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15,500 | In population genetics, a fixed allele is an allele that is the only variant that exists for that gene in a population. A fixed allele is homozygous for all members of the population. The process by which alleles become fixed is called fixation. A population of a hypothetical species can be conceived to exemplify the c... | Fixed allele | 0.814375 |
15,501 | Recent work demonstrates MTTF prediction using a machine learning model. The work uses a neural network-based supervised learning approach with current density, interconnect length, interconnect temperature as input features to the model. | Electromigration | 0.814374 |
15,502 | Particular attention must be paid to vias and contact holes. The current carrying capacity of a via is much less than a metallic wire of same length. Hence multiple vias are often used, whereby the geometry of the via array is very significant: multiple vias must be organized such that the resulting current is distribu... | Electromigration | 0.814374 |
15,503 | The complete mathematical model describing electromigration consists of several partial differential equations (PDEs) which need to be solved for three-dimensional geometrical domains representing segments of an interconnect structure. Such a mathematical model forms the basis for simulation of electromigration in mode... | Electromigration | 0.814374 |
15,504 | In late 2019, Zapata computing claimed to have factored 1,099,551,473,989, and in 2021 released a paper describing this computation.In December 2022, the 48-bit factorisation 261 , 980 , 999 , 226 , 229 = 15538213 × 16860433 {\displaystyle 261,980,999,226,229=15538213\times 16860433} was completed using a 10-qubit flip... | Integer factorization records | 0.814374 |
15,505 | As of the end of 2007, thanks to the constant decline in memory prices, the ready availability of multi-core 64-bit computers, and the availability of the efficient sieving code (developed by Thorsten Kleinjung of the Bonn group) via ggnfs and of robust open-source software such as msieve for the finishing stages, spec... | Integer factorization records | 0.814374 |
15,506 | Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography. The difficulty depends on both the size and form of the number and its prime factors; it is currently very difficult to factorize large semiprimes (and, indeed, m... | Integer factorization records | 0.814373 |
15,507 | In medicine, public health, and biology, transmission is the passing of a pathogen causing communicable disease from an infected host individual or group to a particular individual or group, regardless of whether the other individual was previously infected. The term strictly refers to the transmission of microorganism... | Disease spread | 0.814368 |
15,508 | The foremost example of a full-solution method is the nested fixed point (NFXP) algorithm developed by John Rust in 1987. The NFXP algorithm is described in great detail in its documentation manual.A recent work by Che-Lin Su and Kenneth Judd in 2012 implements another approach (dismissed as intractable by Rust in 1987... | Dynamic discrete choice | 0.814365 |
15,509 | Given the distributional assumption on q ( d ξ ′ ∣ x ′ , θ ) {\displaystyle q(d\xi '\mid x',\theta )} , the probability of particular choice d {\displaystyle d} is given by P ( d ∣ x , θ ) = exp { u ( x , d , θ ) + β E V ( x , d , θ ) } ∑ d ′ ∈ D ( x ) exp { u ( x , d ′ , θ ) + β E V ( x , d ′ , θ ) } {\displaystyl... | Dynamic discrete choice | 0.814365 |
15,510 | 3. The optimization problem follows a Markov decision processThe states x t {\displaystyle x_{t}} follow a Markov chain. That is, attainment of state x t {\displaystyle x_{t}} depends only on the state x t − 1 {\displaystyle x_{t-1}} and not x t − 2 {\displaystyle x_{t-2}} or any prior state. | Dynamic discrete choice | 0.814365 |
15,511 | In the nested fixed point algorithm, P ( d ∣ x , θ ) {\displaystyle P(d\mid x,\theta )} is recalculated for each guess of the parameters θ. The MPEC method instead solves the constrained optimization problem: max L ( θ ) subject to E V ( x , d , θ ) = ∫ p ( x ′ ∣ x , d , θ ) {\displaystyle {\begin{aligned}\max &\qquad... | Dynamic discrete choice | 0.814365 |
15,512 | Virtual screening is a very useful application when it comes to identifying hit molecules as a beginning for medicinal chemistry. As the virtual screening approach begins to become a more vital and substantial technique within the medicinal chemistry industry the approach has had an expeditious increase. | Virtual screening | 0.814361 |
15,513 | An efficient substructure analysis is used for structures that have similarities to a multi-level building or tower. Geometry is used for numbering boundary joints for a given structure in the onset and towards the climax. When the method of special static condensation and substitutions routines are developed this meth... | Virtual screening | 0.814361 |
