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99,300 | The baseline design of the LHeC consists in two superconducting linear particle accelerators ("linacs") each about 1 km long, arranged in a racetrack configuration tangential to the LHC. Each linac provides about 10 GV acceleration, therefore the electrons makes three turns in the racetrack reaching an energy of about ... | LHeC | 0.776854 |
99,301 | The Large Hadron Electron Collider (LHeC) is an accelerator study for a possible upgrade of the existing LHC storage ring - the currently highest energy proton accelerator operating at CERN in Geneva. By adding to the proton accelerator ring a new electron accelerator, the LHeC would enable the investigation of electro... | LHeC | 0.776854 |
99,302 | Galaxy diameters are included and the classifications and descriptions are given in such a way as to provide as accurate an account as possible of the appearance of the galaxies on the prints. The accuracy of coordinates is only what is necessary for identifications purposes. The catalogue was edited by Peter Nilson, a... | Uppsala General Catalogue Addendum | 0.776854 |
99,303 | The book introduced new topics such as rainbow Ramsey theory, an “inequality” version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of t... | Aaron Robertson (mathematician) | 0.776851 |
99,304 | The common routes of transmission for the disease-causing bacteria are fecal-oral, person-to-person sexual contact, ingestion of contaminated food (generally unpasteurized (raw) milk and undercooked or poorly handled poultry), and waterborne (i.e., through contaminated drinking water). Contact with contaminated poultry... | Campylobacter enteritis | 0.77685 |
99,305 | Toxic metals can be present in the aqueous environment at trace or ultra-trace concentrations, yet still be toxicologically significant and thus cause harm to humans or the environment. Because these concentrations are so low, they would fall beyond the detection limits of most analytical instruments if the media had b... | Stabilized liquid membrane devices | 0.77685 |
99,306 | SLMDs are known to accumulate cadmium, cobalt, copper, nickel, lead, and zinc, and have been deployed in freshwater monitoring studies by The Washington State Department of Ecology (Ecology) and the USGS. Ecology deployed SLMDs in upper and lower Indian Creek for 28 and 27 days respectively. Metal concentrations on the... | Stabilized liquid membrane devices | 0.77685 |
99,307 | For a transition involving a nonlinear change in perturbation variable or time-dependent coupling between the diabatic states, the equations of motion for the system dynamics cannot be solved analytically. The diabatic transition probability can still be obtained using one of the wide variety of numerical solution algo... | Adiabatic theorem | 0.77685 |
99,308 | If an atom is initially in state | ϕ 2 ( t 0 ) ⟩ {\displaystyle |\phi _{2}(t_{0})\rangle } in zero magnetic field (on the red curve, at the extreme left), an adiabatic increase in magnetic field ( d B d t → 0 ) {\textstyle \left({\frac {dB}{dt}}\to 0\right)} will ensure the system remains in an eigenstate of the Hamilt... | Adiabatic theorem | 0.77685 |
99,309 | For a more widely applicable example, consider a 2-level atom subjected to an external magnetic field. The states, labelled | 1 ⟩ {\displaystyle |1\rangle } and | 2 ⟩ {\displaystyle |2\rangle } using bra–ket notation, can be thought of as atomic angular-momentum states, each with a particular geometry. For reasons that... | Adiabatic theorem | 0.77685 |
99,310 | The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Ha... | Adiabatic theorem | 0.776849 |
99,311 | Often a solid crystal is modeled as a set of independent valence electrons moving in a mean perfectly periodic potential generated by a rigid lattice of ions. With the Adiabatic theorem we can also include instead the motion of the valence electrons across the crystal and the thermal motion of the ions as in the Born–O... | Adiabatic theorem | 0.776849 |
99,312 | In materials science, work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context. This strengthening occurs because of dislocation movements and dislocation generation withi... | Cold pressing | 0.776847 |
