1 is not primarily due to singular distributions ρ, but due to the variation δρ having singular parts, i.e., due to an unbounded δρ. Note, that for bounded δρ to exist, ρ also has to be non-singular. To keep dx[ρ(x)] q and dx[ρ(x)] q O finite, we further restrict ρ to be bounded. \n1/q − 1) q/γ (B q−γ O ∞ O −1 ∞ ) −1/γ >δ > 0, where γ = (m − q)/(m − 1), then there exists a constant 0 < R < ∞, such that |Q[ρ] −Q[ρ + δρ]| < Rδ γ/q ,(6)\nand R does not depend on the choice of ρ. Theorem 2 states that, for positive bounded observables, q-expectation values are robust whenever the distributions ρ are uniformly bounded 4 . Excluding unbounded variations from consideration therefore is 3 When all considered ρ are bounded by the same bound 0 < ρ < B, then the constant c does not depend on the choice of ρ andQ is absolutely continuous on this domain. 4 When all considered distributions are bounded by the same upper bound (m → ∞ and γ → 1), then R can be chosen independent of ρ andQ becomes uniformly continuous.\n\n\n20005-p3\n\nsufficient to guarantee stability for the q > 1 case in a general setting. In the corresponding example in [15], when formulated in the continuum limit, stability is violated by using unbounded variations 5 .\n\nBoth theorems in [16] are analytical statements about the continuity properties of the q-expectation value as a non-linear functional without any reference to thermodynamics. They provide a useful and flexible mathematical tool to analyze continuity properties for discrete sets as well as for the continuous case on [0, ∞].\n\nStability criteria for the q-expectation value for discrete finite probability functions. -We can now use the above theorems to prove the robustness of q-expectations for bounded observables on finite discrete sets i ∈ I W ≡ {1, 2, . . . , W }. For this we map the discrete probability distribution onto the continuous interval x ∈ [0, 1] by identifying probabilities Since the observable f (x) is bounded, all conditions needed for Theorems 1 and 2 are met. Let γ = q for 0 < q < 1 and γ = 1/q for q > 1. For some given constant 0 <δ there exists a constant C, such that for all |ρ − ρ | < δ <δ it follows that\n{p i } W i=1 with probability densities ρ(x) = W p i for x ∈ [(i − 1)/W, i/W ],Cδ γ > |Q[ρ] −Q[ρ ]| whereQ[ρ] = 1 0 dx [ρ(x)] q f (x)/ 1 0 dx [ρ(x)] q is the q-expectation for the continuous case. NowQ[ρ] = W i=1 W −1 [W p i ] q O i / W i=1 W −1 [W p i ] q = W i=1 p i O i / W i=1 p q i = Q[p], where Q[p]\nis the q-expectation on I W . Moreover,\nρ 1 = 1 0 dx |ρ(x)| = W i=1\n|p i | = p 1 and consequently one can pull back the result to the discrete case, which completes the proof.\n\nComments on discrete infinite probability functions. -For discrete infinite distribution functions it was shown [15] that the q-expectation value is unstable. However, it is possible to state conditions under which robustness can be ensured. This can be done, for instance, in the following way.\n\nDiscrete finite sets are closely related to continuous compact sets in the sense that discrete sequences can be mapped into the compact interval with step functions, as discussed above. In the same spirit, discrete infinite sets are intimately related to the continuous unbounded set [0, ∞], since again one can map the discrete infinite sequence into the continuous case in terms of step functions. If one can find conditions which define classes of distribution functions on [0, ∞] that guarantee continuity or absolute continuity of the functional, i.e., the q-expectation, the same conditions are sufficient for probabilities on infinite discrete sets. Such classes can simply be derived by using suitable differentiable monotonous functions, g : [0, ∞] → [0, 1]. Let g denote the derivative of g and g −1 the inverse function of g. This maps the distribution function ρ, defined on [0, ∞], to a distribution functionρ(y) = ρ(g −1 (y))g (g −1 (y)) −1 on [0, 1] and also the observable O on [0, ∞] gets mapped tõ O(y) = O(g −1 (y))g (g −1 (y)) q−1 . Now one can apply the conditions used for the Theorems 1 and 2 on [0, 1] and pull them back to [0, ∞]. It should be noted that different maps g lead to different, yet consistent boundedness conditions and decay properties for observables O and distributions ρ on [0, 1].\n\nTo give an explicit example, let us consider the following problem. Suppose we considerq -exponential distributions of the form ρ(x) ∝ eq(−βx) ≡ [1 − (1 −q)βx] 1 1−q forq 1 and some β > β 0 , and we want its first N moments under the q-expectation,\nx m q ≡ dx[ρ(x)] q x m dx[ρ(x)] q ,(7)\nto be robust with respect to g, (m N ). For a more detailed discussion on moments under q-expectations, see [18]. Assuming q > 1, let us take g(x) = 1 − 1/(1 + x) γ ; then g (x) = γ(1 + x) −γ−1 . The boundedness condition for the observables immediately requires γ > N/(q − 1) − 1 and the decay property for the distributions implies q < 1 + 1/(γ + 1). Forq = 1 and m = 1 the example is the q-expectation value of the energy of the quantum harmonic oscillator,\nE q = ∞ n=1 n[e −βn 1 ] q ∞ n=1 [e −βn 1 ] q = 1 4 sinh −2 βq 2 ,(8)\nwhich shows continuity in β and robustness of the q-expectation under variations of the exponential distribution 6 .\n\nRobustness of Rényi entropy for continuous and discrete finite distribution functions. -Here it suffices to discuss the case 0 < q < 1 since for q > 1 Rényi entropy\nS R q = ln W i=1 p q i 1 − q(9)\n6 In what concerns the use of continuous distributions for calculating entropies and similar quantities, such as eq. (7), the reader must be aware of a relatively well-known difficulty. If we make a change of variables y = f (x), say in eq. (7), we immediately see that the result is not invariant. In the spirit of Kullback and Leibler entropy [19] the problem is easily resolved in terms of a reference distribution r(x), which, except at infinity, nowhere vanishes. For example, for q > 0, the quantity in eq. (7) would be replaced by Table 1: Table of stability/Lesche-stability and robustness for the functionals Sq, S R q and the q-expectation value for the underlying nature of the distribution function, i.e. continuous, discrete finite or discrete infinite. In the continuum, admissible means that a non-negative entropy is required. Boundedness automatically guarantees robustness [16]. The term Lesche-stable is used for infinite distribution functions when eq. (1) holds, stable is used when there is no division by a maximum taken in eq. (1). Robustness is used for bounded distributions in the continuum and for discrete finite probability functions. For the q-expectations for the discrete infinite case, robustness is understood under the decay properties of the distributions, as specified in the text. Lesche-stability and stability are sufficient but not necessary for robustness. SBG and standard expectation values (q = 1) are Lesche-stable and stable, respectively. S q , for q > 0 S R q , for q > 0 q-expectation value, for q > 0 bounded continuous (physically admissible) robust robust robust [16] discrete finite (W finite) robust robust robust discrete infinite Lesche-unstable [1]; robust unstable [15]; robust for (lim W → ∞)\ndxr(x)[ρ(x)/r(x)] q x m dxr(x)[ρ(x)/r(x)] q .\n\n20005-p4\n\nLesche-stable [2] for typical physical cases typical physical cases strictly speaking ceases to be a proper entropy because it is not concave. Substituting the probabilities p i by step\nfunctions ρ (W ) (x) = W p i W for x ∈ [(i − 1)/W, i/W ]\nwhich represent the discrete probability p i as a probability density on [0, 1], we get\nS R q = ln W + ln 1 0 dx [ρ (W ) (x)] q 1 − q .(10)\nBoundedness of the distributions allows to use propositions (4), (6) and (8) in [16] which have been used to prove Theorem 1. Note that, due to the upper bound W , it follows that dxρ(x) W q−1 . Letδ = µW q−1 /4 and δρ 1 = δ <δ, as in [16]. Now we get\n|S R q [ρ] − S R q [ρ + δρ]| = ln 1 0 dx [ρ(x)] q 1 0 dx [ρ(x) + δρ(x)] q .(11)\nUsing propositions (4) and (6) from [16] one finds 1−aδ q < | 1 0 dx ρ(x) q / 1 0 dx (ρ(x) + δρ(x)) q | < 1 + aδ q and a = 4W 1−q /(1 − µ). Since |ln(1 + x)| < 2|x|, for |x| 1 it follows that for sufficiently small δ,\n|S R q [ρ] − S R q [ρ + δρ]| < 2aδ q .(12)\nThis shows both the uniform continuity of the continuous Rényi entropy for the class of uniformly bounded probability distributions in L 1 ([0, 1]), and the absolute continuity of Rényi entropy for probabilities on finite sets. Similar arguments show robustness also for q > 1, despite lack of concavity of S R q . Robustness of the entropy S q for continuous and discrete finite distribution functions. -One can prove robustness of the nonadditive entropy \nS q = 1 − W i=1 p q i q − 1(13)= δ, where δ is sufficiently small. Now, |S q [ρ] − S q [ρ + δρ]| = |q − 1| −1 | 1 0 dx ρ q − 1 0 dx (ρ + δρ) q |.\nIt therefore is an immediate consequence of propositions (6) and (4) in [16], that for 0 < q < 1, |S q [ρ] − S q [ρ + δρ]| < 4δ q . For q > 1 we use propositions (11) and (13) to\nfind |S q [ρ] − S q [ρ + δρ]| < Rδ 1 q .\nIn what concerns discrete infinite distribution functions, S q has been shown to be Lesche-stable [2].\n\nConclusion. -To summarize, we discussed the concept of physical robustness in contrast to the more restrictive mathematical stability of thermostatistical functionals under variations of their underlying distribution functions. We argue that while several important functionals, such as the Rényi entropy or the q-expectation value are unstable in the strict sense, restriction to physically relevant distribution functions, ensures robustness of these functionals. For a distribution to be physically relevant we require that its associated entropy be non-negative. We further restrict to distributions which are bounded in the continuum. This excludes, for example, distributions involving Dirac deltas. Our results are summarized in table 1, where we indicate the type of stability, Lesche-stability or robustness for the functionals S q , Rényi entropy S R q and the q-expectation value, for the paradigmatic types of distribution functions -continuum, discrete finite, and discrete infinite-that we have focused on here. The term Lesche-stable is used when eq. (1) holds, stable refers to the situation where no division by a maximum is taken in eq. (1), and robustness -in the above-defined sense-is found for admissible (non-negative entropy) and bounded distributions in the continuum and for discrete finite probability functions. In the case for discrete infinite distribution functions which are known to cause instabilities for some functionals [1,15], one can show that there exist paradigmatic robust examples once decay properties of the distributions are specified. In this context one can show that systems such as the harmonic oscillator are robust under variations of the (inverse) temperature. One can of course think of physical distribution functions which have positive BG entropy but are unbounded, such as, e.g., power law divergences. These cases remain to be discussed but exceed the present scope.\n\nWe conclude by stating that the concept of stability might be overly strict for physical applications. This is in accordance to conclusions drawn in [20]. When limited to the class of physically admissible and bounded distribution functions, it is conceivable that physical robustness of virtually all thermodynamic functionals will be guaranteed. * * * We acknowledge fruitful remarks by E. M. F. Curado and C. Beck. RH and ST acknowledge great hospitality at CBPF. This work was partially supported by Faperj and CNPq (Brazilian agencies), and Austrian Science Fund FWF Project P19132.\n\nTheorem 2 .\n2Let q > 1 and let m > 0 be an arbitrary but fixed constant. Let 0 < ρ be a probability distribution on I = [0, 1]. Let δρ be variations of ρ, i.e. ρ + δρ > 0. Let B > 0 be an arbitrary but fixed constant. Let the variations δρ be uniformly bounded in the m-norm, i.e. δρ m < B, by this constant B. Further, let δρ 1 = δ and let 0 < O be a strictly positive bounded observable on I. Letδ be an upper bound for the size of the variations δ such that, (2\n\n\ni.e. step functions on [0, 1]. The observable {O i } W i=1 gets identified with the step function f (x) = O i for the associated interval x ∈ [(i − 1)/W, i/W ]. Clearly, 0 ρ W for all possible distributions of this kind and so are all possible variations since |ρ(x) − ρ (x)| < W .\n\n\nwhere ρ denotes a continuous probability distribution. The expectation value of an observable O(x) under this measure is Q[ρ] = dxP (q) (x)O(x), and its total variation reads δQ[ρ] =Q[ρ + δρ] −Q[ρ]. Here we useQ[ρ] to distinguish from the discrete case.\n\n\nfor discrete finite sets by mapping the probabilities{p i } W i=1onto a distribution on ρ on [0, 1] by step functions, as above. Since all step functions ρ that represent some{p i } W i=1are bounded by W , it is sufficient to prove robustness for the continuous case. ρ is from a uniformly bounded class of distribution functions on [0, 1], i.e., there is a constant W > 0 such that all ρ are bounded by W . Consider variations δρ = ρ − ρ such that both ρ and ρ are bounded by W and δρ 1\nIn the continuum, entropy functionals such as the BG, Rényi and others are well known to become negative for distributions which include too narrow peaks, a situation which typically corresponds to the low-temperature limit, where the quantum nature of physical systems must be taken into account.2 If a functional is stable it is always safe to use. Inversely, instability points at the fact that the domain of safe usage is limited. Here, robustness is never used in the sense of trajectories or attractors, as done in other contexts.\nThe proof was carried out on the unit interval I ∈ [0, 1]. This does not present a loss of generality, since the proofs can be extended to any bounded interval. For unbounded intervals, the proof gets more involved and requires to fix conditions that relate boundedness conditions of the observable and the decay properties of ρ.\n\n. B Lesche, J. Stat. Phys. 27419Lesche B., J. Stat. Phys., 27 (1982) 419.\n\n. Abe S , Phys. Rev. E. 6646134Abe S., Phys. Rev. E, 66 (2002) 046134.\n\n. A G Bashkirov, Phys. Rev. E. 7228101Bashkirov A. G., Phys. Rev. E, 72 (2005) 028101.\n\n. Abe S , Phys. Rev. E. 7228102Abe S., Phys. Rev. E, 72 (2005) 028102.\n\n. B Lesche, Phys. Rev. E. 7017102Lesche B., Phys. Rev. E, 70 (2004) 017102.\n\n. T Yamano, Phys. Lett. A. 329268Yamano T., Phys. Lett. A, 329 (2004) 268.\n\n. G Kaniadakis, A M Scarfone, Physica A. 340102Kaniadakis G. and Scarfone A. M., Physica A, 340 (2004) 102.\n\n. E M F Curado, F D Nobre, Physica A. 33594Curado E. M. F. and Nobre F. D., Physica A, 335 (2004) 94.\n\n. C Tsallis, J. Stat. Phys. 52479Tsallis C., J. Stat. Phys., 52 (1988) 479.\n\n. C Tsallis, R S Mendes, A R Plastino, Physica A. 261534Tsallis C., Mendes R. S. and Plastino A. R., Physica A, 261 (1998) 534.\n\n. J Naudts, J. Inequal. Pure Appl. Math. 5102Naudts J., J. Inequal. Pure Appl. Math., 5 (2004) 102.\n\n. S Abe, G B Bagci, Phys. Rev. E. 7116139Abe S. and Bagci G. B., Phys. Rev. E, 71 (2005) 016139.\n\nC Beck, F Schlögl, Thermodynamics of Chaotic Systems -An Introduction. CambridgeCambridge University PressBeck C. and Schlögl F., Thermodynamics of Chaotic Systems -An Introduction (Cambridge University Press, Cambridge) 1993.\n\n. D Prato, C Tsallis, Phys. Rev. E. 602398Prato D. and Tsallis C., Phys. Rev. E, 60 (1999) 2398.\n\n. Abe S , EPL. 8460006Abe S., EPL, 84 (2008) 60006.\n\n. R Hanel, S Thurner, arXiv:0808.4158Hanel R. and Thurner S., arXiv:0808.4158.\n\n. C Tsallis, E Brigatti, Contin. Mech. Thermodyn. 16223Tsallis C. and Brigatti E., Contin. Mech. Thermodyn., 16 (2004) 223.\n\n. C Tsallis, A R Plastino, R F Alvarez-Estrada, arXiv:0802.1698Tsallis C., Plastino A. R. and Alvarez-Estrada R. F., arXiv:0802.1698.\n\n. S Kullback, R A Leibler, Ann. Math. Stat. 2279Kullback S. and Leibler R. A., Ann. Math. Stat., 22 (1961) 79.\n\n. P Jizba, T Arimitsu, Phys. Rev. E. 6926128Jizba P. and Arimitsu T., Phys. Rev. E, 69 (2004) 026128.\n"},"corpus_id":{"kind":"number","value":15090091,"string":"15,090,091"},"external_ids":{"kind":"string","value":"{\n \"arxiv\": \"0812.3855\",\n \"mag\": 2040164803,\n \"acl\": null,\n \"pubmed\": null,\n \"pubmedcentral\": null,\n \"dblp\": null,\n \"doi\": \"10.1209/0295-5075/85/20005\"\n}"},"source":{"kind":"string","value":"{\n \"pdf_urls\": [],\n \"pdf_sha\": \"f6527493c9b306ee999fc629384911184f813a08\",\n \"open_access\": {\n \"license\": null,\n \"url\": \"http://arxiv.org/pdf/0812.3855\",\n \"status\": \"GREEN\"\n }\n}"},"title":{"kind":"string","value":"On the robustness of q-expectation values and Rényi entropy"},"authors":{"kind":"list like","value":["R Hanel \nComplex Systems Research Group\nHNO\nMedical University of Vienna\nWähringer Gürtel 18-20A-1090EUAustria","S Thurner \nComplex Systems Research Group\nHNO\nMedical University of Vienna\nWähringer Gürtel 18-20A-1090EUAustria\n\nSanta Fe Institute\n1399 Hyde Park Road, Santa Fe87501NMUSA","C Tsallis \nCentro Brasileiro de Pesquisas Físicas\nNational Institute of Science and Technology for Complex Systems Rua\nXavier Sigaud 15022290-180Rio de Janeiro-RJBrazil\n\nSanta Fe Institute\n1399 Hyde Park Road, Santa Fe87501NMUSA"],"string":"[\n \"R Hanel \\nComplex Systems Research Group\\nHNO\\nMedical University of Vienna\\nWähringer Gürtel 18-20A-1090EUAustria\",\n \"S Thurner \\nComplex Systems Research Group\\nHNO\\nMedical University of Vienna\\nWähringer Gürtel 18-20A-1090EUAustria\\n\\nSanta Fe Institute\\n1399 Hyde Park Road, Santa Fe87501NMUSA\",\n \"C Tsallis \\nCentro Brasileiro de Pesquisas Físicas\\nNational Institute of Science and Technology for Complex Systems Rua\\nXavier Sigaud 15022290-180Rio de Janeiro-RJBrazil\\n\\nSanta Fe Institute\\n1399 Hyde Park Road, Santa Fe87501NMUSA\"\n]","isConversational":false},"abstract":{"kind":"string","value":"We study the robustness of the functionals of probability distributions such as the Rényi and nonadditive Sq entropies, as well as the q-expectation values under small variations of the distributions. We focus on three important types of distribution functions, namely i) continuous bounded, ii) discrete with finite number of states, and iii) discrete with infinite number of states. The physical concept of robustness is contrasted with the mathematically stronger condition of stability and Lesche-stability for functionals. We explicitly demonstrate that, in the case of continuous distributions, once unbounded distributions and those leading to negative entropy are excluded, both Rényi and nonadditive Sq entropies as well as the q-expectation values are robust. For the discrete finite case, the Rényi and nonadditive Sq entropies and the q-expectation values are robust as well. For the infinite discrete case, where both Rényi entropy and q-expectations are known to violate Lesche-stability and stability, respectively, we show that one can nevertheless state conditions which guarantee physical robustness."},"sections":{"kind":"list like","value":[{"title":"20005-p3","content":"sufficient to guarantee stability for the q > 1 case in a general setting. In the corresponding example in [15], when formulated in the continuum limit, stability is violated by using unbounded variations 5 .\nBoth theorems in [16] are analytical statements about the continuity properties of the q-expectation value as a non-linear functional without any reference to thermodynamics. They provide a useful and flexible mathematical tool to analyze continuity properties for discrete sets as well as for the continuous case on [0, ∞].\nStability criteria for the q-expectation value for discrete finite probability functions. -We can now use the above theorems to prove the robustness of q-expectations for bounded observables on finite discrete sets i ∈ I W ≡ {1, 2, . . . , W }. For this we map the discrete probability distribution onto the continuous interval x ∈ [0, 1] by identifying probabilities Since the observable f (x) is bounded, all conditions needed for Theorems 1 and 2 are met. Let γ = q for 0 < q < 1 and γ = 1/q for q > 1. For some given constant 0 <δ there exists a constant C, such that for all |ρ − ρ | < δ <δ it follows that\nis the q-expectation on I W . Moreover,\n|p i | = p 1 and consequently one can pull back the result to the discrete case, which completes the proof.\nComments on discrete infinite probability functions. -For discrete infinite distribution functions it was shown [15] that the q-expectation value is unstable. However, it is possible to state conditions under which robustness can be ensured. This can be done, for instance, in the following way.\nDiscrete finite sets are closely related to continuous compact sets in the sense that discrete sequences can be mapped into the compact interval with step functions, as discussed above. In the same spirit, discrete infinite sets are intimately related to the continuous unbounded set [0, ∞], since again one can map the discrete infinite sequence into the continuous case in terms of step functions. If one can find conditions which define classes of distribution functions on [0, ∞] that guarantee continuity or absolute continuity of the functional, i.e., the q-expectation, the same conditions are sufficient for probabilities on infinite discrete sets. Such classes can simply be derived by using suitable differentiable monotonous functions, g : [0, ∞] → [0, 1]. Let g denote the derivative of g and g −1 the inverse function of g. This maps the distribution function ρ, defined on [0, ∞], to a distribution functionρ(y) = ρ(g −1 (y))g (g −1 (y)) −1 on [0, 1] and also the observable O on [0, ∞] gets mapped tõ O(y) = O(g −1 (y))g (g −1 (y)) q−1 . Now one can apply the conditions used for the Theorems 1 and 2 on [0, 1] and pull them back to [0, ∞]. It should be noted that different maps g lead to different, yet consistent boundedness conditions and decay properties for observables O and distributions ρ on [0, 1].\nTo give an explicit example, let us consider the following problem. Suppose we considerq -exponential distributions of the form ρ(x) ∝ eq(−βx) ≡ [1 − (1 −q)βx] 1 1−q forq 1 and some β > β 0 , and we want its first N moments under the q-expectation,\nto be robust with respect to g, (m N ). For a more detailed discussion on moments under q-expectations, see [18]. Assuming q > 1, let us take g(x) = 1 − 1/(1 + x) γ ; then g (x) = γ(1 + x) −γ−1 . The boundedness condition for the observables immediately requires γ > N/(q − 1) − 1 and the decay property for the distributions implies q < 1 + 1/(γ + 1). Forq = 1 and m = 1 the example is the q-expectation value of the energy of the quantum harmonic oscillator,\nwhich shows continuity in β and robustness of the q-expectation under variations of the exponential distribution 6 .\nRobustness of Rényi entropy for continuous and discrete finite distribution functions. -Here it suffices to discuss the case 0 < q < 1 since for q > 1 Rényi entropy\n6 In what concerns the use of continuous distributions for calculating entropies and similar quantities, such as eq. (7), the reader must be aware of a relatively well-known difficulty. If we make a change of variables y = f (x), say in eq. (7), we immediately see that the result is not invariant. In the spirit of Kullback and Leibler entropy [19] the problem is easily resolved in terms of a reference distribution r(x), which, except at infinity, nowhere vanishes. For example, for q > 0, the quantity in eq. (7) would be replaced by Table 1: Table of stability/Lesche-stability and robustness for the functionals Sq, S R q and the q-expectation value for the underlying nature of the distribution function, i.e. continuous, discrete finite or discrete infinite. In the continuum, admissible means that a non-negative entropy is required. Boundedness automatically guarantees robustness [16]. The term Lesche-stable is used for infinite distribution functions when eq. (1) holds, stable is used when there is no division by a maximum taken in eq. (1). Robustness is used for bounded distributions in the continuum and for discrete finite probability functions. For the q-expectations for the discrete infinite case, robustness is understood under the decay properties of the distributions, as specified in the text. Lesche-stability and stability are sufficient but not necessary for robustness. SBG and standard expectation values (q = 1) are Lesche-stable and stable, respectively. S q , for q > 0 S R q , for q > 0 q-expectation value, for q > 0 bounded continuous (physically admissible) robust robust robust [16] discrete finite (W finite) robust robust robust discrete infinite Lesche-unstable [1]; robust unstable [15]; robust for (lim W → ∞)"},{"title":"20005-p4","content":"Lesche-stable [2] for typical physical cases typical physical cases strictly speaking ceases to be a proper entropy because it is not concave. Substituting the probabilities p i by step\nwhich represent the discrete probability p i as a probability density on [0, 1], we get\nBoundedness of the distributions allows to use propositions (4), (6) and (8) in [16] which have been used to prove Theorem 1. Note that, due to the upper bound W , it follows that dxρ(x) W q−1 . Letδ = µW q−1 /4 and δρ 1 = δ <δ, as in [16]. Now we get\nUsing propositions (4) and (6) from [16] one finds 1−aδ q < | 1 0 dx ρ(x) q / 1 0 dx (ρ(x) + δρ(x)) q | < 1 + aδ q and a = 4W 1−q /(1 − µ). Since |ln(1 + x)| < 2|x|, for |x| 1 it follows that for sufficiently small δ,\nThis shows both the uniform continuity of the continuous Rényi entropy for the class of uniformly bounded probability distributions in L 1 ([0, 1]), and the absolute continuity of Rényi entropy for probabilities on finite sets. Similar arguments show robustness also for q > 1, despite lack of concavity of S R q . Robustness of the entropy S q for continuous and discrete finite distribution functions. -One can prove robustness of the nonadditive entropy\nIt therefore is an immediate consequence of propositions (6) and (4) in [16], that for 0 < q < 1, |S q [ρ] − S q [ρ + δρ]| < 4δ q . For q > 1 we use propositions (11) and (13) to\nIn what concerns discrete infinite distribution functions, S q has been shown to be Lesche-stable [2].\nConclusion. -To summarize, we discussed the concept of physical robustness in contrast to the more restrictive mathematical stability of thermostatistical functionals under variations of their underlying distribution functions. We argue that while several important functionals, such as the Rényi entropy or the q-expectation value are unstable in the strict sense, restriction to physically relevant distribution functions, ensures robustness of these functionals. For a distribution to be physically relevant we require that its associated entropy be non-negative. We further restrict to distributions which are bounded in the continuum. This excludes, for example, distributions involving Dirac deltas. Our results are summarized in table 1, where we indicate the type of stability, Lesche-stability or robustness for the functionals S q , Rényi entropy S R q and the q-expectation value, for the paradigmatic types of distribution functions -continuum, discrete finite, and discrete infinite-that we have focused on here. The term Lesche-stable is used when eq. (1) holds, stable refers to the situation where no division by a maximum is taken in eq. (1), and robustness -in the above-defined sense-is found for admissible (non-negative entropy) and bounded distributions in the continuum and for discrete finite probability functions. In the case for discrete infinite distribution functions which are known to cause instabilities for some functionals [1,15], one can show that there exist paradigmatic robust examples once decay properties of the distributions are specified. In this context one can show that systems such as the harmonic oscillator are robust under variations of the (inverse) temperature. One can of course think of physical distribution functions which have positive BG entropy but are unbounded, such as, e.g., power law divergences. These cases remain to be discussed but exceed the present scope.\nWe conclude by stating that the concept of stability might be overly strict for physical applications. This is in accordance to conclusions drawn in [20]. When limited to the class of physically admissible and bounded distribution functions, it is conceivable that physical robustness of virtually all thermodynamic functionals will be guaranteed. * * * We acknowledge fruitful remarks by E. M. F. Curado and C. Beck. RH and ST acknowledge great hospitality at CBPF. This work was partially supported by Faperj and CNPq (Brazilian agencies), and Austrian Science Fund FWF Project P19132."},{"title":"Theorem 2 .","content":""}],"string":"[\n {\n \"title\": \"20005-p3\",\n \"content\": \"sufficient to guarantee stability for the q > 1 case in a general setting. In the corresponding example in [15], when formulated in the continuum limit, stability is violated by using unbounded variations 5 .\\nBoth theorems in [16] are analytical statements about the continuity properties of the q-expectation value as a non-linear functional without any reference to thermodynamics. They provide a useful and flexible mathematical tool to analyze continuity properties for discrete sets as well as for the continuous case on [0, ∞].\\nStability criteria for the q-expectation value for discrete finite probability functions. -We can now use the above theorems to prove the robustness of q-expectations for bounded observables on finite discrete sets i ∈ I W ≡ {1, 2, . . . , W }. For this we map the discrete probability distribution onto the continuous interval x ∈ [0, 1] by identifying probabilities Since the observable f (x) is bounded, all conditions needed for Theorems 1 and 2 are met. Let γ = q for 0 < q < 1 and γ = 1/q for q > 1. For some given constant 0 <δ there exists a constant C, such that for all |ρ − ρ | < δ <δ it follows that\\nis the q-expectation on I W . Moreover,\\n|p i | = p 1 and consequently one can pull back the result to the discrete case, which completes the proof.\\nComments on discrete infinite probability functions. -For discrete infinite distribution functions it was shown [15] that the q-expectation value is unstable. However, it is possible to state conditions under which robustness can be ensured. This can be done, for instance, in the following way.\\nDiscrete finite sets are closely related to continuous compact sets in the sense that discrete sequences can be mapped into the compact interval with step functions, as discussed above. In the same spirit, discrete infinite sets are intimately related to the continuous unbounded set [0, ∞], since again one can map the discrete infinite sequence into the continuous case in terms of step functions. If one can find conditions which define classes of distribution functions on [0, ∞] that guarantee continuity or absolute continuity of the functional, i.e., the q-expectation, the same conditions are sufficient for probabilities on infinite discrete sets. Such classes can simply be derived by using suitable differentiable monotonous functions, g : [0, ∞] → [0, 1]. Let g denote the derivative of g and g −1 the inverse function of g. This maps the distribution function ρ, defined on [0, ∞], to a distribution functionρ(y) = ρ(g −1 (y))g (g −1 (y)) −1 on [0, 1] and also the observable O on [0, ∞] gets mapped tõ O(y) = O(g −1 (y))g (g −1 (y)) q−1 . Now one can apply the conditions used for the Theorems 1 and 2 on [0, 1] and pull them back to [0, ∞]. It should be noted that different maps g lead to different, yet consistent boundedness conditions and decay properties for observables O and distributions ρ on [0, 1].\\nTo give an explicit example, let us consider the following problem. Suppose we considerq -exponential distributions of the form ρ(x) ∝ eq(−βx) ≡ [1 − (1 −q)βx] 1 1−q forq 1 and some β > β 0 , and we want its first N moments under the q-expectation,\\nto be robust with respect to g, (m N ). For a more detailed discussion on moments under q-expectations, see [18]. Assuming q > 1, let us take g(x) = 1 − 1/(1 + x) γ ; then g (x) = γ(1 + x) −γ−1 . The boundedness condition for the observables immediately requires γ > N/(q − 1) − 1 and the decay property for the distributions implies q < 1 + 1/(γ + 1). Forq = 1 and m = 1 the example is the q-expectation value of the energy of the quantum harmonic oscillator,\\nwhich shows continuity in β and robustness of the q-expectation under variations of the exponential distribution 6 .\\nRobustness of Rényi entropy for continuous and discrete finite distribution functions. -Here it suffices to discuss the case 0 < q < 1 since for q > 1 Rényi entropy\\n6 In what concerns the use of continuous distributions for calculating entropies and similar quantities, such as eq. (7), the reader must be aware of a relatively well-known difficulty. If we make a change of variables y = f (x), say in eq. (7), we immediately see that the result is not invariant. In the spirit of Kullback and Leibler entropy [19] the problem is easily resolved in terms of a reference distribution r(x), which, except at infinity, nowhere vanishes. For example, for q > 0, the quantity in eq. (7) would be replaced by Table 1: Table of stability/Lesche-stability and robustness for the functionals Sq, S R q and the q-expectation value for the underlying nature of the distribution function, i.e. continuous, discrete finite or discrete infinite. In the continuum, admissible means that a non-negative entropy is required. Boundedness automatically guarantees robustness [16]. The term Lesche-stable is used for infinite distribution functions when eq. (1) holds, stable is used when there is no division by a maximum taken in eq. (1). Robustness is used for bounded distributions in the continuum and for discrete finite probability functions. For the q-expectations for the discrete infinite case, robustness is understood under the decay properties of the distributions, as specified in the text. Lesche-stability and stability are sufficient but not necessary for robustness. SBG and standard expectation values (q = 1) are Lesche-stable and stable, respectively. S q , for q > 0 S R q , for q > 0 q-expectation value, for q > 0 bounded continuous (physically admissible) robust robust robust [16] discrete finite (W finite) robust robust robust discrete infinite Lesche-unstable [1]; robust unstable [15]; robust for (lim W → ∞)\"\n },\n {\n \"title\": \"20005-p4\",\n \"content\": \"Lesche-stable [2] for typical physical cases typical physical cases strictly speaking ceases to be a proper entropy because it is not concave. Substituting the probabilities p i by step\\nwhich represent the discrete probability p i as a probability density on [0, 1], we get\\nBoundedness of the distributions allows to use propositions (4), (6) and (8) in [16] which have been used to prove Theorem 1. Note that, due to the upper bound W , it follows that dxρ(x) W q−1 . Letδ = µW q−1 /4 and δρ 1 = δ <δ, as in [16]. Now we get\\nUsing propositions (4) and (6) from [16] one finds 1−aδ q < | 1 0 dx ρ(x) q / 1 0 dx (ρ(x) + δρ(x)) q | < 1 + aδ q and a = 4W 1−q /(1 − µ). Since |ln(1 + x)| < 2|x|, for |x| 1 it follows that for sufficiently small δ,\\nThis shows both the uniform continuity of the continuous Rényi entropy for the class of uniformly bounded probability distributions in L 1 ([0, 1]), and the absolute continuity of Rényi entropy for probabilities on finite sets. Similar arguments show robustness also for q > 1, despite lack of concavity of S R q . Robustness of the entropy S q for continuous and discrete finite distribution functions. -One can prove robustness of the nonadditive entropy\\nIt therefore is an immediate consequence of propositions (6) and (4) in [16], that for 0 < q < 1, |S q [ρ] − S q [ρ + δρ]| < 4δ q . For q > 1 we use propositions (11) and (13) to\\nIn what concerns discrete infinite distribution functions, S q has been shown to be Lesche-stable [2].\\nConclusion. -To summarize, we discussed the concept of physical robustness in contrast to the more restrictive mathematical stability of thermostatistical functionals under variations of their underlying distribution functions. We argue that while several important functionals, such as the Rényi entropy or the q-expectation value are unstable in the strict sense, restriction to physically relevant distribution functions, ensures robustness of these functionals. For a distribution to be physically relevant we require that its associated entropy be non-negative. We further restrict to distributions which are bounded in the continuum. This excludes, for example, distributions involving Dirac deltas. Our results are summarized in table 1, where we indicate the type of stability, Lesche-stability or robustness for the functionals S q , Rényi entropy S R q and the q-expectation value, for the paradigmatic types of distribution functions -continuum, discrete finite, and discrete infinite-that we have focused on here. The term Lesche-stable is used when eq. (1) holds, stable refers to the situation where no division by a maximum is taken in eq. (1), and robustness -in the above-defined sense-is found for admissible (non-negative entropy) and bounded distributions in the continuum and for discrete finite probability functions. In the case for discrete infinite distribution functions which are known to cause instabilities for some functionals [1,15], one can show that there exist paradigmatic robust examples once decay properties of the distributions are specified. In this context one can show that systems such as the harmonic oscillator are robust under variations of the (inverse) temperature. One can of course think of physical distribution functions which have positive BG entropy but are unbounded, such as, e.g., power law divergences. These cases remain to be discussed but exceed the present scope.\\nWe conclude by stating that the concept of stability might be overly strict for physical applications. This is in accordance to conclusions drawn in [20]. When limited to the class of physically admissible and bounded distribution functions, it is conceivable that physical robustness of virtually all thermodynamic functionals will be guaranteed. * * * We acknowledge fruitful remarks by E. M. F. Curado and C. Beck. RH and ST acknowledge great hospitality at CBPF. This work was partially supported by Faperj and CNPq (Brazilian agencies), and Austrian Science Fund FWF Project P19132.\"\n },\n {\n \"title\": \"Theorem 2 .\",\n \"content\": \"\"\n }\n]","isConversational":false},"figures":{"kind":"list like","value":[{"id":"","caption":"Let q > 1 and let m > 0 be an arbitrary but fixed constant. Let 0 < ρ be a probability distribution on I = [0, 1]. Let δρ be variations of ρ, i.e. ρ + δρ > 0. Let B > 0 be an arbitrary but fixed constant. Let the variations δρ be uniformly bounded in the m-norm, i.e. δρ m < B, by this constant B. Further, let δρ 1 = δ and let 0 < O be a strictly positive bounded observable on I. Letδ be an upper bound for the size of the variations δ such that, (2","content":"Theorem 2 .\n2Let q > 1 and let m > 0 be an arbitrary but fixed constant. Let 0 < ρ be a probability distribution on I = [0, 1]. Let δρ be variations of ρ, i.e. ρ + δρ > 0. Let B > 0 be an arbitrary but fixed constant. Let the variations δρ be uniformly bounded in the m-norm, i.e. δρ m < B, by this constant B. Further, let δρ 1 = δ and let 0 < O be a strictly positive bounded observable on I. Letδ be an upper bound for the size of the variations δ such that, (2"},{"id":"","caption":"i.e. step functions on [0, 1]. The observable {O i } W i=1 gets identified with the step function f (x) = O i for the associated interval x ∈ [(i − 1)/W, i/W ]. Clearly, 0 ρ W for all possible distributions of this kind and so are all possible variations since |ρ(x) − ρ (x)| < W .","content":"i.e. step functions on [0, 1]. The observable {O i } W i=1 gets identified with the step function f (x) = O i for the associated interval x ∈ [(i − 1)/W, i/W ]. Clearly, 0 ρ W for all possible distributions of this kind and so are all possible variations since |ρ(x) − ρ (x)| < W ."},{"id":"","caption":"where ρ denotes a continuous probability distribution. The expectation value of an observable O(x) under this measure is Q[ρ] = dxP (q) (x)O(x), and its total variation reads δQ[ρ] =Q[ρ + δρ] −Q[ρ]. Here we useQ[ρ] to distinguish from the discrete case.","content":"where ρ denotes a continuous probability distribution. The expectation value of an observable O(x) under this measure is Q[ρ] = dxP (q) (x)O(x), and its total variation reads δQ[ρ] =Q[ρ + δρ] −Q[ρ]. Here we useQ[ρ] to distinguish from the discrete case."},{"id":"","caption":"for discrete finite sets by mapping the probabilities{p i } W i=1onto a distribution on ρ on [0, 1] by step functions, as above. Since all step functions ρ that represent some{p i } W i=1are bounded by W , it is sufficient to prove robustness for the continuous case. ρ is from a uniformly bounded class of distribution functions on [0, 1], i.e., there is a constant W > 0 such that all ρ are bounded by W . Consider variations δρ = ρ − ρ such that both ρ and ρ are bounded by W and δρ 1","content":"for discrete finite sets by mapping the probabilities{p i } W i=1onto a distribution on ρ on [0, 1] by step functions, as above. Since all step functions ρ that represent some{p i } W i=1are bounded by W , it is sufficient to prove robustness for the continuous case. ρ is from a uniformly bounded class of distribution functions on [0, 1], i.e., there is a constant W > 0 such that all ρ are bounded by W . Consider variations δρ = ρ − ρ such that both ρ and ρ are bounded by W and δρ 1"}],"string":"[\n {\n \"id\": \"\",\n \"caption\": \"Let q > 1 and let m > 0 be an arbitrary but fixed constant. Let 0 < ρ be a probability distribution on I = [0, 1]. Let δρ be variations of ρ, i.e. ρ + δρ > 0. Let B > 0 be an arbitrary but fixed constant. Let the variations δρ be uniformly bounded in the m-norm, i.e. δρ m < B, by this constant B. Further, let δρ 1 = δ and let 0 < O be a strictly positive bounded observable on I. Letδ be an upper bound for the size of the variations δ such that, (2\",\n \"content\": \"Theorem 2 .\\n2Let q > 1 and let m > 0 be an arbitrary but fixed constant. Let 0 < ρ be a probability distribution on I = [0, 1]. Let δρ be variations of ρ, i.e. ρ + δρ > 0. Let B > 0 be an arbitrary but fixed constant. Let the variations δρ be uniformly bounded in the m-norm, i.e. δρ m < B, by this constant B. Further, let δρ 1 = δ and let 0 < O be a strictly positive bounded observable on I. Letδ be an upper bound for the size of the variations δ such that, (2\"\n },\n {\n \"id\": \"\",\n \"caption\": \"i.e. step functions on [0, 1]. The observable {O i } W i=1 gets identified with the step function f (x) = O i for the associated interval x ∈ [(i − 1)/W, i/W ]. Clearly, 0 ρ W for all possible distributions of this kind and so are all possible variations since |ρ(x) − ρ (x)| < W .\",\n \"content\": \"i.e. step functions on [0, 1]. The observable {O i } W i=1 gets identified with the step function f (x) = O i for the associated interval x ∈ [(i − 1)/W, i/W ]. Clearly, 0 ρ W for all possible distributions of this kind and so are all possible variations since |ρ(x) − ρ (x)| < W .\"\n },\n {\n \"id\": \"\",\n \"caption\": \"where ρ denotes a continuous probability distribution. The expectation value of an observable O(x) under this measure is Q[ρ] = dxP (q) (x)O(x), and its total variation reads δQ[ρ] =Q[ρ + δρ] −Q[ρ]. Here we useQ[ρ] to distinguish from the discrete case.\",\n \"content\": \"where ρ denotes a continuous probability distribution. The expectation value of an observable O(x) under this measure is Q[ρ] = dxP (q) (x)O(x), and its total variation reads δQ[ρ] =Q[ρ + δρ] −Q[ρ]. Here we useQ[ρ] to distinguish from the discrete case.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"for discrete finite sets by mapping the probabilities{p i } W i=1onto a distribution on ρ on [0, 1] by step functions, as above. Since all step functions ρ that represent some{p i } W i=1are bounded by W , it is sufficient to prove robustness for the continuous case. ρ is from a uniformly bounded class of distribution functions on [0, 1], i.e., there is a constant W > 0 such that all ρ are bounded by W . Consider variations δρ = ρ − ρ such that both ρ and ρ are bounded by W and δρ 1\",\n \"content\": \"for discrete finite sets by mapping the probabilities{p i } W i=1onto a distribution on ρ on [0, 1] by step functions, as above. Since all step functions ρ that represent some{p i } W i=1are bounded by W , it is sufficient to prove robustness for the continuous case. ρ is from a uniformly bounded class of distribution functions on [0, 1], i.e., there is a constant W > 0 such that all ρ are bounded by W . Consider variations δρ = ρ − ρ such that both ρ and ρ are bounded by W and δρ 1\"\n }\n]","isConversational":false},"references":{"kind":"list like","value":[{"text":". B Lesche, J. Stat. Phys. 27419Lesche B., J. Stat. Phys., 27 (1982) 419.","doi":""},{"text":". Abe S , Phys. Rev. E. 6646134Abe S., Phys. Rev. E, 66 (2002) 046134.","doi":""},{"text":". A G Bashkirov, Phys. Rev. E. 7228101Bashkirov A. G., Phys. Rev. E, 72 (2005) 028101.","doi":""},{"text":". Abe S , Phys. Rev. E. 7228102Abe S., Phys. Rev. E, 72 (2005) 028102.","doi":""},{"text":". B Lesche, Phys. Rev. E. 7017102Lesche B., Phys. Rev. E, 70 (2004) 017102.","doi":""},{"text":". T Yamano, Phys. Lett. A. 329268Yamano T., Phys. Lett. A, 329 (2004) 268.","doi":""},{"text":". G Kaniadakis, A M Scarfone, Physica A. 340102Kaniadakis G. and Scarfone A. M., Physica A, 340 (2004) 102.","doi":""},{"text":". E M F Curado, F D Nobre, Physica A. 33594Curado E. M. F. and Nobre F. D., Physica A, 335 (2004) 94.","doi":""},{"text":". C Tsallis, J. Stat. Phys. 52479Tsallis C., J. Stat. Phys., 52 (1988) 479.","doi":""},{"text":". C Tsallis, R S Mendes, A R Plastino, Physica A. 261534Tsallis C., Mendes R. S. and Plastino A. R., Physica A, 261 (1998) 534.","doi":""},{"text":". J Naudts, J. Inequal. Pure Appl. Math. 5102Naudts J., J. Inequal. Pure Appl. Math., 5 (2004) 102.","doi":""},{"text":". S Abe, G B Bagci, Phys. Rev. E. 7116139Abe S. and Bagci G. B., Phys. Rev. E, 71 (2005) 016139.","doi":""},{"text":"C Beck, F Schlögl, Thermodynamics of Chaotic Systems -An Introduction. CambridgeCambridge University PressBeck C. and Schlögl F., Thermodynamics of Chaotic Systems -An Introduction (Cambridge University Press, Cambridge) 1993.","doi":""},{"text":". D Prato, C Tsallis, Phys. Rev. E. 602398Prato D. and Tsallis C., Phys. Rev. E, 60 (1999) 2398.","doi":""},{"text":". Abe S , EPL. 8460006Abe S., EPL, 84 (2008) 60006.","doi":""},{"text":". R Hanel, S Thurner, arXiv:0808.4158Hanel R. and Thurner S., arXiv:0808.4158.","doi":""},{"text":". C Tsallis, E Brigatti, Contin. Mech. Thermodyn. 16223Tsallis C. and Brigatti E., Contin. Mech. Thermodyn., 16 (2004) 223.","doi":""},{"text":". C Tsallis, A R Plastino, R F Alvarez-Estrada, arXiv:0802.1698Tsallis C., Plastino A. R. and Alvarez-Estrada R. F., arXiv:0802.1698.","doi":""},{"text":". S Kullback, R A Leibler, Ann. Math. Stat. 2279Kullback S. and Leibler R. A., Ann. Math. Stat., 22 (1961) 79.","doi":""},{"text":". P Jizba, T Arimitsu, Phys. Rev. E. 6926128Jizba P. and Arimitsu T., Phys. Rev. E, 69 (2004) 026128.","doi":""}],"string":"[\n {\n \"text\": \". B Lesche, J. Stat. Phys. 27419Lesche B., J. Stat. Phys., 27 (1982) 419.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". Abe S , Phys. Rev. E. 6646134Abe S., Phys. Rev. E, 66 (2002) 046134.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". A G Bashkirov, Phys. Rev. E. 7228101Bashkirov A. G., Phys. Rev. E, 72 (2005) 028101.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". Abe S , Phys. Rev. E. 7228102Abe S., Phys. Rev. E, 72 (2005) 028102.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". B Lesche, Phys. Rev. E. 7017102Lesche B., Phys. Rev. E, 70 (2004) 017102.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". T Yamano, Phys. Lett. A. 329268Yamano T., Phys. Lett. A, 329 (2004) 268.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". G Kaniadakis, A M Scarfone, Physica A. 340102Kaniadakis G. and Scarfone A. M., Physica A, 340 (2004) 102.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". E M F Curado, F D Nobre, Physica A. 33594Curado E. M. F. and Nobre F. D., Physica A, 335 (2004) 94.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". C Tsallis, J. Stat. Phys. 52479Tsallis C., J. Stat. Phys., 52 (1988) 479.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". C Tsallis, R S Mendes, A R Plastino, Physica A. 261534Tsallis C., Mendes R. S. and Plastino A. R., Physica A, 261 (1998) 534.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". J Naudts, J. Inequal. Pure Appl. Math. 5102Naudts J., J. Inequal. Pure Appl. Math., 5 (2004) 102.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". S Abe, G B Bagci, Phys. Rev. E. 7116139Abe S. and Bagci G. B., Phys. Rev. E, 71 (2005) 016139.\",\n \"doi\": \"\"\n },\n {\n \"text\": \"C Beck, F Schlögl, Thermodynamics of Chaotic Systems -An Introduction. CambridgeCambridge University PressBeck C. and Schlögl F., Thermodynamics of Chaotic Systems -An Introduction (Cambridge University Press, Cambridge) 1993.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". D Prato, C Tsallis, Phys. Rev. E. 602398Prato D. and Tsallis C., Phys. Rev. E, 60 (1999) 2398.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". Abe S , EPL. 8460006Abe S., EPL, 84 (2008) 60006.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". R Hanel, S Thurner, arXiv:0808.4158Hanel R. and Thurner S., arXiv:0808.4158.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". C Tsallis, E Brigatti, Contin. Mech. Thermodyn. 16223Tsallis C. and Brigatti E., Contin. Mech. Thermodyn., 16 (2004) 223.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". C Tsallis, A R Plastino, R F Alvarez-Estrada, arXiv:0802.1698Tsallis C., Plastino A. R. and Alvarez-Estrada R. F., arXiv:0802.1698.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". S Kullback, R A Leibler, Ann. Math. Stat. 2279Kullback S. and Leibler R. A., Ann. Math. Stat., 22 (1961) 79.\",\n \"doi\": \"\"\n },\n {\n \"text\": \". P Jizba, T Arimitsu, Phys. Rev. E. 6926128Jizba P. and Arimitsu T., Phys. Rev. E, 69 (2004) 026128.\",\n \"doi\": \"\"\n }\n]","isConversational":false}}},{"rowIdx":295,"cells":{"text":{"kind":"string","value":"\nEvolution speed in some coupled-spin models\n7 Apr 2004\n\nR F Sawyer \nDepartment of Physics\nUniversity of California at Santa Barbara\n93106Santa BarbaraCalifornia\n\nEvolution speed in some coupled-spin models\n7 Apr 2004numbers: 0365-w0365Ud0367-a\nWe investigate the time evolution of some models with N spins and pairwise couplings, for the case of large N, in order to compare evolution times with \"speed limit\" minima derived in the literature. Both in a (symmetric) case with couplings of the same strength between each pair and in a case of broken symmetry, the times necessary for evolution to a state in which the simplest initial state has evolved into a nearly orthogonal state are proportional to 1/N, as is the speed limit time. However the coefficient in the broken symmetry case comes much closer to the speed limit value. Introducing a different criterion for evolution speed, based on macroscopic changes in occupation, we find a corresponding enhancement in rates in the asymmetric case as compared to the symmetric case.\n\nINTRODUCTION\n\nIn a recent series of papers, Giovannetti, Lloyd, and Maccone [1]- [3] have elucidated the role of entanglement in approaching theoretical minima of the times required for quantum systems to progress from a prescribed initial state to a state that is orthogonal or nearly orthogonal to the initial state. The criterion for evaluating the outcome is the reduction of the square of the overlap of the initial and final wave-functions to some value less than ǫ, where ǫ is fairly small, but not necessarily infinitesimal, P (t) ≡ Ψ(t)|Ψ(0) < ǫ. The \"theoretical minimum\" of evolution times that we refer to depends on the lesser of the two quantities,\n∆E ≡ H 2 − H 2 ,(1)\nand E − E 0 ≡< H > −E 0 , where E 0 is the ground state energy of the system and the brackets <> in all cases stand for the expectation value in the initial state. In terms of these quantities the fastest evolution time for meeting the criterion P (τ ) = ǫ, as derived in refs. [4]- [7] and sharpened in refs. [1]- [3] is given by, 1\nτ ≥ max πα(ǫ) 2(E − E 0 ) , πβ(ǫ) 2 ∆E ,(2)\nwhere, α(ǫ) and β(ǫ) = 2arccos( √ ǫ)/π are functions that are equal to unity at ǫ = 0 and are plotted in ref. [2]. The time for which the equality holds in (2) will be referred to as the speed limit time.\n\nAs shown in ref. [1], it is easy to find models in which this limit is approached when one chooses initial states in which most of the energy resources are concentrated in one subsystem of sufficient simplicity. It also easy to construct coherent combinations of basis states that are individually of the form of products of subsystem states, in order to achieve fast evolution. But as the authors demonstrate, when the system is composed of multiple simple subsystems with a Hamiltonian that is relatively homogeneous across the range of subsystems, and when the system begins in an initial product state, then the interaction must generate entanglement among the subsystems in order to approach the speed limit for the evolution. Ref. [2] gives an example in a system of N spins, where one of the terms in the Hamiltonian is a product of the operators for all spin states,\nH = ω 0 N k=1 (1 − σ (k) 1 ) + ω(1 − Π N k=1 σ (k) 1 ) ,(3)\nand where the speed limit is realized for choice of parameters such that ω >> √ N ω 0 . In the present work we give some examples of quite different systems that can approach the speed limit, again involving quite homogeneous Hamiltonians and beginning from a separable initial state. But our models are based on a more conventional pairwise coupling among the spins,\nH = G N i,j λ i,j (σ (i) + σ (j) − + σ (i) − σ (j) + ) ,(4)\nwhere σ + and σ − are the usual raising and lowering operators for an individual spin, and where we will discuss different choices for the λ i,j couplings. Within the context of these systems we define an alternative, and rougher, measure of speed of evolution, different from the speed limit rate. This alternative definition might, for some purposes, better characterize the system's rate of undergoing macroscopic changes. We illustrate by dividing the spin sites into an \"upper\" tier with j = 1, 2..., n 1 and a \"lower\" tier j = n1+1, n1+2..., n1+n2, where n 1 +n 2 = N . We consider initial states in which all of the upper tier of spins are pointed up and all in the lower tier are pointed down,\n|Ψ(0) = | ↑ 1 ⊗ | ↑ 2 ⊗ ...| ↑ n1 ⊗ | ↓ n1+1 ⊗ ...| ↓ n1+n2 .\n(5) Then, to define two different kinds of evolution time, we ask the questions:\n\n1. Following refs [2], [3], for a system with the initial state given by (5) and governed by one of the Hamiltonians that we shall introduce later, what is the time required to evolve to a configuration in which,\nP (t) = Ψ(t)|Q 1 |Ψ(t) < ǫ ,(6)\nwhere\nQ 1 = |Ψ(0) Ψ(0)| ,(7)\nand where ǫ is a fairly small number? This is the time that defines the speed limit.\n\n2. For the same system, what is the time required for the occupancy of, say, the upper tier of states to evolve from the initial condition of all-spins-up to a condition in which the upper tier has much different occupancy? To quantify this question, we define\nR(t) = Ψ(t)|Q 2 |Ψ(t)(8)\nwhere\nQ 2 = (2n 1 ) −1 n1 i=1 (1 + σ (i) 3 ),(9)\nand ask, for example, for the time at which R(t) = .5. The function R is equal to the average fraction of the upper-tier spins that remain pointed up.\n\nFor the Hamiltonian of (3) in the limit of parameters for which the speed limit is approached, the two times defined by the above questions are of the same order of magnitude. But for our Hamiltonians, they can differ greatly, one from the other, in a way that appears to depend on the symmetry of the Hamiltonian. Before turning to specific cases we note that in the first definition of evolution time it would suffice for a single spin in the system to be flipped to obtain an orthogonal configuration. For our case of a system of a large number of spins this would change the average occupancy of the upper tier almost not at all. Alternatively, we could think of evolution to a product wave-function in which each upper-tier single-spin state, originally spinup, is 4 % mixed (in probability) with the spin-down state, so that if we had 100 states in the upper tier the overlap, P , that enters the first criterion, above, would be ≈ exp(−4); whereas, looking at the second criterion, the mixing of the entire upper tier would be only 4%. In this case the speed-limit time is much shorter than the mixing time.\n\nWe shall be particulary interested in the limit of a large number, N , of spins, in our pair-interaction models. The speed limit time τ will turn out to be proportional to N −1 in these systems, keeping coupling constants fixed.\n\n\nMODELS AND THEIR SPEED LIMITS\n\nIn what follows we will consider two possible choices for the coupling-constant function in (4), λ i,j .\n\nCase A: λ i,j = 1/2. This case has complete permutational symmetry among the spins. We can write the Hamiltonian as,\nH A = 1 2 G(J + J − + J − J + ) ,(10)\nwhere\nJ ± = i σ (i) ± ,(11)\nare the raising and lowering operators for the total spin of the system. We specialize to the case n 1 = n 2 ≡ n, for simplicity. Then we obtain the values:\nE 0 = 0, E = nG, ∆E = √ 2nG\n. In this case the speed limit will be thus given by the term involving E − E 0 in (2),\nτ A ≥ πα(ǫ) 2nG .(12)\nCase B: We let the upper set of spins interact with the lower set exactly as in case A, but take no interactions between pairs of spins both in the upper tier, or both in the lower tier. Taking λ i,j = 1/2 for all upper-lower connections and λ i,j = 0 for the intra-tier connections, and defining,\nK ± = n j=1 σ (i) ± , L ± = 2n j=n+1 σ (i) ± ,(13)\nthe Hamiltonian of (4) is,\nH B = G(K + L − + K − L + ).(14)\nIn this case we readily find ∆E = nG and E=0. Determination of the ground state energy E 0 requires a numerical calculation which we discuss later. It will turn out that in this case the speed limit is determined by the ∆E term in (2),\nτ B ≥ πβ(ǫ) 2nG .(15)\nBefore solving these models we consider some possible outcomes for the case of large n. Since G is the only dimensional quantity in the theory, characteristic times are of the form,\nτ = [G h(n)] −1 .(16)\nFor the evolution to proceed at a finite fraction of the speed limits (12) and (15) requires h(n) = const × n for either case. For small times the simple perturbative probability for a single spin to have changed its state is of the form,\nprob = const. × G 2 t 2 n ,(17)\ngiving a characteristic time for appreciable change of single-spin occupation probability of,\nτ 2 = const. × (G √ n) −1 .(18)\nIn this kind of model, as we indicated earlier, reaching a given P (t) < ǫ in the case of large n requires only a change of single state probability of order const./n, and the perturbative time to realize this change is, from (17) of order τ 1 = const. × (Gn) −1 . Thus we expect to get the same dependence on G and n as in the above speed limit times, but with a constant that must be calculated. In contrast the perturbative estimate of the characteristic time for change in R(t) is τ 2 = const. × (G √ n) −1 . When we find, for example, that the evolution for large n is faster, for example going like 1/n or log(n)/n, we shall refer to the phenomenon as a \"speed-up\".\n\n\nSOLUTION FOR MODEL A\n\nWe take n 1 = n 2 = n to define the initial configuration, and we rewrite H A with J = K + L as,\nH A = G[( K + L) · ( K + L) − (K 3 + L 3 ) 2 ] .(19)\nSince we are beginning in an eigenstate of (K 3 + L 3 ), which is conserved and equal to zero, we can discard the final term on the RHS of (19). Next we note that K · K and L · L are separately conserved under H A . The initial state is an eigenstate of these two operators with eigenvalues (n/2)(n/2+1). The eigenvalues of H A are given by Gj(j +1), associated with the states in which the angular momentum K has been added to the angular momentum L to give the total angular momentum quantum number, j. Thus to follow the time evolution it is only necessary to resolve the initial state into eigenstates of J · J, and let the system develop for some period of time. We then take the expectation value of whatever operator, Q, we wish to represent the mixing of the system. To address the criterion #1 (i.e. to compare with the speed limit) we calculate P (t), defined in (6),\nP (t) = n j=0 e −iG j(j+1)t [C −n/2, n/2, 0 n/2, n/2, j ] 2 2 ,(20)\nwhere we have used the notation, C m1,m2,m j1,j2,j for the Clebsch-Gordan coefficient.\n\nFor large n and for t < bG −1 n −1/2 , where b is some number smaller than unity, a sufficiently accurate asymptotic estimate of the Clebsch-Gordan coefficients to be used in (20) is given by,\nC −n/2, n/2, 0 n/2, n/2, j 2 ≈ j n exp[− j 2 2n ] ,(21)\nleading directly to the result,\nP (t) = (1 + G 2 n 2 t 2 ) −1 (1 + O(G √ n t) ,(22)\nwhich holds for times less than those of order (G √ n) −1 .\n\nWe have confirmed the limiting result (22) with direct numerical calculations. In fig.1 we plot the function P against the dimensionless coordinate, n G t. On the same plot we indicate the speed limit rate implied by (12),\nplotting the function ǫ(t), where t = πα[ǫ(t)]/2(E − E 0 ), E − E 0 = nG,\nand we have used the approximation α(ǫ) ≈ β(ǫ) 2 suggested in ref. [3]. We see from fig.1 that the evolution in the model procedes at roughly half the speed-limit rate. We have confirmed the analytic approximations leading to (22) by direct numerical calculations, and find that the curves for P are essentially congruent for all n ≥ 4. A numerical calculation over a longer time interval shows that after a time of order G −1 n −1/2 , where the approximations of (22) fail, the function P (t) remains at a small value for an extended time that is of order (Gn) −1 , then reversing its earlier decline in a symmetric fashion; the function is periodic with a period 2π/G, as is clear from (20).\n\nTo address criterion #2, based on the evolution of the expectation value of the z-component of the total spin of the upper tier, we calculate R(t) defined in (8), obtaining,\nR(t) = 1 − n k=0\nk n n j=0 e −iG j(j+1)t C −n/2+k, n/2−k, 0 n/2, n/2, j C −n/2, n/2, 0 n/2, n/2, j 2 .\n\n(23)\n\nIn fig.2, we show plots of numerical results for n = 8, 16, 32, 64, 128, 256, in the region in which R(t) declines from unity to a value less than .6. The time required to reach R(Gnt) = .6 is strongly dependent on n, as we see in fig.2. If R were to have developed at a fixed fraction of the speed limit rate (as did P in the previous example), then the value of the dimensionless variable Gnt required to reach this point would have been independent of n . Friedland and Lunardini [9] have established that for large n the evolution time behaves as (G √ n) −1 , with a coefficient of order unity; so that the characteristic values of Gnt increase as √ n . This is essentially the perturbative time dependence that we defined above 2 , and is already roughly borne out in a fit to the intercepts of the curves shown in fig. 2 with the line R = .6.\n\n2 This result is again obtainable by using the asymptotic forms of Clebsch-Gordan coefficients. In place of |Q| , Friedland and Lunardini consider the probability that a single, typical spin is flipped, summed over all possible fates for the remaining system, and ingeniously reduce the problem in such a way that only a single sum analogous to that in (23) need be performed.\n\n\nSOLUTIONS FOR MODEL B\n\nFirst we enumerate the set of states that are dynamically connected, given the initial state (5) with n 1 = n 2 = n and the Hamiltonian (14). The initial state is an eigenstate of K 2 , and L 2 , each of which commutes with the Hamiltonian, and each with the same eigenvalue, (n/2)(n/2 + 1). The totalẑ component \"angular momentum\", K 3 + L 3 is also conserved and equal to zero for our set of states. Any number of the n spins in the upper tier, all initially up, may be flipped, leading to n+1 possibilities for K 3 for this tier by itself. For each such configuration there is also only a single state of the lower tier. Thus we can index the states by the number of flips plus one, i, where i takes on the values 1, 2...n + 1. We express the operator products that occur in the Hamiltonian in this basis as,\ni|K − L + |i − 1 = (n − i + 1)(i); i = 1, 2...n + 1 i − 1|K + L − |i = (n − i + 2)(i − 1); i = 1, 2...n + 1 ,(24)\nwhich come directly from the standard angular momentum matrices. We now solve numerically for a (n + 1) component wave function Ψ(t), using the Hamiltonian (14) with the substitution (24) and the initial condition Ψ i (0) = δ i,1 . We then calculate both of our measures of change,\nP (t) = |Ψ 1 (t)| 2 ,(25)\nand\nR(t) = n+1 i=1 |Ψ i (t)| 2 (n − i + 1)n −1 .(26)\nWe also solve numerically for the ground state energy, to confirm that it is the ∆E condition of(2) that applies. We find that the approximation,\nE 0 = −0.34n − 0.49n 2 ,(27)\nfits the energies to within 1% over the range n = 4 − 100.\n\nThus we have E − E 0 > ∆E over the whole range that we consider, and the speed limit is determined from the term in (2) involving ∆E. In fig.3 we plot P (t) for n = 64 against the variable gN t. On the same plot we indicate the limitation imposed by (15) by plotting the function ǫ(t) that is the solution to the equation t = πβ(ǫ)/(2 ∆E) where ∆E = nG. Comparing with the case of model A, we see that the evolution proceeds at much more nearly the speed limit rate. The plots of P are almost identical for all n ≥ 4.\n\nIn line R = .4 occur at very nearly equally spaced points. Equal spacing indicates a mixing time decreasing with n as τ ∝ log(n)/n. This is in contrast to the symmetrical model A in which characteristic time decreases as τ ∝ 1/ √ n, which we defined as the \"perturbative\" time. Thus we have a large speed-up over the perturbative estimate, as n increases. For the case n = 128, if we define the characteristic time according to criterion #2, the speed-up over the perturbative rate is a factor of approximately 4. \n\n\nDISCUSSION\n\nWe have considered large spin systems with couplings among pairs such that the quantum speed limit time is proportional to the inverse of the number of spins, τ ∝ N −1 , where we taken an initial state which is completely separable. We have shown that the time required for the squared overlap , P (t), of the evolved state with the initial state to become small is indeed proportional to N −1 , with a coefficient which in model A is about twice the speed limit value, and in model B is only 10-20% greater than the speed limit time, depending on the value of ǫ one chooses for purposes of comparison.\n\nWe have also looked at the time scale for change of another attribute of these systems, R(t), the fraction of upper tier spins that have been flipped. Here the results were drastically different for the two models; in model A, where there were couplings among all of the spins, the evolution time for R(t) is proportional to N −1/2 , which we characterize as the \"perturbative\" time, rather than to N −1 . But in model B, with breaking of permutational symmetry 3 the evolution time is reduced to a time of order N −1 log[N ], a speed-up to near the N −1 level of the speed-limit time. It is tempting to conjecture that with more breaking of the symmetry we could lose the log, and perhaps even approach speed-limit rates. The curves shown in ref. [8], however, for the case of completely broken symmetry, were inconclusive in this regard, due to computational limitations. More generally, it would seem to us to be of some interest first to define \"macroscopic change\" more precisely in a large N limit, and then to try to find general results, analogous to the speed-limit results, on the limitations for the rates for this macroscopic change.\n\nWe should note that we have tested models in which n 1 = n 2 and find results qualitatively the same as those reported for the two models treated in this paper. We set out, in calculating R(t) to get an estimate of the rate at which the average totalẑ component spin of the upper tier, K 3 , changes. But see that in model B the measure R(t) is very nearly zero at the first minimum, indicating that almost all the spins have been flipped. We could compare the results, where (up to logarithms) the characteristic time for evolution is of order (GN ) −1 , to the results for the simplest Hamiltonian that will flip each spin in time (GN ) −1 , namely,\nH C = π 2 GN N i=1 σ (i) 1 .(28)\nMeasuring the \"energy resources\" of this Hamiltonian by ∆E = (π/2)GN 3/2 , and comparing to ∆E = G(N/2) for the Hamiltonian (14), we conclude that the model with pair couplings and consequent many-body entanglements does indeed succeed in rotating the complete ensemble of spins in a very efficient way, for large n. Finally, we comment on the question as to how much substance is contained in the statement that \"entanglement is the key to speed-up of rates\" a paraphrase of a point emphasized in [1] and also in a quite different context in [8]. Of course, states do become entangled during the evolution under the interactions that we have taken in our models. But there is no general agreement known to us on the quantification of entanglement in the case of multicomponent systems, even in the case of pure states. We can, however, perhaps rather arbitrarily, consider the entanglement of two systems, U and L, where U contains all of the upper tier spins and L contains the lower tier states. Then a measure of entanglement between the two systems is given by the entropy of entanglement obtained by tracing out one subsystem's coordinates in the density matrix, say the U subsystem, to define a reduced density matrix ρ L for the L subsystem, and then calculating the von-Neumann entropy corresponding to ρ L [10] [11],\nS e = −T rρ L log[ρ L ] .(29)\nWe have calculated S e as a function of time for models A and B, using the wave-function solutions underlying the calculations discussed above. At a time Gnt = 1, at which P ≈ .5 in either model, we find that, so defined, the entanglement is about 30% more for the case with broken symmetry than for the completely symmetric case, and relatively independent of the number of particles. Thus in our models there is an perhaps an indication of a correlation between the rate of growth of entanglement and the efficiency of transformation. Of course, in the pure states that we have considered, the entanglement, as defined above, can both increase and decrease in time, and comparisons will depend on the time of the sampling.\n\nFIG. 1 :\n1The time evolution of the function P (t) for model A (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.\n\nFIG. 2 :\n2The time evolution of the function R(t) for model A, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256. The curves for higher values of n lie progressively to the right of the lower n curves.\n\nFIG. 3 :\n3fig 4.we show plots of the scaled function R(t) for n = 8, 16, 32, 64, 128, 256, 512, again plotting against the variable Gnt. Note that the intersections with the The time evolution of the function P (t) for model B (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.\n\nFIG. 4 :\n4The time evolution of the function R(t) for model B, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256, 512. The curves for higher values of n lie progressively to the right of the lower n curves.\nNote that we broke the spin states into two sets both for the purpose of breaking the permutation symmetry by setting to zero the intraset interactions, and for the purpose defining which states were initially up and which down. We used the same division for the two purposes only to be able (for large N ) to reduce the evolution problem to calculable dimensions. This is an example of how very minimal is our breaking of the symmetries of the symmetric model.\n\n. V Giovannetti, S Lloyd, L Maccone, quant-ph/0206001Europhys. Lett. 62615V. Giovannetti, S.Lloyd, L. Maccone, Europhys. Lett. 62, 615 (2003), quant-ph/0206001\n\n. V Giovannetti, S Lloyd, L Maccone, quant-ph/0210197Phys. Rev. 6752109V. Giovannetti, S.Lloyd, L. Maccone, Phys. Rev. A67, 052109 (2003), quant-ph/0210197\n\nFluctuations and Noise in Photonics and Quantum Optics. V Giovannetti, S Lloyd, L Maccone ; Bott, D , quant-ph/0303085Proceedings of the SPIE. 5111V. Giovannetti, S.Lloyd, L. Maccone, Fluctuations and Noise in Photonics and Quantum Optics. Edited by Ab- bott, D. et al. Proceedings of the SPIE, Volume 5111, pp. 1-6 (2003), quant-ph/0303085\n\n. K Bhattacharya, J. Phys. 162993K. Bhattacharya, J. Phys. A16, 2993 (1983)\n\n. P Pfeifer, Phys. Rev. Lett. 703365P. Pfeifer, Phys. Rev. Lett. 70, 3365 (1993)\n\n. L Mandelstam, I G Tamm, J. Phys. USSR. 9249L. Mandelstam and I. G. Tamm, J. Phys. USSR 9, 249 (1945)\n\n. N Margulus, L B Levitan, Physica. 120188N. Margulus and L. B. Levitan, Physica D120, 188 (1998)\n\n. N F Bell, A A Rawlinson, R F Sawyer, Phys.Lett. 57386N. F. Bell, A. A. Rawlinson, and R. F. Sawyer, Phys.Lett. B573, 86 (2003)\n\n. A Friedland, C Lunardini, quant-ph/0303085031043A. Friedland and C. Lunardini, JHEP0310, 043 (2003) ;quant-ph/0303085\n\n. C H Bennett, H J Bernstein, S Popescu, B Schumacher, Phys. Rev. A. 532046C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schu- macher, Phys. Rev. A 53, 2046 (1996).\n\n. S Hill, W K Wootters, Phys. Rev. Lett. 785022S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997);\n\n. W K Wootters, 802245W. K. Wootters, ibid. 80, 2245 (1998)\n"},"corpus_id":{"kind":"number","value":119486081,"string":"119,486,081"},"external_ids":{"kind":"string","value":"{\n \"arxiv\": \"quant-ph/0312217\",\n \"mag\": 2142484020,\n \"acl\": null,\n \"pubmed\": null,\n \"pubmedcentral\": null,\n \"dblp\": null,\n \"doi\": \"10.1103/physreva.70.022308\"\n}"},"source":{"kind":"string","value":"{\n \"pdf_urls\": [\n \"https://export.arxiv.org/pdf/quant-ph/0312217v3.pdf\"\n ],\n \"pdf_sha\": \"f566d4f2a99036ecbd8d401432b8ff6a747087d6\",\n \"open_access\": {\n \"license\": null,\n \"url\": \"http://arxiv.org/pdf/quant-ph/0312217\",\n \"status\": \"GREEN\"\n }\n}"},"title":{"kind":"string","value":"Evolution speed in some coupled-spin models"},"authors":{"kind":"list like","value":["R F Sawyer \nDepartment of Physics\nUniversity of California at Santa Barbara\n93106Santa BarbaraCalifornia"],"string":"[\n \"R F Sawyer \\nDepartment of Physics\\nUniversity of California at Santa Barbara\\n93106Santa BarbaraCalifornia\"\n]","isConversational":false},"abstract":{"kind":"string","value":"We investigate the time evolution of some models with N spins and pairwise couplings, for the case of large N, in order to compare evolution times with \"speed limit\" minima derived in the literature. Both in a (symmetric) case with couplings of the same strength between each pair and in a case of broken symmetry, the times necessary for evolution to a state in which the simplest initial state has evolved into a nearly orthogonal state are proportional to 1/N, as is the speed limit time. However the coefficient in the broken symmetry case comes much closer to the speed limit value. Introducing a different criterion for evolution speed, based on macroscopic changes in occupation, we find a corresponding enhancement in rates in the asymmetric case as compared to the symmetric case."},"sections":{"kind":"list like","value":[{"title":"INTRODUCTION","content":"In a recent series of papers, Giovannetti, Lloyd, and Maccone [1]- [3] have elucidated the role of entanglement in approaching theoretical minima of the times required for quantum systems to progress from a prescribed initial state to a state that is orthogonal or nearly orthogonal to the initial state. The criterion for evaluating the outcome is the reduction of the square of the overlap of the initial and final wave-functions to some value less than ǫ, where ǫ is fairly small, but not necessarily infinitesimal, P (t) ≡ Ψ(t)|Ψ(0) < ǫ. The \"theoretical minimum\" of evolution times that we refer to depends on the lesser of the two quantities,\nand E − E 0 ≡< H > −E 0 , where E 0 is the ground state energy of the system and the brackets <> in all cases stand for the expectation value in the initial state. In terms of these quantities the fastest evolution time for meeting the criterion P (τ ) = ǫ, as derived in refs. [4]- [7] and sharpened in refs. [1]- [3] is given by, 1\nwhere, α(ǫ) and β(ǫ) = 2arccos( √ ǫ)/π are functions that are equal to unity at ǫ = 0 and are plotted in ref. [2]. The time for which the equality holds in (2) will be referred to as the speed limit time.\nAs shown in ref. [1], it is easy to find models in which this limit is approached when one chooses initial states in which most of the energy resources are concentrated in one subsystem of sufficient simplicity. It also easy to construct coherent combinations of basis states that are individually of the form of products of subsystem states, in order to achieve fast evolution. But as the authors demonstrate, when the system is composed of multiple simple subsystems with a Hamiltonian that is relatively homogeneous across the range of subsystems, and when the system begins in an initial product state, then the interaction must generate entanglement among the subsystems in order to approach the speed limit for the evolution. Ref. [2] gives an example in a system of N spins, where one of the terms in the Hamiltonian is a product of the operators for all spin states,\nand where the speed limit is realized for choice of parameters such that ω >> √ N ω 0 . In the present work we give some examples of quite different systems that can approach the speed limit, again involving quite homogeneous Hamiltonians and beginning from a separable initial state. But our models are based on a more conventional pairwise coupling among the spins,\nwhere σ + and σ − are the usual raising and lowering operators for an individual spin, and where we will discuss different choices for the λ i,j couplings. Within the context of these systems we define an alternative, and rougher, measure of speed of evolution, different from the speed limit rate. This alternative definition might, for some purposes, better characterize the system's rate of undergoing macroscopic changes. We illustrate by dividing the spin sites into an \"upper\" tier with j = 1, 2..., n 1 and a \"lower\" tier j = n1+1, n1+2..., n1+n2, where n 1 +n 2 = N . We consider initial states in which all of the upper tier of spins are pointed up and all in the lower tier are pointed down,\n(5) Then, to define two different kinds of evolution time, we ask the questions:\n1. Following refs [2], [3], for a system with the initial state given by (5) and governed by one of the Hamiltonians that we shall introduce later, what is the time required to evolve to a configuration in which,\nwhere\nand where ǫ is a fairly small number? This is the time that defines the speed limit.\n2. For the same system, what is the time required for the occupancy of, say, the upper tier of states to evolve from the initial condition of all-spins-up to a condition in which the upper tier has much different occupancy? To quantify this question, we define\nwhere\nand ask, for example, for the time at which R(t) = .5. The function R is equal to the average fraction of the upper-tier spins that remain pointed up.\nFor the Hamiltonian of (3) in the limit of parameters for which the speed limit is approached, the two times defined by the above questions are of the same order of magnitude. But for our Hamiltonians, they can differ greatly, one from the other, in a way that appears to depend on the symmetry of the Hamiltonian. Before turning to specific cases we note that in the first definition of evolution time it would suffice for a single spin in the system to be flipped to obtain an orthogonal configuration. For our case of a system of a large number of spins this would change the average occupancy of the upper tier almost not at all. Alternatively, we could think of evolution to a product wave-function in which each upper-tier single-spin state, originally spinup, is 4 % mixed (in probability) with the spin-down state, so that if we had 100 states in the upper tier the overlap, P , that enters the first criterion, above, would be ≈ exp(−4); whereas, looking at the second criterion, the mixing of the entire upper tier would be only 4%. In this case the speed-limit time is much shorter than the mixing time.\nWe shall be particulary interested in the limit of a large number, N , of spins, in our pair-interaction models. The speed limit time τ will turn out to be proportional to N −1 in these systems, keeping coupling constants fixed."},{"title":"MODELS AND THEIR SPEED LIMITS","content":"In what follows we will consider two possible choices for the coupling-constant function in (4), λ i,j .\nCase A: λ i,j = 1/2. This case has complete permutational symmetry among the spins. We can write the Hamiltonian as,\nwhere\nare the raising and lowering operators for the total spin of the system. We specialize to the case n 1 = n 2 ≡ n, for simplicity. Then we obtain the values:\n. In this case the speed limit will be thus given by the term involving E − E 0 in (2),\nCase B: We let the upper set of spins interact with the lower set exactly as in case A, but take no interactions between pairs of spins both in the upper tier, or both in the lower tier. Taking λ i,j = 1/2 for all upper-lower connections and λ i,j = 0 for the intra-tier connections, and defining,\nthe Hamiltonian of (4) is,\nIn this case we readily find ∆E = nG and E=0. Determination of the ground state energy E 0 requires a numerical calculation which we discuss later. It will turn out that in this case the speed limit is determined by the ∆E term in (2),\nBefore solving these models we consider some possible outcomes for the case of large n. Since G is the only dimensional quantity in the theory, characteristic times are of the form,\nFor the evolution to proceed at a finite fraction of the speed limits (12) and (15) requires h(n) = const × n for either case. For small times the simple perturbative probability for a single spin to have changed its state is of the form,\ngiving a characteristic time for appreciable change of single-spin occupation probability of,\nIn this kind of model, as we indicated earlier, reaching a given P (t) < ǫ in the case of large n requires only a change of single state probability of order const./n, and the perturbative time to realize this change is, from (17) of order τ 1 = const. × (Gn) −1 . Thus we expect to get the same dependence on G and n as in the above speed limit times, but with a constant that must be calculated. In contrast the perturbative estimate of the characteristic time for change in R(t) is τ 2 = const. × (G √ n) −1 . When we find, for example, that the evolution for large n is faster, for example going like 1/n or log(n)/n, we shall refer to the phenomenon as a \"speed-up\"."},{"title":"SOLUTION FOR MODEL A","content":"We take n 1 = n 2 = n to define the initial configuration, and we rewrite H A with J = K + L as,\nSince we are beginning in an eigenstate of (K 3 + L 3 ), which is conserved and equal to zero, we can discard the final term on the RHS of (19). Next we note that K · K and L · L are separately conserved under H A . The initial state is an eigenstate of these two operators with eigenvalues (n/2)(n/2+1). The eigenvalues of H A are given by Gj(j +1), associated with the states in which the angular momentum K has been added to the angular momentum L to give the total angular momentum quantum number, j. Thus to follow the time evolution it is only necessary to resolve the initial state into eigenstates of J · J, and let the system develop for some period of time. We then take the expectation value of whatever operator, Q, we wish to represent the mixing of the system. To address the criterion #1 (i.e. to compare with the speed limit) we calculate P (t), defined in (6),\nwhere we have used the notation, C m1,m2,m j1,j2,j for the Clebsch-Gordan coefficient.\nFor large n and for t < bG −1 n −1/2 , where b is some number smaller than unity, a sufficiently accurate asymptotic estimate of the Clebsch-Gordan coefficients to be used in (20) is given by,\nleading directly to the result,\nwhich holds for times less than those of order (G √ n) −1 .\nWe have confirmed the limiting result (22) with direct numerical calculations. In fig.1 we plot the function P against the dimensionless coordinate, n G t. On the same plot we indicate the speed limit rate implied by (12),\nand we have used the approximation α(ǫ) ≈ β(ǫ) 2 suggested in ref. [3]. We see from fig.1 that the evolution in the model procedes at roughly half the speed-limit rate. We have confirmed the analytic approximations leading to (22) by direct numerical calculations, and find that the curves for P are essentially congruent for all n ≥ 4. A numerical calculation over a longer time interval shows that after a time of order G −1 n −1/2 , where the approximations of (22) fail, the function P (t) remains at a small value for an extended time that is of order (Gn) −1 , then reversing its earlier decline in a symmetric fashion; the function is periodic with a period 2π/G, as is clear from (20).\nTo address criterion #2, based on the evolution of the expectation value of the z-component of the total spin of the upper tier, we calculate R(t) defined in (8), obtaining,\nk n n j=0 e −iG j(j+1)t C −n/2+k, n/2−k, 0 n/2, n/2, j C −n/2, n/2, 0 n/2, n/2, j 2 .\n(23)\nIn fig.2, we show plots of numerical results for n = 8, 16, 32, 64, 128, 256, in the region in which R(t) declines from unity to a value less than .6. The time required to reach R(Gnt) = .6 is strongly dependent on n, as we see in fig.2. If R were to have developed at a fixed fraction of the speed limit rate (as did P in the previous example), then the value of the dimensionless variable Gnt required to reach this point would have been independent of n . Friedland and Lunardini [9] have established that for large n the evolution time behaves as (G √ n) −1 , with a coefficient of order unity; so that the characteristic values of Gnt increase as √ n . This is essentially the perturbative time dependence that we defined above 2 , and is already roughly borne out in a fit to the intercepts of the curves shown in fig. 2 with the line R = .6.