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98,500 | These extra equations express the torsion linearly in terms of the spin tensor associated with the matter source, which entails that the torsion generally be non-zero inside matter. A consequence of the linearity is that outside of matter there is zero torsion, so that the exterior geometry remains the same as what wou... | Einstein–Cartan theory | 0.777269 |
98,501 | It is derived by rewriting the Einstein–Hilbert action in terms of the affine connection and then separately posing a constraint that forces both the torsion and contorsion to be zero, which thus forces the affine connection to be equal to the Levi-Civita connection. Because it is a direct translation of the action and... | Einstein–Cartan theory | 0.777269 |
98,502 | The chief difference between a Riemann–Cartan geometry and Riemannian geometry is that in the former, the affine connection is independent of the metric, while in the latter it is derived from the metric as the Levi-Civita connection, the difference between the two being referred to as the contorsion. In particular, th... | Einstein–Cartan theory | 0.777269 |
98,503 | Nor was there a sufficient awareness of the concept of gauge symmetry to understand that Riemannian geometries do not possess the requisite structure to embody a locally gauged Lorentz symmetry, such as would be required to be able to express continuity equations and conservation laws for rotational and boost symmetrie... | Einstein–Cartan theory | 0.777269 |
98,504 | Einstein–Cartan theory differs from general relativity in two ways: (1) it is formulated within the framework of Riemann–Cartan geometry, which possesses a locally gauged Lorentz symmetry, while general relativity is formulated within the framework of Riemannian geometry, which does not; (2) an additional set of equati... | Einstein–Cartan theory | 0.777269 |
98,505 | Singularity theorems which are premised on and formulated within the setting of Riemannian geometry (e.g. Penrose–Hawking singularity theorems) need not hold in Riemann–Cartan geometry. Consequently, Einstein–Cartan theory is able to avoid the general-relativistic problem of the singularity at the Big Bang. The minimal... | Einstein–Cartan theory | 0.777269 |
98,506 | In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation similar to general relativity. The theory was first proposed by Élie Cartan in 1922. Einstein–Cartan theory is the simplest Poincaré gauge theory. | Einstein–Cartan theory | 0.777269 |
98,507 | The Chicago school of mathematical analysis is a school of thought in mathematics that emphasizes the applications of Fourier analysis to the study of partial differential equations. Mathematician Antoni Zygmund co-founded the school with his doctoral student Alberto Calderón at the University of Chicago in the 1950s. ... | Chicago school (mathematical analysis) | 0.777269 |
98,508 | The decoding of silent speech using a computer played an important role in Arthur C. Clarke's story and Stanley Kubrick's associated film A Space Odyssey. In this, HAL 9000, a computer controlling spaceship Discovery One, bound for Jupiter, discovers a plot to deactivate it by the mission astronauts Dave Bowman and Fra... | Silent speech interface | 0.777268 |
98,509 | Patel's team employed machine learning algorithms and deep neural networks to analyze the EEG data and accurately translate the brain signals into meaningful speech output. One of the remarkable achievements of Patel's NeuroVox was its improved precision in identifying and differentiating speech-related brain patterns,... | Silent speech interface | 0.777268 |
98,510 | By applying this theorem to a two-dimensional version of the Smith–Volterra–Cantor set, it is possible to find an Osgood curve, a Jordan arc or closed Jordan curve whose Lebesgue measure is positive.A related result is the analyst's traveling salesman theorem, describing the point sets that form subsets of curves of fi... | Denjoy–Riesz theorem | 0.777265 |
98,511 | A topological space is zero-dimensional according to the Lebesgue covering dimension if every finite open cover has a refinement that is also an open cover by disjoint sets. A topological space is totally disconnected if it has no nontrivial connected subsets; for points in the plane, being totally disconnected is equi... | Denjoy–Riesz theorem | 0.777265 |
