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31,200 | Mathematically, a token is an element t {\displaystyle t} in a finite (or countably infinite) set T {\displaystyle T} . Suppose we only need to process a finite corpus, then we can put all tokens appearing in the corpus into T {\displaystyle T} , meaning that T {\displaystyle T} is finite. However, suppose we want to p... | Feature hashing | 0.804574 |
31,201 | Now we have an inner product space, with enough structure to describe the geometry of the feature hashing function ϕ: R T → R n {\displaystyle \phi :\mathbb {R} ^{T}\to \mathbb {R} ^{n}} . First, we can see why h {\displaystyle h} is called a "kernel hash": it allows us to define a kernel K: T × T → R {\displaystyle K:... | Feature hashing | 0.804574 |
31,202 | In machine learning, feature hashing, also known as the hashing trick (by analogy to the kernel trick), is a fast and space-efficient way of vectorizing features, i.e. turning arbitrary features into indices in a vector or matrix. It works by applying a hash function to the features and using their hash values as indic... | Feature hashing | 0.804574 |
31,203 | In a typical document classification task, the input to the machine learning algorithm (both during learning and classification) is free text. From this, a bag of words (BOW) representation is constructed: the individual tokens are extracted and counted, and each distinct token in the training set defines a feature (in... | Feature hashing | 0.804574 |
31,204 | Nowadays, it includes quantitative models of symmetry perception and amodal completion, and is theoretically sustained by a perceptually adequate formalization of visual regularity, a quantitative account of viewpoint dependencies, and a powerful form of neurocomputation. SIT has been argued to be the best defined and ... | Structural information theory | 0.804573 |
31,205 | In SIT's formal coding model, candidate interpretations of a stimulus are represented by symbol strings, in which identical symbols refer to identical perceptual primitives (e.g., blobs or edges). Every substring of such a string represents a spatially contiguous part of an interpretation, so that the entire string can... | Structural information theory | 0.804573 |
31,206 | The International Workshop on First-Order Theorem Proving (FTP) is a scientific meeting of researchers interested in automated theorem proving for first-order logic and related fields. FTP workshops are less formal than many conferences, but more formal than most workshops. While FTP proceedings are published informall... | International Workshop on First-Order Theorem Proving | 0.804572 |
31,207 | Engineering management programs typically include instruction in accounting, economics, finance, project management, systems engineering, industrial engineering, mathematical modeling and optimization, management information systems, quality control & six sigma, operations management, operations research, human resourc... | Management engineering | 0.804568 |
31,208 | Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design and manage complex systems over their life cycles. | Management engineering | 0.804568 |
31,209 | Industrial engineering is a branch of engineering which deals with the optimization of complex processes, systems or organizations. Industrial engineers work to eliminate waste of time, money, materials, man-hours, machine time, energy and other resources that do not generate value. | Management engineering | 0.804568 |
31,210 | Thom envisaged applications of this theory to biological systems. Both Smale and Thom worked in direct contact with Maurício Peixoto, who developed Peixoto's theorem in the late 1950s. | Structurally stable | 0.804564 |
31,211 | Structural stability of the system provides a justification for applying the qualitative theory of dynamical systems to analysis of concrete physical systems. The idea of such qualitative analysis goes back to the work of Henri Poincaré on the three-body problem in celestial mechanics. Around the same time, Aleksandr L... | Structurally stable | 0.804564 |
31,212 | This argument fails if y is not fixed: if y is very close to π/2, the value of the fraction may deviate from 0. This leads to another definition of limit, namely the uniform limit. We say the uniform limit of f on T as x approaches p is g, denoted or Alternatively, we may say f tends to g uniformly on T as x approaches... | Epsilon, delta technique | 0.804563 |
31,213 | The condition of acyclicity on a space X implies, for example, for nice spaces—say, simplicial complexes—that any continuous map of X to the circle or to the higher spheres is null-homotopic. If a space X is contractible, then it is also acyclic, by the homotopy invariance of homology. The converse is not true, in gene... | Acyclic space | 0.804563 |