99,313 | The CMP distribution was originally proposed by Conway and Maxwell in 1962 as a solution to handling queueing systems with state-dependent service rates. The CMP distribution was introduced into the statistics literature by Boatwright et al. 2003 and Shmueli et al. (2005). The first detailed investigation into the prob... | Conway–Maxwell–Poisson distribution | 0.776847 |
99,314 | Many important summary statistics, such as moments and cumulants, of the CMP distribution can be expressed in terms of the normalizing constant Z ( λ , ν ) {\displaystyle Z(\lambda ,\nu )} . Indeed, The probability generating function is E s X = Z ( s λ , ν ) / Z ( λ , ν ) {\displaystyle \operatorname {E} s^{X}=Z(s\l... | Conway–Maxwell–Poisson distribution | 0.776847 |
99,315 | In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersio... | Conway–Maxwell–Poisson distribution | 0.776847 |
99,316 | In mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction. It has many interpretations and special cases. For example, the fiber product describes how an algebraic variety over one field determines a variety over a bigger field, or the pullback of a family of varieti... | Fiber product of schemes | 0.776845 |
99,317 | In organic chemistry, a sulfonium ion, also known as sulphonium ion or sulfanium ion, is a positively-charged ion (a "cation") featuring three organic substituents attached to sulfur. These organosulfur compounds have the formula +. Together with a negatively-charged counterion, they give sulfonium salts. They are typi... | Sulfonium | 0.776842 |
99,318 | Let X be a smooth algebraic surface and L be an ample line bundle on X of degree d. The Nagata–Biran conjecture states that for sufficiently large r the Seshadri constant satisfies ε ( p 1 , … , p r ; X , L ) = d r . {\displaystyle \varepsilon (p_{1},\ldots ,p_{r};X,L)={d \over {\sqrt {r}}}.} | Nagata–Biran conjecture | 0.776842 |
99,319 | In probability theory and statistics, the Kronecker delta and Dirac delta function can both be used to represent a discrete distribution. If the support of a distribution consists of points x = { x 1 , ⋯ , x n } {\displaystyle \mathbf {x} =\{x_{1},\cdots ,x_{n}\}} , with corresponding probabilities p 1 , ⋯ , p n {\disp... | Generalized Kronecker delta | 0.776842 |
99,320 | In molecular biology, Small nucleolar RNA MBI-28, also known as SNORA3 and ACA3, is a non-coding RNA (ncRNA) molecule which functions in the biogenesis (modification) of other small nuclear RNAs (snRNAs). This type of modifying RNA is located in the nucleolus of the eukaryotic cell which is a major site of snRNA biogen... | Small nucleolar RNA MBI-28 | 0.77684 |
99,321 | Sand dune ecology describes the biological and physico-chemical interactions that are a characteristic of sand dunes. Sand dune systems are excellent places for biodiversity, partly because they are not very productive for agriculture, and partly because disturbed, stressful, and stable habitats are present in proximit... | Sand dune ecology | 0.776839 |
99,322 | I decided I would check it myself! The next day when he came for the answers I remarked to him, "The arithmetic was apparently correct but I do not know about the formulas for the capture cross sections for oxygen and nitrogen—after all, there could be no experiments at the needed energy levels." He replied, like a phy... | Richard Hamming | 0.776838 |
99,323 | Hamming attempted to rectify the situation with a new text, Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985). In 1993, he remarked that "when I left BTL, I knew that that was the end of my scientific career. | Richard Hamming | 0.776838 |
99,324 | He noted that: The way mathematics is currently taught it is exceedingly dull. In the calculus book we are currently using on my campus, I found no single problem whose answer I felt the student would care about! The problems in the text have the dignity of solving a crossword puzzle – hard to be sure, but the result i... | Richard Hamming | 0.776838 |
99,325 | Looking at a commemorative poster of the Bell Labs' valued achievements, he noted that he had worked on or been associated with nearly all of those listed in the first half of his career at Bell Labs, but none in the second. He therefore resolved to retire in 1976, after thirty years.In 1976 he moved to the Naval Postg... | Richard Hamming | 0.776838 |