98,512 | Kuratowski (1968) credits the result to publications by Frigyes Riesz in 1906, and Arnaud Denjoy in 1910, both in Comptes rendus de l'Académie des sciences. As Moore & Kline (1919) describe, Riesz actually gave an incorrect argument that every totally disconnected set in the plane is a subset of a Jordan arc. This gene... | Denjoy–Riesz theorem | 0.777265 |
98,513 | In topology, the Denjoy–Riesz theorem states that every compact set of totally disconnected points in the Euclidean plane can be covered by a continuous image of the unit interval, without self-intersections (a Jordan arc). | Denjoy–Riesz theorem | 0.777265 |
98,514 | In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, s ( n ) = ∑ d | n , d ≠ n d . {\displaystyle s(n)=\sum \nolimits _{d|n,\ d\neq n}d.} It can be used to characterize the prime numbers, perfect numbers, sociable... | Restricted divisor function | 0.777262 |
98,515 | To summarise: A homeomorphism of the circle is quasi-Möbius if and only if it is quasisymmetric. In this case it and its inverse are Hölder continuous. The quasi-Möbius homeomorphisms form a group under composition.To prove the theorem it suffices to prove that if F = ∂f then there are constants A, B > 0 such that for ... | Busemann function | 0.777261 |
98,516 | To summarise, the above results give the following characterisation of Busemann functions on a Hadamard space:THEOREM. On a Hadamard space, the following conditions on a function f are equivalent: h is a Busemann function. h is a convex function, Lipschitz with constant 1 and h assumes its minimum on any closed ball ce... | Busemann function | 0.777261 |
98,517 | The statement and proof of the property for Busemann functions relies on a fundamental theorem on closed convex subsets of a Hadamard space, which generalises orthogonal projection in a Hilbert space: if C is a closed convex set in a Hadamard space X, then every point x in X has a unique closest point P(x) ≡ PC(x) in C... | Busemann function | 0.777261 |
98,518 | The space X is embedded into Y by sending x to the function fx(y) = d(y,x) – d(x0,x). Let X be the closure of X in Y. Then X is compact (metrisable) and contains X as an open subset; moreover compactifications arising from different choices of basepoint are naturally homeomorphic. Compactness follows from the Arzelà–As... | Busemann function | 0.777261 |
98,519 | The space Y can be topologised by the seminorms ‖ f ‖N = supXN | f |, the topology of uniform convergence on compacta. This is the topology induced by the natural map of C(X) into the direct product of the Banach spaces C(XN). It is give by the metric D(f,g) = Σ 2−N ‖ f − g ‖ N(1 + ‖ f − g ‖ N)−1. | Busemann function | 0.777261 |
98,520 | Before discussing CAT(-1) spaces, this section will describe the Efremovich–Tikhomirova theorem for the unit disk D with the Poincaré metric. It asserts that quasi-isometries of D extend to quasi-Möbius homeomorphisms of the unit disk with the Euclidean metric. The theorem forms the prototype for the more general theor... | Busemann function | 0.777261 |
98,521 | The vector field Vh is thus the gradient vector field for h. The geodesics through any point are the flow lines for the flow αt for Vh, so that αt is the gradient flow for h. THEOREM. On a Hadamard manifold X the following conditions on a continuous function h are equivalent: h is a Busemann function. h is a convex, Li... | Busemann function | 0.777261 |
98,522 | If h is a Busemann function on a Hadamard manifold, then h is continuously differentiable with ‖ dh(y) ‖ = 1 for all y.From the previous properties of h, for each y there is a unique geodesic γ(t) parametrised by arclength with γ(0) = y such that h ∘ γ(t) = h(y) + t. It has the property that it cuts ∂B(y,r) at t = ±r: ... | Busemann function | 0.777261 |
98,523 | In geometric topology, Busemann functions are used to study the large-scale geometry of geodesics in Hadamard spaces and in particular Hadamard manifolds (simply connected complete Riemannian manifolds of nonpositive curvature). They are named after Herbert Busemann, who introduced them; he gave an extensive treatment ... | Busemann function | 0.777261 |
98,524 | On a Hadamard space, the functions F t ( y ) = d ( y , γ ( t ) ) − t {\displaystyle F_{t}(y)=d(y,\gamma (t))-t} converge uniformly to B γ {\displaystyle B_{\gamma }} uniformly on any bounded subset of X {\displaystyle X} .Let h(t) = d(y,γ(t)) − t = Ft(y). Since γ ( t ) {\displaystyle \gamma (t)} is parametrised by arcl... | Busemann function | 0.777261 |