\n2 This result is again obtainable by using the asymptotic forms of Clebsch-Gordan coefficients. In place of |Q| , Friedland and Lunardini consider the probability that a single, typical spin is flipped, summed over all possible fates for the remaining system, and ingeniously reduce the problem in such a way that only a single sum analogous to that in (23) need be performed."},{"title":"SOLUTIONS FOR MODEL B","content":"First we enumerate the set of states that are dynamically connected, given the initial state (5) with n 1 = n 2 = n and the Hamiltonian (14). The initial state is an eigenstate of K 2 , and L 2 , each of which commutes with the Hamiltonian, and each with the same eigenvalue, (n/2)(n/2 + 1). The totalẑ component \"angular momentum\", K 3 + L 3 is also conserved and equal to zero for our set of states. Any number of the n spins in the upper tier, all initially up, may be flipped, leading to n+1 possibilities for K 3 for this tier by itself. For each such configuration there is also only a single state of the lower tier. Thus we can index the states by the number of flips plus one, i, where i takes on the values 1, 2...n + 1. We express the operator products that occur in the Hamiltonian in this basis as,\nwhich come directly from the standard angular momentum matrices. We now solve numerically for a (n + 1) component wave function Ψ(t), using the Hamiltonian (14) with the substitution (24) and the initial condition Ψ i (0) = δ i,1 . We then calculate both of our measures of change,\nand\nWe also solve numerically for the ground state energy, to confirm that it is the ∆E condition of(2) that applies. We find that the approximation,\nfits the energies to within 1% over the range n = 4 − 100.\nThus we have E − E 0 > ∆E over the whole range that we consider, and the speed limit is determined from the term in (2) involving ∆E. In fig.3 we plot P (t) for n = 64 against the variable gN t. On the same plot we indicate the limitation imposed by (15) by plotting the function ǫ(t) that is the solution to the equation t = πβ(ǫ)/(2 ∆E) where ∆E = nG. Comparing with the case of model A, we see that the evolution proceeds at much more nearly the speed limit rate. The plots of P are almost identical for all n ≥ 4.\nIn line R = .4 occur at very nearly equally spaced points. Equal spacing indicates a mixing time decreasing with n as τ ∝ log(n)/n. This is in contrast to the symmetrical model A in which characteristic time decreases as τ ∝ 1/ √ n, which we defined as the \"perturbative\" time. Thus we have a large speed-up over the perturbative estimate, as n increases. For the case n = 128, if we define the characteristic time according to criterion #2, the speed-up over the perturbative rate is a factor of approximately 4."},{"title":"DISCUSSION","content":"We have considered large spin systems with couplings among pairs such that the quantum speed limit time is proportional to the inverse of the number of spins, τ ∝ N −1 , where we taken an initial state which is completely separable. We have shown that the time required for the squared overlap , P (t), of the evolved state with the initial state to become small is indeed proportional to N −1 , with a coefficient which in model A is about twice the speed limit value, and in model B is only 10-20% greater than the speed limit time, depending on the value of ǫ one chooses for purposes of comparison.\nWe have also looked at the time scale for change of another attribute of these systems, R(t), the fraction of upper tier spins that have been flipped. Here the results were drastically different for the two models; in model A, where there were couplings among all of the spins, the evolution time for R(t) is proportional to N −1/2 , which we characterize as the \"perturbative\" time, rather than to N −1 . But in model B, with breaking of permutational symmetry 3 the evolution time is reduced to a time of order N −1 log[N ], a speed-up to near the N −1 level of the speed-limit time. It is tempting to conjecture that with more breaking of the symmetry we could lose the log, and perhaps even approach speed-limit rates. The curves shown in ref. [8], however, for the case of completely broken symmetry, were inconclusive in this regard, due to computational limitations. More generally, it would seem to us to be of some interest first to define \"macroscopic change\" more precisely in a large N limit, and then to try to find general results, analogous to the speed-limit results, on the limitations for the rates for this macroscopic change.\nWe should note that we have tested models in which n 1 = n 2 and find results qualitatively the same as those reported for the two models treated in this paper. We set out, in calculating R(t) to get an estimate of the rate at which the average totalẑ component spin of the upper tier, K 3 , changes. But see that in model B the measure R(t) is very nearly zero at the first minimum, indicating that almost all the spins have been flipped. We could compare the results, where (up to logarithms) the characteristic time for evolution is of order (GN ) −1 , to the results for the simplest Hamiltonian that will flip each spin in time (GN ) −1 , namely,\nMeasuring the \"energy resources\" of this Hamiltonian by ∆E = (π/2)GN 3/2 , and comparing to ∆E = G(N/2) for the Hamiltonian (14), we conclude that the model with pair couplings and consequent many-body entanglements does indeed succeed in rotating the complete ensemble of spins in a very efficient way, for large n. Finally, we comment on the question as to how much substance is contained in the statement that \"entanglement is the key to speed-up of rates\" a paraphrase of a point emphasized in [1] and also in a quite different context in [8]. Of course, states do become entangled during the evolution under the interactions that we have taken in our models. But there is no general agreement known to us on the quantification of entanglement in the case of multicomponent systems, even in the case of pure states. We can, however, perhaps rather arbitrarily, consider the entanglement of two systems, U and L, where U contains all of the upper tier spins and L contains the lower tier states. Then a measure of entanglement between the two systems is given by the entropy of entanglement obtained by tracing out one subsystem's coordinates in the density matrix, say the U subsystem, to define a reduced density matrix ρ L for the L subsystem, and then calculating the von-Neumann entropy corresponding to ρ L [10] [11],\nWe have calculated S e as a function of time for models A and B, using the wave-function solutions underlying the calculations discussed above. At a time Gnt = 1, at which P ≈ .5 in either model, we find that, so defined, the entanglement is about 30% more for the case with broken symmetry than for the completely symmetric case, and relatively independent of the number of particles. Thus in our models there is an perhaps an indication of a correlation between the rate of growth of entanglement and the efficiency of transformation. Of course, in the pure states that we have considered, the entanglement, as defined above, can both increase and decrease in time, and comparisons will depend on the time of the sampling."},{"title":"FIG. 1 :","content":""},{"title":"FIG. 2 :","content":""},{"title":"FIG. 3 :","content":""},{"title":"FIG. 4 :","content":""}],"string":"[\n {\n \"title\": \"INTRODUCTION\",\n \"content\": \"In a recent series of papers, Giovannetti, Lloyd, and Maccone [1]- [3] have elucidated the role of entanglement in approaching theoretical minima of the times required for quantum systems to progress from a prescribed initial state to a state that is orthogonal or nearly orthogonal to the initial state. The criterion for evaluating the outcome is the reduction of the square of the overlap of the initial and final wave-functions to some value less than ǫ, where ǫ is fairly small, but not necessarily infinitesimal, P (t) ≡ Ψ(t)|Ψ(0) < ǫ. The \\\"theoretical minimum\\\" of evolution times that we refer to depends on the lesser of the two quantities,\\nand E − E 0 ≡< H > −E 0 , where E 0 is the ground state energy of the system and the brackets <> in all cases stand for the expectation value in the initial state. In terms of these quantities the fastest evolution time for meeting the criterion P (τ ) = ǫ, as derived in refs. [4]- [7] and sharpened in refs. [1]- [3] is given by, 1\\nwhere, α(ǫ) and β(ǫ) = 2arccos( √ ǫ)/π are functions that are equal to unity at ǫ = 0 and are plotted in ref. [2]. The time for which the equality holds in (2) will be referred to as the speed limit time.\\nAs shown in ref. [1], it is easy to find models in which this limit is approached when one chooses initial states in which most of the energy resources are concentrated in one subsystem of sufficient simplicity. It also easy to construct coherent combinations of basis states that are individually of the form of products of subsystem states, in order to achieve fast evolution. But as the authors demonstrate, when the system is composed of multiple simple subsystems with a Hamiltonian that is relatively homogeneous across the range of subsystems, and when the system begins in an initial product state, then the interaction must generate entanglement among the subsystems in order to approach the speed limit for the evolution. Ref. [2] gives an example in a system of N spins, where one of the terms in the Hamiltonian is a product of the operators for all spin states,\\nand where the speed limit is realized for choice of parameters such that ω >> √ N ω 0 . In the present work we give some examples of quite different systems that can approach the speed limit, again involving quite homogeneous Hamiltonians and beginning from a separable initial state. But our models are based on a more conventional pairwise coupling among the spins,\\nwhere σ + and σ − are the usual raising and lowering operators for an individual spin, and where we will discuss different choices for the λ i,j couplings. Within the context of these systems we define an alternative, and rougher, measure of speed of evolution, different from the speed limit rate. This alternative definition might, for some purposes, better characterize the system's rate of undergoing macroscopic changes. We illustrate by dividing the spin sites into an \\\"upper\\\" tier with j = 1, 2..., n 1 and a \\\"lower\\\" tier j = n1+1, n1+2..., n1+n2, where n 1 +n 2 = N . We consider initial states in which all of the upper tier of spins are pointed up and all in the lower tier are pointed down,\\n(5) Then, to define two different kinds of evolution time, we ask the questions:\\n1. Following refs [2], [3], for a system with the initial state given by (5) and governed by one of the Hamiltonians that we shall introduce later, what is the time required to evolve to a configuration in which,\\nwhere\\nand where ǫ is a fairly small number? This is the time that defines the speed limit.\\n2. For the same system, what is the time required for the occupancy of, say, the upper tier of states to evolve from the initial condition of all-spins-up to a condition in which the upper tier has much different occupancy? To quantify this question, we define\\nwhere\\nand ask, for example, for the time at which R(t) = .5. The function R is equal to the average fraction of the upper-tier spins that remain pointed up.\\nFor the Hamiltonian of (3) in the limit of parameters for which the speed limit is approached, the two times defined by the above questions are of the same order of magnitude. But for our Hamiltonians, they can differ greatly, one from the other, in a way that appears to depend on the symmetry of the Hamiltonian. Before turning to specific cases we note that in the first definition of evolution time it would suffice for a single spin in the system to be flipped to obtain an orthogonal configuration. For our case of a system of a large number of spins this would change the average occupancy of the upper tier almost not at all. Alternatively, we could think of evolution to a product wave-function in which each upper-tier single-spin state, originally spinup, is 4 % mixed (in probability) with the spin-down state, so that if we had 100 states in the upper tier the overlap, P , that enters the first criterion, above, would be ≈ exp(−4); whereas, looking at the second criterion, the mixing of the entire upper tier would be only 4%. In this case the speed-limit time is much shorter than the mixing time.\\nWe shall be particulary interested in the limit of a large number, N , of spins, in our pair-interaction models. The speed limit time τ will turn out to be proportional to N −1 in these systems, keeping coupling constants fixed.\"\n },\n {\n \"title\": \"MODELS AND THEIR SPEED LIMITS\",\n \"content\": \"In what follows we will consider two possible choices for the coupling-constant function in (4), λ i,j .\\nCase A: λ i,j = 1/2. This case has complete permutational symmetry among the spins. We can write the Hamiltonian as,\\nwhere\\nare the raising and lowering operators for the total spin of the system. We specialize to the case n 1 = n 2 ≡ n, for simplicity. Then we obtain the values:\\n. In this case the speed limit will be thus given by the term involving E − E 0 in (2),\\nCase B: We let the upper set of spins interact with the lower set exactly as in case A, but take no interactions between pairs of spins both in the upper tier, or both in the lower tier. Taking λ i,j = 1/2 for all upper-lower connections and λ i,j = 0 for the intra-tier connections, and defining,\\nthe Hamiltonian of (4) is,\\nIn this case we readily find ∆E = nG and E=0. Determination of the ground state energy E 0 requires a numerical calculation which we discuss later. It will turn out that in this case the speed limit is determined by the ∆E term in (2),\\nBefore solving these models we consider some possible outcomes for the case of large n. Since G is the only dimensional quantity in the theory, characteristic times are of the form,\\nFor the evolution to proceed at a finite fraction of the speed limits (12) and (15) requires h(n) = const × n for either case. For small times the simple perturbative probability for a single spin to have changed its state is of the form,\\ngiving a characteristic time for appreciable change of single-spin occupation probability of,\\nIn this kind of model, as we indicated earlier, reaching a given P (t) < ǫ in the case of large n requires only a change of single state probability of order const./n, and the perturbative time to realize this change is, from (17) of order τ 1 = const. × (Gn) −1 . Thus we expect to get the same dependence on G and n as in the above speed limit times, but with a constant that must be calculated. In contrast the perturbative estimate of the characteristic time for change in R(t) is τ 2 = const. × (G √ n) −1 . When we find, for example, that the evolution for large n is faster, for example going like 1/n or log(n)/n, we shall refer to the phenomenon as a \\\"speed-up\\\".\"\n },\n {\n \"title\": \"SOLUTION FOR MODEL A\",\n \"content\": \"We take n 1 = n 2 = n to define the initial configuration, and we rewrite H A with J = K + L as,\\nSince we are beginning in an eigenstate of (K 3 + L 3 ), which is conserved and equal to zero, we can discard the final term on the RHS of (19). Next we note that K · K and L · L are separately conserved under H A . The initial state is an eigenstate of these two operators with eigenvalues (n/2)(n/2+1). The eigenvalues of H A are given by Gj(j +1), associated with the states in which the angular momentum K has been added to the angular momentum L to give the total angular momentum quantum number, j. Thus to follow the time evolution it is only necessary to resolve the initial state into eigenstates of J · J, and let the system develop for some period of time. We then take the expectation value of whatever operator, Q, we wish to represent the mixing of the system. To address the criterion #1 (i.e. to compare with the speed limit) we calculate P (t), defined in (6),\\nwhere we have used the notation, C m1,m2,m j1,j2,j for the Clebsch-Gordan coefficient.\\nFor large n and for t < bG −1 n −1/2 , where b is some number smaller than unity, a sufficiently accurate asymptotic estimate of the Clebsch-Gordan coefficients to be used in (20) is given by,\\nleading directly to the result,\\nwhich holds for times less than those of order (G √ n) −1 .\\nWe have confirmed the limiting result (22) with direct numerical calculations. In fig.1 we plot the function P against the dimensionless coordinate, n G t. On the same plot we indicate the speed limit rate implied by (12),\\nand we have used the approximation α(ǫ) ≈ β(ǫ) 2 suggested in ref. [3]. We see from fig.1 that the evolution in the model procedes at roughly half the speed-limit rate. We have confirmed the analytic approximations leading to (22) by direct numerical calculations, and find that the curves for P are essentially congruent for all n ≥ 4. A numerical calculation over a longer time interval shows that after a time of order G −1 n −1/2 , where the approximations of (22) fail, the function P (t) remains at a small value for an extended time that is of order (Gn) −1 , then reversing its earlier decline in a symmetric fashion; the function is periodic with a period 2π/G, as is clear from (20).\\nTo address criterion #2, based on the evolution of the expectation value of the z-component of the total spin of the upper tier, we calculate R(t) defined in (8), obtaining,\\nk n n j=0 e −iG j(j+1)t C −n/2+k, n/2−k, 0 n/2, n/2, j C −n/2, n/2, 0 n/2, n/2, j 2 .\\n(23)\\nIn fig.2, we show plots of numerical results for n = 8, 16, 32, 64, 128, 256, in the region in which R(t) declines from unity to a value less than .6. The time required to reach R(Gnt) = .6 is strongly dependent on n, as we see in fig.2. If R were to have developed at a fixed fraction of the speed limit rate (as did P in the previous example), then the value of the dimensionless variable Gnt required to reach this point would have been independent of n . Friedland and Lunardini [9] have established that for large n the evolution time behaves as (G √ n) −1 , with a coefficient of order unity; so that the characteristic values of Gnt increase as √ n . This is essentially the perturbative time dependence that we defined above 2 , and is already roughly borne out in a fit to the intercepts of the curves shown in fig. 2 with the line R = .6.\\n2 This result is again obtainable by using the asymptotic forms of Clebsch-Gordan coefficients. In place of |Q| , Friedland and Lunardini consider the probability that a single, typical spin is flipped, summed over all possible fates for the remaining system, and ingeniously reduce the problem in such a way that only a single sum analogous to that in (23) need be performed.\"\n },\n {\n \"title\": \"SOLUTIONS FOR MODEL B\",\n \"content\": \"First we enumerate the set of states that are dynamically connected, given the initial state (5) with n 1 = n 2 = n and the Hamiltonian (14). The initial state is an eigenstate of K 2 , and L 2 , each of which commutes with the Hamiltonian, and each with the same eigenvalue, (n/2)(n/2 + 1). The totalẑ component \\\"angular momentum\\\", K 3 + L 3 is also conserved and equal to zero for our set of states. Any number of the n spins in the upper tier, all initially up, may be flipped, leading to n+1 possibilities for K 3 for this tier by itself. For each such configuration there is also only a single state of the lower tier. Thus we can index the states by the number of flips plus one, i, where i takes on the values 1, 2...n + 1. We express the operator products that occur in the Hamiltonian in this basis as,\\nwhich come directly from the standard angular momentum matrices. We now solve numerically for a (n + 1) component wave function Ψ(t), using the Hamiltonian (14) with the substitution (24) and the initial condition Ψ i (0) = δ i,1 . We then calculate both of our measures of change,\\nand\\nWe also solve numerically for the ground state energy, to confirm that it is the ∆E condition of(2) that applies. We find that the approximation,\\nfits the energies to within 1% over the range n = 4 − 100.\\nThus we have E − E 0 > ∆E over the whole range that we consider, and the speed limit is determined from the term in (2) involving ∆E. In fig.3 we plot P (t) for n = 64 against the variable gN t. On the same plot we indicate the limitation imposed by (15) by plotting the function ǫ(t) that is the solution to the equation t = πβ(ǫ)/(2 ∆E) where ∆E = nG. Comparing with the case of model A, we see that the evolution proceeds at much more nearly the speed limit rate. The plots of P are almost identical for all n ≥ 4.\\nIn line R = .4 occur at very nearly equally spaced points. Equal spacing indicates a mixing time decreasing with n as τ ∝ log(n)/n. This is in contrast to the symmetrical model A in which characteristic time decreases as τ ∝ 1/ √ n, which we defined as the \\\"perturbative\\\" time. Thus we have a large speed-up over the perturbative estimate, as n increases. For the case n = 128, if we define the characteristic time according to criterion #2, the speed-up over the perturbative rate is a factor of approximately 4.\"\n },\n {\n \"title\": \"DISCUSSION\",\n \"content\": \"We have considered large spin systems with couplings among pairs such that the quantum speed limit time is proportional to the inverse of the number of spins, τ ∝ N −1 , where we taken an initial state which is completely separable. We have shown that the time required for the squared overlap , P (t), of the evolved state with the initial state to become small is indeed proportional to N −1 , with a coefficient which in model A is about twice the speed limit value, and in model B is only 10-20% greater than the speed limit time, depending on the value of ǫ one chooses for purposes of comparison.\\nWe have also looked at the time scale for change of another attribute of these systems, R(t), the fraction of upper tier spins that have been flipped. Here the results were drastically different for the two models; in model A, where there were couplings among all of the spins, the evolution time for R(t) is proportional to N −1/2 , which we characterize as the \\\"perturbative\\\" time, rather than to N −1 . But in model B, with breaking of permutational symmetry 3 the evolution time is reduced to a time of order N −1 log[N ], a speed-up to near the N −1 level of the speed-limit time. It is tempting to conjecture that with more breaking of the symmetry we could lose the log, and perhaps even approach speed-limit rates. The curves shown in ref. [8], however, for the case of completely broken symmetry, were inconclusive in this regard, due to computational limitations. More generally, it would seem to us to be of some interest first to define \\\"macroscopic change\\\" more precisely in a large N limit, and then to try to find general results, analogous to the speed-limit results, on the limitations for the rates for this macroscopic change.\\nWe should note that we have tested models in which n 1 = n 2 and find results qualitatively the same as those reported for the two models treated in this paper. We set out, in calculating R(t) to get an estimate of the rate at which the average totalẑ component spin of the upper tier, K 3 , changes. But see that in model B the measure R(t) is very nearly zero at the first minimum, indicating that almost all the spins have been flipped. We could compare the results, where (up to logarithms) the characteristic time for evolution is of order (GN ) −1 , to the results for the simplest Hamiltonian that will flip each spin in time (GN ) −1 , namely,\\nMeasuring the \\\"energy resources\\\" of this Hamiltonian by ∆E = (π/2)GN 3/2 , and comparing to ∆E = G(N/2) for the Hamiltonian (14), we conclude that the model with pair couplings and consequent many-body entanglements does indeed succeed in rotating the complete ensemble of spins in a very efficient way, for large n. Finally, we comment on the question as to how much substance is contained in the statement that \\\"entanglement is the key to speed-up of rates\\\" a paraphrase of a point emphasized in [1] and also in a quite different context in [8]. Of course, states do become entangled during the evolution under the interactions that we have taken in our models. But there is no general agreement known to us on the quantification of entanglement in the case of multicomponent systems, even in the case of pure states. We can, however, perhaps rather arbitrarily, consider the entanglement of two systems, U and L, where U contains all of the upper tier spins and L contains the lower tier states. Then a measure of entanglement between the two systems is given by the entropy of entanglement obtained by tracing out one subsystem's coordinates in the density matrix, say the U subsystem, to define a reduced density matrix ρ L for the L subsystem, and then calculating the von-Neumann entropy corresponding to ρ L [10] [11],\\nWe have calculated S e as a function of time for models A and B, using the wave-function solutions underlying the calculations discussed above. At a time Gnt = 1, at which P ≈ .5 in either model, we find that, so defined, the entanglement is about 30% more for the case with broken symmetry than for the completely symmetric case, and relatively independent of the number of particles. Thus in our models there is an perhaps an indication of a correlation between the rate of growth of entanglement and the efficiency of transformation. Of course, in the pure states that we have considered, the entanglement, as defined above, can both increase and decrease in time, and comparisons will depend on the time of the sampling.\"\n },\n {\n \"title\": \"FIG. 1 :\",\n \"content\": \"\"\n },\n {\n \"title\": \"FIG. 2 :\",\n \"content\": \"\"\n },\n {\n \"title\": \"FIG. 3 :\",\n \"content\": \"\"\n },\n {\n \"title\": \"FIG. 4 :\",\n \"content\": \"\"\n }\n]","isConversational":false},"figures":{"kind":"list like","value":[{"id":"","caption":"The time evolution of the function P (t) for model A (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.","content":"FIG. 1 :\n1The time evolution of the function P (t) for model A (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit."},{"id":"","caption":"The time evolution of the function R(t) for model A, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256. The curves for higher values of n lie progressively to the right of the lower n curves.","content":"FIG. 2 :\n2The time evolution of the function R(t) for model A, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256. The curves for higher values of n lie progressively to the right of the lower n curves."},{"id":"","caption":"fig 4.we show plots of the scaled function R(t) for n = 8, 16, 32, 64, 128, 256, 512, again plotting against the variable Gnt. Note that the intersections with the The time evolution of the function P (t) for model B (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.","content":"FIG. 3 :\n3fig 4.we show plots of the scaled function R(t) for n = 8, 16, 32, 64, 128, 256, 512, again plotting against the variable Gnt. Note that the intersections with the The time evolution of the function P (t) for model B (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit."},{"id":"","caption":"The time evolution of the function R(t) for model B, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256, 512. The curves for higher values of n lie progressively to the right of the lower n curves.","content":"FIG. 4 :\n4The time evolution of the function R(t) for model B, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256, 512. The curves for higher values of n lie progressively to the right of the lower n curves."}],"string":"[\n {\n \"id\": \"\",\n \"caption\": \"The time evolution of the function P (t) for model A (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.\",\n \"content\": \"FIG. 1 :\\n1The time evolution of the function P (t) for model A (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"The time evolution of the function R(t) for model A, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256. The curves for higher values of n lie progressively to the right of the lower n curves.\",\n \"content\": \"FIG. 2 :\\n2The time evolution of the function R(t) for model A, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256. The curves for higher values of n lie progressively to the right of the lower n curves.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"fig 4.we show plots of the scaled function R(t) for n = 8, 16, 32, 64, 128, 256, 512, again plotting against the variable Gnt. Note that the intersections with the The time evolution of the function P (t) for model B (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.\",\n \"content\": \"FIG. 3 :\\n3fig 4.we show plots of the scaled function R(t) for n = 8, 16, 32, 64, 128, 256, 512, again plotting against the variable Gnt. Note that the intersections with the The time evolution of the function P (t) for model B (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"The time evolution of the function R(t) for model B, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256, 512. The curves for higher values of n lie progressively to the right of the lower n curves.\",\n \"content\": \"FIG. 4 :\\n4The time evolution of the function R(t) for model B, plotted as a function of the dimensionless variable, Gnt, for values n = 8, 16, 32, 64, 128, 256, 512. The curves for higher values of n lie progressively to the right of the lower n curves.\"\n }\n]","isConversational":false},"references":{"kind":"list like","value":[{"text":". V Giovannetti, S Lloyd, L Maccone, quant-ph/0206001Europhys. Lett. 62615V. Giovannetti, S.Lloyd, L. Maccone, Europhys. Lett. 62, 615 (2003), quant-ph/0206001","doi":"quant-ph/0206001"},{"text":". V Giovannetti, S Lloyd, L Maccone, quant-ph/0210197Phys. Rev. 6752109V. Giovannetti, S.Lloyd, L. Maccone, Phys. Rev. A67, 052109 (2003), quant-ph/0210197","doi":"quant-ph/0210197"},{"text":"Fluctuations and Noise in Photonics and Quantum Optics. V Giovannetti, S Lloyd, L Maccone ; Bott, D , quant-ph/0303085Proceedings of the SPIE. 5111V. Giovannetti, S.Lloyd, L. Maccone, Fluctuations and Noise in Photonics and Quantum Optics. Edited by Ab- bott, D. et al. Proceedings of the SPIE, Volume 5111, pp. 1-6 (2003), quant-ph/0303085","doi":"quant-ph/0303085"},{"text":". K Bhattacharya, J. Phys. 162993K. Bhattacharya, J. Phys. A16, 2993 (1983)","doi":""},{"text":". P Pfeifer, Phys. Rev. Lett. 703365P. Pfeifer, Phys. Rev. Lett. 70, 3365 (1993)","doi":""},{"text":". L Mandelstam, I G Tamm, J. Phys. USSR. 9249L. Mandelstam and I. G. Tamm, J. Phys. USSR 9, 249 (1945)","doi":""},{"text":". N Margulus, L B Levitan, Physica. 120188N. Margulus and L. B. Levitan, Physica D120, 188 (1998)","doi":""},{"text":". N F Bell, A A Rawlinson, R F Sawyer, Phys.Lett. 57386N. F. Bell, A. A. Rawlinson, and R. F. Sawyer, Phys.Lett. B573, 86 (2003)","doi":""},{"text":". A Friedland, C Lunardini, quant-ph/0303085031043A. Friedland and C. Lunardini, JHEP0310, 043 (2003) ;quant-ph/0303085","doi":"quant-ph/0303085"},{"text":". C H Bennett, H J Bernstein, S Popescu, B Schumacher, Phys. Rev. A. 532046C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schu- macher, Phys. Rev. A 53, 2046 (1996).","doi":""},{"text":". S Hill, W K Wootters, Phys. Rev. Lett. 785022S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997);","doi":""},{"text":". W K Wootters, 802245W. K. Wootters, ibid. 80, 2245 (1998)","doi":""}],"string":"[\n {\n \"text\": \". V Giovannetti, S Lloyd, L Maccone, quant-ph/0206001Europhys. Lett. 62615V. Giovannetti, S.Lloyd, L. Maccone, Europhys. Lett. 62, 615 (2003), quant-ph/0206001\",\n \"doi\": \"quant-ph/0206001\"\n },\n {\n \"text\": \". V Giovannetti, S Lloyd, L Maccone, quant-ph/0210197Phys. Rev. 6752109V. Giovannetti, S.Lloyd, L. Maccone, Phys. Rev. A67, 052109 (2003), quant-ph/0210197\",\n \"doi\": \"quant-ph/0210197\"\n },\n {\n \"text\": \"Fluctuations and Noise in Photonics and Quantum Optics. V Giovannetti, S Lloyd, L Maccone ; Bott, D , quant-ph/0303085Proceedings of the SPIE. 5111V. Giovannetti, S.Lloyd, L. Maccone, Fluctuations and Noise in Photonics and Quantum Optics. Edited by Ab- bott, D. et al. Proceedings of the SPIE, Volume 5111, pp. 1-6 (2003), quant-ph/0303085\",\n \"doi\": \"quant-ph/0303085\"\n },\n {\n \"text\": \". K Bhattacharya, J. Phys. 162993K. Bhattacharya, J. Phys. A16, 2993 (1983)\",\n \"doi\": \"\"\n },\n {\n \"text\": \". P Pfeifer, Phys. Rev. Lett. 703365P. Pfeifer, Phys. Rev. Lett. 70, 3365 (1993)\",\n \"doi\": \"\"\n },\n {\n \"text\": \". L Mandelstam, I G Tamm, J. Phys. USSR. 9249L. Mandelstam and I. G. Tamm, J. Phys. USSR 9, 249 (1945)\",\n \"doi\": \"\"\n },\n {\n \"text\": \". N Margulus, L B Levitan, Physica. 120188N. Margulus and L. B. Levitan, Physica D120, 188 (1998)\",\n \"doi\": \"\"\n },\n {\n \"text\": \". N F Bell, A A Rawlinson, R F Sawyer, Phys.Lett. 57386N. F. Bell, A. A. Rawlinson, and R. F. Sawyer, Phys.Lett. B573, 86 (2003)\",\n \"doi\": \"\"\n },\n {\n \"text\": \". A Friedland, C Lunardini, quant-ph/0303085031043A. Friedland and C. Lunardini, JHEP0310, 043 (2003) ;quant-ph/0303085\",\n \"doi\": \"quant-ph/0303085\"\n },\n {\n \"text\": \". C H Bennett, H J Bernstein, S Popescu, B Schumacher, Phys. Rev. A. 532046C. H. Bennett, H. J. Bernstein, S. Popescu and B. Schu- macher, Phys. Rev. A 53, 2046 (1996).\",\n \"doi\": \"\"\n },\n {\n \"text\": \". S Hill, W K Wootters, Phys. Rev. Lett. 785022S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997);\",\n \"doi\": \"\"\n },\n {\n \"text\": \". W K Wootters, 802245W. K. Wootters, ibid. 80, 2245 (1998)\",\n \"doi\": \"\"\n }\n]","isConversational":false}}},{"rowIdx":296,"cells":{"text":{"kind":"string","value":"\nAn example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state\n3 Apr 2017\n\nHenryk Fukś \nDepartment of Mathematics and Statistics\nBrock University St\nL2S 3A1CatharinesOntarioCanada\n\nJoel Midgley-Volpato \nDepartment of Mathematics and Statistics\nBrock University St\nL2S 3A1CatharinesOntarioCanada\n\nAn example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state\n3 Apr 201768A274CC1D66E57EF68F783BEF8A554CarXiv:1704.00716v1[nlin.CG]\nIn a recent paper[1]we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems.We also calculated densities of 0, 1 and 2 after n iterations of this rule, using finite state machines to conjecture patterns present in preimage sets.Here we rederive the same formulae in a rigorous way, without resorting to any semiempirical methods.This is done by analyzing the behaviour of continuous clusters of symbols and by considering their interactions.\n\nThe general question of finding the iterates of the Bernoulli measure under a given cellular automaton (CA) has been subject of many recent studies, including, among others, [2,3,4,5,6,7,8] and [9].A more specific question of this type is sometimes called the density response problem: If the probability of occurence of a certain state in the initial configuration drawn from a Bernoulli distribution is given, what is the probability of occurence of this state after n iterations of the CA rule?\n\nOf course, one could ask a similar question about the probability of occurence of longer blocks of symbols after n iterations of the rule.Due to the complexity of CA dynamics, it is clear that questions of this type are rather hopeless if one wants to know the answer for an arbitrary rule.In spite of this, it may still be possible to find the answer if the rule is sufficiently simple.\n\nOne of the methods which can be used to do this is studying the structure of preimages of short blocks and detecting patterns present in them.This approach has been successfully used for a number of deterministic CA rules, such as elementary rules 172, 142, 130 (references [10], [11], and [12] respectively), and several others.It has also been used for a special class of probabilistic CA known as single-transition α-asynchronous rules [13].\n\nCellular automata are infinitely-dimensional dynamical systems, yet a behaviour similar to hyperbolicity in finite-dimensional systems has been observed in many of them.In particular, in some binary cellular automata in one dimension, known as asymptotic emulators of identity, if the initial configuration is drawn from a Bernoulli distribution, the expected proportion of ones (or zeros) usually tends to its stationary value exponentially fast [14].This type of behaviour is quite common in many other dynamical systems.For example, in a linear continuous-time dynamical system given by ẋ = Ax, if x : R → R n and A is a real n × n matrix with all eigenvalues distinct and having negative real parts, x(t) tends to zero exponentially fast as t → ∞.Exponential convergence is also observed in nonlinear systems ẋ = f (x) (where f : R n → R n ) in the vicinity of a hyperbolic fixed point, as long as the Jacobian matrix of f evaluated at the fixed point has only distinct eigenvalues with negative real parts.\n\nIf, on the other hand, the matrix A in ẋ = Ax has degenerate (repeated) eigenvalues, the convergence to the fixed point can be polynomialexponential, that is, of the form P (t)e −bt , where P (t) is a polynomial and b > 0. Finite dimensional discrete-time dynamical systems can exhibit analogous behaviour.Consider, for example, the linear system\nx n+1 y n+1 = 0 1 − 1 4 1 x n y n .(1)\nThe matrix on the right hand side has a degenerate (double) eigenvalue 1 2 , and therefore the convergence to the fixed point (0, 0) is expected to be polynomial-exponential (linear-exponential in this case).Indeed, if we explicitly solve the above equation for x n and y n , we obtain\nx n y n = 1 2 n 1 − n 2n − n 2 1 + n x 0 y 0 ,(2)\nand we can clearly see the aforementioned linear-exponential convergence.\n\nVery recently, a probabilistic CA has been discovered [15] where the density of ones converges to its stationary value in a linear-exponential fashion, just like in the above example of a degenerate hyperbolic fixed point in a finite-dimensional dynamical systems.This probabilistic CA could be viewed as a simple model for diffusion of innovations, spread of rumors, or a similar process involving transport of information between neighbours.More precisely, it consists of an infinite one-dimensional lattice where each site is occupied by an individual who has already adopted the innovation (state 1) or who has not adopted it yet (state 0).Once the individual adopts the innovation, he remains in state 1 forever.Individuals in state 0 can change their states to 1 (adopt the innovation) with probabilities depending on the state of nearest neighbours.This process can be formally described as a radius 1 binary probabilistic CA with the following transition probabilities,\nw(1|000) = 0, w(1|001) = p, w(1|010) = 1, w(1|011) = 1,(3) w(1|100) = q, w(1|101) = r, w(1|110) = 1, w(1|111) = 1,\nwhere p, q, r are fixed parameters of the model, p, q, r ∈ [0, 1].By transition probability w(d|abc) one means the probability that site in state b with neighbours a and c changes its state to d in one time step.One can show that for a certain choice of parameters p, q and r, the expected value of the density of ones converges to its steady state in a linear-exponential fashion.\n\nEven more recently, we found a deterministic rule with three states which exhibits the same kind of behaviour [1].This rule, to be defined in sec.2, will be the subject of our subsequent discussion.In [1] we studied the structure of preimages of 0, 1 and 2 under the action of this rule, and by employing finite state machines, we found some patterns in the preimages sets, which in turn allowed us to derive explicit expressions for densities of 0, 1 and 2 after n iterations.The finite state machines used in the derivation were constructed semi-empirically, and no proof of their correctness was given.In the current paper we wish to fill this gap and present a more formal derivation of the aforementioned expressions, without resorting to finite state machines.\n\n\nBasic definition\n\nWe will start from some basic definitions.For A = {0, 1, 2}, a finite sequence of elements of A, b = b 1 b 2 . . ., b n , will be called a block (or word ) of length n.The set of all blocks of all possible lengths will be denoted by A .\n\nLet f : A 3 → A be a local function of a nearest-neighbour cellular automaton.A block evolution operator corresponding to f is a mapping\nf : A → A defined as follows. Let a = a 1 a 2 . . . a n ∈ A n where n ≥ 3. Then f (a) is a block of length n − 2 defined as f (a) = f (a 1 , a 2 , a 3 )f (a 2 , a 3 , a 4 ) . . . f (a n−2 , a n−1 , a n ). (4)\nIf f (b) = a, than we will say that b is a preimage of a, and write b ∈ f −1 (a).Similarly, if f n (b) = a, than we will say that b is an n-step preimage of a, and write b ∈ f −n (a).\n\nLet the density polynomial associated with a string\nb = b 1 b 2 . . . b n be defined as Ψ b (p, q, r) = p # 0 (b) q # 1 (b) r # 2 (b) ,(5)\nwhere # i (b) is the number of occurrences of symbol i in b.If A is a set of strings, we define the density polynomial associated with A as\nΨ A (p, q, r) = a∈A Ψ a (p, q, r).(6)\nOne can easily show (in a manner similar as done in [14]) that if one starts with a bi-infinite string of symbols drawn from a Bernoulli distribution where probabilities of 0, 1 and 2 are, respectively, p, q and r, then the expected proportion of sites in state k after n iterations of rule f is given by Ψ f −n (k) (p, q, r).This quantity will be called density of symbols k after n iterations of f .\n\n\nThe local rule and its properties\n\nLet us now describe the CA rule which will be the subject of this contribution.While studying properties of various 3-state CA rules, we came across an interesting specimen of a nearest-neighbour (radius 1) rule with a local function defined as follows,\nf (x 1 , x 2 , x 3 ) = x 3 for x 1 = x 2 > x 3 , x 2 otherwise,(7)\nwhere x 1 , x 2 , x 3 ∈ {0, 1, 2}.The origins of this rule have been described in [1].Here we will only note that it can be equivalently defined as\nf (x 1 , x 2 , x 3 ) = 0 for (x 1 , x 2 , x 3 ) = (1, 1, 0) or (x 1 , x 2 , x 3 ) = (2, 2, 0), 1 for (x 1 , x 2 , x 3 ) = (2, 2, 1), x 2 otherwise,(8)\nwhich makes it clear that it differs from the identity rule only on three neighbourhood configurations, (1, 1, 0), (2, 2, 0) and (2, 2, 1). Figure 1 shows an example of a spatio-temporal pattern generated by this rule, using periodic boundary conditions.It has some important properties which will be relevant to further discussion.First of all, note that f (x 1 , x 2 , x 3 ) ≤ x 2 , meaning that the state of a given cell cannot increase.This implies that f ( , 0, ) = 0, where denotes an arbitrary symbol from the set {0, 1, 2}.Zero is thus a quiescent state for this CA.We also have f (0, 1, ) = 1 and f (2, 1, ) = 1, which implies that a site in state 1 located at the beginning of a continuous cluster of 1's of any length (even of length 1, meaning isolated 1) remain in state 1 forever.The same is true for 2: since f (0, 2, ) = 2 and f (1, 2, ) = 2, a site in state 2 located at the beginning of a continuous cluster of 2's stays in state 2 forever.This can be observed in Figure 1.In fact, words such as 01 or 02 remain unchanged when the rule is iterated, and no information can propagate through a pair sites which are in states 01 or 02.We note in passing that in the CA theory such words are called blocking words, and the rules with blocking words are known to be almost equicontinuous [16].\n\nFurther inspection of Figure 1 reveals that a continuous cluster of zeros grows to the left if it is preceded by a cluster of 2's longer than 1, and it also grows to the left if is preceded by a cluster of 1's longer than 1.\n\n\nStructure of preimages of 1\n\nWe want to find all strings b of length 2n + 1 such that f n (b) = 1.We know from the definition of the rule that information can propagate only from the right to the left, thus the first n − 2 entries of b are arbitrary.We will represent n-step preimages of 1 in the form b = . . .\nn−2 a 1 a 2 a 3 c 1 c 2 . . . c n ,\nwhere the allowed values of a 1 , a 2 , a 3 (to be called a prefix ) and c 1 c 2 . . .c n (to be called a postfix ) need to be determined.The central site of the preimage string will be, as in the above, denoted by a bold symbol.Since our CA rule has three states, there are 3 3 = 27 possible values for the prefix a 1 a 2 a 3 .Not all of them are possible, however.Prefixes 000, 010, 020, 100, 110, 120, 200, 210 and 220, which can be represented as 0, cannot occur in any preimage of 1.This is because f ( , 0, ) = 0, meaning that if the central site is in state 0, it will remain in state 0 forever, and consequently f n (b) = 0 for any string b containing one of the above prefixes.\n\nMoreover, prefixes of the type 02 or 12 are not allowed either.This is because for the central site to become 1, as required, the transition f (2, 2, 1) = 1 would have to happen somewhere along the way, and for this the central 2 would have to get 2 as the left neighbour.Since states can only decrease, not increase, and the left neighbour of the central site is 0 or 1, this is not possible.\n\nBy excluding 9 prefixes of the type 0 and 6 prefixes of the type 02 or 12 we are left with 12 possibilities, 001, 011, 021, 101, 111, 121, 201, 211, 221, 022, 122, 222.All of them are allowed in preimages of 1, providing that an appropriate suffix is added.In what follows we will find conditions which these suffices need to satisfy.We will divide the possible prefixes into four different types (the reason for this will soon become clear): For prefixes of type 1, 11 and 221, the central site is in the state 1 already, thus we have to make sure that it stays in the same state after n iterations of the rule.The left neighbour of the central 1 is 1 (for 11) or it will become 1 after one iteration (for 221), thus we could potentially be in a danger of the transition f (1, 1, 0) = 0.This could happen only if the central 1 belongs to a continuous cluster of ones which is followed by 0 -in such a case, the cluster of ones will shrink one symbol per time step and the transition f (1, 1, 0) = 0 will eventually change the central 1 into 0. We have, therefore, two choices in avoiding this scenario: either the central 1 belongs to a cluster of ones followed by 2, which prevents its shrinking due to the fact that f (1, 1, 2) = 1, or it belongs to a cluster of ones which extends all the way to the right.In other words, the postfix for type 2 must be of the form\nc 1 c 2 . . . c n = 1 i 2 . . . n−1−i or c 1 c 2 . . . c n = 1 n ,\nwhere i ∈ {0, 1, . . .n − 1}.In the above and in what follows, 1 n denotes the symbol 1 repeated n times.We will use this convention in the rest of the paper.\n\nFor type 2, 01, 021, and 121, note that the central site could become 0 only by utilizing the transition f (1, 1, 0) = 0, and for this the left neighbour of the central 1 would have to be 1.This is clearly impossible for 01 as the left neighbour 0 will always remain 0. In the case of 021 and 121, the left neighbour is 2, and it could potentially become 0 by transition f (2, 2, 0) = 0.For this, however, we would need the second left neighbour of the central 1 to be in state 2, but this is impossible because site values never increase.Thus all prefixes of type 2 belong to preimages of 1, regardless of the suffix.\n\nFor type 3, 022, 122, the central site is in state 2, and its left neighbour is guaranteed to be in state 2 forever.Consequently, the central 2 must change to 1 at some iteration via the f (2, 2, 1) = 1 transition, and in order for this to happen, we need to have the right neighbour of the central site in state 1 at some point of time.This can happen when the central 2 belongs to a continuous cluster of 2's followed by 1, meaning that the postfix must be of the form\nc 1 c 2 . . . c n = 2 i 1 . . . n−1−i , where i ∈ {0, 1, . . . n − 1}.\nType 4 with the prefix 222 is the most complicated one.Similarly as before, the central site must change from 2 to 1, and this can only happen via the transition f (2, 2, 1) = 1, but we do not have a guarantee that the left neighbour of the central 2 remains in state 2 forever, as it was the the case of type 3. Nevertheless, the necessary condition for the suffix is the same as for type 3, meaning that the central 2 must belong to a continuous cluster of 2's followed by 1.This in not sufficient, however, because what follows is also important.In order to understand this clearly, consider two strings of length 13 iterated 6 times: The first of these strings has prefix 222, and the second one has prefix 122 (thus belonging to type 3).In both of them the central 2 belongs to a continuous cluster of 2's followed by 1, but the first one does not produce 1 after 6 iterations.This is because the zero which follows propagates to the left and eventually makes the central site to change to 0 via the transition f (1, 1, 0) = 0. Any string containing 222 as a prefix must, therefore, satisfy an additional property preventing zeros to propagate to the left.This can be done by a making the last part of the suffix to have the same structure as prefix of type 3, so that the entire suffix takes the form\nc 1 c 2 . . . c n = 2 i 1d 1 d 2 . . . d n−1−i ,(9)\nwhere i ∈ {0, 1, . . .n − 1} and where\nd 1 d 2 . . . d n−1−i = 1 j 2 . . . n−2−i−j or d 1 d 2 . . . d n−1−i = 1 n−1−i ,(10)\nwith j ∈ {0, 2, . . ., n − 2 − i}.\n\nFinally, for prefix 222 there is one more possibility not covered by the above discussion, namely c 1 c 2 . . .c n = 2 n−2 10.Below we summarize all these findings in a form of a single proposition.\n= . . . n−2 a 1 a 2 a 3 1 i 2 . . . n−1−i or b = . . . n−2 a 1 a 2 a 3 1 n ,(11)\nwhere a 1 a 2 a 3 ∈ {011, 111, 211, 221}, i ∈ {0, 1, . . .n − 1};\nType 2: b = . . . n−2 a 1 a 2 a 3 . . . n ,(12)\nwhere where a 1 a 2 a 3 ∈ {001, 101, 201, 121, 021};\nType 3: b = . . . n−2 a 1 a 2 a 3 2 i 1 . . . n−1−i ,(13)\nwhere where\na 1 a 2 a 3 ∈ {022, 122}, i ∈ {0, 1, . . . n − 1} Type 4a: b = . . . n−2 a 1 a 2 a 3 2 i 1c 1 c 2 . . . c n−1−i ,(14)\nwhere a 1 a 2 a 3 = 222, i ∈ {0, 1, . . .n − 1} and where\nc 1 c 2 . . . c n−1−i = 1 j 2 . . . n−2−i−j or c 1 c 2 . . . c n−1−i = 1 n−1−i(15)\nwith j ∈ {0, 2, . . ., n − 2 − i}.\nType 4b: b = . . . n−2 a 1 a 2 a 3 2 n−2 10,(16)\nwhere a 1 a 2 a 3 = 222.\n\n\nDensity polynomials for preimages of 1\n\nLet us now denote the set of strings of type 1 by T 1 , type 2 by T 2 etc., and let us define λ = p + q + r.Density polynomial for T 1 will be given by\nΨ T 1 (p, q, r) = n−1 i=0 λ n−2 (pq 2 + q 3 + rq 2 + r 2 q)q i rλ n−i−1 + λ n−2 (pq 2 + q 3 + rq 2 + r 2 q)q n , (17) which simplifies to Ψ T 1 (p, q, r) = λ 2n−3 r(λq 2 + r 2 q) n−1 i=0 λ −i q i + λ n−2 (λq 2 + r 2 q)q n .(18)\nBy performing summation of the partial geometric sequence in the above, one obtains\nΨ T 1 (p, q, r) = λ n−2 r(λq 2 + r 2 q) λ n − q n p + r + λ n−2 (λq 2 + r 2 q)q n ,(19)\nwhich further simplifies to\nΨ T 1 (p, q, r) = r(λq 2 + r 2 q) λ 2n−2 p + r + λ n−2 (λq 2 + r 2 q) pq n p + r .(20)\nSimilar calculations (omitted here) yield\nΨ T 2 (p, q, r) = (λpq + q 2 r + pqr)λ 2n−2 ,(21)Ψ T 3 (p, q, r) = λ n−2 r 2 q(λ n − r n ). (22)\nThe type 4a is the most complicated.Let us first compute the density polynomial for the set of strings of the form\nc 1 c 2 . . . c k = 1 j 2 . . . k−1−j or c 1 c 2 . . . c k = 1 k (23)\nwith j ∈ {0, 1, . . ., k − 1}.The density polynomial for the above, to be denoted by h k (p, q, r), is given by\nh k (p, q, r) = k−1 j=0 q j rλ k−1−j + q n = r λ k − q k p + r + q k = rλ k p + r + pq k p + r .(24)\nHaving this result, we can write the density polynomial for the entire set T 4a ,\nΨ T 4a (p, q, r) = λ n−2 r 3 n−1 i=0 r i qh n−1−i (p, q, r) = λ n−2 r 3 n−1 i=0 r i q rλ n−1−i p + r + λ n−2 r 3 n−1 i=0 r i q pq n−1−i p + r = λ n−2 qr 4 p + r n−1 i=0 r i λ n−1−i + λ n−2 pqr 3 p + r n−1 i=0 r i q n−1−i = λ n−2 qr 4 (λ n − r n ) (p + r)(p + q) + λ n−2 pqr 3 p + r n−1 i=0 r i q n−1−i .(25)\nWhen q = r, we thus obtain\nΨ T 4a (p, q, r) = λ n−2 qr 4 (λ n − r n ) (p + r)(p + q) + λ n−2 pqr 3 (q n − r n ) (p + r)(q − r) .(26)\nWhen q = r, the last sum becomes n−1 i=0 r i q n−1−i = n−1 i=0 q n−1 = q n−1 n, therefore\nΨ T 4a (p, q, q) = λ n−2 q 5 (λ n − q n ) (p + q) 2 + λ n−2 pq 3 p + q nq n .(27)\nFinally, type 4b is straightforward,\nΨ T 4b (p, q, r) = λ n−2 r n+1 pq.(28)\nWe are now ready to compute the density polynomial of preimages of 1, by summing density polynomials for T 1 , T 2 , T 3 , T 4a and T 4b .This yields, for q = r,\nΨ f −n (1) (p, q, r) = r(λq 2 + r 2 q) λ 2n−2 p + r + λ n−2 (λq 2 + r 2 q) pq n p + r + (λpq + q 2 r + pqr)λ 2n−2 + λ n−2 r 2 q(λ n − r n ) + λ n−2 qr 4 (λ n − r n ) (p + r)(p + q) + λ n−2 pqr 3 (q n − r n ) (p + r)(q − r) + λ n−2 r n+1 pq. (29)\nCollecting together terms for (qλ) n , (rλ) n , and λ 2n we obtain, after some algebra,\nΨ f −n (1) (p, q, r) = pq 2 −pr + pq + q 2 (qλ) n λ 2 (p + r) (q − r) + qr −p 2 r + p 2 q + pq 2 − 2 pqr + r 3 − q 2 r (rλ) n λ 2 (p + q) (q − r) + q p 3 + p 2 q + 2 p 2 r + pr 2 + 3 pqr + r 3 + r 2 q + q 2 r λ 2n λ (p + r) (p + q) ,(30)\nwhich is the same formula as derived in [1].\n\nSimilarly, for q = r, we obtain\nΨ f −n (1) (p, q, q) = q(λq 2 + q 3 ) λ 2n−2 p + q + λ n−2 (λq 2 + q 3 ) pq n p + q + (λpq + q 3 + pq 2 )λ 2n−2 + λ n−2 q 3 (λ n − q n ) λ n−2 q 5 (λ n − q n ) (p + q) 2 + λ n−2 pq 3 p + q nq n + λ n−2 q n+1 pq.(31)\nAfter simplification and reordering of terms this yields Ψ f −n (1) (p, q, q) = pq 3 (n + 1) (qλ) n λ 2 (q + p) + q 2 2 p 3 + 4 p 2 q + pq 2 − 2 q 3 (qλ) n (q + p) 2 λ 2 + p 3 + 3 p 2 q + 4 pq 2 + 3 q 3 qλ 2n λ (q + p) 2 , (32) which, again, agrees with the result \"guessed\" in [1] using finite state machines.\n\n\nPreimages of 2 and their density polynomials\n\nFrom the definition of the rule we know that a site can be in state 2 only if it was in that state at the beginning, that is, sites in state 0 or 1 cannot change to 2.Moreover, f (2, 2, 0) = 0, f (2, 2, 1) = 1, and in all other cases f (a 1 , 2, a 3 ) = 2.This means that a site in state 2 remains in that state forever if it is preceded by 0 or 1.Therefore, any string of the form b = . . .and for r = q, Ψ f −n (0) (p, q, q) = p 3 + 4 p 2 q + 7 q 2 p + 5 q 3 pλ 2n\nλ (p + q) 2 − pq 3 (n + 1) (qλ) n λ 2 (p + q) − q 2 p 3 p 2 + 8 pq + 6 q 2 (qλ) n (p + q) 2 λ 2 .(36)\nAgain, similarly as in the density polynomial for 1, the linear-exponential dependence of the form (n + 1)(qλ) n is present in the second term.\n\n\nDensity of ones\n\nAs already stated, density polynomials Ψ f −n (k) (p, q, r) represent probability of occurence of k after n iterations starting from a Bernoulli distribution with probabilities of 0, 1 and 2 equal to, respectively, p, q, and r, where p + q + r = 1.If one starts with a symmetric Bernoulli distribution where r = q, the probability of occurence of 1 after n steps, to be denoted by P n (1), will be given by eq. ( 32) as long as one substitutes r = q and q = (1 − p)/2.This yields, after simplification, One can see that for 0 < p < 1, P n (1) tends to P ∞ (1) as n → ∞, and that the convergence is linear-exponential in n.Such \"degenerate\" convergence takes place for probability of occurence of 0 as well, as seen in eq. ( 36).On the other hand, when r = q in the initial Bernoulli distribution, the convergence is purely exponential, as in eq. ( 30) and (35).\nP n (1) = P ∞ (1) − (An + B) 1 − p 2 n ,(37) where\n\nConclusions\n\nWe presented an example of a 3-state rule exhibiting, under certain conditions, linear-exponential convergence to the steady state.This phenomenon is remarkably similar to degenerate hyperbolicity in finite dimensional dynamical systems.It is not clear, however, what is the origin of this analogy.One can speculate that \"simple\" CA rules, such as those which are equicontinuous or almost equicontinuous, can be somewhat approximated by finite-dimensional systems.Local structure theory could possibly be applicable in this case, as it allows to construct finite-dimensional systems approximating orbits of Bernoulli measure under the action of a given CA.It is hoped that this contribution inspires further research on this subject.\n\nFig. 1 .\n1\nFig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lighter gray and darker gray cells (blue in color version) correspond, respectively, to 0, 1 and 2.\n\n\nProposition 3 . 1\n31\nBlock b belongs to f −n (1) if and only if it is one of the following four types.Type 1: b\n\n\n\n\nn-step preimage of 2, f n (b) = 2.\n\n\n3 4\n3\np) 2 −p 3 − 5 p − 3 p 2 + 1 , (39) P ∞ (1) = (1 − p) p 3 + 5 p 2 − p +\n\nAcknowledgmentsThe author acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of Discovery Grant.This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca)and Compute/Calcul Canada.What if 2 is preceded by 2? In this case it must be followed by a sufficient number of 2's before the first 0 or 1 appears, as any 0 or 1 at the end of a cluster of 2's shortens such cluster by one on each iteration.Therefore, for n iterations we need n 2's.We thus need, in order for f n (b) = 2 to hold in this case, b = . . .The above observations can be summarized as follows.Proposition 5.1 Block b belongs to f −n (2) if and only if it is one of the following three types:This yields the polynomial Ψ f −n (2) (p, q, r) = (p + q)rλ 2n−1 + λ n−1 r n+2 .(33)Preimages of 0 and their density polynomialsSince everything what is not a preimage of 1 or 2 must be a preimage of 0, we haveAfter simplification, this yields, for r = q,+ p 3 + 2 p 2 q + 2 p 2 r + 2 r 2 p + 3 qpr + 2 q 2 p + r 3 + 2 qr 2 + q 3 + q 2 r pλ 2n (p + q) (p + r) λ ,\nAn example of degenerate hyperbolicity in cellular automaton with 3 states,\" in 21st International Workshop on Cellular Automata and Discrete Complex Systems. H Fukś, J Midgley-Volpato, arXiv:1506.06649TUCS Lecture Notes. J. Kari, I. Törmä, and M. Szabados242015\n\nApplications of ergodic theory and sofic systems to cellular automata. D A Lind, Cellular automata. Los Alamos, N.M.1984. 198310\n\nCesàro mean distribution of group automata starting from measures with summable decay. P A Ferrari, A Maass, S Martínez, P Ney, Ergodic Theory Dynam. Systems. 2062000\n\nEvolution of probability measures by cellular automata on algebraic topological markov chains. A Maass, S Martinez, Biol. Res. 3612003\n\nUniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules. B Host, A Maass, S Martínez, Discrete Contin. Dyn. Syst. 962003\n\nLimit measures for affine cellular automata. M Pivato, R Yassawi, Ergodic Theory Dynam. Systems. 2242002\n\nLimit measures for affine cellular automata. II. M Pivato, R Yassawi, Ergodic Theory Dynam. Systems. 2462004\n\nLimit measures for affine cellular automata on topological markov subgroups. A Maass, S Martínez, M Sobottka, Nonlinearity. 19Sept., 2006\n\nAsymptotic randomization of subgroup shifts by linear cellular automata. A Maass, S Martinez, M Pivato, R Yassawi, Ergodic Theory and Dynamical Systems. 26042006\n\nProbabilistic initial value problem for cellular automaton rule 172. H Fukś, arXiv:1007.1026DMTCS proc. AL. 2010\n\nDynamics of the cellular automaton rule 142. H Fukś, Complex Systems. 162006\n\nResponse curves for cellular automata in one and two dimensions -an example of rigorous calculations. H Fukś, A Skelton, arXiv:1108.1987International Journal of Natural Computing Research. 12010\n\nOrbits of Bernoulli measure in asynchronous cellular automata. H Fukś, A Skelton, Dis. Math. Theor. Comp. Science AP. 2011\n\nExponential convergence to equilibrium in cellular automata asymptotically emulating identity. H Fukś, J.-M G Soto, arXiv:1306.1189Complex Systems. 232014\n\nAn example of computation of the density of ones in probabilistic cellular automata by direct recursion. H Fukś, 2015submitted for publication\n\nTopological dynamics of cellular automata. P Kůrka, Encyclopedia of Complexity and System Science. R A Meyers, Springer2009\n"},"corpus_id":{"kind":"number","value":40066643,"string":"40,066,643"},"external_ids":{"kind":"string","value":"{\n \"arxiv\": \"1704.00716\",\n \"mag\": 2963428220,\n \"acl\": null,\n \"pubmed\": null,\n \"pubmedcentral\": null,\n \"dblp\": null,\n \"doi\": \"10.5506/aphyspolbsupp.9.49\"\n}"},"source":{"kind":"string","value":"{\n \"pdf_urls\": [\n \"https://arxiv.org/pdf/1704.00716v1.pdf\"\n ],\n \"pdf_sha\": \"16743d6fd15c71bec0b19746602ab89c8f624314\",\n \"open_access\": {\n \"license\": null,\n \"url\": \"https://www.actaphys.uj.edu.pl/S/9/1/13/pdf\",\n \"status\": \"BRONZE\"\n }\n}"},"title":{"kind":"string","value":"An example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state"},"authors":{"kind":"list like","value":["Henryk Fukś \nDepartment of Mathematics and Statistics\nBrock University St\nL2S 3A1CatharinesOntarioCanada","Joel Midgley-Volpato \nDepartment of Mathematics and Statistics\nBrock University St\nL2S 3A1CatharinesOntarioCanada"],"string":"[\n \"Henryk Fukś \\nDepartment of Mathematics and Statistics\\nBrock University St\\nL2S 3A1CatharinesOntarioCanada\",\n \"Joel Midgley-Volpato \\nDepartment of Mathematics and Statistics\\nBrock University St\\nL2S 3A1CatharinesOntarioCanada\"\n]","isConversational":false},"abstract":{"kind":"string","value":"In a recent paper[1]we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems.We also calculated densities of 0, 1 and 2 after n iterations of this rule, using finite state machines to conjecture patterns present in preimage sets.Here we rederive the same formulae in a rigorous way, without resorting to any semiempirical methods.This is done by analyzing the behaviour of continuous clusters of symbols and by considering their interactions."},"sections":{"kind":"list like","value":[{"title":"Basic definition","content":"We will start from some basic definitions.For A = {0, 1, 2}, a finite sequence of elements of A, b = b 1 b 2 . . ., b n , will be called a block (or word ) of length n.The set of all blocks of all possible lengths will be denoted by A .\nLet f : A 3 → A be a local function of a nearest-neighbour cellular automaton.A block evolution operator corresponding to f is a mapping\nIf f (b) = a, than we will say that b is a preimage of a, and write b ∈ f −1 (a).Similarly, if f n (b) = a, than we will say that b is an n-step preimage of a, and write b ∈ f −n (a).\nLet the density polynomial associated with a string\nwhere # i (b) is the number of occurrences of symbol i in b.If A is a set of strings, we define the density polynomial associated with A as\nOne can easily show (in a manner similar as done in [14]) that if one starts with a bi-infinite string of symbols drawn from a Bernoulli distribution where probabilities of 0, 1 and 2 are, respectively, p, q and r, then the expected proportion of sites in state k after n iterations of rule f is given by Ψ f −n (k) (p, q, r).This quantity will be called density of symbols k after n iterations of f ."},{"title":"The local rule and its properties","content":"Let us now describe the CA rule which will be the subject of this contribution.While studying properties of various 3-state CA rules, we came across an interesting specimen of a nearest-neighbour (radius 1) rule with a local function defined as follows,\nwhere x 1 , x 2 , x 3 ∈ {0, 1, 2}.The origins of this rule have been described in [1].Here we will only note that it can be equivalently defined as\nwhich makes it clear that it differs from the identity rule only on three neighbourhood configurations, (1, 1, 0), (2, 2, 0) and (2, 2, 1). Figure 1 shows an example of a spatio-temporal pattern generated by this rule, using periodic boundary conditions.It has some important properties which will be relevant to further discussion.First of all, note that f (x 1 , x 2 , x 3 ) ≤ x 2 , meaning that the state of a given cell cannot increase.This implies that f ( , 0, ) = 0, where denotes an arbitrary symbol from the set {0, 1, 2}.Zero is thus a quiescent state for this CA.We also have f (0, 1, ) = 1 and f (2, 1, ) = 1, which implies that a site in state 1 located at the beginning of a continuous cluster of 1's of any length (even of length 1, meaning isolated 1) remain in state 1 forever.The same is true for 2: since f (0, 2, ) = 2 and f (1, 2, ) = 2, a site in state 2 located at the beginning of a continuous cluster of 2's stays in state 2 forever.This can be observed in Figure 1.In fact, words such as 01 or 02 remain unchanged when the rule is iterated, and no information can propagate through a pair sites which are in states 01 or 02.We note in passing that in the CA theory such words are called blocking words, and the rules with blocking words are known to be almost equicontinuous [16].\nFurther inspection of Figure 1 reveals that a continuous cluster of zeros grows to the left if it is preceded by a cluster of 2's longer than 1, and it also grows to the left if is preceded by a cluster of 1's longer than 1."},{"title":"Structure of preimages of 1","content":"We want to find all strings b of length 2n + 1 such that f n (b) = 1.We know from the definition of the rule that information can propagate only from the right to the left, thus the first n − 2 entries of b are arbitrary.We will represent n-step preimages of 1 in the form b = . . .\nwhere the allowed values of a 1 , a 2 , a 3 (to be called a prefix ) and c 1 c 2 . . .c n (to be called a postfix ) need to be determined.The central site of the preimage string will be, as in the above, denoted by a bold symbol.Since our CA rule has three states, there are 3 3 = 27 possible values for the prefix a 1 a 2 a 3 .Not all of them are possible, however.Prefixes 000, 010, 020, 100, 110, 120, 200, 210 and 220, which can be represented as 0, cannot occur in any preimage of 1.This is because f ( , 0, ) = 0, meaning that if the central site is in state 0, it will remain in state 0 forever, and consequently f n (b) = 0 for any string b containing one of the above prefixes.\nMoreover, prefixes of the type 02 or 12 are not allowed either.This is because for the central site to become 1, as required, the transition f (2, 2, 1) = 1 would have to happen somewhere along the way, and for this the central 2 would have to get 2 as the left neighbour.Since states can only decrease, not increase, and the left neighbour of the central site is 0 or 1, this is not possible.\nBy excluding 9 prefixes of the type 0 and 6 prefixes of the type 02 or 12 we are left with 12 possibilities, 001, 011, 021, 101, 111, 121, 201, 211, 221, 022, 122, 222.All of them are allowed in preimages of 1, providing that an appropriate suffix is added.In what follows we will find conditions which these suffices need to satisfy.We will divide the possible prefixes into four different types (the reason for this will soon become clear): For prefixes of type 1, 11 and 221, the central site is in the state 1 already, thus we have to make sure that it stays in the same state after n iterations of the rule.The left neighbour of the central 1 is 1 (for 11) or it will become 1 after one iteration (for 221), thus we could potentially be in a danger of the transition f (1, 1, 0) = 0.This could happen only if the central 1 belongs to a continuous cluster of ones which is followed by 0 -in such a case, the cluster of ones will shrink one symbol per time step and the transition f (1, 1, 0) = 0 will eventually change the central 1 into 0. We have, therefore, two choices in avoiding this scenario: either the central 1 belongs to a cluster of ones followed by 2, which prevents its shrinking due to the fact that f (1, 1, 2) = 1, or it belongs to a cluster of ones which extends all the way to the right.In other words, the postfix for type 2 must be of the form\nwhere i ∈ {0, 1, . . .n − 1}.In the above and in what follows, 1 n denotes the symbol 1 repeated n times.We will use this convention in the rest of the paper.\nFor type 2, 01, 021, and 121, note that the central site could become 0 only by utilizing the transition f (1, 1, 0) = 0, and for this the left neighbour of the central 1 would have to be 1.This is clearly impossible for 01 as the left neighbour 0 will always remain 0. In the case of 021 and 121, the left neighbour is 2, and it could potentially become 0 by transition f (2, 2, 0) = 0.For this, however, we would need the second left neighbour of the central 1 to be in state 2, but this is impossible because site values never increase.Thus all prefixes of type 2 belong to preimages of 1, regardless of the suffix.\nFor type 3, 022, 122, the central site is in state 2, and its left neighbour is guaranteed to be in state 2 forever.Consequently, the central 2 must change to 1 at some iteration via the f (2, 2, 1) = 1 transition, and in order for this to happen, we need to have the right neighbour of the central site in state 1 at some point of time.This can happen when the central 2 belongs to a continuous cluster of 2's followed by 1, meaning that the postfix must be of the form\nType 4 with the prefix 222 is the most complicated one.Similarly as before, the central site must change from 2 to 1, and this can only happen via the transition f (2, 2, 1) = 1, but we do not have a guarantee that the left neighbour of the central 2 remains in state 2 forever, as it was the the case of type 3. Nevertheless, the necessary condition for the suffix is the same as for type 3, meaning that the central 2 must belong to a continuous cluster of 2's followed by 1.This in not sufficient, however, because what follows is also important.In order to understand this clearly, consider two strings of length 13 iterated 6 times: The first of these strings has prefix 222, and the second one has prefix 122 (thus belonging to type 3).In both of them the central 2 belongs to a continuous cluster of 2's followed by 1, but the first one does not produce 1 after 6 iterations.This is because the zero which follows propagates to the left and eventually makes the central site to change to 0 via the transition f (1, 1, 0) = 0. Any string containing 222 as a prefix must, therefore, satisfy an additional property preventing zeros to propagate to the left.This can be done by a making the last part of the suffix to have the same structure as prefix of type 3, so that the entire suffix takes the form\nwhere i ∈ {0, 1, . . .n − 1} and where\nwith j ∈ {0, 2, . . ., n − 2 − i}.\nFinally, for prefix 222 there is one more possibility not covered by the above discussion, namely c 1 c 2 . . .c n = 2 n−2 10.Below we summarize all these findings in a form of a single proposition.\nwhere a 1 a 2 a 3 ∈ {011, 111, 211, 221}, i ∈ {0, 1, . . .n − 1};\nwhere where a 1 a 2 a 3 ∈ {001, 101, 201, 121, 021};\nwhere where\nwhere a 1 a 2 a 3 = 222, i ∈ {0, 1, . . .n − 1} and where\nwith j ∈ {0, 2, . . ., n − 2 − i}.\nwhere a 1 a 2 a 3 = 222."},{"title":"Density polynomials for preimages of 1","content":"Let us now denote the set of strings of type 1 by T 1 , type 2 by T 2 etc., and let us define λ = p + q + r.Density polynomial for T 1 will be given by\nBy performing summation of the partial geometric sequence in the above, one obtains\nwhich further simplifies to\nSimilar calculations (omitted here) yield\nThe type 4a is the most complicated.Let us first compute the density polynomial for the set of strings of the form\nwith j ∈ {0, 1, . . ., k − 1}.The density polynomial for the above, to be denoted by h k (p, q, r), is given by\nHaving this result, we can write the density polynomial for the entire set T 4a ,\nWhen q = r, we thus obtain\nWhen q = r, the last sum becomes n−1 i=0 r i q n−1−i = n−1 i=0 q n−1 = q n−1 n, therefore\nFinally, type 4b is straightforward,\nWe are now ready to compute the density polynomial of preimages of 1, by summing density polynomials for T 1 , T 2 , T 3 , T 4a and T 4b .This yields, for q = r,\nCollecting together terms for (qλ) n , (rλ) n , and λ 2n we obtain, after some algebra,\nwhich is the same formula as derived in [1].\nSimilarly, for q = r, we obtain\nAfter simplification and reordering of terms this yields Ψ f −n (1) (p, q, q) = pq 3 (n + 1) (qλ) n λ 2 (q + p) + q 2 2 p 3 + 4 p 2 q + pq 2 − 2 q 3 (qλ) n (q + p) 2 λ 2 + p 3 + 3 p 2 q + 4 pq 2 + 3 q 3 qλ 2n λ (q + p) 2 , (32) which, again, agrees with the result \"guessed\" in [1] using finite state machines."},{"title":"Preimages of 2 and their density polynomials","content":"From the definition of the rule we know that a site can be in state 2 only if it was in that state at the beginning, that is, sites in state 0 or 1 cannot change to 2.Moreover, f (2, 2, 0) = 0, f (2, 2, 1) = 1, and in all other cases f (a 1 , 2, a 3 ) = 2.This means that a site in state 2 remains in that state forever if it is preceded by 0 or 1.Therefore, any string of the form b = . . .and for r = q, Ψ f −n (0) (p, q, q) = p 3 + 4 p 2 q + 7 q 2 p + 5 q 3 pλ 2n\nAgain, similarly as in the density polynomial for 1, the linear-exponential dependence of the form (n + 1)(qλ) n is present in the second term."},{"title":"Density of ones","content":"As already stated, density polynomials Ψ f −n (k) (p, q, r) represent probability of occurence of k after n iterations starting from a Bernoulli distribution with probabilities of 0, 1 and 2 equal to, respectively, p, q, and r, where p + q + r = 1.If one starts with a symmetric Bernoulli distribution where r = q, the probability of occurence of 1 after n steps, to be denoted by P n (1), will be given by eq. ( 32) as long as one substitutes r = q and q = (1 − p)/2.This yields, after simplification, One can see that for 0 < p < 1, P n (1) tends to P ∞ (1) as n → ∞, and that the convergence is linear-exponential in n.Such \"degenerate\" convergence takes place for probability of occurence of 0 as well, as seen in eq. ( 36).On the other hand, when r = q in the initial Bernoulli distribution, the convergence is purely exponential, as in eq. ( 30) and (35)."},{"title":"Conclusions","content":"We presented an example of a 3-state rule exhibiting, under certain conditions, linear-exponential convergence to the steady state.This phenomenon is remarkably similar to degenerate hyperbolicity in finite dimensional dynamical systems.It is not clear, however, what is the origin of this analogy.One can speculate that \"simple\" CA rules, such as those which are equicontinuous or almost equicontinuous, can be somewhat approximated by finite-dimensional systems.Local structure theory could possibly be applicable in this case, as it allows to construct finite-dimensional systems approximating orbits of Bernoulli measure under the action of a given CA.It is hoped that this contribution inspires further research on this subject."},{"title":"Fig. 1 .","content":"Fig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lighter gray and darker gray cells (blue in color version) correspond, respectively, to 0, 1 and 2."},{"title":"Proposition 3 . 1","content":"Block b belongs to f −n (1) if and only if it is one of the following four types.Type 1: b\nn-step preimage of 2, f n (b) = 2."},{"title":"3 4","content":"p) 2 −p 3 − 5 p − 3 p 2 + 1 , (39) P ∞ (1) = (1 − p) p 3 + 5 p 2 − p +"}],"string":"[\n {\n \"title\": \"Basic definition\",\n \"content\": \"We will start from some basic definitions.For A = {0, 1, 2}, a finite sequence of elements of A, b = b 1 b 2 . . ., b n , will be called a block (or word ) of length n.The set of all blocks of all possible lengths will be denoted by A .\\nLet f : A 3 → A be a local function of a nearest-neighbour cellular automaton.A block evolution operator corresponding to f is a mapping\\nIf f (b) = a, than we will say that b is a preimage of a, and write b ∈ f −1 (a).Similarly, if f n (b) = a, than we will say that b is an n-step preimage of a, and write b ∈ f −n (a).\\nLet the density polynomial associated with a string\\nwhere # i (b) is the number of occurrences of symbol i in b.If A is a set of strings, we define the density polynomial associated with A as\\nOne can easily show (in a manner similar as done in [14]) that if one starts with a bi-infinite string of symbols drawn from a Bernoulli distribution where probabilities of 0, 1 and 2 are, respectively, p, q and r, then the expected proportion of sites in state k after n iterations of rule f is given by Ψ f −n (k) (p, q, r).This quantity will be called density of symbols k after n iterations of f .\"\n },\n {\n \"title\": \"The local rule and its properties\",\n \"content\": \"Let us now describe the CA rule which will be the subject of this contribution.While studying properties of various 3-state CA rules, we came across an interesting specimen of a nearest-neighbour (radius 1) rule with a local function defined as follows,\\nwhere x 1 , x 2 , x 3 ∈ {0, 1, 2}.The origins of this rule have been described in [1].Here we will only note that it can be equivalently defined as\\nwhich makes it clear that it differs from the identity rule only on three neighbourhood configurations, (1, 1, 0), (2, 2, 0) and (2, 2, 1). Figure 1 shows an example of a spatio-temporal pattern generated by this rule, using periodic boundary conditions.It has some important properties which will be relevant to further discussion.First of all, note that f (x 1 , x 2 , x 3 ) ≤ x 2 , meaning that the state of a given cell cannot increase.This implies that f ( , 0, ) = 0, where denotes an arbitrary symbol from the set {0, 1, 2}.Zero is thus a quiescent state for this CA.We also have f (0, 1, ) = 1 and f (2, 1, ) = 1, which implies that a site in state 1 located at the beginning of a continuous cluster of 1's of any length (even of length 1, meaning isolated 1) remain in state 1 forever.The same is true for 2: since f (0, 2, ) = 2 and f (1, 2, ) = 2, a site in state 2 located at the beginning of a continuous cluster of 2's stays in state 2 forever.This can be observed in Figure 1.In fact, words such as 01 or 02 remain unchanged when the rule is iterated, and no information can propagate through a pair sites which are in states 01 or 02.We note in passing that in the CA theory such words are called blocking words, and the rules with blocking words are known to be almost equicontinuous [16].\\nFurther inspection of Figure 1 reveals that a continuous cluster of zeros grows to the left if it is preceded by a cluster of 2's longer than 1, and it also grows to the left if is preceded by a cluster of 1's longer than 1.\"\n },\n {\n \"title\": \"Structure of preimages of 1\",\n \"content\": \"We want to find all strings b of length 2n + 1 such that f n (b) = 1.We know from the definition of the rule that information can propagate only from the right to the left, thus the first n − 2 entries of b are arbitrary.We will represent n-step preimages of 1 in the form b = . . .\\nwhere the allowed values of a 1 , a 2 , a 3 (to be called a prefix ) and c 1 c 2 . . .c n (to be called a postfix ) need to be determined.The central site of the preimage string will be, as in the above, denoted by a bold symbol.Since our CA rule has three states, there are 3 3 = 27 possible values for the prefix a 1 a 2 a 3 .Not all of them are possible, however.Prefixes 000, 010, 020, 100, 110, 120, 200, 210 and 220, which can be represented as 0, cannot occur in any preimage of 1.This is because f ( , 0, ) = 0, meaning that if the central site is in state 0, it will remain in state 0 forever, and consequently f n (b) = 0 for any string b containing one of the above prefixes.\\nMoreover, prefixes of the type 02 or 12 are not allowed either.This is because for the central site to become 1, as required, the transition f (2, 2, 1) = 1 would have to happen somewhere along the way, and for this the central 2 would have to get 2 as the left neighbour.Since states can only decrease, not increase, and the left neighbour of the central site is 0 or 1, this is not possible.\\nBy excluding 9 prefixes of the type 0 and 6 prefixes of the type 02 or 12 we are left with 12 possibilities, 001, 011, 021, 101, 111, 121, 201, 211, 221, 022, 122, 222.All of them are allowed in preimages of 1, providing that an appropriate suffix is added.In what follows we will find conditions which these suffices need to satisfy.We will divide the possible prefixes into four different types (the reason for this will soon become clear): For prefixes of type 1, 11 and 221, the central site is in the state 1 already, thus we have to make sure that it stays in the same state after n iterations of the rule.The left neighbour of the central 1 is 1 (for 11) or it will become 1 after one iteration (for 221), thus we could potentially be in a danger of the transition f (1, 1, 0) = 0.This could happen only if the central 1 belongs to a continuous cluster of ones which is followed by 0 -in such a case, the cluster of ones will shrink one symbol per time step and the transition f (1, 1, 0) = 0 will eventually change the central 1 into 0. We have, therefore, two choices in avoiding this scenario: either the central 1 belongs to a cluster of ones followed by 2, which prevents its shrinking due to the fact that f (1, 1, 2) = 1, or it belongs to a cluster of ones which extends all the way to the right.In other words, the postfix for type 2 must be of the form\\nwhere i ∈ {0, 1, . . .n − 1}.In the above and in what follows, 1 n denotes the symbol 1 repeated n times.We will use this convention in the rest of the paper.\\nFor type 2, 01, 021, and 121, note that the central site could become 0 only by utilizing the transition f (1, 1, 0) = 0, and for this the left neighbour of the central 1 would have to be 1.This is clearly impossible for 01 as the left neighbour 0 will always remain 0. In the case of 021 and 121, the left neighbour is 2, and it could potentially become 0 by transition f (2, 2, 0) = 0.For this, however, we would need the second left neighbour of the central 1 to be in state 2, but this is impossible because site values never increase.Thus all prefixes of type 2 belong to preimages of 1, regardless of the suffix.\\nFor type 3, 022, 122, the central site is in state 2, and its left neighbour is guaranteed to be in state 2 forever.Consequently, the central 2 must change to 1 at some iteration via the f (2, 2, 1) = 1 transition, and in order for this to happen, we need to have the right neighbour of the central site in state 1 at some point of time.This can happen when the central 2 belongs to a continuous cluster of 2's followed by 1, meaning that the postfix must be of the form\\nType 4 with the prefix 222 is the most complicated one.Similarly as before, the central site must change from 2 to 1, and this can only happen via the transition f (2, 2, 1) = 1, but we do not have a guarantee that the left neighbour of the central 2 remains in state 2 forever, as it was the the case of type 3. Nevertheless, the necessary condition for the suffix is the same as for type 3, meaning that the central 2 must belong to a continuous cluster of 2's followed by 1.This in not sufficient, however, because what follows is also important.In order to understand this clearly, consider two strings of length 13 iterated 6 times: The first of these strings has prefix 222, and the second one has prefix 122 (thus belonging to type 3).In both of them the central 2 belongs to a continuous cluster of 2's followed by 1, but the first one does not produce 1 after 6 iterations.This is because the zero which follows propagates to the left and eventually makes the central site to change to 0 via the transition f (1, 1, 0) = 0. Any string containing 222 as a prefix must, therefore, satisfy an additional property preventing zeros to propagate to the left.This can be done by a making the last part of the suffix to have the same structure as prefix of type 3, so that the entire suffix takes the form\\nwhere i ∈ {0, 1, . . .n − 1} and where\\nwith j ∈ {0, 2, . . ., n − 2 − i}.\\nFinally, for prefix 222 there is one more possibility not covered by the above discussion, namely c 1 c 2 . . .c n = 2 n−2 10.Below we summarize all these findings in a form of a single proposition.\\nwhere a 1 a 2 a 3 ∈ {011, 111, 211, 221}, i ∈ {0, 1, . . .n − 1};\\nwhere where a 1 a 2 a 3 ∈ {001, 101, 201, 121, 021};\\nwhere where\\nwhere a 1 a 2 a 3 = 222, i ∈ {0, 1, . . .n − 1} and where\\nwith j ∈ {0, 2, . . ., n − 2 − i}.\\nwhere a 1 a 2 a 3 = 222.\"\n },\n {\n \"title\": \"Density polynomials for preimages of 1\",\n \"content\": \"Let us now denote the set of strings of type 1 by T 1 , type 2 by T 2 etc., and let us define λ = p + q + r.Density polynomial for T 1 will be given by\\nBy performing summation of the partial geometric sequence in the above, one obtains\\nwhich further simplifies to\\nSimilar calculations (omitted here) yield\\nThe type 4a is the most complicated.Let us first compute the density polynomial for the set of strings of the form\\nwith j ∈ {0, 1, . . ., k − 1}.The density polynomial for the above, to be denoted by h k (p, q, r), is given by\\nHaving this result, we can write the density polynomial for the entire set T 4a ,\\nWhen q = r, we thus obtain\\nWhen q = r, the last sum becomes n−1 i=0 r i q n−1−i = n−1 i=0 q n−1 = q n−1 n, therefore\\nFinally, type 4b is straightforward,\\nWe are now ready to compute the density polynomial of preimages of 1, by summing density polynomials for T 1 , T 2 , T 3 , T 4a and T 4b .This yields, for q = r,\\nCollecting together terms for (qλ) n , (rλ) n , and λ 2n we obtain, after some algebra,\\nwhich is the same formula as derived in [1].\\nSimilarly, for q = r, we obtain\\nAfter simplification and reordering of terms this yields Ψ f −n (1) (p, q, q) = pq 3 (n + 1) (qλ) n λ 2 (q + p) + q 2 2 p 3 + 4 p 2 q + pq 2 − 2 q 3 (qλ) n (q + p) 2 λ 2 + p 3 + 3 p 2 q + 4 pq 2 + 3 q 3 qλ 2n λ (q + p) 2 , (32) which, again, agrees with the result \\\"guessed\\\" in [1] using finite state machines.\"\n },\n {\n \"title\": \"Preimages of 2 and their density polynomials\",\n \"content\": \"From the definition of the rule we know that a site can be in state 2 only if it was in that state at the beginning, that is, sites in state 0 or 1 cannot change to 2.Moreover, f (2, 2, 0) = 0, f (2, 2, 1) = 1, and in all other cases f (a 1 , 2, a 3 ) = 2.This means that a site in state 2 remains in that state forever if it is preceded by 0 or 1.Therefore, any string of the form b = . . .and for r = q, Ψ f −n (0) (p, q, q) = p 3 + 4 p 2 q + 7 q 2 p + 5 q 3 pλ 2n\\nAgain, similarly as in the density polynomial for 1, the linear-exponential dependence of the form (n + 1)(qλ) n is present in the second term.