99,326 | It was superseded by Fortran when the Bell Labs' IBM 650 were replaced by the IBM 704 in 1957.In A Discipline of Programming (1976), Edsger Dijkstra attributed to Hamming the problem of efficiently finding regular numbers. The problem became known as "Hamming's problem", and the regular numbers are often referred to as... | Richard Hamming | 0.776838 |
99,327 | A code which attains the Hamming bound is said to be a perfect code. Hamming codes are perfect codes.Returning to differential equations, Hamming studied means of numerically integrating them. | Richard Hamming | 0.776838 |
99,328 | This not only solved an important problem in telecommunications and computer science, it opened up a whole new field of study.The Hamming bound, also known as the sphere-packing or volume bound is a limit on the parameters of an arbitrary block code. It is from an interpretation in terms of sphere packing in the Hammin... | Richard Hamming | 0.776838 |
99,329 | "As an engineer," he said, "I would have been the guy going down manholes instead of having the excitement of frontier research work. "He went on to earn a Master of Arts degree from the University of Nebraska in 1939, and then entered the University of Illinois at Urbana–Champaign, where he wrote his doctoral thesis o... | Richard Hamming | 0.776838 |
99,330 | He left to join the Bell Telephone Laboratories in 1946. Over the next fifteen years, he was involved in nearly all of the laboratories' most prominent achievements. For his work, he received the Turing Award in 1968, being its third recipient.After retiring from the Bell Labs in 1976, Hamming took a position at the Na... | Richard Hamming | 0.776838 |
99,331 | In computer science, iterated functions occur as a special case of recursive functions, which in turn anchor the study of such broad topics as lambda calculus, or narrower ones, such as the denotational semantics of computer programs. | Iterated map | 0.776837 |
99,332 | In mathematics, an iterated function is a function X → X (that is, a function from some set X to itself) which is obtained by composing another function f: X → X with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial o... | Iterated map | 0.776837 |
99,333 | SuHV-1 can be used to analyze neural circuits in the central nervous system (CNS). For this purpose the attenuated (less virulent) Bartha SuHV-1 strain is commonly used and is employed as a retrograde and anterograde transneuronal tracer. In the retrograde direction, SuHV-1-Bartha is transported to a neuronal cell body... | Suid alphaherpesvirus 1 | 0.776835 |
99,334 | A constructed language (shortened to conlang) is a language whose phonology, grammar, and vocabulary, instead of having developed naturally, are consciously devised for some purpose, which may include being devised for a work of fiction. A constructed language may also be referred to as an artificial, planned or invent... | Constructed language | 0.776831 |
99,335 | The original approach of Chevalley (1946) to the complexification of a compact Lie group can be concisely stated within the language of classical invariant theory, described in Weyl (1946). Let G be a closed subgroup of the unitary group U(V) where V is a finite-dimensional complex inner product space. Its Lie algebra ... | Complex structures on homogeneous spaces | 0.776831 |
99,336 | If G is a compact Lie group, the *-algebra A of matrix coefficients of finite-dimensional unitary representations is a uniformly dense *-subalgebra of C(G), the *-algebra of complex-valued continuous functions on G. It is naturally a Hopf algebra with comultiplication given by Δ f ( g , h ) = f ( g h ) . {\displaystyle... | Complex structures on homogeneous spaces | 0.776831 |
99,337 | 𝖓± are nilpotent Lie algebras acting as nilpotent operators; they are each other's adjoints on V. In particular T acts by conjugation of 𝖓+, so that 𝖙C ⊕ 𝖓+ is a semidirect product of a nilpotent Lie algebra by an abelian Lie algebra. By Engel's theorem, if 𝖆 ⊕ 𝖓 is a semidirect product, with 𝖆 abelian and 𝖓 ni... | Complex structures on homogeneous spaces | 0.776831 |
99,338 | In particular there is a correspondence between closed connected subgroups of N± and subalgebras of their Lie algebras. The exponential map is onto in each case, since the polynomial function log ( eA eB ) lies in a given Lie subalgebra if A and B do and are sufficiently small.The Gauss decomposition can be extended to... | Complex structures on homogeneous spaces | 0.776831 |