98,525 | Hence in the Euclidean comparison triangle CA - CB is close to AB with CA large. So the angle at A is small. So the point D on AC at the same distance as AB lies close to B. Hence, by the first comparison theorem for geodesic triangles, d(xn(t),γ(t)) is small. Conversely suppose that for fixed t and n sufficiently larg... | Busemann function | 0.777261 |
98,526 | This is the topology induced by the natural map of C(X) into the direct product of the Banach spaces Cb(XN) of continuous bounded functions on XN. It is give by the metric D(f,g) = Σ 2−N ‖ f − g ‖N(1 +‖ f − g ‖N)−1. The space X is embedded into Y by sending x to the function fx(y) = d(y,x) – d(x0,x). | Busemann function | 0.777261 |
98,527 | Let Y = C(X) be the space of Lipschitz continuous functions on X, i.e. those for which | f(x) – f(y) | ≤ A d(x,y) for some constant A > 0. The space Y can be topologised by the seminorms ‖ f ‖N = supXN | f |, the topology of uniform convergence on bounded sets. The seminorms are finite by the Lipschitz conditions. | Busemann function | 0.777261 |
98,528 | In the previous section it was shown that if X is a Hadamard space and x0 is a fixed point in X then the union of the space of Busemann functions vanishing at x0 and the space of functions hy(x) = d(x,y) − d(x0,y) is closed under taking uniform limits on bounded sets. This result can be formalised in the notion of bord... | Busemann function | 0.777261 |
98,529 | Just because a radioisotope lands on the surface of the soil, does not mean it will enter the human food chain. After release into the environment, radioactive materials can reach humans in a range of different routes, and the chemistry of the element usually dictates the most likely route. | Environmental radioactivity | 0.777259 |
98,530 | Possible sources include electron capture from copper-58 and EC + p from zinc-59. Nickel-59 is a long-lived cosmogenic radionuclide with a half-life of 76,000 years. 59Ni has found many applications in isotope geology. | Nickel-56 | 0.777258 |
98,531 | 1914 – Walter Sydney Adams determines an incredibly high density for Sirius B. 1926 – Ralph Fowler uses Fermi–Dirac statistics to explain white dwarf stars. 1930 – Subrahmanyan Chandrasekhar discovers the white dwarf maximum mass limit. | Timeline of white dwarfs, neutron stars, and supernovae | 0.777258 |
98,532 | In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree. The Stern–Brocot tree was introduced independently by Moritz Stern (1858) and Achille Brocot... | Stern–Brocot tree | 0.777258 |
98,533 | In statistics, the Box–Cox distribution (also known as the power-normal distribution) is the distribution of a random variable X for which the Box–Cox transformation on X follows a truncated normal distribution. It is a continuous probability distribution having probability density function (pdf) given by f ( y ) = 1 (... | Box–Cox distribution | 0.777257 |
98,534 | National Grid Gas has ordered ten suction excavators.As of July 2009 in England, the North West Gas Alliance has three German-made suction excavators. Vacuum-excavation hire provider Utility Site Solutions work with utility and civil engineering companies throughout the UK to provide safer no-dig excavation. Projects i... | Hydro excavation | 0.777257 |
98,535 | As the graph Fourier transform enables the definition of convolution on graphs, it makes possible to adapt the conventional convolutional neural networks (CNN) to work on graphs. Graph structured semi-supervised learning algorithms such as graph convolutional network (GCN), are able to propagate the labels of a graph s... | Graph Fourier Transform | 0.777256 |
98,536 | In mathematics, the graph Fourier transform is a mathematical transform which eigendecomposes the Laplacian matrix of a graph into eigenvalues and eigenvectors. Analogously to the classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what is known as a graph Fourier basis. The Graph F... | Graph Fourier Transform | 0.777256 |
98,537 | Note that this function returns complex values and uses the physics convention for spherical coordinates where θ {\displaystyle \theta } is the zenith angle (angle from the positive Z-axis) and ϕ {\displaystyle \phi } is the azimuth (counter-clockwise angle around the positive Z-axis). The presence of Condon-Shortley p... | Ambisonic data exchange formats | 0.777256 |