\"\n },\n {\n \"title\": \"Density of ones\",\n \"content\": \"As already stated, density polynomials Ψ f −n (k) (p, q, r) represent probability of occurence of k after n iterations starting from a Bernoulli distribution with probabilities of 0, 1 and 2 equal to, respectively, p, q, and r, where p + q + r = 1.If one starts with a symmetric Bernoulli distribution where r = q, the probability of occurence of 1 after n steps, to be denoted by P n (1), will be given by eq. ( 32) as long as one substitutes r = q and q = (1 − p)/2.This yields, after simplification, One can see that for 0 < p < 1, P n (1) tends to P ∞ (1) as n → ∞, and that the convergence is linear-exponential in n.Such \\\"degenerate\\\" convergence takes place for probability of occurence of 0 as well, as seen in eq. ( 36).On the other hand, when r = q in the initial Bernoulli distribution, the convergence is purely exponential, as in eq. ( 30) and (35).\"\n },\n {\n \"title\": \"Conclusions\",\n \"content\": \"We presented an example of a 3-state rule exhibiting, under certain conditions, linear-exponential convergence to the steady state.This phenomenon is remarkably similar to degenerate hyperbolicity in finite dimensional dynamical systems.It is not clear, however, what is the origin of this analogy.One can speculate that \\\"simple\\\" CA rules, such as those which are equicontinuous or almost equicontinuous, can be somewhat approximated by finite-dimensional systems.Local structure theory could possibly be applicable in this case, as it allows to construct finite-dimensional systems approximating orbits of Bernoulli measure under the action of a given CA.It is hoped that this contribution inspires further research on this subject.\"\n },\n {\n \"title\": \"Fig. 1 .\",\n \"content\": \"Fig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lighter gray and darker gray cells (blue in color version) correspond, respectively, to 0, 1 and 2.\"\n },\n {\n \"title\": \"Proposition 3 . 1\",\n \"content\": \"Block b belongs to f −n (1) if and only if it is one of the following four types.Type 1: b\\nn-step preimage of 2, f n (b) = 2.\"\n },\n {\n \"title\": \"3 4\",\n \"content\": \"p) 2 −p 3 − 5 p − 3 p 2 + 1 , (39) P ∞ (1) = (1 − p) p 3 + 5 p 2 − p +\"\n }\n]","isConversational":false},"figures":{"kind":"list like","value":[{"id":"","caption":"Fig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lighter gray and darker gray cells (blue in color version) correspond, respectively, to 0, 1 and 2.","content":"Fig. 1 .\n1\nFig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lighter gray and darker gray cells (blue in color version) correspond, respectively, to 0, 1 and 2."},{"id":"","caption":"Block b belongs to f −n (1) if and only if it is one of the following four types.Type 1: b","content":"Proposition 3 . 1\n31\nBlock b belongs to f −n (1) if and only if it is one of the following four types.Type 1: b"},{"id":"","caption":"n-step preimage of 2, f n (b) = 2.","content":"n-step preimage of 2, f n (b) = 2."},{"id":"","caption":"p) 2 −p 3 − 5 p − 3 p 2 + 1 , (39) P ∞ (1) = (1 − p) p 3 + 5 p 2 − p +","content":"3 4\n3\np) 2 −p 3 − 5 p − 3 p 2 + 1 , (39) P ∞ (1) = (1 − p) p 3 + 5 p 2 − p +"}],"string":"[\n {\n \"id\": \"\",\n \"caption\": \"Fig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lighter gray and darker gray cells (blue in color version) correspond, respectively, to 0, 1 and 2.\",\n \"content\": \"Fig. 1 .\\n1\\nFig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lighter gray and darker gray cells (blue in color version) correspond, respectively, to 0, 1 and 2.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"Block b belongs to f −n (1) if and only if it is one of the following four types.Type 1: b\",\n \"content\": \"Proposition 3 . 1\\n31\\nBlock b belongs to f −n (1) if and only if it is one of the following four types.Type 1: b\"\n },\n {\n \"id\": \"\",\n \"caption\": \"n-step preimage of 2, f n (b) = 2.\",\n \"content\": \"n-step preimage of 2, f n (b) = 2.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"p) 2 −p 3 − 5 p − 3 p 2 + 1 , (39) P ∞ (1) = (1 − p) p 3 + 5 p 2 − p +\",\n \"content\": \"3 4\\n3\\np) 2 −p 3 − 5 p − 3 p 2 + 1 , (39) P ∞ (1) = (1 − p) p 3 + 5 p 2 − p +\"\n }\n]","isConversational":false},"references":{"kind":"list like","value":[{"text":"An example of degenerate hyperbolicity in cellular automaton with 3 states,\" in 21st International Workshop on Cellular Automata and Discrete Complex Systems. H Fukś, J Midgley-Volpato, arXiv:1506.06649TUCS Lecture Notes. J. Kari, I. Törmä, and M. Szabados242015","doi":""},{"text":"Applications of ergodic theory and sofic systems to cellular automata. D A Lind, Cellular automata. Los Alamos, N.M.1984. 198310","doi":""},{"text":"Cesàro mean distribution of group automata starting from measures with summable decay. P A Ferrari, A Maass, S Martínez, P Ney, Ergodic Theory Dynam. Systems. 2062000","doi":""},{"text":"Evolution of probability measures by cellular automata on algebraic topological markov chains. A Maass, S Martinez, Biol. Res. 3612003","doi":""},{"text":"Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules. B Host, A Maass, S Martínez, Discrete Contin. Dyn. Syst. 962003","doi":""},{"text":"Limit measures for affine cellular automata. M Pivato, R Yassawi, Ergodic Theory Dynam. Systems. 2242002","doi":""},{"text":"Limit measures for affine cellular automata. II. M Pivato, R Yassawi, Ergodic Theory Dynam. Systems. 2462004","doi":""},{"text":"Limit measures for affine cellular automata on topological markov subgroups. A Maass, S Martínez, M Sobottka, Nonlinearity. 19Sept., 2006","doi":""},{"text":"Asymptotic randomization of subgroup shifts by linear cellular automata. A Maass, S Martinez, M Pivato, R Yassawi, Ergodic Theory and Dynamical Systems. 26042006","doi":""},{"text":"Probabilistic initial value problem for cellular automaton rule 172. H Fukś, arXiv:1007.1026DMTCS proc. AL. 2010","doi":""},{"text":"Dynamics of the cellular automaton rule 142. H Fukś, Complex Systems. 162006","doi":""},{"text":"Response curves for cellular automata in one and two dimensions -an example of rigorous calculations. H Fukś, A Skelton, arXiv:1108.1987International Journal of Natural Computing Research. 12010","doi":""},{"text":"Orbits of Bernoulli measure in asynchronous cellular automata. H Fukś, A Skelton, Dis. Math. Theor. Comp. Science AP. 2011","doi":""},{"text":"Exponential convergence to equilibrium in cellular automata asymptotically emulating identity. H Fukś, J.-M G Soto, arXiv:1306.1189Complex Systems. 232014","doi":""},{"text":"An example of computation of the density of ones in probabilistic cellular automata by direct recursion. H Fukś, 2015submitted for publication","doi":""},{"text":"Topological dynamics of cellular automata. P Kůrka, Encyclopedia of Complexity and System Science. R A Meyers, Springer2009","doi":""}],"string":"[\n {\n \"text\": \"An example of degenerate hyperbolicity in cellular automaton with 3 states,\\\" in 21st International Workshop on Cellular Automata and Discrete Complex Systems. H Fukś, J Midgley-Volpato, arXiv:1506.06649TUCS Lecture Notes. J. Kari, I. Törmä, and M. Szabados242015\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Applications of ergodic theory and sofic systems to cellular automata. D A Lind, Cellular automata. Los Alamos, N.M.1984. 198310\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Cesàro mean distribution of group automata starting from measures with summable decay. P A Ferrari, A Maass, S Martínez, P Ney, Ergodic Theory Dynam. Systems. 2062000\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Evolution of probability measures by cellular automata on algebraic topological markov chains. A Maass, S Martinez, Biol. Res. 3612003\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Uniform Bernoulli measure in dynamics of permutative cellular automata with algebraic local rules. B Host, A Maass, S Martínez, Discrete Contin. Dyn. Syst. 962003\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Limit measures for affine cellular automata. M Pivato, R Yassawi, Ergodic Theory Dynam. Systems. 2242002\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Limit measures for affine cellular automata. II. M Pivato, R Yassawi, Ergodic Theory Dynam. Systems. 2462004\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Limit measures for affine cellular automata on topological markov subgroups. A Maass, S Martínez, M Sobottka, Nonlinearity. 19Sept., 2006\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Asymptotic randomization of subgroup shifts by linear cellular automata. A Maass, S Martinez, M Pivato, R Yassawi, Ergodic Theory and Dynamical Systems. 26042006\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Probabilistic initial value problem for cellular automaton rule 172. H Fukś, arXiv:1007.1026DMTCS proc. AL. 2010\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Dynamics of the cellular automaton rule 142. H Fukś, Complex Systems. 162006\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Response curves for cellular automata in one and two dimensions -an example of rigorous calculations. H Fukś, A Skelton, arXiv:1108.1987International Journal of Natural Computing Research. 12010\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Orbits of Bernoulli measure in asynchronous cellular automata. H Fukś, A Skelton, Dis. Math. Theor. Comp. Science AP. 2011\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Exponential convergence to equilibrium in cellular automata asymptotically emulating identity. H Fukś, J.-M G Soto, arXiv:1306.1189Complex Systems. 232014\",\n \"doi\": \"\"\n },\n {\n \"text\": \"An example of computation of the density of ones in probabilistic cellular automata by direct recursion. H Fukś, 2015submitted for publication\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Topological dynamics of cellular automata. P Kůrka, Encyclopedia of Complexity and System Science. R A Meyers, Springer2009\",\n \"doi\": \"\"\n }\n]","isConversational":false}}},{"rowIdx":297,"cells":{"text":{"kind":"string","value":"\nMULTIPLE GENUS 2 HEEGAARD SPLITTINGS: A MISSED CASE\n1 Mar 2010\n\nJohn Berge \nMartin Scharlemann \nMULTIPLE GENUS 2 HEEGAARD SPLITTINGS: A MISSED CASE\n1 Mar 2010arXiv:0910.3921v2 [math.GT]\nA gap in [RS] is explored: new examples are found of closed orientable 3-manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in [RS] are not universally shared by the new examples: some of the new examples have Hempel distance 3, and it is not clear that a single stabilization always makes the multiple splittings isotopic.1 The error is on p. 533: The last sentence of the first paragraph of Case 2 should have read, \"The same curves cannot then be twisted in X since M is hyperbolike.\" This leaves open an additional possibility for P X , P Y , which appears as Subcase B in Section 5 below.\n\nIntroduction\n\nIn 1998, Rubinstein and the second author [RS] studied the question of when there could be more than one distinct genus 2 Heegaard splitting of the same closed orientable 3-manifold. The goal of the project was modest: to provide a complete list of ways in which such multiple splittings could be constructed, but with no claim that each example on the list did in fact have multiple non-isotopic splittings (there could be isotopies from one splitting to another that are not apparent). Nor was there a claim that the list had no redundancies; a 3-manifold and its multiple splittings might appear more than once on the list. Such a list would still be useful, for if every example on the list could be shown to have a certain property, then that property would be true for any closed orientable 3-manifold M that has multiple genus 2 splittings. Two examples were given in [RS]:\n\n• If M is atoroidal then the hyperelliptic involutions determined by the two genus 2 Heegaard splittings commute. • Any two genus 2 Heegaard splittings of M become isotopic after a single stabilization.\n\nDespite this modest goal, the argument in [RS] contains a gap. In 2008, the first author discovered a class of examples that do not appear on the list and which, moreover, have mathematical properties that distinguish them in important ways from the examples that do Date: March 1, 2010. Second author partially supported by an NSF grant. appear in [RS]. It is true that, even for the new examples, the hyperelliptic involutions commute. But we know of no argument showing that the new examples all share the second property above; that is, we cannot show that the newly discovered multiple splittings necessarily become isotopic after a single stabilization (though they do after two stabilizations).\n\nA third property, shared by all examples in [RS] but not by some of the new examples, is not listed above because the notion of Hempel distance of Heegaard splittings (see [He]) did not exist at the time [RS] was written. But a retrospective look (see Section 7 below) will verify that all the splittings described in [RS] have Hempel distance no greater than 2, whereas results of the first author [Be2] illustrate that at least some of the new examples have Hempel distance 3. (This also verifies that the gap in the argument in [RS] actually led to missed examples.)\n\nThe present paper serves as an erratum to [RS] 1 and describes the new examples. Here is an outline: In Section 2 we describe a general method for constructing closed orientable 3-manifolds that appear to have multiple genus 2 Heegaard splittings; these examples (called Dehnderived) are based around Dehn surgery on a pair of strategically placed curves. It follows from the construction that always the hyperelliptic involutions of the alternate splittings coincide.\n\nIt is not immediately obvious that curves supporting Dehn-derived examples can be found, but in Sections 3 and 4 we give three specific classes of examples. The classes are denoted M H (Section 3), M ×I and M hybrid (Section 4). (M H can be viewed as a third variation of [RS,Example 4.2].) For the examples M H and M hybrid a single stabilization suffices to make the alternate splittings equivalent, but this property is at least not apparent in most cases of M ×I .\n\nSection 5 describes how the proof of [RS,Lemma 9.5, Case 2] went astray and how it needs to be altered to fix the gap. The upshot is that Dehn-derived examples, as described in Section 2, do fill the gap in the original proof. In Section 6 it is further shown, using new results in [Be], that any Dehn-derived example is in fact of type M H , M ×I or M hybrid . Finally, in Section 7 we verify that all of the old examples that are listed in [RS] are of Hempel distance 2, whereas at least some Dehn-derived examples are of distance 3. (It is easy to see that all Dehn-derived examples are of distance no more than 3.)\n\n\nDehn derived multiple splittings\n\nA primitive k-tuple of curves in the boundary of a genus g handlebody H is a collection λ 1 , ...λ k ⊂ ∂H of k ≤ g disjoint simple closed curves so that, for some properly embedded collection D 1 , ..., D k of disks in H, |λ i ∩ D j | = δ ij , 1 ≤ i, j ≤ k. It is easy to see that the closed complement in H of such a collection of meridian disks is a genus g − k handlebody. In particular, if k = g then λ 1 , ...λ g is called a complete set of primitive curves and the corresponding collection of disks D 1 , ..., D g is called a complete set of meridian disks. The closed complement of a complete set of meridian disks in H is a 3-ball.\n\nSuppose Λ = λ 1 , ...λ k ⊂ ∂H is a primitive k-tuple of curves in H and let α 1 , ..., α k be the properly embedded collection of curves in H obtained by pushing Λ slightly into the interior of H. We can view H as the boundary connect sum of a genus g − k handlebody H ′ and k solid tori W 1 , ..., W k , with λ i a longitude of W i and so α i a core curve of W i . Then Dehn surgery on α i ⊂ W i still gives a solid torus. Hence any Dehn surgery on the family of curves α 1 , ..., α k leaves H still a handlebody.\nDefinition 2.1. Suppose M 0 = H a ∪ S H b is a Heegaard splitting of a closed 3-manifold M 0 . A simple closed curve λ ⊂ S is doubly primitive if λ is a primitive curve in both handlebodies H a and H b .\nSuppose M 0 is a closed orientable 3-manifold and that M 0 = H a ∪ S H b is a genus 2 Heegaard splitting of M 0 . Suppose further that λ 1 , λ 2 ⊂ S are two disjoint doubly primitive curves in S.\n\nProposition 2.2. Suppose M is a manifold obtained by some specified Dehn surgeries on λ 1 and λ 2 . For i = 1, 2, let A i (resp. B i ) be the manifold obtained from the handlebody H a (resp. H b ) by pushing the curve λ i into int(H a ) (resp int(H b )) and performing the specified Dehn surgery on the curve.\n\nThen A 1 ∪ S B 2 and A 2 ∪ S B 1 are two (possibly different) genus 2 Heegaard splittings of M.\nProof. A i (resp B i ) is obtained from H a (resp H b )\nby Dehn surgery on a pushed in copy α i of a single primitive curve in S. It was just observed that this makes each A i (resp. B i ) a handlebody. Proof. Let M 0 = H a ∪ S H b be the Heegaard split 3-manifold from which the two splittings of M are Dehn derived, via λ 1 ∪ λ 2 ⊂ S. The hyperelliptic involution preserves the isotopy class (though perhaps reversing the orientation) of any simple closed curve in S. We may then position λ i so that the curves are preserved (reversing orientation) by the hyperelliptic involution on M 0 = H a ∪ S H b . Then the hyperelliptic involution on M 0 naturally induces a single hyperelliptic involution on M.\n\n\nA simple set of examples\n\nIt is not immediately obvious how to create examples of a Dehnderived pair of splittings or, very naively, whether examples even exist. In this section we present and briefly discuss an important concrete class of examples.\n\nConsider a genus 2 handlebody H, constructed from two 0-handles by connecting them with three 1-handles. With this structure H has a natural Z 3 symmetry, shown as 2π 3 rotation about the green axis in Figure 1. Let λ 1 ⊂ ∂H be the red curve shown in the figure and λ 2 , λ 3 be the other two simple closed curves to which λ 1 is carried by the Z 3 symmetry. Then each λ i is a primitive curve on ∂H and, indeed, any two of the curves, say λ 1 , λ 2 constitute a complete set of primitive curves (that is, a primitive pair). In this case the corresponding pair of meridian disks are the meridian disks of the two 1-handles through which λ 3 passes.\n\nLet H be the genus 3 handlebody obtained by removing from H a neighborhood of the arc in which the axis of symmetry intersects one of the 0-handles. It is easy to see that in H the collection λ 1 , λ 2 , λ 3 ⊂ ∂H is a complete set of primitive curves, that is a primitive 3-tuple.\n\nTo construct some Dehn-derived pairs of Heegaard splittings, begin with two genus 2 handlebodies A and B, on each of whose boundaries lie three disjoint simple closed curves corresponding to λ 1 , λ 2 , λ 3 ⊂ ∂H. Let λ ia ⊂ ∂A (resp λ ib ⊂ ∂B) be the curve corresponding to λ i in A (resp B), for each 1 ≤ i ≤ 3. Adopting (for comparison purposes) notation from [RS,Section 4.2], let α na , α sa , ρ a ⊂ A be the triple of curves obtained by pushing λ 1a , λ 2a , λ 3a into the interior of A and let α nb , α sb , ρ b ⊂ B be the triple of curves obtained by pushing λ 1b , λ 2b , λ 3b into the interior of B. Let N be a manifold constructed by identifying an annular neighborhood of λ 1a in ∂A with an annular neighborhood of λ 1b in ∂B and an annular neighborhood of λ 2a in ∂A with an annular neighborhood of λ 2b in ∂B. (After the identification, call the annuli A n and A s with core curves λ 1 , λ 2 respectively .) Then identify the two 4-punctured spheres ∂A − (A n ∪ A s ) and ∂B − (A n ∪ A s ) by any homeomorphism.\n\nThis construction defines a genus 2 Heegaard structure on N, of course, but it also defines a genus 2 Heegaard splitting on M 0 , the manifold obtained from N by arbitrary Dehn surgery on just the two curves ρ a ⊂ A and ρ b ⊂ B, for surgery on these pushed-in primitive curves leaves A and B still handlebodies, handlebodies which we denote respectively H a and H b . What's more, the curves λ 1 , λ 2 are each primitive in both H a and H b (though they are not necessarily a primitive pair in either). Thus the Heegaard splitting M 0 = H a ∪ H b gives rise to two potentially different genus 2 Heegaard structures on any manifold M H that is obtained by simultaneously doing further Dehn surgery on the two curves λ 1 , λ 2 . That is, a manifold M H obtained by arbitrary Dehn surgery on all four curves λ 1 , λ 2 , ρ a , ρ b ⊂ N has two possibly distinct genus 2 Heegaard splittings, Dehn derived from the Heegaard splitting M 0 = H a ∪ H b . One Heegaard structure M H = A 1 ∪ B 2 is obtained by pushing λ 1 to α na ⊂ intA and λ 2 to α sb ⊂ intB before doing Dehn surgeries on the four curves; the other M H = A 2 ∪ B 1 is obtained by pushing λ 1 to α nb ⊂ intB and λ 2 to α sa ⊂ intA before doing the Dehn surgeries. In each case, exactly two of the four Dehn surgered curves lie in each handlebody A and B before the Dehn surgery, and in that handlebody are a pushed-in primitive pair.\n\nProposition 3.1. The two Heegaard splittings A 1 ∪ B 2 and A 2 ∪ B 1 of M H become isotopic after at most a single stabilization.\n\nProof. Let A and B be the genus 3 handlebodies derived from A and B respectively, just as H was derived from H. Here is a natural genus 3 Heegaard splitting of M H : in contrast to the construction above, push both λ 1 to α na and λ 2 to α sa , so both curves (as well as ρ a ) lie in A before doing the Dehn surgeries. Although A may no longer be a handlebody after the Dehn surgeries, it follows from the discussion above that the result on A of the surgery on the three curves\nα na , α sa , ρ a ⊂ A ⊂ A is still a genus three handlebody A ′ . The complement of A ′ in M H is also a handlebody B ′ : a single 1-handle is added to B and surgery is done on the single curve ρ b ⊂ B. Thus M H = A ′ ∪ B ′ is a genus 3 Heegaard splitting of M H .\nIt's fairly easy to see that this Heegaard splitting is a stabilization of A 1 ∪ B 2 (and so, symmetrically, A 2 ∪ B 1 ). Indeed, an alternate way to construct A ′ ∪ B ′ is to begin with A 1 ∪ B 2 and add to A 1 (and so subtract from B 2 ) a regular neighborhood of the curve α sb ⊂ int(B) and a straight arc from ∂B to α sb . From this point of view, the inclusion B ′ ⊂ B 2 defines a genus 3 Heegaard splitting of the genus 2 handlebody B 2 , and any such Heegaard splitting is necessarily stabilized (see [ST,Lemma 2.7]). The pair of stabilizing disks are also a pair of stabilizing disks for A ′ ∪ B ′\n\n\nA second construction, and a hybrid\n\nHere is another natural, but less naive, way to find disjoint pairs of primitive curves on the boundary of a genus 2-handlebody and so to create a Dehn-derived pair of Heegaard splittings. Let F denote a torus with the interior of a disk removed. Then F × I is a genus 2-handlebody. For γ any properly embedded essential simple closed curve in F , γ × {0} (or symmetrically γ × {1}) is a primitive curve in the handlebody F × I. Indeed, for δ a properly embedded arc in F intersecting γ once, δ × I is a meridian disk in F × I that intersects γ × {0} exactly once.\n\nFollowing this observation, and the example of the previous section, here is a recipe for constructing candidate 3-manifolds. Begin with two copies A and B of the surface F and choose two essential (not necessarily disjoint) simple closed curves α 0 , α 1 ⊂ A and two essential (not necessarily disjoint) simple closed curves\nβ 0 , β 1 ⊂ B. Let λ 0a = α 0 × {0} ⊂ ∂(A × I), λ 1a = α 1 × {1} ⊂ ∂(A × I), λ 0b = β 0 × {0} ⊂ ∂(B × I), λ 1b = β 1 × {1} ⊂ ∂(B × I).\nIdentify an annular neighborhood of λ 0a in A×{0} with an annular neighborhood of λ 0b in B×{0} and call the core curve of the resulting annulus λ 0 . Similarly identify an annular neighborhood of λ 1a in A × {1} with an annular neighborhood of λ 1b in B × {1} and call the core curve of the resulting annulus λ 1 . Complete the identification of ∂(A × I) with ∂(B × I) along the remaining 4punctured sphere arbitrarily. Call the resulting closed 3-manifold M 0 , with Heegaard splitting M 0 = (A × I) ∪ (B × I).\n\nThe 3-manifold M ×I obtained from M 0 by doing arbitrary Dehn surgeries to the simple closed curves λ 0 and λ 1 has a Dehn-derived pair of Heegaard splittings: one comes from first pushing λ 0 into A × I and λ 1 into B × I before the Dehn surgery, the other comes from first pushing λ 1 into A × I and λ 0 into B × I before the Dehn surgery.\n\nRemarks on stabilization It is not apparent to us that a single stabilization will make the two Dehn-derived splittings of M ×I equivalent. The argument of Proposition 3.1 does not immediately carry over: if both curves λ 0a and λ 1a are pushed into A × I there is no apparent arc so that the complement A × I of a neighborhood of the arc in A × I is a genus 3 handlebody after an arbitrary Dehn surgery on the pushed in λ 0a and λ 1a . If there is a proper arc γ in A that intersects both curves α 0 ⊂ A and α 1 ⊂ A in a single point, then the complement A × I after pushing the interior of γ into A × I is a genus 3 handlebody, and so a single stabilization suffices, but having such an arc γ is not the general situation. (What is required for such an arc γ to exist is that the slopes of α 0 α 1 in A are a distance at most two apart in the Farey graph [Mi, Figure 1]. In that case γ has the slope that is incident to the slopes of both α 0 and α 1 in the Farey graph.)\n\nOn the other hand, it is relatively easy to show that two stabilizations suffice to make the two splittings equivalent. To see this, push both λ 0 and λ 1 into A×I and connect them to respectively A×{0} and A×{1} by straight arcs. Then add a regular neighborhood of the arcs and of the pushed in curves λ 0 and λ 1 to B ×I to create a genus 4 handlebody B × I and simultaneously subtract the regular neighborhood from A×I to get the genus 4 handlebody A × I. The resulting genus 4 Heegaard splitting M 0 = A × I ∪ B × I becomes a Heegaard splitting H + a ∪ H + b of M ×I after the prescribed Dehn surgery on λ 0 and λ 1 . Using the argument of Proposition 3.1 it is easy to see that the Heegaard splitting H + a ∪ H + b destablizes to the genus 3 splitting obtained by instead pushing λ 0 into B × I and then adding to B × I a regular neighborhood of λ 1 ⊂ (A × I) and a straight arc attaching it to A × {1}. The argument of Proposition 3.1 applied again shows that this Heegaard splitting destabilizes to the genus 2 splitting in which λ 0 is pushed into B ×I and λ 1 into A×I, one of the Dehn-derived splittings. But this destabilization process is clearly symmetric: we could equally well have destabilized to the other genus 2 splitting, in which λ 0 is pushed into A×I and λ 1 into B ×I, and this is the other Dehn-derived splitting.\n\nA further, call it a hybrid example of a Dehn-derived pair of splittings comes by combining the two constructions above: Identify annular neighborhoods of λ 1 , λ 2 ⊂ ∂H from Section 3 with annular neighborhoods of λ 0b , λ 1b ⊂ ∂(B × I) and identify the rest of ∂H with the rest of ∂(B × I) in any way. This gives a closed 3-manifold N with a Heegaard splitting H ∪ (B × I). Let M 0 be a 3-manifold obtained by doing an arbitrary Dehn surgery on λ 3 ⊂ ∂H, after pushing it into int(H). Then M 0 has the genus 2 Heegaard splitting (exploiting the notation used above) M 0 = H a ∪ (B × I). Let M hybrid be a closed 3-manifold obtained from M 0 by arbitrary Dehn surgeries on the two remaining curves λ 1 , λ 2 ⊂ ∂H a ⊂ M 0 . The Dehn-derived pair of Heegaard splittings for M hybrid is obtained by alternatively pushing λ 1 into H a and λ 2 into B × I or vice versa. A single stabilization suffices to make the two splittings equivalent, essentially by the same argument as for M H , in Proposition 3.1. [RS] The gap in [RS] arises because of a faulty sentence in the midst of a long and technical argument which would be difficult to summarize. We see no good alternative to simply jumping into that argument at a reasonable breaking point and inserting the argument we now believe to be complete. The jumping in point is on p. 533, in the midst of trying to prove that all cases of multiple genus 2 Heegaard splittings have been covered in the earlier examples listed in that paper. Here M is a closed hyperbolike 3-manifold with Heegaard splittings M = A ∪ P B = X ∪ Q Y . The two splitting surfaces P and Q have been made to coincide on sub-surfaces P 0 ⊂ P and Q 0 ⊂ Q. Then P − P 0 consists of annular components P X and P Y properly embedded in the handlebodies X and Y respectively, and Q − Q 0 consists of annular components Q A , Q B properly embedded in the handlebodies A, B respectively. With this as background, we now re-enter the proof of [RS,Theorem 9.4, Case 2] on page 533, at first echoing what is written there as the proof of Subcase A below. In filling the gap in the argument we also broaden the possible outcome, as expressed in Proposition 5.1:\n\n\nFilling the gap in\n\nCase 2: P X and P Y are both non-empty and the end of each curve in ∂P X ∪ ∂P Y is parallel to one of c 1 or c 2 .\n\nProposition 5.1. In this case, either I) the splittings M = A ∪ P B = X ∪ Q Y are related as in [RS,Example 4.4] or II) the two splittings M = A ∪ P B = X ∪ Q Y are Dehn-derived from a single genus 2 Heegaard splitting of another manifold M 0 .\n\nProof. If at least one annulus in each of P X or P Y is non-separating, then together they would give a non-separating, hence essential, torus in M. This contradicts our assumption that M is hyperbolike. So we may as well assume that each annulus in P Y is separating. Hence the ends of P Y are twisted in Y (see [RS,Definition 5.4]). No end of P Y can also be twisted in X, for the union along the curve of the solid tori (one in X, one in Y ) on which the curve is a torus knot would be a Seifert submanifold of M, contradicting the assumption that M is hyperbolike.\n\nSubcase A: Some end of P Y is parallel to an end of P X . [The gap in [RS] was to view this as the only possibility.]\n\nIn this case, by [RS,Lemma 5.6] all of P X is a collection of parallel non-separating longitudinal annuli in X. If P Y has ends at both c 1 and c 2 then neither curve can be twisted in X. In this case each annulus in P X is non-separating and so has ends that are non-parallel in Q. This implies that each annulus in P X has one end at c 1 and one at c 2 . Attach such an annulus in X to the tori in Y on which the c i are twisted. The boundary of the thickened result would exhibit a Seifert manifold in M, again contradicting the assumption that M is hyperbolike. We conclude that P Y has ends only at c 2 , say.\n\nIf there were three or more annuli in P Y (hence six or more ends of ∂P Y at c 2 ) then there would be at least four ends of P X at c 2 . No annulus in P X could have both ends at c 2 (since c 2 is not twisted in X) so there would also be at least four ends of P X at c 1 . This would contradict [RS,Lemma 9.5]. So we conclude that P Y is made up of one or two annuli. If it's two annuli, necessarily separating and parallel in Y , then, again by [RS,Lemma 9.5] some annulus in P X has an end at c 2 . It cannot have both ends at c 2 and must be non-separating and longitudinal in X, since c 2 is not twisted in X. In this case the relation between P and Q can be seen as follows (See [RS,Figure 32]): In [RS,Example 4.4,Variation 2], let P be the splitting given there with Dehn surgery curve in µ a + and Q be the same splitting given there but with Dehn surgery curve in µ a − . To view these simultaneously as splittings of the same manifold M, of course, the Dehn surgery curve has to be moved from µ a + to µ a − , dragging some annuli along, until the splitting surfaces P and Q intersect as described.\n\nSuppose then that P Y is a single annulus. It may have both ends on P 0 or it may have one end on P 0 and one end on an end of P X . (If both ends of P Y were also ends of P X then these, together with ends of P X at ∂P 0 parallel to c 2 would exhibit more than two annuli in P X , hence more than two ends of P X at c 1 , contradicting [RS,Lemma 9.5].) If P Y has one end on P 0 and one end on an end of P X , the initial splitting by Q is as in [RS,Example 4.4, Variation 1] (X = A − ∪ σ), with a Dehn surgery curve lying in µ b + , say. If the splitting is altered by first putting the Dehn surgery curve in µ a + (yielding the same manifold M), then altering as in [RS,Example 4.4] (i. e. considering A ∪ P B where B = B − ∪ σ) and then dragging the Dehn surgery curve from µ a + to µ b + , pushing before it an annulus from the 4-punctured sphere along which A − and B − are identified, we get the splitting surface P , intersecting Q as required. (See [RS,Figure 33].) This completes the proof that I) holds in Subcase A.\n\nSubcase B: No end of P Y is parallel to an end of P X .\n\nIn view of [RS,Lemma 9.5], in this subcase P Y and P X each consist of exactly one separating annulus, P Y twisted in Y with boundary curves parallel to c 2 (say) and P X twisted in X with boundary curves parallel to c 1 . This case is symmetric: the annulus in Q lying between the ends of P Y is Q A (say) and the annulus in Q lying between the ends of P X is exactly Q B . The annulus P Y cannot be parallel to the annulus Q A (else P 0 and Q 0 could be extended to include both) but rather the region between them is a solid torus W 2 = A ∩ Y on whose boundary the cores of the annuli are torus knots. Similarly B ∩ X is a solid torus W 1 on whose boundary the cores of the annuli Q B and P X are torus knots. The annulus P Y ∂-compresses in Y to become a separating disk; it follows that Y − W 2 = B ∩ Y is a genus 2 handlebody H BY on which the core a 2 of the annulus P Y is primitive. Symmetrically, the curve c 1 (viewed as the core of the annulus Q B ) is primitive in H BY , the curve c 2 is primitive in the genus 2 handlebody H AX = X − W 1 = X ∩ A, as is the core curve a 1 of P X .\n\nHere is another way to describe the manifold M above: begin with the two genus 2 handlebodies H AX (which contains disjoint primitive simple closed curves a 1 , c 2 on its boundary) and H BY (which contains disjoint primitive simple closed curves a 2 , c 1 on its boundary). Construct a closed 3-manifold M 0 by identifying ∂H AX to ∂H BY by a homeomorphism that identifies a i with c i , i = 1, 2. Call the resulting curves α 1 , α 2 . Now recover M from M 0 by removing a tubular neighborhood of each α i and replacing with the solid torus W i ; equivalently, do an appropriate surgery on each α i in M 0 . The two Heegaard splittings of M are then seen as follows: if α 1 is pushed into H AX and α 2 into H BY before the surgery on the curves, then the resulting Heegaard splitting is M = X ∪ Q Y ; if α 1 is pushed into H BY and α 2 into H AX before the surgery then the resulting splitting is M = A ∪ P B. That is, the splittings of M are both Dehn-derived from the Heegaard splitting M 0 = H AX ∪ H BY . Thus II) holds in Subcase B.\n\n\nA taxonomy of Dehn-derived splittings\n\nSections 3 and 4 give concrete examples of pairs of Dehn-derived fillings. In this section we show that these examples in fact constitute all pairs of Dehn-derived splittings. The argument exploits Berge's classification of pairs of primitive curves on genus 2 handlebodies [Be], though the classification here is slightly different.\n\nLet H be a genus 2 handlebody, with λ 1 , λ 2 , λ 3 ⊂ ∂H the disjoint simple closed curves described in Section 3. Denote by ρ the curve in the interior of H obtained by pushing λ 3 into H and let H surg denote the handlebody obtained from H by a specified Dehn surgery on ρ ⊂ int(H). As in Section 4, let F denote a torus with the interior of a disk removed.\n\nProposition 6.1 (Berge). Suppose α and β are disjoint non-parallel primitive curves on the boundary of a genus 2 handlebody H. Then either A) there is a Dehn surgery on ρ ⊂ H and a homeomorphism h :\nH → H surg so that h(α) = λ 1 ⊂ ∂H surg and h(β) = λ 2 ⊂ ∂H surg or B) there is a homeomorphism h : H → F ×I so that h(α) ⊂ F ×{0} and h(β) ⊂ F × {1}.\nProof. This classification is a variant of that described in [Be]. The Type II pair there, as well as some pairs of Type I, are exactly as described in alternative B). The interest is in the third example of a Type I pair, in [Be,Lemma 3.8 (3) via Figure 3]. In that example, H is viewed as divided into two solid tori by a separating disk D; let λ a and λ b be longitudes of the two solid tori into which D divides H. Then β is parallel to λ b , and α is the band sum, via a band that crosses D once, of λ b with a torus knot on the solid torus containing λ a . This picture is equivalent to letting α be the band sum λ a #λ b (through D) of λ b with λ a , and then performing a Dehn surgery on a disjoint copy of λ a that has been pushed into H, to become a core of the solid torus on which λ a lies. Now translate: relabel λ b ⊂ ∂H as λ 2 and λ a ⊂ ∂H as λ 3 . Then λ a #λ b corresponds to λ 1 . The construction just described is then to push λ 3 into the interior of H and perform some surgery to get H surg . Afterwards α corresponds to λ 1 ⊂ ∂H surg and β corresponds to λ 2 ⊂ ∂H surg . This is exactly alternative A).\n\nFollowing Propositions 5.1 and 6.1 there is a fairly clear description of the cases of multiple Heegaard splittings that are missing from [RS]. According to Proposition 5.1 the only missing cases are pairs of splittings that are Dehn-derived from an initial splitting H AX ∪ H BY of a manifold M 0 . First determine which of alternatives A) and B) apply to the pairs of surgery curves as they lie on the boundaries of the respective handlebodies: {a 1 , c 2 } ⊂ H AX or {a 2 , c 1 } ⊂ H BY . If both are of type A) then the pair of splittings is Dehn-derived as in the construction of M H in Section 3. If both are of type B) then the pair of splittings is Dehn-derived as in the construction of M ×I in Section 4. If one is of type A) and one of type B) then the pair of splittings is Dehn-derived as in the construction of M hybrid in Section 4.\n\nIt is worth mentioning that there is another view of a pair of primitive curves lying on a handlebody as in A) of Proposition 6.1, a view that more closely resembles that in B): Let α, β, γ be simple closed curves in F so that each pair of curves intersects in exactly one point. (For example, choose curves in F of slopes 0, 1, ∞.) Then it is fairly easy to see that the three curves α × {0}, β × {1}, γ × { 1 2 } lie in the handlebody F × I just as λ 1 , λ 2 , ρ lie in H in the description preceding Proposition 6.1. So the primitive curves in description A) can be made to look like a special case of those in description B), but with the cost that an extra Dehn surgery has to be performed on a specific curve in the interior of F × I. This is the twisted product view of [Be,3.2].\n\n\nDistance\n\nIt would seem possible that the Dehn-derived pairs of Heegaard splittings exhibited above could coincidentally all be contained among the examples already listed in [RS], for there is no claim that the types of examples of multiple Heegaard splittings we have offered here and in [RS] do not overlap. But in fact there is an invariant which does show that at least some Dehn-derived pairs of Heegaard splittings described above did not already occur in a different guise in [RS]. This invariant had not yet been introduced when [RS] was written and is called the (Hempel) distance of the Heegaard splitting [He]. We briefly review:\n\nDefinition 7.1. A Heegaard splitting H 1 ∪ S H 2 has Hempel distance at most n if there is a sequence c 0 , ..., c n of essential simple closed curves in the splitting surface S so that • for each i = 1, ..., n, c i ∩ c i−1 = ∅ • c 0 bounds a disk in H 1 • c n bounds a disk in H 2 If the splitting has distance ≤ n but not ≤ n − 1, then the distance d(S) = n.\n\nA Heegaard splitting of distance 0 is called reducible; one of distance ≤ 1 is called weakly reducible. Any Heegaard splitting of a reducible manifold is reducible. A Heegaard splitting of distance ≤ 2 is said to have the disjoint curve property [Th]; any Heegaard splitting of a toroidal 3-manifold has the disjoint curve property ( [He], [Th]). A weakly reducible genus 2 Heegaard splitting is also reducible, so an irreducible Heegaard splitting of genus 2 has distance at least 2 ( [Th]).\n\nIn the other direction we have:\n\nProposition 7.2. Suppose the manifold M has a Dehn-derived pair of Heegaard splittings. Then each of these Heegaard splittings has Hempel distance at most 3.\n\nProof. Suppose the splittings are Dehn-derived from a splitting M 0 = H a ∪ S H b via the disjoint pair of simple closed curves λ 1 , λ 2 ⊂ S. With no loss of generality, consider the splitting M = A ∪ S B obtained by pushing λ 1 into int(H a ) and λ 2 into int(H b ) before doing Dehn surgery on the λ i . Since λ 1 is primitive in H a there is a properly embedded essential disk D a ⊂ H a that is disjoint from λ 1 . (For example D a can be obtained from a meridian disk D 1 ⊂ H a that intersects λ 1 in a single point by band-summing together two copies of D 1 along a subarc of λ 1 − D 1 .) D a is then also disjoint from the curve α 1 ⊂ H a obtained by pushing λ 1 into int(H a ), so D a remains intact as a meridian of A after surgery on α 1 . Hence ∂D a and λ 1 are disjoint curves in ∂A.\n\nSymmetrically, there is a meridian D b ⊂ B so that ∂D b and λ 2 are disjoint curves in ∂B. Then the sequence ∂D a , λ 1 , λ 2 , ∂D b shows that the splitting A ∪ S B has distance at most 3. Proof. Following the comments above we can restrict attention to irreducible, atoroidal manifolds. We briefly run through the examples as they appear in [RS,Section 4]. Typically the description of an example H 1 ∪ S H 2 in [RS] consists of two parts: A collection of annuli A ⊂ S along which ∂H 1 and ∂H 2 are identified, followed by an arbitrary identification of ∂H 1 − A with ∂H 2 − A. From this point of view the simple closed curves ∂A ⊂ S that separate one sort of region from the other will be called the seams of the Heegaard splitting. We will observe that in [RS] some seam is always disjoint from an essential disk in H 1 and an essential disk in H 2 . This demonstrates that the splitting has the disjoint curve property and so has distance ≤ 2.\n\nTo be specific: In [RS,Subsection 4.1], [RS,Subsection 4.2, Variation 1] and [RS,Subsection 4.4, Variations 1 and 2], the meridians of the 1-handles e a and e b are disjoint from the seams. [RS,Subsection 4.2, Variation 2] is slightly more complicated. It is a bit like the construction in Section 3 above: Handlebodies A and B are identified along neighborhoods of all three curves λ i , i = 1, 2, 3, Dehn surgery is done to all three, with λ 1 , λ 2 pushed into A and λ 3 into B (then vice versa). But there is a meridian of A disjoint from λ 1 and λ 2 and a meridian of B disjoint from λ 1 and λ 3 , so a seam parallel to λ 1 demonstrates that the splitting of [RS,Subsection 4.2,Variation 2] has the disjoint curve property.\n\nThe manifolds in [RS,Subsection 4.3] and [RS,Subsection 4.4,Variations 3,4,and 7] are all toroidal, so they are of distance ≤ 2. What remains are [RS,Subsection 4.4,Variations 5 and 6] and we adopt the terminology there. In Variation 5, with, say, ρ a ⊂ A − , the seams that are the boundary of the 4-punctured sphere ∂A − ∩ ∂Γ are all disjoint from the meridian of the 1-handle e b ⊂ B and, in A − , any one of these seams together with ρ a lie in A − as two of the λ i 's of Section 3 above lie in H. In particular, there is a meridian of A − disjoint from both the seam and from ρ a . Thus that seam again illustrates that the splitting has the disjoint curve property.\n\nThe argument for Variation 6 is much the same. First note that if, in that Variation, Dehn surgeries are done on two curves parallel to σ, then the resulting manifold has a Seifert piece and so has distance ≤ 2. So the only change we need to consider from Variation 5 is Dehn surgery on a single curve parallel to σ. If that curve lies in B the argument for Variation 5 suffices; if it is in A − this merely forces us to pick a specific seam in the argument for Variation 5, a seam parallel to the new surgery curve.\n\nIn contrast, some of the examples constructed in this paper can be shown to have distance 3, so they cannot have appeared in any case considered in [RS]. See [Be2] (also [Sc]) for details.\n\nDefinition 2 . 3 .\n23Two genus 2 Heegaard splittings X ∪ Q Y and A ∪ P B of a closed 3-manifold M are called Dehn derived (from the splitting M 0 = H a ∪ S H b via λ 1 ∪ λ 2 ⊂ S) if the two splittings are created as in Proposition 2.2.\n\nCorollary 2 . 4 .\n24Suppose M = A ∪ P B = X ∪ Q Y are a Dehn-derived pair of Heegaard splittings. Then the two hyperelliptic involutions of M, one determined by the Heegaard splitting A ∪ P B and the other by the Heegaard splitting X ∪ Q Y , coincide.\n\nFigure 1 .\n1Figure 1.\n\nProposition 7 . 3 .\n73All examples of multiple Heegaard splittings appearing in[RS, Section 4] have Hempel distance ≤ 2.\n\nA classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody. J Berge, arXiv:0910.3038J. Berge, A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody, arXiv:0910.3038.\n\nA closed orientable 3-manifold with distinct distance three genus two Heegaard splittings. J Berge, to appearJ. Berge, A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings, to appear.\n\n3-manifolds as viewed from the curve complex. J Hempel, Topology. 40J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (2001) 631-657.\n\nThe classification of punctured-torus groups. Y Minsky, Annals of Math. 149Y. Minsky, The classification of punctured-torus groups, Annals of Math 149 (1999) 559-626.\n\nGenus two Heegaard splittings of orientable 3-manifolds. H Rubinstein, M Scharlemann, Proceedings of the 1998 Kirbyfest, Geometry and Topology Monographs. the 1998 Kirbyfest, Geometry and Topology Monographs2H. Rubinstein and M. Scharlemann, Genus two Heegaard splittings of ori- entable 3-manifolds, in Proceedings of the 1998 Kirbyfest, Geometry and Topol- ogy Monographs 2 (1999) 489-553.\n\nBerge's distance 3 pairs of genus 2 Heegaard splittings. M Scharlemann, ArXiv preprint 1002.4887M. Scharlemann, Berge's distance 3 pairs of genus 2 Heegaard splittings, ArXiv preprint 1002.4887\n\nHeegaard splittings of (surface) x I are standard. M Scharlemann, A Thompson, Math. Ann. 295M. Scharlemann, A. Thompson, Heegaard splittings of (surface) x I are stan- dard, Math. Ann. 295 (1993) 549-564.\n\nThe disjoint curve property and genus 2 manifolds. A Thompson, Topology Appl. 97A. Thompson, The disjoint curve property and genus 2 manifolds, Topology Appl. 97 (1999) 273-279.\n"},"corpus_id":{"kind":"number","value":16107171,"string":"16,107,171"},"external_ids":{"kind":"string","value":"{\n \"arxiv\": \"0910.3921\",\n \"mag\": 2135452356,\n \"acl\": null,\n \"pubmed\": null,\n \"pubmedcentral\": null,\n \"dblp\": null,\n \"doi\": \"10.2140/agt.2011.11.1781\"\n}"},"source":{"kind":"string","value":"{\n \"pdf_urls\": [\n \"https://arxiv.org/pdf/0910.3921v2.pdf\"\n ],\n \"pdf_sha\": \"767f2a222eb7bcc86040bfa3be6ec7d40168ed93\",\n \"open_access\": {\n \"license\": null,\n \"url\": \"http://msp.org/agt/2011/11-3/agt-v11-n3-p20-s.pdf\",\n \"status\": \"BRONZE\"\n }\n}"},"title":{"kind":"string","value":"MULTIPLE GENUS 2 HEEGAARD SPLITTINGS: A MISSED CASE"},"authors":{"kind":"list like","value":["John Berge","Martin Scharlemann"],"string":"[\n \"John Berge\",\n \"Martin Scharlemann\"\n]","isConversational":false},"abstract":{"kind":"string","value":"A gap in [RS] is explored: new examples are found of closed orientable 3-manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in [RS] are not universally shared by the new examples: some of the new examples have Hempel distance 3, and it is not clear that a single stabilization always makes the multiple splittings isotopic.1 The error is on p. 533: The last sentence of the first paragraph of Case 2 should have read, \"The same curves cannot then be twisted in X since M is hyperbolike.\" This leaves open an additional possibility for P X , P Y , which appears as Subcase B in Section 5 below."},"sections":{"kind":"list like","value":[{"title":"Introduction","content":"In 1998, Rubinstein and the second author [RS] studied the question of when there could be more than one distinct genus 2 Heegaard splitting of the same closed orientable 3-manifold. The goal of the project was modest: to provide a complete list of ways in which such multiple splittings could be constructed, but with no claim that each example on the list did in fact have multiple non-isotopic splittings (there could be isotopies from one splitting to another that are not apparent). Nor was there a claim that the list had no redundancies; a 3-manifold and its multiple splittings might appear more than once on the list. Such a list would still be useful, for if every example on the list could be shown to have a certain property, then that property would be true for any closed orientable 3-manifold M that has multiple genus 2 splittings. Two examples were given in [RS]:\n• If M is atoroidal then the hyperelliptic involutions determined by the two genus 2 Heegaard splittings commute. • Any two genus 2 Heegaard splittings of M become isotopic after a single stabilization.\nDespite this modest goal, the argument in [RS] contains a gap. In 2008, the first author discovered a class of examples that do not appear on the list and which, moreover, have mathematical properties that distinguish them in important ways from the examples that do Date: March 1, 2010. Second author partially supported by an NSF grant. appear in [RS]. It is true that, even for the new examples, the hyperelliptic involutions commute. But we know of no argument showing that the new examples all share the second property above; that is, we cannot show that the newly discovered multiple splittings necessarily become isotopic after a single stabilization (though they do after two stabilizations).\nA third property, shared by all examples in [RS] but not by some of the new examples, is not listed above because the notion of Hempel distance of Heegaard splittings (see [He]) did not exist at the time [RS] was written. But a retrospective look (see Section 7 below) will verify that all the splittings described in [RS] have Hempel distance no greater than 2, whereas results of the first author [Be2] illustrate that at least some of the new examples have Hempel distance 3. (This also verifies that the gap in the argument in [RS] actually led to missed examples.)\nThe present paper serves as an erratum to [RS] 1 and describes the new examples. Here is an outline: In Section 2 we describe a general method for constructing closed orientable 3-manifolds that appear to have multiple genus 2 Heegaard splittings; these examples (called Dehnderived) are based around Dehn surgery on a pair of strategically placed curves. It follows from the construction that always the hyperelliptic involutions of the alternate splittings coincide.\nIt is not immediately obvious that curves supporting Dehn-derived examples can be found, but in Sections 3 and 4 we give three specific classes of examples. The classes are denoted M H (Section 3), M ×I and M hybrid (Section 4). (M H can be viewed as a third variation of [RS,Example 4.2].) For the examples M H and M hybrid a single stabilization suffices to make the alternate splittings equivalent, but this property is at least not apparent in most cases of M ×I .\nSection 5 describes how the proof of [RS,Lemma 9.5, Case 2] went astray and how it needs to be altered to fix the gap. The upshot is that Dehn-derived examples, as described in Section 2, do fill the gap in the original proof. In Section 6 it is further shown, using new results in [Be], that any Dehn-derived example is in fact of type M H , M ×I or M hybrid . Finally, in Section 7 we verify that all of the old examples that are listed in [RS] are of Hempel distance 2, whereas at least some Dehn-derived examples are of distance 3. (It is easy to see that all Dehn-derived examples are of distance no more than 3.)"},{"title":"Dehn derived multiple splittings","content":"A primitive k-tuple of curves in the boundary of a genus g handlebody H is a collection λ 1 , ...λ k ⊂ ∂H of k ≤ g disjoint simple closed curves so that, for some properly embedded collection D 1 , ..., D k of disks in H, |λ i ∩ D j | = δ ij , 1 ≤ i, j ≤ k. It is easy to see that the closed complement in H of such a collection of meridian disks is a genus g − k handlebody. In particular, if k = g then λ 1 , ...λ g is called a complete set of primitive curves and the corresponding collection of disks D 1 , ..., D g is called a complete set of meridian disks. The closed complement of a complete set of meridian disks in H is a 3-ball.\nSuppose Λ = λ 1 , ...λ k ⊂ ∂H is a primitive k-tuple of curves in H and let α 1 , ..., α k be the properly embedded collection of curves in H obtained by pushing Λ slightly into the interior of H. We can view H as the boundary connect sum of a genus g − k handlebody H ′ and k solid tori W 1 , ..., W k , with λ i a longitude of W i and so α i a core curve of W i . Then Dehn surgery on α i ⊂ W i still gives a solid torus. Hence any Dehn surgery on the family of curves α 1 , ..., α k leaves H still a handlebody.\nSuppose M 0 is a closed orientable 3-manifold and that M 0 = H a ∪ S H b is a genus 2 Heegaard splitting of M 0 . Suppose further that λ 1 , λ 2 ⊂ S are two disjoint doubly primitive curves in S.\nProposition 2.2. Suppose M is a manifold obtained by some specified Dehn surgeries on λ 1 and λ 2 . For i = 1, 2, let A i (resp. B i ) be the manifold obtained from the handlebody H a (resp. H b ) by pushing the curve λ i into int(H a ) (resp int(H b )) and performing the specified Dehn surgery on the curve.\nThen A 1 ∪ S B 2 and A 2 ∪ S B 1 are two (possibly different) genus 2 Heegaard splittings of M.\nby Dehn surgery on a pushed in copy α i of a single primitive curve in S. It was just observed that this makes each A i (resp. B i ) a handlebody. Proof. Let M 0 = H a ∪ S H b be the Heegaard split 3-manifold from which the two splittings of M are Dehn derived, via λ 1 ∪ λ 2 ⊂ S. The hyperelliptic involution preserves the isotopy class (though perhaps reversing the orientation) of any simple closed curve in S. We may then position λ i so that the curves are preserved (reversing orientation) by the hyperelliptic involution on M 0 = H a ∪ S H b . Then the hyperelliptic involution on M 0 naturally induces a single hyperelliptic involution on M."},{"title":"A simple set of examples","content":"It is not immediately obvious how to create examples of a Dehnderived pair of splittings or, very naively, whether examples even exist. In this section we present and briefly discuss an important concrete class of examples.\nConsider a genus 2 handlebody H, constructed from two 0-handles by connecting them with three 1-handles. With this structure H has a natural Z 3 symmetry, shown as 2π 3 rotation about the green axis in Figure 1. Let λ 1 ⊂ ∂H be the red curve shown in the figure and λ 2 , λ 3 be the other two simple closed curves to which λ 1 is carried by the Z 3 symmetry. Then each λ i is a primitive curve on ∂H and, indeed, any two of the curves, say λ 1 , λ 2 constitute a complete set of primitive curves (that is, a primitive pair). In this case the corresponding pair of meridian disks are the meridian disks of the two 1-handles through which λ 3 passes.\nLet H be the genus 3 handlebody obtained by removing from H a neighborhood of the arc in which the axis of symmetry intersects one of the 0-handles. It is easy to see that in H the collection λ 1 , λ 2 , λ 3 ⊂ ∂H is a complete set of primitive curves, that is a primitive 3-tuple.\nTo construct some Dehn-derived pairs of Heegaard splittings, begin with two genus 2 handlebodies A and B, on each of whose boundaries lie three disjoint simple closed curves corresponding to λ 1 , λ 2 , λ 3 ⊂ ∂H. Let λ ia ⊂ ∂A (resp λ ib ⊂ ∂B) be the curve corresponding to λ i in A (resp B), for each 1 ≤ i ≤ 3. Adopting (for comparison purposes) notation from [RS,Section 4.2], let α na , α sa , ρ a ⊂ A be the triple of curves obtained by pushing λ 1a , λ 2a , λ 3a into the interior of A and let α nb , α sb , ρ b ⊂ B be the triple of curves obtained by pushing λ 1b , λ 2b , λ 3b into the interior of B. Let N be a manifold constructed by identifying an annular neighborhood of λ 1a in ∂A with an annular neighborhood of λ 1b in ∂B and an annular neighborhood of λ 2a in ∂A with an annular neighborhood of λ 2b in ∂B. (After the identification, call the annuli A n and A s with core curves λ 1 , λ 2 respectively .) Then identify the two 4-punctured spheres ∂A − (A n ∪ A s ) and ∂B − (A n ∪ A s ) by any homeomorphism.\nThis construction defines a genus 2 Heegaard structure on N, of course, but it also defines a genus 2 Heegaard splitting on M 0 , the manifold obtained from N by arbitrary Dehn surgery on just the two curves ρ a ⊂ A and ρ b ⊂ B, for surgery on these pushed-in primitive curves leaves A and B still handlebodies, handlebodies which we denote respectively H a and H b . What's more, the curves λ 1 , λ 2 are each primitive in both H a and H b (though they are not necessarily a primitive pair in either). Thus the Heegaard splitting M 0 = H a ∪ H b gives rise to two potentially different genus 2 Heegaard structures on any manifold M H that is obtained by simultaneously doing further Dehn surgery on the two curves λ 1 , λ 2 . That is, a manifold M H obtained by arbitrary Dehn surgery on all four curves λ 1 , λ 2 , ρ a , ρ b ⊂ N has two possibly distinct genus 2 Heegaard splittings, Dehn derived from the Heegaard splitting M 0 = H a ∪ H b . One Heegaard structure M H = A 1 ∪ B 2 is obtained by pushing λ 1 to α na ⊂ intA and λ 2 to α sb ⊂ intB before doing Dehn surgeries on the four curves; the other M H = A 2 ∪ B 1 is obtained by pushing λ 1 to α nb ⊂ intB and λ 2 to α sa ⊂ intA before doing the Dehn surgeries. In each case, exactly two of the four Dehn surgered curves lie in each handlebody A and B before the Dehn surgery, and in that handlebody are a pushed-in primitive pair.\nProposition 3.1. The two Heegaard splittings A 1 ∪ B 2 and A 2 ∪ B 1 of M H become isotopic after at most a single stabilization.\nProof. Let A and B be the genus 3 handlebodies derived from A and B respectively, just as H was derived from H. Here is a natural genus 3 Heegaard splitting of M H : in contrast to the construction above, push both λ 1 to α na and λ 2 to α sa , so both curves (as well as ρ a ) lie in A before doing the Dehn surgeries. Although A may no longer be a handlebody after the Dehn surgeries, it follows from the discussion above that the result on A of the surgery on the three curves\nIt's fairly easy to see that this Heegaard splitting is a stabilization of A 1 ∪ B 2 (and so, symmetrically, A 2 ∪ B 1 ). Indeed, an alternate way to construct A ′ ∪ B ′ is to begin with A 1 ∪ B 2 and add to A 1 (and so subtract from B 2 ) a regular neighborhood of the curve α sb ⊂ int(B) and a straight arc from ∂B to α sb . From this point of view, the inclusion B ′ ⊂ B 2 defines a genus 3 Heegaard splitting of the genus 2 handlebody B 2 , and any such Heegaard splitting is necessarily stabilized (see [ST,Lemma 2.7]). The pair of stabilizing disks are also a pair of stabilizing disks for A ′ ∪ B ′"},{"title":"A second construction, and a hybrid","content":"Here is another natural, but less naive, way to find disjoint pairs of primitive curves on the boundary of a genus 2-handlebody and so to create a Dehn-derived pair of Heegaard splittings. Let F denote a torus with the interior of a disk removed. Then F × I is a genus 2-handlebody. For γ any properly embedded essential simple closed curve in F , γ × {0} (or symmetrically γ × {1}) is a primitive curve in the handlebody F × I. Indeed, for δ a properly embedded arc in F intersecting γ once, δ × I is a meridian disk in F × I that intersects γ × {0} exactly once.\nFollowing this observation, and the example of the previous section, here is a recipe for constructing candidate 3-manifolds. Begin with two copies A and B of the surface F and choose two essential (not necessarily disjoint) simple closed curves α 0 , α 1 ⊂ A and two essential (not necessarily disjoint) simple closed curves\nIdentify an annular neighborhood of λ 0a in A×{0} with an annular neighborhood of λ 0b in B×{0} and call the core curve of the resulting annulus λ 0 . Similarly identify an annular neighborhood of λ 1a in A × {1} with an annular neighborhood of λ 1b in B × {1} and call the core curve of the resulting annulus λ 1 . Complete the identification of ∂(A × I) with ∂(B × I) along the remaining 4punctured sphere arbitrarily. Call the resulting closed 3-manifold M 0 , with Heegaard splitting M 0 = (A × I) ∪ (B × I).\nThe 3-manifold M ×I obtained from M 0 by doing arbitrary Dehn surgeries to the simple closed curves λ 0 and λ 1 has a Dehn-derived pair of Heegaard splittings: one comes from first pushing λ 0 into A × I and λ 1 into B × I before the Dehn surgery, the other comes from first pushing λ 1 into A × I and λ 0 into B × I before the Dehn surgery.\nRemarks on stabilization It is not apparent to us that a single stabilization will make the two Dehn-derived splittings of M ×I equivalent. The argument of Proposition 3.1 does not immediately carry over: if both curves λ 0a and λ 1a are pushed into A × I there is no apparent arc so that the complement A × I of a neighborhood of the arc in A × I is a genus 3 handlebody after an arbitrary Dehn surgery on the pushed in λ 0a and λ 1a . If there is a proper arc γ in A that intersects both curves α 0 ⊂ A and α 1 ⊂ A in a single point, then the complement A × I after pushing the interior of γ into A × I is a genus 3 handlebody, and so a single stabilization suffices, but having such an arc γ is not the general situation. (What is required for such an arc γ to exist is that the slopes of α 0 α 1 in A are a distance at most two apart in the Farey graph [Mi, Figure 1]. In that case γ has the slope that is incident to the slopes of both α 0 and α 1 in the Farey graph.)\nOn the other hand, it is relatively easy to show that two stabilizations suffice to make the two splittings equivalent. To see this, push both λ 0 and λ 1 into A×I and connect them to respectively A×{0} and A×{1} by straight arcs. Then add a regular neighborhood of the arcs and of the pushed in curves λ 0 and λ 1 to B ×I to create a genus 4 handlebody B × I and simultaneously subtract the regular neighborhood from A×I to get the genus 4 handlebody A × I. The resulting genus 4 Heegaard splitting M 0 = A × I ∪ B × I becomes a Heegaard splitting H + a ∪ H + b of M ×I after the prescribed Dehn surgery on λ 0 and λ 1 . Using the argument of Proposition 3.1 it is easy to see that the Heegaard splitting H + a ∪ H + b destablizes to the genus 3 splitting obtained by instead pushing λ 0 into B × I and then adding to B × I a regular neighborhood of λ 1 ⊂ (A × I) and a straight arc attaching it to A × {1}. The argument of Proposition 3.1 applied again shows that this Heegaard splitting destabilizes to the genus 2 splitting in which λ 0 is pushed into B ×I and λ 1 into A×I, one of the Dehn-derived splittings. But this destabilization process is clearly symmetric: we could equally well have destabilized to the other genus 2 splitting, in which λ 0 is pushed into A×I and λ 1 into B ×I, and this is the other Dehn-derived splitting.\nA further, call it a hybrid example of a Dehn-derived pair of splittings comes by combining the two constructions above: Identify annular neighborhoods of λ 1 , λ 2 ⊂ ∂H from Section 3 with annular neighborhoods of λ 0b , λ 1b ⊂ ∂(B × I) and identify the rest of ∂H with the rest of ∂(B × I) in any way. This gives a closed 3-manifold N with a Heegaard splitting H ∪ (B × I). Let M 0 be a 3-manifold obtained by doing an arbitrary Dehn surgery on λ 3 ⊂ ∂H, after pushing it into int(H). Then M 0 has the genus 2 Heegaard splitting (exploiting the notation used above) M 0 = H a ∪ (B × I). Let M hybrid be a closed 3-manifold obtained from M 0 by arbitrary Dehn surgeries on the two remaining curves λ 1 , λ 2 ⊂ ∂H a ⊂ M 0 . The Dehn-derived pair of Heegaard splittings for M hybrid is obtained by alternatively pushing λ 1 into H a and λ 2 into B × I or vice versa. A single stabilization suffices to make the two splittings equivalent, essentially by the same argument as for M H , in Proposition 3.1. [RS] The gap in [RS] arises because of a faulty sentence in the midst of a long and technical argument which would be difficult to summarize. We see no good alternative to simply jumping into that argument at a reasonable breaking point and inserting the argument we now believe to be complete. The jumping in point is on p. 533, in the midst of trying to prove that all cases of multiple genus 2 Heegaard splittings have been covered in the earlier examples listed in that paper. Here M is a closed hyperbolike 3-manifold with Heegaard splittings M = A ∪ P B = X ∪ Q Y . The two splitting surfaces P and Q have been made to coincide on sub-surfaces P 0 ⊂ P and Q 0 ⊂ Q. Then P − P 0 consists of annular components P X and P Y properly embedded in the handlebodies X and Y respectively, and Q − Q 0 consists of annular components Q A , Q B properly embedded in the handlebodies A, B respectively. With this as background, we now re-enter the proof of [RS,Theorem 9.4, Case 2] on page 533, at first echoing what is written there as the proof of Subcase A below. In filling the gap in the argument we also broaden the possible outcome, as expressed in Proposition 5.1:"},{"title":"Filling the gap in","content":"Case 2: P X and P Y are both non-empty and the end of each curve in ∂P X ∪ ∂P Y is parallel to one of c 1 or c 2 .\nProposition 5.1. In this case, either I) the splittings M = A ∪ P B = X ∪ Q Y are related as in [RS,Example 4.4] or II) the two splittings M = A ∪ P B = X ∪ Q Y are Dehn-derived from a single genus 2 Heegaard splitting of another manifold M 0 .\nProof. If at least one annulus in each of P X or P Y is non-separating, then together they would give a non-separating, hence essential, torus in M. This contradicts our assumption that M is hyperbolike. So we may as well assume that each annulus in P Y is separating. Hence the ends of P Y are twisted in Y (see [RS,Definition 5.4]). No end of P Y can also be twisted in X, for the union along the curve of the solid tori (one in X, one in Y ) on which the curve is a torus knot would be a Seifert submanifold of M, contradicting the assumption that M is hyperbolike.\nSubcase A: Some end of P Y is parallel to an end of P X . [The gap in [RS] was to view this as the only possibility.]\nIn this case, by [RS,Lemma 5.6] all of P X is a collection of parallel non-separating longitudinal annuli in X. If P Y has ends at both c 1 and c 2 then neither curve can be twisted in X. In this case each annulus in P X is non-separating and so has ends that are non-parallel in Q. This implies that each annulus in P X has one end at c 1 and one at c 2 . Attach such an annulus in X to the tori in Y on which the c i are twisted. The boundary of the thickened result would exhibit a Seifert manifold in M, again contradicting the assumption that M is hyperbolike. We conclude that P Y has ends only at c 2 , say.\nIf there were three or more annuli in P Y (hence six or more ends of ∂P Y at c 2 ) then there would be at least four ends of P X at c 2 . No annulus in P X could have both ends at c 2 (since c 2 is not twisted in X) so there would also be at least four ends of P X at c 1 . This would contradict [RS,Lemma 9.5]. So we conclude that P Y is made up of one or two annuli. If it's two annuli, necessarily separating and parallel in Y , then, again by [RS,Lemma 9.5] some annulus in P X has an end at c 2 . It cannot have both ends at c 2 and must be non-separating and longitudinal in X, since c 2 is not twisted in X. In this case the relation between P and Q can be seen as follows (See [RS,Figure 32]): In [RS,Example 4.4,Variation 2], let P be the splitting given there with Dehn surgery curve in µ a + and Q be the same splitting given there but with Dehn surgery curve in µ a − . To view these simultaneously as splittings of the same manifold M, of course, the Dehn surgery curve has to be moved from µ a + to µ a − , dragging some annuli along, until the splitting surfaces P and Q intersect as described.\nSuppose then that P Y is a single annulus. It may have both ends on P 0 or it may have one end on P 0 and one end on an end of P X . (If both ends of P Y were also ends of P X then these, together with ends of P X at ∂P 0 parallel to c 2 would exhibit more than two annuli in P X , hence more than two ends of P X at c 1 , contradicting [RS,Lemma 9.5].) If P Y has one end on P 0 and one end on an end of P X , the initial splitting by Q is as in [RS,Example 4.4, Variation 1] (X = A − ∪ σ), with a Dehn surgery curve lying in µ b + , say. If the splitting is altered by first putting the Dehn surgery curve in µ a + (yielding the same manifold M), then altering as in [RS,Example 4.4] (i. e. considering A ∪ P B where B = B − ∪ σ) and then dragging the Dehn surgery curve from µ a + to µ b + , pushing before it an annulus from the 4-punctured sphere along which A − and B − are identified, we get the splitting surface P , intersecting Q as required. (See [RS,Figure 33].) This completes the proof that I) holds in Subcase A.\nSubcase B: No end of P Y is parallel to an end of P X .\nIn view of [RS,Lemma 9.5], in this subcase P Y and P X each consist of exactly one separating annulus, P Y twisted in Y with boundary curves parallel to c 2 (say) and P X twisted in X with boundary curves parallel to c 1 . This case is symmetric: the annulus in Q lying between the ends of P Y is Q A (say) and the annulus in Q lying between the ends of P X is exactly Q B . The annulus P Y cannot be parallel to the annulus Q A (else P 0 and Q 0 could be extended to include both) but rather the region between them is a solid torus W 2 = A ∩ Y on whose boundary the cores of the annuli are torus knots. Similarly B ∩ X is a solid torus W 1 on whose boundary the cores of the annuli Q B and P X are torus knots. The annulus P Y ∂-compresses in Y to become a separating disk; it follows that Y − W 2 = B ∩ Y is a genus 2 handlebody H BY on which the core a 2 of the annulus P Y is primitive. Symmetrically, the curve c 1 (viewed as the core of the annulus Q B ) is primitive in H BY , the curve c 2 is primitive in the genus 2 handlebody H AX = X − W 1 = X ∩ A, as is the core curve a 1 of P X .\nHere is another way to describe the manifold M above: begin with the two genus 2 handlebodies H AX (which contains disjoint primitive simple closed curves a 1 , c 2 on its boundary) and H BY (which contains disjoint primitive simple closed curves a 2 , c 1 on its boundary). Construct a closed 3-manifold M 0 by identifying ∂H AX to ∂H BY by a homeomorphism that identifies a i with c i , i = 1, 2. Call the resulting curves α 1 , α 2 . Now recover M from M 0 by removing a tubular neighborhood of each α i and replacing with the solid torus W i ; equivalently, do an appropriate surgery on each α i in M 0 . The two Heegaard splittings of M are then seen as follows: if α 1 is pushed into H AX and α 2 into H BY before the surgery on the curves, then the resulting Heegaard splitting is M = X ∪ Q Y ; if α 1 is pushed into H BY and α 2 into H AX before the surgery then the resulting splitting is M = A ∪ P B. That is, the splittings of M are both Dehn-derived from the Heegaard splitting M 0 = H AX ∪ H BY . Thus II) holds in Subcase B."},{"title":"A taxonomy of Dehn-derived splittings","content":"Sections 3 and 4 give concrete examples of pairs of Dehn-derived fillings. In this section we show that these examples in fact constitute all pairs of Dehn-derived splittings. The argument exploits Berge's classification of pairs of primitive curves on genus 2 handlebodies [Be], though the classification here is slightly different.\nLet H be a genus 2 handlebody, with λ 1 , λ 2 , λ 3 ⊂ ∂H the disjoint simple closed curves described in Section 3. Denote by ρ the curve in the interior of H obtained by pushing λ 3 into H and let H surg denote the handlebody obtained from H by a specified Dehn surgery on ρ ⊂ int(H). As in Section 4, let F denote a torus with the interior of a disk removed.\nProposition 6.1 (Berge). Suppose α and β are disjoint non-parallel primitive curves on the boundary of a genus 2 handlebody H. Then either A) there is a Dehn surgery on ρ ⊂ H and a homeomorphism h :\nProof. This classification is a variant of that described in [Be]. The Type II pair there, as well as some pairs of Type I, are exactly as described in alternative B). The interest is in the third example of a Type I pair, in [Be,Lemma 3.8 (3) via Figure 3]. In that example, H is viewed as divided into two solid tori by a separating disk D; let λ a and λ b be longitudes of the two solid tori into which D divides H. Then β is parallel to λ b , and α is the band sum, via a band that crosses D once, of λ b with a torus knot on the solid torus containing λ a . This picture is equivalent to letting α be the band sum λ a #λ b (through D) of λ b with λ a , and then performing a Dehn surgery on a disjoint copy of λ a that has been pushed into H, to become a core of the solid torus on which λ a lies. Now translate: relabel λ b ⊂ ∂H as λ 2 and λ a ⊂ ∂H as λ 3 . Then λ a #λ b corresponds to λ 1 . The construction just described is then to push λ 3 into the interior of H and perform some surgery to get H surg . Afterwards α corresponds to λ 1 ⊂ ∂H surg and β corresponds to λ 2 ⊂ ∂H surg . This is exactly alternative A).\nFollowing Propositions 5.1 and 6.1 there is a fairly clear description of the cases of multiple Heegaard splittings that are missing from [RS]. According to Proposition 5.1 the only missing cases are pairs of splittings that are Dehn-derived from an initial splitting H AX ∪ H BY of a manifold M 0 . First determine which of alternatives A) and B) apply to the pairs of surgery curves as they lie on the boundaries of the respective handlebodies: {a 1 , c 2 } ⊂ H AX or {a 2 , c 1 } ⊂ H BY . If both are of type A) then the pair of splittings is Dehn-derived as in the construction of M H in Section 3. If both are of type B) then the pair of splittings is Dehn-derived as in the construction of M ×I in Section 4. If one is of type A) and one of type B) then the pair of splittings is Dehn-derived as in the construction of M hybrid in Section 4.\nIt is worth mentioning that there is another view of a pair of primitive curves lying on a handlebody as in A) of Proposition 6.1, a view that more closely resembles that in B): Let α, β, γ be simple closed curves in F so that each pair of curves intersects in exactly one point. (For example, choose curves in F of slopes 0, 1, ∞.) Then it is fairly easy to see that the three curves α × {0}, β × {1}, γ × { 1 2 } lie in the handlebody F × I just as λ 1 , λ 2 , ρ lie in H in the description preceding Proposition 6.1. So the primitive curves in description A) can be made to look like a special case of those in description B), but with the cost that an extra Dehn surgery has to be performed on a specific curve in the interior of F × I. This is the twisted product view of [Be,3.2]."},{"title":"Distance","content":"It would seem possible that the Dehn-derived pairs of Heegaard splittings exhibited above could coincidentally all be contained among the examples already listed in [RS], for there is no claim that the types of examples of multiple Heegaard splittings we have offered here and in [RS] do not overlap. But in fact there is an invariant which does show that at least some Dehn-derived pairs of Heegaard splittings described above did not already occur in a different guise in [RS]. This invariant had not yet been introduced when [RS] was written and is called the (Hempel) distance of the Heegaard splitting [He]. We briefly review:\nDefinition 7.1. A Heegaard splitting H 1 ∪ S H 2 has Hempel distance at most n if there is a sequence c 0 , ..., c n of essential simple closed curves in the splitting surface S so that • for each i = 1, ..., n, c i ∩ c i−1 = ∅ • c 0 bounds a disk in H 1 • c n bounds a disk in H 2 If the splitting has distance ≤ n but not ≤ n − 1, then the distance d(S) = n.\nA Heegaard splitting of distance 0 is called reducible; one of distance ≤ 1 is called weakly reducible. Any Heegaard splitting of a reducible manifold is reducible. A Heegaard splitting of distance ≤ 2 is said to have the disjoint curve property [Th]; any Heegaard splitting of a toroidal 3-manifold has the disjoint curve property ( [He], [Th]). A weakly reducible genus 2 Heegaard splitting is also reducible, so an irreducible Heegaard splitting of genus 2 has distance at least 2 ( [Th]).\nIn the other direction we have:\nProposition 7.2. Suppose the manifold M has a Dehn-derived pair of Heegaard splittings. Then each of these Heegaard splittings has Hempel distance at most 3.\nProof. Suppose the splittings are Dehn-derived from a splitting M 0 = H a ∪ S H b via the disjoint pair of simple closed curves λ 1 , λ 2 ⊂ S. With no loss of generality, consider the splitting M = A ∪ S B obtained by pushing λ 1 into int(H a ) and λ 2 into int(H b ) before doing Dehn surgery on the λ i . Since λ 1 is primitive in H a there is a properly embedded essential disk D a ⊂ H a that is disjoint from λ 1 . (For example D a can be obtained from a meridian disk D 1 ⊂ H a that intersects λ 1 in a single point by band-summing together two copies of D 1 along a subarc of λ 1 − D 1 .) D a is then also disjoint from the curve α 1 ⊂ H a obtained by pushing λ 1 into int(H a ), so D a remains intact as a meridian of A after surgery on α 1 . Hence ∂D a and λ 1 are disjoint curves in ∂A.\nSymmetrically, there is a meridian D b ⊂ B so that ∂D b and λ 2 are disjoint curves in ∂B. Then the sequence ∂D a , λ 1 , λ 2 , ∂D b shows that the splitting A ∪ S B has distance at most 3. Proof. Following the comments above we can restrict attention to irreducible, atoroidal manifolds. We briefly run through the examples as they appear in [RS,Section 4]. Typically the description of an example H 1 ∪ S H 2 in [RS] consists of two parts: A collection of annuli A ⊂ S along which ∂H 1 and ∂H 2 are identified, followed by an arbitrary identification of ∂H 1 − A with ∂H 2 − A. From this point of view the simple closed curves ∂A ⊂ S that separate one sort of region from the other will be called the seams of the Heegaard splitting. We will observe that in [RS] some seam is always disjoint from an essential disk in H 1 and an essential disk in H 2 . This demonstrates that the splitting has the disjoint curve property and so has distance ≤ 2.\nTo be specific: In [RS,Subsection 4.1], [RS,Subsection 4.2, Variation 1] and [RS,Subsection 4.4, Variations 1 and 2], the meridians of the 1-handles e a and e b are disjoint from the seams. [RS,Subsection 4.2, Variation 2] is slightly more complicated. It is a bit like the construction in Section 3 above: Handlebodies A and B are identified along neighborhoods of all three curves λ i , i = 1, 2, 3, Dehn surgery is done to all three, with λ 1 , λ 2 pushed into A and λ 3 into B (then vice versa). But there is a meridian of A disjoint from λ 1 and λ 2 and a meridian of B disjoint from λ 1 and λ 3 , so a seam parallel to λ 1 demonstrates that the splitting of [RS,Subsection 4.2,Variation 2] has the disjoint curve property.\nThe manifolds in [RS,Subsection 4.3] and [RS,Subsection 4.4,Variations 3,4,and 7] are all toroidal, so they are of distance ≤ 2. What remains are [RS,Subsection 4.4,Variations 5 and 6] and we adopt the terminology there. In Variation 5, with, say, ρ a ⊂ A − , the seams that are the boundary of the 4-punctured sphere ∂A − ∩ ∂Γ are all disjoint from the meridian of the 1-handle e b ⊂ B and, in A − , any one of these seams together with ρ a lie in A − as two of the λ i 's of Section 3 above lie in H. In particular, there is a meridian of A − disjoint from both the seam and from ρ a . Thus that seam again illustrates that the splitting has the disjoint curve property.\nThe argument for Variation 6 is much the same. First note that if, in that Variation, Dehn surgeries are done on two curves parallel to σ, then the resulting manifold has a Seifert piece and so has distance ≤ 2. So the only change we need to consider from Variation 5 is Dehn surgery on a single curve parallel to σ. If that curve lies in B the argument for Variation 5 suffices; if it is in A − this merely forces us to pick a specific seam in the argument for Variation 5, a seam parallel to the new surgery curve.\nIn contrast, some of the examples constructed in this paper can be shown to have distance 3, so they cannot have appeared in any case considered in [RS]. See [Be2] (also [Sc]) for details."},{"title":"Definition 2 . 3 .","content":""},{"title":"Corollary 2 . 4 .","content":""},{"title":"Figure 1 .","content":""},{"title":"Proposition 7 . 3 .","content":""}],"string":"[\n {\n \"title\": \"Introduction\",\n \"content\": \"In 1998, Rubinstein and the second author [RS] studied the question of when there could be more than one distinct genus 2 Heegaard splitting of the same closed orientable 3-manifold. The goal of the project was modest: to provide a complete list of ways in which such multiple splittings could be constructed, but with no claim that each example on the list did in fact have multiple non-isotopic splittings (there could be isotopies from one splitting to another that are not apparent). Nor was there a claim that the list had no redundancies; a 3-manifold and its multiple splittings might appear more than once on the list. Such a list would still be useful, for if every example on the list could be shown to have a certain property, then that property would be true for any closed orientable 3-manifold M that has multiple genus 2 splittings. Two examples were given in [RS]:\\n• If M is atoroidal then the hyperelliptic involutions determined by the two genus 2 Heegaard splittings commute. • Any two genus 2 Heegaard splittings of M become isotopic after a single stabilization.\\nDespite this modest goal, the argument in [RS] contains a gap. In 2008, the first author discovered a class of examples that do not appear on the list and which, moreover, have mathematical properties that distinguish them in important ways from the examples that do Date: March 1, 2010. Second author partially supported by an NSF grant. appear in [RS]. It is true that, even for the new examples, the hyperelliptic involutions commute. But we know of no argument showing that the new examples all share the second property above; that is, we cannot show that the newly discovered multiple splittings necessarily become isotopic after a single stabilization (though they do after two stabilizations).\\nA third property, shared by all examples in [RS] but not by some of the new examples, is not listed above because the notion of Hempel distance of Heegaard splittings (see [He]) did not exist at the time [RS] was written. But a retrospective look (see Section 7 below) will verify that all the splittings described in [RS] have Hempel distance no greater than 2, whereas results of the first author [Be2] illustrate that at least some of the new examples have Hempel distance 3. (This also verifies that the gap in the argument in [RS] actually led to missed examples.)\\nThe present paper serves as an erratum to [RS] 1 and describes the new examples. Here is an outline: In Section 2 we describe a general method for constructing closed orientable 3-manifolds that appear to have multiple genus 2 Heegaard splittings; these examples (called Dehnderived) are based around Dehn surgery on a pair of strategically placed curves. It follows from the construction that always the hyperelliptic involutions of the alternate splittings coincide.\\nIt is not immediately obvious that curves supporting Dehn-derived examples can be found, but in Sections 3 and 4 we give three specific classes of examples. The classes are denoted M H (Section 3), M ×I and M hybrid (Section 4). (M H can be viewed as a third variation of [RS,Example 4.2].) For the examples M H and M hybrid a single stabilization suffices to make the alternate splittings equivalent, but this property is at least not apparent in most cases of M ×I .\\nSection 5 describes how the proof of [RS,Lemma 9.5, Case 2] went astray and how it needs to be altered to fix the gap. The upshot is that Dehn-derived examples, as described in Section 2, do fill the gap in the original proof. In Section 6 it is further shown, using new results in [Be], that any Dehn-derived example is in fact of type M H , M ×I or M hybrid . Finally, in Section 7 we verify that all of the old examples that are listed in [RS] are of Hempel distance 2, whereas at least some Dehn-derived examples are of distance 3. (It is easy to see that all Dehn-derived examples are of distance no more than 3.)\"\n },\n {\n \"title\": \"Dehn derived multiple splittings\",\n \"content\": \"A primitive k-tuple of curves in the boundary of a genus g handlebody H is a collection λ 1 , ...λ k ⊂ ∂H of k ≤ g disjoint simple closed curves so that, for some properly embedded collection D 1 , ..., D k of disks in H, |λ i ∩ D j | = δ ij , 1 ≤ i, j ≤ k. It is easy to see that the closed complement in H of such a collection of meridian disks is a genus g − k handlebody. In particular, if k = g then λ 1 , ...λ g is called a complete set of primitive curves and the corresponding collection of disks D 1 , ..., D g is called a complete set of meridian disks. The closed complement of a complete set of meridian disks in H is a 3-ball.\\nSuppose Λ = λ 1 , ...λ k ⊂ ∂H is a primitive k-tuple of curves in H and let α 1 , ..., α k be the properly embedded collection of curves in H obtained by pushing Λ slightly into the interior of H. We can view H as the boundary connect sum of a genus g − k handlebody H ′ and k solid tori W 1 , ..., W k , with λ i a longitude of W i and so α i a core curve of W i . Then Dehn surgery on α i ⊂ W i still gives a solid torus. Hence any Dehn surgery on the family of curves α 1 , ..., α k leaves H still a handlebody.\\nSuppose M 0 is a closed orientable 3-manifold and that M 0 = H a ∪ S H b is a genus 2 Heegaard splitting of M 0 . Suppose further that λ 1 , λ 2 ⊂ S are two disjoint doubly primitive curves in S.\\nProposition 2.2. Suppose M is a manifold obtained by some specified Dehn surgeries on λ 1 and λ 2 . For i = 1, 2, let A i (resp. B i ) be the manifold obtained from the handlebody H a (resp. H b ) by pushing the curve λ i into int(H a ) (resp int(H b )) and performing the specified Dehn surgery on the curve.