15,514 | The first Machine Learning model used on large datasets is the Substructure Analysis that was created in 1973. Each fragment substructure make a continuous contribution an activity of specific type. Substructure is a method that overcomes the difficulty of massive dimensionality when it comes to analyzing structures in... | Virtual screening | 0.814361 |
15,515 | Machine learning algorithms have been widely used in virtual screening approaches. Supervised learning techniques use a training and test datasets composed of known active and known inactive compounds. Different ML algorithms have been applied with success in virtual screening strategies, such as recursive partitioning... | Virtual screening | 0.814361 |
15,516 | Often in areas of physics and mathematics, a vector evolves in time, meaning that it depends on a time parameter t. For instance, if r represents the position vector of a particle, then r(t) gives a parametric representation of the trajectory of the particle. Vector-valued functions can be differentiated and integrated... | Vector components | 0.814357 |
15,517 | A Lie algebra g {\displaystyle {\mathfrak {g}}} is called completely solvable or split solvable if it has an elementary sequence{(V) As above definition} of ideals in g {\displaystyle {\mathfrak {g}}} from 0 {\displaystyle 0} to g {\displaystyle {\mathfrak {g}}} . A finite-dimensional nilpotent Lie algebra is completel... | Derived algebra | 0.814357 |
15,518 | Another class of examples comes from nilpotent Lie algebras since the adjoint representation is solvable. Some examples include the upper-diagonal matrices, such as the class of matrices of the form { } {\displaystyle \left\{{\begin{bmatrix}0&*&*\\0&0&*\\0&0&0\end{bmatrix}}\right\}} called the Lie algebra of strictly ... | Derived algebra | 0.814356 |
15,519 | (vi) There is a finite sequence of subalgebras g i {\displaystyle {\mathfrak {g}}_{i}} of g {\displaystyle {\mathfrak {g}}} , g = g 0 ⊃ g 1 ⊃ . . . | Derived algebra | 0.814356 |
15,520 | (iv) {\displaystyle } is nilpotent. (v) For g {\displaystyle {\mathfrak {g}}} n {\displaystyle n} -dimensional, there is a finite sequence of subalgebras a i {\displaystyle {\mathfrak {a}}_{i}} of g {\displaystyle {\mathfrak {g}}}: g = a 0 ⊃ a 1 ⊃ . . | Derived algebra | 0.814356 |
15,521 | Let g {\displaystyle {\mathfrak {g}}} be a finite-dimensional Lie algebra over a field of characteristic 0. The following are equivalent. (i) g {\displaystyle {\mathfrak {g}}} is solvable. (ii) a d ( g ) {\displaystyle {\rm {ad}}({\mathfrak {g}})} , the adjoint representation of g {\displaystyle {\mathfrak {g}}} , is s... | Derived algebra | 0.814356 |
15,522 | The first hitting time, also called first passage time, of the barrier set B {\displaystyle B} with respect to an instance of a stochastic process is the time until the stochastic process first enters B {\displaystyle B} . More colloquially, a first passage time in a stochastic system, is the time taken for a state var... | First-hitting-time model | 0.814352 |
15,523 | Events are often triggered when a stochastic or random process first encounters a threshold. The threshold can be a barrier, boundary or specified state of a system. The amount of time required for a stochastic process, starting from some initial state, to encounter a threshold for the first time is referred to various... | First-hitting-time model | 0.814352 |
15,524 | This probability density is calculable from the Survival probability (a more common probability measure in statistics). Consider the absorbing boundary condition p ( x c , t ) = 0 {\displaystyle p(x_{c},t)=0} (The subscript c for the absorption point x c {\displaystyle x_{c}} is an abbreviation for cliff used in many t... | First-hitting-time model | 0.814352 |
15,525 | The BKS potential is a force field that may be used to simulate the interatomic potential between Silica glass atoms. Rather than relying only on experimental data, the BKS potential is derived by combining ab initio quantum chemistry methods on small silica clusters to describe accurate interaction between nearest-nei... | Buckingham potential | 0.814351 |
15,526 | In theoretical chemistry, the Buckingham potential is a formula proposed by Richard Buckingham which describes the Pauli exclusion principle and van der Waals energy Φ 12 ( r ) {\displaystyle \Phi _{12}(r)} for the interaction of two atoms that are not directly bonded as a function of the interatomic distance r {\displ... | Buckingham potential | 0.814351 |
15,527 | A charge-generated E-field can be expressed as the gradient of a scalar field that is a solution to Poisson's equation, and has a zero path integral. See gradient theorem. The integral equation is true for any path ∂Σ through space, and any surface Σ for which that path is a boundary. If the surface Σ is not changing i... | Faraday's induction law | 0.814348 |