98,538 | SN3D stands for Schmidt semi-normalisation and is commonly used in geology and magnetics. The weighting coefficients are N ℓ , m SN3D = ( 2 − δ m ) ( ℓ − | m | ) ! ( ℓ + | m | ) ! , δ m { 1 if m = 0 0 if m ≠ 0 {\displaystyle N_{\ell ,m}^{\text{SN3D}}={\sqrt {{(2-\delta _{m})}{(\ell -|m|)! | Ambisonic data exchange formats | 0.777256 |
98,539 | Obvious significance for solving decoding problems (3D reconstruction). "The relation to SN3D is N ℓ , m N3D = N ℓ , m SN3D 2 ℓ + 1 {\displaystyle N_{\ell ,m}^{\text{N3D}}=N_{\ell ,m}^{\text{SN3D}}{\sqrt {2\ell +1}}} .This normalisation is standard in Physics and Mathematics and is supported by some Ambisonic software... | Ambisonic data exchange formats | 0.777256 |
98,540 | Data exchange formats for Ambisonics have undergone radical changes since the early days of four-track magnetic tape. Researchers working on very high-order systems found no straightforward way to extend the traditional formats to suit their needs. Furthermore, there was no widely accepted formulation of spherical harm... | Ambisonic data exchange formats | 0.777256 |
98,541 | A moron, in the context of bacteriophage genetics, is an extra gene in a prophage genome without a function in the phage's lysogenic cycle. These genes may code for products beneficial to the phage's bacterial host, as with the example of gp15 of phage HK97 serving as a superinfection exclusion protein. The term moron ... | Moron (bacteriophage) | 0.777255 |
98,542 | The chondritic uniform reservoir model are tightly constrained in order to use Lu–Hf system for age determination. Chondrites represent primitive materials from solar nebula which later accrete to form planetesimals, and to further extent meaning the primitive undifferentiated Earth. Chondritic uniform reservoir are us... | Lutetium–hafnium dating | 0.777254 |
98,543 | The 2009 Nobel Prize in Physics, divided between three recipients over two disciplines, led to some omissions. Charles Kuen Kao's award for his work in fiber optics led to claims that Narinder Singh Kapany's previous work had been overlooked. Willard Boyle and George E. Smith's award for the development of the charge-c... | Nobel Prize controversies | 0.777253 |
98,544 | The 1974 prize went to Martin Ryle and Antony Hewish "for their pioneering research in radio astrophysics: Ryle for his observations and inventions, in particular of the aperture synthesis technique, and Hewish for his decisive role in the discovery of pulsars". Jocelyn Bell Burnell, Hewish's graduate student, was not ... | Nobel Prize controversies | 0.777253 |
98,545 | None of the contributors to the discovery of nuclear fission won the prize for Physics. Instead, the prize for Chemistry was awarded to Otto Hahn for his discovery of fission in Berlin in 1938. Lise Meitner also contributed to the discovery of nuclear fission, through her collaboration with Hahn. From the beginning, sh... | Nobel Prize controversies | 0.777253 |
98,546 | Half of the 1983 prize went to William Alfred Fowler "for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe". Fowler acknowledged Fred Hoyle as the pioneer of the concept of stellar nucleosynthesis but Hoyle did not receive a share ... | Nobel Prize controversies | 0.777252 |
98,547 | Albert Einstein's 1921 Nobel Prize Award mainly recognized his 1905 discovery of the mechanism of the photoelectric effect and "for his services to Theoretical Physics". The Nobel committee passed on several nominations for his many other seminal contributions, although these led to prizes for others who later applied ... | Nobel Prize controversies | 0.777252 |
98,548 | But the influence of the economist that mainly matters is an influence over laymen: politicians, journalists, civil servants and the public generally. "The Kluge Prize, a $1 million prize given by the John W. Kluge Center at the Library of Congress, is awarded for lifetime achievement in fields of humanistic and social... | Nobel Prize controversies | 0.777252 |
98,549 | Since the Institute had already prepared his medal and diploma before the second letter arrived, they were able to award them to him later, during the 1947 Nobel festival. Domagk was the first to decline a prize. Due to his refusal, the procedures changed so that if a laureate declined the prize or failed to collect th... | Nobel Prize controversies | 0.777252 |
98,550 | While fascism had few supporters outside Italy, Spain, and Germany, those who did not necessarily sympathize felt that it was wrong to (deliberately) offend Germany.Hitler's decree prevented three Germans from accepting their prizes: Gerhard Domagk (1939 Nobel Prize in Physiology or Medicine), Richard Kuhn (1938 Nobel ... | Nobel Prize controversies | 0.777252 |