\\nThen A 1 ∪ S B 2 and A 2 ∪ S B 1 are two (possibly different) genus 2 Heegaard splittings of M.\\nby Dehn surgery on a pushed in copy α i of a single primitive curve in S. It was just observed that this makes each A i (resp. B i ) a handlebody. Proof. Let M 0 = H a ∪ S H b be the Heegaard split 3-manifold from which the two splittings of M are Dehn derived, via λ 1 ∪ λ 2 ⊂ S. The hyperelliptic involution preserves the isotopy class (though perhaps reversing the orientation) of any simple closed curve in S. We may then position λ i so that the curves are preserved (reversing orientation) by the hyperelliptic involution on M 0 = H a ∪ S H b . Then the hyperelliptic involution on M 0 naturally induces a single hyperelliptic involution on M.\"\n },\n {\n \"title\": \"A simple set of examples\",\n \"content\": \"It is not immediately obvious how to create examples of a Dehnderived pair of splittings or, very naively, whether examples even exist. In this section we present and briefly discuss an important concrete class of examples.\\nConsider a genus 2 handlebody H, constructed from two 0-handles by connecting them with three 1-handles. With this structure H has a natural Z 3 symmetry, shown as 2π 3 rotation about the green axis in Figure 1. Let λ 1 ⊂ ∂H be the red curve shown in the figure and λ 2 , λ 3 be the other two simple closed curves to which λ 1 is carried by the Z 3 symmetry. Then each λ i is a primitive curve on ∂H and, indeed, any two of the curves, say λ 1 , λ 2 constitute a complete set of primitive curves (that is, a primitive pair). In this case the corresponding pair of meridian disks are the meridian disks of the two 1-handles through which λ 3 passes.\\nLet H be the genus 3 handlebody obtained by removing from H a neighborhood of the arc in which the axis of symmetry intersects one of the 0-handles. It is easy to see that in H the collection λ 1 , λ 2 , λ 3 ⊂ ∂H is a complete set of primitive curves, that is a primitive 3-tuple.\\nTo construct some Dehn-derived pairs of Heegaard splittings, begin with two genus 2 handlebodies A and B, on each of whose boundaries lie three disjoint simple closed curves corresponding to λ 1 , λ 2 , λ 3 ⊂ ∂H. Let λ ia ⊂ ∂A (resp λ ib ⊂ ∂B) be the curve corresponding to λ i in A (resp B), for each 1 ≤ i ≤ 3. Adopting (for comparison purposes) notation from [RS,Section 4.2], let α na , α sa , ρ a ⊂ A be the triple of curves obtained by pushing λ 1a , λ 2a , λ 3a into the interior of A and let α nb , α sb , ρ b ⊂ B be the triple of curves obtained by pushing λ 1b , λ 2b , λ 3b into the interior of B. Let N be a manifold constructed by identifying an annular neighborhood of λ 1a in ∂A with an annular neighborhood of λ 1b in ∂B and an annular neighborhood of λ 2a in ∂A with an annular neighborhood of λ 2b in ∂B. (After the identification, call the annuli A n and A s with core curves λ 1 , λ 2 respectively .) Then identify the two 4-punctured spheres ∂A − (A n ∪ A s ) and ∂B − (A n ∪ A s ) by any homeomorphism.\\nThis construction defines a genus 2 Heegaard structure on N, of course, but it also defines a genus 2 Heegaard splitting on M 0 , the manifold obtained from N by arbitrary Dehn surgery on just the two curves ρ a ⊂ A and ρ b ⊂ B, for surgery on these pushed-in primitive curves leaves A and B still handlebodies, handlebodies which we denote respectively H a and H b . What's more, the curves λ 1 , λ 2 are each primitive in both H a and H b (though they are not necessarily a primitive pair in either). Thus the Heegaard splitting M 0 = H a ∪ H b gives rise to two potentially different genus 2 Heegaard structures on any manifold M H that is obtained by simultaneously doing further Dehn surgery on the two curves λ 1 , λ 2 . That is, a manifold M H obtained by arbitrary Dehn surgery on all four curves λ 1 , λ 2 , ρ a , ρ b ⊂ N has two possibly distinct genus 2 Heegaard splittings, Dehn derived from the Heegaard splitting M 0 = H a ∪ H b . One Heegaard structure M H = A 1 ∪ B 2 is obtained by pushing λ 1 to α na ⊂ intA and λ 2 to α sb ⊂ intB before doing Dehn surgeries on the four curves; the other M H = A 2 ∪ B 1 is obtained by pushing λ 1 to α nb ⊂ intB and λ 2 to α sa ⊂ intA before doing the Dehn surgeries. In each case, exactly two of the four Dehn surgered curves lie in each handlebody A and B before the Dehn surgery, and in that handlebody are a pushed-in primitive pair.\\nProposition 3.1. The two Heegaard splittings A 1 ∪ B 2 and A 2 ∪ B 1 of M H become isotopic after at most a single stabilization.\\nProof. Let A and B be the genus 3 handlebodies derived from A and B respectively, just as H was derived from H. Here is a natural genus 3 Heegaard splitting of M H : in contrast to the construction above, push both λ 1 to α na and λ 2 to α sa , so both curves (as well as ρ a ) lie in A before doing the Dehn surgeries. Although A may no longer be a handlebody after the Dehn surgeries, it follows from the discussion above that the result on A of the surgery on the three curves\\nIt's fairly easy to see that this Heegaard splitting is a stabilization of A 1 ∪ B 2 (and so, symmetrically, A 2 ∪ B 1 ). Indeed, an alternate way to construct A ′ ∪ B ′ is to begin with A 1 ∪ B 2 and add to A 1 (and so subtract from B 2 ) a regular neighborhood of the curve α sb ⊂ int(B) and a straight arc from ∂B to α sb . From this point of view, the inclusion B ′ ⊂ B 2 defines a genus 3 Heegaard splitting of the genus 2 handlebody B 2 , and any such Heegaard splitting is necessarily stabilized (see [ST,Lemma 2.7]). The pair of stabilizing disks are also a pair of stabilizing disks for A ′ ∪ B ′\"\n },\n {\n \"title\": \"A second construction, and a hybrid\",\n \"content\": \"Here is another natural, but less naive, way to find disjoint pairs of primitive curves on the boundary of a genus 2-handlebody and so to create a Dehn-derived pair of Heegaard splittings. Let F denote a torus with the interior of a disk removed. Then F × I is a genus 2-handlebody. For γ any properly embedded essential simple closed curve in F , γ × {0} (or symmetrically γ × {1}) is a primitive curve in the handlebody F × I. Indeed, for δ a properly embedded arc in F intersecting γ once, δ × I is a meridian disk in F × I that intersects γ × {0} exactly once.\\nFollowing this observation, and the example of the previous section, here is a recipe for constructing candidate 3-manifolds. Begin with two copies A and B of the surface F and choose two essential (not necessarily disjoint) simple closed curves α 0 , α 1 ⊂ A and two essential (not necessarily disjoint) simple closed curves\\nIdentify an annular neighborhood of λ 0a in A×{0} with an annular neighborhood of λ 0b in B×{0} and call the core curve of the resulting annulus λ 0 . Similarly identify an annular neighborhood of λ 1a in A × {1} with an annular neighborhood of λ 1b in B × {1} and call the core curve of the resulting annulus λ 1 . Complete the identification of ∂(A × I) with ∂(B × I) along the remaining 4punctured sphere arbitrarily. Call the resulting closed 3-manifold M 0 , with Heegaard splitting M 0 = (A × I) ∪ (B × I).\\nThe 3-manifold M ×I obtained from M 0 by doing arbitrary Dehn surgeries to the simple closed curves λ 0 and λ 1 has a Dehn-derived pair of Heegaard splittings: one comes from first pushing λ 0 into A × I and λ 1 into B × I before the Dehn surgery, the other comes from first pushing λ 1 into A × I and λ 0 into B × I before the Dehn surgery.\\nRemarks on stabilization It is not apparent to us that a single stabilization will make the two Dehn-derived splittings of M ×I equivalent. The argument of Proposition 3.1 does not immediately carry over: if both curves λ 0a and λ 1a are pushed into A × I there is no apparent arc so that the complement A × I of a neighborhood of the arc in A × I is a genus 3 handlebody after an arbitrary Dehn surgery on the pushed in λ 0a and λ 1a . If there is a proper arc γ in A that intersects both curves α 0 ⊂ A and α 1 ⊂ A in a single point, then the complement A × I after pushing the interior of γ into A × I is a genus 3 handlebody, and so a single stabilization suffices, but having such an arc γ is not the general situation. (What is required for such an arc γ to exist is that the slopes of α 0 α 1 in A are a distance at most two apart in the Farey graph [Mi, Figure 1]. In that case γ has the slope that is incident to the slopes of both α 0 and α 1 in the Farey graph.)\\nOn the other hand, it is relatively easy to show that two stabilizations suffice to make the two splittings equivalent. To see this, push both λ 0 and λ 1 into A×I and connect them to respectively A×{0} and A×{1} by straight arcs. Then add a regular neighborhood of the arcs and of the pushed in curves λ 0 and λ 1 to B ×I to create a genus 4 handlebody B × I and simultaneously subtract the regular neighborhood from A×I to get the genus 4 handlebody A × I. The resulting genus 4 Heegaard splitting M 0 = A × I ∪ B × I becomes a Heegaard splitting H + a ∪ H + b of M ×I after the prescribed Dehn surgery on λ 0 and λ 1 . Using the argument of Proposition 3.1 it is easy to see that the Heegaard splitting H + a ∪ H + b destablizes to the genus 3 splitting obtained by instead pushing λ 0 into B × I and then adding to B × I a regular neighborhood of λ 1 ⊂ (A × I) and a straight arc attaching it to A × {1}. The argument of Proposition 3.1 applied again shows that this Heegaard splitting destabilizes to the genus 2 splitting in which λ 0 is pushed into B ×I and λ 1 into A×I, one of the Dehn-derived splittings. But this destabilization process is clearly symmetric: we could equally well have destabilized to the other genus 2 splitting, in which λ 0 is pushed into A×I and λ 1 into B ×I, and this is the other Dehn-derived splitting.\\nA further, call it a hybrid example of a Dehn-derived pair of splittings comes by combining the two constructions above: Identify annular neighborhoods of λ 1 , λ 2 ⊂ ∂H from Section 3 with annular neighborhoods of λ 0b , λ 1b ⊂ ∂(B × I) and identify the rest of ∂H with the rest of ∂(B × I) in any way. This gives a closed 3-manifold N with a Heegaard splitting H ∪ (B × I). Let M 0 be a 3-manifold obtained by doing an arbitrary Dehn surgery on λ 3 ⊂ ∂H, after pushing it into int(H). Then M 0 has the genus 2 Heegaard splitting (exploiting the notation used above) M 0 = H a ∪ (B × I). Let M hybrid be a closed 3-manifold obtained from M 0 by arbitrary Dehn surgeries on the two remaining curves λ 1 , λ 2 ⊂ ∂H a ⊂ M 0 . The Dehn-derived pair of Heegaard splittings for M hybrid is obtained by alternatively pushing λ 1 into H a and λ 2 into B × I or vice versa. A single stabilization suffices to make the two splittings equivalent, essentially by the same argument as for M H , in Proposition 3.1. [RS] The gap in [RS] arises because of a faulty sentence in the midst of a long and technical argument which would be difficult to summarize. We see no good alternative to simply jumping into that argument at a reasonable breaking point and inserting the argument we now believe to be complete. The jumping in point is on p. 533, in the midst of trying to prove that all cases of multiple genus 2 Heegaard splittings have been covered in the earlier examples listed in that paper. Here M is a closed hyperbolike 3-manifold with Heegaard splittings M = A ∪ P B = X ∪ Q Y . The two splitting surfaces P and Q have been made to coincide on sub-surfaces P 0 ⊂ P and Q 0 ⊂ Q. Then P − P 0 consists of annular components P X and P Y properly embedded in the handlebodies X and Y respectively, and Q − Q 0 consists of annular components Q A , Q B properly embedded in the handlebodies A, B respectively. With this as background, we now re-enter the proof of [RS,Theorem 9.4, Case 2] on page 533, at first echoing what is written there as the proof of Subcase A below. In filling the gap in the argument we also broaden the possible outcome, as expressed in Proposition 5.1:\"\n },\n {\n \"title\": \"Filling the gap in\",\n \"content\": \"Case 2: P X and P Y are both non-empty and the end of each curve in ∂P X ∪ ∂P Y is parallel to one of c 1 or c 2 .\\nProposition 5.1. In this case, either I) the splittings M = A ∪ P B = X ∪ Q Y are related as in [RS,Example 4.4] or II) the two splittings M = A ∪ P B = X ∪ Q Y are Dehn-derived from a single genus 2 Heegaard splitting of another manifold M 0 .\\nProof. If at least one annulus in each of P X or P Y is non-separating, then together they would give a non-separating, hence essential, torus in M. This contradicts our assumption that M is hyperbolike. So we may as well assume that each annulus in P Y is separating. Hence the ends of P Y are twisted in Y (see [RS,Definition 5.4]). No end of P Y can also be twisted in X, for the union along the curve of the solid tori (one in X, one in Y ) on which the curve is a torus knot would be a Seifert submanifold of M, contradicting the assumption that M is hyperbolike.\\nSubcase A: Some end of P Y is parallel to an end of P X . [The gap in [RS] was to view this as the only possibility.]\\nIn this case, by [RS,Lemma 5.6] all of P X is a collection of parallel non-separating longitudinal annuli in X. If P Y has ends at both c 1 and c 2 then neither curve can be twisted in X. In this case each annulus in P X is non-separating and so has ends that are non-parallel in Q. This implies that each annulus in P X has one end at c 1 and one at c 2 . Attach such an annulus in X to the tori in Y on which the c i are twisted. The boundary of the thickened result would exhibit a Seifert manifold in M, again contradicting the assumption that M is hyperbolike. We conclude that P Y has ends only at c 2 , say.\\nIf there were three or more annuli in P Y (hence six or more ends of ∂P Y at c 2 ) then there would be at least four ends of P X at c 2 . No annulus in P X could have both ends at c 2 (since c 2 is not twisted in X) so there would also be at least four ends of P X at c 1 . This would contradict [RS,Lemma 9.5]. So we conclude that P Y is made up of one or two annuli. If it's two annuli, necessarily separating and parallel in Y , then, again by [RS,Lemma 9.5] some annulus in P X has an end at c 2 . It cannot have both ends at c 2 and must be non-separating and longitudinal in X, since c 2 is not twisted in X. In this case the relation between P and Q can be seen as follows (See [RS,Figure 32]): In [RS,Example 4.4,Variation 2], let P be the splitting given there with Dehn surgery curve in µ a + and Q be the same splitting given there but with Dehn surgery curve in µ a − . To view these simultaneously as splittings of the same manifold M, of course, the Dehn surgery curve has to be moved from µ a + to µ a − , dragging some annuli along, until the splitting surfaces P and Q intersect as described.\\nSuppose then that P Y is a single annulus. It may have both ends on P 0 or it may have one end on P 0 and one end on an end of P X . (If both ends of P Y were also ends of P X then these, together with ends of P X at ∂P 0 parallel to c 2 would exhibit more than two annuli in P X , hence more than two ends of P X at c 1 , contradicting [RS,Lemma 9.5].) If P Y has one end on P 0 and one end on an end of P X , the initial splitting by Q is as in [RS,Example 4.4, Variation 1] (X = A − ∪ σ), with a Dehn surgery curve lying in µ b + , say. If the splitting is altered by first putting the Dehn surgery curve in µ a + (yielding the same manifold M), then altering as in [RS,Example 4.4] (i. e. considering A ∪ P B where B = B − ∪ σ) and then dragging the Dehn surgery curve from µ a + to µ b + , pushing before it an annulus from the 4-punctured sphere along which A − and B − are identified, we get the splitting surface P , intersecting Q as required. (See [RS,Figure 33].) This completes the proof that I) holds in Subcase A.\\nSubcase B: No end of P Y is parallel to an end of P X .\\nIn view of [RS,Lemma 9.5], in this subcase P Y and P X each consist of exactly one separating annulus, P Y twisted in Y with boundary curves parallel to c 2 (say) and P X twisted in X with boundary curves parallel to c 1 . This case is symmetric: the annulus in Q lying between the ends of P Y is Q A (say) and the annulus in Q lying between the ends of P X is exactly Q B . The annulus P Y cannot be parallel to the annulus Q A (else P 0 and Q 0 could be extended to include both) but rather the region between them is a solid torus W 2 = A ∩ Y on whose boundary the cores of the annuli are torus knots. Similarly B ∩ X is a solid torus W 1 on whose boundary the cores of the annuli Q B and P X are torus knots. The annulus P Y ∂-compresses in Y to become a separating disk; it follows that Y − W 2 = B ∩ Y is a genus 2 handlebody H BY on which the core a 2 of the annulus P Y is primitive. Symmetrically, the curve c 1 (viewed as the core of the annulus Q B ) is primitive in H BY , the curve c 2 is primitive in the genus 2 handlebody H AX = X − W 1 = X ∩ A, as is the core curve a 1 of P X .\\nHere is another way to describe the manifold M above: begin with the two genus 2 handlebodies H AX (which contains disjoint primitive simple closed curves a 1 , c 2 on its boundary) and H BY (which contains disjoint primitive simple closed curves a 2 , c 1 on its boundary). Construct a closed 3-manifold M 0 by identifying ∂H AX to ∂H BY by a homeomorphism that identifies a i with c i , i = 1, 2. Call the resulting curves α 1 , α 2 . Now recover M from M 0 by removing a tubular neighborhood of each α i and replacing with the solid torus W i ; equivalently, do an appropriate surgery on each α i in M 0 . The two Heegaard splittings of M are then seen as follows: if α 1 is pushed into H AX and α 2 into H BY before the surgery on the curves, then the resulting Heegaard splitting is M = X ∪ Q Y ; if α 1 is pushed into H BY and α 2 into H AX before the surgery then the resulting splitting is M = A ∪ P B. That is, the splittings of M are both Dehn-derived from the Heegaard splitting M 0 = H AX ∪ H BY . Thus II) holds in Subcase B.\"\n },\n {\n \"title\": \"A taxonomy of Dehn-derived splittings\",\n \"content\": \"Sections 3 and 4 give concrete examples of pairs of Dehn-derived fillings. In this section we show that these examples in fact constitute all pairs of Dehn-derived splittings. The argument exploits Berge's classification of pairs of primitive curves on genus 2 handlebodies [Be], though the classification here is slightly different.\\nLet H be a genus 2 handlebody, with λ 1 , λ 2 , λ 3 ⊂ ∂H the disjoint simple closed curves described in Section 3. Denote by ρ the curve in the interior of H obtained by pushing λ 3 into H and let H surg denote the handlebody obtained from H by a specified Dehn surgery on ρ ⊂ int(H). As in Section 4, let F denote a torus with the interior of a disk removed.\\nProposition 6.1 (Berge). Suppose α and β are disjoint non-parallel primitive curves on the boundary of a genus 2 handlebody H. Then either A) there is a Dehn surgery on ρ ⊂ H and a homeomorphism h :\\nProof. This classification is a variant of that described in [Be]. The Type II pair there, as well as some pairs of Type I, are exactly as described in alternative B). The interest is in the third example of a Type I pair, in [Be,Lemma 3.8 (3) via Figure 3]. In that example, H is viewed as divided into two solid tori by a separating disk D; let λ a and λ b be longitudes of the two solid tori into which D divides H. Then β is parallel to λ b , and α is the band sum, via a band that crosses D once, of λ b with a torus knot on the solid torus containing λ a . This picture is equivalent to letting α be the band sum λ a #λ b (through D) of λ b with λ a , and then performing a Dehn surgery on a disjoint copy of λ a that has been pushed into H, to become a core of the solid torus on which λ a lies. Now translate: relabel λ b ⊂ ∂H as λ 2 and λ a ⊂ ∂H as λ 3 . Then λ a #λ b corresponds to λ 1 . The construction just described is then to push λ 3 into the interior of H and perform some surgery to get H surg . Afterwards α corresponds to λ 1 ⊂ ∂H surg and β corresponds to λ 2 ⊂ ∂H surg . This is exactly alternative A).\\nFollowing Propositions 5.1 and 6.1 there is a fairly clear description of the cases of multiple Heegaard splittings that are missing from [RS]. According to Proposition 5.1 the only missing cases are pairs of splittings that are Dehn-derived from an initial splitting H AX ∪ H BY of a manifold M 0 . First determine which of alternatives A) and B) apply to the pairs of surgery curves as they lie on the boundaries of the respective handlebodies: {a 1 , c 2 } ⊂ H AX or {a 2 , c 1 } ⊂ H BY . If both are of type A) then the pair of splittings is Dehn-derived as in the construction of M H in Section 3. If both are of type B) then the pair of splittings is Dehn-derived as in the construction of M ×I in Section 4. If one is of type A) and one of type B) then the pair of splittings is Dehn-derived as in the construction of M hybrid in Section 4.\\nIt is worth mentioning that there is another view of a pair of primitive curves lying on a handlebody as in A) of Proposition 6.1, a view that more closely resembles that in B): Let α, β, γ be simple closed curves in F so that each pair of curves intersects in exactly one point. (For example, choose curves in F of slopes 0, 1, ∞.) Then it is fairly easy to see that the three curves α × {0}, β × {1}, γ × { 1 2 } lie in the handlebody F × I just as λ 1 , λ 2 , ρ lie in H in the description preceding Proposition 6.1. So the primitive curves in description A) can be made to look like a special case of those in description B), but with the cost that an extra Dehn surgery has to be performed on a specific curve in the interior of F × I. This is the twisted product view of [Be,3.2].\"\n },\n {\n \"title\": \"Distance\",\n \"content\": \"It would seem possible that the Dehn-derived pairs of Heegaard splittings exhibited above could coincidentally all be contained among the examples already listed in [RS], for there is no claim that the types of examples of multiple Heegaard splittings we have offered here and in [RS] do not overlap. But in fact there is an invariant which does show that at least some Dehn-derived pairs of Heegaard splittings described above did not already occur in a different guise in [RS]. This invariant had not yet been introduced when [RS] was written and is called the (Hempel) distance of the Heegaard splitting [He]. We briefly review:\\nDefinition 7.1. A Heegaard splitting H 1 ∪ S H 2 has Hempel distance at most n if there is a sequence c 0 , ..., c n of essential simple closed curves in the splitting surface S so that • for each i = 1, ..., n, c i ∩ c i−1 = ∅ • c 0 bounds a disk in H 1 • c n bounds a disk in H 2 If the splitting has distance ≤ n but not ≤ n − 1, then the distance d(S) = n.\\nA Heegaard splitting of distance 0 is called reducible; one of distance ≤ 1 is called weakly reducible. Any Heegaard splitting of a reducible manifold is reducible. A Heegaard splitting of distance ≤ 2 is said to have the disjoint curve property [Th]; any Heegaard splitting of a toroidal 3-manifold has the disjoint curve property ( [He], [Th]). A weakly reducible genus 2 Heegaard splitting is also reducible, so an irreducible Heegaard splitting of genus 2 has distance at least 2 ( [Th]).\\nIn the other direction we have:\\nProposition 7.2. Suppose the manifold M has a Dehn-derived pair of Heegaard splittings. Then each of these Heegaard splittings has Hempel distance at most 3.\\nProof. Suppose the splittings are Dehn-derived from a splitting M 0 = H a ∪ S H b via the disjoint pair of simple closed curves λ 1 , λ 2 ⊂ S. With no loss of generality, consider the splitting M = A ∪ S B obtained by pushing λ 1 into int(H a ) and λ 2 into int(H b ) before doing Dehn surgery on the λ i . Since λ 1 is primitive in H a there is a properly embedded essential disk D a ⊂ H a that is disjoint from λ 1 . (For example D a can be obtained from a meridian disk D 1 ⊂ H a that intersects λ 1 in a single point by band-summing together two copies of D 1 along a subarc of λ 1 − D 1 .) D a is then also disjoint from the curve α 1 ⊂ H a obtained by pushing λ 1 into int(H a ), so D a remains intact as a meridian of A after surgery on α 1 . Hence ∂D a and λ 1 are disjoint curves in ∂A.\\nSymmetrically, there is a meridian D b ⊂ B so that ∂D b and λ 2 are disjoint curves in ∂B. Then the sequence ∂D a , λ 1 , λ 2 , ∂D b shows that the splitting A ∪ S B has distance at most 3. Proof. Following the comments above we can restrict attention to irreducible, atoroidal manifolds. We briefly run through the examples as they appear in [RS,Section 4]. Typically the description of an example H 1 ∪ S H 2 in [RS] consists of two parts: A collection of annuli A ⊂ S along which ∂H 1 and ∂H 2 are identified, followed by an arbitrary identification of ∂H 1 − A with ∂H 2 − A. From this point of view the simple closed curves ∂A ⊂ S that separate one sort of region from the other will be called the seams of the Heegaard splitting. We will observe that in [RS] some seam is always disjoint from an essential disk in H 1 and an essential disk in H 2 . This demonstrates that the splitting has the disjoint curve property and so has distance ≤ 2.\\nTo be specific: In [RS,Subsection 4.1], [RS,Subsection 4.2, Variation 1] and [RS,Subsection 4.4, Variations 1 and 2], the meridians of the 1-handles e a and e b are disjoint from the seams. [RS,Subsection 4.2, Variation 2] is slightly more complicated. It is a bit like the construction in Section 3 above: Handlebodies A and B are identified along neighborhoods of all three curves λ i , i = 1, 2, 3, Dehn surgery is done to all three, with λ 1 , λ 2 pushed into A and λ 3 into B (then vice versa). But there is a meridian of A disjoint from λ 1 and λ 2 and a meridian of B disjoint from λ 1 and λ 3 , so a seam parallel to λ 1 demonstrates that the splitting of [RS,Subsection 4.2,Variation 2] has the disjoint curve property.\\nThe manifolds in [RS,Subsection 4.3] and [RS,Subsection 4.4,Variations 3,4,and 7] are all toroidal, so they are of distance ≤ 2. What remains are [RS,Subsection 4.4,Variations 5 and 6] and we adopt the terminology there. In Variation 5, with, say, ρ a ⊂ A − , the seams that are the boundary of the 4-punctured sphere ∂A − ∩ ∂Γ are all disjoint from the meridian of the 1-handle e b ⊂ B and, in A − , any one of these seams together with ρ a lie in A − as two of the λ i 's of Section 3 above lie in H. In particular, there is a meridian of A − disjoint from both the seam and from ρ a . Thus that seam again illustrates that the splitting has the disjoint curve property.\\nThe argument for Variation 6 is much the same. First note that if, in that Variation, Dehn surgeries are done on two curves parallel to σ, then the resulting manifold has a Seifert piece and so has distance ≤ 2. So the only change we need to consider from Variation 5 is Dehn surgery on a single curve parallel to σ. If that curve lies in B the argument for Variation 5 suffices; if it is in A − this merely forces us to pick a specific seam in the argument for Variation 5, a seam parallel to the new surgery curve.\\nIn contrast, some of the examples constructed in this paper can be shown to have distance 3, so they cannot have appeared in any case considered in [RS]. See [Be2] (also [Sc]) for details.\"\n },\n {\n \"title\": \"Definition 2 . 3 .\",\n \"content\": \"\"\n },\n {\n \"title\": \"Corollary 2 . 4 .\",\n \"content\": \"\"\n },\n {\n \"title\": \"Figure 1 .\",\n \"content\": \"\"\n },\n {\n \"title\": \"Proposition 7 . 3 .\",\n \"content\": \"\"\n }\n]","isConversational":false},"figures":{"kind":"list like","value":[{"id":"","caption":"Two genus 2 Heegaard splittings X ∪ Q Y and A ∪ P B of a closed 3-manifold M are called Dehn derived (from the splitting M 0 = H a ∪ S H b via λ 1 ∪ λ 2 ⊂ S) if the two splittings are created as in Proposition 2.2.","content":"Definition 2 . 3 .\n23Two genus 2 Heegaard splittings X ∪ Q Y and A ∪ P B of a closed 3-manifold M are called Dehn derived (from the splitting M 0 = H a ∪ S H b via λ 1 ∪ λ 2 ⊂ S) if the two splittings are created as in Proposition 2.2."},{"id":"","caption":"Suppose M = A ∪ P B = X ∪ Q Y are a Dehn-derived pair of Heegaard splittings. Then the two hyperelliptic involutions of M, one determined by the Heegaard splitting A ∪ P B and the other by the Heegaard splitting X ∪ Q Y , coincide.","content":"Corollary 2 . 4 .\n24Suppose M = A ∪ P B = X ∪ Q Y are a Dehn-derived pair of Heegaard splittings. Then the two hyperelliptic involutions of M, one determined by the Heegaard splitting A ∪ P B and the other by the Heegaard splitting X ∪ Q Y , coincide."},{"id":"","caption":"Figure 1.","content":"Figure 1 .\n1Figure 1."},{"id":"","caption":"All examples of multiple Heegaard splittings appearing in[RS, Section 4] have Hempel distance ≤ 2.","content":"Proposition 7 . 3 .\n73All examples of multiple Heegaard splittings appearing in[RS, Section 4] have Hempel distance ≤ 2."}],"string":"[\n {\n \"id\": \"\",\n \"caption\": \"Two genus 2 Heegaard splittings X ∪ Q Y and A ∪ P B of a closed 3-manifold M are called Dehn derived (from the splitting M 0 = H a ∪ S H b via λ 1 ∪ λ 2 ⊂ S) if the two splittings are created as in Proposition 2.2.\",\n \"content\": \"Definition 2 . 3 .\\n23Two genus 2 Heegaard splittings X ∪ Q Y and A ∪ P B of a closed 3-manifold M are called Dehn derived (from the splitting M 0 = H a ∪ S H b via λ 1 ∪ λ 2 ⊂ S) if the two splittings are created as in Proposition 2.2.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"Suppose M = A ∪ P B = X ∪ Q Y are a Dehn-derived pair of Heegaard splittings. Then the two hyperelliptic involutions of M, one determined by the Heegaard splitting A ∪ P B and the other by the Heegaard splitting X ∪ Q Y , coincide.\",\n \"content\": \"Corollary 2 . 4 .\\n24Suppose M = A ∪ P B = X ∪ Q Y are a Dehn-derived pair of Heegaard splittings. Then the two hyperelliptic involutions of M, one determined by the Heegaard splitting A ∪ P B and the other by the Heegaard splitting X ∪ Q Y , coincide.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"Figure 1.\",\n \"content\": \"Figure 1 .\\n1Figure 1.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"All examples of multiple Heegaard splittings appearing in[RS, Section 4] have Hempel distance ≤ 2.\",\n \"content\": \"Proposition 7 . 3 .\\n73All examples of multiple Heegaard splittings appearing in[RS, Section 4] have Hempel distance ≤ 2.\"\n }\n]","isConversational":false},"references":{"kind":"list like","value":[{"text":"A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody. J Berge, arXiv:0910.3038J. Berge, A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody, arXiv:0910.3038.","doi":"arXiv:0910.3038"},{"text":"A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings. J Berge, to appearJ. Berge, A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings, to appear.","doi":""},{"text":"3-manifolds as viewed from the curve complex. J Hempel, Topology. 40J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (2001) 631-657.","doi":""},{"text":"The classification of punctured-torus groups. Y Minsky, Annals of Math. 149Y. Minsky, The classification of punctured-torus groups, Annals of Math 149 (1999) 559-626.","doi":""},{"text":"Genus two Heegaard splittings of orientable 3-manifolds. H Rubinstein, M Scharlemann, Proceedings of the 1998 Kirbyfest, Geometry and Topology Monographs. the 1998 Kirbyfest, Geometry and Topology Monographs2H. Rubinstein and M. Scharlemann, Genus two Heegaard splittings of ori- entable 3-manifolds, in Proceedings of the 1998 Kirbyfest, Geometry and Topol- ogy Monographs 2 (1999) 489-553.","doi":""},{"text":"Berge's distance 3 pairs of genus 2 Heegaard splittings. M Scharlemann, ArXiv preprint 1002.4887M. Scharlemann, Berge's distance 3 pairs of genus 2 Heegaard splittings, ArXiv preprint 1002.4887","doi":"ArXiv preprint 1002.4887"},{"text":"Heegaard splittings of (surface) x I are standard. M Scharlemann, A Thompson, Math. Ann. 295M. Scharlemann, A. Thompson, Heegaard splittings of (surface) x I are stan- dard, Math. Ann. 295 (1993) 549-564.","doi":""},{"text":"The disjoint curve property and genus 2 manifolds. A Thompson, Topology Appl. 97A. Thompson, The disjoint curve property and genus 2 manifolds, Topology Appl. 97 (1999) 273-279.","doi":""}],"string":"[\n {\n \"text\": \"A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody. J Berge, arXiv:0910.3038J. Berge, A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody, arXiv:0910.3038.\",\n \"doi\": \"arXiv:0910.3038\"\n },\n {\n \"text\": \"A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings. J Berge, to appearJ. Berge, A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings, to appear.\",\n \"doi\": \"\"\n },\n {\n \"text\": \"3-manifolds as viewed from the curve complex. J Hempel, Topology. 40J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (2001) 631-657.\",\n \"doi\": \"\"\n },\n {\n \"text\": \"The classification of punctured-torus groups. Y Minsky, Annals of Math. 149Y. Minsky, The classification of punctured-torus groups, Annals of Math 149 (1999) 559-626.\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Genus two Heegaard splittings of orientable 3-manifolds. H Rubinstein, M Scharlemann, Proceedings of the 1998 Kirbyfest, Geometry and Topology Monographs. the 1998 Kirbyfest, Geometry and Topology Monographs2H. Rubinstein and M. Scharlemann, Genus two Heegaard splittings of ori- entable 3-manifolds, in Proceedings of the 1998 Kirbyfest, Geometry and Topol- ogy Monographs 2 (1999) 489-553.\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Berge's distance 3 pairs of genus 2 Heegaard splittings. M Scharlemann, ArXiv preprint 1002.4887M. Scharlemann, Berge's distance 3 pairs of genus 2 Heegaard splittings, ArXiv preprint 1002.4887\",\n \"doi\": \"ArXiv preprint 1002.4887\"\n },\n {\n \"text\": \"Heegaard splittings of (surface) x I are standard. M Scharlemann, A Thompson, Math. Ann. 295M. Scharlemann, A. Thompson, Heegaard splittings of (surface) x I are stan- dard, Math. Ann. 295 (1993) 549-564.\",\n \"doi\": \"\"\n },\n {\n \"text\": \"The disjoint curve property and genus 2 manifolds. A Thompson, Topology Appl. 97A. Thompson, The disjoint curve property and genus 2 manifolds, Topology Appl. 97 (1999) 273-279.\",\n \"doi\": \"\"\n }\n]","isConversational":false}}},{"rowIdx":298,"cells":{"text":{"kind":"string","value":"\nDNA LOSSLESS DIFFERENTIAL COMPRESSION ALGORITHM BASED ON SIMILARITY OF GENOMIC SEQUENCE DATABASE\n\n\nHeba Afify hebaaffify@yahoo.com \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt\n\nMuhammad Islam \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt\n\nManal Abdel Wahed \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt\n\nDNA LOSSLESS DIFFERENTIAL COMPRESSION ALGORITHM BASED ON SIMILARITY OF GENOMIC SEQUENCE DATABASE\n2E2F727440755CDCC66E61EA585ACD0010.5121/ijcsit.2011.3412Data compressionGenomic sequencesDifferential compression algorithm\nModern biological science produces vast amounts of genomic sequence data.This is fuelling the need for efficient algorithms for sequence compression and analysis.Data compression and the associated techniques coming from information theory are often perceived as being of interest for data communication and storage.In recent years, a substantial effort has been made for the application of textual data compression techniques to various computational biology tasks, ranging from storage and indexing of large datasets to comparison of genomic databases.This paper presents a differential compression algorithm that is based on production of difference sequences according to op-code table in order to optimize the compression of homologous sequences in dataset.Therefore, the stored data are composed of reference sequence, the set of differences, and differences locations, instead of storing each sequence individually.This algorithm does not require a priori knowledge about the statistics of the sequence set.The algorithm was applied to three different datasets of genomic sequences, it achieved up to 195-fold compression rate corresponding to 99.4% space saving.\n\nINTRODUCTION\n\nThe compression of genomic sequences remains a challenging problem, with profound implications in biology and with important technological impact when the use of genomic data will become a daily practice in health and medicine.As such, it will certainly be investigated further due to several reasons: benefits when storing or transmitting the genome files; possibilities for comparison of entire genomes by similarity metrics approximating Kolmogorov similarity [1,2]; and discovering statistically significant relationships among various sequences.\n\nData compression and the related information-theoretic techniques find a wide use for investigation in computational biology.Such a pervasive use has grounds in some outstanding notions that deeply characterizes data compression, in particular universality and quantification of statistical dependence via information measures.These notions give rise to methods that need very few assumptions on the data models and, as a consequence, very minor parameter estimations for their application.This seems to be a major advantage for computational biology applications, where the statistical modeling of the data is a highly non-trivial task.In addition, the low-computational demand of these methods allows them to scale well with dataset size, even on a genomic scale.Obviously, data structure, data modeling and speed are the main advantages for the use of data compression in biological investigations [3].\n\nThe amount of DNA being extracted from organisms and sequenced is increasing exponentially [4].This yields two problems: storage and comprehension.Despite the prevalence of broadband network connections, there still exists a need for compact representation of data to speed up transmission.Transferring a single sequence that is millions of characters long may take ten to fifteen minutes over a dial-up connection.Compression of genomic sequences can decrease the storage requirements, and increase the transmission speed.\n\nUnderstanding genomic sequences has wide applications, from the synthesis of medicines to genetic screening and engineering.The knowledge of the structure of a sequence is important for its comprehension.If a set of sequences have a common structural property that is shared by another sequence, it is possible that they are related in some way, or that the knowledge that applies to one may also be useful for the other.Compression can help to show both the structure of a sequence and how it is related to other sequences.\n\nDNA is composed of four bases (A, T, G, C), and can be coded using two bits per base.According to functionality, DNA manifests different properties from other kinds of data.Standard compression algorithms for text or image files exploit small repeated patterns and contextual similarities to achieve compression.However, repeated patterns in DNA sequences are typically much longer and less frequent, so standard compression algorithms perform poorly on DNA.The most popular general-purpose encoders of today, such as gzip [5], which is based on the Lempel-Ziv algorithm [6], and bzip2, based on the Burrows-Wheeler Transform [7], which usually produces more than two bits per base to achieve the un-encoded representation [8].Hence, the quest for efficient DNA compression programs started to become popular in the competition-driven community of data compression enthusiasts.DNA sequences are compressible, so they are not random.But they are not highly compressible.It is therefore necessary for coding methods to be as efficient as possible.In the context of compression, missing structure will lead to inefficient compression.\n\nIn the last two decades, compression of genomic sequences can be divided into two categories: Specific compression algorithms developed for efficiently compressing sequence data for the sake of reduced resource consumption (disk space or network usage) [8][9][10][11][12][13]; and investigations of the usefulness of compressibility as a measure of information content, for the purpose of making inferences about sequences (such as the relatedness of two sequences) [1,14].Specific compression algorithms have been proposed for DNA compression by using particular characteristics such as exact or approximate repeats measures within a single DNA sequence that are based on relations between subsequences only.Compression gains afforded by these algorithms are ultimately not sufficient to justify their adoption for large databases.While much research has been done on compressing individual DNA sequences, surprisingly little has focused on the compression of entire databases [3].The results of compressing genomic sequences can be applied to the problem of evolution derivation [15].Compression-based distance measures (CBMs) that depend on probabilities of mismatching locations [16], are not distinct enough among different classes.However, researches have been suffering from the poor modeling to characterize the relationship between sequences.\n\nAlgorithms for Compressing DNA sequences, such as GenCompress [11] ,Biocompress [10] and Cfact [17] were available to compress DNA sequences.Their compression rate was about 1.74 bits per base i.e., 78% in compression rate.Hence, a compression algorithm named \"GenBit Compress Tool\" [18] is presented, whose compression rate was below 1.2 bits per byte (for Best case) , 1.727 bits/bytes (for Average Case), 2.238 bits/bytes (Worst case ) even for larger genome (nearly 2,00,000 characters).Recently, P. Raja Rajeswari, and A. Apparao [19] presented a new compression algorithm named \"DNABIT Compress\" whose compression rate was below 1.56 bits per base (for Best case) even for larger genome.DNABIT Compress algorithm was the best among the remaining compression algorithms and significantly improves the running time of all previous DNA compression programs.\n\nResearchers have worked in entropy estimation for genomic sequences, either by computing frequency of n-mers for long enough inputs, called Shannon entropy [20], or by adopting compression methods to obtain an upper bound on entropy [8].Loewenstern [21,22] introduced a compression method CDNA by considering inexact match in finding patterns.Importantly, Lanctot and Yang [23] improved the compression further by exploiting the reverse complement property of DNA sequences.Also, this latter method produces a good estimation of entropy, e.g., the estimate approaches the actual entropy for long enough input.Badger and Chen [1] proposed a distance function with nice properties for cluster related sequences.\n\nInterestingly, difference compression schemes targets the efficient compression of entire databases of sequences.DNAzip [24] was first algorithm introducing the important idea of only storing differences to a reference sequence, but in this case for storing an entire, assembled genome as a series of difference.This algorithm [24] did not consider the process of generating the variations, which can be a challenging problem in itself, but assume that the variation data have been provided.Difference compression schemes, which compress entire sets of homologous sequences by encoding only the differences between a genomic sequences and a reference sequence, are also suggested in [25].Brandon et al [25] found that selecting the reference sequence is important for having an effective compression of dataset.With only a partial level of optimization, 3615 genome sequences occupying 56MB in GenBank are compressed down to only 167 KB, achieving a 345-fold compression rate, using the revised Cambridge Reference Sequence as the reference sequence.Using the consensus sequence as the reference sequence, the data can be stored using only 133 KB, corresponding to a 433-fold level of compression, roughly a 23% improvement.On the other hand, C. Wang [26] implemented a generic tool, GRS, for de novo compression of genome resequencing data which does not need the reference SNPs map.When its performance was tested on the first Korean personal genome sequence dataset, GRS was able to achieve 159-fold compression, reducing the size of the data from 2986.8 to 18.8 MB.While being tested against the sequencing data from rice and Arabidopsis thaliana, GRS compressed the 361.0 MB rice genome data to 4.4 MB, and the A. thaliana genome data from 115.1MB to 6.5 KB.DNAEncodeWG [27] also presented how to compress DNA sequence data using the whole genome sequence of an organism to identify differences between DNA sequences if a repository of the whole genome sequence of the organism is accessible through the Web.It encoded the sequences 10-fold better than the other standard algorithms.Kozanitis [28] focused on fragment compression as opposed to sequence compression by using SLIMGENE.H. Afify [29] presented another algorithm in which for each pair of similar sequences, a third sequence can be generated; representing the difference between them, and the entropy of the generated difference sequence can be estimated.Difference sequence can help in building phylogenic tree, while the entropy can help in selecting appropriate compression reference for short dataset.\n\nFor difference compression scheme to be appropriate, it should be suitable for the way the set is being used.When an entire set is archived or transmitted, the concern will be focused on the compression rate.In this situation, a reference sequence is stored, and the next sequence is generated from this reference and the appropriate difference sequence.Newly generated sequences may be used as references for subsequent sequences.When the set is being actively used, in addition to the compression rate, the speed of decompression is of comparable importance, where any sequence may be repeatedly fetched at any moment.To speed up sequence decompression, it is preferable to have a single reference for the whole set.\n\nIn this study, we describe another solution to the compression of genomic sequence dataset which compresses the dataset based on comparing it with a reference sequence.We focus our study on large sets of sequences that belong to the same class.If two genomes are, e.g., more than 99% identical, it is much more efficient to store one genome as a variation from the other; in which case, only that 1% representing the variation needs to be stored.A differentially compressed set is a set where a single reference sequence is stored, along with information about the difference between this sequence and the rest of the set.To evaluate the suggested selection method, the compression of the differences, compression of difference locations and the size of the compressed set are examined, as is explained in the next section.\n\n\nMATERIAL AND METHOD\n\n\nData Extraction\n\nThe data used in our work consists of three different datasets of genomic sequences including 3615 human mitochondrial genomic sequences, 500 human virus sequences H1N1, and 100 mouse sequences Mus Musculus Dmesticus.\n\nMitochondrial dataset takes 56MB size in GenBank, and is downloadable from the GenBank database, HapMap web site and the MITOMAO database [30].Among the sequences, 2671 correspond to complete genome, while the remaining 944 correspond only to the coding region sequence, which is about 1100bp shorter than the full genome sequence.Virus dataset takes 601KB size in GenBank, and is downloaded from Influenza Research Database [31].Mouse datasets takes 106KB in GenBank, and is downloaded from Mouse Genome Database (MGD) [32].References were selected as follows: Cambridge sequence NC_012920 sequence for human mitochondrial dataset, HM17663 for virus dataset, and AJ843867 for mouse dataset.\n\n\nOperation Code Generation\n\nThe DNA is constructed of a double helix held together by hydrogen bonds.Each strand of the helix is a biomolecule consisting of many linked components called nucleotides.Each nucleotide is one of four possible types: adenine (A), cytosine (C), guanine (G) and thymine (T).The two strands of the helix are exact complement of each other.Each nucleotide of one strand matches to its complement on the other strand, where A pairs with T and G pairs with C, DNA strands that are complementary to themselves are called self-complementary or palindromes.\n\nTo generate an operation code of differences between a target sequence and its reference, the base at every location of the target is compared with the corresponding bases at the reference.A difference between the two bases can be due to one of three modifications to the target: a base insertion, a base deletion, or a replacement.Table 1 summarizes the operation codes.Table 1.Operation code generation.\n\n\nCorresponding Bases\n\nOperation Op-codes The same Similarity\n\"0\" A T G C Replacement \"1\" A G C T \"2\" A C G T \"3\"\nA or T or G or C '-' Deletion \"4\" '-' G Insertion \"5\" '-' A \"6\" '-' C \"7\" '-' T \"8\"\n\n\nDifferential Compression Algorithm\n\nThe proposed differential compression algorithm consists of three main steps: Alignment, Differences recording and differences compression.\n\n\nAlignment\n\nWe start by aligning each sequence in the dataset with the reference sequence using local Sequence Alignment.The sole purpose of sequence alignments is to place homologous positions of homologous sequences into the same column by inserting gapes.Gaps reflect the occurrence of insertions/deletions or other rearrangements during the process.Also, the alignment of similar sequences can help in discovering patterns and relationships between sequences, consequently improve their compression ratio [33].\n\n\nDifferences Recording\n\nIn this step, differences and differences locations vectors are recorded.Difference vector is achieved by storing only the op-code of the different bases between the aligned reference sequence and the aligned genomic sequence; these will be according to Table 2 ranging from 1 to 8. Difference locations with respect to the unaligned reference sequence are recorded.It is to be noted out that an insertion in the aligned reference sequence will not change the recorded unaligned reference sequence base location, while any other operation in the aligned genomic sequence will increment to the next recorded unaligned reference sequence base location.\n\n\nDifference Compression\n\nThe proposed compression algorithm can be divided into two phases, the differences are coded, and the codes are compressed in the first phase, while their locations are compressed in the second.To improve the compression of differences locations, the distance between successive locations are stored.\n\nTo compare the results obtained after the compression of both differences codes and locations, we used compression ratio which is the ratio between the compressed size and the uncompressed size, and space saving which is defined as the reduction in size relative to the uncompressed size (1-compression ratio) [34], as measures for the compression process.Figure 1 shows the architecture of the proposed differential compression algorithm.\n\nTable 2. Op-codes of differences.\n\n\nAligned Reference Sequence Bases\nG A C T - Aligned Genomic Sequence Bases G 0 2 1 3 5 A 2 0 3 1 6 C 1 3 0 2 7 T 3 1 2 0 8 - 4 4 4 4 0\n\nRESULTS AND DISCUSSION\n\nWe have tested the proposed differential compression algorithm on the three genomic sequences datasets.Difference codes were compressed using two lossless compression algorithms namely, Huffman [35] and ZLIB Deflator algorithm [36].Table 3 shows the generated Huffman codes.Table 4 shows the size of the compressed difference codes.It also shows that ZLIB Deflator algorithm achieved better compression ratio than Huffman algorithm in human data, while Huffman algorithm achieved slightly better compression ratio in virus and mouse data.\n\nDifference locations are compressed using ZLIB Deflator algorithm.Table 5 summarizes the compression ratio and space saving of our algorithm on the three datasets.The results confirm that mitochondria dataset that occupies 56MB size in GenBank can be stored using only 294.3KB, corresponding to 195-fold compression rate.While virus dataset that occupies 601KB size in GenBank can be stored using only 212.9KB, corresponding to 3-fold level of compression.Mouse datasets that occupies 106KB size in GenBank can be stored using only 9.6KB, corresponding to 11-fold level of compression.It should be noted that compression of mitochondria dataset is better than virus and mouse database because it has high similarity between genomic sequences.The most popular algorithms, including specific compression algorithms: DNACompress [12], XM [13], and difference compression scheme: DNAEncodeWG [27], are not suitable for compression of entire databases.We believe that DNAEncodeWG is superior for a single sequence.It should be mentioned that Brandon et al. algorithm [25], was done by using extra reference sequence and based on statistics of the sequence set that are not valid for other sets.\n\nThe compression result of our algorithm is better than C. Wang [26] that achieved 159-fold compression on Korean personal genome.Our results confirm that the proposed method compresses a 56MB human data file to 294.4KB, with a space savings of 99.4%.For virus data, a 601KB file was compressed to 212.9KB, with a space savings of 64.6%.For mouse data, a 106KB file was compressed to 9.6KB, with a space savings of 91%.\n\nAs can be observed, high similarity between genomic sequences is essential to improve the compression.For each dataset, the compression ratio achieved is a measure of the similarity between its sequences.In other words, it is possible to measure how much information one sequence gives about the other.\n\nAn important point should be mentioned here is that the proposed method does not require a priori knowledge about that statistics of the sequence set.This will be a big advantage when the updated sequences have different statistics.\n\nThe execution time of the differential compression is depending on the length of the difference sequence needed to be compressed.As the difference sequence length increases, the execution time increases.On the other hand, decoding speed is similar since both encoder and decoder do essentially the same computation.Therefore, our current implementation has been optimized for encoding and decoding speed, when the sequence set is under heavy usage.\n\nThe differential compression method has been used for lossless compression.Through our investigation, we have found that the use of this method could open new frontiers in quickly identifying unknown sequence related to the set of sequences.This method can potentially be modified to include variable references instead of using a single reference to improve the difference compression.It also extends to update the set with new similar sequences.Further investigation of the new method is needed to further assess its practical value.Moreover, when individuals have complete genome sequences available as part of their personal health records, the focus will shift to difference sequence-level compression.It seems likely that improvement of difference compression will continue to be important to advance knowledge of human genetic variation, and is the pressing problem faced by researchers today.\n\n\nCONCLUSIONS\n\nThe differential compression method that is based on the differences and locations of differences between each sequence in a genomic dataset and its reference sequence is presented.This method is simple, universal which does not depend on the statistics of the dataset.and could achieve up to 195-fold compression.Compression methods are undergoing rapid development making it tempting to store sequencing data for long periods of time so that the data can be re-analyzed with the latest techniques.The challenging open research problems, huge influx of data, and rapidly improving analysis techniques have created the need to store and transfer very large volumes of data.More work is needed to select the prefect reference for huge data to improve difference compression generation, and to further investigate the use of the new method in practical genomic applications.\n\nFigure 1 .\n1\nFigure 1.Architecture of the differential compression algorithm\n\n\nTable 4 .\n4\nSize of compressed differences for different compression algorithms\nDatasetUncompressedHuffmanZLIB DeflatorsizealgorithmalgorithmHuman1.08MB156.6KB35.6KBVirus374.7KB81.6KB84.3KBMouse11.8KB4.3KB5.2KB\n\nTable 3 .\n3\nHuffman codes for difference operations.\nHuman dataVirus dataMouse dataRelevantProbability EncodingProbability EncodingProbability Encodingnumbervaluevaluevalue10.0011111010.06411100.0718001120.0942100.06531010.0906001030.002111110.05501110.0483011140.895700.721800.0696011050.000211100010.0237100010.1911060.00071110010.025100000.18491170.0051100.0221100110.159501080.000511100000.0225100100.1839\n\nTable 5 .\n5\nComparison of compression ratios and space saving\nDatasetUncompressedDifferences Locations CompressionSpacesizeratiosavingHuman56MB35.6KB258.7KB0.00599.4%Virus601KB81.6KB131.3KB0.35464.6%Mouse106KB4.3KB5.3KB0.0991.0%\n\nAn Information Based Sequence Distance and its Application to Whole Mitochondrial Genome. M Li, J Badger, X Chen, S Kwong, P Kearney, H Zhang, Bioinformatics. 1722001\n\nThe Similarity Metric. M Li, X Chen, X Li, B Ma, P Vitanyi, Proc. 14th Ann. ACM-SIAM Symp. Discrete Algorithms. 14th Ann. ACM-SIAM Symp. Discrete Algorithms2003\n\nTextual Data Compression in Computational Biology: a synopsis. R Giancarlo, D Scaturro, F Utro, Bioinformatics. 25132009\n\nSequencing the Human Genome. L Rowen, G Mahairas, L Hood, Science. 2781997\n\ngzip (GNUzip) compression utility. J Gailly, M Adler, \n\nA Universal Algorithm for Sequential Data Compression. J Ziv, A Lempel, IEEE Trans. Information Theory. 231977\n\nA Block Sorting Lossless Data Compression Algorithm. M Burrows, D J Wheeler, 1241994Digital System Research CenterTechnical Report\n\nBiological Sequence Compression Algorithms. T Matsumoto, K Sadakane, H Imai, Genome Informatics. 112000\n\nCompression of DNA Sequences. S Grumbach, F Tahi, Proc. IEEE Symp. Data Compression. IEEE Symp. Data CompressionSnowbird, UT1993\n\nA New Challenge for Compression Algorithms: Genetic Sequences. S Grumbach, F Tahi, Information Processing Management. 199430\n\nA Compression Algorithm for DNA Sequences and its Applications in Genome Comparison. X Chen, S Kwong, M Li, Proc. 4 th Ann. International Conf. Computational Molecular Biology. 4 th Ann. International Conf. Computational Molecular Biology2000107\n\nDNACompress: Fast and Effective DNA Sequence Compression. X Chen, M Li, B Ma, J Tromp, Bioinformatics. 18122002\n\nA Simple Statistical Algorithm for Biological Sequence Compression. M D Cao, T I Dix, L Allison, Proc. IEEE Data Compression Conference (DCC '07). IEEE Data Compression Conference (DCC '07)2007\n\nApplication of Compression-Based Distance Measures to Protein Sequence Classification: A Methodology Study. A Kocsor, A Kertesz-Farkas, L Kajan, S Pongor, Bioinformatics. 222006\n\nProtien is Compressible. A Hatengan, I Tabus, Proc. 6 th Nordic Signal Processing Symposium. 6 th Nordic Signal essing Symposium2004\n\nClustering by Compression. R Cilibrasi, P M B Vitanyi, IEEE Trans. Information Theory. 514April 2005\n\nA Guarantee DNA Sequences for Repetitive DNA Sequences. E Rivals, J P Delahaye, M Dauchet, O Delgrange, IT-2851995LIFL Lille I UniversityTechnical Report\n\nGENBIT Compress Tool (GBC): A Java -Based Tool to Compress DNA Sequences and Compute Compression Ratio (BITS/BASE) Of Genomes. P Raja Rajeswari, A Apparao, International Journal of Computer Science and Information Technology. 2June 2010\n\nDNABIT Compress -Genome Compression Algorithm. P Raja Rajeswari1, A Apparao, Bioinformation. 582011\n\nA Mathematical Theory of Communications. C E Shannon, Bell System Technology Journal. 271948\n\nDNA Sequence Classification Using Compression-based Induction. D M Loewenstern, H Hirsh, P Yianilos, M Noordewier, 95-041995DIMACSTechnical Report\n\nSignificantly Lower Entropy Estimates for Natural DNA Sequences. D M Loewenstern, P N Yianilos, Proc. IEEE Data Compression Conference (DCC '97). IEEE Data Compression Conference (DCC '97)1997\n\nEstimating DNA Sequence Entropy. J K Lanctot, M Li, E H Yang, Proc. 11 th Annul. ACM-SIAM Symp. Discrete Algorithms. 11 th Annul. ACM-SIAM Symp. Discrete Algorithms2000\n\nHuman Genomes as Email Attachments. S Christley, Y Lu, C Li, X Xie, Bioinformatics. 2522009\n\nData Structures and Compression algorithms for Genomic Sequence data. C Brandon, D C Wallace, P Baldi, Bioinformatics. 25142009\n\nA Novel Compression Tool for Efficient Storage of Genome Resequencing Ddata. C Wang, D Zhang, 10.1093/nar/gkr009Nucleic Acids Research. January 2011\n\nDNA Data Compression Based on the Whole Genome Sequence. H Do Kim, Ju-Han Kim, Journal of Convergence Information Technology. 432009\n\nCompressing Genomic Sequence Fragments Using SLIMGENE. C Kozanitis, C Saunders, S Kruglyak, V Bafna, G Varghese, 2010RECCOMB\n\nGenomic Sequences Differential Compression Model. H Afify, M Islam, M Abdel, Y M Wahed, Kadah, 27 th National Radio Science Conference, NRSC'2010. Menouf, EgyptMarch 16-18, 2010\n\nMITOMAP: a human mitochondrial genome database-2004. M Brandon, Nucleic Acids Res. 332005\n\nBasic Local Alignment Search. S F Altschul, W Gish, W Miller, E W Myers, D J Lipman, J. Molecular Biology. 2151990\n\nIntroduction to Data Compression. Khalid Sayood, 20063University of Nebraskard ed.\n"},"corpus_id":{"kind":"number","value":699920,"string":"699,920"},"external_ids":{"kind":"string","value":"{\n \"arxiv\": \"1109.0094\",\n \"mag\": 2963562425,\n \"acl\": null,\n \"pubmed\": null,\n \"pubmedcentral\": null,\n \"dblp\": \"journals/corr/abs-1109-0094\",\n \"doi\": \"10.5121/ijcsit.2011.3412\"\n}"},"source":{"kind":"string","value":"{\n \"pdf_urls\": [\n \"https://arxiv.org/pdf/1109.0094v1.pdf\"\n ],\n \"pdf_sha\": \"5934644d27fc4faee46b3d3b0753e3d8e76c70f1\",\n \"open_access\": {\n \"license\": null,\n \"url\": \"https://doi.org/10.5121/ijcsit.2011.3412\",\n \"status\": \"BRONZE\"\n }\n}"},"title":{"kind":"string","value":"DNA LOSSLESS DIFFERENTIAL COMPRESSION ALGORITHM BASED ON SIMILARITY OF GENOMIC SEQUENCE DATABASE"},"authors":{"kind":"list like","value":["Heba Afify hebaaffify@yahoo.com \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt","Muhammad Islam \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt","Manal Abdel Wahed \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt"],"string":"[\n \"Heba Afify hebaaffify@yahoo.com \\nDepartment of Systems and Biomedical Engineering\\nCairo University\\nEgypt\",\n \"Muhammad Islam \\nDepartment of Systems and Biomedical Engineering\\nCairo University\\nEgypt\",\n \"Manal Abdel Wahed \\nDepartment of Systems and Biomedical Engineering\\nCairo University\\nEgypt\"\n]","isConversational":false},"abstract":{"kind":"string","value":"Modern biological science produces vast amounts of genomic sequence data.This is fuelling the need for efficient algorithms for sequence compression and analysis.Data compression and the associated techniques coming from information theory are often perceived as being of interest for data communication and storage.In recent years, a substantial effort has been made for the application of textual data compression techniques to various computational biology tasks, ranging from storage and indexing of large datasets to comparison of genomic databases.This paper presents a differential compression algorithm that is based on production of difference sequences according to op-code table in order to optimize the compression of homologous sequences in dataset.Therefore, the stored data are composed of reference sequence, the set of differences, and differences locations, instead of storing each sequence individually.This algorithm does not require a priori knowledge about the statistics of the sequence set.The algorithm was applied to three different datasets of genomic sequences, it achieved up to 195-fold compression rate corresponding to 99.4% space saving."},"sections":{"kind":"list like","value":[{"title":"INTRODUCTION","content":"The compression of genomic sequences remains a challenging problem, with profound implications in biology and with important technological impact when the use of genomic data will become a daily practice in health and medicine.As such, it will certainly be investigated further due to several reasons: benefits when storing or transmitting the genome files; possibilities for comparison of entire genomes by similarity metrics approximating Kolmogorov similarity [1,2]; and discovering statistically significant relationships among various sequences.\nData compression and the related information-theoretic techniques find a wide use for investigation in computational biology.Such a pervasive use has grounds in some outstanding notions that deeply characterizes data compression, in particular universality and quantification of statistical dependence via information measures.These notions give rise to methods that need very few assumptions on the data models and, as a consequence, very minor parameter estimations for their application.This seems to be a major advantage for computational biology applications, where the statistical modeling of the data is a highly non-trivial task.In addition, the low-computational demand of these methods allows them to scale well with dataset size, even on a genomic scale.Obviously, data structure, data modeling and speed are the main advantages for the use of data compression in biological investigations [3].\nThe amount of DNA being extracted from organisms and sequenced is increasing exponentially [4].This yields two problems: storage and comprehension.Despite the prevalence of broadband network connections, there still exists a need for compact representation of data to speed up transmission.Transferring a single sequence that is millions of characters long may take ten to fifteen minutes over a dial-up connection.Compression of genomic sequences can decrease the storage requirements, and increase the transmission speed.\nUnderstanding genomic sequences has wide applications, from the synthesis of medicines to genetic screening and engineering.The knowledge of the structure of a sequence is important for its comprehension.If a set of sequences have a common structural property that is shared by another sequence, it is possible that they are related in some way, or that the knowledge that applies to one may also be useful for the other.Compression can help to show both the structure of a sequence and how it is related to other sequences.\nDNA is composed of four bases (A, T, G, C), and can be coded using two bits per base.According to functionality, DNA manifests different properties from other kinds of data.Standard compression algorithms for text or image files exploit small repeated patterns and contextual similarities to achieve compression.However, repeated patterns in DNA sequences are typically much longer and less frequent, so standard compression algorithms perform poorly on DNA.The most popular general-purpose encoders of today, such as gzip [5], which is based on the Lempel-Ziv algorithm [6], and bzip2, based on the Burrows-Wheeler Transform [7], which usually produces more than two bits per base to achieve the un-encoded representation [8].Hence, the quest for efficient DNA compression programs started to become popular in the competition-driven community of data compression enthusiasts.DNA sequences are compressible, so they are not random.But they are not highly compressible.It is therefore necessary for coding methods to be as efficient as possible.In the context of compression, missing structure will lead to inefficient compression.\nIn the last two decades, compression of genomic sequences can be divided into two categories: Specific compression algorithms developed for efficiently compressing sequence data for the sake of reduced resource consumption (disk space or network usage) [8][9][10][11][12][13]; and investigations of the usefulness of compressibility as a measure of information content, for the purpose of making inferences about sequences (such as the relatedness of two sequences) [1,14].Specific compression algorithms have been proposed for DNA compression by using particular characteristics such as exact or approximate repeats measures within a single DNA sequence that are based on relations between subsequences only.Compression gains afforded by these algorithms are ultimately not sufficient to justify their adoption for large databases.While much research has been done on compressing individual DNA sequences, surprisingly little has focused on the compression of entire databases [3].The results of compressing genomic sequences can be applied to the problem of evolution derivation [15].Compression-based distance measures (CBMs) that depend on probabilities of mismatching locations [16], are not distinct enough among different classes.However, researches have been suffering from the poor modeling to characterize the relationship between sequences.\nAlgorithms for Compressing DNA sequences, such as GenCompress [11] ,Biocompress [10] and Cfact [17] were available to compress DNA sequences.Their compression rate was about 1.74 bits per base i.e., 78% in compression rate.Hence, a compression algorithm named \"GenBit Compress Tool\" [18] is presented, whose compression rate was below 1.2 bits per byte (for Best case) , 1.727 bits/bytes (for Average Case), 2.238 bits/bytes (Worst case ) even for larger genome (nearly 2,00,000 characters).Recently, P. Raja Rajeswari, and A. Apparao [19] presented a new compression algorithm named \"DNABIT Compress\" whose compression rate was below 1.56 bits per base (for Best case) even for larger genome.DNABIT Compress algorithm was the best among the remaining compression algorithms and significantly improves the running time of all previous DNA compression programs.\nResearchers have worked in entropy estimation for genomic sequences, either by computing frequency of n-mers for long enough inputs, called Shannon entropy [20], or by adopting compression methods to obtain an upper bound on entropy [8].Loewenstern [21,22] introduced a compression method CDNA by considering inexact match in finding patterns.Importantly, Lanctot and Yang [23] improved the compression further by exploiting the reverse complement property of DNA sequences.Also, this latter method produces a good estimation of entropy, e.g., the estimate approaches the actual entropy for long enough input.Badger and Chen [1] proposed a distance function with nice properties for cluster related sequences.\nInterestingly, difference compression schemes targets the efficient compression of entire databases of sequences.DNAzip [24] was first algorithm introducing the important idea of only storing differences to a reference sequence, but in this case for storing an entire, assembled genome as a series of difference.This algorithm [24] did not consider the process of generating the variations, which can be a challenging problem in itself, but assume that the variation data have been provided.Difference compression schemes, which compress entire sets of homologous sequences by encoding only the differences between a genomic sequences and a reference sequence, are also suggested in [25].Brandon et al [25] found that selecting the reference sequence is important for having an effective compression of dataset.With only a partial level of optimization, 3615 genome sequences occupying 56MB in GenBank are compressed down to only 167 KB, achieving a 345-fold compression rate, using the revised Cambridge Reference Sequence as the reference sequence.Using the consensus sequence as the reference sequence, the data can be stored using only 133 KB, corresponding to a 433-fold level of compression, roughly a 23% improvement.On the other hand, C. Wang [26] implemented a generic tool, GRS, for de novo compression of genome resequencing data which does not need the reference SNPs map.When its performance was tested on the first Korean personal genome sequence dataset, GRS was able to achieve 159-fold compression, reducing the size of the data from 2986.8 to 18.8 MB.While being tested against the sequencing data from rice and Arabidopsis thaliana, GRS compressed the 361.0 MB rice genome data to 4.4 MB, and the A. thaliana genome data from 115.1MB to 6.5 KB.DNAEncodeWG [27] also presented how to compress DNA sequence data using the whole genome sequence of an organism to identify differences between DNA sequences if a repository of the whole genome sequence of the organism is accessible through the Web.It encoded the sequences 10-fold better than the other standard algorithms.Kozanitis [28] focused on fragment compression as opposed to sequence compression by using SLIMGENE.H. Afify [29] presented another algorithm in which for each pair of similar sequences, a third sequence can be generated; representing the difference between them, and the entropy of the generated difference sequence can be estimated.Difference sequence can help in building phylogenic tree, while the entropy can help in selecting appropriate compression reference for short dataset.\nFor difference compression scheme to be appropriate, it should be suitable for the way the set is being used.When an entire set is archived or transmitted, the concern will be focused on the compression rate.In this situation, a reference sequence is stored, and the next sequence is generated from this reference and the appropriate difference sequence.Newly generated sequences may be used as references for subsequent sequences.When the set is being actively used, in addition to the compression rate, the speed of decompression is of comparable importance, where any sequence may be repeatedly fetched at any moment.To speed up sequence decompression, it is preferable to have a single reference for the whole set.\nIn this study, we describe another solution to the compression of genomic sequence dataset which compresses the dataset based on comparing it with a reference sequence.We focus our study on large sets of sequences that belong to the same class.If two genomes are, e.g., more than 99% identical, it is much more efficient to store one genome as a variation from the other; in which case, only that 1% representing the variation needs to be stored.A differentially compressed set is a set where a single reference sequence is stored, along with information about the difference between this sequence and the rest of the set.To evaluate the suggested selection method, the compression of the differences, compression of difference locations and the size of the compressed set are examined, as is explained in the next section."},{"title":"MATERIAL AND METHOD","content":""},{"title":"Data Extraction","content":"The data used in our work consists of three different datasets of genomic sequences including 3615 human mitochondrial genomic sequences, 500 human virus sequences H1N1, and 100 mouse sequences Mus Musculus Dmesticus.\nMitochondrial dataset takes 56MB size in GenBank, and is downloadable from the GenBank database, HapMap web site and the MITOMAO database [30].Among the sequences, 2671 correspond to complete genome, while the remaining 944 correspond only to the coding region sequence, which is about 1100bp shorter than the full genome sequence.Virus dataset takes 601KB size in GenBank, and is downloaded from Influenza Research Database [31].Mouse datasets takes 106KB in GenBank, and is downloaded from Mouse Genome Database (MGD) [32].References were selected as follows: Cambridge sequence NC_012920 sequence for human mitochondrial dataset, HM17663 for virus dataset, and AJ843867 for mouse dataset."},{"title":"Operation Code Generation","content":"The DNA is constructed of a double helix held together by hydrogen bonds.Each strand of the helix is a biomolecule consisting of many linked components called nucleotides.Each nucleotide is one of four possible types: adenine (A), cytosine (C), guanine (G) and thymine (T).The two strands of the helix are exact complement of each other.Each nucleotide of one strand matches to its complement on the other strand, where A pairs with T and G pairs with C, DNA strands that are complementary to themselves are called self-complementary or palindromes.\nTo generate an operation code of differences between a target sequence and its reference, the base at every location of the target is compared with the corresponding bases at the reference.A difference between the two bases can be due to one of three modifications to the target: a base insertion, a base deletion, or a replacement.Table 1 summarizes the operation codes.Table 1.Operation code generation."},{"title":"Corresponding Bases","content":"Operation Op-codes The same Similarity\nA or T or G or C '-' Deletion \"4\" '-' G Insertion \"5\" '-' A \"6\" '-' C \"7\" '-' T \"8\""},{"title":"Differential Compression Algorithm","content":"The proposed differential compression algorithm consists of three main steps: Alignment, Differences recording and differences compression."},{"title":"Alignment","content":"We start by aligning each sequence in the dataset with the reference sequence using local Sequence Alignment.The sole purpose of sequence alignments is to place homologous positions of homologous sequences into the same column by inserting gapes.Gaps reflect the occurrence of insertions/deletions or other rearrangements during the process.Also, the alignment of similar sequences can help in discovering patterns and relationships between sequences, consequently improve their compression ratio [33]."},{"title":"Differences Recording","content":"In this step, differences and differences locations vectors are recorded.Difference vector is achieved by storing only the op-code of the different bases between the aligned reference sequence and the aligned genomic sequence; these will be according to Table 2 ranging from 1 to 8. Difference locations with respect to the unaligned reference sequence are recorded.It is to be noted out that an insertion in the aligned reference sequence will not change the recorded unaligned reference sequence base location, while any other operation in the aligned genomic sequence will increment to the next recorded unaligned reference sequence base location."},{"title":"Difference Compression","content":"The proposed compression algorithm can be divided into two phases, the differences are coded, and the codes are compressed in the first phase, while their locations are compressed in the second.To improve the compression of differences locations, the distance between successive locations are stored.\nTo compare the results obtained after the compression of both differences codes and locations, we used compression ratio which is the ratio between the compressed size and the uncompressed size, and space saving which is defined as the reduction in size relative to the uncompressed size (1-compression ratio) [34], as measures for the compression process.Figure 1 shows the architecture of the proposed differential compression algorithm.\nTable 2. Op-codes of differences."},{"title":"Aligned Reference Sequence Bases","content":""},{"title":"RESULTS AND DISCUSSION","content":"We have tested the proposed differential compression algorithm on the three genomic sequences datasets.Difference codes were compressed using two lossless compression algorithms namely, Huffman [35] and ZLIB Deflator algorithm [36].Table 3 shows the generated Huffman codes.Table 4 shows the size of the compressed difference codes.It also shows that ZLIB Deflator algorithm achieved better compression ratio than Huffman algorithm in human data, while Huffman algorithm achieved slightly better compression ratio in virus and mouse data.\nDifference locations are compressed using ZLIB Deflator algorithm.Table 5 summarizes the compression ratio and space saving of our algorithm on the three datasets.The results confirm that mitochondria dataset that occupies 56MB size in GenBank can be stored using only 294.3KB, corresponding to 195-fold compression rate.While virus dataset that occupies 601KB size in GenBank can be stored using only 212.9KB, corresponding to 3-fold level of compression.Mouse datasets that occupies 106KB size in GenBank can be stored using only 9.6KB, corresponding to 11-fold level of compression.It should be noted that compression of mitochondria dataset is better than virus and mouse database because it has high similarity between genomic sequences.The most popular algorithms, including specific compression algorithms: DNACompress [12], XM [13], and difference compression scheme: DNAEncodeWG [27], are not suitable for compression of entire databases.We believe that DNAEncodeWG is superior for a single sequence.It should be mentioned that Brandon et al. algorithm [25], was done by using extra reference sequence and based on statistics of the sequence set that are not valid for other sets.\nThe compression result of our algorithm is better than C. Wang [26] that achieved 159-fold compression on Korean personal genome.Our results confirm that the proposed method compresses a 56MB human data file to 294.4KB, with a space savings of 99.4%.For virus data, a 601KB file was compressed to 212.9KB, with a space savings of 64.6%.For mouse data, a 106KB file was compressed to 9.6KB, with a space savings of 91%.\nAs can be observed, high similarity between genomic sequences is essential to improve the compression.For each dataset, the compression ratio achieved is a measure of the similarity between its sequences.In other words, it is possible to measure how much information one sequence gives about the other.\nAn important point should be mentioned here is that the proposed method does not require a priori knowledge about that statistics of the sequence set.This will be a big advantage when the updated sequences have different statistics.\nThe execution time of the differential compression is depending on the length of the difference sequence needed to be compressed.As the difference sequence length increases, the execution time increases.On the other hand, decoding speed is similar since both encoder and decoder do essentially the same computation.Therefore, our current implementation has been optimized for encoding and decoding speed, when the sequence set is under heavy usage.\nThe differential compression method has been used for lossless compression.Through our investigation, we have found that the use of this method could open new frontiers in quickly identifying unknown sequence related to the set of sequences.This method can potentially be modified to include variable references instead of using a single reference to improve the difference compression.It also extends to update the set with new similar sequences.Further investigation of the new method is needed to further assess its practical value.Moreover, when individuals have complete genome sequences available as part of their personal health records, the focus will shift to difference sequence-level compression.It seems likely that improvement of difference compression will continue to be important to advance knowledge of human genetic variation, and is the pressing problem faced by researchers today."},{"title":"CONCLUSIONS","content":"The differential compression method that is based on the differences and locations of differences between each sequence in a genomic dataset and its reference sequence is presented.This method is simple, universal which does not depend on the statistics of the dataset.and could achieve up to 195-fold compression.Compression methods are undergoing rapid development making it tempting to store sequencing data for long periods of time so that the data can be re-analyzed with the latest techniques.The challenging open research problems, huge influx of data, and rapidly improving analysis techniques have created the need to store and transfer very large volumes of data.More work is needed to select the prefect reference for huge data to improve difference compression generation, and to further investigate the use of the new method in practical genomic applications."},{"title":"Figure 1 .","content":"Figure 1.Architecture of the differential compression algorithm"},{"title":"Table 4 .","content":"Size of compressed differences for different compression algorithms"},{"title":"Table 3 .","content":"Huffman codes for difference operations."},{"title":"Table 5 .","content":"Comparison of compression ratios and space saving"}],"string":"[\n {\n \"title\": \"INTRODUCTION\",\n \"content\": \"The compression of genomic sequences remains a challenging problem, with profound implications in biology and with important technological impact when the use of genomic data will become a daily practice in health and medicine.As such, it will certainly be investigated further due to several reasons: benefits when storing or transmitting the genome files; possibilities for comparison of entire genomes by similarity metrics approximating Kolmogorov similarity [1,2]; and discovering statistically significant relationships among various sequences.\\nData compression and the related information-theoretic techniques find a wide use for investigation in computational biology.Such a pervasive use has grounds in some outstanding notions that deeply characterizes data compression, in particular universality and quantification of statistical dependence via information measures.These notions give rise to methods that need very few assumptions on the data models and, as a consequence, very minor parameter estimations for their application.This seems to be a major advantage for computational biology applications, where the statistical modeling of the data is a highly non-trivial task.In addition, the low-computational demand of these methods allows them to scale well with dataset size, even on a genomic scale.Obviously, data structure, data modeling and speed are the main advantages for the use of data compression in biological investigations [3].\\nThe amount of DNA being extracted from organisms and sequenced is increasing exponentially [4].This yields two problems: storage and comprehension.Despite the prevalence of broadband network connections, there still exists a need for compact representation of data to speed up transmission.Transferring a single sequence that is millions of characters long may take ten to fifteen minutes over a dial-up connection.Compression of genomic sequences can decrease the storage requirements, and increase the transmission speed.