99,339 | Their Lie algebras consist of upper and lower strictly triangular matrices. The exponential mapping is a polynomial mapping from the Lie algebra to the corresponding subgroup by nilpotence. The inverse is given by the logarithm mapping which by unipotence is also a polynomial mapping. | Complex structures on homogeneous spaces | 0.776831 |
99,340 | By the functional calculus for polynomial functions it follows that h⊗N lies in the commutant of AN if h = exp z T with z in C. In particular taking z purely imaginary, T must have the form iX with X in the Lie algebra of G. Since every finite-dimensional representation of G occurs as a direct summand of W⊗N, it is lef... | Complex structures on homogeneous spaces | 0.776831 |
99,341 | The defining relations (as a commutant) show that G is an algebraic subgroup. Its intersection with U(V) coincides with G, since it is a priori a larger compact group for which the irreducible representations stay irreducible and inequivalent when restricted to G. Since AN is generated by unitaries, an invertible opera... | Complex structures on homogeneous spaces | 0.776831 |
99,342 | The commutant (or centralizer algebra) is denoted by AN = EndG W⊗N. It is generated as a *-algebra by its unitary operators and its commutant is the *-algebra spanned by the operators u⊗N. The complexification GC of G consists of all operators g in GL(V) such that g⊗N commutes with AN and g acts trivially on the second... | Complex structures on homogeneous spaces | 0.776831 |
99,343 | The decomposition derived from the polar decomposition G C = G ⋅ P = G ⋅ exp i g , {\displaystyle \displaystyle {G_{\mathbf {C} }=G\cdot P=G\cdot \exp i{\mathfrak {g}},}} where 𝖌 is the Lie algebra of G, is called the Cartan decomposition of GC. The exponential factor P is invariant under conjugation by G but is not... | Complex structures on homogeneous spaces | 0.776831 |
99,344 | Neurexin and neuroligin "shake hands," resulting in the connection between the two neurons and the production of a synapse. Neurexins mediate signaling across the synapse, and influence the properties of neural networks by synapse specificity. Neurexins were discovered as receptors for α-latrotoxin, a vertebrate-specif... | Neurexin | 0.77683 |
99,345 | In organic chemistry, the term ethynyl designates a functional group with a double bond with 2 carbon atoms both with sp hybridisation and a triple bond (1 sigma and 2 pi bonds). It is a species similar to acetylene (or in IUPAC ethyne ) with a less H atom thus joined to root chain. An ethynyl group (HC≡C–), also desig... | Ethynyl | 0.776829 |
99,346 | In 2018 IBM reported that there were over 80,000 users of the IBM Quantum Experience, who have collectively run over 3 million experiments.Many academic papers have been published by researchers who have conducted experiments using the service.University professors have integrated examples and experiments based on the ... | IBM Quantum Experience | 0.776829 |
99,347 | This service can be used to run algorithms and experiments, and explore tutorials and simulations around what might be possible with quantum computing. IBM's quantum processors are made up of superconducting transmon qubits, located in dilution refrigerators at the IBM Research headquarters at the Thomas J. Watson Rese... | IBM Quantum Experience | 0.776829 |
99,348 | The IBM Quantum Composer and the IBM Quantum Lab (previously known collectively as the IBM Quantum Experience) form an online platform allowing public and premium access to cloud-based quantum computing services provided by IBM Quantum. This includes access to a set of IBM's prototype quantum processors, a set of tutor... | IBM Quantum Experience | 0.776829 |
99,349 | In algebraic geometry, a torsor or a principal bundle is an analog of a principal bundle in algebraic topology. Because there are few open sets in Zariski topology, it is more common to consider torsors in étale topology or some other flat topologies. The notion also generalizes a Galois extension in abstract algebra. ... | Torsor (algebraic geometry) | 0.776829 |
99,350 | Given a smooth algebraic group G, a G-torsor (or a principal G-bundle) P over a scheme X is a scheme (or even algebraic space) with an action of G that is locally trivial in the given Grothendieck topology in the sense that the base change Y × X P {\displaystyle Y\times _{X}P} along some covering map Y → X {\displaysty... | Torsor (algebraic geometry) | 0.776829 |