98,551 | Cabibbo arguably merited a share of the award. The recipient of the other half of the 2008 prize was Yoichiro Nambu for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics. The fundamental step in this field is the Nambu–Jona-Lasinio model (NJL model), developed together with the Italian ... | Nobel Prize controversies | 0.777252 |
98,552 | Gerhard Ertl, who was the sole recipient of the 2007 Nobel Prize in Chemistry for his studies of the catalytic effects of metal surfaces, has expressed surprise and disappointment that Gábor Somorjai, a foundational pioneer in modern surface science and catalysis, did not share the prize. Somorjai and Ertl had previous... | Nobel Prize controversies | 0.777252 |
98,553 | From 1922 to 1946, Gilbert N. Lewis, who was widely known for his coining of the covalent bond, electron pair, Lewis structure and other seminal contributions that have become near-universal conventions in chemistry, was nominated 41 times for the Nobel Prize in Chemistry but never won. It has been speculated that whil... | Nobel Prize controversies | 0.777252 |
98,554 | 1915 saw a newspaper rumor (starting with a 6 November Reuters report from London) along the lines that the Nobel Prize in Physics was to be awarded to both Thomas Edison and Nikola Tesla. The story had gone to press in many publications before a 15 November Reuters story from Stockholm with the announcement that the p... | Nobel Prize controversies | 0.777252 |
98,555 | The 2017 Nobel Prize in Physics was awarded to Reiner Weiss, Kip Thorne, and Barry Barish for their contribution to LIGO, which led to the detection of gravitational waves. Despite the contributions of the upwards of a thousand scientists and engineers in LIGO, the Nobel Committee continued its tradition of awarding th... | Nobel Prize controversies | 0.777252 |
98,556 | The 2014 Nobel Prize in Physics, awarded to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura for the blue light-emitting diode, did not recognize the decades of incremental work in developing the LED by other pioneers such as Oleg Losev, Nick Holonyak, and Gertrude Neumark and overlooked a prior claim for invention of t... | Nobel Prize controversies | 0.777252 |
98,557 | The 2010 Nobel Prize in Physics was awarded to Andre Geim and Konstantin Novoselov of the University of Manchester "for groundbreaking experiments regarding the two-dimensional material graphene". Several problems with the factual accuracy of the supporting documents issued by the Nobel committee have been pointed out,... | Nobel Prize controversies | 0.777252 |
98,558 | The 1935 prize was awarded to Hans Spemann "for his discovery of the organizer effect in embryonic development". In 1991 Howard M. Lenhoff, then Professor of Developmental and Cell Biology at the University of California, published a paper pointing out that Ethel Browne Harvey should have shared in Spemann's Nobel Priz... | Nobel Prize controversies | 0.777252 |
98,559 | Banting's original method of isolating insulin required performing surgery on living dogs, which was too labor-intensive to produce insulin on a large scale. Best then set about finding a biochemical extraction method, while James Collip, a chemistry professor on sabbatical from the University of Alberta, joined Macleo... | Nobel Prize controversies | 0.777252 |
98,560 | The 1918 Nobel Prize in Chemistry was awarded to Fritz Haber for his invention of the Haber–Bosch process, which allowed for the efficient synthesis of ammonia, leading to the economical mass production of chemical fertilizers. The award was controversial, as Haber had overseen Germany's chemical weapons program during... | Nobel Prize controversies | 0.777252 |
98,561 | Beyond disputes over which contributor's work was more worthy, critics most often discerned political bias and Eurocentrism in the result. The interpretation of Nobel's original words concerning the Literature prize has also undergone repeated revisions.A major controversies-generating factor for the more recent scient... | Nobel Prize controversies | 0.777252 |
98,562 | Awards committees have historically rewarded discoveries over inventions: up to 2004, 77 per cent of Nobel Prizes in physics have been given to discoveries, compared with only 23 per cent to inventions. In addition, the scientific prizes typically reward contributions over an entire career rather than a single year.No ... | Nobel Prize controversies | 0.777252 |