\\nUnderstanding genomic sequences has wide applications, from the synthesis of medicines to genetic screening and engineering.The knowledge of the structure of a sequence is important for its comprehension.If a set of sequences have a common structural property that is shared by another sequence, it is possible that they are related in some way, or that the knowledge that applies to one may also be useful for the other.Compression can help to show both the structure of a sequence and how it is related to other sequences.\\nDNA is composed of four bases (A, T, G, C), and can be coded using two bits per base.According to functionality, DNA manifests different properties from other kinds of data.Standard compression algorithms for text or image files exploit small repeated patterns and contextual similarities to achieve compression.However, repeated patterns in DNA sequences are typically much longer and less frequent, so standard compression algorithms perform poorly on DNA.The most popular general-purpose encoders of today, such as gzip [5], which is based on the Lempel-Ziv algorithm [6], and bzip2, based on the Burrows-Wheeler Transform [7], which usually produces more than two bits per base to achieve the un-encoded representation [8].Hence, the quest for efficient DNA compression programs started to become popular in the competition-driven community of data compression enthusiasts.DNA sequences are compressible, so they are not random.But they are not highly compressible.It is therefore necessary for coding methods to be as efficient as possible.In the context of compression, missing structure will lead to inefficient compression.\\nIn the last two decades, compression of genomic sequences can be divided into two categories: Specific compression algorithms developed for efficiently compressing sequence data for the sake of reduced resource consumption (disk space or network usage) [8][9][10][11][12][13]; and investigations of the usefulness of compressibility as a measure of information content, for the purpose of making inferences about sequences (such as the relatedness of two sequences) [1,14].Specific compression algorithms have been proposed for DNA compression by using particular characteristics such as exact or approximate repeats measures within a single DNA sequence that are based on relations between subsequences only.Compression gains afforded by these algorithms are ultimately not sufficient to justify their adoption for large databases.While much research has been done on compressing individual DNA sequences, surprisingly little has focused on the compression of entire databases [3].The results of compressing genomic sequences can be applied to the problem of evolution derivation [15].Compression-based distance measures (CBMs) that depend on probabilities of mismatching locations [16], are not distinct enough among different classes.However, researches have been suffering from the poor modeling to characterize the relationship between sequences.\\nAlgorithms for Compressing DNA sequences, such as GenCompress [11] ,Biocompress [10] and Cfact [17] were available to compress DNA sequences.Their compression rate was about 1.74 bits per base i.e., 78% in compression rate.Hence, a compression algorithm named \\\"GenBit Compress Tool\\\" [18] is presented, whose compression rate was below 1.2 bits per byte (for Best case) , 1.727 bits/bytes (for Average Case), 2.238 bits/bytes (Worst case ) even for larger genome (nearly 2,00,000 characters).Recently, P. Raja Rajeswari, and A. Apparao [19] presented a new compression algorithm named \\\"DNABIT Compress\\\" whose compression rate was below 1.56 bits per base (for Best case) even for larger genome.DNABIT Compress algorithm was the best among the remaining compression algorithms and significantly improves the running time of all previous DNA compression programs.\\nResearchers have worked in entropy estimation for genomic sequences, either by computing frequency of n-mers for long enough inputs, called Shannon entropy [20], or by adopting compression methods to obtain an upper bound on entropy [8].Loewenstern [21,22] introduced a compression method CDNA by considering inexact match in finding patterns.Importantly, Lanctot and Yang [23] improved the compression further by exploiting the reverse complement property of DNA sequences.Also, this latter method produces a good estimation of entropy, e.g., the estimate approaches the actual entropy for long enough input.Badger and Chen [1] proposed a distance function with nice properties for cluster related sequences.\\nInterestingly, difference compression schemes targets the efficient compression of entire databases of sequences.DNAzip [24] was first algorithm introducing the important idea of only storing differences to a reference sequence, but in this case for storing an entire, assembled genome as a series of difference.This algorithm [24] did not consider the process of generating the variations, which can be a challenging problem in itself, but assume that the variation data have been provided.Difference compression schemes, which compress entire sets of homologous sequences by encoding only the differences between a genomic sequences and a reference sequence, are also suggested in [25].Brandon et al [25] found that selecting the reference sequence is important for having an effective compression of dataset.With only a partial level of optimization, 3615 genome sequences occupying 56MB in GenBank are compressed down to only 167 KB, achieving a 345-fold compression rate, using the revised Cambridge Reference Sequence as the reference sequence.Using the consensus sequence as the reference sequence, the data can be stored using only 133 KB, corresponding to a 433-fold level of compression, roughly a 23% improvement.On the other hand, C. Wang [26] implemented a generic tool, GRS, for de novo compression of genome resequencing data which does not need the reference SNPs map.When its performance was tested on the first Korean personal genome sequence dataset, GRS was able to achieve 159-fold compression, reducing the size of the data from 2986.8 to 18.8 MB.While being tested against the sequencing data from rice and Arabidopsis thaliana, GRS compressed the 361.0 MB rice genome data to 4.4 MB, and the A. thaliana genome data from 115.1MB to 6.5 KB.DNAEncodeWG [27] also presented how to compress DNA sequence data using the whole genome sequence of an organism to identify differences between DNA sequences if a repository of the whole genome sequence of the organism is accessible through the Web.It encoded the sequences 10-fold better than the other standard algorithms.Kozanitis [28] focused on fragment compression as opposed to sequence compression by using SLIMGENE.H. Afify [29] presented another algorithm in which for each pair of similar sequences, a third sequence can be generated; representing the difference between them, and the entropy of the generated difference sequence can be estimated.Difference sequence can help in building phylogenic tree, while the entropy can help in selecting appropriate compression reference for short dataset.\\nFor difference compression scheme to be appropriate, it should be suitable for the way the set is being used.When an entire set is archived or transmitted, the concern will be focused on the compression rate.In this situation, a reference sequence is stored, and the next sequence is generated from this reference and the appropriate difference sequence.Newly generated sequences may be used as references for subsequent sequences.When the set is being actively used, in addition to the compression rate, the speed of decompression is of comparable importance, where any sequence may be repeatedly fetched at any moment.To speed up sequence decompression, it is preferable to have a single reference for the whole set.\\nIn this study, we describe another solution to the compression of genomic sequence dataset which compresses the dataset based on comparing it with a reference sequence.We focus our study on large sets of sequences that belong to the same class.If two genomes are, e.g., more than 99% identical, it is much more efficient to store one genome as a variation from the other; in which case, only that 1% representing the variation needs to be stored.A differentially compressed set is a set where a single reference sequence is stored, along with information about the difference between this sequence and the rest of the set.To evaluate the suggested selection method, the compression of the differences, compression of difference locations and the size of the compressed set are examined, as is explained in the next section.\"\n },\n {\n \"title\": \"MATERIAL AND METHOD\",\n \"content\": \"\"\n },\n {\n \"title\": \"Data Extraction\",\n \"content\": \"The data used in our work consists of three different datasets of genomic sequences including 3615 human mitochondrial genomic sequences, 500 human virus sequences H1N1, and 100 mouse sequences Mus Musculus Dmesticus.\\nMitochondrial dataset takes 56MB size in GenBank, and is downloadable from the GenBank database, HapMap web site and the MITOMAO database [30].Among the sequences, 2671 correspond to complete genome, while the remaining 944 correspond only to the coding region sequence, which is about 1100bp shorter than the full genome sequence.Virus dataset takes 601KB size in GenBank, and is downloaded from Influenza Research Database [31].Mouse datasets takes 106KB in GenBank, and is downloaded from Mouse Genome Database (MGD) [32].References were selected as follows: Cambridge sequence NC_012920 sequence for human mitochondrial dataset, HM17663 for virus dataset, and AJ843867 for mouse dataset.\"\n },\n {\n \"title\": \"Operation Code Generation\",\n \"content\": \"The DNA is constructed of a double helix held together by hydrogen bonds.Each strand of the helix is a biomolecule consisting of many linked components called nucleotides.Each nucleotide is one of four possible types: adenine (A), cytosine (C), guanine (G) and thymine (T).The two strands of the helix are exact complement of each other.Each nucleotide of one strand matches to its complement on the other strand, where A pairs with T and G pairs with C, DNA strands that are complementary to themselves are called self-complementary or palindromes.\\nTo generate an operation code of differences between a target sequence and its reference, the base at every location of the target is compared with the corresponding bases at the reference.A difference between the two bases can be due to one of three modifications to the target: a base insertion, a base deletion, or a replacement.Table 1 summarizes the operation codes.Table 1.Operation code generation.\"\n },\n {\n \"title\": \"Corresponding Bases\",\n \"content\": \"Operation Op-codes The same Similarity\\nA or T or G or C '-' Deletion \\\"4\\\" '-' G Insertion \\\"5\\\" '-' A \\\"6\\\" '-' C \\\"7\\\" '-' T \\\"8\\\"\"\n },\n {\n \"title\": \"Differential Compression Algorithm\",\n \"content\": \"The proposed differential compression algorithm consists of three main steps: Alignment, Differences recording and differences compression.\"\n },\n {\n \"title\": \"Alignment\",\n \"content\": \"We start by aligning each sequence in the dataset with the reference sequence using local Sequence Alignment.The sole purpose of sequence alignments is to place homologous positions of homologous sequences into the same column by inserting gapes.Gaps reflect the occurrence of insertions/deletions or other rearrangements during the process.Also, the alignment of similar sequences can help in discovering patterns and relationships between sequences, consequently improve their compression ratio [33].\"\n },\n {\n \"title\": \"Differences Recording\",\n \"content\": \"In this step, differences and differences locations vectors are recorded.Difference vector is achieved by storing only the op-code of the different bases between the aligned reference sequence and the aligned genomic sequence; these will be according to Table 2 ranging from 1 to 8. Difference locations with respect to the unaligned reference sequence are recorded.It is to be noted out that an insertion in the aligned reference sequence will not change the recorded unaligned reference sequence base location, while any other operation in the aligned genomic sequence will increment to the next recorded unaligned reference sequence base location.\"\n },\n {\n \"title\": \"Difference Compression\",\n \"content\": \"The proposed compression algorithm can be divided into two phases, the differences are coded, and the codes are compressed in the first phase, while their locations are compressed in the second.To improve the compression of differences locations, the distance between successive locations are stored.\\nTo compare the results obtained after the compression of both differences codes and locations, we used compression ratio which is the ratio between the compressed size and the uncompressed size, and space saving which is defined as the reduction in size relative to the uncompressed size (1-compression ratio) [34], as measures for the compression process.Figure 1 shows the architecture of the proposed differential compression algorithm.\\nTable 2. Op-codes of differences.\"\n },\n {\n \"title\": \"Aligned Reference Sequence Bases\",\n \"content\": \"\"\n },\n {\n \"title\": \"RESULTS AND DISCUSSION\",\n \"content\": \"We have tested the proposed differential compression algorithm on the three genomic sequences datasets.Difference codes were compressed using two lossless compression algorithms namely, Huffman [35] and ZLIB Deflator algorithm [36].Table 3 shows the generated Huffman codes.Table 4 shows the size of the compressed difference codes.It also shows that ZLIB Deflator algorithm achieved better compression ratio than Huffman algorithm in human data, while Huffman algorithm achieved slightly better compression ratio in virus and mouse data.\\nDifference locations are compressed using ZLIB Deflator algorithm.Table 5 summarizes the compression ratio and space saving of our algorithm on the three datasets.The results confirm that mitochondria dataset that occupies 56MB size in GenBank can be stored using only 294.3KB, corresponding to 195-fold compression rate.While virus dataset that occupies 601KB size in GenBank can be stored using only 212.9KB, corresponding to 3-fold level of compression.Mouse datasets that occupies 106KB size in GenBank can be stored using only 9.6KB, corresponding to 11-fold level of compression.It should be noted that compression of mitochondria dataset is better than virus and mouse database because it has high similarity between genomic sequences.The most popular algorithms, including specific compression algorithms: DNACompress [12], XM [13], and difference compression scheme: DNAEncodeWG [27], are not suitable for compression of entire databases.We believe that DNAEncodeWG is superior for a single sequence.It should be mentioned that Brandon et al. algorithm [25], was done by using extra reference sequence and based on statistics of the sequence set that are not valid for other sets.\\nThe compression result of our algorithm is better than C. Wang [26] that achieved 159-fold compression on Korean personal genome.Our results confirm that the proposed method compresses a 56MB human data file to 294.4KB, with a space savings of 99.4%.For virus data, a 601KB file was compressed to 212.9KB, with a space savings of 64.6%.For mouse data, a 106KB file was compressed to 9.6KB, with a space savings of 91%.\\nAs can be observed, high similarity between genomic sequences is essential to improve the compression.For each dataset, the compression ratio achieved is a measure of the similarity between its sequences.In other words, it is possible to measure how much information one sequence gives about the other.\\nAn important point should be mentioned here is that the proposed method does not require a priori knowledge about that statistics of the sequence set.This will be a big advantage when the updated sequences have different statistics.\\nThe execution time of the differential compression is depending on the length of the difference sequence needed to be compressed.As the difference sequence length increases, the execution time increases.On the other hand, decoding speed is similar since both encoder and decoder do essentially the same computation.Therefore, our current implementation has been optimized for encoding and decoding speed, when the sequence set is under heavy usage.\\nThe differential compression method has been used for lossless compression.Through our investigation, we have found that the use of this method could open new frontiers in quickly identifying unknown sequence related to the set of sequences.This method can potentially be modified to include variable references instead of using a single reference to improve the difference compression.It also extends to update the set with new similar sequences.Further investigation of the new method is needed to further assess its practical value.Moreover, when individuals have complete genome sequences available as part of their personal health records, the focus will shift to difference sequence-level compression.It seems likely that improvement of difference compression will continue to be important to advance knowledge of human genetic variation, and is the pressing problem faced by researchers today.\"\n },\n {\n \"title\": \"CONCLUSIONS\",\n \"content\": \"The differential compression method that is based on the differences and locations of differences between each sequence in a genomic dataset and its reference sequence is presented.This method is simple, universal which does not depend on the statistics of the dataset.and could achieve up to 195-fold compression.Compression methods are undergoing rapid development making it tempting to store sequencing data for long periods of time so that the data can be re-analyzed with the latest techniques.The challenging open research problems, huge influx of data, and rapidly improving analysis techniques have created the need to store and transfer very large volumes of data.More work is needed to select the prefect reference for huge data to improve difference compression generation, and to further investigate the use of the new method in practical genomic applications.\"\n },\n {\n \"title\": \"Figure 1 .\",\n \"content\": \"Figure 1.Architecture of the differential compression algorithm\"\n },\n {\n \"title\": \"Table 4 .\",\n \"content\": \"Size of compressed differences for different compression algorithms\"\n },\n {\n \"title\": \"Table 3 .\",\n \"content\": \"Huffman codes for difference operations.\"\n },\n {\n \"title\": \"Table 5 .\",\n \"content\": \"Comparison of compression ratios and space saving\"\n }\n]","isConversational":false},"figures":{"kind":"list like","value":[{"id":"","caption":"Figure 1.Architecture of the differential compression algorithm","content":"Figure 1 .\n1\nFigure 1.Architecture of the differential compression algorithm"},{"id":"","caption":"Size of compressed differences for different compression algorithms","content":"Table 4 .\n4\nSize of compressed differences for different compression algorithms\nDatasetUncompressedHuffmanZLIB DeflatorsizealgorithmalgorithmHuman1.08MB156.6KB35.6KBVirus374.7KB81.6KB84.3KBMouse11.8KB4.3KB5.2KB"},{"id":"","caption":"Huffman codes for difference operations.","content":"Table 3 .\n3\nHuffman codes for difference operations.\nHuman dataVirus dataMouse dataRelevantProbability EncodingProbability EncodingProbability Encodingnumbervaluevaluevalue10.0011111010.06411100.0718001120.0942100.06531010.0906001030.002111110.05501110.0483011140.895700.721800.0696011050.000211100010.0237100010.1911060.00071110010.025100000.18491170.0051100.0221100110.159501080.000511100000.0225100100.1839"},{"id":"","caption":"Comparison of compression ratios and space saving","content":"Table 5 .\n5\nComparison of compression ratios and space saving\nDatasetUncompressedDifferences Locations CompressionSpacesizeratiosavingHuman56MB35.6KB258.7KB0.00599.4%Virus601KB81.6KB131.3KB0.35464.6%Mouse106KB4.3KB5.3KB0.0991.0%"}],"string":"[\n {\n \"id\": \"\",\n \"caption\": \"Figure 1.Architecture of the differential compression algorithm\",\n \"content\": \"Figure 1 .\\n1\\nFigure 1.Architecture of the differential compression algorithm\"\n },\n {\n \"id\": \"\",\n \"caption\": \"Size of compressed differences for different compression algorithms\",\n \"content\": \"Table 4 .\\n4\\nSize of compressed differences for different compression algorithms\\nDatasetUncompressedHuffmanZLIB DeflatorsizealgorithmalgorithmHuman1.08MB156.6KB35.6KBVirus374.7KB81.6KB84.3KBMouse11.8KB4.3KB5.2KB\"\n },\n {\n \"id\": \"\",\n \"caption\": \"Huffman codes for difference operations.\",\n \"content\": \"Table 3 .\\n3\\nHuffman codes for difference operations.\\nHuman dataVirus dataMouse dataRelevantProbability EncodingProbability EncodingProbability Encodingnumbervaluevaluevalue10.0011111010.06411100.0718001120.0942100.06531010.0906001030.002111110.05501110.0483011140.895700.721800.0696011050.000211100010.0237100010.1911060.00071110010.025100000.18491170.0051100.0221100110.159501080.000511100000.0225100100.1839\"\n },\n {\n \"id\": \"\",\n \"caption\": \"Comparison of compression ratios and space saving\",\n \"content\": \"Table 5 .\\n5\\nComparison of compression ratios and space saving\\nDatasetUncompressedDifferences Locations CompressionSpacesizeratiosavingHuman56MB35.6KB258.7KB0.00599.4%Virus601KB81.6KB131.3KB0.35464.6%Mouse106KB4.3KB5.3KB0.0991.0%\"\n }\n]","isConversational":false},"references":{"kind":"list like","value":[{"text":"An Information Based Sequence Distance and its Application to Whole Mitochondrial Genome. M Li, J Badger, X Chen, S Kwong, P Kearney, H Zhang, Bioinformatics. 1722001","doi":""},{"text":"The Similarity Metric. M Li, X Chen, X Li, B Ma, P Vitanyi, Proc. 14th Ann. ACM-SIAM Symp. Discrete Algorithms. 14th Ann. ACM-SIAM Symp. Discrete Algorithms2003","doi":""},{"text":"Textual Data Compression in Computational Biology: a synopsis. R Giancarlo, D Scaturro, F Utro, Bioinformatics. 25132009","doi":""},{"text":"Sequencing the Human Genome. L Rowen, G Mahairas, L Hood, Science. 2781997","doi":""},{"text":"gzip (GNUzip) compression utility. J Gailly, M Adler,","doi":""},{"text":"A Universal Algorithm for Sequential Data Compression. J Ziv, A Lempel, IEEE Trans. Information Theory. 231977","doi":""},{"text":"A Block Sorting Lossless Data Compression Algorithm. M Burrows, D J Wheeler, 1241994Digital System Research CenterTechnical Report","doi":""},{"text":"Biological Sequence Compression Algorithms. T Matsumoto, K Sadakane, H Imai, Genome Informatics. 112000","doi":""},{"text":"Compression of DNA Sequences. S Grumbach, F Tahi, Proc. IEEE Symp. Data Compression. IEEE Symp. Data CompressionSnowbird, UT1993","doi":""},{"text":"A New Challenge for Compression Algorithms: Genetic Sequences. S Grumbach, F Tahi, Information Processing Management. 199430","doi":""},{"text":"A Compression Algorithm for DNA Sequences and its Applications in Genome Comparison. X Chen, S Kwong, M Li, Proc. 4 th Ann. International Conf. Computational Molecular Biology. 4 th Ann. International Conf. Computational Molecular Biology2000107","doi":""},{"text":"DNACompress: Fast and Effective DNA Sequence Compression. X Chen, M Li, B Ma, J Tromp, Bioinformatics. 18122002","doi":""},{"text":"A Simple Statistical Algorithm for Biological Sequence Compression. M D Cao, T I Dix, L Allison, Proc. IEEE Data Compression Conference (DCC '07). IEEE Data Compression Conference (DCC '07)2007","doi":""},{"text":"Application of Compression-Based Distance Measures to Protein Sequence Classification: A Methodology Study. A Kocsor, A Kertesz-Farkas, L Kajan, S Pongor, Bioinformatics. 222006","doi":""},{"text":"Protien is Compressible. A Hatengan, I Tabus, Proc. 6 th Nordic Signal Processing Symposium. 6 th Nordic Signal essing Symposium2004","doi":""},{"text":"Clustering by Compression. R Cilibrasi, P M B Vitanyi, IEEE Trans. Information Theory. 514April 2005","doi":""},{"text":"A Guarantee DNA Sequences for Repetitive DNA Sequences. E Rivals, J P Delahaye, M Dauchet, O Delgrange, IT-2851995LIFL Lille I UniversityTechnical Report","doi":""},{"text":"GENBIT Compress Tool (GBC): A Java -Based Tool to Compress DNA Sequences and Compute Compression Ratio (BITS/BASE) Of Genomes. P Raja Rajeswari, A Apparao, International Journal of Computer Science and Information Technology. 2June 2010","doi":""},{"text":"DNABIT Compress -Genome Compression Algorithm. P Raja Rajeswari1, A Apparao, Bioinformation. 582011","doi":""},{"text":"A Mathematical Theory of Communications. C E Shannon, Bell System Technology Journal. 271948","doi":""},{"text":"DNA Sequence Classification Using Compression-based Induction. D M Loewenstern, H Hirsh, P Yianilos, M Noordewier, 95-041995DIMACSTechnical Report","doi":""},{"text":"Significantly Lower Entropy Estimates for Natural DNA Sequences. D M Loewenstern, P N Yianilos, Proc. IEEE Data Compression Conference (DCC '97). IEEE Data Compression Conference (DCC '97)1997","doi":""},{"text":"Estimating DNA Sequence Entropy. J K Lanctot, M Li, E H Yang, Proc. 11 th Annul. ACM-SIAM Symp. Discrete Algorithms. 11 th Annul. ACM-SIAM Symp. Discrete Algorithms2000","doi":""},{"text":"Human Genomes as Email Attachments. S Christley, Y Lu, C Li, X Xie, Bioinformatics. 2522009","doi":""},{"text":"Data Structures and Compression algorithms for Genomic Sequence data. C Brandon, D C Wallace, P Baldi, Bioinformatics. 25142009","doi":""},{"text":"A Novel Compression Tool for Efficient Storage of Genome Resequencing Ddata. C Wang, D Zhang, 10.1093/nar/gkr009Nucleic Acids Research. January 2011","doi":""},{"text":"DNA Data Compression Based on the Whole Genome Sequence. H Do Kim, Ju-Han Kim, Journal of Convergence Information Technology. 432009","doi":""},{"text":"Compressing Genomic Sequence Fragments Using SLIMGENE. C Kozanitis, C Saunders, S Kruglyak, V Bafna, G Varghese, 2010RECCOMB","doi":""},{"text":"Genomic Sequences Differential Compression Model. H Afify, M Islam, M Abdel, Y M Wahed, Kadah, 27 th National Radio Science Conference, NRSC'2010. Menouf, EgyptMarch 16-18, 2010","doi":""},{"text":"MITOMAP: a human mitochondrial genome database-2004. M Brandon, Nucleic Acids Res. 332005","doi":""},{"text":"Basic Local Alignment Search. S F Altschul, W Gish, W Miller, E W Myers, D J Lipman, J. Molecular Biology. 2151990","doi":""},{"text":"Introduction to Data Compression. Khalid Sayood, 20063University of Nebraskard ed.","doi":""}],"string":"[\n {\n \"text\": \"An Information Based Sequence Distance and its Application to Whole Mitochondrial Genome. M Li, J Badger, X Chen, S Kwong, P Kearney, H Zhang, Bioinformatics. 1722001\",\n \"doi\": \"\"\n },\n {\n \"text\": \"The Similarity Metric. M Li, X Chen, X Li, B Ma, P Vitanyi, Proc. 14th Ann. ACM-SIAM Symp. Discrete Algorithms. 14th Ann. ACM-SIAM Symp. Discrete Algorithms2003\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Textual Data Compression in Computational Biology: a synopsis. R Giancarlo, D Scaturro, F Utro, Bioinformatics. 25132009\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Sequencing the Human Genome. L Rowen, G Mahairas, L Hood, Science. 2781997\",\n \"doi\": \"\"\n },\n {\n \"text\": \"gzip (GNUzip) compression utility. J Gailly, M Adler,\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A Universal Algorithm for Sequential Data Compression. J Ziv, A Lempel, IEEE Trans. Information Theory. 231977\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A Block Sorting Lossless Data Compression Algorithm. M Burrows, D J Wheeler, 1241994Digital System Research CenterTechnical Report\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Biological Sequence Compression Algorithms. T Matsumoto, K Sadakane, H Imai, Genome Informatics. 112000\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Compression of DNA Sequences. S Grumbach, F Tahi, Proc. IEEE Symp. Data Compression. IEEE Symp. Data CompressionSnowbird, UT1993\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A New Challenge for Compression Algorithms: Genetic Sequences. S Grumbach, F Tahi, Information Processing Management. 199430\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A Compression Algorithm for DNA Sequences and its Applications in Genome Comparison. X Chen, S Kwong, M Li, Proc. 4 th Ann. International Conf. Computational Molecular Biology. 4 th Ann. International Conf. Computational Molecular Biology2000107\",\n \"doi\": \"\"\n },\n {\n \"text\": \"DNACompress: Fast and Effective DNA Sequence Compression. X Chen, M Li, B Ma, J Tromp, Bioinformatics. 18122002\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A Simple Statistical Algorithm for Biological Sequence Compression. M D Cao, T I Dix, L Allison, Proc. IEEE Data Compression Conference (DCC '07). IEEE Data Compression Conference (DCC '07)2007\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Application of Compression-Based Distance Measures to Protein Sequence Classification: A Methodology Study. A Kocsor, A Kertesz-Farkas, L Kajan, S Pongor, Bioinformatics. 222006\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Protien is Compressible. A Hatengan, I Tabus, Proc. 6 th Nordic Signal Processing Symposium. 6 th Nordic Signal essing Symposium2004\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Clustering by Compression. R Cilibrasi, P M B Vitanyi, IEEE Trans. Information Theory. 514April 2005\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A Guarantee DNA Sequences for Repetitive DNA Sequences. E Rivals, J P Delahaye, M Dauchet, O Delgrange, IT-2851995LIFL Lille I UniversityTechnical Report\",\n \"doi\": \"\"\n },\n {\n \"text\": \"GENBIT Compress Tool (GBC): A Java -Based Tool to Compress DNA Sequences and Compute Compression Ratio (BITS/BASE) Of Genomes. P Raja Rajeswari, A Apparao, International Journal of Computer Science and Information Technology. 2June 2010\",\n \"doi\": \"\"\n },\n {\n \"text\": \"DNABIT Compress -Genome Compression Algorithm. P Raja Rajeswari1, A Apparao, Bioinformation. 582011\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A Mathematical Theory of Communications. C E Shannon, Bell System Technology Journal. 271948\",\n \"doi\": \"\"\n },\n {\n \"text\": \"DNA Sequence Classification Using Compression-based Induction. D M Loewenstern, H Hirsh, P Yianilos, M Noordewier, 95-041995DIMACSTechnical Report\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Significantly Lower Entropy Estimates for Natural DNA Sequences. D M Loewenstern, P N Yianilos, Proc. IEEE Data Compression Conference (DCC '97). IEEE Data Compression Conference (DCC '97)1997\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Estimating DNA Sequence Entropy. J K Lanctot, M Li, E H Yang, Proc. 11 th Annul. ACM-SIAM Symp. Discrete Algorithms. 11 th Annul. ACM-SIAM Symp. Discrete Algorithms2000\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Human Genomes as Email Attachments. S Christley, Y Lu, C Li, X Xie, Bioinformatics. 2522009\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Data Structures and Compression algorithms for Genomic Sequence data. C Brandon, D C Wallace, P Baldi, Bioinformatics. 25142009\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A Novel Compression Tool for Efficient Storage of Genome Resequencing Ddata. C Wang, D Zhang, 10.1093/nar/gkr009Nucleic Acids Research. January 2011\",\n \"doi\": \"\"\n },\n {\n \"text\": \"DNA Data Compression Based on the Whole Genome Sequence. H Do Kim, Ju-Han Kim, Journal of Convergence Information Technology. 432009\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Compressing Genomic Sequence Fragments Using SLIMGENE. C Kozanitis, C Saunders, S Kruglyak, V Bafna, G Varghese, 2010RECCOMB\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Genomic Sequences Differential Compression Model. H Afify, M Islam, M Abdel, Y M Wahed, Kadah, 27 th National Radio Science Conference, NRSC'2010. Menouf, EgyptMarch 16-18, 2010\",\n \"doi\": \"\"\n },\n {\n \"text\": \"MITOMAP: a human mitochondrial genome database-2004. M Brandon, Nucleic Acids Res. 332005\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Basic Local Alignment Search. S F Altschul, W Gish, W Miller, E W Myers, D J Lipman, J. Molecular Biology. 2151990\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Introduction to Data Compression. Khalid Sayood, 20063University of Nebraskard ed.\",\n \"doi\": \"\"\n }\n]","isConversational":false}}},{"rowIdx":299,"cells":{"text":{"kind":"string","value":"\nFine-Tuning Automatic Speech Recognition for People with Parkinson's: An Effective Strategy for Enhancing Speech Technology Accessibility\n\n\nXiuwen Zheng xiuwenz2@illinois.edu \nDepartment of Electrical and Computer Engineering\nUniversity of Illinois Urbana-Champaign\n\n\nBornali Phukon bornalip@illinois.edu \nDepartment of Electrical and Computer Engineering\nUniversity of Illinois Urbana-Champaign\n\n\nMark Hasegawa-Johnson \nDepartment of Electrical and Computer Engineering\nUniversity of Illinois Urbana-Champaign\n\n\nFine-Tuning Automatic Speech Recognition for People with Parkinson's: An Effective Strategy for Enhancing Speech Technology Accessibility\n5EFEE0CFDBE3C3E98F91CDDD7347DD4Ddysarthriadysphoniaaccessibilityautomatic speech recognitionwav2vec 2.0speaker clustering\nThis paper enhances dysarthric and dysphonic speech recognition by fine-tuning pretrained automatic speech recognition (ASR) models on the 2023-10-05 data package of the Speech Accessibility Project (SAP), which contains the speech of 253 people with Parkinson's disease.Experiments tested methods that have been effective for Cerebral Palsy, including the use of speaker clustering and severity-dependent models, weighted fine-tuning, and multi-task learning.Best results were obtained using a multi-task learning model, in which the ASR is trained to produce an estimate of the speaker's impairment severity as an auxiliary output.The resulting word error rates are considerably improved relative to a baseline model fine-tuned using only Librispeech data, with word error rate improvements of 37.62% and 26.97% compared to fine-tuning on 100h and 960h of LibriSpeech data, respectively.\n\nIntroduction\n\nSpeech recognition technology has revolutionized how we interact with digital devices, and can be an especially useful computer input modality for people with motor disorders [1,2].However, many individuals with motor disorders face challenges in effectively using these devices due to dysarthria and dysphonia, i.e., impaired articulation and phonation caused by neuromotor disorder [3,4].\n\nDespite ongoing efforts by researchers [5,6,7,8,9,10,11,12], current ASR systems encounter notable challenges in accurately recognizing dysarthric and dysphonic impaired speech primarily due to differences between impaired speech and typical speech and the unavailability of adequate training data.Initiatives like the Nemours database of dysarthric speech [13], the Universal Access speech corpus [14], the TORGO database of acoustic and articulatory speech [15], the Neurovoz [16] and GITA [17] Spanish-language corpora of speech with Parkinson's, and Project Euphonia [18] have been instrumental in advancing impaired speech recognition.However, while dysarthric ASR error rates have dropped by a factor of three in the past fifteen years ([19] vs. [20]), non-dysarthric ASR error rates have dropped by a factor of five over the same period ([21] vs. [22]).The accelerated enhancements in nondysarthric ASR can be partly credited to the greater accessibility of standardized data for both training and testing.To address these limitations, the Speech Accessibility Project (SAP [23]) is collecting, and distributing to researchers, a large corpus of impaired speech.In this paper, we report the results of fine-tuning ASR using the first partial release of SAP data.\n\nIn the context of impaired speech recognition, fine-tuning a pre-trained model using transcribed impaired speech is a widely explored technique that has shown promising results for speech accessibility [24].In particular, the wav2vec 2.0 base model has been fine-tuned to UA-Speech using low-rank adaptation [25] and using system fusion methods in which wav2vec rescores a conformer or TDNN [26].Auxiliary speaker attributes can improve dysarthric ASR, e.g., hidden Markov model (HMM) ASR using UA-Speech was improved by first clustering speaker attribute vectors, then training cluster-dependent ASR for the speakers in each cluster [27].Deep neural network (DNN) ASR is improved by providing automatic dysarthria severity estimates as auxiliary inputs [28] or outputs [19] of the ASR, or by providing automatically inferred estimates of the visual [29] or articulatory [28] features corresponding to an acoustic dysarthric utterance.Inspired by these results, we aim to explore the potential benefits of fine-tuning the wav2vec 2.0 model by speaker clusters for dysarthric speech recognition.We explore two types of speaker clusters-(1) Speaker feature-based.\n\n(2) Speech impairment severity-based.We have evaluated the performance of these experiments by comparing to a baseline wav2vec 2.0 ASR fine-tuned using only LibriSpeech data.\n\nFrom the various experimental setups, it is observed that fine-tuning the wav2vec 2.0 base model on the SAP dataset yields a notable 36.70% and 25.90% improvement in Word Error Rate (WER) compared to fine-tuning on 100h and 960h of LibriSpeech data, respectively.Error rates for high-severity test speakers are harmed if the training corpus includes only high-severity speakers, but are improved if the training algorithm emphasizes speakers with a low or moderate degree of impairment.Optimum results are achieved using either clusterweighted training (all training data are used, but some are weighted more than others) or a form of multi-task training in which speaker severity level serves as an auxiliary model output.Cluster-weighted and multi-task training give identical low error rates averaged across the entire test set, and both give substantial improvements especially for the test speakers with the most severe impairment.\n\n\nData\n\nThe Speech Accessibility Project (SAP) aims to support research and development in impaired speech recognition by collecting, transcribing, and sharing speech samples from contributors with disabilities.The first partial data release was made available to members of the six participating institutions on 2023-10-05, and is scheduled for release to other researchers on 2024-04-05.We will refer to the SAP 2023-10-05 partial corpus as SAP-1005 throughout this paper.\n\nSAP data sets differ in many ways from existing corpora of impaired speech.First, unlike UA-Speech, Nemours, and TORGO, SAP is designed for speaker-independent ASR.The 2023-10-05 data package includes 253 speakers, of whom 190 are allocated to a training set, 21 to a development set, and 42 to a test set.The development and test sets are each further divided into shared and unshared subsets, depending on whether or not the utterance text was also read by some of the training speakers; all results in this paper report WER using only the unshared subset of the test corpus.Second, the types of impairment in SAP are quite different from those in existing corpora.UA-Speech and TORGO include speakers with spastic or mixed dysarthria as symptoms of cerebral palsy (CP) or amyotrophic lateral sclerosis (ALS).Although SAP will eventually include speakers with CP or ALS [23], the 2023-10-05 data package includes only speakers with Parkinson's disease.It has been demonstrated that even relatively mild Parkinson's disease can cause significant increases in the WER of an ASR [30].Some of these speakers exhibit hypokinetic dysarthria (reduced intelligibility caused by reduced articulatory movement): perceptual ratings by professional speech pathologists using the differential diagnostic scales of [31] indicate that 63 of the 253 speakers have imprecise consonants, while 54 have less than normal intelligibility.Dysphonia (disordered phonation) is a more frequent symptom: 207 of the 253 speakers have monotone pitch or loudness (monopitch or monoloudness), while 243 have speech that is rated as other than the normal level of overall naturalness.\n\nIn order to protect participant privacy, with limited exceptions, participant-provided metadata is not distributed with the corpus.In particular, participant gender is not specified in the corpus distribution.\n\n\nMethods\n\nIn this section, we present the methodologies adopted for finetuning the Wav2Vec 2.0 model on the SAP-1005 corpus, along with the speaker clustering strategies.We first introduce the architecture of the Wav2Vec 2.0 base model and then delve into the fine-tuning and speaker clustering strategies applied to enhance its performance in the context of dysarthric and dysphonic speech.\n\n3.1.Wav2Vec 2.0 pre-trained model Wav2Vec 2.0 [32] is a set of Transformer-based speech recognition models pre-trained using self-supervised learning.The model initiates by processing the raw waveform X of speech audio using a multilayer convolutional neural network (CNN), producing latent audio representations zt of 25ms duration each: zt = CNN(X).These representations are then simultaneously passed through a quantizer and a transformer.The quantizer selects a speech unit qt from a learned inventory of units: qt = Quantizer(zt).Approximately half of the audio representations undergo masking before entering the transformer, which integrates information from the entire audio sequence, resulting in contextualized representations ct: ct = Transformer(zmasked).Finally, the output of the transformer is optimized contrastively to select the appropriate quantized speech units corresponding to the masked positions.\n\nDuring the fine-tuning phase, a randomly initialized new linear projection layer is added on top of the context network to project representation into C classes, which corresponds to the target vocabulary.The optimization process involves minimizing the Connectionist Temporal Classification (CTC) loss LCT C [33]\n\n\nFine-tuning on impaired speech\n\nTo assess the effectiveness of the SAP-1005 corpus in dysarthric speech recognition, we first fine-tune an ASR to SAP data.The wav2vec 2.0 base model, previously pre-trained using Librispeech 960h as described in Section 3.1, is further fine-tuned using the training subset of SAP-1005.Fine-tuning is performed using the fairseq open-source repository1 .\n\n\nSpeaker clustering\n\nMotivated by [27], where the authors observed noticeable enhancements in HMM-based dysathric ASR through selective speaker training based on speaker clusters, in this paper we investigate whether this observation extends to DNN-based speech recognition systems.We extract X-vectors [34], one of the most widely used deep speaker embeddings, using the pretrained VoxCeleb Xvector System 1a2 through kaldi.This system trained on augmented VoxCeleb 1 and VoxCeleb 2 corpus achieves a 3.1% equal error-rate (EER) in the speaker recognition task and outperforms any other previous X-vector systems.The wav2vec 2.0 base system described in Section 3.1 is fine-tuned separately for each speaker cluster in order to create speaker-cluster-dependent ASR.X-vectors are also extracted from the recordings of each speaker in the development and test set.Each speaker in the development or test set is then assigned to the cluster-dependent ASR with the nearest X-vector centroid, which is used to transcribe their speech.\n\n\nSeverity-dependent ASR\n\nClassical papers about hypokinetic dysarthric and dysphonia (e.g., [31]) describe them using a relatively compact set of perceptual features (e.g., monopitch and monoloudness).It is possible that speakers with similar levels of impairment severity may have acoustically similar speech, and that severitydependent ASR models may therefore outperform severityindependent models.Rather than depending on human severity annotations, we measure the impairment severity of a speaker according to the average character error rate (CER) with which the Wav2Vec 2.0 base system fine-tuned on Librispeech 960h transcribes that person's speech.Dividing the 190 training speakers into three equal-sized groups yields CER thresholds of approximately 10% and 20%.However, since there exists considerable inter-speaker variability within the most severe group, i.e., among those individuals with a CER exceeding 20%, an additional threshold at 40% is introduced.Consequently we use four severity levels: very low (VL: < 10% CER), low (L: 10 − 20% CER), median (M: 20 − 40% CER), and high (H: > 40% CER).Table 1 gives the frequency of each severity level.Subsequently, fine-tuning experiments are conducted on a severity basis, utilizing one or multiple clusters of severity.Since the severity level of a development or test speaker cannot be determined without the availability of reference transcriptions, we perform experiments in which every category of dev and test speakers is transcribed using each of the four severity-dependent ASRs, in order to determine whether applying the wrong ASR to a test speaker increases or decreases the resulting WER.\n\n\nFine-tuning with weighted clusters\n\nAs an alternative to training an ASR using data from only a subset of speakers, we also train a set of models that are finetuned using the full training set, but with extra weight placed on the correctness of transcriptions for speakers of a given severity.With n denoting the total number of clusters, the general structure of the loss function is as follows:\nL ctc,total = n k=1 ω k • L ctc,k(1)\nwhere ω k is a hyperparameter specifying the weight given to the k th cluster of training speakers, and L ctc,k is the corresponding CTC loss.\n\n\nMulti-task learning with severity classification\n\nPrevious studies [19] have suggested that, instead of dividing the training data by severity level, dysarthric ASR can be improved by training the ASR using a multi-task training criterion in which the severity level of a speaker is estimated as an auxiliary output of the neural net.Employing the same multitask learning (MTL) strategy on the SAP-1005 corpus, we experiment with an interpolation between the initial transcription loss, Lctc, and the cross-entropy loss of an auxiliary network output estimating impairment severity, Lseve 3 :\nLMT L = ω1 • Lctc + ω2 • Lseve (2)\nThe auxiliary network is a linear transformation of the outputs of the last transformer layer, passed through a logistic sigmoid.Three different placements of the auxiliary network were tested: \"first-token\" (linear transform of the first transformer output), \"max\" (linear transform of the maximum, across time, of each element of the transformer output vector), and \"mean\" (linear transform of the mean, across time, of each element of the transformer output).\n\n\nResults and Discussion\n\nThe evaluation results, as presented in Table 2: WER (%) of Wav2Vec 2.0 base models fine-tuned by different corpora and splits, using speaker clustering with two clusters.The two clusters are described in the Table as \"Male\" and \"Female\" based on post-hoc perceptual evaluation.SA=training data augmented using SpecAugment.X-vector clustering results in clusters of speakers each of whom sounds somewhat like the others in the same cluster.When there are only two clusters, the two clusters seem to naturally divide the training speakers into two genders: post-hoc perceptual evaluation of the speakers in each cluster indicates that the speakers in one cluster are all male, while those in the other are all female, though this cannot be verified because the corpus distribution does not include gender metadata.As shown in Figure 1, average x-vectors for each speaker are well separated between the clusters, and x-vectors computed from each utterance show a clear boundary between those from cluster 1 and those from cluster 2. Table 1 gives detailed number of speakers in each of the two clusters, where the clusters have been labeled \"Male\" and \"Female\" based on post-hoc perceptual evaluation.Based on this finding, we conduct fine-tuning experiments using two speaker clusters.In one experimental setting, SpecAugment [35] is used to increase the amount of training data in each cluster and to make the training data quantities similar in the two clusters.With data augmentation, approximately 151.47 hours of training data are selected for each experiment, aligning with all training data of the SAP-1005 corpus.Table 3: WER (%) of Wav2Vec 2.0 base models fine-tuned by different corpora and splits, with severity clustering.\n\nMatched testing (each test speaker is assigned to the cluster with the closest X-vector centroid) produces much lower WER than mismatched testing (in which each test speaker is assigned to the cluster with the farther X-vector centroid).Specifically, fine-tuning on the male split leads to a 25.90% WER reduction for males, but only 8.6% for females, compared to the system fine-tuned on Librispeech.Conversely, fine-tuning on the female split yields a 17.75% WER reduction for females, but 13.34% for males.However, in contrast to the findings of Christensen et al., [27], where HMM-based speech systems trained by selecting speakers based on speech similarity outperformed those trained on all speakers, utilizing data from all speakers in our experiments led to enhanced model performance both generally and gender-specifically.\n\nThe evaluation results of fine-tuning by severity are presented in Table 3. Starting from a single cluster, we first compare models fine-tuned on the SAP-1005 \"VL,\" \"L\" and \"M+H\" subsets to ensure the amount of training data is comparable.Among these, while fine-tuning on \"VL\" leads to the expected superior performance for \"VL\" in the test split, fine-tuning on \"L\" produces the best WER on every other severity levels except \"VL.\"Furthermore, we evaluate models fine-tuned on \"M\" and \"H\" splits separately.Compared to the \"M+H\" model, the \"M\" model benefits the overall performance, and the performance for test speakers with \"M\" severity.On the other hand, test speakers with \"H\" severity are transcribed least accurately using an ASR fine-tuned using only \"H\" training speakers.The set of \"H\" speakers in the training set contains 12.79 hours of speech, and previous publications suggest that 12.79 hours is sufficient to fine-tune an ASR with low WER [32], therefore we tentatively conclude that the very high WER of the system fine-tuned using \"H\" speakers is caused by their very high interspeaker variability.\n\nIn general, feeding more data to the network leads to better performance, regardless of the severity level.Compared to the model fine-tuned on LibriSpeech 960h, Figure 2 shows the WER reduction of the best performing models fine-tuned with data from 1, 2, 3, or 4 distinct severity levels.While \"L\" is the most powerful among all the models fine-tuned by a single cluster (30.13% overall WER), as we enlarge the training data by combining two of the three major classes, the \"VL+L\" model achieves the best overall WER of 27.51% with an 8.70% relative improvement compared to \"L\" alone.Although adding \"VL\" to \"L\" leads to improvements among all severity levels, the influence decreases as the severity level increases, i.e., the WER reduction decreases from 11.93%, 8.07%, 6.37%, to 3.22% for \"VL,\" \"L,\" \"M,\" and \"H,\" respectively.This further indicates the mismatch between speech of different impairment severity levels.Combining three training groups (\"VL+L+M\") further decreases the WER of individuals with \"M\" and \"H\" sever- Table 4: WER (%) using SAP-1005 unshared test corpus.For weighted fine-tuning, the cluster along with adjusted weight are listed as parameters.For multitask learning, location of the auxiliary severity classifier is listed as a parameter.\n\nity, without hurting performance for those with lower severity, leading to a 26.92% overall test WER.Adding \"H\" on top of \"VL+L+M\" does not further enhance overall performance: there is no WER gain for test speakers in the \"H\" severity class, and WER changes are minimal for speakers in other categories.Table 4 compares cluster-weighted fine-tuning and multitask learning strategies to full-train-set fine-tuning.By adding reasonable weights to the \"L\" class, we achieve our best average WER of 26.53% at ωL = 1.2, while setting ωL = 1.6 yields an improved 59.16% WER for testing group \"H.\"Among all types of pooling layers for severity classification, first-tokenbased multitask learning yields the best overall WER (26.53%), and the best WER for \"H\"-severity test speakers (58.64%).\n\n\nConclusion\n\nThis work 4 investigates the effectiveness of fine-tuning the wav2vec 2.0 model using the 2023-10-05 partial data release of the Speech Accessibility Project.Our experiment demonstrates that fine-tuning using one group of speakers with Parkinson's disease (the SAP-1005 training speakers) substantially reduces WER for other speakers with Parkinson's disease (the SAP-1005 test speakers).Cluster-based fine-tuning does not further improve performance, but multi-task training, in which speaker severity level is an auxiliary output of the ASR, gives small additional benefits in performance, especially for test speakers with the most severe impairments.\n\nFigure 1 :\n1\nFigure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker level; Bottom: utterance level.\n\n\nFigure 2 :\n2\nFigure 2: Relative improvements per severity level of the best performing models fine-tuned by 1, 2, 3 and 4 severity classes of the SAP-1005 corpus, compared to the model fine-tuned by 960 hours of LibriSpeech.\n\n\nTable 1 :\n1\non labeled speech data.With a Transformer lan-Number of speakers in the Speech Accessibility\nSplitAllGenderSeverity#spk|durM FVL L M HTrain 190|151.47h109 8170 54 48 18Dev21|23.32h10118742Test42|39.84h261613 13 115Project Corpus, 2023-10-05 release. Gender and impair-ment severity are automatically estimated using methods de-scribed in the text.guage model, fine-tuning the Wav2Vec 2.0 base model with thecomplete 960 hours of labeled LibriSpeech data yielded a 1.8%WER on the LibriSpeech test-clean set.\n\nTable 2\n2, demonstrate aremarkable improvement in Word Error Rate (WER) when fine-tuning on SAP-1005 compared to LibriSpeech. ASR fine-tunedusing the SAP-1005 training set achieves 36.70% less WERthan ASR fine-tuned using Librispeech 100h, and 25.90% lessthan ASR fine-tuned using LibriSpeech 960h. Unlike most pre-vious published results for impaired ASR, this is not speaker-dependent training: These results demonstrate that fine-tuningusing one set of speakers with Parkinson's (the SAP-1005 train-ing set) substantially reduces WER for another set of speakerswith Parkinson's (the SAP-1005 test set).2\n3Empirically, ω 1 = ω 2 = 1\n\n\n\n\n.72 36.5761.4985.88 960h 36.33 18.36 30.23 54.16 79.71 SAP-1005 All 26.92 13.58 21.15 41.10 60.34 VL+L+M 26.92 13.53 20.79 41.58 60.41 VL+L 27.51 13.64 21.08 42.5762.93 L+M+H 29.00 15.71 23.48 43.04 62.06 L+M 28.75 15.30 22.72 43.32 62.45\nFine-tuningtestWERCorpusSplitAllVLLMHLibriSpeech 100h 42.53 23VL 30.97 14.46 24.15 48.89 70.68L30.13 15.83 23.52 46.02 65.50M+H33.90 19.81 28.98 48.28 66.99M32.92 18.74 26.90 48.06 68.00H51.70 37.56 46.51 64.10 82.39\nhttps://github.com/facebookresearch/fairseq\nhttps://kaldi-asr.org/models/m7\nThis work utilizes resources supported by the National Science Foundation's Major Research Instrumentation program, grant #1725729, as well as the University of Illinois at Urbana-Champaign[36] \n\nVoice recognition device as a computer interface for motor and speech impaired people. 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S Liu, M Geng, S Hu, X Xie, M Cui, J Yu, H Meng, IEEE/ACM TASLP. 292021\n\nExploiting cross-domain visual feature generation for disordered speech recognition. S Liu, X Xie, J Yu, S Hu, M Geng, R Su, H Meng, Proc. Interspeech. ISCA. Interspeech. ISCA2020\n\nStudy of the performance of automatic speech recognition systems in speakers with parkinson's disease. L Moro-Velazquez, J Cho, S Watanabe, M A Hasegawa-Johnson, O Scharenborg, H Kim, N Dehak, Proc. Interspeech 2019. ISCA. Interspeech 2019. ISCA2019\n\nDifferential diagnostic patterns of dysarthria. F L Darley, A E Aronson, J R Brown, JSLHR. 121969\n\nwav2vec 2.0: A framework for self-supervised learning of speech representations. A Baevski, Y Zhou, A Mohamed, M Auli, Advances in neural information processing systems. 202033460\n\nConnectionist temporal classification: labelling unsegmented sequence data with recurrent neural networks. A Graves, S Fernández, F Gomez, J Schmidhuber, Proceedings of the 23rd ICML. the 23rd ICML2006\n\nX-vectors: Robust dnn embeddings for speaker recognition. D Snyder, D Garcia-Romero, G Sell, D Povey, S Khudanpur, IEEE ICASSP. 2018. 2018\n\nSpecAugment: A Simple Data Augmentation Method for Automatic Speech Recognition. D S Park, W Chan, Y Zhang, C.-C Chiu, B Zoph, E D Cubuk, Q V Le, Proc. Interspeech 2019. ISCA. Interspeech 2019. ISCA2019\n\nHal: Computer system for scalable deep learning. V Kindratenko, D Mu, Y Zhan, J Maloney, S H Hashemi, 10.1145/3311790.3396649Practice and Experience in Advanced Research Computing, ser. PEARC '20. New York, NY, USAAssociation for Computing Machinery2020\n"},"corpus_id":{"kind":"number","value":272352029,"string":"272,352,029"},"external_ids":{"kind":"string","value":"{\n \"arxiv\": \"2409.19818\",\n \"mag\": null,\n \"acl\": null,\n \"pubmed\": null,\n \"pubmedcentral\": null,\n \"dblp\": \"journals/corr/abs-2409-19818\",\n \"doi\": \"10.21437/interspeech.2024-1969\"\n}"},"source":{"kind":"string","value":"{\n \"pdf_urls\": [\n \"https://export.arxiv.org/pdf/2409.19818v1.pdf\"\n ],\n \"pdf_sha\": \"ab8fcce92679cb03c802044e080a36d2c8fe107d\",\n \"open_access\": {\n \"license\": null,\n \"url\": null,\n \"status\": \"CLOSED\"\n }\n}"},"title":{"kind":"string","value":"Fine-Tuning Automatic Speech Recognition for People with Parkinson's: An Effective Strategy for Enhancing Speech Technology Accessibility"},"authors":{"kind":"list like","value":["Xiuwen Zheng xiuwenz2@illinois.edu \nDepartment of Electrical and Computer Engineering\nUniversity of Illinois Urbana-Champaign","Bornali Phukon bornalip@illinois.edu \nDepartment of Electrical and Computer Engineering\nUniversity of Illinois Urbana-Champaign","Mark Hasegawa-Johnson \nDepartment of Electrical and Computer Engineering\nUniversity of Illinois Urbana-Champaign"],"string":"[\n \"Xiuwen Zheng xiuwenz2@illinois.edu \\nDepartment of Electrical and Computer Engineering\\nUniversity of Illinois Urbana-Champaign\",\n \"Bornali Phukon bornalip@illinois.edu \\nDepartment of Electrical and Computer Engineering\\nUniversity of Illinois Urbana-Champaign\",\n \"Mark Hasegawa-Johnson \\nDepartment of Electrical and Computer Engineering\\nUniversity of Illinois Urbana-Champaign\"\n]","isConversational":false},"abstract":{"kind":"string","value":"This paper enhances dysarthric and dysphonic speech recognition by fine-tuning pretrained automatic speech recognition (ASR) models on the 2023-10-05 data package of the Speech Accessibility Project (SAP), which contains the speech of 253 people with Parkinson's disease.Experiments tested methods that have been effective for Cerebral Palsy, including the use of speaker clustering and severity-dependent models, weighted fine-tuning, and multi-task learning.Best results were obtained using a multi-task learning model, in which the ASR is trained to produce an estimate of the speaker's impairment severity as an auxiliary output.The resulting word error rates are considerably improved relative to a baseline model fine-tuned using only Librispeech data, with word error rate improvements of 37.62% and 26.97% compared to fine-tuning on 100h and 960h of LibriSpeech data, respectively."},"sections":{"kind":"list like","value":[{"title":"Introduction","content":"Speech recognition technology has revolutionized how we interact with digital devices, and can be an especially useful computer input modality for people with motor disorders [1,2].However, many individuals with motor disorders face challenges in effectively using these devices due to dysarthria and dysphonia, i.e., impaired articulation and phonation caused by neuromotor disorder [3,4].\nDespite ongoing efforts by researchers [5,6,7,8,9,10,11,12], current ASR systems encounter notable challenges in accurately recognizing dysarthric and dysphonic impaired speech primarily due to differences between impaired speech and typical speech and the unavailability of adequate training data.Initiatives like the Nemours database of dysarthric speech [13], the Universal Access speech corpus [14], the TORGO database of acoustic and articulatory speech [15], the Neurovoz [16] and GITA [17] Spanish-language corpora of speech with Parkinson's, and Project Euphonia [18] have been instrumental in advancing impaired speech recognition.However, while dysarthric ASR error rates have dropped by a factor of three in the past fifteen years ([19] vs. [20]), non-dysarthric ASR error rates have dropped by a factor of five over the same period ([21] vs. [22]).The accelerated enhancements in nondysarthric ASR can be partly credited to the greater accessibility of standardized data for both training and testing.To address these limitations, the Speech Accessibility Project (SAP [23]) is collecting, and distributing to researchers, a large corpus of impaired speech.In this paper, we report the results of fine-tuning ASR using the first partial release of SAP data.\nIn the context of impaired speech recognition, fine-tuning a pre-trained model using transcribed impaired speech is a widely explored technique that has shown promising results for speech accessibility [24].In particular, the wav2vec 2.0 base model has been fine-tuned to UA-Speech using low-rank adaptation [25] and using system fusion methods in which wav2vec rescores a conformer or TDNN [26].Auxiliary speaker attributes can improve dysarthric ASR, e.g., hidden Markov model (HMM) ASR using UA-Speech was improved by first clustering speaker attribute vectors, then training cluster-dependent ASR for the speakers in each cluster [27].Deep neural network (DNN) ASR is improved by providing automatic dysarthria severity estimates as auxiliary inputs [28] or outputs [19] of the ASR, or by providing automatically inferred estimates of the visual [29] or articulatory [28] features corresponding to an acoustic dysarthric utterance.Inspired by these results, we aim to explore the potential benefits of fine-tuning the wav2vec 2.0 model by speaker clusters for dysarthric speech recognition.We explore two types of speaker clusters-(1) Speaker feature-based.\n(2) Speech impairment severity-based.We have evaluated the performance of these experiments by comparing to a baseline wav2vec 2.0 ASR fine-tuned using only LibriSpeech data.\nFrom the various experimental setups, it is observed that fine-tuning the wav2vec 2.0 base model on the SAP dataset yields a notable 36.70% and 25.90% improvement in Word Error Rate (WER) compared to fine-tuning on 100h and 960h of LibriSpeech data, respectively.Error rates for high-severity test speakers are harmed if the training corpus includes only high-severity speakers, but are improved if the training algorithm emphasizes speakers with a low or moderate degree of impairment.Optimum results are achieved using either clusterweighted training (all training data are used, but some are weighted more than others) or a form of multi-task training in which speaker severity level serves as an auxiliary model output.Cluster-weighted and multi-task training give identical low error rates averaged across the entire test set, and both give substantial improvements especially for the test speakers with the most severe impairment."},{"title":"Data","content":"The Speech Accessibility Project (SAP) aims to support research and development in impaired speech recognition by collecting, transcribing, and sharing speech samples from contributors with disabilities.The first partial data release was made available to members of the six participating institutions on 2023-10-05, and is scheduled for release to other researchers on 2024-04-05.We will refer to the SAP 2023-10-05 partial corpus as SAP-1005 throughout this paper.\nSAP data sets differ in many ways from existing corpora of impaired speech.First, unlike UA-Speech, Nemours, and TORGO, SAP is designed for speaker-independent ASR.The 2023-10-05 data package includes 253 speakers, of whom 190 are allocated to a training set, 21 to a development set, and 42 to a test set.The development and test sets are each further divided into shared and unshared subsets, depending on whether or not the utterance text was also read by some of the training speakers; all results in this paper report WER using only the unshared subset of the test corpus.Second, the types of impairment in SAP are quite different from those in existing corpora.UA-Speech and TORGO include speakers with spastic or mixed dysarthria as symptoms of cerebral palsy (CP) or amyotrophic lateral sclerosis (ALS).Although SAP will eventually include speakers with CP or ALS [23], the 2023-10-05 data package includes only speakers with Parkinson's disease.It has been demonstrated that even relatively mild Parkinson's disease can cause significant increases in the WER of an ASR [30].Some of these speakers exhibit hypokinetic dysarthria (reduced intelligibility caused by reduced articulatory movement): perceptual ratings by professional speech pathologists using the differential diagnostic scales of [31] indicate that 63 of the 253 speakers have imprecise consonants, while 54 have less than normal intelligibility.Dysphonia (disordered phonation) is a more frequent symptom: 207 of the 253 speakers have monotone pitch or loudness (monopitch or monoloudness), while 243 have speech that is rated as other than the normal level of overall naturalness.\nIn order to protect participant privacy, with limited exceptions, participant-provided metadata is not distributed with the corpus.In particular, participant gender is not specified in the corpus distribution."},{"title":"Methods","content":"In this section, we present the methodologies adopted for finetuning the Wav2Vec 2.0 model on the SAP-1005 corpus, along with the speaker clustering strategies.We first introduce the architecture of the Wav2Vec 2.0 base model and then delve into the fine-tuning and speaker clustering strategies applied to enhance its performance in the context of dysarthric and dysphonic speech.\n3.1.Wav2Vec 2.0 pre-trained model Wav2Vec 2.0 [32] is a set of Transformer-based speech recognition models pre-trained using self-supervised learning.The model initiates by processing the raw waveform X of speech audio using a multilayer convolutional neural network (CNN), producing latent audio representations zt of 25ms duration each: zt = CNN(X).These representations are then simultaneously passed through a quantizer and a transformer.The quantizer selects a speech unit qt from a learned inventory of units: qt = Quantizer(zt).Approximately half of the audio representations undergo masking before entering the transformer, which integrates information from the entire audio sequence, resulting in contextualized representations ct: ct = Transformer(zmasked).Finally, the output of the transformer is optimized contrastively to select the appropriate quantized speech units corresponding to the masked positions.\nDuring the fine-tuning phase, a randomly initialized new linear projection layer is added on top of the context network to project representation into C classes, which corresponds to the target vocabulary.The optimization process involves minimizing the Connectionist Temporal Classification (CTC) loss LCT C [33]"},{"title":"Fine-tuning on impaired speech","content":"To assess the effectiveness of the SAP-1005 corpus in dysarthric speech recognition, we first fine-tune an ASR to SAP data.The wav2vec 2.0 base model, previously pre-trained using Librispeech 960h as described in Section 3.1, is further fine-tuned using the training subset of SAP-1005.Fine-tuning is performed using the fairseq open-source repository1 ."},{"title":"Speaker clustering","content":"Motivated by [27], where the authors observed noticeable enhancements in HMM-based dysathric ASR through selective speaker training based on speaker clusters, in this paper we investigate whether this observation extends to DNN-based speech recognition systems.We extract X-vectors [34], one of the most widely used deep speaker embeddings, using the pretrained VoxCeleb Xvector System 1a2 through kaldi.This system trained on augmented VoxCeleb 1 and VoxCeleb 2 corpus achieves a 3.1% equal error-rate (EER) in the speaker recognition task and outperforms any other previous X-vector systems.The wav2vec 2.0 base system described in Section 3.1 is fine-tuned separately for each speaker cluster in order to create speaker-cluster-dependent ASR.X-vectors are also extracted from the recordings of each speaker in the development and test set.Each speaker in the development or test set is then assigned to the cluster-dependent ASR with the nearest X-vector centroid, which is used to transcribe their speech."},{"title":"Severity-dependent ASR","content":"Classical papers about hypokinetic dysarthric and dysphonia (e.g., [31]) describe them using a relatively compact set of perceptual features (e.g., monopitch and monoloudness).It is possible that speakers with similar levels of impairment severity may have acoustically similar speech, and that severitydependent ASR models may therefore outperform severityindependent models.Rather than depending on human severity annotations, we measure the impairment severity of a speaker according to the average character error rate (CER) with which the Wav2Vec 2.0 base system fine-tuned on Librispeech 960h transcribes that person's speech.Dividing the 190 training speakers into three equal-sized groups yields CER thresholds of approximately 10% and 20%.However, since there exists considerable inter-speaker variability within the most severe group, i.e., among those individuals with a CER exceeding 20%, an additional threshold at 40% is introduced.Consequently we use four severity levels: very low (VL: < 10% CER), low (L: 10 − 20% CER), median (M: 20 − 40% CER), and high (H: > 40% CER).Table 1 gives the frequency of each severity level.Subsequently, fine-tuning experiments are conducted on a severity basis, utilizing one or multiple clusters of severity.Since the severity level of a development or test speaker cannot be determined without the availability of reference transcriptions, we perform experiments in which every category of dev and test speakers is transcribed using each of the four severity-dependent ASRs, in order to determine whether applying the wrong ASR to a test speaker increases or decreases the resulting WER."},{"title":"Fine-tuning with weighted clusters","content":"As an alternative to training an ASR using data from only a subset of speakers, we also train a set of models that are finetuned using the full training set, but with extra weight placed on the correctness of transcriptions for speakers of a given severity.With n denoting the total number of clusters, the general structure of the loss function is as follows:\nwhere ω k is a hyperparameter specifying the weight given to the k th cluster of training speakers, and L ctc,k is the corresponding CTC loss."},{"title":"Multi-task learning with severity classification","content":"Previous studies [19] have suggested that, instead of dividing the training data by severity level, dysarthric ASR can be improved by training the ASR using a multi-task training criterion in which the severity level of a speaker is estimated as an auxiliary output of the neural net.Employing the same multitask learning (MTL) strategy on the SAP-1005 corpus, we experiment with an interpolation between the initial transcription loss, Lctc, and the cross-entropy loss of an auxiliary network output estimating impairment severity, Lseve 3 :\nThe auxiliary network is a linear transformation of the outputs of the last transformer layer, passed through a logistic sigmoid.Three different placements of the auxiliary network were tested: \"first-token\" (linear transform of the first transformer output), \"max\" (linear transform of the maximum, across time, of each element of the transformer output vector), and \"mean\" (linear transform of the mean, across time, of each element of the transformer output)."},{"title":"Results and Discussion","content":"The evaluation results, as presented in Table 2: WER (%) of Wav2Vec 2.0 base models fine-tuned by different corpora and splits, using speaker clustering with two clusters.The two clusters are described in the Table as \"Male\" and \"Female\" based on post-hoc perceptual evaluation.SA=training data augmented using SpecAugment.X-vector clustering results in clusters of speakers each of whom sounds somewhat like the others in the same cluster.When there are only two clusters, the two clusters seem to naturally divide the training speakers into two genders: post-hoc perceptual evaluation of the speakers in each cluster indicates that the speakers in one cluster are all male, while those in the other are all female, though this cannot be verified because the corpus distribution does not include gender metadata.As shown in Figure 1, average x-vectors for each speaker are well separated between the clusters, and x-vectors computed from each utterance show a clear boundary between those from cluster 1 and those from cluster 2. Table 1 gives detailed number of speakers in each of the two clusters, where the clusters have been labeled \"Male\" and \"Female\" based on post-hoc perceptual evaluation.Based on this finding, we conduct fine-tuning experiments using two speaker clusters.In one experimental setting, SpecAugment [35] is used to increase the amount of training data in each cluster and to make the training data quantities similar in the two clusters.With data augmentation, approximately 151.47 hours of training data are selected for each experiment, aligning with all training data of the SAP-1005 corpus.Table 3: WER (%) of Wav2Vec 2.0 base models fine-tuned by different corpora and splits, with severity clustering.\nMatched testing (each test speaker is assigned to the cluster with the closest X-vector centroid) produces much lower WER than mismatched testing (in which each test speaker is assigned to the cluster with the farther X-vector centroid).Specifically, fine-tuning on the male split leads to a 25.90% WER reduction for males, but only 8.6% for females, compared to the system fine-tuned on Librispeech.Conversely, fine-tuning on the female split yields a 17.75% WER reduction for females, but 13.34% for males.However, in contrast to the findings of Christensen et al., [27], where HMM-based speech systems trained by selecting speakers based on speech similarity outperformed those trained on all speakers, utilizing data from all speakers in our experiments led to enhanced model performance both generally and gender-specifically.\nThe evaluation results of fine-tuning by severity are presented in Table 3. Starting from a single cluster, we first compare models fine-tuned on the SAP-1005 \"VL,\" \"L\" and \"M+H\" subsets to ensure the amount of training data is comparable.Among these, while fine-tuning on \"VL\" leads to the expected superior performance for \"VL\" in the test split, fine-tuning on \"L\" produces the best WER on every other severity levels except \"VL.\"Furthermore, we evaluate models fine-tuned on \"M\" and \"H\" splits separately.Compared to the \"M+H\" model, the \"M\" model benefits the overall performance, and the performance for test speakers with \"M\" severity.On the other hand, test speakers with \"H\" severity are transcribed least accurately using an ASR fine-tuned using only \"H\" training speakers.The set of \"H\" speakers in the training set contains 12.79 hours of speech, and previous publications suggest that 12.79 hours is sufficient to fine-tune an ASR with low WER [32], therefore we tentatively conclude that the very high WER of the system fine-tuned using \"H\" speakers is caused by their very high interspeaker variability.\nIn general, feeding more data to the network leads to better performance, regardless of the severity level.Compared to the model fine-tuned on LibriSpeech 960h, Figure 2 shows the WER reduction of the best performing models fine-tuned with data from 1, 2, 3, or 4 distinct severity levels.While \"L\" is the most powerful among all the models fine-tuned by a single cluster (30.13% overall WER), as we enlarge the training data by combining two of the three major classes, the \"VL+L\" model achieves the best overall WER of 27.51% with an 8.70% relative improvement compared to \"L\" alone.Although adding \"VL\" to \"L\" leads to improvements among all severity levels, the influence decreases as the severity level increases, i.e., the WER reduction decreases from 11.93%, 8.07%, 6.37%, to 3.22% for \"VL,\" \"L,\" \"M,\" and \"H,\" respectively.This further indicates the mismatch between speech of different impairment severity levels.Combining three training groups (\"VL+L+M\") further decreases the WER of individuals with \"M\" and \"H\" sever- Table 4: WER (%) using SAP-1005 unshared test corpus.For weighted fine-tuning, the cluster along with adjusted weight are listed as parameters.For multitask learning, location of the auxiliary severity classifier is listed as a parameter.\nity, without hurting performance for those with lower severity, leading to a 26.92% overall test WER.Adding \"H\" on top of \"VL+L+M\" does not further enhance overall performance: there is no WER gain for test speakers in the \"H\" severity class, and WER changes are minimal for speakers in other categories.Table 4 compares cluster-weighted fine-tuning and multitask learning strategies to full-train-set fine-tuning.By adding reasonable weights to the \"L\" class, we achieve our best average WER of 26.53% at ωL = 1.2, while setting ωL = 1.6 yields an improved 59.16% WER for testing group \"H.\"Among all types of pooling layers for severity classification, first-tokenbased multitask learning yields the best overall WER (26.53%), and the best WER for \"H\"-severity test speakers (58.64%)."},{"title":"Conclusion","content":"This work 4 investigates the effectiveness of fine-tuning the wav2vec 2.0 model using the 2023-10-05 partial data release of the Speech Accessibility Project.Our experiment demonstrates that fine-tuning using one group of speakers with Parkinson's disease (the SAP-1005 training speakers) substantially reduces WER for other speakers with Parkinson's disease (the SAP-1005 test speakers).Cluster-based fine-tuning does not further improve performance, but multi-task training, in which speaker severity level is an auxiliary output of the ASR, gives small additional benefits in performance, especially for test speakers with the most severe impairments."},{"title":"Figure 1 :","content":"Figure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker level; Bottom: utterance level."},{"title":"Figure 2 :","content":"Figure 2: Relative improvements per severity level of the best performing models fine-tuned by 1, 2, 3 and 4 severity classes of the SAP-1005 corpus, compared to the model fine-tuned by 960 hours of LibriSpeech."},{"title":"Table 1 :","content":"on labeled speech data.With a Transformer lan-Number of speakers in the Speech Accessibility"},{"title":"Table 2","content":"3Empirically, ω 1 = ω 2 = 1\n.72 36.5761.4985.88 960h 36.33 18.36 30.23 54.16 79.71 SAP-1005 All 26.92 13.58 21.15 41.10 60.34 VL+L+M 26.92 13.53 20.79 41.58 60.41 VL+L 27.51 13.64 21.08 42.5762.93 L+M+H 29.00 15.71 23.48 43.04 62.06 L+M 28.75 15.30 22.72 43.32 62.45"}],"string":"[\n {\n \"title\": \"Introduction\",\n \"content\": \"Speech recognition technology has revolutionized how we interact with digital devices, and can be an especially useful computer input modality for people with motor disorders [1,2].However, many individuals with motor disorders face challenges in effectively using these devices due to dysarthria and dysphonia, i.e., impaired articulation and phonation caused by neuromotor disorder [3,4].\\nDespite ongoing efforts by researchers [5,6,7,8,9,10,11,12], current ASR systems encounter notable challenges in accurately recognizing dysarthric and dysphonic impaired speech primarily due to differences between impaired speech and typical speech and the unavailability of adequate training data.Initiatives like the Nemours database of dysarthric speech [13], the Universal Access speech corpus [14], the TORGO database of acoustic and articulatory speech [15], the Neurovoz [16] and GITA [17] Spanish-language corpora of speech with Parkinson's, and Project Euphonia [18] have been instrumental in advancing impaired speech recognition.However, while dysarthric ASR error rates have dropped by a factor of three in the past fifteen years ([19] vs. [20]), non-dysarthric ASR error rates have dropped by a factor of five over the same period ([21] vs. [22]).The accelerated enhancements in nondysarthric ASR can be partly credited to the greater accessibility of standardized data for both training and testing.To address these limitations, the Speech Accessibility Project (SAP [23]) is collecting, and distributing to researchers, a large corpus of impaired speech.In this paper, we report the results of fine-tuning ASR using the first partial release of SAP data.\\nIn the context of impaired speech recognition, fine-tuning a pre-trained model using transcribed impaired speech is a widely explored technique that has shown promising results for speech accessibility [24].In particular, the wav2vec 2.0 base model has been fine-tuned to UA-Speech using low-rank adaptation [25] and using system fusion methods in which wav2vec rescores a conformer or TDNN [26].Auxiliary speaker attributes can improve dysarthric ASR, e.g., hidden Markov model (HMM) ASR using UA-Speech was improved by first clustering speaker attribute vectors, then training cluster-dependent ASR for the speakers in each cluster [27].Deep neural network (DNN) ASR is improved by providing automatic dysarthria severity estimates as auxiliary inputs [28] or outputs [19] of the ASR, or by providing automatically inferred estimates of the visual [29] or articulatory [28] features corresponding to an acoustic dysarthric utterance.Inspired by these results, we aim to explore the potential benefits of fine-tuning the wav2vec 2.0 model by speaker clusters for dysarthric speech recognition.We explore two types of speaker clusters-(1) Speaker feature-based.\\n(2) Speech impairment severity-based.We have evaluated the performance of these experiments by comparing to a baseline wav2vec 2.0 ASR fine-tuned using only LibriSpeech data.\\nFrom the various experimental setups, it is observed that fine-tuning the wav2vec 2.0 base model on the SAP dataset yields a notable 36.70% and 25.90% improvement in Word Error Rate (WER) compared to fine-tuning on 100h and 960h of LibriSpeech data, respectively.Error rates for high-severity test speakers are harmed if the training corpus includes only high-severity speakers, but are improved if the training algorithm emphasizes speakers with a low or moderate degree of impairment.Optimum results are achieved using either clusterweighted training (all training data are used, but some are weighted more than others) or a form of multi-task training in which speaker severity level serves as an auxiliary model output.Cluster-weighted and multi-task training give identical low error rates averaged across the entire test set, and both give substantial improvements especially for the test speakers with the most severe impairment.\"\n },\n {\n \"title\": \"Data\",\n \"content\": \"The Speech Accessibility Project (SAP) aims to support research and development in impaired speech recognition by collecting, transcribing, and sharing speech samples from contributors with disabilities.The first partial data release was made available to members of the six participating institutions on 2023-10-05, and is scheduled for release to other researchers on 2024-04-05.We will refer to the SAP 2023-10-05 partial corpus as SAP-1005 throughout this paper.\\nSAP data sets differ in many ways from existing corpora of impaired speech.First, unlike UA-Speech, Nemours, and TORGO, SAP is designed for speaker-independent ASR.The 2023-10-05 data package includes 253 speakers, of whom 190 are allocated to a training set, 21 to a development set, and 42 to a test set.The development and test sets are each further divided into shared and unshared subsets, depending on whether or not the utterance text was also read by some of the training speakers; all results in this paper report WER using only the unshared subset of the test corpus.Second, the types of impairment in SAP are quite different from those in existing corpora.UA-Speech and TORGO include speakers with spastic or mixed dysarthria as symptoms of cerebral palsy (CP) or amyotrophic lateral sclerosis (ALS).Although SAP will eventually include speakers with CP or ALS [23], the 2023-10-05 data package includes only speakers with Parkinson's disease.It has been demonstrated that even relatively mild Parkinson's disease can cause significant increases in the WER of an ASR [30].Some of these speakers exhibit hypokinetic dysarthria (reduced intelligibility caused by reduced articulatory movement): perceptual ratings by professional speech pathologists using the differential diagnostic scales of [31] indicate that 63 of the 253 speakers have imprecise consonants, while 54 have less than normal intelligibility.Dysphonia (disordered phonation) is a more frequent symptom: 207 of the 253 speakers have monotone pitch or loudness (monopitch or monoloudness), while 243 have speech that is rated as other than the normal level of overall naturalness.\\nIn order to protect participant privacy, with limited exceptions, participant-provided metadata is not distributed with the corpus.In particular, participant gender is not specified in the corpus distribution.