15,528 | Both dl and dA have a sign ambiguity; to get the correct sign, the right-hand rule is used, as explained in the article Kelvin–Stokes theorem. For a planar surface Σ, a positive path element dl of curve ∂Σ is defined by the right-hand rule as one that points with the fingers of the right hand when the thumb points in t... | Faraday's induction law | 0.814348 |
15,529 | The Maxwell–Faraday equation states that a time-varying magnetic field always accompanies a spatially varying (also possibly time-varying), non-conservative electric field, and vice versa. The Maxwell–Faraday equation is (in SI units) where ∇ × is the curl operator and again E(r, t) is the electric field and B(r, t) is... | Faraday's induction law | 0.814348 |
15,530 | Matrices can be used to condense multiple linear equations as above into one vector equation, namely where A = {\displaystyle A={\begin{bmatrix}1&3&1\\4&2&2\end{bmatrix}}} is the matrix containing the coefficients of the given equations, x {\displaystyle \mathbf {x} } is the vector ( a , b , c ) , {\displaystyle (a,b,... | Coordinate vector space | 0.814347 |
15,531 | The four-spin of a particle is defined in the rest frame of a particle to be where s is the spin pseudovector. In quantum mechanics, not all three components of this vector are simultaneously measurable, only one component is. The timelike component is zero in the particle's rest frame, but not in any other frame. This... | Position four-vector | 0.814346 |
15,532 | These coordinates are the components of the position four-vector for the event. The displacement four-vector is defined to be an "arrow" linking two events: For the differential four-position on a world line we have, using a norm notation: defining the differential line element ds and differential proper time increment... | Position four-vector | 0.814346 |
15,533 | In spacetime algebra, another example of Clifford algebra, the gamma matrices can also form a basis. (They are also called the Dirac matrices, owing to their appearance in the Dirac equation). There is more than one way to express the gamma matrices, detailed in that main article. The Feynman slash notation is a shorth... | Position four-vector | 0.814346 |
15,534 | In quantum mechanics, the four-probability current or probability four-current is analogous to the electromagnetic four-current: where ρ is the probability density function corresponding to the time component, and j is the probability current vector. In non-relativistic quantum mechanics, this current is always well de... | Position four-vector | 0.814346 |
15,535 | Cold Spring Harbor Laboratory Press was founded in 1933 to aid in Cold Spring Harbor Laboratory's purpose of furthering the advance and spread of scientific knowledge. CSHL Press publishes monographs, technical manuals, handbooks, review volumes, conference proceedings, scholarly journals and videotapes. These examine ... | Cold Spring Harbor Molecular Case Studies | 0.814346 |
15,536 | The Cold Spring Harbor Press monograph series is a series of advanced comprehensive volumes giving the state of the art on the most important model organisms and systems for research in molecular biology. The series began in 1970 with The Lactose Operon edited by David Zipser and Jonathan Beckwith OCLC 67611756 | Cold Spring Harbor Molecular Case Studies | 0.814346 |
15,537 | Scientific journals published by CSHL Press: Cold Spring Harbor Molecular Case Studies Cold Spring Harbor Perspectives in Biology Cold Spring Harbor Perspectives in Medicine Cold Spring Harbor Protocols Cold Spring Harbor Symposia on Quantitative Biology Genes & Development Genome Research Learning & Memory Life Scienc... | Cold Spring Harbor Molecular Case Studies | 0.814346 |
15,538 | Some facts about homology groups can be derived directly from the axioms, such as the fact that homotopically equivalent spaces have isomorphic homology groups. The homology of some relatively simple spaces, such as n-spheres, can be calculated directly from the axioms. From this it can be easily shown that the (n − 1)... | Eilenberg–Steenrod axioms | 0.814341 |
15,539 | In photochemistry, photohydrogen is hydrogen produced with the help of artificial or natural light. This is how the leaf of a tree splits water molecules into protons (hydrogen ions), electrons (to make carbohydrates) and oxygen (released into the air as a waste product). Photohydrogen may also be produced by the photo... | Photohydrogen | 0.814341 |
15,540 | This daily cycle is interrupted for tests and additional topics. From Algebra 1/2 on, the higher level books remove the mental math problems and incorporate testing more frequently. Saxon Publishers has also published a phonics and spelling curriculum. | Saxon math | 0.814337 |