98,563 | Since the first award in 1901, conferment of the Nobel Prize has occasionally engendered criticism and controversy. After his death in 1896, the will of Swedish industrialist Alfred Nobel established that an annual prize be awarded for service to humanity in the fields of physics, chemistry, physiology or medicine, lit... | Nobel Prize controversies | 0.777252 |
98,564 | Several Nobel Prizes were awarded for research related to the concepts of the boson, Bose–Einstein statistics and Bose–Einstein condensate—the latest being the 2001 Nobel Prize in Physics given for advancing the theory of Bose–Einstein condensates although Satyendra Nath Bose himself was not awarded the Nobel Prize. In... | Nobel Prize controversies | 0.777252 |
98,565 | Physics 1989—The Nobel Committee mistakenly phoned Washington DC economist Norman Ramsey, trying to award him the Nobel Prize in Physics. They meant to call the Harvard University physicist Norman Foster Ramsey Jr..Chemistry 1987—The Nobel Committee mistakenly phoned Southern California carpet cleaner Donald O. Cram, t... | Nobel Prize controversies | 0.777252 |
98,566 | Peter Higgs and François Englert were awarded the 2013 Nobel Prize in Physics for their theoretical predictions related to the Higgs boson. This ran into the problem of the Nobel only awarding three individuals since three separate 1964 PRL symmetry breaking papers have been credited with the discovery of the Higgs mec... | Nobel Prize controversies | 0.777252 |
98,567 | Bohr nominated both for this work, in addition to recommending the Chemistry prize for Hahn. Hahn's assistant, Fritz Strassmann, was not considered for the Physics prize.Chien-Shiung Wu disproved the law of the conservation of parity (1956) and was the first Wolf Prize winner in physics. | Nobel Prize controversies | 0.777252 |
98,568 | The term radar has since entered English and other languages as a common noun, losing all capitalization. The modern uses of radar are highly diverse, including air and terrestrial traffic control, radar astronomy, air-defense systems, anti-missile systems, marine radars to locate landmarks and other ships, aircraft an... | Microwave radar | 0.777252 |
98,569 | "Randomized simplex algorithms on Klee-Minty cubes". Proceedings 35th Annual Symposium on Foundations of Computer Science. IEEE. | Klee–Minty cube | 0.777251 |
98,570 | The first two links have both an algebraic construction and a picture of a three-dimensional Klee–Minty cube: Deza, Antoine; Nematollahi, Eissa; Terlaky, Tamás (May 2008). "How good are interior point methods? Klee–Minty cubes tighten iteration-complexity bounds" (PDF). Mathematical Programming. | Klee–Minty cube | 0.777251 |
98,571 | The Klee–Minty cube was originally specified with a parameterized system of linear inequalities, with the dimension as the parameter. When the dimension is two, the "cube" is a squashed square. When the dimension is three, the "cube" is a squashed cube. Illustrations of the "cube" have appeared besides algebraic descri... | Klee–Minty cube | 0.777251 |
98,572 | In particular, many optimization algorithms for linear optimization exhibit poor performance when applied to the Klee–Minty cube. In 1973 Klee and Minty showed that Dantzig's simplex algorithm was not a polynomial-time algorithm when applied to their cube. Later, modifications of the Klee–Minty cube have shown poor beh... | Klee–Minty cube | 0.777251 |
98,573 | Further modifications of the Klee–Minty cube have shown poor performance of central-path–following algorithms for linear optimization, in that the central path comes arbitrarily close to each of the corners of a cube. This "vertex-stalking" performance is surprising, because such path-following algorithms have polynomi... | Klee–Minty cube | 0.777251 |
98,574 | In mathematical optimization, the Klee–Minty cube is an example that shows the worst-case computational complexity of many algorithms of linear optimization. It is a deformed cube with exactly 2D corners in dimension D. Klee and Minty showed that Dantzig's simplex algorithm visits all corners of a (perturbed) cube in d... | Klee–Minty cube | 0.777251 |
98,575 | A chorochromatic or area-class map represents a categorical or nominal variable distributed over space (also known as a discrete field), by using different area symbols (usually color hue) to represent regions of homogeneous value. Common examples include maps of surface geology, soil, vegetation, land use, city zoning... | Thematic map | 0.77725 |