99,351 | Conversely, it is easy to see any class in H 1 ( X , G ) {\displaystyle H^{1}(X,G)} defines a G-torsor on X, unique up to an isomorphism. If G is a connected algebraic group over a finite field F q {\displaystyle \mathbf {F} _{q}} , then any G-bundle over Spec F q {\displaystyle \operatorname {Spec} \mathbf {F} _{q}}... | Torsor (algebraic geometry) | 0.776829 |
99,352 | Let P be a G-torsor with a local trivialization { U i → X } {\displaystyle \{U_{i}\to X\}} in étale topology. A trivial torsor admits a section: thus, there are elements s i ∈ P ( U i ) {\displaystyle s_{i}\in P(U_{i})} . Fixing such sections s i {\displaystyle s_{i}} , we can write uniquely s i g i j = s j {\displayst... | Torsor (algebraic geometry) | 0.776829 |
99,353 | If P is a parabolic subgroup of a smooth affine group scheme G with connected fibers, then its degree of instability, denoted by deg i ( P ) {\displaystyle \deg _{i}(P)} , is the degree of its Lie algebra Lie ( P ) {\displaystyle \operatorname {Lie} (P)} as a vector bundle on X. The degree of instability of G is th... | Torsor (algebraic geometry) | 0.776829 |
99,354 | According to John Baez, energy, voltage, position and the phase of a quantum-mechanical wavefunction are all examples of torsors in everyday physics; in each case, only relative comparisons can be measured, but a reference point must be chosen arbitrarily to make absolute values meaningful. However, the comparative val... | Torsor (algebraic geometry) | 0.776829 |
99,355 | Most of constructions and terminology regarding principal bundles in algebraic topology carry over in verbatim to G-bundles. For example, if P → X {\displaystyle P\to X} is a G-bundle and G acts from the left on a scheme F, then one can form the associated bundle P × G F → X {\displaystyle P\times ^{G}F\to X} with fibe... | Torsor (algebraic geometry) | 0.776829 |
99,356 | Some past and present programs and activities include: Microcontroller Workshops and Projects: Microcontroller Mondays, AVR Class 3D Printing, printer assembly and repair, 3D part design using ImplicitCAD. FPGA Workshops and Projects Kit Builds and Kit Designing Nikolas's LED heart kit, Adafruit game of life kit build ... | HacDC | 0.776829 |
99,357 | Perform calibration and validation of surface observations made by Mars Reconnaissance Orbiter (MRO) instruments. This will help determine the accuracy and effectiveness of various instruments that survey Martian geology from orbit. Search for iron-containing minerals, and to identify and quantify relative amounts of s... | Mars Exploration Rover | 0.776828 |
99,358 | Determine what geologic processes have shaped the local terrain and influenced the chemistry. Such processes could include water or wind erosion, sedimentation, hydrothermal mechanisms, volcanism, and cratering. | Mars Exploration Rover | 0.776828 |
99,359 | The Microscopic Imager is a combination of a microscope and a CCD camera. Rock Abrasion Tool (RAT), developed by Honeybee Robotics, for removing dusty and weathered rock surfaces and exposing fresh material for examination by instruments on board. It was able to create a hole around 2 inches (45 millimeters) in diamete... | Mars Exploration Rover | 0.776828 |
99,360 | Development was led by Ken Herkenhoff's team at the U.S. Geological Survey Astrogeology Research Program. | Mars Exploration Rover | 0.776828 |
99,361 | Alpha particle X-ray spectrometer (APXS), developed by the Max Planck Institute for Chemistry in Mainz, Germany, was used to determines the elemental chemistry of rocks and soils using alpha particles and X-rays. Most APXS measurements were taken at night and required at least 10 hours of accumulation time. Magnet arra... | Mars Exploration Rover | 0.776828 |
99,362 | NASA's Mars Exploration Rover (MER) mission was a robotic space mission involving two Mars rovers, Spirit and Opportunity, exploring the planet Mars. It began in 2003 with the launch of the two rovers to explore the Martian surface and geology; both landed on Mars at separate locations in January 2004. Both rovers far ... | Mars Exploration Rover | 0.776828 |
99,363 | Larssens are used in foundation pits, coastline strengthening, bridge construction, piers, tide control, flood protection, agriculture irrigation, water reservoir and other work requiring extremely strong support in a narrow geometry. == References == | Larssen sheet piling | 0.776827 |