\"\n },\n {\n \"title\": \"Methods\",\n \"content\": \"In this section, we present the methodologies adopted for finetuning the Wav2Vec 2.0 model on the SAP-1005 corpus, along with the speaker clustering strategies.We first introduce the architecture of the Wav2Vec 2.0 base model and then delve into the fine-tuning and speaker clustering strategies applied to enhance its performance in the context of dysarthric and dysphonic speech.\\n3.1.Wav2Vec 2.0 pre-trained model Wav2Vec 2.0 [32] is a set of Transformer-based speech recognition models pre-trained using self-supervised learning.The model initiates by processing the raw waveform X of speech audio using a multilayer convolutional neural network (CNN), producing latent audio representations zt of 25ms duration each: zt = CNN(X).These representations are then simultaneously passed through a quantizer and a transformer.The quantizer selects a speech unit qt from a learned inventory of units: qt = Quantizer(zt).Approximately half of the audio representations undergo masking before entering the transformer, which integrates information from the entire audio sequence, resulting in contextualized representations ct: ct = Transformer(zmasked).Finally, the output of the transformer is optimized contrastively to select the appropriate quantized speech units corresponding to the masked positions.\\nDuring the fine-tuning phase, a randomly initialized new linear projection layer is added on top of the context network to project representation into C classes, which corresponds to the target vocabulary.The optimization process involves minimizing the Connectionist Temporal Classification (CTC) loss LCT C [33]\"\n },\n {\n \"title\": \"Fine-tuning on impaired speech\",\n \"content\": \"To assess the effectiveness of the SAP-1005 corpus in dysarthric speech recognition, we first fine-tune an ASR to SAP data.The wav2vec 2.0 base model, previously pre-trained using Librispeech 960h as described in Section 3.1, is further fine-tuned using the training subset of SAP-1005.Fine-tuning is performed using the fairseq open-source repository1 .\"\n },\n {\n \"title\": \"Speaker clustering\",\n \"content\": \"Motivated by [27], where the authors observed noticeable enhancements in HMM-based dysathric ASR through selective speaker training based on speaker clusters, in this paper we investigate whether this observation extends to DNN-based speech recognition systems.We extract X-vectors [34], one of the most widely used deep speaker embeddings, using the pretrained VoxCeleb Xvector System 1a2 through kaldi.This system trained on augmented VoxCeleb 1 and VoxCeleb 2 corpus achieves a 3.1% equal error-rate (EER) in the speaker recognition task and outperforms any other previous X-vector systems.The wav2vec 2.0 base system described in Section 3.1 is fine-tuned separately for each speaker cluster in order to create speaker-cluster-dependent ASR.X-vectors are also extracted from the recordings of each speaker in the development and test set.Each speaker in the development or test set is then assigned to the cluster-dependent ASR with the nearest X-vector centroid, which is used to transcribe their speech.\"\n },\n {\n \"title\": \"Severity-dependent ASR\",\n \"content\": \"Classical papers about hypokinetic dysarthric and dysphonia (e.g., [31]) describe them using a relatively compact set of perceptual features (e.g., monopitch and monoloudness).It is possible that speakers with similar levels of impairment severity may have acoustically similar speech, and that severitydependent ASR models may therefore outperform severityindependent models.Rather than depending on human severity annotations, we measure the impairment severity of a speaker according to the average character error rate (CER) with which the Wav2Vec 2.0 base system fine-tuned on Librispeech 960h transcribes that person's speech.Dividing the 190 training speakers into three equal-sized groups yields CER thresholds of approximately 10% and 20%.However, since there exists considerable inter-speaker variability within the most severe group, i.e., among those individuals with a CER exceeding 20%, an additional threshold at 40% is introduced.Consequently we use four severity levels: very low (VL: < 10% CER), low (L: 10 − 20% CER), median (M: 20 − 40% CER), and high (H: > 40% CER).Table 1 gives the frequency of each severity level.Subsequently, fine-tuning experiments are conducted on a severity basis, utilizing one or multiple clusters of severity.Since the severity level of a development or test speaker cannot be determined without the availability of reference transcriptions, we perform experiments in which every category of dev and test speakers is transcribed using each of the four severity-dependent ASRs, in order to determine whether applying the wrong ASR to a test speaker increases or decreases the resulting WER.\"\n },\n {\n \"title\": \"Fine-tuning with weighted clusters\",\n \"content\": \"As an alternative to training an ASR using data from only a subset of speakers, we also train a set of models that are finetuned using the full training set, but with extra weight placed on the correctness of transcriptions for speakers of a given severity.With n denoting the total number of clusters, the general structure of the loss function is as follows:\\nwhere ω k is a hyperparameter specifying the weight given to the k th cluster of training speakers, and L ctc,k is the corresponding CTC loss.\"\n },\n {\n \"title\": \"Multi-task learning with severity classification\",\n \"content\": \"Previous studies [19] have suggested that, instead of dividing the training data by severity level, dysarthric ASR can be improved by training the ASR using a multi-task training criterion in which the severity level of a speaker is estimated as an auxiliary output of the neural net.Employing the same multitask learning (MTL) strategy on the SAP-1005 corpus, we experiment with an interpolation between the initial transcription loss, Lctc, and the cross-entropy loss of an auxiliary network output estimating impairment severity, Lseve 3 :\\nThe auxiliary network is a linear transformation of the outputs of the last transformer layer, passed through a logistic sigmoid.Three different placements of the auxiliary network were tested: \\\"first-token\\\" (linear transform of the first transformer output), \\\"max\\\" (linear transform of the maximum, across time, of each element of the transformer output vector), and \\\"mean\\\" (linear transform of the mean, across time, of each element of the transformer output).\"\n },\n {\n \"title\": \"Results and Discussion\",\n \"content\": \"The evaluation results, as presented in Table 2: WER (%) of Wav2Vec 2.0 base models fine-tuned by different corpora and splits, using speaker clustering with two clusters.The two clusters are described in the Table as \\\"Male\\\" and \\\"Female\\\" based on post-hoc perceptual evaluation.SA=training data augmented using SpecAugment.X-vector clustering results in clusters of speakers each of whom sounds somewhat like the others in the same cluster.When there are only two clusters, the two clusters seem to naturally divide the training speakers into two genders: post-hoc perceptual evaluation of the speakers in each cluster indicates that the speakers in one cluster are all male, while those in the other are all female, though this cannot be verified because the corpus distribution does not include gender metadata.As shown in Figure 1, average x-vectors for each speaker are well separated between the clusters, and x-vectors computed from each utterance show a clear boundary between those from cluster 1 and those from cluster 2. Table 1 gives detailed number of speakers in each of the two clusters, where the clusters have been labeled \\\"Male\\\" and \\\"Female\\\" based on post-hoc perceptual evaluation.Based on this finding, we conduct fine-tuning experiments using two speaker clusters.In one experimental setting, SpecAugment [35] is used to increase the amount of training data in each cluster and to make the training data quantities similar in the two clusters.With data augmentation, approximately 151.47 hours of training data are selected for each experiment, aligning with all training data of the SAP-1005 corpus.Table 3: WER (%) of Wav2Vec 2.0 base models fine-tuned by different corpora and splits, with severity clustering.\\nMatched testing (each test speaker is assigned to the cluster with the closest X-vector centroid) produces much lower WER than mismatched testing (in which each test speaker is assigned to the cluster with the farther X-vector centroid).Specifically, fine-tuning on the male split leads to a 25.90% WER reduction for males, but only 8.6% for females, compared to the system fine-tuned on Librispeech.Conversely, fine-tuning on the female split yields a 17.75% WER reduction for females, but 13.34% for males.However, in contrast to the findings of Christensen et al., [27], where HMM-based speech systems trained by selecting speakers based on speech similarity outperformed those trained on all speakers, utilizing data from all speakers in our experiments led to enhanced model performance both generally and gender-specifically.\\nThe evaluation results of fine-tuning by severity are presented in Table 3. Starting from a single cluster, we first compare models fine-tuned on the SAP-1005 \\\"VL,\\\" \\\"L\\\" and \\\"M+H\\\" subsets to ensure the amount of training data is comparable.Among these, while fine-tuning on \\\"VL\\\" leads to the expected superior performance for \\\"VL\\\" in the test split, fine-tuning on \\\"L\\\" produces the best WER on every other severity levels except \\\"VL.\\\"Furthermore, we evaluate models fine-tuned on \\\"M\\\" and \\\"H\\\" splits separately.Compared to the \\\"M+H\\\" model, the \\\"M\\\" model benefits the overall performance, and the performance for test speakers with \\\"M\\\" severity.On the other hand, test speakers with \\\"H\\\" severity are transcribed least accurately using an ASR fine-tuned using only \\\"H\\\" training speakers.The set of \\\"H\\\" speakers in the training set contains 12.79 hours of speech, and previous publications suggest that 12.79 hours is sufficient to fine-tune an ASR with low WER [32], therefore we tentatively conclude that the very high WER of the system fine-tuned using \\\"H\\\" speakers is caused by their very high interspeaker variability.\\nIn general, feeding more data to the network leads to better performance, regardless of the severity level.Compared to the model fine-tuned on LibriSpeech 960h, Figure 2 shows the WER reduction of the best performing models fine-tuned with data from 1, 2, 3, or 4 distinct severity levels.While \\\"L\\\" is the most powerful among all the models fine-tuned by a single cluster (30.13% overall WER), as we enlarge the training data by combining two of the three major classes, the \\\"VL+L\\\" model achieves the best overall WER of 27.51% with an 8.70% relative improvement compared to \\\"L\\\" alone.Although adding \\\"VL\\\" to \\\"L\\\" leads to improvements among all severity levels, the influence decreases as the severity level increases, i.e., the WER reduction decreases from 11.93%, 8.07%, 6.37%, to 3.22% for \\\"VL,\\\" \\\"L,\\\" \\\"M,\\\" and \\\"H,\\\" respectively.This further indicates the mismatch between speech of different impairment severity levels.Combining three training groups (\\\"VL+L+M\\\") further decreases the WER of individuals with \\\"M\\\" and \\\"H\\\" sever- Table 4: WER (%) using SAP-1005 unshared test corpus.For weighted fine-tuning, the cluster along with adjusted weight are listed as parameters.For multitask learning, location of the auxiliary severity classifier is listed as a parameter.\\nity, without hurting performance for those with lower severity, leading to a 26.92% overall test WER.Adding \\\"H\\\" on top of \\\"VL+L+M\\\" does not further enhance overall performance: there is no WER gain for test speakers in the \\\"H\\\" severity class, and WER changes are minimal for speakers in other categories.Table 4 compares cluster-weighted fine-tuning and multitask learning strategies to full-train-set fine-tuning.By adding reasonable weights to the \\\"L\\\" class, we achieve our best average WER of 26.53% at ωL = 1.2, while setting ωL = 1.6 yields an improved 59.16% WER for testing group \\\"H.\\\"Among all types of pooling layers for severity classification, first-tokenbased multitask learning yields the best overall WER (26.53%), and the best WER for \\\"H\\\"-severity test speakers (58.64%).\"\n },\n {\n \"title\": \"Conclusion\",\n \"content\": \"This work 4 investigates the effectiveness of fine-tuning the wav2vec 2.0 model using the 2023-10-05 partial data release of the Speech Accessibility Project.Our experiment demonstrates that fine-tuning using one group of speakers with Parkinson's disease (the SAP-1005 training speakers) substantially reduces WER for other speakers with Parkinson's disease (the SAP-1005 test speakers).Cluster-based fine-tuning does not further improve performance, but multi-task training, in which speaker severity level is an auxiliary output of the ASR, gives small additional benefits in performance, especially for test speakers with the most severe impairments.\"\n },\n {\n \"title\": \"Figure 1 :\",\n \"content\": \"Figure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker level; Bottom: utterance level.\"\n },\n {\n \"title\": \"Figure 2 :\",\n \"content\": \"Figure 2: Relative improvements per severity level of the best performing models fine-tuned by 1, 2, 3 and 4 severity classes of the SAP-1005 corpus, compared to the model fine-tuned by 960 hours of LibriSpeech.\"\n },\n {\n \"title\": \"Table 1 :\",\n \"content\": \"on labeled speech data.With a Transformer lan-Number of speakers in the Speech Accessibility\"\n },\n {\n \"title\": \"Table 2\",\n \"content\": \"3Empirically, ω 1 = ω 2 = 1\\n.72 36.5761.4985.88 960h 36.33 18.36 30.23 54.16 79.71 SAP-1005 All 26.92 13.58 21.15 41.10 60.34 VL+L+M 26.92 13.53 20.79 41.58 60.41 VL+L 27.51 13.64 21.08 42.5762.93 L+M+H 29.00 15.71 23.48 43.04 62.06 L+M 28.75 15.30 22.72 43.32 62.45\"\n }\n]","isConversational":false},"figures":{"kind":"list like","value":[{"id":"","caption":"Figure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker level; Bottom: utterance level.","content":"Figure 1 :\n1\nFigure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker level; Bottom: utterance level."},{"id":"","caption":"Figure 2: Relative improvements per severity level of the best performing models fine-tuned by 1, 2, 3 and 4 severity classes of the SAP-1005 corpus, compared to the model fine-tuned by 960 hours of LibriSpeech.","content":"Figure 2 :\n2\nFigure 2: Relative improvements per severity level of the best performing models fine-tuned by 1, 2, 3 and 4 severity classes of the SAP-1005 corpus, compared to the model fine-tuned by 960 hours of LibriSpeech."},{"id":"","caption":"on labeled speech data.With a Transformer lan-Number of speakers in the Speech Accessibility","content":"Table 1 :\n1\non labeled speech data.With a Transformer lan-Number of speakers in the Speech Accessibility\nSplitAllGenderSeverity#spk|durM FVL L M HTrain 190|151.47h109 8170 54 48 18Dev21|23.32h10118742Test42|39.84h261613 13 115Project Corpus, 2023-10-05 release. Gender and impair-ment severity are automatically estimated using methods de-scribed in the text.guage model, fine-tuning the Wav2Vec 2.0 base model with thecomplete 960 hours of labeled LibriSpeech data yielded a 1.8%WER on the LibriSpeech test-clean set."},{"id":"","caption":".72 36.5761.4985.88 960h 36.33 18.36 30.23 54.16 79.71 SAP-1005 All 26.92 13.58 21.15 41.10 60.34 VL+L+M 26.92 13.53 20.79 41.58 60.41 VL+L 27.51 13.64 21.08 42.5762.93 L+M+H 29.00 15.71 23.48 43.04 62.06 L+M 28.75 15.30 22.72 43.32 62.45","content":"Table 2\n2, demonstrate aremarkable improvement in Word Error Rate (WER) when fine-tuning on SAP-1005 compared to LibriSpeech. ASR fine-tunedusing the SAP-1005 training set achieves 36.70% less WERthan ASR fine-tuned using Librispeech 100h, and 25.90% lessthan ASR fine-tuned using LibriSpeech 960h. Unlike most pre-vious published results for impaired ASR, this is not speaker-dependent training: These results demonstrate that fine-tuningusing one set of speakers with Parkinson's (the SAP-1005 train-ing set) substantially reduces WER for another set of speakerswith Parkinson's (the SAP-1005 test set).2\n3Empirically, ω 1 = ω 2 = 1"}],"string":"[\n {\n \"id\": \"\",\n \"caption\": \"Figure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker level; Bottom: utterance level.\",\n \"content\": \"Figure 1 :\\n1\\nFigure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker level; Bottom: utterance level.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"Figure 2: Relative improvements per severity level of the best performing models fine-tuned by 1, 2, 3 and 4 severity classes of the SAP-1005 corpus, compared to the model fine-tuned by 960 hours of LibriSpeech.\",\n \"content\": \"Figure 2 :\\n2\\nFigure 2: Relative improvements per severity level of the best performing models fine-tuned by 1, 2, 3 and 4 severity classes of the SAP-1005 corpus, compared to the model fine-tuned by 960 hours of LibriSpeech.\"\n },\n {\n \"id\": \"\",\n \"caption\": \"on labeled speech data.With a Transformer lan-Number of speakers in the Speech Accessibility\",\n \"content\": \"Table 1 :\\n1\\non labeled speech data.With a Transformer lan-Number of speakers in the Speech Accessibility\\nSplitAllGenderSeverity#spk|durM FVL L M HTrain 190|151.47h109 8170 54 48 18Dev21|23.32h10118742Test42|39.84h261613 13 115Project Corpus, 2023-10-05 release. Gender and impair-ment severity are automatically estimated using methods de-scribed in the text.guage model, fine-tuning the Wav2Vec 2.0 base model with thecomplete 960 hours of labeled LibriSpeech data yielded a 1.8%WER on the LibriSpeech test-clean set.\"\n },\n {\n \"id\": \"\",\n \"caption\": \".72 36.5761.4985.88 960h 36.33 18.36 30.23 54.16 79.71 SAP-1005 All 26.92 13.58 21.15 41.10 60.34 VL+L+M 26.92 13.53 20.79 41.58 60.41 VL+L 27.51 13.64 21.08 42.5762.93 L+M+H 29.00 15.71 23.48 43.04 62.06 L+M 28.75 15.30 22.72 43.32 62.45\",\n \"content\": \"Table 2\\n2, demonstrate aremarkable improvement in Word Error Rate (WER) when fine-tuning on SAP-1005 compared to LibriSpeech. ASR fine-tunedusing the SAP-1005 training set achieves 36.70% less WERthan ASR fine-tuned using Librispeech 100h, and 25.90% lessthan ASR fine-tuned using LibriSpeech 960h. Unlike most pre-vious published results for impaired ASR, this is not speaker-dependent training: These results demonstrate that fine-tuningusing one set of speakers with Parkinson's (the SAP-1005 train-ing set) substantially reduces WER for another set of speakerswith Parkinson's (the SAP-1005 test set).2\\n3Empirically, ω 1 = ω 2 = 1\"\n }\n]","isConversational":false},"references":{"kind":"list like","value":[{"text":"Voice recognition device as a computer interface for motor and speech impaired people. M Fried-Oken, Archives of physical medicine and rehabilitation. 66101985","doi":""},{"text":"Automatic speech recognition and training for severely dysarthric users of assistive technology: The STARDUST project. M Parker, S Cunningham, P Enderby, M Hawley, P Green, Clinical Linguistics & Phonetics. 202/32006","doi":""},{"text":"On the use of hidden Markov modelling for recognition of dysarthric speech. J R DellerJr, D Hsu, L J Ferrier, CMPB. 3521991","doi":""},{"text":"Computer recognition of the speech of adults with cerebral palsy and dysarthria. C Coleman, L Meyers, Augmentative and Alternative Communication. 711991","doi":""},{"text":"Adaptive neuro-fuzzy inference system for evaluating dysarthric automatic speech recognition (asr) systems: a case study on mvml-based asr. A Asemi, S S B Salim, S R Shahamiri, A Asemi, N Houshangi, Soft Computing. 23102019","doi":""},{"text":"Modelling errors in automatic speech recognition for dysarthric speakers. C Morales, S Omar, S J Cox, EURASIP Journal on Advances in Signal Processing. 2009","doi":""},{"text":"Severity-based adaptation with limited data for asr to aid dysarthric speakers. M B Mustafa, S S Salim, N Mohamed, B Al-Qatab, C E Siong, PloS one. 91e862852014","doi":""},{"text":"Model adaptation and adaptive training for the recognition of dysarthric speech. S Sehgal, S Cunningham, 6th Workshop on SLPAT. ISCA. 2015","doi":""},{"text":"A multi-views multi-learners approach towards dysarthric speech recognition using multi-nets artificial neural networks. S R Shahamiri, S S B Salim, IEEE TNSRE. 2252014","doi":""},{"text":"End-to-end dysarthric speech recognition using multiple databases. Y Takashima, T Takiguchi, Y Ariki, Proc. ICASSP. ICASSP2019","doi":""},{"text":"Data augmentation using healthy speech for dysarthric speech recognition. B Vachhani, C Bhat, S K Kopparapu, Proc. Interspeech. Interspeech2018","doi":""},{"text":"Development of the CUHK dysarthric speech recognition system for the UA Speech corpus. J Yu, X Xie, S Liu, S Hu, M W Lam, X Wu, H Meng, Proc. Interspeech. ISCA. Interspeech. ISCA2018","doi":""},{"text":"The Nemours database of dysarthric speech. X Menendez-Pidal, J B Polikoff, S M Peters, J E Leonzio, H T Bunnell, Proc. of Fourth ICSLP'96. of Fourth ICSLP'96IEEE19963","doi":""},{"text":"Dysarthric speech database for universal access research. H Kim, M Hasegawa-Johnson, A Perlman, J Gunderson, T S Huang, K Watkin, S Frame, Proc. Interspeech. ISCA. Interspeech. ISCA2008","doi":""},{"text":"The TORGO database of acoustic and articulatory speech from speakers with dysarthria. F Rudzicz, A K Namasivayam, T Wolff, LRE. 462012","doi":""},{"text":"Study of the automatic detection of parkison's disease based on speaker recognition technologies and allophonic distillation. L Moro-Velazquez, J A Gomez-Garcia, J I Godino-Llorente, J Rusz, S Skodda, 40th EMBC. IEEE2018","doi":""},{"text":"New spanish speech corpus database for the analysis of people suffering from parkinson's disease. J R Orozco-Arroyave, J D Arias-Londoño, J F Vargas-Bonilla, M C Gonzalez-Rátiva, E Nöth, LREC. 2014","doi":""},{"text":"Disordered speech data collection: Lessons learned at 1 million utterances from project Euphonia. R L Macdonald, P.-P Jiang, J Cattiau, R Heywood, R Cave, Proc. Interspeech. Interspeech2021","doi":""},{"text":"Use of speech impairment severity for dysarthric speech recognition. M Geng, Z Jin, T Wang, S Hu, J Deng, arXiv:2305.106592023arXiv preprint","doi":""},{"text":"State-transition interpolation and MAP adaptation for HMM-based dysarthric speech recognition. H Sharma, M Hasegawa-Johnson, HLT/NAACL Workshop on SLPAT. 2010","doi":""},{"text":"Comparison of soft and hard target RNN-T distillation for large-scale ASR. D Hwang, K C Sim, Y Zhang, T Strohman, Proc. ICASSP. IEEE. ICASSP. IEEE6","doi":""},{"text":"The BBN RT04 English broadcast news transcription system. L Nguyen, B Xiang, M Afify, S Abdou, S Matsoukas, R Schwartz, J Makhoul, Proc. Interspeech. ISCA. Interspeech. ISCA2005","doi":""},{"text":"UIUC leads effort to make speech recognition technology more inclusive. L O'malley, Insight Into Diversity. 11 2023","doi":""},{"text":"Automatic speech recognition of disordered speech: Personalized models outperforming human listeners on short phrases. J Green, R L Macdonald, P.-P Jiang, J Cattiau, R Heywood, Proc. Interspeech. Interspeech2021","doi":""},{"text":"Speaker adaptation for wav2vec2 based dysarthric ASR. M K Baskar, T Herzig, D Nguyen, M Diez, T Polzehl, L Burget, J Černocký, Proc. Interspeech. ISCA. Interspeech. ISCA2022","doi":""},{"text":"Exploring self-supervised pre-trained ASR models for dysarthric and elderly speech recognition. S Hu, X Xie, Z Jin, M Geng, Y Wang, Proc. ICASSP. IEEE. ICASSP. IEEE2023","doi":""},{"text":"Automatic selection of speakers for improved acoustic modelling: recognition of disordered speech with sparse data. H Christensen, I Casanueva, S Cunningham, P Green, T Hain, IEEE SLT. 2014. 2014","doi":""},{"text":"Recent progress in the CUHK dysarthric speech recognition system. S Liu, M Geng, S Hu, X Xie, M Cui, J Yu, H Meng, IEEE/ACM TASLP. 292021","doi":""},{"text":"Exploiting cross-domain visual feature generation for disordered speech recognition. S Liu, X Xie, J Yu, S Hu, M Geng, R Su, H Meng, Proc. Interspeech. ISCA. Interspeech. ISCA2020","doi":""},{"text":"Study of the performance of automatic speech recognition systems in speakers with parkinson's disease. L Moro-Velazquez, J Cho, S Watanabe, M A Hasegawa-Johnson, O Scharenborg, H Kim, N Dehak, Proc. Interspeech 2019. ISCA. Interspeech 2019. ISCA2019","doi":""},{"text":"Differential diagnostic patterns of dysarthria. F L Darley, A E Aronson, J R Brown, JSLHR. 121969","doi":""},{"text":"wav2vec 2.0: A framework for self-supervised learning of speech representations. A Baevski, Y Zhou, A Mohamed, M Auli, Advances in neural information processing systems. 202033460","doi":""},{"text":"Connectionist temporal classification: labelling unsegmented sequence data with recurrent neural networks. A Graves, S Fernández, F Gomez, J Schmidhuber, Proceedings of the 23rd ICML. the 23rd ICML2006","doi":""},{"text":"X-vectors: Robust dnn embeddings for speaker recognition. D Snyder, D Garcia-Romero, G Sell, D Povey, S Khudanpur, IEEE ICASSP. 2018. 2018","doi":""},{"text":"SpecAugment: A Simple Data Augmentation Method for Automatic Speech Recognition. D S Park, W Chan, Y Zhang, C.-C Chiu, B Zoph, E D Cubuk, Q V Le, Proc. Interspeech 2019. ISCA. Interspeech 2019. ISCA2019","doi":""},{"text":"Hal: Computer system for scalable deep learning. V Kindratenko, D Mu, Y Zhan, J Maloney, S H Hashemi, 10.1145/3311790.3396649Practice and Experience in Advanced Research Computing, ser. PEARC '20. New York, NY, USAAssociation for Computing Machinery2020","doi":""}],"string":"[\n {\n \"text\": \"Voice recognition device as a computer interface for motor and speech impaired people. M Fried-Oken, Archives of physical medicine and rehabilitation. 66101985\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Automatic speech recognition and training for severely dysarthric users of assistive technology: The STARDUST project. M Parker, S Cunningham, P Enderby, M Hawley, P Green, Clinical Linguistics & Phonetics. 202/32006\",\n \"doi\": \"\"\n },\n {\n \"text\": \"On the use of hidden Markov modelling for recognition of dysarthric speech. J R DellerJr, D Hsu, L J Ferrier, CMPB. 3521991\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Computer recognition of the speech of adults with cerebral palsy and dysarthria. C Coleman, L Meyers, Augmentative and Alternative Communication. 711991\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Adaptive neuro-fuzzy inference system for evaluating dysarthric automatic speech recognition (asr) systems: a case study on mvml-based asr. A Asemi, S S B Salim, S R Shahamiri, A Asemi, N Houshangi, Soft Computing. 23102019\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Modelling errors in automatic speech recognition for dysarthric speakers. C Morales, S Omar, S J Cox, EURASIP Journal on Advances in Signal Processing. 2009\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Severity-based adaptation with limited data for asr to aid dysarthric speakers. M B Mustafa, S S Salim, N Mohamed, B Al-Qatab, C E Siong, PloS one. 91e862852014\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Model adaptation and adaptive training for the recognition of dysarthric speech. S Sehgal, S Cunningham, 6th Workshop on SLPAT. ISCA. 2015\",\n \"doi\": \"\"\n },\n {\n \"text\": \"A multi-views multi-learners approach towards dysarthric speech recognition using multi-nets artificial neural networks. S R Shahamiri, S S B Salim, IEEE TNSRE. 2252014\",\n \"doi\": \"\"\n },\n {\n \"text\": \"End-to-end dysarthric speech recognition using multiple databases. Y Takashima, T Takiguchi, Y Ariki, Proc. ICASSP. ICASSP2019\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Data augmentation using healthy speech for dysarthric speech recognition. B Vachhani, C Bhat, S K Kopparapu, Proc. Interspeech. Interspeech2018\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Development of the CUHK dysarthric speech recognition system for the UA Speech corpus. J Yu, X Xie, S Liu, S Hu, M W Lam, X Wu, H Meng, Proc. Interspeech. ISCA. Interspeech. ISCA2018\",\n \"doi\": \"\"\n },\n {\n \"text\": \"The Nemours database of dysarthric speech. X Menendez-Pidal, J B Polikoff, S M Peters, J E Leonzio, H T Bunnell, Proc. of Fourth ICSLP'96. of Fourth ICSLP'96IEEE19963\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Dysarthric speech database for universal access research. H Kim, M Hasegawa-Johnson, A Perlman, J Gunderson, T S Huang, K Watkin, S Frame, Proc. Interspeech. ISCA. Interspeech. ISCA2008\",\n \"doi\": \"\"\n },\n {\n \"text\": \"The TORGO database of acoustic and articulatory speech from speakers with dysarthria. F Rudzicz, A K Namasivayam, T Wolff, LRE. 462012\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Study of the automatic detection of parkison's disease based on speaker recognition technologies and allophonic distillation. L Moro-Velazquez, J A Gomez-Garcia, J I Godino-Llorente, J Rusz, S Skodda, 40th EMBC. IEEE2018\",\n \"doi\": \"\"\n },\n {\n \"text\": \"New spanish speech corpus database for the analysis of people suffering from parkinson's disease. J R Orozco-Arroyave, J D Arias-Londoño, J F Vargas-Bonilla, M C Gonzalez-Rátiva, E Nöth, LREC. 2014\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Disordered speech data collection: Lessons learned at 1 million utterances from project Euphonia. R L Macdonald, P.-P Jiang, J Cattiau, R Heywood, R Cave, Proc. Interspeech. Interspeech2021\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Use of speech impairment severity for dysarthric speech recognition. M Geng, Z Jin, T Wang, S Hu, J Deng, arXiv:2305.106592023arXiv preprint\",\n \"doi\": \"\"\n },\n {\n \"text\": \"State-transition interpolation and MAP adaptation for HMM-based dysarthric speech recognition. H Sharma, M Hasegawa-Johnson, HLT/NAACL Workshop on SLPAT. 2010\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Comparison of soft and hard target RNN-T distillation for large-scale ASR. D Hwang, K C Sim, Y Zhang, T Strohman, Proc. ICASSP. IEEE. ICASSP. IEEE6\",\n \"doi\": \"\"\n },\n {\n \"text\": \"The BBN RT04 English broadcast news transcription system. L Nguyen, B Xiang, M Afify, S Abdou, S Matsoukas, R Schwartz, J Makhoul, Proc. Interspeech. ISCA. Interspeech. ISCA2005\",\n \"doi\": \"\"\n },\n {\n \"text\": \"UIUC leads effort to make speech recognition technology more inclusive. L O'malley, Insight Into Diversity. 11 2023\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Automatic speech recognition of disordered speech: Personalized models outperforming human listeners on short phrases. J Green, R L Macdonald, P.-P Jiang, J Cattiau, R Heywood, Proc. Interspeech. Interspeech2021\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Speaker adaptation for wav2vec2 based dysarthric ASR. M K Baskar, T Herzig, D Nguyen, M Diez, T Polzehl, L Burget, J Černocký, Proc. Interspeech. ISCA. Interspeech. ISCA2022\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Exploring self-supervised pre-trained ASR models for dysarthric and elderly speech recognition. S Hu, X Xie, Z Jin, M Geng, Y Wang, Proc. ICASSP. IEEE. ICASSP. IEEE2023\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Automatic selection of speakers for improved acoustic modelling: recognition of disordered speech with sparse data. H Christensen, I Casanueva, S Cunningham, P Green, T Hain, IEEE SLT. 2014. 2014\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Recent progress in the CUHK dysarthric speech recognition system. S Liu, M Geng, S Hu, X Xie, M Cui, J Yu, H Meng, IEEE/ACM TASLP. 292021\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Exploiting cross-domain visual feature generation for disordered speech recognition. S Liu, X Xie, J Yu, S Hu, M Geng, R Su, H Meng, Proc. Interspeech. ISCA. Interspeech. ISCA2020\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Study of the performance of automatic speech recognition systems in speakers with parkinson's disease. L Moro-Velazquez, J Cho, S Watanabe, M A Hasegawa-Johnson, O Scharenborg, H Kim, N Dehak, Proc. Interspeech 2019. ISCA. Interspeech 2019. ISCA2019\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Differential diagnostic patterns of dysarthria. F L Darley, A E Aronson, J R Brown, JSLHR. 121969\",\n \"doi\": \"\"\n },\n {\n \"text\": \"wav2vec 2.0: A framework for self-supervised learning of speech representations. A Baevski, Y Zhou, A Mohamed, M Auli, Advances in neural information processing systems. 202033460\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Connectionist temporal classification: labelling unsegmented sequence data with recurrent neural networks. A Graves, S Fernández, F Gomez, J Schmidhuber, Proceedings of the 23rd ICML. the 23rd ICML2006\",\n \"doi\": \"\"\n },\n {\n \"text\": \"X-vectors: Robust dnn embeddings for speaker recognition. D Snyder, D Garcia-Romero, G Sell, D Povey, S Khudanpur, IEEE ICASSP. 2018. 2018\",\n \"doi\": \"\"\n },\n {\n \"text\": \"SpecAugment: A Simple Data Augmentation Method for Automatic Speech Recognition. D S Park, W Chan, Y Zhang, C.-C Chiu, B Zoph, E D Cubuk, Q V Le, Proc. Interspeech 2019. ISCA. Interspeech 2019. ISCA2019\",\n \"doi\": \"\"\n },\n {\n \"text\": \"Hal: Computer system for scalable deep learning. V Kindratenko, D Mu, Y Zhan, J Maloney, S H Hashemi, 10.1145/3311790.3396649Practice and Experience in Advanced Research Computing, ser. PEARC '20. 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6 Aug 2010
Yuke Li
Department of Physics
Zhejiang University
310027HangzhouChina
Jun Tong
Department of Physics
Zhejiang University
310027HangzhouChina
Qian Tao
Department of Physics
Zhejiang University
310027HangzhouChina
Chunmu Feng
Department of Physics
Zhejiang University
310027HangzhouChina
Guanghan Cao... | 4,943,614 | {
"arxiv": "1001.4317",
"mag": 1710002617,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1088/1367-2630/12/8/083008"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1001.4317v2.pdf"
],
"pdf_sha": "ae805dd27947e8ae45f5d7bd0354681a2090cc00",
"open_access": {
"license": "CCBY",
"url": "https://doi.org/10.1088/1367-2630/12/8/083008",
"status": "GOLD"
}
} | [
"Yuke Li \nDepartment of Physics\nZhejiang University\n310027HangzhouChina",
"Jun Tong \nDepartment of Physics\nZhejiang University\n310027HangzhouChina",
"Qian Tao \nDepartment of Physics\nZhejiang University\n310027HangzhouChina",
"Chunmu Feng \nDepartment of Physics\nZhejiang University\n310027HangzhouChin... | The effect of non-magnetic Zn impurity on superconductivity in LaFe 1−y Zn y AsO 1−x F x system is studied systematically. In the presence of Zn impurity, the superconducting transition temperature increases in the under-doped regime, remains unchanged in the optimally doped regime, and is severely suppressed in the ov... | [
{
"title": "Introduction",
"content": "Discovery of iron-based superconductivity [1] has generated great interest in condensedmatter physics. Similar to the high transition temperature superconducting (SC) copper oxides, the parent compounds of the iron pnictide are antiferromagnet. Superconductivity emerge... | [
{
"id": "",
"caption": "(color online). Structural characterization of LaFe 1−y Zn y AsO 1−x F x samples. (a) and (b) Powder X-ray diffraction patterns for x=0.05 and 0.15, respectively. Inset: Lattice parameters as functions of Zn content.",
"content": "Figure 1 .\n1(color online). Structural character... | [
{
"text": ". Y Kamihara, T Watanabe, M Hirano, H Hosono, J. Am. Chem. Soc. 1303296Kamihara Y, Watanabe T, Hirano M, and Hosono H 2006 J. Am. Chem. Soc. 130 3296",
"doi": ""
},
{
"text": ". C C Tsuei, J R Kirtley, C Chi, Phys. Rev. Lett. 73593Tsuei C C, Kirtley J R, Chi C C 1994 Phys. Rev. Lett. 73 5... | |
Supplementary Information: A single-hole spin qubit
(Dated: May 18, 2020)
N W Hendrickx
Kavli Institute of Nanoscience
Delft University of Technology
P.O. Box 50462600 GADelftThe Netherlands
W I L Lawrie
Kavli Institute of Nanoscience
Delft University of Technology
P.O. Box 50462600 GADelftThe Netherlands
L Petit... | 209,444,224 | {
"arxiv": "1912.10426",
"mag": 3098730138,
"acl": null,
"pubmed": "32651363",
"pubmedcentral": 7351715,
"dblp": null,
"doi": "10.1038/s41467-020-17211-7"
} | {
"pdf_urls": [],
"pdf_sha": "e2c8c10ca7a2ca079b2da5325932c9ecbcb1018f",
"open_access": {
"license": "CCBY",
"url": "https://www.nature.com/articles/s41467-020-17211-7.pdf",
"status": "GOLD"
}
} | Supplementary Information: A single-hole spin qubit | [
"N W Hendrickx \nKavli Institute of Nanoscience\nDelft University of Technology\nP.O. Box 50462600 GADelftThe Netherlands",
"W I L Lawrie \nKavli Institute of Nanoscience\nDelft University of Technology\nP.O. Box 50462600 GADelftThe Netherlands",
"L Petit \nKavli Institute of Nanoscience\nDelft University of Te... | mV) 0 0.01 0.02 | S 12 | (a.u.) Supplementary Fig. 1. Depletion of a hole double quantum dot in germanium. Colour map of the sensor signal as a function of the voltages on plunger gates P1 and P2. No extra addition lines can be observed beyond VP1 ≈ −1100 and VP2 ≈ −1260, indicating the double quantum dot is fully depl... | [
{
"title": "Fig. 1 .",
"content": ""
},
{
"title": "Fig. 2 .. 3 .",
"content": ""
},
{
"title": "Fig. 4 .",
"content": ""
},
{
"title": "-",
"content": ""
}
] | [
{
"id": "",
"caption": "Depletion of a hole double quantum dot in germanium. Colour map of the sensor signal as a function of the voltages on plunger gates P1 and P2. No extra addition lines can be observed beyond VP1 ≈ −1100 and VP2 ≈ −1260, indicating the double quantum dot is fully depleted. This is the ... | [
{
"text": "Differential Charge Sensing and Charge Delocalization in a Tunable Double Quantum Dot. L Dicarlo, Phys. Rev. Lett. 92226801DiCarlo, L. et al. Differential Charge Sensing and Charge Delocalization in a Tunable Double Quantum Dot. Phys. Rev. Lett. 92, 226801 (2004).",
"doi": ""
},
{
"text":... |
Aging dynamics in interacting many-body systems
November 18, 2013
Lloyd P Sanders
Department of Astronomy and Theoretical Physics
Lund University
LundSweden
Michael A Lomholt
MEMPHYS -Center for Biomembrane Physics
Department of Physics and Chemistry
University of Southern Denmark
OdenseDenmark
Ludvig Lizana
Int... | 51,944,821 | {
"arxiv": "1311.3790",
"mag": 3100244936,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1088/1367-2630/16/11/113050"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1311.3790v1.pdf"
],
"pdf_sha": "cd8bb939b4cd34b68f201acf2226c7578d490023",
"open_access": {
"license": "CCBY",
"url": "https://doi.org/10.1088/1367-2630/16/11/113050",
"status": "GOLD"
}
} | Aging dynamics in interacting many-body systems | [
"Lloyd P Sanders \nDepartment of Astronomy and Theoretical Physics\nLund University\nLundSweden",
"Michael A Lomholt \nMEMPHYS -Center for Biomembrane Physics\nDepartment of Physics and Chemistry\nUniversity of Southern Denmark\nOdenseDenmark",
"Ludvig Lizana \nIntegrated Science Lab\nDepartment of Physics\nUme... | Low-dimensional, complex systems are often characterized by logarithmically slow dynamics.We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly disordered, one-dimensional environment.Each particle in this single file is trapped for a ... | [
{
"title": "FIG. 1 :",
"content": "FIG. 1: Schematic of a narrow channel containing a single file of N colloidal particles particles.Regular particles in a bare channel perform single file motion characterized by Harris' law x 2 (t) t 1/2 (top), in the case of functionalized, sticky particles (bottom) the m... | [
{
"id": "",
"caption": "FIG. 1: Schematic of a narrow channel containing a single file of N colloidal particles particles.Regular particles in a bare channel perform single file motion characterized by Harris' law x 2 (t) t 1/2 (top), in the case of functionalized, sticky particles (bottom) the motion becom... | [
{
"text": ". K Matan, R B Williams, T A Witten, S R Nagel, Phys. Rev. Lett. 88761012002",
"doi": ""
},
{
"text": ". E B Brauns, M L Madaras, R S Coleman, C J Murphy, M A Berg, Phys. Rev. Lett. 881581012002",
"doi": ""
},
{
"text": ". O Ben-David, S M Rubinstein, J Fineberg, Nature. 46376... |
Sudden death and revival of Gaussian Einstein-Podolsky-Rosen steering in noisy channels
May 2021
Xiaowei Deng
Shenzhen Institute for Quantum Science and Engineering
Southern University of Science and Technology
518055ShenzhenChina
Institute of Opto-Electronics
State Key Laboratory of Quantum Optics and Quantum Opti... | 233,416,841 | {
"arxiv": "2105.06065",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1038/s41534-021-00399-x"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2105.06065v1.pdf"
],
"pdf_sha": "616d73ebcf6d0a2b8f43889996fdfd5c75d9d0de",
"open_access": {
"license": "CCBY",
"url": "https://www.nature.com/articles/s41534-021-00399-x.pdf",
"status": "GOLD"
}
} | Sudden death and revival of Gaussian Einstein-Podolsky-Rosen steering in noisy channels | [
"Xiaowei Deng \nShenzhen Institute for Quantum Science and Engineering\nSouthern University of Science and Technology\n518055ShenzhenChina\n\nInstitute of Opto-Electronics\nState Key Laboratory of Quantum Optics and Quantum Optics Devices\nShanxi University\n030006TaiyuanChina",
"Yang Liu \nInstitute of Opto-Elec... | Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum information tasks. It is crucial to investigate the effect of inevitable loss and noise in quantum channels on EPR steering. We analyze and experimentally demonstrate the influence of purity of quantum states and excess noise on Gaussian EPR... | [
{
"title": "INTRODUCTION",
"content": "Nonlocality, which challenges our comprehension and intuition about the nature, is a key and distinctive feature of quantum world. Three different types of nonlocal correlations: Bell nonlocality [1], Einstein-Podolsky-Rosen (EPR) steering [2][3][4][5][6] and entanglem... | [
{
"id": "",
"caption": "The influence of purity of TMSS on the Gaussian EPR steering in a lossy channel. a, Steering parameter quantified by Eq. (4). b, Steering certification according to Eq. (5). The region under the bound of 1 (black dotted line) indicates the existence of steerability. Theoretical resul... | [
{
"text": "On the Einstein-Podolsky-Rosen paradox. J S Bell, Physics. 1Bell, J. S. On the Einstein-Podolsky-Rosen paradox. Physics 1, 195-200 (1964).",
"doi": ""
},
{
"text": "Discussion of probability relations between separated systems. E Schrödinger, Math. Proc. Cambridge Philos. Soc. 31Schröding... |
Integrating epigenomic data and 3D genomic structure with a new measure of chromatin assortativity
Vera Pancaldi
Enrique Carrillo-De-Santa-Pau
Biola Maria Javierre
David Juan
Peter Fraser
Mikhail Spivakov
Alfonso Valencia
Daniel Rico
Integrating epigenomic data and 3D genomic structure with a new measure of ... | 13,977,606 | {
"arxiv": "1512.00268",
"mag": 2950099363,
"acl": null,
"pubmed": "27391817",
"pubmedcentral": 4939006,
"dblp": null,
"doi": "10.1186/s13059-016-1003-3"
} | {
"pdf_urls": [],
"pdf_sha": "adc71859c9fd44080b918c41c8340144569288d8",
"open_access": {
"license": "CCBY",
"url": "https://genomebiology.biomedcentral.com/track/pdf/10.1186/s13059-016-1003-3",
"status": "GOLD"
}
} | Integrating epigenomic data and 3D genomic structure with a new measure of chromatin assortativity | [
"Vera Pancaldi",
"Enrique Carrillo-De-Santa-Pau",
"Biola Maria Javierre",
"David Juan",
"Peter Fraser",
"Mikhail Spivakov",
"Alfonso Valencia",
"Daniel Rico"
] | Background: Network analysis is a powerful way of modeling chromatin interactions. Assortativity is a network property used in social sciences to identify factors affecting how people establish social ties. We propose a new approach, using chromatin assortativity, to integrate the epigenomic landscape of a specific cel... | [
{
"title": "Background",
"content": "Advances in chromatin interaction mapping have allowed us to refine our vision of the genome, leading us to a more realistic, well organized tension globule picture with extrusions of chromatin loops [1,2]. The resolution of available contact maps has increased from a me... | [
{
"id": "",
"caption": "Chromatin assortativity (ChAs) of epigenomic features in a network of chromatin contacts. a Largest connected component of PCHi-C chromatin interaction network in mESCs. Nodes are colored by proportion of fragment covered by EZH2, which highlights the neighborhoods in which the prote... | [
{
"text": "Formation of chromosomal domains by loop extrusion. G Fudenberg, M Imakaev, C Lu, A Goloborodko, N Abdennur, L A Mirny, bioRxiv. 2015: 024620Fudenberg G, Imakaev M, Lu C, Goloborodko A, Abdennur N, Mirny LA. Formation of chromosomal domains by loop extrusion. bioRxiv. 2015: 024620.",
"doi": "bioR... |
Schrödinger's problem with cats: measurements and states in the Groupoid Picture of Quantum Mechanics
F M Ciaglia
Max Planck Institute for Mathematics in the Sciences
LeipzigGermany
F Di Cosmo
ICMAT
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)
Depto. de Matemáticas
Univ. Carlos III de Madrid
Leganés, M... | 229,331,942 | {
"arxiv": "2012.10284",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.3390/e22111292"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2012.10284v1.pdf"
],
"pdf_sha": "dfeea64195a8e496222eb0775c965c32f4871583",
"open_access": {
"license": "CCBY",
"url": "https://www.mdpi.com/1099-4300/22/11/1292/pdf",
"status": "GOLD"
}
} | Schrödinger's problem with cats: measurements and states in the Groupoid Picture of Quantum Mechanics | [
"F M Ciaglia \nMax Planck Institute for Mathematics in the Sciences\nLeipzigGermany",
"F Di Cosmo \nICMAT\nInstituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)\n\n\nDepto. de Matemáticas\nUniv. Carlos III de Madrid\nLeganés, MadridSpain",
"A Ibort \nICMAT\nInstituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)\... | Schrödinger's famous Gedankenexperiment involving a cat is used as a motivation to discuss the evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently. It is shown that the notion of classical system, in the sense of Birkhoff and von Ne... | [
{
"title": "Introduction",
"content": "Erwin Schrödinger shared with Einstein an enormous puzzlement about the implications of the laws that were being uncovered in the investigation of atomic processes. In their Gedankenexperiment [12], Einstein, Podolski and Rosen showed the conflicting relation between \... | [
{
"id": "",
"caption": "satisfies the following axioms: • Associativity: M (a , a ) • (M (a , a ) • M (a , a)) = (M (a , a ) • M (a , a )) • M (a , a); • Units: M (a , a ) • M (a , a) = M (a , a) and M (a , a) • M (a, a) = M (a , a); • Inverse: M (a, a ) • M (a , a) = M (a, a) and M (a , a) • M (a, a ) = M ... | [
{
"text": "Foundations and Interpretations of Quantum Mechanics. G Auletta, World Scientific CoAuletta, G. Foundations and Interpretations of Quantum Mechanics; World Scientific Co., 2001. ↓ 3",
"doi": ""
},
{
"text": "Bell's Inequality for C * -Algebras. J Baez, Letters in Mathematical Physics. 13B... |
M-band Imaging of the HR 8799 Planetary System Using an Innovative LOCI-based Background Subtraction Technique
5 Jul 2011
Raphaël Galicher raphael.galicher@nrc-cnrc.gc.ca
National Research Council Canada
Herzberg Institute of Astrophysics
5071 West Saanich RoadV9E 2E7VictoriaBCCanada
Dept. de Physique
Université de... | 118,502,188 | {
"arxiv": "1107.0967",
"mag": 2015932208,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1088/2041-8205/739/2/l41"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1107.0967v1.pdf"
],
"pdf_sha": "635eaee46f7449d3c4fd3c97a648a67f26f66aee",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1107.0967",
"status": "GREEN"
}
} | M-band Imaging of the HR 8799 Planetary System Using an Innovative LOCI-based Background Subtraction Technique | [
"Raphaël Galicher raphael.galicher@nrc-cnrc.gc.ca \nNational Research Council Canada\nHerzberg Institute of Astrophysics\n5071 West Saanich RoadV9E 2E7VictoriaBCCanada\n\nDept. de Physique\nUniversité de Montréal\nSucc. Centre-ville\nC.P. 6128H3C 3J7MontréalQcCanada",
"Christian Marois \nNational Research Council... | Multi-wavelength observations/spectroscopy of exoplanetary atmospheres are the basis of the emerging exciting field of comparative exoplanetology. The HR 8799 planetary system is an ideal laboratory to study our current knowledge gap between massive field brown dwarfs and the cold 5-Gyr old Solar system planets. The HR... | [
{
"title": "Introduction",
"content": "After more than a decade of searching, the direct exoplanet imaging quest was finally successful in 2008 with the discovery of three planetary systems (Marois et al. 2008;Kalas et al. 2008;Lagrange et al. 2009). One key advantage of this technique is the detection of t... | [
{
"id": "",
"caption": ". 1.-Image I p where the background has to be subtracted (left) and the D region inside which the LOCI coefficients are optimized using the reference background dither images (right).",
"content": "Fig\n. 1.-Image I p where the background has to be subtracted (left) and the D reg... | [
{
"text": ". I Baraffe, Astronomy and Astrophysics. 402Baraffe, I., et al., 2003, Astronomy and As- trophysics, 402, 701-712.",
"doi": ""
},
{
"text": ". T Barman, The Astrophysical Journal. 73365Barman, T., et al., 2011, The Astrophysi- cal Journal, 733, 65-.",
"doi": ""
},
{
"text": ".... |
Off equilibrium properties of vortex creep in superconductors
May 2001
Henrik Jeldtoft Jensen
Department of Mathematics
Imperial College
180 Queen's GateSW7 2BZLondonUK
Mario Nicodemi
Department of Mathematics
Imperial College
180 Queen's GateSW7 2BZLondonUK
Dip. Scienze Fisiche, INFM and INFN
Universitá di Napol... | 119,495,159 | {
"arxiv": "cond-mat/0006491",
"mag": 2018737459,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1209/epl/i2001-00285-3"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/cond-mat/0006491v2.pdf"
],
"pdf_sha": "00c2e0358193228a7311884c4f1161c39bf61c9a",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/cond-mat/0006491",
"status": "GREEN"
}
} | Off equilibrium properties of vortex creep in superconductors | [
"Henrik Jeldtoft Jensen \nDepartment of Mathematics\nImperial College\n180 Queen's GateSW7 2BZLondonUK",
"Mario Nicodemi \nDepartment of Mathematics\nImperial College\n180 Queen's GateSW7 2BZLondonUK\n\nDip. Scienze Fisiche, INFM and INFN\nUniversitá di Napoli \"Federico II\"\nVia Cintia80126NapoliItaly"
] | We study a model for the dynamics of vortices in type II superconductors. In particular, we discuss glassy "off equilibrium" properties and "aging" in magnetic creep. At low temperatures a crossover point is found, Tg, where relaxation times seem to divergeá la Vogel-Tamman-Fulcher. Magnetic creep changes by crossing T... | [
{
"title": "FIG. 1 .",
"content": ""
},
{
"title": "FIG. 2 .",
"content": ""
}
] | [
{
"id": "",
"caption": "Main frame The two time magnetic correlation function C(t, tw) recorded at T = 1.0 for the shown values of the external field and waiting times tw. All data are collapsed on the same curve when plotted as a function of (t − tw)/τ . Here τ (Next, T ) is the characteristic creep time. ... | [
{
"text": ". G Blatter, M V Feigel'man, V B Geshkenbein, A I , G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I.",
"doi": ""
},
{
"text": ". V M Larkin, Vinokur, Rev. Mod. Phys. 661125Larkin, V.M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).",
"doi": ""
},
{
"text": ". E H Brandt, Re... |
A Conditional Singular Value Decomposition
Qi Deng dengq@sacredheart.edu
College of Artificial Intelligence
Hubei University of Automotive Technology
ShiyanChina
Jack Welch College of Business & Technology
Sacred Heart University
FairfieldCTUSA
School of Accounting, Economics and Finance
University of Portsmouth
... | 268,509,915 | {
"arxiv": "2403.09696",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.2139/ssrn.4736134"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2403.09696v1.pdf"
],
"pdf_sha": "1d0951bcb6a700eb52746a984955036d26871968",
"open_access": {
"license": null,
"url": "https://arxiv.org/pdf/2403.09696",
"status": "GREEN"
}
} | A Conditional Singular Value Decomposition | [
"Qi Deng dengq@sacredheart.edu \nCollege of Artificial Intelligence\nHubei University of Automotive Technology\nShiyanChina\n\nJack Welch College of Business & Technology\nSacred Heart University\nFairfieldCTUSA\n\nSchool of Accounting, Economics and Finance\nUniversity of Portsmouth\nPortsmouthUK\n\nCofintelligenc... | We propose a Conditional Singular Value Decomposition in the form of {"#} = {"%} {%&} {&#} * for given general matrices {"#} and {%&} . | [
{
"title": "Introduction",
"content": "The Singular Value Decomposition (SVD) given as {\"#} = ( {\"\"} ( {\"$} ( {$$} * is unconditional.However, in financial econometrics applications, there is need to decompose the covariance matrix of one multivariate time series with that of another.To generalize, ... | [
{
"id": "",
"caption": "13) ℎ: ℎ ℎ ⇒ ( = * * = * ⇒ = ( ( * ,. ) substituting ( in Equation 12a with the RHS of Equation 13 we get: = ( ( * * ) ( * ⇒ = ( ( ) * ( ( ) * (15a) Also, substitute in Equation 11 with the RHS of Equation 12b: = ( * * * * ) * ⇒ = ( * ) * ( * ) * (15b) By com... | [
{
"text": "On the early history of the singular value decomposition. G W Stewart, 10.1137/1035134SIAM review. 3541993",
"doi": ""
},
{
"text": "G W Stewart, Matrix algorithms: volume 1: basic decompositions. 1998. August 1, 19981st edition",
"doi": ""
}
] |
The stress-energy tensor for trans-Planckian cosmology
arXiv:hep-th/0109128v2 9 Oct 2001
Martin Lemoine
Institut d'Astrophysique de Paris
CNRS
98bis Bd. AragoF-75014ParisFrance) (
Musongela Lubo
) Mécanique et Gravitation
Université de Mons-Hainaut
6 avenue du Champ de MarsB-7000MonsBelgium) (
Jérôme Martin
Inst... | 13,505,150 | {
"arxiv": "hep-th/0109128",
"mag": 2125400604,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevd.65.023510"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/hep-th/0109128v2.pdf"
],
"pdf_sha": "ab32be2a8a7b5d5890d742b49f95f96bc7889c45",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/hep-th/0109128",
"status": "GREEN"
}
} | The stress-energy tensor for trans-Planckian cosmology | [
"Martin Lemoine \nInstitut d'Astrophysique de Paris\nCNRS\n98bis Bd. AragoF-75014ParisFrance) (",
"Musongela Lubo \n) Mécanique et Gravitation\nUniversité de Mons-Hainaut\n6 avenue du Champ de MarsB-7000MonsBelgium) (",
"Jérôme Martin \nInstitut d'Astrophysique de Paris\nCNRS\n98bis Bd. AragoF-75014ParisFrance)... | This article presents the derivation of the stress-energy tensor of a free scalar field with a general non-linear dispersion relation in curved spacetime. This dispersion relation is used as a phenomelogical description of the short distance structure of spacetime following the conventional approach of trans-Planckian ... | [
{
"title": "I. INTRODUCTION",
"content": "The inflationary paradigm provides an appealing framework to describe the very early phase of the evolution of the Universe, notably because it produces in a natural way the seeds necessary to the formation of the cosmological large scale structures [1]. These initi... | [
{
"id": "",
"caption": "where we have used Eq. (32) to express K + /(ak c ). If k c is of order of the Planck scale, with H 0 /M Pl ≃ 10 −61 , then one obtains today ω ≃ −186.",
"content": "where we have used Eq. (32) to express K + /(ak c ). If k c is of order of the Planck scale, with H 0 /M Pl ≃ 10 −... | [
{
"text": ". A Guth, Phys. Rev. 23347A. Guth, Phys. Rev. D23 (1981) 347;",
"doi": ""
},
{
"text": ". A Linde, Phys. Lett. 108389A. Linde, Phys. Lett. B108 (1982) 389;",
"doi": ""
},
{
"text": ". A Albrecht, P J Steinhardt, Phys. Rev. Lett. 481220A. Albrecht and P. J. Steinhardt, Phys. Re... |
Exploring the Links between the Fundamental Lemma and Kernel Regression
13 Sep 2024
Oleksii Molodchyk 0009-0001-1659-1891
Timm Faulwasser 0000-0002-6892-7406
Exploring the Links between the Fundamental Lemma and Kernel Regression
13 Sep 2024A7EC9B1426855A198258B357D694F72C10.1109/LCSYS.2024.3406053arXiv:2403.05368v2[... | 268,297,348 | {
"arxiv": "2403.05368",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/csysl/MolodchykF24",
"doi": "10.1109/lcsys.2024.3406053"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2403.05368v2.pdf"
],
"pdf_sha": "2852587b96bafea0b14bdde12f4cfc8af05c6381",
"open_access": {
"license": null,
"url": "https://arxiv.org/pdf/2403.05368",
"status": "GREEN"
}
} | Exploring the Links between the Fundamental Lemma and Kernel Regression | [
"Oleksii Molodchyk 0009-0001-1659-1891",
"Timm Faulwasser 0000-0002-6892-7406"
] | Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research.In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the fundamental lemma.Applying a transformation to the usual linear equation in Hankel matric... | [
{
"title": "I. INTRODUCTION",
"content": "Any dynamic system can be associated with its behavior, i.e., with the set of all input-output-state trajectories it can generate.Direct data-driven methods exploit this to bypass the identification of model parameters and the usage of parametric state-space models.... | [
{
"id": "",
"caption": "For w : N 0 → R nw and a, b ∈ N 0 : b ≥ a, the restriction of w to I [a,b] .= [a, b] ∩ N 0 is denoted as w [a,b] .We identify T .= b − a + 1 as the length of w [a,b] .Whenever no confusion can arise, we interpret w [a,b] as the column-stacked vector w [a,b]",
"content": "Notation... | [
{
"text": "A note on persistency of excitation. J C Willems, P Rapisarda, I Markovsky, B L De Moor, Syst. Control Lett. 5442005",
"doi": ""
},
{
"text": "Behavioral systems theory in data-driven analysis, signal processing, and control. I Markovsky, F Dörfler, Ann. Rev. Control. 522021",
"doi": ... |
Chondrules in Enstatite Chondrites Chondrules in enstatite chondrites
American Museum of Natural HistoryCopyright American Museum of Natural History2018. 11235. 10016
Enstatite Chondrules In
Chondrites
S Sara
Russell
C Harold
Connolly Jr
N Alexander
Krot
Chondrules in Enstatite Chondrites Chondrules in enstati... | 119,475,347 | {
"arxiv": "1710.01174",
"mag": 2994271864,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1017/9781108284073.007"
} | {
"pdf_urls": [],
"pdf_sha": "2bc2ce608495b010d19ef9ee88f0f66788940a7b",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1710.01174",
"status": "GREEN"
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} | Chondrules in Enstatite Chondrites Chondrules in enstatite chondrites | [
"Enstatite Chondrules In",
"Chondrites",
"S Sara",
"Russell",
"C Harold",
"Connolly Jr",
"N Alexander",
"Krot"
] | We review silicate chondrules and metal-sulfide nodules in unequilibrated enstatite chondrites (EH3 and EL3). Their unique mineralogical assemblage, with a wide diversity of opaque phases, nitrides, nearly FeO-free enstatite etc. testify to exceptionally reduced conditions. While those have long been ascribed to a cond... | [
{
"title": "Introduction",
"content": "When thinking about the chondrule enigma, it is customary to concentrate on the common ferromagnesian, porphyritic chondrules found in ordinary or carbonaceous chondrites. Still, less usual chondrules (e.g. Al-rich, silica-rich, metallic…) can also offer their share of... | [
{
"id": "",
"caption": "Mg-Ca-Al (red-green-blue) composite element map of the (a) ALH 81189 (,3) EH3 chondrite and (b) QUE 93351 (,6) EL3 chondrite showing chondrules of different textures and mineral abundances. In each image, the more common reds are dominantly enstatite, minor brightest reds are olivine... | [
{
"text": "Elemental fractionations among enstatite chondrites. P A Baedecker, J T Wasson, Geochimica et Cosmochimica Acta. 39Baedecker, P. A. & Wasson, J. T. (1975), 'Elemental fractionations among enstatite chondrites', Geochimica et Cosmochimica Acta 39, 735-765.",
"doi": ""
},
{
"text": "The lit... |
arXiv:hep-ph/9801399v2 17 Mar 1999
I Dadić dadic@faust.irb.hr
Ruder Bošković Institute
ZagrebCroatia
Fakultät für Physik
Universität Bielefeld
Germany
arXiv:hep-ph/9801399v2 17 Mar 1999Two mechanisms for the elimination of pinch singularities in out of equilibrium thermal field theories
We analyze ill-defined pinc... | 18,603,635 | {
"arxiv": "hep-ph/9801399",
"mag": 2052304311,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
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"doi": "10.1103/physrevd.59.125012"
} | {
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} | [
"I Dadić dadic@faust.irb.hr \nRuder Bošković Institute\nZagrebCroatia\n\nFakultät für Physik\nUniversität Bielefeld\nGermany"
] | We analyze ill-defined pinch singularities characteristic of out of equilibrium thermal field theories. We identify two mechanisms that eliminate pinching even at the single selfenergy insertion approximation to the propagator: the first is based on the vanishing of phase space at the singular point (threshold effect).... | [
{
"title": "Introduction",
"content": "Out of equilibrium thermal field theories have recently attracted much interest. From the experimental point of view, various aspects of heavy-ion collisions and the related hot QCD plasma are of considerable interest, in particular the supposedly gluon-dominated stage... | [
{
"id": "",
"caption": "− m 2 D ) 1 behavior near m 2 D . This case (for m 2 = m 2 D ) is promising. The elimination of pinching in the electron propagator, considered in Sec.IV, is one of important examples.",
"content": "(q 2\n2− m 2 D ) 1 behavior near m 2 D . This case (for m 2 = m 2 D ) is promisin... | [
{
"text": ". N P Landsman, Ch G Van Weert, Phys. Rep. 145141N. P. Landsman and Ch. G. van Weert, Phys. Rep. 145, 141 (1987).",
"doi": ""
},
{
"text": "M , Le Bellac, Thermal Field Theory. CambridgeCambridge University PressM. Le Bellac, \"Thermal Field Theory\", (Cambridge University Press, Cambridg... | |
Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion
Christopher W Curtis
Department of Applied Mathematics
University of Colorado
80309BoulderColoradoUSA
David M Bortz
Department of Applied Mathematics
University of Colorado
80309BoulderColoradoUSA
Propagation of fronts in th... | 23,652,142 | {
"arxiv": "1207.1097",
"mag": 2057712034,
"acl": null,
"pubmed": "23368005",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physreve.86.066108"
} | {
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"https://arxiv.org/pdf/1207.1097v2.pdf"
],
"pdf_sha": "1a298d041cf579e3a05359ef8c960781ac5cfb95",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1207.1097",
"status": "GREEN"
}
} | Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion | [
"Christopher W Curtis \nDepartment of Applied Mathematics\nUniversity of Colorado\n80309BoulderColoradoUSA",
"David M Bortz \nDepartment of Applied Mathematics\nUniversity of Colorado\n80309BoulderColoradoUSA"
] | The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that describes propagation of the front up to the minimum of the diffusion coefficient. We al... | [
{
"title": "I. INTRODUCTION",
"content": "Front propagation in reaction-diffusion equations (RDEs) is an important topic in the physical and biological sciences. These models appear throughout biology [1,2], ecology [3], cancer research [4], chemical kinetics [5], and geochemistry [6]. While classically con... | [
{
"id": "",
"caption": "σ 0 (0)φ 0 (e t − 1)) 2 .Thus, on timescales T = O(1/ ), or t = O(1), one has u(x, T, t) = u 0 (x, T, t) + O( ).",
"content": "σ 0 (0)φ 0 (e t − 1)) 2 .Thus, on timescales T = O(1/ ), or t = O(1), one has u(x, T, t) = u 0 (x, T, t) + O( )."
},
{
"id": "",
"caption": "... | [
{
"text": "Mathematical Biology I: An Introduction. J D Murray, Interdisciplinary Applied Math. 17Springer-Verlag3rd edJ. D. Murray, Mathematical Biology I: An Introduc- tion, vol. 17 of Interdisciplinary Applied Math. (Springer- Verlag, New York, NY, 2001), 3rd ed.",
"doi": ""
},
{
"text": ". J D M... |
B-meson decay constants with domain-wall light quarks and nonperturbatively tuned relativistic b-quarks
July 29 -August 3, 2013 23 Dec 2013
Oliver Witzel owitzel@bu.edu
Center for Computational Science
Boston University
3 Cummington Mall02215Boston, MainzMAUSA, Germany
B-meson decay constants with domain-wall light... | 119,115,855 | {
"arxiv": "1311.0276",
"mag": 2952796358,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1063/1.4826794"
} | {
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"https://arxiv.org/pdf/1311.0276v2.pdf"
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"url": "http://arxiv.org/pdf/1311.0276",
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} | B-meson decay constants with domain-wall light quarks and nonperturbatively tuned relativistic b-quarks | [
"Oliver Witzel owitzel@bu.edu \nCenter for Computational Science\nBoston University\n3 Cummington Mall02215Boston, MainzMAUSA, Germany"
] | We report on our progress to obtain the decay constants f B and f B s from lattice-QCD simulations on the RBC-UKQCD Collaborations 2+1 flavor domain-wall Iwasaki lattices. Using domain-wall light quarks and relativistic b-quarks we analyze data with several partially quenched light-quark masses at two lattice spacings ... | [
{
"title": "Motivation",
"content": "B-physics plays a central role in the global efforts to constrain the CKM unitarity triangle. The ratio of neutral B-meson mixing, e.g., is used in the unitarity triangle fits [1][2][3]. Neutral B-mesons mix with their anti-particle under the exchange of two W -bosons as... | [
{
"id": "",
"caption": "Example plot for the determination of the flavor-conserving renormalization factor Z bb V on the finer, 32 3 ensemble with m l sea = 0.006.",
"content": "Figure 4 :\n4Example plot for the determination of the flavor-conserving renormalization factor Z bb V on the finer, 32 3 ense... | [
{
"text": ". J Charles, CKMfitter Group10.1140/epjc/s2005-02169-1arXiv:hep-ph/0406184Eur.Phys.J. 41J. Charles et al. (CKMfitter Group), Eur.Phys.J. C41, 1 (2005), arXiv:hep-ph/0406184, http://ckmfitter. in2p3.fr/",
"doi": ""
},
{
"text": ". M Bona, UTfit10.1088/1126-6708/2005/07/028arXiv:hep-ph/0501... |
Description and comparison of algorithms for correcting anisotropic magnification in cryo-EM images
January 29, 2015
Jianhua Zhao
Molecular Structure and Function Program
The Hospital for Sick Children
Department of Medical Biophysics
University of Toronto
Marcus A Brubaker
Department of Computer Science
Univer... | 6,082,134 | {
"arxiv": "1501.05928",
"mag": 2963681239,
"acl": null,
"pubmed": "26087140",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1016/j.jsb.2015.06.014"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1501.05928v3.pdf"
],
"pdf_sha": "dfcd0014e48c447cd85b0c9f054c23d24a02e8b2",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1501.05928",
"status": "GREEN"
}
} | Description and comparison of algorithms for correcting anisotropic magnification in cryo-EM images | [
"Jianhua Zhao \nMolecular Structure and Function Program\nThe Hospital for Sick Children\n\n\nDepartment of Medical Biophysics\nUniversity of Toronto",
"Marcus A Brubaker \nDepartment of Computer Science\nUniversity of Toronto",
"Samir Benlekbir \nMolecular Structure and Function Program\nThe Hospital for Sick ... | Single particle electron cryomicroscopy (cryo-EM) allows for structures of proteins and protein complexes to be determined from images of non-crystalline specimens.Cryo-EM data analysis requires electron microscope images of randomly oriented ice-embedded protein particles to be rotated and translated to allow for cohe... | [
{
"title": "Introduction",
"content": "Anisotropic magnification in electron microscope images of 2-D crystals was first described more than 30 years ago [1] but more recently has not been a problem with most modern electron microscopes used under conditions typical for cryo-EM with film or charge-coupled d... | [
{
"id": "",
"caption": "Figure1: Anisotropic magnification in images.A, A thallous chloride particle in a 512 × 512 image.Interatomic planes are apparent in the image.The scale bar corresponds to 100 Å. B, The calculated power spectrum from the image in part A shows diffraction peaks.The expected distance f... | [
{
"text": "Measurement and evaluation of electron diffraction patterns from two-dimensional crystals. J Baldwin, R Henderson, Ultramicroscopy. 1441984",
"doi": ""
},
{
"text": "The resolution revolution. W Kühlbrandt, Science. 34361782014",
"doi": ""
},
{
"text": "Beyond blob-ology. M T ... |
CONTRACTIVE IDEMPOTENTS ON LOCALLY COMPACT QUANTUM GROUPS
7 Mar 2013
Matthias Neufang
Pekka Salmi
ANDAdam Skalski
Nico Spronk
CONTRACTIVE IDEMPOTENTS ON LOCALLY COMPACT QUANTUM GROUPS
7 Mar 2013arXiv:1209.6508v2 [math.OA]
A general form of contractive idempotent functionals on coamenable locally compact quantum g... | 119,154,798 | {
"arxiv": "1209.6508",
"mag": 2963017824,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1512/iumj.2013.62.5178"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1209.6508v2.pdf"
],
"pdf_sha": "54cc2fb87f0e598fe2e7662d82cdc4523bf9ae20",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1209.6508.pdf",
"status": "GREEN"
}
} | CONTRACTIVE IDEMPOTENTS ON LOCALLY COMPACT QUANTUM GROUPS | [
"Matthias Neufang",
"Pekka Salmi",
"ANDAdam Skalski",
"Nico Spronk"
] | A general form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a contractive idempotent is shown to be a ternary ring of operators. As... | [
{
"title": "Introduction",
"content": "Idempotent probability measures on locally compact groups arise naturally as limit distributions of random walks and have been studied in this context at least since the 1940s (for the history of the investigations of such idempotent measures we refer to the recent sur... | [
{
"id": "",
"caption": "Let ω be a contractive idempotent in M(G). Then the absolute values |ω| r and |ω| l are idempotent states and there exists v ∈ C 0 (G) such that ω = |ω| l .v = v.|ω| r and",
"content": "Theorem 2. 3 .\n3Let ω be a contractive idempotent in M(G). Then the absolute values |ω| r and... | [
{
"text": "Amenability and co-amenability for locally compact quantum groups, Internat. E Bédos, L Tuset, J. Math. 14E. Bédos and L. Tuset, Amenability and co-amenability for locally compact quantum groups, Inter- nat. J. Math. 14 (2003), 865-884.",
"doi": ""
},
{
"text": "Harmonic functions on grou... |
Decentralized Control of Constrained Linear Systems via Assume-Guarantee Contracts
7 Apr 2020
Weixuan Lin
Eilyan Bitar
Decentralized Control of Constrained Linear Systems via Assume-Guarantee Contracts
7 Apr 2020arXiv:2004.03262v1 [math.OC]
We consider the decentralized control of a discretetime, linear system subj... | 215,238,637 | {
"arxiv": "2004.03262",
"mag": 3045499690,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "conf/amcc/LinB20",
"doi": "10.23919/acc45564.2020.9147215"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2004.03262v1.pdf"
],
"pdf_sha": "7951911837a0059e40a9c53f9e0c8d135bf5ec99",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/2004.03262",
"status": "GREEN"
}
} | Decentralized Control of Constrained Linear Systems via Assume-Guarantee Contracts | [
"Weixuan Lin",
"Eilyan Bitar"
] | We consider the decentralized control of a discretetime, linear system subject to exogenous disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of dynamically coupled subsystems, where each subsystem is assumed to have a dedicated local c... | [
{
"title": "I. INTRODUCTION",
"content": "We investigate the design of affine decentralized control policies for stochastic discrete-time, linear systems that evolve over a finite horizon, and are subject to polyhedral constraints on the state and input trajectories. The computational tractability of such p... | [
{
"id": "",
"caption": "and the matrices ( B, L) in Eq. (17) are defined according to",
"content": "and the matrices ( B, L) in Eq. (17) are defined according to"
},
{
"id": "",
"caption": "). The condition that [Q(t, s)Y (s, r)] ij = 0 implies that there exists k ∈ V such that the blocks [Q... | [
{
"text": "Solution of some nonclassical LQG stochastic decision problems. N R SandellJr, M Athans, IEEE Transactions on. 192Automatic ControlN. R. Sandell Jr and M. Athans, \"Solution of some nonclassical LQG stochastic decision problems,\" Automatic Control, IEEE Transactions on, vol. 19, no. 2, pp. 108-116, ... |
The Mean Pulse Profile of PSR J0737−3039A
arXiv:astro-ph/0501665v1 31 Jan 2005
R N Manchester
M Kramer
A Possenti
A G Lyne
M Burgay
I H Stairs
A W Hotan
M A Mclaughlin
D R Lorimer
G B Hobbs
J M Sarkissian
N D'amico
F Camilo
B C Joshi
P C C Freire
The Mean Pulse Profile of PSR J0737−3039A
arXiv:ast... | 55,439,819 | {
"arxiv": "astro-ph/0501665",
"mag": 2021759142,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1086/429128"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/astro-ph/0501665v1.pdf"
],
"pdf_sha": "db2bdffd74a56da53f329c423131ef201a4ff6f1",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/astro-ph/0501665v1.pdf",
"status": "GREEN"
}
} | The Mean Pulse Profile of PSR J0737−3039A | [
"R N Manchester",
"M Kramer",
"A Possenti",
"A G Lyne",
"M Burgay",
"I H Stairs",
"A W Hotan",
"M A Mclaughlin",
"D R Lorimer",
"G B Hobbs",
"J M Sarkissian",
"N D'amico",
"F Camilo",
"B C Joshi",
"P C C Freire"
] | General relativity predicts that the spin axes of the pulsars in the double-pulsar system (PSR J0737−3039A/B) will precess rapidly, in general leading to a change in the observed pulse profiles. We have observed this system over a one-year interval using the Parkes 64-m radio telescope at three frequencies: 680, 1390 a... | [
{
"title": "Introduction",
"content": "The double-pulsar system PSR J0737−3039A/B (Burgay et al. 2003;Lyne et al. 2004) provides a wonderful laboratory for investigations of rela-tivistic gravity ) as well as the physics of pulsar magnetospheres (e.g., McLaughlin et al. 2004). The system consists of a 22-ms... | [
{
"id": "",
"caption": "-Mean pulse profiles for PSR J0737−3039A at three frequencies, where 360 • of longitude corresponds to the pulse period. The 680-MHz and 3030-MHz profiles were aligned to give maximum cross-correlation with the 1390-MHz profile.",
"content": "Fig. 1 .\n1-Mean pulse profiles for P... | [
{
"text": ". B M Barker, R F O'connell, ApJ. 19925Barker, B. M. & O'Connell, R. F. 1975, ApJ, 199, L25",
"doi": ""
},
{
"text": ". J D Biggs, MNRAS. 245514Biggs, J. D. 1990, MNRAS, 245, 514",
"doi": ""
},
{
"text": ". M Burgay, N D'amico, A Possenti, R N Manchester, A G Lyne, B... |
Strong Phase and D 0 − D 0 mixing at BES-III
18 Apr 2007 (Dated: February 1, 2008)
Xiao-Dong Cheng
Institute of High Energy Physics
P.O.Box 918100049BeijingChina
Department of Physics
Henan Normal University
453007XinXiangHenanChina
Kang-Lin He
Hai-Bo Li
Institute of High Energy Physics
P.O.Box 918100049BeijingC... | 119,310,175 | {
"arxiv": "0704.0120",
"mag": 2920213920,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevd.75.094019"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0704.0120v3.pdf"
],
"pdf_sha": "56ddf90e497b27c1f54b219f104fa64cc9d43c95",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/0704.0120",
"status": "GREEN"
}
} | Strong Phase and D 0 − D 0 mixing at BES-III | [
"Xiao-Dong Cheng \nInstitute of High Energy Physics\nP.O.Box 918100049BeijingChina\n\nDepartment of Physics\nHenan Normal University\n453007XinXiangHenanChina",
"Kang-Lin He",
"Hai-Bo Li \nInstitute of High Energy Physics\nP.O.Box 918100049BeijingChina",
"Yi-Fang Wang \nInstitute of High Energy Physics\nP.O.B... | Most recently, both BaBar and Belle experiments found evidences of neutral D mixing. In this paper, we discuss the constraints on the strong phase difference in D 0 → Kπ decay from the measurements of the mixing parameters, y ′ , yCP and x at the B factories. With CP tag technique at ψ(3770) peak, the extraction of the... | [
{
"title": "FIG. 1 :",
"content": ""
},
{
"title": "TABLE I :",
"content": ""
},
{
"title": "TABLE II :",
"content": ""
},
{
"title": "TABLE III :",
"content": ""
}
] | [
{
"id": "",
"caption": "Illustrative plot of the expected error (∆δ) of the strong phase with various central values of cosδ. The expected error of cosδ is 0.04 by ssuming 20f b −1 data at ψ(3770) peak at BES-III. The two asterisks correspond to δ = 19 0 and −82 0 , respectively.",
"content": "FIG. 1 :\... | [
{
"text": "ing us many numerical results based on GEANT4 simulation. This work is supported in part by the National Natural Science Foundation of China under contracts Nos. 10205017, 10575108,10521003, and the Knowledge Innovation Project of CAS under contract Nos. 530IHEPing us many numerical results based on ... |
Comment on "Coherence measures for heralded single-photon sources"
8 Nov 2009
Stefano Bettelli
Romanogasse 29/151200WienÖsterreich
Comment on "Coherence measures for heralded single-photon sources"
8 Nov 2009numbers: 4250Dv0367Dd4250Ar4265Lm
A recent Brief Report [Phys. Rev. A 79, 035801 (2009)] investigates two f... | 118,504,621 | {
"arxiv": "0911.1478",
"mag": 2054831486,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physreva.81.037801"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0911.1478v1.pdf"
],
"pdf_sha": "fb68fabc219b5f7ce452c2b58e354f5e1ca2eee2",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/0911.1478",
"status": "GREEN"
}
} | Comment on "Coherence measures for heralded single-photon sources" | [
"Stefano Bettelli \nRomanogasse 29/151200WienÖsterreich"
] | A recent Brief Report [Phys. Rev. A 79, 035801 (2009)] investigates two figures of merit for heralded photon sources based on spontaneous parametric down-conversion with a continuous pump, namely the time-averaged temporal coherence between the signal and idler beams and the timeaveraged conditioned second-order degre... | [
{
"title": "Preliminaries",
"content": "The authors of [2] assume a theoretical model for a low-gain frequency-degenerate type-II SPDC process predicting that all auto-and cross-correlations of the source arms can be expressed by means of the two real even functions R(τ ) and C(τ ) shown in Fig.1. In practi... | [
{
"id": "",
"caption": "The triple-coincidence rate Pssi(τ ), and the secondorder correlation function g",
"content": "}FIG. 3 :\n3The triple-coincidence rate Pssi(τ ), and the secondorder correlation function g"
},
{
"id": "",
"caption": "(τ ) for an idler photon arriving at time ti and two... | [
{
"text": "Photon bunching in parametric down-conversion with continuous wave excitation. B Blauensteiner, I Herbauts, S Bettelli, A Poppe, H Hübel, Phys. Rev. A. 7963846B. Blauensteiner, I. Herbauts, S. Bettelli, A. Poppe, and H. Hübel, Photon bunching in parametric down-conversion with continuous wave excitat... |
Covariant L-S Scheme for the effective N * N M couplings
arXiv:hep-ph/0210164v1 10 Oct 2002
B S Zou
CCAST (World Laboratory)
P.O. Box 8730100080Beijing
Institute of High Energy Physics
CAS
P. O. Box 918(4)100039BeijingChina
Abdus Salam International Centre for Theoretical Physics
TriesteItaly
F Hussain
Abdus Sal... | 16,381,199 | {
"arxiv": "hep-ph/0210164",
"mag": 2195587785,
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"doi": "10.1103/physrevc.67.015204"
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} | Covariant L-S Scheme for the effective N * N M couplings | [
"B S Zou \nCCAST (World Laboratory)\nP.O. Box 8730100080Beijing\n\nInstitute of High Energy Physics\nCAS\nP. O. Box 918(4)100039BeijingChina\n\nAbdus Salam International Centre for Theoretical Physics\nTriesteItaly",
"F Hussain \nAbdus Salam International Centre for Theoretical Physics\nTriesteItaly"
] | For excited nucleon states N * of arbitrary spin coupling to nucleon (N) and meson (M), we propose a Lorentz covariant orbital-spin (L-S) scheme for the effective N * N M couplings. To be used for the partial wave analysis of various N * production and decay processes, it combines merits of two conventional schemes, i.... | [
{
"title": "Introduction",
"content": "The study of the nucleon and its excited states N * can provide us with critical insights into the nature of QCD in the confinement domain [1]. They are the simplest system in which the three colors of QCD neutralize into colorless objects and the essential nonabelian ... | [
{
"id": "",
"caption": "wave with S AB = 4; and so on. Then the effective N * Nπ couplings in the covariant L-S scheme are",
"content": "wave with S AB = 4; and so on. Then the effective N * Nπ couplings in the covariant L-S scheme are"
},
{
"id": "",
"caption": "[S A × S B ] S AB × S C ] LM... | [
{
"text": "N Isgur, ; V Burkert, nucl-th/0007008Excited nucleons and hadronic structure. SingaporeWorld ScientificN.Isgur, nucl-th/0007008, in Excited nucleons and hadronic structure, ed V. Burkert et al., (Singapore: World Scientific).",
"doi": ""
},
{
"text": ". Euro. Phys. J. 151Particle Data Gro... |
20 Jan 2020
E V L De Mello brazil**correspondingauthor:evandro@if.uff.br
Instituto de Física
Universidade Federal Fluminense
24210-346NiteróiRJ
20 Jan 2020
A single theory to charge order, pseudo and superconducting gap, critical temperature and pairing interaction of cuprate superconductors
We have developed a co... | 210,838,803 | {
"arxiv": "2001.07245",
"mag": 3106065626,
"acl": null,
"pubmed": "32580169",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1088/1361-648x/ab9fd5"
} | {
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"https://arxiv.org/pdf/2001.07245v1.pdf"
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"url": "http://arxiv.org/pdf/2001.07245",
"status": "GREEN"
}
} | [
"E V L De Mello brazil**correspondingauthor:evandro@if.uff.br \nInstituto de Física\nUniversidade Federal Fluminense\n24210-346NiteróiRJ"
] | A single theory to charge order, pseudo and superconducting gap, critical temperature and pairing interaction of cuprate superconductors | [
{
"title": "FIG. 1 .",
"content": ""
},
{
"title": "FIG. 3 .",
"content": ""
},
{
"title": "FIG. 5 .",
"content": ""
}
] | [
{
"id": "",
"caption": "(a) Low temperature simulation of a checkerboard charge density pattern for Bi2212 p = 0.16 and ∆p ≈ 10 −2 on 100 vs.100 sites and (b) the VGL(r) that yields this density map. The inset shows how VGL(x) evolves with the temperature below T * or with the time of simulation δt. (c) The... | [
{
"text": ". E Fradkin, S A Kivelson, J M Tranquada, 10.1103/RevModPhys.87.457Rev. Mod. Phys. 87457E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Rev. Mod. Phys. 87, 457 (2015).",
"doi": ""
},
{
"text": ". S Huefner, M A Hossain, A Damascelli, G A Sawatzky, Rep. Prog. Phys. 7162501S. Huefner, M. A... | |
Overrelaxation Algorithm for coupled Gauge-Higgs Systems
9403024v2 23 Mar 1994 March 1994
Zoltán Fodor
On leave from Institute for Theoretical Physics
Eötvös University
BudapestHungary
Karl Jansen
Deutsches Elektronen-Synchrotron DESY
HamburgGermany
Overrelaxation Algorithm for coupled Gauge-Higgs Systems
940302... | 119,091,091 | {
"arxiv": "hep-lat/9403024",
"mag": 2192400212,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1016/0370-2693(94)90951-2"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/hep-lat/9403024v2.pdf"
],
"pdf_sha": "557e0159b09e74c80fa47d55709f91bc8726b48b",
"open_access": {
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"url": "http://arxiv.org/pdf/hep-lat/9403024",
"status": "GREEN"
}
} | Overrelaxation Algorithm for coupled Gauge-Higgs Systems | [
"Zoltán Fodor \nOn leave from Institute for Theoretical Physics\nEötvös University\nBudapestHungary",
"Karl Jansen",
"Deutsches Elektronen-Synchrotron DESY\nHamburgGermany"
] | In this letter we extent the overrelaxation algorithm, known to be very efficient in gauge theories, to coupled gauge-Higgs systems with a particular emphasis on the update of the radial mode of the Higgs field. Our numerical tests of the algorithm show that the autocorrelation times can be reduced substantially.The el... | [
{
"title": "4",
"content": "In simulations of the SU(2)-Higgs model, which is the most relevant part for studies of the electroweak phase transition, using a Metropolis algorithm one detects large autocorrelation times already on small lattices. In order to be able to have reliable numerical results it is t... | [
{
"id": "",
"caption": "we plot the autocorrelation function Γ ρ for the length of the Higgs field ρ. This operator in general shows the longest autocorrelation time in the SU(2)-Higgs model. The solid line corresponds to a pure Metropolis simulation and the dashed line shows the result of a hybrid overrela... | [
{
"text": ". A G Cohen, D B Kaplan, A E Nelson, Annu.Rev.Nucl. Part.Sci. 4327A.G. Cohen, D.B. Kaplan and A.E. Nelson, Annu.Rev.Nucl. Part.Sci. 43 (1993) 27.",
"doi": ""
},
{
"text": ". P Arnold, O Espinosa, Phys.Rev. 473546P. Arnold and O. Espinosa, Phys.Rev.D47 (1993) 3546;",
"doi": ""
},
{... |
The second order spin-2 system in flat space near space-like and null-infinity
December 12, 2013
Georgios Doulis
Jörg Frauendiener
The second order spin-2 system in flat space near space-like and null-infinity
December 12, 2013GRG manuscript No. (will be inserted by the editor)
In previous work, the numerical solut... | 119,210,666 | {
"arxiv": "1301.4286",
"mag": 2034497646,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1007/s10714-013-1532-y"
} | {
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"https://arxiv.org/pdf/1301.4286v2.pdf"
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"license": null,
"url": "http://arxiv.org/pdf/1301.4286",
"status": "GREEN"
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} | The second order spin-2 system in flat space near space-like and null-infinity | [
"Georgios Doulis",
"Jörg Frauendiener"
] | In previous work, the numerical solution of the linearized gravitational field equations near space-like and null-infinity was discussed in the form of the spin-2 zero-rest-mass equation for the perturbations of the conformal Weyl curvature. The motivation was to study the behavior of the field and properties of the nu... | [
{
"title": "Introduction",
"content": "In a recent paper [1] we studied the behaviour of gravitational perturbations on Minkowski space near space-like infinity. For this purpose we used the spin-2 zerorest-mass equation which governs the perturbations of the Weyl curvature. The system was studied using a c... | [
{
"id": "",
"caption": "The neighborhood of the cylinder I for the horizontal and the diagonal conformal representations.",
"content": "Fig. 1\n1The neighborhood of the cylinder I for the horizontal and the diagonal conformal representations."