15,541 | It uses a steady review of all previous material, with a focus on students who struggle with retaining the math they previously learned. However, it has sometimes been criticized for its heavy emphasis on rote rather than conceptual learning.The Saxon Math 1 to Algebra 1/2 (the equivalent of a Pre-Algebra book) curricu... | Saxon math | 0.814337 |
15,542 | ( ( E 1 E 2 ) E 3 ) . . . E n ) {\displaystyle (...((E_{1}E_{2})E_{3})...E_{n})} . This is the same general convention (left-associativity) as for multiple application in lambda calculus. | Combinatory Logic | 0.814335 |
15,543 | A distinction must be made between the CLK as described in this article and the CLI calculus. The distinction corresponds to that between the λK and the λI calculus. Unlike the λK calculus, the λI calculus restricts abstractions to: λx.E where x has at least one free occurrence in E.As a consequence, combinator K is no... | Combinatory Logic | 0.814335 |
15,544 | In mathematics, a cyclotomic unit (or circular unit) is a unit of an algebraic number field which is the product of numbers of the form (ζan − 1) for ζn an nth root of unity and 0 < a < n. | Cyclotomic unit | 0.814334 |
15,545 | Static linking does naturally lend to the concept of LTO, but it only works with library archives that contain IR objects as opposed to machine-code only object files. Due to performance concerns, not even the entire unit is always directly used—a program could be partitioned in a divide-and-conquer style LTO such as G... | Interprocedural optimization | 0.81433 |
15,546 | Whole program optimization (WPO) is the compiler optimization of a program using information about all the modules in the program. Normally, optimizations are performed on a per module, "compiland", basis; but this approach, while easier to write and test and less demanding of resources during the compilation itself, d... | Interprocedural optimization | 0.81433 |
15,547 | For procedural languages like ALGOL, interprocedural analysis and optimization appear to have entered commercial practice in the early 1970s. IBM's PL/I Optimizing Compiler performed interprocedural analysis to understand the side effects of both procedure calls and exceptions (cast, in PL/I terms as "on conditions") a... | Interprocedural optimization | 0.81433 |
15,548 | Modern compilers offer IPO as an option at compile-time. The actual IPO process may occur at any step between the human-readable source code and producing a finished executable binary program. For languages that compile on a file-by-file basis, effective IPO across translation units (module files) requires knowledge of... | Interprocedural optimization | 0.81433 |
15,549 | Additionally, IPO may re-order the routines for better memory layout and locality. IPO may also include typical compiler optimizations applied on a whole-program level, for example dead code elimination (DCE), which removes code that is never executed. IPO also tries to ensure better use of constants. | Interprocedural optimization | 0.81433 |
15,550 | Interprocedural optimization (IPO) is a collection of compiler techniques used in computer programming to improve performance in programs containing many frequently used functions of small or medium length. IPO differs from other compiler optimizations by analyzing the entire program as opposed to a single function or ... | Interprocedural optimization | 0.81433 |
15,551 | Tail recursion modulo cons is a generalization of tail-recursion optimization introduced by David H. D. Warren in the context of compilation of Prolog, seen as an explicitly set once language. It was described (though not named) by Daniel P. Friedman and David S. Wise in 1974 as a LISP compilation technique. As the nam... | Tail call optimization | 0.81433 |
15,552 | This expands the scope of interprocedural optimizations to encompass the whole program (or, rather, everything that is visible at link time). With link-time optimization, the compiler can apply various forms of interprocedural optimization to the whole program, allowing for deeper analysis, more optimization, and ultim... | Interprocedural optimization | 0.81433 |
15,553 | This simple optimization is foiled the moment that the implementation of F(x) becomes impure; that is, its execution involves reference to parameters other than the explicit argument 6 that have been changed between the invocations, or side effects such as printing some message to a log, counting the number of evaluati... | Interprocedural optimization | 0.81433 |
15,554 | Interprocedural optimization represents an attempt at reducing this waste. Suppose there is a procedure that evaluates F(x), and that F is a pure function, and the code requests the result of F(6) and then later, F(6) again. This second evaluation is almost certainly unnecessary: the result could have instead been save... | Interprocedural optimization | 0.81433 |