98,576 | In 1701 he published the "New and Correct Chart Shewing the Variations of the Compass", see first image, the first chart to show lines of equal magnetic variation and possibly the first isarithmic map. Early chorochromatic (nominal area-class) maps also appeared in the late 18th century as scientific instruments for ex... | Thematic map | 0.77725 |
98,577 | The Experimental Station was founded as an effort to move the DuPont Company from gunpowder and explosives into chemistry. The site overlooks the original powder mills upon which the company was founded – now Hagley Museum and Library. The Experimental Station is east from Hagley Museum and west-southwest from Nemours ... | DuPont Experimental Station | 0.777249 |
98,578 | Fast prototyping of wheeled and legged robots Research on robot locomotion Swarm intelligence (Multi-robot simulations) Artificial life and evolutionary robotics Simulation of adaptive behaviour Self-Reconfiguring Modular Robotics Experimental environment for computer vision Teaching and robot programming contests | Webots | 0.777249 |
98,579 | A complete and up-to-date list is provided in the Webots user guide. AIBO ERS7 and ERS210, Sony Corporation BIOLOID (dog), Robotis Boe-Bot DARwIn-OP, Robotis E-puck Hemisson HOAP-2, Fujitsu Limited iCub, RobotCub Consortium iRobot Create, iRobot Katana IPR, Neuronics AG Khepera mobile robot I, II, III, K-Team Corporati... | Webots | 0.777249 |
98,580 | Since August 18, 2017, the robotbenchmark.net website has offered free access to a series of robotics benchmarks based on Webots simulations through the Webots web interface. Webots instances are running in the cloud and the 3D views are displayed in the user browser. From this web interface, users can program robots i... | Webots | 0.777249 |
98,581 | A United States patent with multinational collaborative recognition was applied for on 10/26/2009, and published 10/4/2012, for the rights to BDBV. The patent is listed under six different numbers, including one assigned a US appellation, as well as one Canadian (CA), two European Patent Office (EP), and two World Inte... | Bundibugyo virus | 0.777248 |
98,582 | The ecology of BDBV is currently unclear and no reservoir host has yet been identified. Therefore, it remains unclear how BDBV was introduced into the human population. Bats are suspected to harbor the virus because infectious Marburg virus (MARV) and Ravn virus (RAVV), two distantly related filoviruses, have been isol... | Bundibugyo virus | 0.777248 |
98,583 | He found the existence of the infinitely many fixed points (equilibrium points) for the first two versions. He concluded that these versions of AFDEs are structurally unstable systems mathematically by using an extension of the Peixoto Theorem for two-dimensional manifolds to a four-dimensional manifold. Moreover, he o... | Quantitative behavioral finance | 0.777246 |
98,584 | Research continues on efforts to optimize the parameters of the asset flow equations in order to forecast near term prices (see Duran and Caginalp ). It is important to classify the behavior of solutions for the dynamical system of nonlinear differential equations. Duran studied the stability analysis of the solutions ... | Quantitative behavioral finance | 0.777246 |
98,585 | For example, suppose many traders are anticipating positive news and buy the stock. If the positive news does not materialize they are inclined to sell in large numbers, thereby suppressing the price significantly below the previous levels. This interpretation is inconsistent with EMH but is consistent with asset flow ... | Quantitative behavioral finance | 0.777246 |
98,586 | White showed that using neural networks with 500 days of IBM stock was unsuccessful in terms of short term forecasts. In both of these examples, the level of “noise” or changes in valuation apparently exceeds any possible behavioral effects. A methodology that avoids this pitfall has been developed during the past deca... | Quantitative behavioral finance | 0.777246 |
98,587 | The challenge of using these ideas to forecast price dynamics in financial markets has been the focus of some of the recent work that has merged two different mathematical methods. The differential equations can be used in conjunction with statistical methods to provide short term forecasts. One of the difficulties in ... | Quantitative behavioral finance | 0.777246 |