31,214 | The difference of the theorems is the following: in McKean's result the P {\displaystyle P} -null sets, where the statement is not true, depends on the choice of A {\displaystyle A} . Kaufman's result on the other hand is true for all choices of A {\displaystyle A} simultaneously. This means Kaufman's theorem can also ... | Dimension doubling theorem | 0.804561 |
31,215 | In probability theory, the dimension doubling theorems are two results about the Hausdorff dimension of an image of a Brownian motion. In their core both statements say, that the dimension of a set A {\displaystyle A} under a Brownian motion doubles almost surely. The first result is due to Henry P. McKean jr and hence... | Dimension doubling theorem | 0.804561 |
31,216 | The Open Biological and Biomedical Ontologies (OBO) Foundry is a group of people dedicated to build and maintain ontologies related to the life sciences. The OBO Foundry establishes a set of principles for ontology development for creating a suite of interoperable reference ontologies in the biomedical domain. Currentl... | Relation Ontology | 0.804559 |
31,217 | Locally connected does not imply connected, nor does locally path-connected imply path connected. A simple example of a locally connected (and locally path-connected) space that is not connected (or path-connected) is the union of two separated intervals in R {\displaystyle \mathbb {R} } , such as ( 0 , 1 ) ∪ ( 2 , 3 )... | Totally separated space | 0.804555 |
31,218 | Main theorem of connectedness: Let X {\displaystyle X} and Y {\displaystyle Y} be topological spaces and let f: X → Y {\displaystyle f:X\rightarrow Y} be a continuous function. If X {\displaystyle X} is (path-)connected then the image f ( X ) {\displaystyle f(X)} is (path-)connected. This result can be considered a gen... | Totally separated space | 0.804555 |
31,219 | Stable algebraic topology flourished between 1945 and 1966 with many important results. In 1953 George W. Whitehead showed that there is a metastable range for the homotopy groups of spheres. Jean-Pierre Serre used spectral sequences to show that most of these groups are finite, the exceptions being πn(Sn) and π4n−1(S2... | Stable stem | 0.804554 |
31,220 | An important method for calculating the various groups is the concept of stable algebraic topology, which finds properties that are independent of the dimensions. Typically these only hold for larger dimensions. The first such result was Hans Freudenthal's suspension theorem, published in 1937. | Stable stem | 0.804554 |
31,221 | In the late 19th century Camille Jordan introduced the notion of homotopy and used the notion of a homotopy group, without using the language of group theory. A more rigorous approach was adopted by Henri Poincaré in his 1895 set of papers Analysis situs where the related concepts of homology and the fundamental group ... | Stable stem | 0.804554 |
31,222 | Čech, Eduard (1932), "Höherdimensionale Homotopiegruppen", Verhandlungen des Internationalen Mathematikerkongress, Zürich. Hopf, Heinz (1931), "Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche", Mathematische Annalen, 104 (1): 637–665, doi:10.1007/BF01457962, S2CID 123533891. May, J. Peter (1999a),... | Stable stem | 0.804554 |
31,223 | The Gheorghe–Wang–Xu theorem identifies the motivic Adams spectral sequence for the cofiber of τ as the algebraic Novikov spectral sequence for BP*, which allows one to deduce motivic Adams differentials for the cofiber of τ from purely algebraic data. One can then pullback these motivic Adams differentials to the moti... | Stable stem | 0.804554 |
31,224 | The classical Adams spectral sequence has E2 term given by the Ext groups Ext∗,∗A(p)(Zp, Zp) over the mod p Steenrod algebra A(p), and converges to something closely related to the p-component of the stable homotopy groups. The initial terms of the Adams spectral sequence are themselves quite hard to compute: this is s... | Stable stem | 0.804554 |
31,225 | He used the fact that taking the loop space of a well behaved space shifts all the homotopy groups down by 1, so the nth homotopy group of a space X is the first homotopy group of its (n−1)-fold repeated loop space, which is equal to the first homology group of the (n−1)-fold loop space by the Hurewicz theorem. This re... | Stable stem | 0.804554 |
31,226 | "The method of killing homotopy groups", due to Cartan and Serre (1952a, 1952b) involves repeatedly using the Hurewicz theorem to compute the first non-trivial homotopy group and then killing (eliminating) it with a fibration involving an Eilenberg–MacLane space. In principle this gives an effective algorithm for compu... | Stable stem | 0.804554 |