15,555 | The objective of any optimization for speed is to have the program run as swiftly as possible; the problem is that it is not possible for a compiler to correctly analyze a program and determine what it will do, much less what the programmer intended for it to do. By contrast, human programmers start at the other end wi... | Interprocedural optimization | 0.81433 |
15,556 | The GNU Compiler Collection has function inlining at all optimization levels. At -O1 this only applies to those only called once (-finline-functions-once), at -O2 this constraint is relaxed (-finline-functions). By default this is a single-file-only behavior, but with link-time optimization -flto it becomes whole progr... | Interprocedural optimization | 0.81433 |
15,557 | Most of ILP work addresses a wider class of problems, as the focus is not only on recursive logic programs but on machine learning of symbolic hypotheses from logical representations. However, there were some encouraging results on learning recursive Prolog programs such as quicksort from examples together with suitabl... | Inductive programming | 0.81433 |
15,558 | The first workshop on Approaches and Applications of Inductive Programming (AAIP) held in conjunction with ICML 2005 identified all applications where "learning of programs or recursive rules are called for, first in the domain of software engineering where structural learning, software assistants and software agents ... | Inductive programming | 0.81433 |
15,559 | In other cases, inductive programming is seen as a more general area where any declarative programming or representation language can be used and we may even have some degree of error in the examples, as in general machine learning, the more specific area of structure mining or the area of symbolic artificial intellige... | Inductive programming | 0.81433 |
15,560 | Inductive programming (IP) is a special area of automatic programming, covering research from artificial intelligence and programming, which addresses learning of typically declarative (logic or functional) and often recursive programs from incomplete specifications, such as input/output examples or constraints. Depend... | Inductive programming | 0.81433 |
15,561 | Stack search (also known as Stack decoding algorithm) is a search algorithm similar to beam search. It can be used to explore tree-structured search spaces and is often employed in Natural language processing applications, such as parsing of natural languages, or for decoding of error correcting codes where the techniq... | Stack search | 0.814329 |
15,562 | In astrophysics, wherever there is evidence of shocks (standing, propagating or oscillating), the flow close by must be transonic, as only supersonic flows form shocks. All black hole accretions are transonic. Many such flows also have shocks very close to the black holes. The outflows or jets from young stellar object... | Transonic flight | 0.814329 |
15,563 | Prior to the advent of powerful computers, even the simplest forms of the compressible flow equations were difficult to solve due to their nonlinearity. A common assumption used to circumvent this nonlinearity is that disturbances within the flow are relatively small, which allows mathematicians and engineers to linear... | Transonic flight | 0.814329 |
15,564 | In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration. The concentration can refer to any kind of chemical mixture, bu... | Concentration measurements | 0.814321 |
15,565 | Normality is defined as the molar concentration c i {\displaystyle c_{i}} divided by an equivalence factor f e q {\displaystyle f_{\mathrm {eq} }} . Since the definition of the equivalence factor depends on context (which reaction is being studied), the International Union of Pure and Applied Chemistry and National Ins... | Concentration measurements | 0.814321 |
15,566 | In topology, a metric space can be constructed by defining a similarity instead of a distance. The similarity is a function such that its value is greater when two points are closer (contrary to the distance, which is a measure of dissimilarity: the closer the points, the lesser the distance). The definition of the sim... | Geometrically similar | 0.814316 |
15,567 | In plasma physics, an electromagnetic electron wave is a wave in a plasma which has a magnetic field component and in which primarily the electrons oscillate. In an unmagnetized plasma, an electromagnetic electron wave is simply a light wave modified by the plasma. In a magnetized plasma, there are two modes perpendicu... | Over-dense plasma | 0.814313 |
15,568 | A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, engineering, chemistry and biology to economics, psychology, cognitive science and computer science. The system under stu... | Computational model | 0.814312 |
15,569 | Polynomial regression is one example of regression analysis using basis functions to model a functional relationship between two quantities. More specifically, it replaces x ∈ R d x {\displaystyle x\in \mathbb {R} ^{d_{x}}} in linear regression with polynomial basis φ ( x ) ∈ R d φ {\displaystyle \varphi (x)\in \mathbb... | Polynomial least squares | 0.814312 |