98,588 | One of the predictions of this theory by Caginalp and Balenovich (1999) was that a larger supply of cash per share would result in a larger bubble. Experiments by Caginalp, Porter and Smith (1998) confirmed that doubling the level of cash, for example, while maintaining constant number of shares essentially doubles the... | Quantitative behavioral finance | 0.777246 |
98,589 | The attempt to quantify basic biases and to use them in mathematical models is the subject of Quantitative Behavioral Finance. Caginalp and collaborators have used both statistical and mathematical methods on both the world market data and experimental economics data in order to make quantitative predictions. In a seri... | Quantitative behavioral finance | 0.777246 |
98,590 | Data obtained from CRC Handbook of Chemistry and Physics, 44th ed. pages 2560–2561, except for critical temperature line (31.1 °C) and temperatures −30 °C and below, which are taken from Lange's Handbook of Chemistry, 10th ed. page 1463. | Carbon dioxide (data page) | 0.777246 |
98,591 | Table data obtained from CRC Handbook of Chemistry and Physics 44th ed. Annotation "(s)" indicates equilibrium temperature of vapor over solid. Otherwise temperature is equilibrium of vapor over liquid. For kPa values, where datum is whole numbers of atmospheres exact kPa values are given, elsewhere 2 significant figur... | Carbon dioxide (data page) | 0.777246 |
98,592 | The UOP Riverside research and development laboratory in McCook, Illinois was conceived in 1921 by Hiram J. Halle, the chief executive officer of Universal Oil Products (now simply UOP), as a focal point where the best and brightest scientists could create new products and provide scientific support for the oil refinin... | UOP LLC | 0.777246 |
98,593 | A map f: X → Y {\displaystyle f:X\to Y} is called a relatively closed map if whenever C {\displaystyle C} is a closed subset of the domain X {\displaystyle X} then f ( C ) {\displaystyle f(C)} is a closed subset of f {\displaystyle f} 's image Im f := f ( X ) , {\displaystyle \operatorname {Im} f:=f(X),} where as usu... | Open mapping | 0.777241 |
98,594 | The condition f(x1, ..., xn) = f(|x1|, ..., |xn|) ensures that X1, ..., Xn are of zero mean and uncorrelated; still, they need not be independent, nor even pairwise independent. By the way, pairwise independence cannot replace independence in the classical central limit theorem.Here is a Berry–Esseen type result. The d... | Lyapunov's central limit theorem | 0.777239 |
98,595 | These two εn-close distributions have densities (in fact, log-concave densities), thus, the total variance distance between them is the integral of the absolute value of the difference between the densities. Convergence in total variation is stronger than weak convergence. An important example of a log-concave density ... | Lyapunov's central limit theorem | 0.777239 |
98,596 | A sum of discrete random variables is still a discrete random variable, so that we are confronted with a sequence of discrete random variables whose cumulative probability distribution function converges towards a cumulative probability distribution function corresponding to a continuous variable (namely that of the no... | Lyapunov's central limit theorem | 0.777239 |
98,597 | The central limit theorem gives only an asymptotic distribution. As an approximation for a finite number of observations, it provides a reasonable approximation only when close to the peak of the normal distribution; it requires a very large number of observations to stretch into the tails.The convergence in the centra... | Lyapunov's central limit theorem | 0.777239 |
98,598 | If each Xi has finite mean μ, then by the law of large numbers, Sn/n → μ. If in addition each Xi has finite variance σ2, then by the central limit theorem, where ξ is distributed as N(0,σ2). This provides values of the first two constants in the informal expansion In the case where the Xi do not have finite mean or var... | Lyapunov's central limit theorem | 0.777239 |
98,599 | Taking the difference between f(n) and its approximation and then dividing by the next term in the expansion, we arrive at a more refined statement about f(n): Here one can say that the difference between the function and its approximation grows approximately as a2φ2(n). The idea is that dividing the function by approp... | Lyapunov's central limit theorem | 0.777239 |
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