},
{
"id": "",
"caption": "Characteristic curves... | [
{
"text": "Numerical space-times near space-like and null infinity. The spin-2 system on Minkowski space. F Beyer, G Doulis, J Frauendiener, B Whale, Classical and Quantum Gravity. 292413Beyer, F., Doulis, G., Frauendiener, J., Whale, B.: Numerical space-times near space-like and null infinity. The spin-2 syste... |
On Fractional Quantum Hall Solitons and Chern-Simons Quiver Gauge Theories
24 Mar 2012 March 27, 2012
Adil Belhaj
Centre of Physics and Mathematics
Groupement National de Physique des Hautes Energies
CPM-CNESTENRabat, RabatMorocco, Morocco
On Fractional Quantum Hall Solitons and Chern-Simons Quiver Gauge Theories
2... | 119,261,366 | {
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"mag": 2163618575,
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"doi": "10.1088/0264-9381/29/9/095013"
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"license": null,
"url": "http://arxiv.org/pdf/1111.1878",
"status": "GREEN"
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} | On Fractional Quantum Hall Solitons and Chern-Simons Quiver Gauge Theories | [
"Adil Belhaj \nCentre of Physics and Mathematics\nGroupement National de Physique des Hautes Energies\nCPM-CNESTENRabat, RabatMorocco, Morocco"
] | We investigate a class of hierarchical multiple layers of fractional quantum Hall soliton (FQHS) systems from Chern-Simons quivers embedded in M-theory on the cotangent on a 2-dimensional complex toric variety V 2 , which is dual to type IIA superstring on a 3-dimensional complex manifold CP 1 × V 2 fibered over a real... | [
{
"title": "Introduction",
"content": "Three dimensional Quantum Hall Systems (QHS) of condensed matter physics can be modeled using D-branes of type II superstrings [1,2,3]. The first ten dimensional superstring picture of Quantum Hall Effect (QHE) in (1+2)-dimensions has been given in terms of a stack of ... | [
{
"id": "",
"caption": "k gauge symmetry or more generally in toric CS quiver gauge theories. For simplicity, we first consider the case of the U(1) k CS gauge theory in ABJM theory. Indeed, this model can be obtained from a D6-brane wrapping a four-cycle class [C 4 ] in H 4 (CP 3 , Z) which is one-dimensio... | [
{
"text": "How Bob Laughlin Tamed the Giant Graviton from Taub-NUT space. B A Bernevig, J Brodie, L Susskind, N Toumbas, hep-th/001010501023B. A. Bernevig, J. Brodie, L. Susskind and N. Toumbas, How Bob Laughlin Tamed the Giant Graviton from Taub-NUT space, JHEP0102(2001)003, hep-th/0010105.",
"doi": "hep-t... |
Do You Trust What You See? Toward A Multidimensional Measure of Trust in Visualization
Saugat Pandey
Oen G Mckinley
R Jordan Crouser jcrouser@smith.edu
Alvitta Ottley alvitta@wustl.edu
Washington University
St. Louis
Smith College
Washington University
St. Louis
Do You Trust What You See? Toward A Multidi... | 260,735,558 | {
"arxiv": "2308.04727",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "conf/visualization/PandeyMCO23",
"doi": "10.1109/vis54172.2023.00014"
} | {
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"https://export.arxiv.org/pdf/2308.04727v1.pdf"
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"url": "https://arxiv.org/pdf/2308.04727",
"status": "GREEN"
}
} | Do You Trust What You See? Toward A Multidimensional Measure of Trust in Visualization | [
"Saugat Pandey",
"Oen G Mckinley",
"R Jordan Crouser jcrouser@smith.edu",
"Alvitta Ottley alvitta@wustl.edu",
"Washington University\nSt. Louis",
"Smith College",
"Washington University\nSt. Louis"
] | Figure 1: An illustrative overview of our experiments.Participants rated a diverse set of visualizations based on their FAMILIARITY, CLARITY, CREDIBILITY, RELIABILITY, and CONFIDENCE.We examined how these ratings align with visual features and trust rankings. | [
{
"title": "INTRODUCTION",
"content": "Trust is an amorphous concept but is also an integral part of human interactions with machines.Many fields in Computer Science and Engineering have explored the topic of trust in recent decades, including Machine Learning [43], Automation and Robotics [1], and Informat... | [
{
"id": "",
"caption": "Figure 3: Comparing trust ratings from Exp. 2 to the three with the highest and lowest mean scores for the dimensions in Exp. 1.",
"content": "Figure 3 :\n3\nFigure 3: Comparing trust ratings from Exp. 2 to the three with the highest and lowest mean scores for the dimensions in E... | [
{
"text": "Real-time estimation of drivers' trust in automated driving systems. H Azevedo-Sa, S K Jayaraman, C T Esterwood, X J Yang, L P Robert, D M Tilbury, International Journal of Social Robotics. 2020",
"doi": ""
},
{
"text": "Let's gamble: How a poor visualization can elicit risky behavior. M ... |
Supersymmetry approach to Wishart correlation matrices: Exact results
31 Aug 2012
Christian Recher christian.recher@uni-due.de
Mario Kieburg mario.kieburg@stonybrook.edu
Thomas Guhr thomas.guhr@uni-due.de
Martin R Zirnbauer zirnbauer@uni-koeln.de
T Guhr
M R Zirnbauer
Fakultät für Physik
M. Kieburg Department o... | 56,003,812 | {
"arxiv": "1012.1234",
"mag": 2079505262,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1007/s10955-012-0567-x"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1012.1234v3.pdf"
],
"pdf_sha": "5b4f07a655ecd8bd3aa84e535404b5790ab91e13",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1012.1234",
"status": "GREEN"
}
} | Supersymmetry approach to Wishart correlation matrices: Exact results | [
"Christian Recher christian.recher@uni-due.de",
"Mario Kieburg mario.kieburg@stonybrook.edu",
"Thomas Guhr thomas.guhr@uni-due.de",
"Martin R Zirnbauer zirnbauer@uni-koeln.de",
"T Guhr",
"M R Zirnbauer",
"Fakultät für Physik\nM. Kieburg Department of Physics and Astronomy State University of New York St... | We calculate the 'one-point function', meaning the marginal probability density function for any single eigenvalue, of real and complex Wishart correlation matrices. No explicit expression had been obtained for the real case so far. We succeed in doing so by using supersymmetry techniques to express the one-point funct... | [
{
"title": "Introduction",
"content": "Complex systems of many different kinds are in the focus of modern research [1,2,3,4]. Correlation matrices obtained from data sampling are a key tool to study such systems [5,6]. A standard approach in multivariate statistics is to use random matrix theory (RMT) to mo... | [
{
"id": "",
"caption": "1 4/β + iQΛ j .Q is formally identical to the supermatrix of Sec. 3.3. The only difference is in the domain of integration: the present Q-integral is over a Riemannian symmetric superspace (of Cartan type A) with invariant (or Berezin-Haar) measure DQ. This is to say that Q runs over... | [
{
"text": ". T Guhr, A Müller-Groeling, H A Weidenmüller, Phys. Rep. 299189T. Guhr, A. Müller-Groeling, and H.A. Weidenmüller. Phys. Rep., 299:189, 1998.",
"doi": ""
},
{
"text": ". A Tulino, S Verdú, Found. trends commun. inf. theory 1. 1A. Tulino and S. Verdú. Found. trends commun. inf. theory 1. ... |
B → K * γ from D → K * lν
10 May 1999
Zoltan Ligeti
Theory Group
P.O. Box 50060510Fermilab, BataviaIL
Mark B Wise
California Institute of Technology
91125PasadenaCA
B → K * γ from D → K * lν
10 May 1999DF385B9BDC772A799D542C129735B04AarXiv:hep-ph/9905277v1
The B → K * γ branching fraction is predicted using heavy... | 209,850,444 | {
"arxiv": "hep-ph/9905277",
"mag": 2994615659,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevd.60.117506"
} | {
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"https://export.arxiv.org/pdf/hep-ph/9905277v1.pdf"
],
"pdf_sha": "398b9ca27f84c7d59b8a0f66f07889582c3b4832",
"open_access": {
"license": null,
"url": "https://arxiv.org/pdf/hep-ph/9905277",
"status": "GREEN"
}
} | B → K * γ from D → K * lν | [
"Zoltan Ligeti \nTheory Group\nP.O. Box 50060510Fermilab, BataviaIL",
"Mark B Wise \nCalifornia Institute of Technology\n91125PasadenaCA"
] | The B → K * γ branching fraction is predicted using heavy quark spin symmetry at large recoil to relate the tensor and (axial-)vector form factors, using heavy quark flavor symmetry to relate the B decay form factors to the measured D → K * lν form factors, and extrapolating the semileptonic B decay form factors to lar... | [
{
"title": "(B→K * ) + ( 3 .",
"content": "05) = 0.38.Then Eq. (4) gives the following prediction for the B → K * γ branching fraction B( B → K * γ) = 4.1 × 10 −5 .(10) To evaluate Eq. (4), we used τ B = 1.6 ps, |C 7 | = 0.31, |V tb V * ts | = 0.04, and m b = 4.2 GeV.This result compares unexpectedly well w... | [
{
"id": "",
"caption": "05) = 0.38.Then Eq. (4) gives the following prediction for the B → K * γ branching fraction B( B → K * γ) = 4.1 × 10 −5 .(10) To evaluate Eq. (4), we used τ B = 1.6 ps, |C 7 | = 0.31, |V tb V * ts | = 0.04, and m b = 4.2 GeV.This result compares unexpectedly well with the CLEO measur... | [
{
"text": ". F Bartelt, CLEO CollaborationPhys. Rev. Lett. 7141111993",
"doi": ""
},
{
"text": ". J Alexander, CLEO CollaborationPhys. Rev. Lett. 7750001996",
"doi": ""
},
{
"text": ". A F Falk, Z Ligeti, M B Wise, Phys. Lett. 4062251997",
"doi": ""
},
{
"text": ". R D Dikema... |
Early Biomarkers and Intervention Programs for the Infant Exposed to Prenatal Stress
Marta C Antonelli
Martin G 2#
Department of Obstetrics and Gynecology
Klinikum rechts der Isar
Technical University of Munich
Germany
Frasch
Department of Obstetrics and Gynecology
Center on Human Development and Disability
Univ... | 218,595,960 | {
"arxiv": "2005.05787",
"mag": 3025602991,
"acl": null,
"pubmed": "33550974",
"pubmedcentral": 9199558,
"dblp": null,
"doi": "10.2174/1570159x19666210125150955"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2005.05787v1.pdf"
],
"pdf_sha": "e3459d2e344759cc1b158be37148d76758b47d0e",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/2005.05787",
"status": "GREEN"
}
} | Early Biomarkers and Intervention Programs for the Infant Exposed to Prenatal Stress | [
"Marta C Antonelli",
"Martin G 2# \nDepartment of Obstetrics and Gynecology\nKlinikum rechts der Isar\nTechnical University of Munich\nGermany",
"Frasch \nDepartment of Obstetrics and Gynecology\nCenter on Human Development and Disability\nUniversity of Washington\nSeattleWAUSA\n\nUniversity of Washington\nSeat... | Functional development of affective and reward circuits, cognition and response inhibition later in life exhibits vulnerability periods during gestation and early childhood. Extensive evidence supports the model that exposure to stressors in the gestational period and early postnatal life increases an individual's susc... | [
{
"title": "GESTATIONAL ENVIRONMENT AND EARLY PARENTING",
"content": "The spread and depth of evidence from both animal and human studies leave nowadays little doubt about the impact of the gestational environment on the fetal brain development; a concept tha ha bee a ed fe a g a g [1,2]. Prenatal stress (P... | [
{
"id": "",
"caption": "FIGURE LEGENDS FIGURE 1",
"content": "FIGURE LEGENDS FIGURE 1"
},
{
"id": "",
"caption": "The concepts derived from these studies contributed to the emphasis on maternal health as a global priority for the World Health",
"content": "The concepts derived from these... | [
{
"text": "Fetal nutrition and cardiovascular disease in adult life. D J Barker, P D Gluckman, K M Godfrey, J E Harding, J A Owens, J S Robinson, Lancet. 8850Barker, D.J.; Gluckman, P.D.; Godfrey, K.M.; Harding, J.E.; Owens, J.A.; Robinson, J.S. Fetal nutrition and cardiovascular disease in adult life. Lancet, ... |
Semi-classical model for the dephasing of a two-electron spin qubit coupled to a coherently evolving nuclear spin bath
5 Sep 2011
Izhar Neder
Department of Physics
Harvard University
02138CambridgeMAUSA
Mark S Rudner
Department of Physics
Harvard University
02138CambridgeMAUSA
Hendrik Bluhm
Department of Physics... | 36,251,398 | {
"arxiv": "1103.4862",
"mag": 2136207178,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevb.84.035441"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1103.4862v2.pdf"
],
"pdf_sha": "3ca0459f49541e8469951089bef734f16c166bec",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1103.4862",
"status": "GREEN"
}
} | Semi-classical model for the dephasing of a two-electron spin qubit coupled to a coherently evolving nuclear spin bath | [
"Izhar Neder \nDepartment of Physics\nHarvard University\n02138CambridgeMAUSA",
"Mark S Rudner \nDepartment of Physics\nHarvard University\n02138CambridgeMAUSA",
"Hendrik Bluhm \nDepartment of Physics\nHarvard University\n02138CambridgeMAUSA",
"Sandra Foletti \nDepartment of Physics\nHarvard University\n02138... | We study electron spin decoherence in a two-electron double quantum dot due to the hyperfine interaction, under spin-echo conditions as studied in recent experiments. We develop a semi-classical model for the interaction between the electron and nuclear spins, in which the time-dependent Overhauser fields induced by th... | [
{
"title": "I. INTRODUCTION",
"content": "In recent years, electron spin qubits in solid-state quantum dots have emerged as promising candidates for the implementation of quantum information processing [1][2][3][4][5][6][7][8] . The confined electrons in these devices can be precisely manipulated using micr... | [
{
"id": "",
"caption": "Hermitian matrix T in Eq.(21) corresponds to that of Ref.32. Because T is Hermitian and is similar to an antisymmetric matrix, it has one zero eigenvalue, λ 1,d = 0, and a pair of eigenvaluesλ 2(3),d = ± α>β |T αβ,d | 2 .Inserting these eigenvalues into Eq.(22), and using Eq. (21) fo... | [
{
"text": ". J R Petta, A C Johnson, J M Taylor, E A Laird, A Yacoby, M D Lukin, C M Marcus, M P Hanson, A C Gossard, Science. 3092180J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Science 309, 2180 (2005).",
"doi": ""
},
{
... |
Enhancing Trace Visualizations for Microservices Performance Analysis *
24 Feb 2023
University of L '
Luca Traini
Enhancing Trace Visualizations for Microservices Performance Analysis *
24 Feb 2023662128F61337E5E45A6D9D21C8236EA210.1145/3578245.3584729arXiv:2302.12734v1[cs.SE]MicroservicesDistributed TracingPerform... | 257,205,724 | {
"arxiv": "2302.12734",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "conf/wosp/LeoneT23",
"doi": "10.1145/3578245.3584729"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2302.12734v1.pdf"
],
"pdf_sha": "7ca921521cbc8f5875450b5ea873fd0e6d70320b",
"open_access": {
"license": null,
"url": "https://dl.acm.org/doi/pdf/10.1145/3578245.3584729",
"status": "BRONZE"
}
} | Enhancing Trace Visualizations for Microservices Performance Analysis * | [
"University of L '\nLuca Traini"
] | Performance analysis of microservices can be a challenging task, as a typical request to these systems involves multiple Remote Procedure Calls (RPC) spanning across independent services and machines.Practitioners primarily rely on distributed tracing tools to closely monitor microservices performance.These tools enabl... | [
{
"title": "INTRODUCTION",
"content": "Microservices have emerged as a paradigm shift in software development, enabling the efficient testing and deployment of new software features and improvements [28].Due to their modular nature, microservices are particularly well-suited for today's software market, whe... | [
{
"id": "",
"caption": "Figure 1: Swimlane visualization.",
"content": "Figure 1 :\n1\nFigure 1: Swimlane visualization."
},
{
"id": "",
"caption": "Figure 2: End-to-end response time distribution.",
"content": "Figure 2 :Figure 3 :\n23\nFigure 2: End-to-end response time distribution."
... | [
{
"text": "Studying the Effectiveness of Application Performance Management (APM) Tools for Detecting Performance Regressions for Web Applications: An Experience Report. M Tarek, Cor-Paul Ahmed, Tse-Hsun Bezemer, Ahmed E Chen, Weiyi Hassan, Shang, 10.1145/2901739.2901774Proceedings of the 13th International Con... |
The nature of the X-ray pulsar in M31: an intermediate mass X-ray binary?
17 Aug 2016. 2014
Shigeyuki Karino *e-mail:karino@ip.kyusan-u.ac.jp
Kyushu Sangyo Univ. Dept. of Engineering
Matsukadai 2-3-1813-8503FukuokaJapan
The nature of the X-ray pulsar in M31: an intermediate mass X-ray binary?
Publ. Astron. Soc. Ja... | 118,552,414 | {
"arxiv": "1608.05276",
"mag": 3100803128,
"acl": null,
"pubmed": null,
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"dblp": null,
"doi": "10.1093/pasj/psw084"
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} | The nature of the X-ray pulsar in M31: an intermediate mass X-ray binary? | [
"Shigeyuki Karino *e-mail:karino@ip.kyusan-u.ac.jp \nKyushu Sangyo Univ. Dept. of Engineering\nMatsukadai 2-3-1813-8503FukuokaJapan"
] | Recently the first finding of a spin period of an accreting neutron star in M31 is reported. The observed spin period is 1.2 s and it shows 1.27 d modulations due to orbital motion. From the orbital information, the mass donor could not be a giant massive star. On the other hand, the observed properties are quite odd f... | [
{
"title": "Introduction",
"content": "Recently, in EXTraS project with XMM Newton (De Luca et al. 2015), periodic pulsations from an X-ray point source, 3XMM J004301.4+413017 (hereafter, we refer as gM31 XBPh), in an external arm of M31 have been found (Esposito et al. 2015). This object shows 1.2 second p... | [
{
"id": "",
"caption": "The RLOF condition (shown by shaded area). We show the orbital radius given by Eq. (2) (dashed curve) and the Roche lobe radius given by Eq.(1) (solid curve). At the same time, stellar radii of the mass donor as functions of stellar mass are shown at ZAMS phase (filled squares), TMS ... | [
{
"text": ". M Bachetti, Nature. 514202Bachetti, M. et al. 2014, Nature, 514, 202",
"doi": ""
},
{
"text": ". M M Basko, R A Sunyaev, A & A. 42315Basko, M. M. & Sunyaev, R. A. 1975, A & A, 42, 315",
"doi": ""
},
{
"text": ". K Belczynski, V Kalogera, T Bulik, ApJ. 572407Belczynski, K., K... |
14 May 2014
F E Brochero Martínez
STRUCTURE OF FINITE DIHEDRAL GROUP ALGEBRA
14 May 2014and phrases Central idempotent, Dihedral group
In this article, we show the relation between the irreducible idempotents of the cyclic group algebra FqCn and the central irreducible idempotents of the group algebras FqD 2n , wh... | 20,439,494 | {
"arxiv": "1405.3716",
"mag": 1895237144,
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"dblp": "journals/ffa/Martinez15",
"doi": "10.1016/j.ffa.2015.05.002"
} | {
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} | [
"F E Brochero Martínez \nSTRUCTURE OF FINITE DIHEDRAL GROUP ALGEBRA"
] | In this article, we show the relation between the irreducible idempotents of the cyclic group algebra FqCn and the central irreducible idempotents of the group algebras FqD 2n , where Fq is a finite field with q elements and D 2n is the dihedral group of order 2n, where gcd(q, n) = 1.In addition, if every divisor of n ... | [
{
"title": "Introduction",
"content": "Let K be a field and G be a group with n elements. It is known that, if char(K) ∤ n, then the group algebra KG is semisimple and as consequence of Wedderburn Theorem, we have that KG is isomorphic to a direct sum of matrix algebras over division rings, such that each d... | [
{
"id": "",
"caption": "The cyclic group ring R n has r + 2s irreducible idempotents of the form e f given by Lemma 2.1, where the polynomials f 's are the irreducible factors of",
"content": "Corollary 2. 3 .\n3The cyclic group ring R n has r + 2s irreducible idempotents of the form e f given by Lemma ... | [
{
"text": "Minimal Codes of Prime-Power Length. S K Arora, M Pruthi, Finite Fields Appl. 3Arora, S. K., Pruthi M. Minimal Codes of Prime-Power Length. Finite Fields Appl. 3 (1997) 99-113",
"doi": ""
},
{
"text": "Wedderburn decomposition of finite group algebras. O Broche, Á Del Río, Finite Fields A... | |
Challenges of GPT-3-based Conversational Agents for Healthcare
29 Aug 2023
Fabian Lechner fabian.lechner@uni-marburg.de
Department of Mathematics and Computer Science
Conversational AI and Social Analytics (CAISA) Lab Bonn-Aachen International Center for Information Technology (b-it)
University of Bonn
University of... | 261,242,619 | {
"arxiv": "2308.14641",
"mag": null,
"acl": "2023.ranlp-1.67",
"pubmed": null,
"pubmedcentral": null,
"dblp": "conf/ranlp/LechnerLWF23",
"doi": "10.26615/978-954-452-092-2_067"
} | {
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"https://export.arxiv.org/pdf/2308.14641v2.pdf"
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"license": null,
"url": "https://doi.org/10.26615/978-954-452-092-2_067",
"status": "BRONZE"
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} | Challenges of GPT-3-based Conversational Agents for Healthcare | [
"Fabian Lechner fabian.lechner@uni-marburg.de \nDepartment of Mathematics and Computer Science\nConversational AI and Social Analytics (CAISA) Lab Bonn-Aachen International Center for Information Technology (b-it)\nUniversity of Bonn\nUniversity of Marburg ⋆ University Hospital Gießen and Marburg (UKGM)",
"Alliso... | The potential to provide patients with faster information access while allowing medical specialists to concentrate on critical tasks makes medical domain dialog agents appealing.However, the integration of largelanguage models (LLMs) into these agents presents certain limitations that may result in serious consequences... | [
{
"title": "Introduction",
"content": "There is growing interest in medical dialogue systems that can support patients with health goals, extend access to health services such as information seeking, and improve the quality of patient care (Amith et al., 2020;Zeng et al., 2020).However, there are many risks... | [
{
"id": "",
"caption": "Initialization prompt for subsequent experiments and congruence in patient communication.Such systems should thus be assessed for sensitivity and accommodation toward the patient's intellectual and emotional needs.",
"content": "Table 1 :\n1\nInitialization prompt for subsequent ... | [
{
"text": "Towards an ontology-based medication conversational agent for PrEP and PEP. Muhammad Amith, Licong Cui, Kirk Roberts, Cui Tao, Proceedings of the First Workshop on Natural Language Processing for Medical Conversations. the First Workshop on Natural Language Processing for Medical ConversationsOnline.... |
Encoding Higher Level Extensions of Petri Nets in Answer Set Programming
Saadat Anwar
SCIDSE
Arizona State University
699 S Mill Ave85281TempeAZUSA
Chitta Baral
SCIDSE
Arizona State University
699 S Mill Ave85281TempeAZUSA
Katsumi Inoue
Principles of Informatics Research Divisions
National Institute of Informat... | 8,747,015 | {
"arxiv": "1306.3548",
"mag": 2952134500,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/AnwarBI13a",
"doi": "10.1007/978-3-642-40564-8_12"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1306.3548v2.pdf"
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"pdf_sha": "dad21f679ecd01a80cc4ff1f3d1c24b1dad5b0b4",
"open_access": {
"license": null,
"url": null,
"status": "CLOSED"
}
} | Encoding Higher Level Extensions of Petri Nets in Answer Set Programming | [
"Saadat Anwar \nSCIDSE\nArizona State University\n699 S Mill Ave85281TempeAZUSA",
"Chitta Baral \nSCIDSE\nArizona State University\n699 S Mill Ave85281TempeAZUSA",
"Katsumi Inoue \nPrinciples of Informatics Research Divisions\nNational Institute of Informatics\nJapan"
] | Answering realistic questions about biological systems and pathways similar to the ones used by text books to test understanding of students about biological systems is one of our long term research goals.Often these questions require simulation based reasoning.To answer such questions, we need formalisms to build path... | [
{
"title": "Introduction",
"content": "One of our long term research objectives is to develop a system that can answer questions similar to the ones given in the biological texts, used to test the understanding of the students.In order to answer such questions, we have to model pathways, add interventions /... | [
{
"id": "",
"caption": "Fig. 2.An extended version of the Petri Net model from Fig. 1.The new transitions tq, tcytc have a duration of 2 each (shown in square brackets (\"[ ]\") next to the transition).When missing, transition duration is assumed to be 1.",
"content": "Fig. 2 .\n2\nFig. 2.An extended ve... | [
{
"text": "T , Ts0 ) Num(n), Ts1>ts0 Tparc(t, P , N , C , Ts0 , D ) , e5: notenabled(T,TS1):-firescol(C), time(TS0), time(TS1). S1",
"doi": ""
},
{
"text": "As.",
"doi": ""
},
{
"text": "Kommunikation mit Automaten. C A Petri, 1962Bonn, GermanyInstitut für Instrumentelle MathematikTechni... |
A Time-Aware Approach to Early Detection of Anorexia: UNSL at eRisk 2024
23 Oct 2024
Horacio Thompson hjthompson@unsl.edu.ar
Universidad Nacional de San Luis (UNSL)
Ejército de Los Andes 950C.P. 5700San LuisArgentina
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
San LuisArgentina
Marcelo Err... | 271,866,129 | {
"arxiv": "2410.17963",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/abs-2410-17963",
"doi": "10.48550/arxiv.2410.17963"
} | {
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"https://export.arxiv.org/pdf/2410.17963v1.pdf"
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"pdf_sha": "09d755a2ef73f5384c55d306798760406549185d",
"open_access": {
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} | A Time-Aware Approach to Early Detection of Anorexia: UNSL at eRisk 2024 | [
"Horacio Thompson hjthompson@unsl.edu.ar \nUniversidad Nacional de San Luis (UNSL)\nEjército de Los Andes 950C.P. 5700San LuisArgentina\n\nConsejo Nacional de Investigaciones Científicas y Técnicas (CONICET)\nSan LuisArgentina",
"Marcelo Errecalde \nUniversidad Nacional de San Luis (UNSL)\nEjército de Los Andes 9... | The eRisk laboratory aims to address issues related to early risk detection on the Web.In this year's edition, three tasks were proposed, where Task 2 was about early detection of signs of anorexia.Early risk detection is a problem where precision and speed are two crucial objectives.Our research group solved Task 2 by... | [
{
"title": "Introduction",
"content": "According to the World Health Organization, approximately one in every eight people worldwide suffers from a mental disorder, with anxiety, depression, bipolar disorder, and eating disorders being the most prevalent [1].Multiple studies have underscored the correlation... | [
{
"id": "",
"caption": "The [TIME] token is added to the model architecture, separating the post content of the moment it was read.For example, I don't feel like eating evaluated at = 10, the model would receive [CLS] I don't feel like eating [TIME] 10 [SEP].",
"content": "The [TIME] token is added to ... | [
{
"text": "New who prevalence estimates of mental disorders in conflict settings: a systematic review and meta-analysis. F Charlson, M Van Ommeren, A Flaxman, J Cornett, H Whiteford, S Saxena, The Lancet. 3942019",
"doi": ""
},
{
"text": "Social networks and internet emotional relationships on menta... |
How does chemical functionalization affect the thermal transport of antimony films?
June 26, 2016
Tian Zhang
Institute of Atomic and Molecular Physics
College of Physical Science and Technology
Sichuan University
610065ChengduChina
Yuan-Yuan Qi
College of Science
Henan University of Technology
450001ZhengzhouChina... | 264,967,161 | {
"arxiv": "1607.01094",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1607.01094v1.pdf"
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"pdf_sha": "c132ab1128afb86e20ed754712ff22fe1e67962c",
"open_access": {
"license": null,
"url": null,
"status": null
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} | How does chemical functionalization affect the thermal transport of antimony films? | [
"Tian Zhang \nInstitute of Atomic and Molecular Physics\nCollege of Physical Science and Technology\nSichuan University\n610065ChengduChina",
"Yuan-Yuan Qi \nCollege of Science\nHenan University of Technology\n450001ZhengzhouChina",
"Xiang-Rong Chen \nInstitute of Atomic and Molecular Physics\nCollege of Physic... | Chemical functionalization is an effective means to tune electronic and crystal structure of twodimensional material, but very little is known regarding its correlation with thermal transport.Based on the first-principle calculation and an iterative solution of Boltzmann transport equation, we find that antimony films ... | [
{
"title": "FIG. 2 :",
"content": "FIG. 2: (Color online) Phonon spectrum ω( k) of (a) the antimonene Sb.ZA and TA are the transverse acoustic phonon branches, and LA is the longitudinal acoustic phonon branch.G, M and K refer to special points in the first Brillouin zone.(b) The enlarged view of phonon spe... | [
{
"id": "",
"caption": "FIG. 1: (Color online) Top and side view of (a) the antimonene structure and (b) the decorated antimonene structure.X represents the chemical functional group.(c) The calculated lattice thermal conductivities k for antimonene and decorated antimonene.",
"content": "FIG. 1: (Color... | [
{
"text": ". F H L Koppens, Nat. Nanotechnol. 97802014",
"doi": ""
},
{
"text": ". Y. -C Lin, D O Dumcenco, Y. -S Huang, K Suenaga, Nat. Nanotechnol. 93912014",
"doi": ""
},
{
"text": ". K S Novoselov, Nature. 4381972005",
"doi": ""
},
{
"text": ". L Lindsay, Phys. Rev. B. 89... |
Asynchronous Perception-Action-Communication with Graph Neural Networks
Saurav Agarwal
Alejandro Ribeiro
Vijay Kumar
Asynchronous Perception-Action-Communication with Graph Neural Networks
Index Terms-Graph Neural NetworksDecentralized ControlMulti-Robot SystemsRobot Swarms
Collaboration in large robot swarms to ... | 261,945,190 | {
"arxiv": "2309.10164",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/abs-2309-10164",
"doi": "10.48550/arxiv.2309.10164"
} | {
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"https://export.arxiv.org/pdf/2309.10164v1.pdf"
],
"pdf_sha": "92fdffc51075adf344bd6c003bfa8f52a856ffbe",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Asynchronous Perception-Action-Communication with Graph Neural Networks | [
"Saurav Agarwal",
"Alejandro Ribeiro",
"Vijay Kumar"
] | Collaboration in large robot swarms to achieve a common global objective is a challenging problem in large environments due to limited sensing and communication capabilities. The robots must execute a Perception-Action-Communication (PAC) loop-they perceive their local environment, communicate with other robots, and ta... | [
{
"title": "I. INTRODUCTION",
"content": "Decentralized collaboration for navigation of robot swarms through an environment requires high-fidelity algorithms that can efficiently and reliably handle Perception-Action-Communication (PAC) in a feedback loop (Figure 1). The primary challenge in such systems is... | [
{
"id": "",
"caption": "Learning Perception-Action-Communication (PAC) loops using an architecture composed of three Neural Networks (NN):",
"content": "Fig. 2 .\n2Learning Perception-Action-Communication (PAC) loops using an architecture composed of three Neural Networks (NN):"
},
{
"id": "",
... | [
{
"text": "Semi-Supervised Classification with Graph Convolutional Networks. T N Kipf, M Welling, International Conference on Learning Representations. T. N. Kipf and M. Welling, \"Semi-Supervised Classification with Graph Convolutional Networks,\" in International Conference on Learning Representations, 2017."... |
Information of Interest
20 May 2009
Dorje C Brody
Department of Mathematics
Imperial College London
SW7 2BZLondonUK
Robyn L Friedman robyn.freidman@rbs.com
Department of Mathematics
Imperial College London
SW7 2BZLondonUK
Royal Bank of Scotland
135 BishopsgateEC2M 3URLondonUK
Information of Interest
20 May 2009W... | 59,568,636 | {
"arxiv": "0905.0072",
"mag": 2951996696,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0905.0072v2.pdf"
],
"pdf_sha": "8727ded62a8615b488084db2b1dba3ba9687a811",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Information of Interest | [
"Dorje C Brody \nDepartment of Mathematics\nImperial College London\nSW7 2BZLondonUK",
"Robyn L Friedman robyn.freidman@rbs.com \nDepartment of Mathematics\nImperial College London\nSW7 2BZLondonUK\n\nRoyal Bank of Scotland\n135 BishopsgateEC2M 3URLondonUK"
] | A pricing formula for discount bonds, based on the consideration of the market perception of future liquidity risk, is established. An information-based model for liquidity is then introduced, which is used to obtain an expression for the bond price. Analysis of the bond price dynamics shows that the bond volatility is... | [
{
"title": "Introduction.",
"content": "We would like to present here an idea concerning how to generate interest rate dynamics from elementary economic considerations. There are of course numerous economic factors that affect the movement of interest rates, and causal relations that hold between these fact... | [
{
"id": "",
"caption": "Sample paths of the discount function",
"content": "FIG. 1 :\n1Sample paths of the discount function"
},
{
"id": "",
"caption": "Price of a call option on a discount bond. The bond maturity is 5 years. The informationadjusting function is set as φ(x) = e −0.05x , and ... | [
{
"text": "T R Bielecki, M Rutkowski, Credit Risk: Modelling, Valuation and Hedging. BerlinSpringer-VarlagBielecki, T. R. & Rutkowski, M. Credit Risk: Modelling, Valuation and Hedging (Berlin: Springer-Varlag 2002).",
"doi": ""
},
{
"text": "Interest rates and information geometry. D C Brody, L P Hu... |
Protracted Kondo coherence with dilute carrier density in Cerium based nickel pnictides
Peng Zhang
Department of Physics
School of Science
Xi'an Jiaotong University
710049Xi'an, ShaanxiChina
School of Science
MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter
Xi'an Jiaotong Universi... | 203,593,774 | {
"arxiv": "1909.13251",
"mag": 2976459430,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1016/j.physleta.2024.129924"
} | {
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"https://export.arxiv.org/pdf/1909.13251v1.pdf"
],
"pdf_sha": "b3d3956c368e666107f7b34128e512f4cbac3832",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Protracted Kondo coherence with dilute carrier density in Cerium based nickel pnictides | [
"Peng Zhang \nDepartment of Physics\nSchool of Science\nXi'an Jiaotong University\n710049Xi'an, ShaanxiChina\n\nSchool of Science\nMOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter\nXi'an Jiaotong University\n710049Xi'anShaanxiChina",
"Bo Liu \nDepartment of Physics\nSchool of Sci... | Nozières' exhaustion theory argues the temperature for coherently screening of all local moments in Kondo lattice could be much lower than the temperature of single moment screening with insufficient number of conduction electrons.Recent experiment [Luo et al, PNAS, 112,13520 (2015)] indicates the cerium based nickel p... | [
{
"title": "1 FIG. 1 .FIG. 2 .",
"content": "FIG. 1. (Color online).The total and the partial DOS of CeN i2As2 and CeN i2P2 at 300 K (upper panels) and at 38 K (lower panels).DOS of (a-b) CeN i2As2 at the ambient pressure, (c-d) CeN i2As2 at 4.8 GPa, and (e-f) CeN i2P2 at the ambient pressure.The total DOS ... | [
{
"id": "",
"caption": "with continuous time quantum arXiv:1909.13251v1[cond-mat.str-el]29 Sep 2019",
"content": "with continuous time quantum arXiv:1909.13251v1[cond-mat.str-el]29 Sep 2019"
},
{
"id": "",
"caption": "FIG. 1. (Color online).The total and the partial DOS of CeN i2As2 and CeN ... | [
{
"text": ". F Lu, J Zhao, H Weng, Z Fang, X Dai, 10.1103/PhysRevLett.110.096401Phys. Rev. Lett. 110964012013",
"doi": ""
},
{
"text": ". Y Xu, C Yue, H Weng, X Dai, 10.1103/PhysRevX.7.011027Phys. Rev. X. 7110272017",
"doi": ""
},
{
"text": ". S Dzsaber, L Prochaska, A Sidorenko, G Eguch... |
Posterior Uncertainty Estimation via a Monte Carlo Procedure Specialized for Data Assimilation
15 Nov 2023
Michael Stanley mcstanle@andrew.cmu.edu
Department of Statistics and Data Science
Carnegie Mellon University
PittsburghPAUSA
Mikael Kuusela mkuusela@andrew.cmu.edu
Department of Statistics and Data Science
Ca... | 263,605,646 | {
"arxiv": "2310.01397",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2310.01397v1.pdf"
],
"pdf_sha": "3a4a06527aa40ae01045dff517b2434e62416a07",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Posterior Uncertainty Estimation via a Monte Carlo Procedure Specialized for Data Assimilation | [
"Michael Stanley mcstanle@andrew.cmu.edu \nDepartment of Statistics and Data Science\nCarnegie Mellon University\nPittsburghPAUSA",
"Mikael Kuusela mkuusela@andrew.cmu.edu \nDepartment of Statistics and Data Science\nCarnegie Mellon University\nPittsburghPAUSA",
"Brendan Byrne brendan.k.byrne@jpl.nasa.gov \nJet... | Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix.However, in modern settings involving high-dimensional and computationally expensive forward models, posterior covariance knowledge must be relaxed to deterministic or stoc... | [
{
"title": "Introduction",
"content": "Uncertainty quantification (UQ) for data assimilation (DA) tasks is often non-trivial, but scientifically paramount to their understanding and interpretation.Since DA broadly describes methods combining observations with a computational model of a physical system, a Ba... | [
{
"id": "",
"caption": "(d) S[k] ← c k M AP .3. Estimate Posterior Functional Variance: (a) Compute the mean Monte Carlo sample functional: φ = 1 M M k=1 φ k , where φ k = h ⊤ c k M AP .(b) Compute the empirical posterior functional variance:",
"content": "(d) S[k] ← c k M AP .3. Estimate Posterior Func... | [
{
"text": "Optimal and scalable methods to approximate the solutions of large-scale Bayesian problems: theory and application to atmospheric inversion and data assimilation. N Bousserez, D K Henze, Quarterly Journal of the Royal Meteorological Society. 1442018",
"doi": ""
},
{
"text": "A limited mem... |
Automated Detection of Equine Facial Action Units
Zhenghong Li zhenghong.li@stonybrook.edu
KTH Royal Institute of Technology
Sweden
Stony Brook University
USA
Sofia Broomé sbroome@kth.se
KTH Royal Institute of Technology
Sweden
Pia Haubro Andersen pia.haubro.andersen@slu.se
Swedish University of Agricultural S... | 231,951,697 | {
"arxiv": "2102.08983",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/abs-2102-08983",
"doi": null
} | {
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"https://arxiv.org/pdf/2102.08983v2.pdf"
],
"pdf_sha": "7fcafa0a6f95566fc889f7a4ee61e2ba67d7c3be",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Automated Detection of Equine Facial Action Units | [
"Zhenghong Li zhenghong.li@stonybrook.edu \nKTH Royal Institute of Technology\nSweden\n\nStony Brook University\nUSA",
"Sofia Broomé sbroome@kth.se \nKTH Royal Institute of Technology\nSweden",
"Pia Haubro Andersen pia.haubro.andersen@slu.se \nSwedish University of Agricultural Sciences\nSweden",
"Hedvig Kjel... | The recently developed Equine Facial Coding System (EquiFACS) provides a precise and exhaustive, but laborious, manual labelling method of facial action units of the horse. To automate parts of this process, we propose a Deep Learning-based method to detect EquiFACS units automatically from images. We use a cascade fra... | [
{
"title": "I. INTRODUCTION",
"content": "The horse is a highly social species, and facial communication is of utmost importance for the function of the herd. In accordance, the horse has a remarkable repertoire of facial expressions which may be described by 17 degrees of freedom, so called actions units [... | [
{
"id": "",
"caption": "A raw example of AD1 eye white increase in our datasetFig. 2. Our cascade framework for EquiFACS recognition. Note that each part is trained separately",
"content": "Fig. 1 .\n1A raw example of AD1 eye white increase in our datasetFig. 2. Our cascade framework for EquiFACS recogn... | [
{
"text": "Dynamics are important for the recognition of equine pain in video. S Broomé, K B Gleerup, P H Andersen, H Kjellström, IEEE Conference on Computer Vision and Pattern Recognition. S. Broomé, K. B. Gleerup, P. H. Andersen, and H. Kjellström. Dynamics are important for the recognition of equine pain in ... |
7 Apr 2008 September 10-14, 2007
Patrick Achenbach patrick@kph.uni-mainz.de
Institut für Kernphysik Johannes Gutenberg-Universität J.-J
Becher-Weg 45D-55099MainzGermany
7 Apr 2008 September 10-14, 2007The Physics Program at MAMI-C the Structure of the Nucleon IKP, Forschungzentrum Jülich, Germany
In February 2007, ... | 16,710,273 | {
"arxiv": "0802.2870",
"mag": 1766017985,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0802.2870v2.pdf"
],
"pdf_sha": "e01e18c79f09a0878d38c419d6c4399b41b42e09",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | [
"Patrick Achenbach patrick@kph.uni-mainz.de \nInstitut für Kernphysik Johannes Gutenberg-Universität J.-J\nBecher-Weg 45D-55099MainzGermany"
] | In February 2007, the fourth stage of the Mainz Microtron, MAMI-C, started operations with a first experiment. The new Harmonic Double-Sided Microtron delivers an electron beam with energies up to 1.5 GeV while preserving the excellent beam quality of the previous stages. The experimental program at MAMI is focused on ... | [
{
"title": "Selection A: Polarized η Electroproduction",
"content": "The electromagnetic production of η mesons is a selective probe to study the resonance structure of the nucleon. The polarized target asymmetry was measured in Bonn at the PHOENICS experiment [6]. This measurement showed a surprising angul... | [
{
"id": "",
"caption": "The new 1.5 GeV Harmonic Double-Sided Microtron as the Fourth Stage of MAMI",
"content": "1\nThe new 1.5 GeV Harmonic Double-Sided Microtron as the Fourth Stage of MAMI"
},
{
"id": "",
"caption": "For the operation of Kaos/A1 as a double spectrometer trajectories of p... | [
{
"text": "Funding proposal for Collaborative Research Centre 443: Many-body structure of strongly interacting systems. Joh. Gutenberg-University. Funding proposal for Collaborative Research Centre 443: Many-body structure of strongly interacting systems, Joh. Gutenberg-University (Mainz, 2007).",
"doi": ""... | |
ν Electroweak Baryogenesis
4 May 2021
S Rosauro-Alcaraz
Departamento de Física Teórica and Instituto de Física Teórica
IFT-UAM/CSIC
Universidad Autónoma de Madrid
28049Cantoblanco, MadridSpain
ν Electroweak Baryogenesis
4 May 2021F4D14AE4C7D8E2B336D6380FFCD3EE51arXiv:2105.01452v1[hep-ph]
We investigate if the CP vi... | 225,536,131 | {
"arxiv": "2105.01452",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2105.01452v1.pdf"
],
"pdf_sha": "eb29ceff1914608c37ce0b0dda255d75e3a6b0d7",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | ν Electroweak Baryogenesis | [
"S Rosauro-Alcaraz \nDepartamento de Física Teórica and Instituto de Física Teórica\nIFT-UAM/CSIC\nUniversidad Autónoma de Madrid\n28049Cantoblanco, MadridSpain"
] | We investigate if the CP violation necessary for successful electroweak baryogenesis may be sourced by the neutrino Yukawa couplings.In particular, we consider an electroweak scale Seesaw realisation with sizeable Yukawas where the new neutrino singlets form (pseudo)-Dirac pairs.We find that flavour effects critically ... | [
{
"title": "Introduction",
"content": "The origin of the baryon asymmetry of the Universe (BAU) remains one of the most intriguing open questions of the Standard Model (SM).It has been measured 1 to be\nwhere n b (nb) is the (anti)baryon number density and s is the entropy density.To dynamically generate th... | [
{
"id": "",
"caption": "Figure 1 -Sketch of the reflection of an incoming NR off the bubble wall to a νL and its subsequent conversion to baryons through sphaleron transitions.",
"content": "BFigure 1 -\n1\nFigure 1 -Sketch of the reflection of an incoming NR off the bubble wall to a νL and its subseque... | [
{
"text": ". N Aghanim, VI. Cosmological parameters. 2018. 2018",
"doi": ""
},
{
"text": "Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe. A D Sakharov, Pisma Zh. Eksp. Teor. Fiz. 5241967. 1967JETP Lett.",
"doi": ""
},
{
"text": ". Sov. Phys. Usp. 3453921991... |
Search for the Kaluza-Klein Dark Matter with the AMANDA/IceCube Detectors
2009
Matthias Danninger
Department of Physics
Stockholm University
AlbaNovaS-10691StockholmSweden
Kahae Han
IceCube Collaboration
Department of Physics and Astronomy
University of Canterbury
Pr. Bag4800ChristchurchNew Zealand
Search for... | 18,673,201 | {
"arxiv": "0906.3969",
"mag": 2130988751,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0906.3969v1.pdf"
],
"pdf_sha": "d5b3d31579c09dfae1b71a44378708e941afaa97",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Search for the Kaluza-Klein Dark Matter with the AMANDA/IceCube Detectors | [
"Matthias Danninger \nDepartment of Physics\nStockholm University\nAlbaNovaS-10691StockholmSweden",
"Kahae Han",
"IceCube Collaboration",
"Department of Physics and Astronomy\nUniversity of Canterbury\nPr. Bag4800ChristchurchNew Zealand"
] | A viable WIMP candidate, the lightest Kaluza-Klein particle (LKP), is motivated by theories of universal extra dimensions. LKPs can scatter off nuclei in large celestial bodies, like the Sun, and become trapped within their deep gravitational wells, leading to high WIMP densities in the object's core. Pair-wise LKP ann... | [
{
"title": "I. INTRODUCTION",
"content": "Kaluza-Klein weakly interacting massive particles (WIMP) arising from theories with extra dimensions have come under increased scrutiny [1] alongside WIMP candidates from supersymmetric particle theories, e.g. the neutralino. Several analyses [2], [3] performed on t... | [
{
"id": "",
"caption": "Top view of the 2007 IceCube+AMANDA detector configuration. The IceCube-22 strings (squares) enclose the AMANDA strings (circles).",
"content": "Fig. 1 .\n1Top view of the 2007 IceCube+AMANDA detector configuration. The IceCube-22 strings (squares) enclose the AMANDA strings (cir... | [
{
"text": "The PAMELA and ATIC Signals from Kaluza-Klein Dark Matter. D Hooper, D.Hooper et al. , The PAMELA and ATIC Signals from Kaluza- Klein Dark Matter http://arxiv.org/abs/0902.0593 .",
"doi": ""
},
{
"text": "J Braun, Searches for WIMP DM from the Sun with AMANDA) ICRC. J.Braun et al. , (Sear... |
SNS Vacuum Instrumentation and Control System*
J Y Tang
L A Smart
H C Hseuh
P S Marroquin
L R Dalesio
S A Lewis
C A Lionberger
K Kishiyama
Lawrence
D P Gurd
OakM Hechler
W Schneider
Thomas Jefferson
Los Alamos National Laboratory
Brookhaven National Laboratory
UptonLos AlamosNY, NMUSA, USA
Lawrence B... | 118,895,076 | {
"arxiv": "physics/0111101",
"mag": 1655168687,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/physics/0111101v1.pdf"
],
"pdf_sha": "42e9d85828ba3b03e048718869cb51b53fcb40ea",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | SNS Vacuum Instrumentation and Control System* | [
"J Y Tang",
"L A Smart",
"H C Hseuh",
"P S Marroquin",
"L R Dalesio",
"S A Lewis",
"C A Lionberger",
"K Kishiyama",
"Lawrence",
"D P Gurd",
"OakM Hechler",
"W Schneider",
"Thomas Jefferson",
"Los Alamos National Laboratory\nBrookhaven National Laboratory\nUptonLos AlamosNY, NMUSA, USA",
... | The Spallation Neutron Source (SNS) vacuum instrumentation and control systems are being designed at Lawrence Berkeley National Laboratory (LBNL), Brookhaven National Laboratory (BNL), Thomas Jefferson National Accelerator facility (TJNAF) and Los Alamos National Laboratory (LANL). Each participating lab is responsible... | [
{
"title": "SNS VACUUM SYSTEM",
"content": ""
},
{
"title": "SNS VACUUM SYSTEM",
"content": ""
},
{
"title": "Vacuum System Requirements",
"content": ""
},
{
"title": "Vacuum System Requirements",
"content": "The successful operation of SNS is dependent upon the reliable ... | [
{
"id": "",
"caption": "SNS Vacuum Control System Architecture.",
"content": "Figure 1 .\n1SNS Vacuum Control System Architecture."
},
{
"id": "",
"caption": "SNS Vacuum Control System Architecture.",
"content": "Figure 1 .\n1SNS Vacuum Control System Architecture."
},
{
"id": ""... | [
{
"text": "Design of the SNS Accumulator Ring Vacuum Systems. H C Hseuh, PAC'99. New York, p1345H. C. Hseuh, et al, \"Design of the SNS Accumulator Ring Vacuum Systems\", PAC'99, New York, p1345, (1999)",
"doi": ""
},
{
"text": "Status of the Control System for the Front-End of the Spallation Neutro... |
The intercept of symmetric multigluon configurations in the variational approach
October 1994
N Armesto
M A Braun
Departamento de Física de Partículas
Department of High Energy Physics
Universidade de Santiago de Compostela
15706-Santiago de CompostelaSpain
University of St
Pe-tersburg198904St. PetersburgRussia
... | 16,319,716 | {
"arxiv": "hep-ph/9410411",
"mag": 1677444501,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://arxiv.org/pdf/hep-ph/9410411v1.pdf"
],
"pdf_sha": "758b2b597050d1a58ff8b1dcab9af7f1fd2ef252",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | The intercept of symmetric multigluon configurations in the variational approach | [
"N Armesto",
"M A Braun",
"Departamento de Física de Partículas\nDepartment of High Energy Physics\nUniversidade de Santiago de Compostela\n15706-Santiago de CompostelaSpain",
"University of St\nPe-tersburg198904St. PetersburgRussia"
] | To calculate the intercept of the multigluon system in a symmetric spatial configuration a variational method is developed based on a complete system of one-gluon functions. The method is applied to two-and three-gluon cases to compare with the known results. The convergence turns out rather slow. Ways to improve resul... | [
{
"title": "Introduction",
"content": "Much attention has recently been devoted to the perturbative \"hard\", or BFKL, pomeron [1], especially in relation to the study of the small x behaviour of the deep inelastic scattering structure functions (see a recent review in [2]). In application to soft phenomena... | [
{
"id": "",
"caption": "more gluons solutions do not presumably possess such simple symmetry properties, since Eq. (1) mixes colour and space variables. Among various solutions there certainly are those which correspond to a number of BFKL pomerons weakly interacting with each other (multipomeron cuts in th... | [
{
"text": ". E A Kuraev, L N Lipatov, V S Fadin, Sov. Phys. JETP. 44433E. A. Kuraev, L. N. Lipatov and V. S. Fadin, Sov. Phys. JETP 44 (1976) 433; 45 (1977)",
"doi": ""
},
{
"text": ". Ya, Ya, L N Balitzky, Lipatov, Sov. J. Nucl. Phys. 28822Ya. Ya. Balitzky and L. N. Lipatov, Sov. J. Nucl. Phys. 28 ... |
Error analysis of regularized trigonometric linear regression with unbounded sampling: a statistical learning viewpoint
16 Mar 2023
Anna Scampicchio
Elena Arcari
Melanie N Zeilinger
Error analysis of regularized trigonometric linear regression with unbounded sampling: a statistical learning viewpoint
16 Mar 2023
T... | 257,557,673 | {
"arxiv": "2303.09206",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/csysl/ScampicchioAZ23",
"doi": "10.1109/lcsys.2023.3291690"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2303.09206v1.pdf"
],
"pdf_sha": "d8e38519090f1233a7135b5d3dbec1166a0e2d1b",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Error analysis of regularized trigonometric linear regression with unbounded sampling: a statistical learning viewpoint | [
"Anna Scampicchio",
"Elena Arcari",
"Melanie N Zeilinger"
] | The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques based on sparse spectrum Gaussian processes, we focus on models given by regula... | [
{
"title": "I. INTRODUCTION",
"content": "Non-parametric approaches for regularized function estimation are a key tool in machine learning, and have been successfully applied to, e.g., system identification [1] and learning-based control [2], [3]. Nevertheless, their applicability in real-time scenarios is ... | [
{
"id": "",
"caption": "Statistics of the difference between bound and true sample error, normalized by true sample error, in logarithmic scale. Top panel: behaviour of the mean value over the Monte Carlo iterations as a function of ε. Bottom panel: boxplots over the Monte Carlo runs for the case ε = 0.95. ... | [
{
"text": "Kernel methods in system identification, machine learning and function estimation: A survey. G Pillonetto, F Dinuzzo, T Chen, G De Nicolao, L Ljung, Automatica. 503G. Pillonetto, F. Dinuzzo, T. Chen, G. De Nicolao, and L. Ljung, \"Ker- nel methods in system identification, machine learning and functi... |
Memorie della Stellar Variability in Ground-Based Photometric Surveys: An Overview
M Catelan mcatelan@astro.puc.cl
Instituto de Astrofísica
Facultad de Física
Pontificia Universidad Católica de Chile
Av. Vicuña Mackenna 48607820436Macul, SantiagoChile
Millennium Institute of Astrophysics
Nuncio Monseñor Sotero San... | 256,598,121 | {
"arxiv": "2302.01436",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2302.01436v1.pdf"
],
"pdf_sha": "9f6510de8c84f2f76fc1d2d56adb42a8e5365d02",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Memorie della Stellar Variability in Ground-Based Photometric Surveys: An Overview | [
"M Catelan mcatelan@astro.puc.cl \nInstituto de Astrofísica\nFacultad de Física\nPontificia Universidad Católica de Chile\nAv. Vicuña Mackenna 48607820436Macul, SantiagoChile\n\nMillennium Institute of Astrophysics\nNuncio Monseñor Sotero Sanz 100, Of. 104Providencia, SantiagoChile"
] | Time-resolved ground-based surveys in general, and photometric ones in particular, have played a crucial role in building up our knowledge of the properties, physical nature, and the very existence of the many different classes of variable stars and transient events that are currently known. Here I provide a brief over... | [
{
"title": "Prologue",
"content": "This paper provides a brief overview of the early developments, current state, and future of ground-based, wide-field, visual and nearinfrared (IR) photometric time-series surveys. Surveys that have been carried out from space, in other wavelength regimes, and/or using spe... | [
{
"id": "",
"caption": "Non-exhaustive list of acronyms (surveys, telescopes, follow-up projects, alert brokers, etc.).",
"content": "Fig. 1 .\n1Non-exhaustive list of acronyms (surveys, telescopes, follow-up projects, alert brokers, etc.)."
},
{
"id": "",
"caption": "Other groups have chose... | [
{
"text": "F Abe, W Allen, T Banks, Variables Stars and the Astrophysical Returns of the Microlensing Surveys. R. Ferlet, J.-P. Maillard, & B. Raban75Abe, F., Allen, W., Banks, T., et al. 1997, in Variables Stars and the Astrophysical Returns of the Microlensing Surveys, ed. R. Ferlet, J.-P. Maillard, & B. Raba... |
Continuously Expanding the Response Frequency of Rydberg Atom-Based Microwave Sensor by Using Quantum Mixer
Sheng-Xian Xiao
Tao Wang
Chongqing Key Laboratory for Strongly Coupled Physics
Chongqing University
401331ChongqingChina
Center of Modern Physics
Institute for Smart City of Chongqing University in Liyang... | 271,404,133 | {
"arxiv": "2407.17088",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2407.17088v1.pdf"
],
"pdf_sha": "50ac477c6f020a04c164bc23e2881697670979bd",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Continuously Expanding the Response Frequency of Rydberg Atom-Based Microwave Sensor by Using Quantum Mixer | [
"Sheng-Xian Xiao",
"Tao Wang",
"Chongqing Key Laboratory for Strongly Coupled Physics\nChongqing University\n401331ChongqingChina",
"Center of Modern Physics\nInstitute for Smart City of Chongqing University in Liyang\n213300LiyangChina"
] | Microwave electric (MW) field measurements utilizing Rydberg atoms have witnessed significant advancements, achieving remarkable sensitivity, albeit limited to discrete MW frequencies resonant with Rydberg states.Recently, various continuous-frequency measurement schemes have emerged.However, when the MW detuning surpa... | [
{
"title": "I. INTRODUCTION",
"content": "Over the past decade, microwave (MW) field sensing based on Rydberg atoms has rapidly developed due to their exceptional sensitivity to electric fields [1][2][3].This technology leverages the four-level electromagnetically induced transparency (EIT) [4] and Autler-T... | [
{
"id": "",
"caption": "where δ c = ∆ c −A− δ M 2 and ∆ ef f M = ∆ M −a−kω+δ M are the effective detunings of coupling laser and MW field, respectively.By precisely adjusting the coupling laser and the RF field, δ c and ∆ ef f M can be set to 0. Therefore, the EIT",
"content": "where δ c = ∆ c −A− δ M 2... | [
{
"text": ". H Fan, S Kumar, J Sedlacek, H Kübler, S Karimkashi, J P Shaffer, 10.1088/0953-4075/48/20/202001Journal of Physics B: Atomic, Molecular and Optical Physics. 482020012015",
"doi": ""
},
{
"text": ". J Yuan, W Yang, M Jing, H Zhang, Y Jiao, W Li, L Zhang, L Xiao, S Jia, 10.1088/1361-6633/a... |
Systematic modification of functionality in disordered elastic networks through free energy surface tailoring
Dan Mendels
M AT E R I A L S S C I E N C E
Fabian Byléhn
M AT E R I A L S S C I E N C E
Timothy W Sirk
M AT E R I A L S S C I E N C E
Juan J De Pablo
M AT E R I A L S S C I E N C E
Systematic mod... | 250,407,890 | {
"arxiv": "2207.03861",
"mag": null,
"acl": null,
"pubmed": "37285442",
"pubmedcentral": 10246901,
"dblp": null,
"doi": "10.1126/sciadv.adf7541"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2207.03861v3.pdf"
],
"pdf_sha": "a2125371781858d1a88aa9f45caf4d7f9e701a0a",
"open_access": {
"license": "CCBYNC",
"url": null,
"status": null
}
} | Systematic modification of functionality in disordered elastic networks through free energy surface tailoring | [
"Dan Mendels \nM AT E R I A L S S C I E N C E",
"Fabian Byléhn \nM AT E R I A L S S C I E N C E",
"Timothy W Sirk \nM AT E R I A L S S C I E N C E",
"Juan J De Pablo \nM AT E R I A L S S C I E N C E"
] | A combined machine learning-physics-based approach is explored for molecular and materials engineering. Specifically, collective variables, akin to those used in enhanced sampled simulations, are constructed using a machine learning model trained on data gathered from a single system. Through the constructed collective... | [
{
"title": "INTRODUCTION",
"content": "Progress in the manufacturing and characterization of complex molecular and material systems is often hampered by the complexity of such systems and the enormity of the available design space. Engineering systems at molecular length scales remains a challenging, costly... | [
{
"id": "",
"caption": "Illustration of a simulated network from which 12 bonds were removed to embed allosteric response between the indicated sites. (A) The source (top) and target (bottom) beads are represented by the black circles. (B) Magnified view of the network in its activated state (in blue) overl... | [
{
"text": "Perspective: Materials informatics and big data: Realization of the \"fourth paradigm\" of science in materials science. A Agrawal, A Choudhary, APL Mater. 453208A. Agrawal, A. Choudhary, Perspective: Materials informatics and big data: Realization of the \"fourth paradigm\" of science in materials s... |
Satisfiability of Almost Disjoint CNF Formulas
10 Jul 2008 July 10, 2008
Dominik Scheder dscheder@inf.ethz.ch
Theoretical Computer Science
ETH Zürich
CH-8092ZürichSwitzerland
Satisfiability of Almost Disjoint CNF Formulas
10 Jul 2008 July 10, 2008
We call a CNF formula linear if any two clauses have at most one var... | 18,306,424 | {
"arxiv": "0807.1282",
"mag": 1673530647,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/abs-0807-1282",
"doi": null
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0807.1282v2.pdf"
],
"pdf_sha": "60e0dca10e27b0a4fa05ca75ee1968ccdc0d4c9a",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Satisfiability of Almost Disjoint CNF Formulas | [
"Dominik Scheder dscheder@inf.ethz.ch \nTheoretical Computer Science\nETH Zürich\nCH-8092ZürichSwitzerland"
] | We call a CNF formula linear if any two clauses have at most one variable in common. Let m(k) be the largest integer m such that any linear k-CNF formula with ≤ m clauses is satisfiable. We show that 4 k 4e 2 k 3 ≤ m(k) < ln(2)k 4 4 k . More generally, a (k, d)-CSP is a constraint satisfaction problem in conjunctive no... | [
{
"title": "Introduction",
"content": "How difficult is it to come up with an unsatisfiable CNF formula? Stupid question, you might think: {{x}, {x}}, here is one. Two clauses, each containing one literal, and unsatisfiable. Well, yes, but what if we want a k-CNF formula, i.e., we require that every clause ... | [
{
"id": "",
"caption": "Lovász Local Lemma). Let E 1 , . . . , E n be events in a probability space with Pr[E i ] ≤ p for every i. If each event E i is independent of all other events except at most d many, and ep(d + 1) ≤ 1, then Pr[ E i ] < 1.",
"content": "Lemma 2. 1 (\n1Lovász Local Lemma). Let E 1 ... | [
{
"text": "A simplified NP-complete satisfiability problem. C A Tovey, Discrete Appl. Math. 81Tovey, C.A.: A simplified NP-complete satisfiability problem. Discrete Appl. Math. 8(1) (1984) 85-89",
"doi": ""
},
{
"text": "One more occurrence of variables makes satisfiability jump from trivial to NP-c... |
Inner-Heliosphere Signatures of Ion-Scale Dissipation and Nonlinear Interaction
Trevor A Bowen
Space Sciences Laboratory
University of California
94720-7450BerkeleyCAUSA
Alfred Mallet
Space Sciences Laboratory
University of California
94720-7450BerkeleyCAUSA
Stuart D Bale
Space Sciences Laboratory
University of... | 210,718,317 | {
"arxiv": "2001.05081",
"mag": 2999205548,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": null
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2001.05081v1.pdf"
],
"pdf_sha": "8578eed304ae1c4badbe10bfc95f218e43a15c44",
"open_access": {
"license": null,
"url": null,
"status": null
}
} | Inner-Heliosphere Signatures of Ion-Scale Dissipation and Nonlinear Interaction | [
"Trevor A Bowen \nSpace Sciences Laboratory\nUniversity of California\n94720-7450BerkeleyCAUSA",
"Alfred Mallet \nSpace Sciences Laboratory\nUniversity of California\n94720-7450BerkeleyCAUSA",
"Stuart D Bale \nSpace Sciences Laboratory\nUniversity of California\n94720-7450BerkeleyCAUSA\n\nPhysics Department\nUn... | We perform a statistical study of the turbulent power spectrum at inertial and kinetic scales observed during the first perihelion encounter of Parker Solar Probe. We find that often there is an extremely steep scaling range of the power spectrum just above the ion-kinetic scales, similar to prior observations at 1 AU,... | [
{
"title": "PACS numbers:",
"content": "Introduction.-In many astrophysical settings, the background plasma is both highly turbulent and nearly collisionless. The dissipation of this collisionless turbulence is important for heating the plasma [1][2][3][4][5][6], but the precise physical mechanisms involved... | [
{
"id": "",
"caption": "(a,b) Examples of PSP/FIELDS magnetic field spectra with 3PL (blue) and 2PL fits (orange). Black dashed lines show measured 3PL spectral breaks. (c,d) spectral indices computed from data (black), 3PL (blue) and 2PL fits (orange). Dashed lines are shown corresponding to spectral indic... | [
{
"text": "Radial evolution of the solar wind from IMP 8 to Voyager 2. Geophys. Research Letters. John D Richardson, Karolen I Paularena, Alan J Lazarus, John W Belcher, doi: 10.1029/ 94GL0327322John D. Richardson, Karolen I. Paularena, Alan J. Lazarus, and John W. Belcher. Radial evolution of the solar wind fr... |
The role of object-centric representations, guided attention, and external memory on generalizing visual relations
Guillermo Puebla
National Center for Artificial Intelligence
School of Psychological Science
Vicuña Mackenna
4860MaculChile
Guillermo Puebla@cenia
National Center for Artificial Intelligence
School o... | 258,170,271 | {
"arxiv": "2304.07091",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/abs-2304-07091",
"doi": "10.32470/ccn.2023.1499-0"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2304.07091v1.pdf"
],
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"open_access": {
"license": null,
"url": null,
"status": null
}
} | The role of object-centric representations, guided attention, and external memory on generalizing visual relations | [
"Guillermo Puebla \nNational Center for Artificial Intelligence\nSchool of Psychological Science\nVicuña Mackenna\n4860MaculChile",
"Guillermo Puebla@cenia \nNational Center for Artificial Intelligence\nSchool of Psychological Science\nVicuña Mackenna\n4860MaculChile",
"Jeffrey S Bowers j.bowers@bristol.ac.uk \... | Visual reasoning is a long-term goal of vision research. In the last decade, several works have attempted to apply deep neural networks (DNNs) to the task of learning visual relations from images, with modest results in terms of the generalization of the relations learned. In recent years, several innovations in DNNs h... | [
{
"title": "Introduction",
"content": "Detecting relations is one of the fundamental operations of the visual system. This allows us to form a coherent representation of the environment as sets of relations between objects (Vo, Boettcher, & Draschkow, 2019). It is also the basis of robust object recognition... | [
{
"id": "",
"caption": "Example images of all datasets tested.",
"content": "Figure 1 :\n1Example images of all datasets tested."
},
{
"id": "",
"caption": "Mean accuracy on 10 runs of each model per condition. Error bars are standard errors of the mean.",
"content": "Figure 2 :\n2Mean a... | [
{
"text": "A brain-inspired object-based attention network for multi-object recognition and visual reasoning. bioRxiv. H Adeli, S Ahn, G J Zelinsky, Adeli, H., Ahn, S., & Zelinsky, G. J. (2022). A brain-inspired object-based attention network for multi-object recognition and visual reasoning. bioRxiv , 2022-04.... |
Intra-cavity gain shaping of mode-locked Ti:Sapphire laser oscillations
1 Jan 2015
Shai Yefet
Department of physics
BINA Center of nano-technology
Bar-Ilan universityRamat-Gan 52900Israel
Avi Na'aman Amer
Department of physics
BINA Center of nano-technology
Bar-Ilan universityRamat-Gan 52900Israel
Pe'er... | 6,004,144 | {
"arxiv": "1501.00272",
"mag": 2951647535,
"acl": null,
"pubmed": "22535091",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1364/oe.20.009991"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1501.00272v1.pdf"
],
"pdf_sha": "28901dc6b173992072376415d36bb2510f4ced14",
"open_access": {
"license": "CCBY",
"url": "https://doi.org/10.1364/oe.20.009991",
"status": "GOLD"
}
} | Intra-cavity gain shaping of mode-locked Ti:Sapphire laser oscillations | [
"Shai Yefet \nDepartment of physics\nBINA Center of nano-technology\nBar-Ilan universityRamat-Gan 52900Israel",
"Avi Na'aman Amer \nDepartment of physics\nBINA Center of nano-technology\nBar-Ilan universityRamat-Gan 52900Israel",
"Pe'er \nDepartment of physics\nBINA Center of nano-technology\nBar-Ilan... | The gain properties of an oscillator strongly affect its behavior. When the gain is homogeneous, different modes compete for gain resources in a 'winner takes all' manner, whereas with inhomogeneous gain, modes can coexist if they utilize different gain resources. We demonstrate precise control over the mode competitio... | [
{
"title": "Introduction",
"content": "Active oscillators, and in particular laser oscillators, which produce precise, stable oscillations are a major concept in physics and engineering. Due to the highly nonlinear interplay between positive feedback, loss, gain saturation (and possibly additional nonlinear... | [
{
"id": "",
"caption": "Block diagram illustrating the core principle of intra-cavity gain shaping.",
"content": "Figure 1 :\n1Block diagram illustrating the core principle of intra-cavity gain shaping."