31,227 | The AWM–Microsoft Research Prize in Algebra and Number Theory and is a prize given every other year by the Association for Women in Mathematics to an outstanding young female researcher in algebra or number theory. It was funded in 2012 by Microsoft Research and first issued in 2014. | AWM–Microsoft Research Prize in Algebra and Number Theory | 0.804551 |
31,228 | Sophie Morel (2014), for her research in number theory, particularly her contributions to the Langlands program, an application of her results on weighted cohomology, and a new proof of Brenti's combinatorial formula for Kazhdan-Lusztig polynomials. Lauren Williams (2016), for her research in algebraic combinatorics, p... | AWM–Microsoft Research Prize in Algebra and Number Theory | 0.804551 |
31,229 | A more accurate analysis considering the statistics of electrons provides the following result for the size of the depletion region w = 1 / 2 {\displaystyle w={\left\lbrack {\frac {2\varepsilon }{{\mathit {qN}}_{D}}}\left({V}_{\text{bi}}+V-{\frac {{k}_{B}T}{q}}\right)\right\rbrack }^{1/2}} (5) in this case the Mott–Sc... | Mott–Schottky plot | 0.80455 |
31,230 | In semiconductor electrochemistry, a Mott–Schottky plot describes the reciprocal of the square of capacitance ( 1 / C 2 ) {\displaystyle (1/C^{2})} versus the potential difference between bulk semiconductor and bulk electrolyte. In many theories, and in many experimental measurements, the plot is linear. The use of Mot... | Mott–Schottky plot | 0.80455 |
31,231 | Skolem's paradox is the seeming contradiction that on the one hand, the set of real numbers is uncountable (and this is provable from ZFC, or even from a small finite subsystem ZFC' of ZFC), while on the other hand there are countable transitive models of ZFC' (this is provable in ZFC), and the set of real numbers in s... | Absoluteness (logic) | 0.80455 |
31,232 | - includes examples of gerbes on complex tori Ben-Bassat, Oren (2013). "Equivariant gerbes on complex tori". Journal of Geometry and Physics. | Complex torus | 0.804549 |
31,233 | Ben-Bassat, Oren (2012). "Gerbes and the holomorphic Brauer group of complex tori". Journal of Noncommutative Geometry. 6 (3): 407–455. | Complex torus | 0.804549 |
31,234 | One way to define complex tori is as a compact connected complex Lie group G {\displaystyle G} . These are Lie groups where the structure maps are holomorphic maps of complex manifolds. It turns out that all such compact connected Lie groups are commutative, and are isomorphic to a quotient of their Lie algebra g = T 0... | Complex torus | 0.804549 |
31,235 | For n > 1 Bernhard Riemann found necessary and sufficient conditions for a complex torus to be an algebraic variety; those that are varieties can be embedded into complex projective space, and are the abelian varieties. The actual projective embeddings are complicated (see equations defining abelian varieties) when n >... | Complex torus | 0.804549 |
31,236 | Tablets kept in the British Museum provide evidence that the Babylonians even went so far as to have a concept of objects in an abstract mathematical space. The tablets date from between 350 and 50 B.C.E., revealing that the Babylonians understood and used geometry even earlier than previously thought. The Babylonians ... | Babylonian geometry | 0.804548 |
31,237 | Babylonian mathematics remained constant, in character and content, for over a millennium.In contrast to the scarcity of sources in Egyptian mathematics, knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed while the cla... | Babylonian geometry | 0.804548 |
31,238 | The Journal of Commutative Algebra is a peer-reviewed academic journal of mathematical research that specializes in commutative algebra and closely related fields. It has been published by the Rocky Mountain Mathematics Consortium (RMMC) since its establishment in 2009. It is currently published four times per year.His... | Journal of Commutative Algebra | 0.804548 |
31,239 | Multiplying the equation by a2 and dividing by b3 gives: ( a x b ) 3 + ( a x b ) 2 = c a 2 b 3 . {\displaystyle \left({\frac {ax}{b}}\right)^{3}+\left({\frac {ax}{b}}\right)^{2}={\frac {ca^{2}}{b^{3}}}.} Substituting y = ax/b gives: y 3 + y 2 = c a 2 b 3 {\displaystyle y^{3}+y^{2}={\frac {ca^{2}}{b^{3}}}} which could n... | Babylonian geometry | 0.804548 |
31,240 | The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of √2 in four sexagesimal figures, 1;24,51,10, which is accurate to about six decimal digits, and is the closest possible three-place sexagesimal representation of √2: 1 + 24 60 + 51 60 2 + 10 60 3 = 30547 21600 = 1.41421 296 ¯ . {\displaystyl... | Babylonian geometry | 0.804548 |