99,364 | More generally, data depth, gives a center-outward ordering of data points, and thereby provides a mechanism for constructing rank statistics of various kinds of multidimensional data. For instance, functional data examples can be ordered using the method of band depth or a modified band depth. In contour data analysis... | Contour boxplot | 0.776825 |
99,365 | In statistical graphics and scientific visualization, the contour boxplot is an exploratory tool that has been proposed for visualizing ensembles of feature-sets determined by a threshold on some scalar function (e.g. level-sets, isocontours). Analogous to the classical boxplot and considered an expansion of the concep... | Contour boxplot | 0.776825 |
99,366 | He received his AM (Astronomy) in 1992 and then PhD (Astronomy) in 1993 from Harvard University. Schmidt's PhD thesis was supervised by Robert Kirshner and used Type II Supernovae to measure the Hubble Constant.While at Harvard, he met his future wife, the Australian (Jenny) Jennifer M. Gordon who was a PhD student in ... | Brian Schmidt | 0.776822 |
99,367 | But I guess I was just a little naive about what being a meteorologist meant." His decision to study astronomy, which he had seen as "a minor pastime", was made just before he enrolled at university. Even then, he was not fully committed: he said "I'll do astronomy and change into something else later", and just never ... | Brian Schmidt | 0.776822 |
99,368 | He has often voiced his concern that the current year-to-year uncertainty and lack of co-ordination make it difficult to establish and staff large facilities, or to participate in multi-national ventures, and that scientists spend too much time applying for funding instead of doing research. Interviewed by the Australi... | Brian Schmidt | 0.776822 |
99,369 | Brian Paul Schmidt (born 24 February 1967) is the Vice-Chancellor of the Australian National University (ANU). He was previously a Distinguished Professor, Australian Research Council Laureate Fellow and astrophysicist at the University's Mount Stromlo Observatory and Research School of Astronomy and Astrophysics. He i... | Brian Schmidt | 0.776822 |
99,370 | The corroborating evidence between the two competing studies led to the acceptance of the accelerating universe theory and initiated new research to understand the nature of the universe, such as the existence of dark energy. The discovery of the accelerating universe was named 'Breakthrough of the Year' by Science in ... | Brian Schmidt | 0.776822 |
99,371 | Schmidt was a postdoctoral research Fellow at the Center for Astrophysics | Harvard & Smithsonian (1993–1994) before moving on to the ANU's Mount Stromlo Observatory in 1995. In 1994, Schmidt and Nicholas B. Suntzeff formed the High-Z Supernova Search Team to measure the expected deceleration of the universe and the de... | Brian Schmidt | 0.776822 |
99,372 | Schmidt is married to Jennifer Gordon. They met while they were both studying for their PhDs at Harvard – he in astrophysics and she in economics. They decided to settle in Australia, which he had already visited on several occasions to visit family. He now holds dual citizenship of Australia and the United States.He i... | Brian Schmidt | 0.776822 |
99,373 | He was elected a Fellow of the Royal Society (FRS) in 2012; his certificate of election to the Royal Society reads: Brian Schmidt is an internationally renowned researcher in cosmology and also in the physics of supernovae and gamma ray bursts. In particular, Schmidt's formation and leadership of the High-z Supernova S... | Brian Schmidt | 0.776822 |
99,374 | He was called "Australian of the Year" for 2011 by The Australian newspaper. He is a Fellow and council member of the Australian Academy of Science, The United States National Academy of Sciences, the Royal Society, and Foreign Member of the Spanish Royal Academy of Sciences.Schmidt, Adam Riess, and the High-Z Supernov... | Brian Schmidt | 0.776822 |
99,375 | Schmidt has received the Australian Government's inaugural Malcolm McIntosh Prize for achievement in the Physical Sciences in 2000, Harvard University's Bok Prize in 2000, the Australian Academy of Science's Pawsey Medal Medal in 2001, and the Astronomical Society of India's Vainu Bappu Medal in 2002. He was the Marc A... | Brian Schmidt | 0.776822 |