},
{
"id": "",
"caption": "(a) Schematic of the standard design of a TiS oscillator. A l... | [
{
"text": ". A E Siegman, Lasers (University Science Books. A. E. Siegman, Lasers (University Science Books, 1986).",
"doi": ""
},
{
"text": "A Yariv, Quantum Electronics. John Wiley & SonsA. Yariv, Quantum Electronics (John Wiley & Sons, 1989).",
"doi": ""
},
{
"text": "60 channel wdm t... |
Relationships Between Journal Metrics
March 2024
William H Mischo w-mischo@illinois.edu
Mary C Schlembach schlemba@illinois.edu
Elisandro Cabada cabada@illinois.edu
Chemistry Library
William H. Mischo is Berthold Family Professor Emeritus in Information Access and Discovery and Head, Grainger Engineering Library I... | 257,039,064 | {
"arxiv": "2302.09130",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/crl/MischoSC24",
"doi": "10.5860/crl.85.2.234"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2302.09130v1.pdf"
],
"pdf_sha": "f16959aec22ba845efa87b7cf835d49dd24343c5",
"open_access": {
"license": "CCBYNC",
"url": "https://crl.acrl.org/index.php/crl/article/download/26229/34168",
"status": "GOLD"
}
} | Relationships Between Journal Metrics | [
"William H Mischo w-mischo@illinois.edu",
"Mary C Schlembach schlemba@illinois.edu",
"Elisandro Cabada cabada@illinois.edu \nChemistry Library\nWilliam H. Mischo is Berthold Family Professor Emeritus in Information Access and Discovery and Head, Grainger Engineering Library Information Center\nUniversity of Ill... | This study examines the correlational relationships between local journal authorship, local and external citation counts, full-text downloads, link-resolver clicks, and four global journal impact factor indices within an all-disciplines journal collection of 12,200 titles and six subject subsets at the University of Il... | [
{
"title": "Introduction",
"content": "There has been a great deal of interest in attempting to determine correlational relationships between various individual journal title metrics within a collection, including local publication, citation, and usage (now download) measures and journal global impact facto... | [
{
"id": "",
"caption": "a title and an ISI subject descriptor; and (5) several tables of 14,338 journal titles showing the number of times outside authors have cited articles written by UIUC authors.",
"content": "a title and an ISI subject descriptor; and (5) several tables of 14,338 journal titles sho... | [
{
"text": "Where to Spend our E-journal Money? Defining a University Library's Core Collection Through Citation Analysis. Philip M Davis, 10.1353/pla.2002.0009Portal: Libraries & the Academy. 212002",
"doi": ""
},
{
"text": "Level 1 COUNTER Compliant Vendor Statistics are a Reliable Measure of Journ... |
QED2 boson description of the X17 particle and dark matter
Cheuk-Yin Wong
Physics Division
Oak Ridge National Laboratory
37831Oak RidgeTNUSA
QED2 boson description of the X17 particle and dark matter
(Dated: January 15, 2020)
The oscillations of the color charges and electric charges of the quark and antiquarks of... | 210,473,441 | {
"arxiv": "2001.04864",
"mag": 3101674158,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1007/jhep08(2020)165"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2001.04864v1.pdf"
],
"pdf_sha": "7278eed784f7e50aa1eabe412f8822040165e37d",
"open_access": {
"license": "CCBY",
"url": "https://link.springer.com/content/pdf/10.1007/JHEP08(2020)165.pdf",
"status": "GOLD"
}
} | QED2 boson description of the X17 particle and dark matter | [
"Cheuk-Yin Wong \nPhysics Division\nOak Ridge National Laboratory\n37831Oak RidgeTNUSA"
] | The oscillations of the color charges and electric charges of the quark and antiquarks of the underlying vacuum in a flux tube generate QCD2 bosons (mesons) and QED2 bosons (Phys.Rev.C81,064903(2010)). The predicted mass of the isoscalar QED2 boson in the flux tube environment is close to the X17 mass, leading to the s... | [
{
"title": "I. INTRODUCTION",
"content": "Recent observation of a light, neutral boson with a mass of about 17 MeV in the electromagnetic M1 decay of the excited I(J π )=0(1 + ) state of 8 Be has generated a great deal of interest [1]. Supporting evidence for the existence of the hypothetical X17 particle h... | [
{
"id": "",
"caption": "I. Comparison of experimental and theoretical spin S=0 boson masses obtained with the semi-empirical mass formula of Eq. (6) using strong coupling constant αs=0.5 and a flux tube radius RT =0.42 fm. Exp Theory Semi-empirical I S [I(J π )] mass massless (Eq.+ )? 17.01 † X17 (0 − )? 16... | [
{
"text": "A re-evaluation of evidence for light neutral bosons in nuclear emulsions. F Boer, C A Fields, arXiv:1001.3897Int. J. mod. Phys. E. 20F. de Boer, C. A. Fields, A re-evaluation of evidence for light neutral bosons in nuclear emulsions, Int. J. mod. Phys. E 20 (2011) 1787-1803, arXiv:1001.3897.",
"... |
Many bioinformatics programming tasks can be automated with ChatGPT
Stephen R Piccolo stephen_piccolo@byu.edu
Department of Biology
Brigham Young University
ProvoUTUSA
Paul Denny
School of Computer Science
The University of Auckland
AucklandNew Zealand
Andrew Luxton-Reilly
School of Computer Science
The Univers... | 257,757,225 | {
"arxiv": "2303.13528",
"mag": null,
"acl": null,
"pubmed": "37769024v1",
"pubmedcentral": 10564134,
"dblp": "journals/ploscb/PiccoloDLPR23",
"doi": "10.1371/journal.pcbi.1011511"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2303.13528v1.pdf"
],
"pdf_sha": "94ac118c522c065e24d9090b9f7827b83e8ff2f4",
"open_access": {
"license": "CCBY",
"url": "https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1011511&type=printable",
"status": "GOLD"
}
} | Many bioinformatics programming tasks can be automated with ChatGPT | [
"Stephen R Piccolo stephen_piccolo@byu.edu \nDepartment of Biology\nBrigham Young University\nProvoUTUSA",
"Paul Denny \nSchool of Computer Science\nThe University of Auckland\nAucklandNew Zealand",
"Andrew Luxton-Reilly \nSchool of Computer Science\nThe University of Auckland\nAucklandNew Zealand",
"Samuel P... | Computer programming is a fundamental tool for life scientists, allowing them to carry out many essential research tasks.However, despite a variety of educational efforts, learning to write code can be a challenging endeavor for both researchers and students in life science disciplines.Recent advances in artificial int... | [
{
"title": "Introduction",
"content": "For decades, the life-sciences community has called for researchers to gain a greater awareness of \"computing in all its forms\" 1 .This need is now greater than ever.A 2016 survey of principal investigators from diverse biology disciplines revealed that almost 90% of... | [
{
"id": "",
"caption": "Figure 2: Number of ChatGPT iterations per exercise.For each exercise prompt, we gave ChatGPT up to 10 attempts at generating a code solution that successfully passed the tests.The counts above each bar represents the number of exercises that required a particular number of attempts.... | [
{
"text": ". R J Beynon, 10.1093/bioinformatics/1.1.1CABIOS editorial. Bioinformatics. 11985",
"doi": ""
},
{
"text": "Unmet needs for analyzing biological big data: A survey of 704 NSF principal investigators. L Barone, J Williams, D Micklos, 10.1371/journal.pcbi.1005755PLOS Computational Biology. ... |
The Legendre-Hadamard condition in Cosserat elasticity theory
2 Jun 2020 20 May, 2020
Milad Shirani amiladshirani@berkeley.edu
Department of Mechanical Engineering
University of California Berkeley
CA. 94720USA
David J Steigmann bdsteigmann@berkeley.edu
Department of Mechanical Engineering
University of California... | 219,179,811 | {
"arxiv": "2006.01539",
"mag": 3034006412,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1093/qjmam/hbaa013"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2006.01539v1.pdf"
],
"pdf_sha": "8564c0a793bc2c8f1f73bb9081462bc2bd14453c",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/2006.01539",
"status": "GREEN"
}
} | The Legendre-Hadamard condition in Cosserat elasticity theory | [
"Milad Shirani amiladshirani@berkeley.edu \nDepartment of Mechanical Engineering\nUniversity of California Berkeley\nCA. 94720USA",
"David J Steigmann bdsteigmann@berkeley.edu \nDepartment of Mechanical Engineering\nUniversity of California Berkeley\nCA. 94720USA",
"Patrizio Neff patrizio.neff@uni-due.de \nChai... | The Legendre-Hadamard necessary condition for energy minimizers is derived in the framework of Cosserat elasticity theory. | [
{
"title": "Introduction",
"content": "Cosserat elasticity [1] is enjoying a resurgence as a framework for the modeling and analysis of scale effects in solids associated with the presence of microstructure. Definitive modern treatments of the subject may be found in [2][3][4][5][6][7][8][9][10][11]. Here w... | [
{
"id": "",
"caption": "(Rσ)ν on ∂κ t and c = (Rµ)ν on ∂κ c , (2.21)",
"content": "(Rσ)ν on ∂κ t and c = (Rµ)ν on ∂κ c , (2.21)"
},
{
"id": "",
"caption": "[10] to model isotropic materials, where µ, µ c , λ and a 1−3 are material constants and I is the identity. Using the variational formul... | [
{
"text": "Théorie des corps déformables. E Cosserat, F Cosserat, HermanParisE. Cosserat and F. Cosserat. Théorie des corps déformables. Herman, Paris, (1909).",
"doi": ""
},
{
"text": "Theories of elasticity with couple-stress. R A Toupin, Arch. Ration. Mech. Anal. 17R. A. Toupin. Theories of elast... |
10 Aug 2004
10 Aug 2004
F inite tem perature super uid density in very underdoped cuprates Igor F. H erbut and M atthew J. C ase D epartm ent of Physics, Sim on Fraser U niversity, B urnaby, B ritish C ol um bia, C anada V 5A 1S6T he com bi nati on of a l arge gap, l ow transi ti on tem perature, and quasi tw o-di m ... | 119,481,694 | {
"arxiv": "cond-mat/0401101",
"mag": 1984414605,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevb.70.094516"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/cond-mat/0401101v2.pdf"
],
"pdf_sha": "0c68441e34efde3879bc5ce8ddea0fdb0c444a2d",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/cond-mat/0401101",
"status": "GREEN"
}
} | [] | F inite tem perature super uid density in very underdoped cuprates Igor F. H erbut and M atthew J. C ase D epartm ent of Physics, Sim on Fraser U niversity, B urnaby, B ritish C ol um bia, C anada V 5A 1S6T he com bi nati on of a l arge gap, l ow transi ti on tem perature, and quasi tw o-di m ensi onal i ty i n strongl... | [
{
"title": "1",
"content": ". W e have taken v F = 2: 5 10 7 cm /s. T he dotted l i ne represents then the Eq. 12 w i th d = 10 A and z = 1 and no tti ng param eters. A som ew hat better agreem ent i s obtai ned by assum i ng z = T c =C w i th C = 79K ,w hi ch we show as the ful ll i ne,as an i l l ustrati ... | [
{
"id": "",
"caption": "F i s a di m ensi onl ess functi on ofi ts three di m ensi onl ess argum ents and 0 = 0 (J;e ; ) i s the hel i ci ty H el i ci ty m odul us vs. tem perature i n the sel fconsi stent G aussi an approxi m ati on, for 2D X Y m odel ( = e = 0),and w i th C oul om b i nteracti on ( = 0,e ... | [
{
"text": ". M Sutherl, D G Thorn, R W , F Onni Ng, S Aki M Oto, H Zhang, C Proust, E Oakni N, C Lupi En, L Tai L L Efer, R Li Ang, D A Onn, W N Ardy, R Agnon, N E Ussey, T K I M Ura, M Ohara, H Takagi, Phys.R ev.B. 67174520M . Sutherl and, D . G . H aw thorn, R . W . H i l l , F. R on- ni ng,S.W aki m oto,H .Z... | |
Tightly Localized Stationary Pulses in Multi-Level Atomic System
arXiv:quant-ph/0606051v4 18 Jan 2007
Xiong-Jun Liu
Department of Physics
National University of Singapore
2 Science Drive 3117542Singapore
Xin Liu
Department of Physics
Texas A&M University
77843-4242College Station, TexasUSA
Zheng-Xin Liu
Theoreti... | 119,502,538 | {
"arxiv": "quant-ph/0606051",
"mag": 2012725790,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physreva.75.023809"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/quant-ph/0606051v4.pdf"
],
"pdf_sha": "fe158b8ad00cec4d27103c148ba93dc019970b08",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/quant-ph/0606051",
"status": "GREEN"
}
} | Tightly Localized Stationary Pulses in Multi-Level Atomic System | [
"Xiong-Jun Liu \nDepartment of Physics\nNational University of Singapore\n2 Science Drive 3117542Singapore",
"Xin Liu \nDepartment of Physics\nTexas A&M University\n77843-4242College Station, TexasUSA",
"Zheng-Xin Liu \nTheoretical Physics Division\nNankai Institute of Mathematics\nNankai University\n300071Tian... | We show the pulse matching phenomenon can be obtained in the general multi-level system with electromagnetically induced transparency (EIT). For this we find a novel way to create tightly localized stationary pulses by using counter-propagating pump fields. The present process is a spatial compression of excitation so ... | [
{
"title": "FIG",
"content": ""
},
{
"title": "FIG. 2 :",
"content": ""
},
{
"title": "FIG. 3 :",
"content": ""
}
] | [
{
"id": "",
"caption": ". 1: (color online) (a) General m-level atomic system coupled to m − 2 quantized probe and classical pump fields which propagate in +z or −z directions. (b) No. 1 to No. m − 3 pump/probe pulses propagate in the +z direction, while No. m − 2 pump/probe pulse propagates in the −z direc... | [
{
"text": ". S E Harris, J E Field, A Kasapi, Phys. Rev. A. 4629S. E. Harris, J. E. Field and A. Kasapi, Phys. Rev. A 46, R29 (1992);",
"doi": ""
},
{
"text": "M O Scully, M S Zubairy, Quantum Optics. CambridgeCambridge University PressM. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge Univer... |
Compartmental analysis of dynamic nuclear medicine data: regularization procedure and application to physiology
Fabrice Delbary
Institut für Mathematik
Johannes Gutenberg-Universität Mainz
Mainz
Sara Garbarino
Centre for Medical Image Computing
Department of Computer Science
University College London
London
Comp... | 247,760,360 | {
"arxiv": "1608.01825",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1080/17415977.2018.1512603"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1608.01825v1.pdf"
],
"pdf_sha": "dfb0e593cbbf27ce906b74c185af7708cc80b089",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1608.01825",
"status": "GREEN"
}
} | Compartmental analysis of dynamic nuclear medicine data: regularization procedure and application to physiology | [
"Fabrice Delbary \nInstitut für Mathematik\nJohannes Gutenberg-Universität Mainz\nMainz",
"Sara Garbarino \nCentre for Medical Image Computing\nDepartment of Computer Science\nUniversity College London\nLondon"
] | Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the second of a series of two that deal with the problem of tracer coefficient estimation via comp... | [
{
"title": "Introduction",
"content": "Nuclear medicine imaging is a class of functional imaging modality that utilizes radioactive tracers to investigate specific physiological processes. Such tracers are in general short-lived isotopes that are injected in the subject's blood and linked to chemical compou... | [
{
"id": "",
"caption": "2-compartment catenary model",
"content": "Figure 2 .\n22-compartment catenary model"
},
{
"id": "",
"caption": "2-compartment model with 2 input functions (liver)",
"content": "Figure 3 .\n32-compartment model with 2 input functions (liver)"
},
{
"id": ""... | [
{
"text": ". J M Ollinger, J A Fessler, IEEE Signal Processing Magazine. 14Ollinger J M and Fessler J A 1997 IEEE Signal Processing Magazine 14 43-55",
"doi": ""
},
{
"text": ". G Antoch, N Saoudi, H Kuehl, G Dahmen, S P Mueller, T Beyer, A Bockisch, J Debatin, L S Freudenberg, Journal of Clinical O... |
Analyticity, Unitarity and One-loop Graviton Corrections to Compton Scattering
30 Jul 2012
Hovhannes R Grigoryan es:hg41@nyu.edu
Center for Cosmology and Particle Physics Department of Physics
New York University
10003Washington Place, New YorkNYUSA
Analyticity, Unitarity and One-loop Graviton Corrections to Comp... | 119,244,057 | {
"arxiv": "1207.7095",
"mag": 2063976604,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1007/jhep10(2012)030"
} | {
"pdf_urls": [
"http://export.arxiv.org/pdf/1207.7095"
],
"pdf_sha": "b2296bb1aeb63b2b7d8ad31f3a36480f5b81aec0",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1207.7095",
"status": "GREEN"
}
} | Analyticity, Unitarity and One-loop Graviton Corrections to Compton Scattering | [
"Hovhannes R Grigoryan es:hg41@nyu.edu \nCenter for Cosmology and Particle Physics Department of Physics\nNew York University\n\n\n10003Washington Place, New YorkNYUSA"
] | We compute spin-flip cross section for graviton photoproduction on a spin-1/2 target of finite mass. Using this tree-level result, we find one-loop graviton correction to the spin-flip lowenergy forward Compton scattering amplitude by using Gerasimov-Drell-Hearn sum rule. We show that this result agrees with the corres... | [
{
"title": "Introduction",
"content": "It has been known for a long time that in computing the one-loop graviton corrections to the anomalous magnetic moment of a charged lepton miraculous cancellations occur, rendering to a finite result. In four dimensions this has been shown first by Berends and Gastmans... | [
{
"id": "",
"caption": "One-loop graviton diagrams that contribute to the anomalous magnetic moment of lepton. The wavy lines represent photons, dashed lines -gravitons, and solid lines -leptons.",
"content": "Figure 1 :\n1One-loop graviton diagrams that contribute to the anomalous magnetic moment of le... | [
{
"text": "Quantum Gravity And The Electron And Muon Anomalous Magnetic Moments. F A Berends, R Gastmans, Phys. Lett. B. 55311F. A. Berends and R. Gastmans, \"Quantum Gravity And The Electron And Muon Anomalous Magnetic Moments,\" Phys. Lett. B 55, 311 (1975).",
"doi": ""
},
{
"text": "Extra Dimensi... |
Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type
20 Jul 2020
Leithold L Aurazo-Alvarez
IMECC-Department of Mathematics CEP
University of Campinas
13083-859CampinasSPBrazil
Lucas C F Ferreira
IMECC-Department of Mathematics CEP
University o... | 220,646,980 | {
"arxiv": "2007.09840",
"mag": 3194304176,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1007/s42985-021-00109-4"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2007.09840v1.pdf"
],
"pdf_sha": "a5dcecc616226f13e8f9ad15706e93a2d2632e67",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/2007.09840",
"status": "GREEN"
}
} | Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type | [
"Leithold L Aurazo-Alvarez \nIMECC-Department of Mathematics CEP\nUniversity of Campinas\n13083-859CampinasSPBrazil",
"Lucas C F Ferreira \nIMECC-Department of Mathematics CEP\nUniversity of Campinas\n13083-859CampinasSPBrazil"
] | We establish the global well-posedness of the 3D fractional Boussinesq-Coriolis system with stratification in a framework of Fourier type, namely spaces of Fourier-Besov type with underlying space being Morrey spaces (FBM-spaces, for short). Under suitable conditions and rescaled density fluctuation, the result is unif... | [
{
"title": "Introduction",
"content": "We are concerned with the initial value problem (IVP) for the 3D fractional Boussinesq-Coriolis equations with stratification (FBCS)\nu(x, 0) = u 0 (x), θ(0, x) = θ 0 (x) for x ∈ R 3 , where u = (u 1 (x, t), u 2 (x, t), u 3 (x, t)), θ = θ(x, t) and p = p(x, t) stand fo... | [
{
"id": "",
"caption": "Similar computations, using the fractional Stokes-Coriolis semigroup S α Ω (t), instead of the fractional Boussinesq-Coriolis-Stratification semigroup, which is defined via the Fourier transform as [S α Ω (t)f ]ˆ(ξ) = e −νt|ξ| 2α cos(",
"content": "Remark 3. 2 .\n2Similar computa... | [
{
"text": "Uniform global well-posedness of the Navier-Stokes-Coriolis system in a new critical space. M F De Almeida, L C F Ferreira, L S M Lima, Mathematische Zeitschrift. 2873-4M.F. de Almeida, L.C.F. Ferreira, and L.S.M. Lima, Uniform global well-posedness of the Navier- Stokes-Coriolis system in a new crit... |
18 Nov 1999
S Daul
Institute for Theoretical Physics
University of California
93106Santa-BarbaraCA
D J Scalapino
Physics Department
University of California
93106Santa-BarbaraCA
Steven R White
Department of Physics and Astronomy
University of California
92697IrvineCA
18 Nov 1999Effect of the W -term for a t − U... | 119,339,826 | {
"arxiv": "cond-mat/9911290",
"mag": 3021479299,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevb.61.15526"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/cond-mat/9911290v1.pdf"
],
"pdf_sha": "6737aa2307f1528ece7c7ea2a084d815f6e82a2c",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/cond-mat/9911290",
"status": "GREEN"
}
} | [
"S Daul \nInstitute for Theoretical Physics\nUniversity of California\n93106Santa-BarbaraCA",
"D J Scalapino \nPhysics Department\nUniversity of California\n93106Santa-BarbaraCA",
"Steven R White \nDepartment of Physics and Astronomy\nUniversity of California\n92697IrvineCA"
] | Antiferromagnetic and d x 2 −y 2 -pairing correlations appear delicately balanced in the 2D Hubbard model. Whether doping can tip the balance to pairing is unclear and models with additional interaction terms have been studied. In one of these, the square of a local hopping kinetic energy HW was found to favor pairing.... | [
{
"title": "S(q x )",
"content": "FIG. 4. Structure factor S(q) of the spin-spin correlation function versus qx for the half-filled system and qy = π. The inset shows an enlargement of the region near (π, π).\nWe now turn to the doped case and consider the same lattice with U = 4 and 8 holes corresponding t... | [
{
"id": "",
"caption": "The rung-rung singlet pairing correlation function Dyy(ℓ) versus ℓ on a half-filled ladder with U = 4 for (a) all Wi = 0, only W5 = 0.25 and all Wi = 0.25 and (b) all Wi = 0 and only one Wi = 0.25.",
"content": "FIG. 1 .\n1The rung-rung singlet pairing correlation function Dyy(ℓ)... | [
{
"text": "Proc. 10 th Anniversary HTS Workshop on Physics, Materials and Applications. Ed. B. Batlogg, C. W. Chu, W.10 th Anniversary HTS Workshop on Physics, Materials and ApplicationsProc. 10 th Anniversary HTS Workshop on Physics, Ma- terials and Applications (Ed. B. Batlogg, C. W. Chu, W.",
"doi": ""
... | |
The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
9 Jan 2015
O Götze
Institut für Theoretische Physik
Universität Magdeburg
39016MagdeburgGermany
J Richter
Institut für Theoretische Physik
Universität Magdeburg
39016MagdeburgGermany
The ground-state phase diagram of ... | 119,111,267 | {
"arxiv": "1501.02146",
"mag": 2315383617,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevb.91.104402"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1501.02146v1.pdf"
],
"pdf_sha": "f9b18822c4de28a39aada02c3297dbea33462023",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1501.02146",
"status": "GREEN"
}
} | The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study | [
"O Götze \nInstitut für Theoretische Physik\nUniversität Magdeburg\n39016MagdeburgGermany",
"J Richter \nInstitut für Theoretische Physik\nUniversität Magdeburg\n39016MagdeburgGermany"
] | We use the coupled cluster method to high orders of approximation in order to calculate the ground-state phase diagram of the XXZ spin-s kagome antiferromagnet with easy-plane anisotropy, i.e. the anisotropy parameter ∆ varies between ∆ = 1 (isotropic Heisenberg model) and ∆ = 0 (XY model). We find that for the extreme... | [
{
"title": "FIG. 1 .",
"content": ""
},
{
"title": "FIG. 2 .",
"content": ""
},
{
"title": "FIG. 4 .",
"content": ""
},
{
"title": "TABLE I .",
"content": ""
}
] | [
{
"id": "",
"caption": "The extrapolated CCM GS energy per spin e0|n→∞ using the √ 3× √ 3 reference state (left) and the q = 0 reference state (right) as a function of the anisotropy parameter ∆ for spin quantum numbers s = 1/2, 1, 3/2, . . . , 9/2, 5.",
"content": "FIG. 1 .\n1The extrapolated CCM GS en... | [
{
"text": ". S Sachdev, Phys. Rev. B. 4512377S. Sachdev, Phys. Rev. B 45, 12377 (1992).",
"doi": ""
},
{
"text": ". A Chubukov, Phys. Rev. Lett. 69832A. Chubukov, Phys. Rev. Lett. 69, 832 (1992).",
"doi": ""
},
{
"text": ". J N Reimers, A J Berlinsky, Phys. Rev. B. 489539J. N. Reimers an... |
Probing the plateau-insulator quantum phase transition in the quantum Hall regime
2 Dec 1998
R T F Van Schaijk
A De Visser
S Olsthoorn
H P Wei
A M M Pruisken
Waals-Zeeman Institute
High Field Magnet Laboratory
University of Amsterdam
Valckenierstraat 651018 XEAmsterdamThe Netherlands
Department of Physics
Uni... | 8,942,936 | {
"arxiv": "cond-mat/9812035",
"mag": 1991494774,
"acl": null,
"pubmed": "11017569",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevlett.84.1567"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/cond-mat/9812035v1.pdf"
],
"pdf_sha": "b31d94d9d87d2ffec570dd28b9456deb0873362a",
"open_access": {
"license": null,
"url": "https://pure.uva.nl/ws/files/3014703/12615_88238y.pdf",
"status": "GREEN"
}
} | Probing the plateau-insulator quantum phase transition in the quantum Hall regime | [
"R T F Van Schaijk",
"A De Visser",
"S Olsthoorn",
"H P Wei",
"A M M Pruisken",
"Waals-Zeeman Institute\nHigh Field Magnet Laboratory\nUniversity of Amsterdam\nValckenierstraat 651018 XEAmsterdamThe Netherlands",
"Department of Physics\nUniversity of Nijmegen\nSwain Hall West6525 EDToernooiveld, Nijmege... | We report quantum Hall experiments on the plateau-insulator transition in a low mobility In.53Ga.47As/InP heterostructure. The data for the longitudinal resistance ρxx follow an exponential law and we extract a critical exponent κ = .55 ± .05 which is slightly different from the established value κ = .42±.04 for the pl... | [
{
"title": "FIG. 1 . 0 .",
"content": ""
},
{
"title": "FIG. 3 .",
"content": ""
}
] | [
{
"id": "",
"caption": "ρxx and ρxy data with varying B. The curves are labelled a, b, . . . , n and the corresponding T 's are 0.13, Bc is the critical B (see text).",
"content": "FIG. 1 . 0 .\n10ρxx and ρxy data with varying B. The curves are labelled a, b, . . . , n and the corresponding T 's are 0.1... | [
{
"text": ". H P Wei, Phys. Rev. Lett. 611294H.P.Wei et al., Phys. Rev. Lett. 61 1294 (1988);",
"doi": ""
},
{
"text": "Pruisken in Localization and confinement of electrons in semiconductors. H P Wei, D C Tsui, A M , Kuchar, H. Heinrich and G. Bauer edsSpringer VerlagBerlinH.P.Wei, D.C. Tsui and A.... |
A non-absorbing SIR stochastic lattice gas model on hybrid lattices
30 Nov 2021
Carlos Handrey
Exact and Natural Sciences Center
Universidade Federal Rural do Semi-Árido-UFERSA
PO Box 013759625-900MossoróCEP, RNBrazil
Araujo Ferraz
Exact and Natural Sciences Center
Universidade Federal Rural do Semi-Árido-UFERSA
P... | 238,259,855 | {
"arxiv": "2110.01054",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1016/j.physleta.2021.127871"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2110.01054v2.pdf"
],
"pdf_sha": "1521a967d7b2782cfd4c8127d6c7b5f9b1402a23",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/2110.01054",
"status": "GREEN"
}
} | A non-absorbing SIR stochastic lattice gas model on hybrid lattices | [
"Carlos Handrey \nExact and Natural Sciences Center\nUniversidade Federal Rural do Semi-Árido-UFERSA\nPO Box 013759625-900MossoróCEP, RNBrazil",
"Araujo Ferraz \nExact and Natural Sciences Center\nUniversidade Federal Rural do Semi-Árido-UFERSA\nPO Box 013759625-900MossoróCEP, RNBrazil"
] | In this paper, we perform Monte Carlo calculations to study the critical behavior of the spread of infectious diseases through a novel approach to the SIR epidemiological model. A stochastic lattice gas version of the model was applied on hybrid lattices which, in turn, are generated from typical square lattices when i... | [
{
"title": "Introduction",
"content": "In the late 1920s, Kermack and McKendrick [1] proposed a system of ordinary differential equations for determining the temporal evolution of the population of individuals who interacted with each other when exposed to an infectious disease. These individuals were initi... | [
{
"id": "",
"caption": "Typical spanning clusters along with few smaller clusters formed close to the epidemic threshold λ c on a 100×100 lattice for two different p cases. (a) Case p = 0 (at λ = 0.16) and (b) Case p = 1/2 (at λ = 0.21). Susceptible, infected, and recovered individuals are represented by bl... | [
{
"text": ". W , W. .",
"doi": ""
},
{
"text": ". A G Kermack, Mckendrick, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 115Kermack, A. G. Mckendrick, Proceedings of the Royal So- ciety of London. Series A, Containing Papers of a Ma... |
Speckle-free laser imaging
Brandon Redding brandon.redding@yale.edu
Department of Applied Physics
Yale University
06511New HavenCTUSA
Michael A Choma
Departments of Diagnostic Radiology and of Pediatrics
Yale School of Medicine
06520New HavenCTUSA
Department of Biomedical Engineering
Yale University
06511New Hav... | 11,366,036 | {
"arxiv": "1110.6860",
"mag": 2779507318,
"acl": null,
"pubmed": "24570762",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1038/nphoton.2012.90"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1110.6860v1.pdf"
],
"pdf_sha": "191d65aae86809ac669c9f09c1e824ae0b6fb101",
"open_access": {
"license": null,
"url": "https://europepmc.org/articles/pmc3932313?pdf=render",
"status": "GREEN"
}
} | Speckle-free laser imaging | [
"Brandon Redding brandon.redding@yale.edu \nDepartment of Applied Physics\nYale University\n06511New HavenCTUSA",
"Michael A Choma \nDepartments of Diagnostic Radiology and of Pediatrics\nYale School of Medicine\n06520New HavenCTUSA\n\nDepartment of Biomedical Engineering\nYale University\n06511New HavenCTUSA",
... | Many imaging applications require increasingly bright illumination sources, motivating the replacement of conventional thermal light sources with light emitting diodes (LEDs), superluminescent diodes (SLDs) and lasers. Despite their brightness, lasers and SLDs are poorly suited for full-field imaging applications becau... | [
{
"title": "Fig. 1 .",
"content": ""
},
{
"title": "Fig. 2 .",
"content": ""
},
{
"title": "Fig. 3 .",
"content": ""
},
{
"title": "Fig. 4 .",
"content": ""
}
] | [
{
"id": "",
"caption": "Light sources for imaging. Light sources are compared in terms of the two parameters most relevant to full-field, non-scanning imaging: the photon degeneracy and the spatial coherence. Random lasers represent a new class of light source with high photon degeneracy and low spatial coh... | [
{
"text": "Sparkling spots and random diffraction. B M Oliver, Proc IEEE. 51Oliver, B. M. Sparkling spots and random diffraction. Proc IEEE 51, 220-221 (1963).",
"doi": ""
},
{
"text": "Optical methods for suppressing speckle in Speckle phenomena in optics. J W Goodman, Roberts & CompanyGoodman, J. ... |
Quantum Friction of Micromechanical Resonators at Low Temperatures
15 Jan 2003
Kang-Hun Ahn
School of Physics
Seoul National University
151-747SeoulKorea
Pritiraj Mohanty
Department of Physics
Boston University
02215BostonMA
Quantum Friction of Micromechanical Resonators at Low Temperatures
15 Jan 2003(Dated: Mar... | 17,088,605 | {
"arxiv": "cond-mat/0301255",
"mag": 2004742719,
"acl": null,
"pubmed": "12633438",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevlett.90.085504"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/cond-mat/0301255v1.pdf"
],
"pdf_sha": "9087c4f8005fbd2bf2393be0f7fdeb2ab5a935a6",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/cond-mat/0301255",
"status": "GREEN"
}
} | Quantum Friction of Micromechanical Resonators at Low Temperatures | [
"Kang-Hun Ahn \nSchool of Physics\nSeoul National University\n151-747SeoulKorea",
"Pritiraj Mohanty \nDepartment of Physics\nBoston University\n02215BostonMA"
] | Dissipation of micro-and nano-scale mechanical structures is dominated by quantum-mechanical tunneling of two-level defects intrinsically present in the system. We find that at high frequenciesusually, for smaller, micron-scale structures-a novel mechanism of phonon pumping of two-level defects gives rise to weakly tem... | [
{
"title": "12",
"content": "). Q −1 shows a weak temperature dependence with decreasing temperature, as Q −1 1 becomes more important than Q −1 2 at low temperatures. The low-temperature saturation value of Q −1 for ωτ ǫ ≥ 1 is well approximated by ∼ 0.3(1/ωτ ǫ )(nγ 2 /ρv 2 ). Now, let us estimate τ ǫ from... | [
{
"id": "",
"caption": "0 , T = 0) = 0. SinceP (∆ s , T = 0) is a smoothly-decaying function of ∆ s , an analytic formula for Q −1 1 (T = The schematic diagram describes the energy-pumping process of the two-level atom from the acoustic wave to phonons. The crossing curves represent the time evolution of th... | [
{
"text": ". D Bishop, Physics Today. 54D. Bishop et al., Physics Today 54, 38 (October)(2001).",
"doi": ""
},
{
"text": ". C A Bolle, Nature. 39943C.A. Bolle et al., Nature 399, 43 (1999).",
"doi": ""
},
{
"text": ". J Fritz, Science. 288316J. Fritz et al., Science 288, 316 (2000).",
... |
Compensating the Noise of a Communication Channel via Asymmetric Encoding of Quantum Information
28 Jan 2010
Marco Lucamarini
CNISM UdR
University of Camerino
Via Madonna delle Carceri 962032CamerinoMCItaly
Giovanni Di Giuseppe
Physics Department
University of Camerino
Via Madonna delle Carceri 962032CamerinoMCIta... | 35,052,760 | {
"arxiv": "1001.5234",
"mag": 2000106249,
"acl": null,
"pubmed": "21230820",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevlett.105.140504"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1001.5234v1.pdf"
],
"pdf_sha": "7a700f14724b08d61d2630a224083825b2d5c12d",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1001.5234",
"status": "GREEN"
}
} | Compensating the Noise of a Communication Channel via Asymmetric Encoding of Quantum Information | [
"Marco Lucamarini \nCNISM UdR\nUniversity of Camerino\nVia Madonna delle Carceri 962032CamerinoMCItaly",
"Giovanni Di Giuseppe \nPhysics Department\nUniversity of Camerino\nVia Madonna delle Carceri 962032CamerinoMCItaly",
"David Vitali \nPhysics Department\nUniversity of Camerino\nVia Madonna delle Carceri 962... | An asymmetric preparation of the quantum states sent through a noisy channel can enable a new way to monitor and actively compensate the channel noise. The paradigm of such an asymmetric treatment of quantum information is the Bennett 1992 protocol, in which the ratio between conclusive and inconclusive counts is in di... | [
{
"title": "FIG. 2 :",
"content": ""
},
{
"title": "FIG. 3 :",
"content": ""
}
] | [
{
"id": "",
"caption": "PACS numbers: 03.67.Dd, 03.65.Hk",
"content": "PACS numbers: 03.67.Dd, 03.65.Hk"
},
{
"id": "",
"caption": "FIG. 1: States of the B92 protocol with a characteristic angle θ = π 12 (15 • ). Left: channel without phase-drift, ε = 0. Center: channel with a phase-drift of... | [
{
"text": ". N Gisin, G Ribordy, W Tittel, H Zbinden, Rev. Mod. Phys. 74145N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).",
"doi": ""
},
{
"text": ". C H Bennett, Phys. Rev. Lett. 683121C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).",
"doi": ""
},
{
"te... |
Phase-matched nonlinear wave-mixing processes in XUV region with multicolor lasers
Anh Khoa
Centre for Quantum and Optical Science
Swinburne University of Technology
3122MelbourneAustralia
Tran
Centre for Quantum and Optical Science
Swinburne University of Technology
3122MelbourneAustralia
Khuong Ba Dinh
Centre... | 90,261,532 | {
"arxiv": "1904.00356",
"mag": 3102268659,
"acl": null,
"pubmed": "31045048",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1364/ao.58.002540"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1904.00356v1.pdf"
],
"pdf_sha": "9574bec2d608b1250f02296aed28fe799e8f70fc",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1904.00356",
"status": "GREEN"
}
} | Phase-matched nonlinear wave-mixing processes in XUV region with multicolor lasers | [
"Anh Khoa \nCentre for Quantum and Optical Science\nSwinburne University of Technology\n3122MelbourneAustralia",
"Tran \nCentre for Quantum and Optical Science\nSwinburne University of Technology\n3122MelbourneAustralia",
"Khuong Ba Dinh \nCentre for Quantum and Optical Science\nSwinburne University of Technolo... | We report here experimental results of perturbative nonlinear optical wave-mixing processes in the extreme ultraviolet region by using two-color and three-color laser fields. Besides the usual odd-harmonic spectrum of high harmonic generation, new spectral components are observed when multiple incommensurate lasers (on... | [
{
"title": "Introduction",
"content": "Recent breakthroughs in ultrafast optical physics [1] allow us to study laser-matter interactions in the strong-field regime, and the quasi-classical model [2] and quantum mechanical calculations [3] for the high harmonic generation (HHG) process make recollisional phy... | [
{
"id": "",
"caption": "Wave-mixing spectra of the 25-Torr krypton gas at 0 fs time delay gated by twocolor fields (800 nm and 1400 nm [blue dashed line], 800 nm and 1860 nm [black triangles]), and three-color fields 800 nm, 1400 nm, and 1860 nm (red solid line). Inset (a) shows the sharp HHG spectrum drive... | [
{
"text": "Compression of amplified chirped optical pulses. D Strickland, G Mourou, Opt. Commun. 56D. Strickland and G. Mourou, \"Compression of amplified chirped optical pulses,\" Opt. Commun. 56, 219-221 (1985).",
"doi": ""
},
{
"text": "Plasma perspective on strong field multiphoton ionization. P... |
Nonlinear susceptibilities and the measurement of a cooperative length
22 May 2008 (Dated: May 23, 2008)
E Lippiello
Dipartimento di Scienze Fisiche
Universitá di Napoli "Federico II"
80125NapoliItaly
F Corberi
Dipartimento di Matematica ed Informatica, via Ponte don Melillo
Università di Salerno
84084FiscianoSAIt... | 118,391,184 | {
"arxiv": "0805.3457",
"mag": 2065032382,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevb.77.212201"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0805.3457v1.pdf"
],
"pdf_sha": "9d3fcbf042345cf20377c8f645c1bda1cf18b357",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/0805.3457",
"status": "GREEN"
}
} | Nonlinear susceptibilities and the measurement of a cooperative length | [
"E Lippiello \nDipartimento di Scienze Fisiche\nUniversitá di Napoli \"Federico II\"\n80125NapoliItaly",
"F Corberi \nDipartimento di Matematica ed Informatica, via Ponte don Melillo\nUniversità di Salerno\n84084FiscianoSAItaly",
"A Sarracino \nDipartimento di Fisica \"E.R.Caianiello\", via S.Allende\nUniversit... | We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which takes a similar form for systems governed by a master equation or by a Langevin equation, can be derived to every order, i... | [
{
"title": "FIG. 1 :",
"content": ""
},
{
"title": "FIG. 2 :",
"content": ""
}
] | [
{
"id": "",
"caption": "namely the counterpart of the standard static equilibrium relation between correlations and susceptibilities. Taking the k = 0 component χ",
"content": "namely the counterpart of the standard static equilibrium relation between correlations and susceptibilities. Taking the k = 0 ... | [
{
"text": ". L F Cugliandolo, J Kurchan, L Peliti, Phys.Rev.E. 553898L.F. Cugliandolo, J. Kurchan, and L. Peliti Phys.Rev.E 55, 3898 (1997).",
"doi": ""
},
{
"text": ". L F Cugliandolo, J Kurchan, Phys.Rev.Lett. 71173L.F. Cugliandolo and J. Kurchan, Phys.Rev.Lett. 71, 173 (1993);",
"doi": ""
}... |
q-ANALOG OF TABLEAU CONTAINMENT
December 6, 2008.
Soo Jang
Kim
q-ANALOG OF TABLEAU CONTAINMENT
December 6, 2008.3B95EF53B0489D692EE3F099A29989E1arXiv:0812.1256v1[math.CO]
We prove a q-analog, which is valid if q is a positive real number, of the following: the probability that, when n tends to infinity, a randomly ... | 17,659,561 | {
"arxiv": "0812.1256",
"mag": 2952880614,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/jct/Kim11b",
"doi": "10.1016/j.jcta.2010.08.011"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0812.1256v2.pdf"
],
"pdf_sha": "6c8810d0b975ce07d84a5265dbb972dca76e8f73",
"open_access": {
"license": null,
"url": "https://arxiv.org/pdf/0812.1256",
"status": "GREEN"
}
} | q-ANALOG OF TABLEAU CONTAINMENT | [
"Soo Jang",
"Kim"
] | We prove a q-analog, which is valid if q is a positive real number, of the following: the probability that, when n tends to infinity, a randomly chosen standard Young tableau of size n contains a fixed standard Young tableau of shape λ ⊢ k is equal to f λ k! (Journal of Combinatorial Theory Series A, volume 97,[117][11... | [
{
"title": "Introduction",
"content": "Let S n denote the set of permutations of [n] = {1, 2, . . ., n}.Let π = π 1 π 2 • • • π n be a permutation in S n .Let π ≤k (resp.π >k ) denote the permutation obtained from π by taking integers i ≤ k (resp.i > k) and by order-preserving relabeling.Let π ≤k (resp.π >k... | [
{
"id": "",
"caption": "(π) = (1, 21, 1, 213, 01, 101, 11010, 0111).It is easy to see that φ a,b is a bijection.Let σ ∈ S a , τ ∈ S b and r ∈ [a+b] b",
"content": "φ 2 , 3\n23\n(π) = (1, 21, 1, 213, 01, 101, 11010, 0111).It is easy to see that φ a,b is a bijection.Let σ ∈ S a , τ ∈ S b and r ∈ [a+b] b"
... | [
{
"text": "Permutation statistics and partitions. A M Garsia, I Gessel, Adv. in Math. 3131979",
"doi": ""
},
{
"text": "Subsequence containment by involutions. Aaron D Jaggard, Electron. J. Combin. 122005Research Paper",
"doi": ""
},
{
"text": "The initial involution patterns of permutat... |
On some approximate methods for nonlinear models
26 Apr 2009
Francisco M Fernández
División Química Teórica
INIFTA (UNLP
CCT La Plata-CONICET)
Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 161900La PlataArgentina
On some approximate methods for nonlinear models
26 Apr 2009
We show that recent applications of ... | 12,373,411 | {
"arxiv": "0904.4044",
"mag": 2952066839,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/amc/Fernandez09",
"doi": "10.1016/j.amc.2009.04.060"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0904.4044v1.pdf"
],
"pdf_sha": "a314cb760ebd38ab3c459b28284dc33100d466cc",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/0904.4044",
"status": "GREEN"
}
} | On some approximate methods for nonlinear models | [
"Francisco M Fernández \nDivisión Química Teórica\nINIFTA (UNLP\nCCT La Plata-CONICET)\nDiag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 161900La PlataArgentina"
] | We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems. | [
{
"title": "Introduction",
"content": "In a series of papers we have shown that some particular applications of some variational and perturbation approaches (VAPA) like, for example, the homotopy perturbation method (HPM), homotopy analysis method (HAM), Adomian decomposition method (ADM) and variational it... | [
{
"id": "",
"caption": "shows the populations for Case I (a = b = d = 1, c = 0.1, x 0 = 14, y 0 = 18) in a time scale larger than that considered in the earlier studies already mentioned above",
"content": "Fig. 1\n1shows the populations for Case I (a = b = d = 1, c = 0.1, x 0 = 14, y 0 = 18) in a time ... | [
{
"text": "F M Fernández, arXiv:0712.3376v1Perturbation Theory for Population Dynamics. F. M. Fernández, Perturbation Theory for Population Dynamics, arXiv:0712.3376v1",
"doi": "arXiv:0712.3376v1"
},
{
"text": "F M Fernández, arXiv:0806.0263v1On Some Perturbation Approaches to Population Dynamics. F... |
Laser Cooling of two trapped ions: Sideband cooling beyond the Lamb-Dicke limit
7 Dec 1998
G Morigi
Institut für Theoretische Physik
Universität Innsbruck
A-6020InnsbruckAUSTRIA, (
J Eschner
Institut für Experimentalphysik
Universität Innsbruck
A-6020InnsbruckAUSTRIA
J I Cirac
Institut für Theoretische Physik
Un... | 42,173,078 | {
"arxiv": "quant-ph/9812014",
"mag": 2170404679,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physreva.59.3797"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/quant-ph/9812014v1.pdf"
],
"pdf_sha": "2fd9d16564d4d01d81efdbe7022c12014b3d360c",
"open_access": {
"license": "CC0",
"url": "https://ddd.uab.cat/pub/artpub/1999/115777/phyreva_a1999m5v59n5p3797.pdf",
"status": "GREEN"
}
} | Laser Cooling of two trapped ions: Sideband cooling beyond the Lamb-Dicke limit | [
"G Morigi \nInstitut für Theoretische Physik\nUniversität Innsbruck\nA-6020InnsbruckAUSTRIA, (",
"J Eschner \nInstitut für Experimentalphysik\nUniversität Innsbruck\nA-6020InnsbruckAUSTRIA",
"J I Cirac \nInstitut für Theoretische Physik\nUniversität Innsbruck\nA-6020InnsbruckAUSTRIA, (",
"P Zoller \nInstitut ... | We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in... | [
{
"title": "I. INTRODUCTION",
"content": "The emergence of schemes that utilize trapped ions or atoms for quantum information, and the interest in quantum statistics of ultra cold atoms, have provided renewed interest and applications for laser cooling techniques [1]. The present goal is to laser cool sever... | [
{
"id": "",
"caption": "(t) = P L0P ρ(t) + t 0 dτ P L1(1 − P ) exp (L0τ ) (1 − P )L1P ρ(t − τ ) (1 − P ) exp (L0τ1) (1 − P )L1 exp (L0(τ2 − τ1)) P ρ(t − τ2)",
"content": "(t) = P L0P ρ(t) + t 0 dτ P L1(1 − P ) exp (L0τ ) (1 − P )L1P ρ(t − τ ) (1 − P ) exp (L0τ1) (1 − P )L1 exp (L0(τ2 − τ1)) P ρ(t − τ2)"... | [
{
"text": "An overview of laser cooling can be found in S. Chu. Rev. Mod. Phys. 70685An overview of laser cooling can be found in S. Chu, Rev. Mod. Phys 70, 685 (1998);",
"doi": ""
},
{
"text": ". C Cohen-Tannoudij, W.D. Phillips70721C. Cohen-Tannoudij, ibidem 70, 707 (1998), W.D. Phillips, ibidem 7... |
Boltzmann approach to high-order transport: the non-linear and non-local responses
M Battiato
Institute of Solid State Physics
Vienna University of Technology
ViennaAustria
V Zlatic
Institute of Physics
ZagrebCroatia
K Held
Institute of Solid State Physics
Vienna University of Technology
ViennaAustria
Boltzman... | 118,311,747 | {
"arxiv": "1606.05084",
"mag": 2621865435,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevb.95.235137"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1606.05084v3.pdf"
],
"pdf_sha": "6f0105650c3d8c9e2215047ed5bcb3bcf2c568d9",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1606.05084",
"status": "GREEN"
}
} | Boltzmann approach to high-order transport: the non-linear and non-local responses | [
"M Battiato \nInstitute of Solid State Physics\nVienna University of Technology\nViennaAustria",
"V Zlatic \nInstitute of Physics\nZagrebCroatia",
"K Held \nInstitute of Solid State Physics\nVienna University of Technology\nViennaAustria"
] | The phenomenological textbook equations for the charge and heat transport are extensively used in a number of fields ranging from semiconductor devices to thermoelectricity. We provide a rigorous derivation of transport equations by solving the Boltzmann equation in the relaxation time approximation and show that the c... | [
{
"title": "I. INTRODUCTION",
"content": "The phenomenological transport equations for the charge and heat currents are at the core of the description of electric and electronic devices of any type. These equations relate the local charge and heat current densities, J(r) and J E (r), to the local thermodyna... | [
{
"id": "",
"caption": "[r, k, T, µ] with respect to its first variable. The spatial part of Eq.(21) is a convection-reaction equation and the solution requires the value of g [0] [r, k, T, µ] on the boundary. The change in the distribution function due to an applied electric field E, is defined by the equa... | [
{
"text": ". L Onsager, Phys. Rev. 37405L. Onsager, Phys. Rev. 37, 405 (1931).",
"doi": ""
},
{
"text": ". R Kubo, J. Phys. Soc. Jpn. 12570R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).",
"doi": ""
},
{
"text": ". J M Luttinger, 10.1103/PhysRev.135.A1505Phys. Rev. 1351505J. M. Luttinger, Ph... |
Bulk-boundary correspondence in soft matter
(Dated: May 16, 2019)
Mehmet Ramazanoglu
Physics Engineering Department
Istanbul Technical University
34469IstanbulMaslakTurkey
Brockhouse Institute for Materials Research
L8S 4M1HamiltonONCanada
Şenerözönder
Physics Engineering Department
Istanbul Technical University
... | 155,091,203 | {
"arxiv": "1905.06163",
"mag": 2970162007,
"acl": null,
"pubmed": "31574595",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physreve.100.020702"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1905.06163v1.pdf"
],
"pdf_sha": "dac28eca82008b91a750e0f54f741c0b8b96082d",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1905.06163",
"status": "GREEN"
}
} | Bulk-boundary correspondence in soft matter | [
"Mehmet Ramazanoglu \nPhysics Engineering Department\nIstanbul Technical University\n34469IstanbulMaslakTurkey\n\nBrockhouse Institute for Materials Research\nL8S 4M1HamiltonONCanada",
"Şenerözönder \nPhysics Engineering Department\nIstanbul Technical University\n34469IstanbulMaslakTurkey",
"Rumeysa Salcı \nPhy... | Bulk-boundary correspondence is the emergence of features at the boundary of a material that are dependent on and yet distinct from the properties of the bulk of the material. The diverse applications of this idea in topological insulators as well as high energy physics prove its universality. However, whether a form o... | [
{
"title": "Analysis",
"content": "Fractal surfaces appear in nature in diverse areas such as fracture in rocks, cancer growth processes, wetting of surfaces, burning of paper and rupturing [27,28]. Fractal surfaces possess self-affine structure, i.e., when observed at different scales the surface looks sel... | [
{
"id": "",
"caption": "lkjf Aerosil and liquid crystal (LC) mixture. (top) A 3D cartoon of dispersed aerosil nanoparticles in LCs.",
"content": "Figure 1 .\n1lkjf Aerosil and liquid crystal (LC) mixture. (top) A 3D cartoon of dispersed aerosil nanoparticles in LCs."
},
{
"id": "",
"caption"... | [
{
"text": "Colloquium: Topological insulators. M Z Hasan, C L Kane, Rev. Mod. Phys. 82Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045-3067 (2010).",
"doi": ""
},
{
"text": "Topological insulators and superconductors. X.-L Qi, S.-C Zhang, Rev. Mod. Phys. 83Qi, ... |
Strong, but not weak, noise correlations are beneficial for population coding
Gabriel Mahuas
Institut de la Vision
Sorbonne Université
CNRS
INSERM
17 rue Moreau75012ParisFrance
Laboratoire de physique de École normale supérieure
CNRS
PSL University
Sorbonne University
Université Paris-Cité
24 rue Lhomond75005Par... | 270,738,002 | {
"arxiv": "2406.18439",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1101/2024.06.26.600826"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2406.18439v1.pdf"
],
"pdf_sha": "de3697ac7c78685426d869333f2685ea2c2076fe",
"open_access": {
"license": null,
"url": "https://arxiv.org/pdf/2406.18439",
"status": "GREEN"
}
} | Strong, but not weak, noise correlations are beneficial for population coding | [
"Gabriel Mahuas \nInstitut de la Vision\nSorbonne Université\nCNRS\nINSERM\n17 rue Moreau75012ParisFrance\n\nLaboratoire de physique de École normale supérieure\nCNRS\nPSL University\n\n\nSorbonne University\nUniversité Paris-Cité\n24 rue Lhomond75005ParisFrance",
"Thomas Buffet \nInstitut de la Vision\nSorbonne ... | Neural correlations play a critical role in sensory information coding.They are of two kinds: signal correlations, when neurons have overlapping sensitivities, and noise correlations from network effects and shared noise.It is commonly thought that stimulus and noise correlations should have opposite signs to improve c... | [
{
"title": "I. INTRODUCTION",
"content": "Neurons from sensory systems encode information about incoming stimuli in their collective spiking activity.This activity is noisy: repetitions of the very same stimulus can drive different responses [1][2][3][4][5][6].It has been shown that the noise is shared amon... | [
{
"id": "",
"caption": "FIG. 1:The effects of noise correlations on information coding depends on the stimulus.A. Example pair of Von Mises tuning curves with moderate signal correlation level (ρs = 0.25).B. Mutual information between stimulus and response for the example pair of A, vs the strength of noise... | [
{
"text": "Correlated neuronal discharge rate and its implications for psychophysical performance. E Zohary, M N Shadlen, W T Newsome, Nature. 3701994",
"doi": ""
},
{
"text": "Concerted signaling by retinal ganglion cells. M Meister, L Lagnado, D A Baylor, Science. 2701995",
"doi": ""
},
{
... |
Super accurate low latency object detection on a surveillance UAV
Maarten Vandersteegen maarten.vandersteegen@kuleuven.be
Van Kristof kristof.vanbeeck@kuleuven.be
Toon Goedemé Beeck
Eavise
Leuven -Campus Ku
De Nayer
Super accurate low latency object detection on a surveillance UAV
Drones have proven to be use... | 102,486,758 | {
"arxiv": "1904.02024",
"mag": 2962897380,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "conf/mva/VandersteegenBG19",
"doi": "10.23919/mva.2019.8758060"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1904.02024v1.pdf"
],
"pdf_sha": "d060acb09074066559484c00840c8c8f62bcc30f",
"open_access": {
"license": null,
"url": "https://lirias.kuleuven.be/bitstream/123456789/638479/2/Super_accurate_low_latency_object_detection_on_a_surveillance_UAV(2).pdf",
"status"... | Super accurate low latency object detection on a surveillance UAV | [
"Maarten Vandersteegen maarten.vandersteegen@kuleuven.be",
"Van Kristof kristof.vanbeeck@kuleuven.be",
"Toon Goedemé Beeck",
"Eavise",
"Leuven -Campus Ku",
"De Nayer"
] | Drones have proven to be useful in many industry segments such as security and surveillance, where e.g. on-board real-time object tracking is a necessity for autonomous flying guards. Tracking and following suspicious objects is therefore required in real-time on limited hardware. With an object detector in the loop, l... | [
{
"title": "Introduction",
"content": "While UAVs are demonstrating their potential to offer support for numerous tasks in different industry sectors, there is a rising need for automating their control. On-board vision sensors combined with detection and tracking algorithms are a promising source of input ... | [
{
"id": "",
"caption": "Examples from the MS COCO (top) and Vis-drone2018 (bottom) training set, with their modified annotations.",
"content": "Figure 2 :\n2Examples from the MS COCO (top) and Vis-drone2018 (bottom) training set, with their modified annotations."
},
{
"id": "",
"caption": "D... | [
{
"text": "Embedded real-time object detection for a UAV warning system. Tijtgat, Tijtgat et al. \"Embedded real-time object detection for a UAV warning system.\" ICCV, 2017. p. 2110-2118.",
"doi": ""
},
{
"text": "Deep Drone: object detection and tracking for smart drones on embedded system. Han, S... |
Tribimaximal Neutrino Mixing from A 4 Replication
12 Jan 2011
Christopher D Carone
Department of Physics
Particle Theory Group
College of William and Mary
23187-8795WilliamsburgVA
Richard F Lebed
Department of Physics
Arizona State University
85287-1504TempeAZ
Tribimaximal Neutrino Mixing from A 4 Replication
12 ... | 119,262,760 | {
"arxiv": "1011.6379",
"mag": 2016190791,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1016/j.physletb.2011.01.004"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1011.6379v2.pdf"
],
"pdf_sha": "256de5fd881f1f6b2614f51ac233717b5b471001",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1011.6379",
"status": "GREEN"
}
} | Tribimaximal Neutrino Mixing from A 4 Replication | [
"Christopher D Carone \nDepartment of Physics\nParticle Theory Group\nCollege of William and Mary\n23187-8795WilliamsburgVA",
"Richard F Lebed \nDepartment of Physics\nArizona State University\n85287-1504TempeAZ"
] | Motivated by dimensional deconstruction, we propose a model of tribimaximal neutrino mixing based on A 4 ×A 4 symmetry. In this model, the two triplet symmetry-breaking fields of conventional A 4 models are taken to transform under different A 4 group factors, but are not distinguished by any other quantum numbers. An ... | [
{
"title": "I. INTRODUCTION",
"content": "The observed pattern of fermion masses and mixing angles remains one of the major unresolved mysteries of the standard model. In the neutral sector, a global analysis of the neutrino oscillation data leads to the mixing angles [1] sin 2 θ 12 = 0.314 +0.019 −0.014 , ... | [
{
"id": "",
"caption": "a trivial singlet (1 0 ) under the A 4 subgroup under which both φ 1 and φ 2 transform identically. The individual A 4 factors are broken by a (3, 1 0 ) triplet φ T with the vev",
"content": "a trivial singlet (1 0 ) under the A 4 subgroup under which both φ 1 and φ 2 transform i... | [
{
"text": ". B Aharmim, SNO CollaborationarXiv:0910.2984Phys. Rev. C. 8155504nucl-exB. Aharmim et al. [SNO Collaboration], Phys. Rev. C 81, 055504 (2010) [arXiv:0910.2984 [nucl-ex]].",
"doi": ""
},
{
"text": ". P F Harrison, D H Perkins, W G Scott, arXiv:hep-ph/0202074Phys. Lett. B. 530167P.F. Harri... |
Vision and Inertial Sensing Fusion for Human Action Recognition: A Review
FEBRUARY 1, 2021
Graduate Student Member, IEEESharmin Majumder
Fellow, IEEENasser Kehtarnavaz
Vision and Inertial Sensing Fusion for Human Action Recognition: A Review
IEEE SENSORS JOURNAL
213FEBRUARY 1, 202110.1109/JSEN.2020.30223262454
Hum... | 220,935,508 | {
"arxiv": "2008.00380",
"mag": 3084394676,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/abs-2008-00380",
"doi": "10.1109/jsen.2020.3022326"
} | {
"pdf_urls": [],
"pdf_sha": "97b15187a5083a3fde36532ea6a4fff4aae221d4",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/2008.00380",
"status": "GREEN"
}
} | Vision and Inertial Sensing Fusion for Human Action Recognition: A Review | [
"Graduate Student Member, IEEESharmin Majumder",
"Fellow, IEEENasser Kehtarnavaz"
] | Human action recognition is used in many applications such as video surveillance, human-computer interaction, assistive living, and gaming. Many papers have appeared in the literature showing that the fusion of vision and inertial sensing improves recognition accuracies compared to the situations when each sensing moda... | [
{
"title": "II. FUSION APPROACHES",
"content": "The fusion of information from different sensing modalities has been conducted in different ways. In general, three fusion approaches are encountered as stated in [95]: (1) raw/data-level fusion, (2) feature-level fusion, and (3) score/decision-level fusion. T... | [
{
"id": "",
"caption": "Single and multimodality sensing for human action recognition; the box indicates the scope of this survey paper.",
"content": "Fig. 2 .\n2Single and multimodality sensing for human action recognition; the box indicates the scope of this survey paper."
},
{
"id": "",
"... | [
{
"text": "Human activity analysis: A review. J K Aggarwal, M S Ryoo, 10.1145/1922649.1922653ACM Comput. Surveys. 433J. K. Aggarwal and M. S. Ryoo, \"Human activity analysis: A review,\" ACM Comput. Surveys, vol. 43, no. 3, pp. 1-43, Apr. 2011, doi: 10.1145/1922649.1922653.",
"doi": "10.1145/1922649.1922653... |
EXTREME-STRIKE ASYMPTOTICS FOR GENERAL GAUSSIAN STOCHASTIC VOLATILITY MODELS
18 Feb 2015
Archil Gulisashvili
ANDFrederi Viens
Xin Zhang
EXTREME-STRIKE ASYMPTOTICS FOR GENERAL GAUSSIAN STOCHASTIC VOLATILITY MODELS
18 Feb 2015arXiv:1502.05442v1 [q-fin.MF]stochastic volatilityimplied volatilitylarge strikeKarhunen-Lo... | 73,601,460 | {
"arxiv": "1502.05442",
"mag": 2951225586,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1007/s10436-018-0338-z"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1502.05442v3.pdf"
],
"pdf_sha": "52276681c90f0488a5a2b31f350e308c856d61fe",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1502.05442",
"status": "GREEN"
}
} | EXTREME-STRIKE ASYMPTOTICS FOR GENERAL GAUSSIAN STOCHASTIC VOLATILITY MODELS | [
"Archil Gulisashvili",
"ANDFrederi Viens",
"Xin Zhang"
] | We consider a stochastic volatility stock price model in which the volatility is a non-centered continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we... | [
{
"title": "Introduction",
"content": "In this article, we characterize the extreme-strike behavior of implied volatility curves for fixed maturity for uncorrelated Gaussian stochastic volatility models. This introduction contains a careful description of the problem's background and of our motivations. Bef... | [
{
"id": "",
"caption": "By exp − Cy 2",
"content": "exp\nBy exp − Cy 2"
},
{
"id": "",
"caption": "The following formula holds for the implied volatility K → I(K) as K → ∞:",
"content": "Theorem 4 .\n4The following formula holds for the implied volatility K → I(K) as K → ∞:"
},
{
... | [
{
"text": "A brief note on the Karhunen-Loève expansion, technical note, available on users. A , A. Alexanderian. A brief note on the Karhunen-Loève expansion, technical note, available on users.ices.utexas.edu/∼alen/articles/KL.pdf",
"doi": ""
},
{
"text": "An introduction to continuity, extrema, a... |
Selfsynchronization and dissipation-induced threshold in collective atomic recoil lasing
2 Feb 2004
C Von Cube
S Slama
D Kruse
C Zimmermann
Ph W Courteille
G R M Robb
Department of Physics
University of Strathclyde
G4 0NGGlasgowScotland
N Piovella
Dipartimento di Fisica, Università Degli Studi di Milano and I... | 6,994,956 | {
"arxiv": "quant-ph/0402013",
"mag": 2130830630,
"acl": null,
"pubmed": "15447183",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevlett.93.083601"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/quant-ph/0402013v1.pdf"
],
"pdf_sha": "8c3e503767cc2d00f9490f54a0c90f18bcb09d4c",
"open_access": {
"license": null,
"url": "https://strathprints.strath.ac.uk/2978/11/vonCube_etal_2004_PRL_Self_synchronization_and_dissipation_induced_threshold_in_collective_atom... | Selfsynchronization and dissipation-induced threshold in collective atomic recoil lasing | [
"C Von Cube",
"S Slama",
"D Kruse",
"C Zimmermann",
"Ph W Courteille",
"G R M Robb \nDepartment of Physics\nUniversity of Strathclyde\nG4 0NGGlasgowScotland",
"N Piovella \nDipartimento di Fisica, Università Degli Studi di Milano and INFM\nVia Celoria 16I-20133MilanoItaly",
"R Bonifacio \nDipartimento... | Networks of globally coupled oscillators exhibit phase transitions from incoherent to coherent states. Atoms interacting with the counterpropagating modes of a unidirectionally pumped highfinesse ring cavity form such a globally coupled network. The coupling mechanism is provided by collective atomic recoil lasing (CAR... | [
{
"title": "Figs. 2(a) and (b)",
"content": "show measurements of the threshold pump power as a function of the laser detuning and the total atom number. Both experimental curves have been obtained from the same data set P +,thr (N, ∆ a ) scaled either to an arbitrarily chosen reference atom number N = 10 6... | [
{
"id": "",
"caption": "PACS numbers: 42.50.Vk, 05.45.Xt, 05.65+b, 05.70.Fh",
"content": "PACS numbers: 42.50.Vk, 05.45.Xt, 05.65+b, 05.70.Fh"
},
{
"id": "",
"caption": "(a) Sectionwise Fourier-transform of the interference signal P beat with the pump laser power being ramped up and down. Th... | [
{
"text": ". R Bonifacio, L Desalvo, Nucl. Instrum. Methods. 341360R. Bonifacio and L. DeSalvo, Nucl. Instrum. Methods 341, 360 (1994);",
"doi": ""
},
{
"text": ". R Bonifacio, L Desalvo, L M Narducci, E J Angelo, Phys. Rev. A. 501716R. Bonifacio, L. DeSalvo, L. M. Nar- ducci, and E. J. D'Angelo, Ph... |
Towards fidelity and scalability in non-vacuum mergers
(Dated: February 19, 2020)
Steven L Liebling
Long Island University
11548BrookvilleNew YorkUSA
Carlos Palenzuela
Departament de Física & IAC3
Universitat de les Illes Balears
E-07122Palma de Mallorca, BalearesSpain
Luis Lehner
Perimeter Institute
31 Caroline... | 211,146,423 | {
"arxiv": "2002.07554",
"mag": 3100972163,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1088/1361-6382/ab8fcd"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2002.07554v1.pdf"
],
"pdf_sha": "c113b7ab204d3c25a22f10cbf4be7c6966a1108a",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/2002.07554",
"status": "GREEN"
}
} | Towards fidelity and scalability in non-vacuum mergers | [
"Steven L Liebling \nLong Island University\n11548BrookvilleNew YorkUSA",
"Carlos Palenzuela \nDepartament de Física & IAC3\nUniversitat de les Illes Balears\nE-07122Palma de Mallorca, BalearesSpain",
"Luis Lehner \nPerimeter Institute\n31 Caroline StN2L 2Y5WaterlooONCanada"
] | We study the evolution of two fiducial configurations for binary neutron stars using two different general relativistic hydrodynamics (GRHD), distributed adaptive mesh codes. One code, Had, has for many years been used to study mergers of compact object binaries, while a new code, MHDuet, has been recently developed wi... | [
{
"title": "I. INTRODUCTION",
"content": "The merger of a binary neutron star (BNS) system produces a wide range of potentially observable signals and hence provides an ideal event for studying high energy astrophysics through gravitational and electromagnetic waves as well as (for sufficiently close system... | [
{
"id": "",
"caption": "II: Details of the various simulations presented here. For each simulation, the name of the code used, the name of the EOS characterizing the fluid, the name we use to refer to the simulation, the number of levels, the number of points in each direction for the coarse level, the fine... | [
{
"text": "Merger and mass ejection of neutron star binaries. M Shibata, K Hotokezaka, 10.1146/annurev-nucl-101918-023625Annual Review of Nuclear and Particle Science. 691M. Shibata and K. Hotokezaka, \"Merger and mass ejection of neutron star binaries,\" Annual Review of Nuclear and Particle Science 69 no. 1, ... |
Global gravitational instability of FLRW backgrounds-interpreting the dark sectors
2011
Xavier Roy roy@obs.univ-lyon1.fr
Centre de Recherche Astrophysique de Lyon
Université Lyon 1
9 avenue Charles AndréF-69230Saint-Genis-LavalFrance
Thomas Buchert buchert@obs.univ-lyon1.fr
Centre de Recherche Astrophysique de Lyo... | 36,957,813 | {
"arxiv": "1103.1146",
"mag": 2057552478,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1088/0264-9381/28/16/165004"
} | {
"pdf_urls": [
"https://web.archive.org/web/20190503110943/https:/hal.archives-ouvertes.fr/hal-00724412/file/PEER_stage2_10.1088%252F0264-9381%252F28%252F16%252F165004.pdf"
],
"pdf_sha": "c01a75fcb10b251d552c35c51d167d210025db39",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1103.... | Global gravitational instability of FLRW backgrounds-interpreting the dark sectors | [
"Xavier Roy roy@obs.univ-lyon1.fr \nCentre de Recherche Astrophysique de Lyon\nUniversité Lyon 1\n9 avenue Charles AndréF-69230Saint-Genis-LavalFrance",
"Thomas Buchert buchert@obs.univ-lyon1.fr \nCentre de Recherche Astrophysique de Lyon\nUniversité Lyon 1\n9 avenue Charles AndréF-69230Saint-Genis-LavalFrance",
... | The standard model of cosmology is based on homogeneous-isotropic solutions of Einstein's equations. These solutions are known to be gravitationally unstable to local inhomogeneous perturbations, commonly described as evolving on a background given by the same solutions. In this picture, the Friedmann-Lemaître-Robertso... | [
{
"title": "Effective description of inhomogeneous cosmologies",
"content": "Let us consider an inhomogeneous, irrotational and pressureless fluid (dust). The spatial average over a compact, rest-mass preserving domain D of the Raychaudhuri equation, the Hamilton constraint and the dust continuity equation ... | [
{
"id": "",
"caption": "under the conservation law (3), if and only if Q D and W D obey the integrability condition",
"content": "under the conservation law (3), if and only if Q D and W D obey the integrability condition"
},
{
"id": "",
"caption": "D m , D X , D k , n , in the corresponding... | [
{
"text": ". D K Arrowsmith, C M Place, An Introduction to Dynamical Systems. Cambridge University PressArrowsmith D K and Place C M 1990 An Introduction to Dynamical Systems (Cambridge: Cambridge University Press)",
"doi": ""
},
{
"text": "On the stability of the Einstein static universe. J D Barro... |
Giant Skyrmions Stabilized by Dipole-Dipole Interactions in Thin Ferromagnetic Films
3 Nov 2010 (Dated: November 4, 2010)
Motohiko Ezawa
Giant Skyrmions Stabilized by Dipole-Dipole Interactions in Thin Ferromagnetic Films
3 Nov 2010 (Dated: November 4, 2010)arXiv:1007.4048v2 [cond-mat.str-el]
Motivated by a recent m... | 18,213,419 | {
"arxiv": "1007.4048",
"mag": 2123131732,
"acl": null,
"pubmed": "21231193",
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevlett.105.197202"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1007.4048v2.pdf"
],
"pdf_sha": "f0952a04bef3e5b87d34267235b14d623fcd7916",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1007.4048",
"status": "GREEN"
}
} | Giant Skyrmions Stabilized by Dipole-Dipole Interactions in Thin Ferromagnetic Films | [
"Motohiko Ezawa"
] | Motivated by a recent magnetization reversal experiment on a TbFeCo thin film, we study a topological excitation in the anisotropic nonlinear sigma model together with the Zeeman and magnetic dipole-dipole interactions. Dipole-dipole interactions turn a ferromagnet into a frustrated spin system, which allows a nontrivi... | [
{
"title": "The ordinary ferromagnet is described by the Hamiltonian",
"content": "On the other hand, the chiral magnet is described by the Hamiltonian\nis the DMI term. It breaks the chiral symmetry explicitly. The use of a continuum approximation and of classical fields to represent the spins is justified... | [
{
"id": "",
"caption": "(Color online) (a) Illustration of a giant skyrmion (∼ 1µm)",
"content": "FIG. 1 .\n1(Color online) (a) Illustration of a giant skyrmion (∼ 1µm)"
},
{
"id": "",
"caption": "(Color online) (a) Illustration of a soliton-lattice solution σ(x) described by the Jacobian el... | [
{
"text": "The Multifaced Skyrmions. G.E. Brown and M. RhoWorld ScientificSingaporeG.E. Brown and M. Rho (eds.), \"The Multifaced Skyrmions\", World Scientific, Singapore (2010).",
"doi": ""
},
{
"text": ". T H R Skyrme, Proc. Roy. Soc. (London) A. 260127T. H. R. Skyrme, Proc. Roy. Soc. (London) A 2... |
Statistical study of gamma-ray bursts with jet break feature in multi-wavelength afterglow emissions
8 Sep 2020
Wen Zhao
School of Physics and Physical Engineering
Qufu Normal University
273165QufuChina
Jia-Chang Zhang
School of Physics and Physical Engineering
Qufu Normal University
273165QufuChina
Qing-Xiang Zh... | 221,534,349 | {
"arxiv": "2009.03550",
"mag": 3100994144,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.3847/1538-4357/aba43a"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2009.03550v1.pdf"
],
"pdf_sha": "46620d012e438496e98967c96a314250e3783ef3",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/2009.03550",
"status": "GREEN"
}
} | Statistical study of gamma-ray bursts with jet break feature in multi-wavelength afterglow emissions | [
"Wen Zhao \nSchool of Physics and Physical Engineering\nQufu Normal University\n273165QufuChina",
"Jia-Chang Zhang \nSchool of Physics and Physical Engineering\nQufu Normal University\n273165QufuChina",
"Qing-Xiang Zhang",
"Jian-Tong Liang \nSchool of Physics and Physical Engineering\nQufu Normal University\n... | It is generally supposed that a transition from the normal decay phase (decay slope ∼ −1) to a steeper phase (decay slope ∼ −2) could be suggested as a jet break. The jet opening angle θ jet is then calculated from the jet break time of the afterglow light curve. This allows the derivation of the collimation-corrected ... | [
{
"title": "Introduction",
"content": "Gamma-ray bursts (GRBs) are supposed to be the most powerful electromagnetic explosions in the universe. These erratic, luminous, transient events are very different from the other astrophysical phenomena. Generally speaking, according to the fireball model, GRBs are b... | [
{
"id": "",
"caption": "-The distributions of the parameters for GRBs with jet breaks.",
"content": "Fig. 1 .\n1-The distributions of the parameters for GRBs with jet breaks."
},
{
"id": "",
"caption": "-The two-dimensional correlations of GRBs claimed in previous papers.",
"content": "F... | [
{
"text": ". B P Abbott, R Abbott, T D Abbott, Phys. Rev. Lett. 119161101Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017, Phys. Rev. Lett., 119, 161101",
"doi": ""
},
{
"text": ". L Amati, F Frontera, M Tavani, A&A. 39081Amati, L., Frontera, F., Tavani, M., et al. 2002, A&A, 390, 81",
"doi... |
Structure functions at large x
2001. June 17-22, 2001
Zhiqing Zhang
CNRS
IN2P3 et Université de Paris-Sud -Bât
200 -BP 34 -91898Orsay cedex
Structure functions at large x
New Trends in HERA Physics
Germany2001. June 17-22, 2001(On behalf of the H1 and ZEUS collaborations) Laboratoire de l'Accélérateur Linéaire
Str... | 17,774,771 | {
"arxiv": "hep-ph/0110231",
"mag": 1964384125,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1088/0954-3899/28/5/304"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/hep-ph/0110231v1.pdf"
],
"pdf_sha": "19d060b5f5912da926f10242fa3d9940763d9525",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/hep-ph/0110231",
"status": "GREEN"
}
} | Structure functions at large x | [
"Zhiqing Zhang \nCNRS\nIN2P3 et Université de Paris-Sud -Bât\n200 -BP 34 -91898Orsay cedex"
] | Structure function data together with other measurements from fixed-target deep inelastic scattering and hadron-hadron collider experiments which contribute to our knowledge of the parton density functions are reviewed. The inclusive cross-section measurements of neutral and charged current interactions at HERA are pre... | [
{
"title": "Introduction",
"content": "Deep inelastic scattering (DIS) experiments have played important roles in understanding the partonic structure of hadrons and in establishing the theory of quantum chromodynamics (QCD), the strong sector of the Standard Model (SM). Our current knowledge of the parton ... | [
{
"id": "",
"caption": "Figure 2. The kinematic coverage [11] of (a) the lepton-pair (Drell-Yan) production from E605 [15], the asymmetry data in the Drell-Yan production from NA51 [16], and the direct photon production data from E706 [17], WA70 [18] and UA6 [19] and of (b) the direct photon (γ) data from U... | [
{
"text": ". T Affolder, CDF CollaborationPhys. Rev. D. 6452001Affolder T et al [CDF Collaboration] 2001 Phys. Rev. D 64 052001;",
"doi": ""
},
{
"text": ". B Abbott, D0 CollaborationPhys. Rev. Lett. 84222Abbott B et al [D0 Collaboration] 2000 Phys. Rev. Lett. 84 222",
"doi": ""
},
{
"te... |
Plasmon localization and relaxation, and thermal transport in one-dimensional conductors
(Dated: February 10, 2022)
M Bard
Institut für Nanotechnologie
Karlsruhe Institute of Technology
76021KarlsruheGermany
I V Protopopov
Department of Theoretical Physics
University of Geneva
1211GenevaSwitzerland
Landau Institu... | 182,952,571 | {
"arxiv": "1906.03968",
"mag": 2975869445,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physrevb.100.115153"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/1906.03968v1.pdf"
],
"pdf_sha": "84854fb48cc440a1009b4f5ef02d35fdd51a28f1",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/1906.03968",
"status": "GREEN"
}
} | Plasmon localization and relaxation, and thermal transport in one-dimensional conductors | [
"M Bard \nInstitut für Nanotechnologie\nKarlsruhe Institute of Technology\n76021KarlsruheGermany",
"I V Protopopov \nDepartment of Theoretical Physics\nUniversity of Geneva\n1211GenevaSwitzerland\n\nLandau Institute for Theoretical Physics\n119334MoscowRussia",
"A D Mirlin \nInstitut für Nanotechnologie\nKarlsr... | We study the localization and decay properties as well as the thermal conductance of onedimensional plasmons. Our model contains a Luttinger-liquid part with spatially random plasmon velocity and interaction parameter as well as a nonlinearity that is cubic in density. The scaling of the decay rate of plasmons is obtai... | [
{
"title": "I. INTRODUCTION",
"content": "One-dimensional (1D) quantum systems show a plenty of fascinating phenomena 1 . Interaction effects are often strong in 1D, so that the proper elementary excitations of the systems are plasmons (collective density fluctuations) and not the genuine constituent partic... | [
{
"id": "",
"caption": "Inelastic relaxation of a plasmonic mode at frequency ω1 via a) decay into two plasmons; b) collision with another plasmon.",
"content": "FIG. 1 .\n1Inelastic relaxation of a plasmonic mode at frequency ω1 via a) decay into two plasmons; b) collision with another plasmon."
},
... | [
{
"text": "Quantum physics in one dimension, International series of monographs on physics. T Giamarchi, Clarendon Press121OxfordT. Giamarchi, Quantum physics in one dimension, Inter- national series of monographs on physics ; 121 (Clarendon Press, Oxford, 2004).",
"doi": ""
},
{
"text": ". M Meschk... |
Clustering-aware Graph Construction: A Joint Learning Perspective
14 Jun 2019
Yuheng Jia yuheng.jia@my.cityu.edu.hk
Hui Liu
Member, IEEEJunhui Hou jh.hou@cityu.edu.hk
Fellow, IEEESam Kwong
Department of Computer Sci-ence
City University of Hong Kong
Kowloon, Hong Kong
Department of Computer Science
City Univer... | 146,120,856 | {
"arxiv": "1905.01446",
"mag": 3019223480,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/tsipn/JiaLHK20",
"doi": "10.1109/tsipn.2020.2988572"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1905.01446v3.pdf"
],
"pdf_sha": "01547ccd95109cd23ca624e531746dfd874d8a77",
"open_access": {
"license": null,
"url": "https://arxiv.org/pdf/1905.01446",
"status": "GREEN"
}
} | Clustering-aware Graph Construction: A Joint Learning Perspective | [
"Yuheng Jia yuheng.jia@my.cityu.edu.hk",
"Hui Liu",
"Member, IEEEJunhui Hou jh.hou@cityu.edu.hk",
"Fellow, IEEESam Kwong",
"Department of Computer Sci-ence\nCity University of Hong Kong\nKowloon, Hong Kong",
"Department of Computer Science\nCity University of Hong Kong\nKowloon, Hong Kong",
"City Univer... | Graph-based clustering methods have demonstrated the effectiveness in various applications.Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the clustering result.However, such a stepwise manner may make the constructed graph not fit... | [
{
"title": "I. INTRODUCTION",
"content": "Clustering aims to partition the input data into different groups, where the samples in the same group are more similar to each other than to those in other groups.Many realworld applications can be formulated as a clustering problem, e.g., image segmentation [1], [... | [
{
"id": "",
"caption": "Fig. 1.Clustering ACC of the proposed model versus α and β on 10 datasets.",
"content": "Fig. 1 .\n1\nFig. 1.Clustering ACC of the proposed model versus α and β on 10 datasets."
},
{
"id": "",
"caption": "Fig. 2. Illustration of objective values against the number of ... | [
{
"text": "An optimal graph theoretic approach to data clustering: Theory and its application to image segmentation. Z Wu, R Leahy, IEEE transactions on pattern analysis and machine intelligence. 199315",
"doi": ""
},
{
"text": "Fuzzy c-means clustering with spatial information for image segmentatio... |
JOINT LEARNING ON THE HIERARCHY REPRESENTATION FOR FINE-GRAINED HUMAN ACTION RECOGNITION
Mei Chee Leong leongmeichee@i2r.a-star.edu.sg
School of Computer Science and Engineering
Nanyang Technological University
Singapore
Hui Li
School of Computer Science and Engineering
Nanyang Technological University
Singapore
... | 238,634,490 | {
"arxiv": "2110.05853",
"mag": 3193621526,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "conf/icip/LeongTZLLL21",
"doi": "10.1109/icip42928.2021.9506157"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/2110.05853v1.pdf"
],
"pdf_sha": "511c335c8966d746cd45479ac30691007c57df94",
"open_access": {
"license": null,
"url": "https://arxiv.org/pdf/2110.05853",
"status": "GREEN"
}
} | JOINT LEARNING ON THE HIERARCHY REPRESENTATION FOR FINE-GRAINED HUMAN ACTION RECOGNITION | [
"Mei Chee Leong leongmeichee@i2r.a-star.edu.sg \nSchool of Computer Science and Engineering\nNanyang Technological University\nSingapore",
"Hui Li \nSchool of Computer Science and Engineering\nNanyang Technological University\nSingapore",
"Haosong Zhang haosong001@e.ntu.edu.sg \nSchool of Computer Science and E... | Fine-grained human action recognition is a core research topic in computer vision.Inspired by the recently proposed hierarchy representation of fine-grained actions in FineGym and SlowFast network for action recognition, we propose a novel multi-task network which exploits the FineGym hierarchy representation to achiev... | [
{
"title": "INTRODUCTION",
"content": "As a fundamental research topic in computer vision, action recognition has always been an important research problem.Driven by advancements in deep learning models, such as 2D and 3D convolutional neural network (CNN) models, record breaking accuracies have been achiev... | [
{
"id": "",
"caption": "Fig. 1.The architecture of our multi-task network for effective representation and joint learning of three-level hierarchy of fine-grained human actions.",
"content": "Fig. 1 .\n1\nFig. 1.The architecture of our multi-task network for effective representation and joint learning o... | [
{
"text": "Activitynet: A large-scale video benchmark for human activity understanding. Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, Juan Carlos Niebles, Proceedings of the ieee conference on computer vision and pattern recognition. the ieee conference on computer vision and pattern recognition2015",
... |
RadiX-Net: Structured Sparse Matrices for Deep Neural Networks
Ryan A Robinett
MIT Department of Mathematics
Jeremy Kepner
MIT Department of Mathematics
MIT Lincoln Laboratory Supercomputing Center
RadiX-Net: Structured Sparse Matrices for Deep Neural Networks
4A6EE1C9C6E0DD80CFCEC1127BEF0707sparse neural ne... | 143,421,515 | {
"arxiv": "1905.00416",
"mag": 3100809954,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "conf/ipps/KepnerR19",
"doi": "10.1109/ipdpsw.2019.00051"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/1905.00416v1.pdf"
],
"pdf_sha": "a14484af29b44a16a52ecbb85929c5210e8eb06d",
"open_access": {
"license": null,
"url": "https://arxiv.org/pdf/1905.00416",
"status": "GREEN"
}
} | RadiX-Net: Structured Sparse Matrices for Deep Neural Networks | [
"Ryan A Robinett \nMIT Department of Mathematics",
"Jeremy Kepner \nMIT Department of Mathematics\n\n\nMIT Lincoln Laboratory Supercomputing Center"
] | The sizes of deep neural networks (DNNs) are rapidly outgrowing the capacity of hardware to store and train them.Research over the past few decades has explored the prospect of sparsifying DNNs before, during, and after training by pruning edges from the underlying topology.The resulting neural network is known as a sp... | [
{
"title": "I. INTRODUCTION",
"content": "As research in artificial neural networks progresses, the sizes of state-of-the-art deep neural network (DNN) architectures put increasing strain on the hardware needed to implement them [1], [2].In the interest of reduced storage and runtime costs, much research ov... | [
{
"id": "",
"caption": "Fig. 1. Construction of the mixed-radix topology defined by N = (2, 2, 2) using overlapping decision trees.(left) A four-layer binary decision tree.(right) A four-layer mixed radix topology composed of eight offset decision trees.",
"content": "Fig. 1 .\n1\nFig. 1. Construction o... | [
{
"text": "Going deeper with convolutions. C Szegedy, W Liu, Y Jia, P Sermanet, S Reed, D Anguelov, D Erhan, V Vanhoucke, A Rabinovich, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). June 2015",
"doi": ""
},
{
"text": "Sparse deep neural network exact solutions. J Kepner, V ... |
On the robustness of q-expectation values and Rényi entropy
January 2009. 2009. 20005
R Hanel
Complex Systems Research Group
HNO
Medical University of Vienna
Währinger Gürtel 18-20A-1090EUAustria
S Thurner
Complex Systems Research Group
HNO
Medical University of Vienna
Währinger Gürtel 18-20A-1090EUAustria
Santa ... | 15,090,091 | {
"arxiv": "0812.3855",
"mag": 2040164803,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1209/0295-5075/85/20005"
} | {
"pdf_urls": [],
"pdf_sha": "f6527493c9b306ee999fc629384911184f813a08",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/0812.3855",
"status": "GREEN"
}
} | On the robustness of q-expectation values and Rényi entropy | [
"R Hanel \nComplex Systems Research Group\nHNO\nMedical University of Vienna\nWähringer Gürtel 18-20A-1090EUAustria",
"S Thurner \nComplex Systems Research Group\nHNO\nMedical University of Vienna\nWähringer Gürtel 18-20A-1090EUAustria\n\nSanta Fe Institute\n1399 Hyde Park Road, Santa Fe87501NMUSA",
"C Tsallis ... | We study the robustness of the functionals of probability distributions such as the Rényi and nonadditive Sq entropies, as well as the q-expectation values under small variations of the distributions. We focus on three important types of distribution functions, namely i) continuous bounded, ii) discrete with finite num... | [
{
"title": "20005-p3",
"content": "sufficient to guarantee stability for the q > 1 case in a general setting. In the corresponding example in [15], when formulated in the continuum limit, stability is violated by using unbounded variations 5 .\nBoth theorems in [16] are analytical statements about the conti... | [
{
"id": "",
"caption": "Let q > 1 and let m > 0 be an arbitrary but fixed constant. Let 0 < ρ be a probability distribution on I = [0, 1]. Let δρ be variations of ρ, i.e. ρ + δρ > 0. Let B > 0 be an arbitrary but fixed constant. Let the variations δρ be uniformly bounded in the m-norm, i.e. δρ m < B, by thi... | [
{
"text": ". B Lesche, J. Stat. Phys. 27419Lesche B., J. Stat. Phys., 27 (1982) 419.",
"doi": ""
},
{
"text": ". Abe S , Phys. Rev. E. 6646134Abe S., Phys. Rev. E, 66 (2002) 046134.",
"doi": ""
},
{
"text": ". A G Bashkirov, Phys. Rev. E. 7228101Bashkirov A. G., Phys. Rev. E, 72 (2005) 0... |
Evolution speed in some coupled-spin models
7 Apr 2004
R F Sawyer
Department of Physics
University of California at Santa Barbara
93106Santa BarbaraCalifornia
Evolution speed in some coupled-spin models
7 Apr 2004numbers: 0365-w0365Ud0367-a
We investigate the time evolution of some models with N spins and pairwise ... | 119,486,081 | {
"arxiv": "quant-ph/0312217",
"mag": 2142484020,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.1103/physreva.70.022308"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/quant-ph/0312217v3.pdf"
],
"pdf_sha": "f566d4f2a99036ecbd8d401432b8ff6a747087d6",
"open_access": {
"license": null,
"url": "http://arxiv.org/pdf/quant-ph/0312217",
"status": "GREEN"
}
} | Evolution speed in some coupled-spin models | [
"R F Sawyer \nDepartment of Physics\nUniversity of California at Santa Barbara\n93106Santa BarbaraCalifornia"
] | We investigate the time evolution of some models with N spins and pairwise couplings, for the case of large N, in order to compare evolution times with "speed limit" minima derived in the literature. Both in a (symmetric) case with couplings of the same strength between each pair and in a case of broken symmetry, the t... | [
{
"title": "INTRODUCTION",
"content": "In a recent series of papers, Giovannetti, Lloyd, and Maccone [1]- [3] have elucidated the role of entanglement in approaching theoretical minima of the times required for quantum systems to progress from a prescribed initial state to a state that is orthogonal or near... | [
{
"id": "",
"caption": "The time evolution of the function P (t) for model A (solid line), plotted as a function of the dimensionless variable, Gnt. The dashed curve shows the evolution that saturates the speed limit.",
"content": "FIG. 1 :\n1The time evolution of the function P (t) for model A (solid l... | [
{
"text": ". V Giovannetti, S Lloyd, L Maccone, quant-ph/0206001Europhys. Lett. 62615V. Giovannetti, S.Lloyd, L. Maccone, Europhys. Lett. 62, 615 (2003), quant-ph/0206001",
"doi": "quant-ph/0206001"
},
{
"text": ". V Giovannetti, S Lloyd, L Maccone, quant-ph/0210197Phys. Rev. 6752109V. Giovannetti, ... |
An example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state
3 Apr 2017
Henryk Fukś
Department of Mathematics and Statistics
Brock University St
L2S 3A1CatharinesOntarioCanada
Joel Midgley-Volpato
Department of Mathematics and Statistics
Brock University St
L2S 3A1... | 40,066,643 | {
"arxiv": "1704.00716",
"mag": 2963428220,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.5506/aphyspolbsupp.9.49"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1704.00716v1.pdf"
],
"pdf_sha": "16743d6fd15c71bec0b19746602ab89c8f624314",
"open_access": {
"license": null,
"url": "https://www.actaphys.uj.edu.pl/S/9/1/13/pdf",
"status": "BRONZE"
}
} | An example of a deterministic cellular automaton exhibiting linear-exponential convergence to the steady state | [
"Henryk Fukś \nDepartment of Mathematics and Statistics\nBrock University St\nL2S 3A1CatharinesOntarioCanada",
"Joel Midgley-Volpato \nDepartment of Mathematics and Statistics\nBrock University St\nL2S 3A1CatharinesOntarioCanada"
] | In a recent paper[1]we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems.We also calculated densities of 0, 1 and 2 after n iterations of this rule, using finite state machines to conjecture patterns... | [
{
"title": "Basic definition",
"content": "We will start from some basic definitions.For A = {0, 1, 2}, a finite sequence of elements of A, b = b 1 b 2 . . ., b n , will be called a block (or word ) of length n.The set of all blocks of all possible lengths will be denoted by A .\nLet f : A 3 → A be a local ... | [
{
"id": "",
"caption": "Fig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lighter gray and darker gray cells (blue in color version) correspond, respectively, to 0, 1 and 2.",
"content": "Fig. 1 .\n1\nFig. 1.Sample spatio-temporal pattern generated by 3-state rule 140.White, lig... | [
{
"text": "An example of degenerate hyperbolicity in cellular automaton with 3 states,\" in 21st International Workshop on Cellular Automata and Discrete Complex Systems. H Fukś, J Midgley-Volpato, arXiv:1506.06649TUCS Lecture Notes. J. Kari, I. Törmä, and M. Szabados242015",
"doi": ""
},
{
"text": ... |
MULTIPLE GENUS 2 HEEGAARD SPLITTINGS: A MISSED CASE
1 Mar 2010
John Berge
Martin Scharlemann
MULTIPLE GENUS 2 HEEGAARD SPLITTINGS: A MISSED CASE
1 Mar 2010arXiv:0910.3921v2 [math.GT]
A gap in [RS] is explored: new examples are found of closed orientable 3-manifolds with possibly multiple genus 2 Heegaard splittings... | 16,107,171 | {
"arxiv": "0910.3921",
"mag": 2135452356,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": null,
"doi": "10.2140/agt.2011.11.1781"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/0910.3921v2.pdf"
],
"pdf_sha": "767f2a222eb7bcc86040bfa3be6ec7d40168ed93",
"open_access": {
"license": null,
"url": "http://msp.org/agt/2011/11-3/agt-v11-n3-p20-s.pdf",
"status": "BRONZE"
}
} | MULTIPLE GENUS 2 HEEGAARD SPLITTINGS: A MISSED CASE | [
"John Berge",
"Martin Scharlemann"
] | A gap in [RS] is explored: new examples are found of closed orientable 3-manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in [RS] are not universally shared by the new examples: some of the new examples have Hempel distance 3, and it is not clear that a single stabiliz... | [
{
"title": "Introduction",
"content": "In 1998, Rubinstein and the second author [RS] studied the question of when there could be more than one distinct genus 2 Heegaard splitting of the same closed orientable 3-manifold. The goal of the project was modest: to provide a complete list of ways in which such m... | [
{
"id": "",
"caption": "Two genus 2 Heegaard splittings X ∪ Q Y and A ∪ P B of a closed 3-manifold M are called Dehn derived (from the splitting M 0 = H a ∪ S H b via λ 1 ∪ λ 2 ⊂ S) if the two splittings are created as in Proposition 2.2.",
"content": "Definition 2 . 3 .\n23Two genus 2 Heegaard splittin... | [
{
"text": "A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody. J Berge, arXiv:0910.3038J. Berge, A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody, arXiv:0910.3038.",
"doi": "arXiv:0910.3038"
},
{
... |
DNA LOSSLESS DIFFERENTIAL COMPRESSION ALGORITHM BASED ON SIMILARITY OF GENOMIC SEQUENCE DATABASE
Heba Afify hebaaffify@yahoo.com
Department of Systems and Biomedical Engineering
Cairo University
Egypt
Muhammad Islam
Department of Systems and Biomedical Engineering
Cairo University
Egypt
Manal Abdel Wahed
Depart... | 699,920 | {
"arxiv": "1109.0094",
"mag": 2963562425,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/abs-1109-0094",
"doi": "10.5121/ijcsit.2011.3412"
} | {
"pdf_urls": [
"https://arxiv.org/pdf/1109.0094v1.pdf"
],
"pdf_sha": "5934644d27fc4faee46b3d3b0753e3d8e76c70f1",
"open_access": {
"license": null,
"url": "https://doi.org/10.5121/ijcsit.2011.3412",
"status": "BRONZE"
}
} | DNA LOSSLESS DIFFERENTIAL COMPRESSION ALGORITHM BASED ON SIMILARITY OF GENOMIC SEQUENCE DATABASE | [
"Heba Afify hebaaffify@yahoo.com \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt",
"Muhammad Islam \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt",
"Manal Abdel Wahed \nDepartment of Systems and Biomedical Engineering\nCairo University\nEgypt"
] | Modern biological science produces vast amounts of genomic sequence data.This is fuelling the need for efficient algorithms for sequence compression and analysis.Data compression and the associated techniques coming from information theory are often perceived as being of interest for data communication and storage.In r... | [
{
"title": "INTRODUCTION",
"content": "The compression of genomic sequences remains a challenging problem, with profound implications in biology and with important technological impact when the use of genomic data will become a daily practice in health and medicine.As such, it will certainly be investigated... | [
{
"id": "",
"caption": "Figure 1.Architecture of the differential compression algorithm",
"content": "Figure 1 .\n1\nFigure 1.Architecture of the differential compression algorithm"
},
{
"id": "",
"caption": "Size of compressed differences for different compression algorithms",
"content"... | [
{
"text": "An Information Based Sequence Distance and its Application to Whole Mitochondrial Genome. M Li, J Badger, X Chen, S Kwong, P Kearney, H Zhang, Bioinformatics. 1722001",
"doi": ""
},
{
"text": "The Similarity Metric. M Li, X Chen, X Li, B Ma, P Vitanyi, Proc. 14th Ann. ACM-SIAM Symp. Discr... |
Fine-Tuning Automatic Speech Recognition for People with Parkinson's: An Effective Strategy for Enhancing Speech Technology Accessibility
Xiuwen Zheng xiuwenz2@illinois.edu
Department of Electrical and Computer Engineering
University of Illinois Urbana-Champaign
Bornali Phukon bornalip@illinois.edu
Department of... | 272,352,029 | {
"arxiv": "2409.19818",
"mag": null,
"acl": null,
"pubmed": null,
"pubmedcentral": null,
"dblp": "journals/corr/abs-2409-19818",
"doi": "10.21437/interspeech.2024-1969"
} | {
"pdf_urls": [
"https://export.arxiv.org/pdf/2409.19818v1.pdf"
],
"pdf_sha": "ab8fcce92679cb03c802044e080a36d2c8fe107d",
"open_access": {
"license": null,
"url": null,
"status": "CLOSED"
}
} | Fine-Tuning Automatic Speech Recognition for People with Parkinson's: An Effective Strategy for Enhancing Speech Technology Accessibility | [
"Xiuwen Zheng xiuwenz2@illinois.edu \nDepartment of Electrical and Computer Engineering\nUniversity of Illinois Urbana-Champaign",
"Bornali Phukon bornalip@illinois.edu \nDepartment of Electrical and Computer Engineering\nUniversity of Illinois Urbana-Champaign",
"Mark Hasegawa-Johnson \nDepartment of Electrica... | This paper enhances dysarthric and dysphonic speech recognition by fine-tuning pretrained automatic speech recognition (ASR) models on the 2023-10-05 data package of the Speech Accessibility Project (SAP), which contains the speech of 253 people with Parkinson's disease.Experiments tested methods that have been effecti... | [
{
"title": "Introduction",
"content": "Speech recognition technology has revolutionized how we interact with digital devices, and can be an especially useful computer input modality for people with motor disorders [1,2].However, many individuals with motor disorders face challenges in effectively using thes... | [
{
"id": "",
"caption": "Figure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker level; Bottom: utterance level.",
"content": "Figure 1 :\n1\nFigure 1: t-SNE plots of x-vectors with K-means clustering (K=2), using SAP-1005 training split.Top: speaker l... | [
{
"text": "Voice recognition device as a computer interface for motor and speech impaired people. M Fried-Oken, Archives of physical medicine and rehabilitation. 66101985",
"doi": ""
},
{
"text": "Automatic speech recognition and training for severely dysarthric users of assistive technology: The ST... |