31,241 | Another generalization of class field theory is anabelian geometry, which studies algorithms to restore the original object (e.g. a number field or a hyperbolic curve over it) from the knowledge of its full absolute Galois group or algebraic fundamental group.Another natural generalization is higher class field theory,... | Abelian number field | 0.804546 |
31,242 | However, the Langlands correspondence does not include as much arithmetical information about finite Galois extensions as class field theory does in the abelian case. It also does not include an analog of the existence theorem in class field theory: the concept of class fields is absent in the Langlands correspondence.... | Abelian number field | 0.804546 |
31,243 | There are three main generalizations, each of great interest. They are: the Langlands program, anabelian geometry, and higher class field theory. Often, the Langlands correspondence is viewed as a nonabelian class field theory. If and when it is fully established, it would contain a certain theory of nonabelian Galois ... | Abelian number field | 0.804546 |
31,244 | In this case the reciprocity isomorphism of class field theory (or Artin reciprocity map) also admits an explicit description due to the Kronecker–Weber theorem. However, principal constructions of such more detailed theories for small algebraic number fields are not extendable to the general case of algebraic number f... | Abelian number field | 0.804546 |
31,245 | The fundamental result of general class field theory states that the group G is naturally isomorphic to the profinite completion of CK, the multiplicative group of a local field or the idele class group of the global field, with respect to the natural topology on CK related to the specific structure of the field K. Equ... | Abelian number field | 0.804546 |
31,246 | In number theory, the ruler function of an integer n {\displaystyle n} can be either of two closely related functions. One of these functions counts the number of times n {\displaystyle n} can be evenly divided by two, which for the numbers 1, 2, 3, ... is Alternatively, the ruler function can be defined as the same nu... | Ruler function | 0.804545 |
31,247 | We consider a single-ported machine. The way the data is routed through the network depends on its underlying topology. We take a look at all-to-all algorithms for common network topologies. | All-to-all (parallel pattern) | 0.804545 |
31,248 | An all-to-all algorithm in a ring topology is very intuitive. Initially a processor sends a message of size m(p-1) to one of its neighbors. Communication is performed in the same direction on all processors. | All-to-all (parallel pattern) | 0.804545 |
31,249 | This approach requires p to be a power of two. Depending on the underlying topology of the network, one approach might be superior to the other. The exclusive or approach is superior, when performing pairwise one-to-one routings in a hypercube or fat-tree. == References == | All-to-all (parallel pattern) | 0.804545 |
31,250 | A hypercube is a network topology, where two processors share a link, if the hamming distance of their indices is one. The idea of an all-to-all algorithm is to combine messages belonging to the same subcube, and then distribute them. | All-to-all (parallel pattern) | 0.804545 |
31,251 | On such a machine, an all-to-all algorithm requires at least ⌈ log 2 n ⌉ {\displaystyle \lceil \log _{2}n\rceil } communication rounds. Further a minimum of ⌈ m ( n − 1 ) ⌉ {\displaystyle \left\lceil m(n-1)\right\rceil } units of data is transferred. Optimum for both these measures can not be achieved simultaneously.... | All-to-all (parallel pattern) | 0.804545 |
31,252 | Weather models that have gridboxes with sizes between 5 and 25 kilometers (3 and 16 mi) can explicitly represent convective clouds, although they need to parameterize cloud microphysics which occur at a smaller scale. The formation of large-scale (stratus-type) clouds is more physically based; they form when the relati... | Numerical Weather Prediction | 0.804543 |
31,253 | Consequently, changes in wind speed, direction, moisture, temperature, or lapse rate at different levels of the atmosphere can have a significant impact on the behavior and growth of a wildfire. Since the wildfire acts as a heat source to the atmospheric flow, the wildfire can modify local advection patterns, introduci... | Numerical Weather Prediction | 0.804543 |
31,254 | Socio-technical systems, such as transport, utilities and their related infrastructures comprise human elements as well as artifacts. Traditional mathematical and physical modeling techniques may not take adequate account of the effects of engineering on people, and culture. The Civil Engineering discipline makes elabo... | Philosophy of engineering | 0.804543 |