15,570 | In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean ... | Polynomial least squares | 0.814312 |
15,571 | Thus, assume a solution u is continuously differentiable on the Euclidean space R2, multiply the equation (1) by a test function φ {\displaystyle \varphi } (smooth of compact support), and integrate: ∫ − ∞ ∞ ∫ − ∞ ∞ ∂ u ( t , x ) ∂ t φ ( t , x ) d t d x + ∫ − ∞ ∞ ∫ − ∞ ∞ ∂ u ( t , x ) ∂ x φ ( t , x ) d t d x = 0. {\dis... | Generalized solution | 0.814307 |
15,572 | Somewhat surprisingly, a differential equation may have solutions which are not differentiable; and the weak formulation allows one to find such solutions. Weak solutions are important because many differential equations encountered in modelling real-world phenomena do not admit of sufficiently smooth solutions, and th... | Generalized solution | 0.814307 |
15,573 | This research suggests that water, or, more specifically, ice, plays a large role in the formation of these eventual starsOthers are researching much more tangible ideas relating to stars and chemistry. Research published in 2010 studied the effects of a strong stellar flare on the atmospheric chemistry of an Earth-lik... | Stellar chemistry | 0.814306 |
15,574 | Stellar chemistry is the study of the chemical composition of astronomical objects; stars in particular, hence the name stellar chemistry. The significance of stellar chemical composition is an open ended question at this point. Some research asserts that a greater abundance of certain elements (such as carbon, sodium,... | Stellar chemistry | 0.814306 |
15,575 | "The Correlation between Relatives on the Supposition of Mendelian Inheritance" is a scientific paper by Ronald Fisher which was published in the Transactions of the Royal Society of Edinburgh in 1918, (volume 52, pages 399–433). In it, Fisher puts forward the "infinitesimal model", a genetics conceptual model showing ... | The Correlation between Relatives on the Supposition of Mendelian Inheritance | 0.814305 |
15,576 | In Euclidean geometry, Apollonius' problem is to construct all the circles that are tangent to three given circles. Special cases of Apollonius' problem are those in which at least one of the given circles is a point or line, i.e., is a circle of zero or infinite radius. The nine types of such limiting cases of Apollon... | Special cases of Apollonius' problem | 0.814303 |
15,577 | PPL problems generally have 2 solutions. If a line m drawn through the given points P and Q is parallel to the given line l, the tangent point T of the circle with l is located at the intersection of the perpendicular bisector of P Q ¯ {\displaystyle {\overline {PQ}}} with l. In that case, the sole solution circle is t... | Special cases of Apollonius' problem | 0.814303 |
15,578 | Like most branches of mathematics, Euclidean geometry is concerned with proofs of general truths from a minimum of postulates. For example, a simple proof would show that at least two angles of an isosceles triangle are equal. One important type of proof in Euclidean geometry is to show that a geometrical object can be... | Special cases of Apollonius' problem | 0.814303 |
15,579 | Expectation values in phase-space quantization are obtained isomorphically to tracing operator observables with the density matrix in Hilbert space: they are obtained by phase-space integrals of observables, with the Wigner quasi-probability distribution effectively serving as a measure. Thus, by expressing quantum mec... | Phase space trajectory | 0.814301 |
15,580 | Every quantum mechanical observable corresponds to a unique function or distribution on phase space, and conversely, as specified by Hermann Weyl (1927) and supplemented by John von Neumann (1931); Eugene Wigner (1932); and, in a grand synthesis, by H. J. Groenewold (1946). With J. E. Moyal (1949), these completed the ... | Phase space trajectory | 0.814301 |
15,581 | In quantum mechanics, the coordinates p and q of phase space normally become Hermitian operators in a Hilbert space. But they may alternatively retain their classical interpretation, provided functions of them compose in novel algebraic ways (through Groenewold's 1946 star product). This is consistent with the uncertai... | Phase space trajectory | 0.814301 |
15,582 | In probability theory, the multidimensional Chebyshev's inequality is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount. Let X {\displaystyle X} be an N {\displaystyle N} -dimensional rand... | Multidimensional Chebyshev's inequality | 0.814296 |
15,583 | Static light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight Mw of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, ... | Static light scattering | 0.814293 |