99,376 | Even though a statistically significant association can be seen between the gene or loci of interest and the trait or disease, no causal relationship can be derived. In order to establish a causal relationship, further studies utilizing a reverse genetics approach for knock-outs of genes or site-directed mutagenesis wo... | Transcriptome-wide association study | 0.77682 |
99,377 | Transcriptome-wide association study (TWAS) is a genetic methodology that can be used to compare the genetic components of gene expression and the genetic components of a trait to determine if an association is present between the two components. TWAS are useful for the identification and prioritization of candidate ca... | Transcriptome-wide association study | 0.77682 |
99,378 | The module structure of a representation of a Hopf algebra H is simply its structure as a module for the underlying associative algebra. The main use of considering the additional structure of a Hopf algebra is when considering all H-modules as a category. The additional structure is also used to define invariant eleme... | Representation theory of Hopf algebras | 0.776818 |
99,379 | In abstract algebra, a representation of a Hopf algebra is a representation of its underlying associative algebra. That is, a representation of a Hopf algebra H over a field K is a K-vector space V with an action H × V → V usually denoted by juxtaposition ( that is, the image of (h,v) is written hv ). The vector space ... | Representation theory of Hopf algebras | 0.776818 |
99,380 | where ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the usual pairing of dual vector spaces. If the map φ: V ⊗ V ∗ → ε H {\displaystyle \varphi :V\otimes V^{*}\rightarrow \varepsilon _{H}} induced by the pairing is to be an H-homomorphism, then for any h in H, x in V and y in V*, φ ( h ( x ⊗ y ) ) = φ ( x ... | Representation theory of Hopf algebras | 0.776818 |
99,381 | This is the motivation for the definition of a bialgebra, where Δ is called the comultiplication and ε is called the counit. In order for each H-module V to have a dual representation V such that the underlying vector spaces are dual and the operation * is functorial over the monoidal category of H-modules, there must ... | Representation theory of Hopf algebras | 0.776818 |
99,382 | The existence of an algebra homomorphism ε satisfying ε ( h ( 1 ) ) h ( 2 ) = h = h ( 1 ) ε ( h ( 2 ) ) {\displaystyle \varepsilon (h_{(1)})h_{(2)}=h=h_{(1)}\varepsilon (h_{(2)})} is a sufficient condition for the existence of the trivial module. It follows that in order for the category of H-modules to be a monoidal c... | Representation theory of Hopf algebras | 0.776818 |
99,383 | The trivial module must be one-dimensional, and so an algebra homomorphism ε: H → F may be defined such that hv = ε(h)v for all v in εH. The trivial module may be identified with F, with 1 being the element such that 1 ⊗ v = v = v ⊗ 1 for all v. It follows that for any v in any H-module V, any c in εH and any h in H, (... | Representation theory of Hopf algebras | 0.776818 |
99,384 | For an associative algebra H, the tensor product V1 ⊗ V2 of two H-modules V1 and V2 is a vector space, but not necessarily an H-module. For the tensor product to be a functorial product operation on H-modules, there must be a linear binary operation Δ: H → H ⊗ H such that for any v in V1 ⊗ V2 and any h in H, h v = Δ h ... | Representation theory of Hopf algebras | 0.776818 |
99,385 | A Hopf algebra also has representations which carry additional structure, namely they are algebras. Let H be a Hopf algebra. If A is an algebra with the product operation μ: A ⊗ A → A, and ρ: H ⊗ A → A is a representation of H on A, then ρ is said to be a representation of H on an algebra if μ is H-equivariant. As spec... | Representation theory of Hopf algebras | 0.776818 |
99,386 | In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called non-conjunction, or alternative denial since it says in effect that at least one of its operand... | Sheffer stroke | 0.776817 |
99,387 | Since the only connective of this logic is |, the symbol | could be discarded altogether, leaving only the parentheses to group the letters. A pair of parentheses must always enclose a pair of WFFs. Examples of theorems in this simplified notation are (p(p(q(q((pq)(pq)))))),(p(p((qq)(pp)))).The notation can be simplifi... | Sheffer stroke | 0.776817 |