31,255 | For this, he proved a very deep dichotomy theorem. Saharon Shelah gave an almost complete solution to the spectrum problem. For a given complete theory T, either I(T,κ) = 2κ for all uncountable cardinals κ, or I ( T , ℵ ξ ) < ℶ ω 1 ( | ξ | ) {\displaystyle \textstyle I(T,\aleph _{\xi })<\beth _{\omega _{1}}(|\xi |)} fo... | Spectrum of a theory | 0.804543 |
31,256 | Morley proved that if I(T,ℵ0) is infinite then it must be ℵ0 or ℵ1 or 2ℵ0. It is not known if it can be ℵ1 if the continuum hypothesis is false: this is called the Vaught conjecture and is the main remaining open problem (in 2005) in the theory of the spectrum. Morley's problem was a conjecture (now a theorem) first pr... | Spectrum of a theory | 0.804543 |
31,257 | In this section T is a countable complete theory and κ is a cardinal. The Löwenheim–Skolem theorem shows that if I(T,κ) is nonzero for one infinite cardinal then it is nonzero for all of them. Morley's categoricity theorem was the first main step in solving the spectrum problem: it states that if I(T,κ) is 1 for some u... | Spectrum of a theory | 0.804543 |
31,258 | The implementation of the spectral method is normally accomplished either with collocation or a Galerkin or a Tau approach . For very small problems, the spectral method is unique in that solutions may be written out symbolically, yielding a practical alternative to series solutions for differential equations. Spectral... | Spectral method | 0.804536 |
31,259 | When applying spectral methods to time-dependent PDEs, the solution is typically written as a sum of basis functions with time-dependent coefficients; substituting this in the PDE yields a system of ODEs in the coefficients which can be solved using any numerical method for ODEs. Eigenvalue problems for ODEs are simila... | Spectral method | 0.804536 |
31,260 | However, there are no known three-dimensional single domain spectral shock capturing results (shock waves are not smooth). In the finite element community, a method where the degree of the elements is very high or increases as the grid parameter h increases is sometimes called a spectral element method. Spectral method... | Spectral method | 0.804536 |
31,261 | By the uniqueness theorem for Fourier expansions, we must then equate the Fourier coefficients term by term, giving which is an explicit formula for the Fourier coefficients aj,k. With periodic boundary conditions, the Poisson equation possesses a solution only if b0,0 = 0. Therefore, we can freely choose a0,0 which wi... | Spectral method | 0.804536 |
31,262 | Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and the... | Spectral method | 0.804536 |
31,263 | "Although the formulation of Turing we have presented is closer in spirit to that originally given by Emil Post, it was Turing's analysis of the computation that has made this formulation seem so appropriate. This language has played a fundamental role in theoretical computer science." (Davis et al. (1994) p. | Post-Turing Model | 0.804535 |
31,264 | The default definition of magnetic remanence is the magnetization remaining in zero field after a large magnetic field is applied (enough to achieve saturation). The effect of a magnetic hysteresis loop is measured using instruments such as a vibrating sample magnetometer; and the zero-field intercept is a measure of t... | Saturation isothermal remanence | 0.804532 |
31,265 | Lagrange's four-square theorem, also known as Bachet's conjecture, states that every natural number can be represented as a sum of four non-negative integer squares. That is, the squares form an additive basis of order four. where the four numbers a , b , c , d {\displaystyle a,b,c,d} are integers. For illustration, 3,... | Four-square theorem | 0.804532 |
31,266 | Lagrange's four-square theorem is a special case of the Fermat polygonal number theorem and Waring's problem. Another possible generalization is the following problem: Given natural numbers a , b , c , d {\displaystyle a,b,c,d} , can we solve for all positive integers n in integers x 1 , x 2 , x 3 , x 4 {\displaystyle ... | Four-square theorem | 0.804532 |
31,267 | If such side effects – including but not limited to memory access timing – are visible to a malicious program, and can be engineered to depend on sensitive data held by the victim process, then these side effects can result in such data becoming discernible. This can happen despite the formal architecture-level securit... | Branch Target Injection | 0.804531 |