15,584 | In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state. It is important in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields. The position of a sin... | Yaw rotation | 0.814291 |
15,585 | LCA may be used in many fields, such as: collaborative filtering, Behavior Genetics and Evaluation of diagnostic tests. | Latent class model | 0.814284 |
15,586 | The origins of Koopman–von Neumann (KvN) theory are tightly connected with the rise of ergodic theory as an independent branch of mathematics, in particular with Boltzmann's ergodic hypothesis. In 1931 Koopman and André Weil independently observed that the phase space of the classical system can be converted into a Hil... | Koopman–von Neumann classical mechanics | 0.814281 |
15,587 | Conversely, it is possible to start from operator postulates, similar to the Hilbert space axioms of quantum mechanics, and derive the equation of motion by specifying how expectation values evolve.The relevant axioms are that as in quantum mechanics (i) the states of a system are represented by normalized vectors of a... | Koopman–von Neumann classical mechanics | 0.814281 |
15,588 | The Koopman–von Neumann mechanics is a description of classical mechanics in terms of Hilbert space, introduced by Bernard Koopman and John von Neumann in 1931 and 1932, respectively.As Koopman and von Neumann demonstrated, a Hilbert space of complex, square-integrable wavefunctions can be defined in which classical me... | Koopman–von Neumann classical mechanics | 0.814281 |
15,589 | The commutativity physically implies that all observables are simultaneously measurable. Contrast this with quantum mechanics, where observables need not commute, which underlines the uncertainty principle, Kochen–Specker theorem, and Bell inequalities.The KvN wavefunction is postulated to evolve according to exactly t... | Koopman–von Neumann classical mechanics | 0.814281 |
15,590 | In the approach of Koopman and von Neumann (KvN), dynamics in phase space is described by a (classical) probability density, recovered from an underlying wavefunction – the Koopman–von Neumann wavefunction – as the square of its absolute value (more precisely, as the amplitude multiplied with its own complex conjugate)... | Koopman–von Neumann classical mechanics | 0.814281 |
15,591 | The Killing fields of Minkowski space are the 3 space translations, time translation, three generators of rotations (the little group) and the three generators of boosts. These are Time and space translations ∂ t , ∂ x , ∂ y , ∂ z ; {\displaystyle \partial _{t}~,\qquad \partial _{x}~,\qquad \partial _{y}~,\qquad \parti... | Killing vector field | 0.814279 |
15,592 | Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement... | Vector direction | 0.814278 |
15,593 | It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from A to B. Many algebraic operations on real numbers such as addition, subtraction, multiplicat... | Vector direction | 0.814278 |
15,594 | In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a... | Vector direction | 0.814278 |
15,595 | The magnification in an atom is due to the projection of ions radially away from the small, sharp tip. Subsequently, in the far-field, the ions will be greatly magnified. This magnification is sufficient to observe field variations due to individual atoms, thus allowing in field ion and field evaporation modes for the ... | Atom Probe | 0.814276 |
15,596 | Materials implicitly control achievable spatial resolution. Specimen geometry during the analysis is uncontrolled, yet controls projection behaviour, hence there is little control over the magnification. This induces distortions into the computer generated 3D dataset. Features of interest might evaporate in a physicall... | Atom Probe | 0.814276 |
15,597 | Metagenomic sequencing and short-read based assembly have revealed the exchange of antibiotic resistance genes between non-pathogenic environmental soil bacteria and clinical pathogens. The portions in the soil bacteria perfectly match the identity of several diverse human pathogens and contain resistance cassettes aga... | Resistome | 0.814273 |
15,598 | {\displaystyle \sum _{i=0}^{n-1}{\frac {\Delta F}{\Delta x}}(a+ih+h/2)\,\Delta x=F(b)-F(a).} Stokes' theorem says that the sum of a form ω {\displaystyle \omega } over the boundary of some orientable manifold Ω {\displaystyle \Omega } is equal to the sum of its exterior derivative d ω {\displaystyle d\omega } over the ... | Discrete calculus | 0.814271 |
15,599 | We also use the calculus notation for the values of the forms: ω ( s ) = ∫ s ω . {\displaystyle \omega (s)=\int _{s}\omega .} Stokes' theorem is a statement about the discrete differential forms on manifolds, which generalizes the fundamental theorem of discrete calculus for a partition of an interval: ∑ i = 0 n − 1 Δ ... | Discrete calculus | 0.814271 |
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