99,388 | Research using V-2 rockets after World War II produced valuable results concerning the nature of cosmic rays, the solar spectrum, and the distribution of atmospheric ozone. However, the limited supply and the expense of assembling and firing the V-2 rockets, as well as the small payload capacity of the first purpose-bu... | Aerobee rocket | 0.776813 |
99,389 | The Witt ring of C, and indeed any algebraically closed field or quadratically closed field, is Z/2Z. The Witt ring of R is Z. The Witt ring of a finite field Fq with q odd is Z/4Z if q ≡ 3 mod 4 and isomorphic to the group ring (Z/2Z) if q ≡ 1 mod 4. The Witt ring of a local field with maximal ideal of norm congruent ... | Witt ring (forms) | 0.776811 |
99,390 | The ring homomorphisms from W(k) to Z correspond to the field orderings of k, by taking signature with respective to the ordering. The Witt ring is a Jacobson ring. It is a Noetherian ring if and only if there are finitely many square classes; that is, if the squares in k form a subgroup of finite index in the multipli... | Witt ring (forms) | 0.776811 |
99,391 | In chemistry, axial chirality is a special case of chirality in which a molecule contains two pairs of chemical groups in a non-planar arrangement about an axis of chirality so that the molecule is not superposable on its mirror image. The axis of chirality (or chiral axis) is usually determined by a chemical bond that... | Helical chirality | 0.776809 |
99,392 | The chirality of a molecule that has a helical, propeller, or screw-shaped geometry is called helicity or helical chirality. The screw axis or the Dn, or Cn principle symmetry axis is considered to be the axis of chirality. Some sources consider helical chirality to be a type of axial chirality, and some do not. | Helical chirality | 0.776809 |
99,393 | Lists of animals Ant genera (alphabetical) British ant species (common names) Non-endemic ant species introduced to Great Britain and Ireland Myrmecology topics Amblypygid genera Birds Santa Cruz County, California Sibley–Monroe checklist Domesticated animals Cat breeds Dog breeds Freshwater aquarium fish species Horse... | Outline of zoology | 0.776806 |
99,394 | In alphabetical order by surname: Louis Agassiz (malacology, ichthyology) Aristotle Pierre Joseph Bonnaterre Archie Carr (herpetology, esp. cheloniology) Eugenie Clark (ichthyology) Jeff Corwin (most animals) Georges Cuvier (founder of comparative morphology) Charles Darwin (formulated modern theory of evolution) Richa... | Outline of zoology | 0.776806 |
99,395 | The following outline is provided as an overview of and topical guide to zoology: Zoology – study of animals. Zoology, or "animal biology", is the branch of biology that relates to the animal kingdom, including the identification, structure, embryology, evolution, classification, habits, and distribution of all animals... | Outline of zoology | 0.776806 |
99,396 | Arthropodology - study of arthropods as a whole Carcinology - the study of crustaceans Myriapodology - study of milli- and centipedes Arachnology - study of spiders and related animals such as scorpions, pseudoscorpions, and harvestmen, collectively called arachnids Acarology - study of mites and ticks Entomology - stu... | Outline of zoology | 0.776806 |
99,397 | Anthrozoology - study of interaction between humans and other animals Behavioral ecology - study of environmental effects on animal behaviors Endocrinology - study of endocrine systems Ethology - study of animal behaviour, usually with a focus on behaviour under natural conditions, and viewing behaviour as an evolution... | Outline of zoology | 0.776806 |
99,398 | A number of 2,4-D-degrading bacteria have been isolated and characterized from a variety of environmental habitats. Metabolic pathways for the compound's degradation have been available for many years, and genes encoding 2,4-D catabolism have been identified for several organisms. As a result of the extensive metadata ... | 2,4-Dichlorophenoxyacetic acid | 0.776804 |
99,399 | This may create an appearance known as “ball in hand” on a sialogram, where the ducts are curved around the mass of the lesion.Sialochemistry The composition of saliva changes in disease states, and analysis of saliva for enzymes, electrolytes, hormones, drugs and immunisation status can be performed.Radioisotope scint... | Parotid gland | 0.776803 |
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