31,268 | Surface engineering is the sub-discipline of materials science which deals with the surface of solid matter. It has applications to chemistry, mechanical engineering, and electrical engineering (particularly in relation to semiconductor manufacturing). Solids are composed of a bulk material covered by a surface. The su... | Surface functionalization | 0.804531 |
31,269 | A carbohydrate () is a biomolecule consisting of carbon (C), hydrogen (H) and oxygen (O) atoms, usually with a hydrogen–oxygen atom ratio of 2:1 (as in water) and thus with the empirical formula Cm(H2O)n (where m may or may not be different from n), which does not mean the H has covalent bonds with O (for example with ... | Carbohydrate | 0.804531 |
31,270 | Formerly the name "carbohydrate" was used in chemistry for any compound with the formula Cm (H2O)n. Following this definition, some chemists considered formaldehyde (CH2O) to be the simplest carbohydrate, while others claimed that title for glycolaldehyde. Today, the term is generally understood in the biochemistry sen... | Carbohydrate | 0.80453 |
31,271 | Pairs of octahedra can be fused in a way that preserves the octahedral coordination geometry by replacing terminal ligands with bridging ligands. Two motifs for fusing octahedra are common: edge-sharing and face-sharing. Edge- and face-shared bioctahedra have the formulas 2 and M2L6(μ-L)3, respectively. Polymeric versi... | Octahedral complex | 0.804529 |
31,272 | While the lines of conceptual understanding between theoretical astrochemistry and theoretical chemical astronomy often become blurred so that the goals and tools are the same, there are subtle differences between the two sciences. Theoretical chemistry as applied to astronomy seeks to find new ways to observe chemical... | Mathematical astronomy | 0.804528 |
31,273 | The sparseness of interstellar and interplanetary space results in some unusual chemistry, since symmetry-forbidden reactions cannot occur except on the longest of timescales. For this reason, molecules and molecular ions which are unstable on earth can be highly abundant in space, for example the H3+ ion. Astrochemist... | Mathematical astronomy | 0.804528 |
31,274 | Astrochemistry, the overlap of the disciplines of astronomy and chemistry, is the study of the abundance and reactions of chemical elements and molecules in space, and their interaction with radiation. The formation, atomic and chemical composition, evolution and fate of molecular gas clouds, is of special interest bec... | Mathematical astronomy | 0.804528 |
31,275 | "An important goal for theoretical astrochemistry is to elucidate which organics are of true interstellar origin, and to identify possible interstellar precursors and reaction pathways for those molecules which are the result of aqueous alterations." One of the ways this goal can be achieved is through the study of car... | Mathematical astronomy | 0.804528 |
31,276 | Geodetic astronomy is the application of astronomical methods into networks and technical projects of geodesy for apparent places of stars, and their proper motions precise astronomical navigation astro-geodetic geoid determination and modelling the rock densities of the topography and of geological layers in the subsu... | Mathematical astronomy | 0.804528 |
31,277 | The Deep Space Network, or DSN, is an international network of large antennas and communication facilities that supports interplanetary spacecraft missions, and radio and radar astronomy observations for the exploration of the Solar System and the universe. The network also supports selected Earth-orbiting missions. DS... | Mathematical astronomy | 0.804528 |
31,278 | Some widely accepted and studied theories and models in astronomy, now included in the Lambda-CDM model are the Big Bang, Cosmic inflation, dark matter, and fundamental theories of physics. A few examples of this process: | Mathematical astronomy | 0.804528 |
31,279 | Most database management systems restrict check constraints to a single row, with access to constants and deterministic functions, but not to data in other tables, or to data invisible to the current transaction because of transaction isolation. Such constraints are not truly table check constraints but rather row chec... | Check Constraint | 0.804526 |
31,280 | A NOT NULL constraint is functionally equivalent to the following check constraint with an IS NOT NULL predicate: CHECK (column IS NOT NULL) Some relational database management systems are able to optimize performance when the NOT NULL constraint syntax is used as opposed to the CHECK constraint syntax given above. | Check Constraint | 0.804526 |
31,281 | Three international organizations are implanted between 1973 and 1988 with the Institut Laue–Langevin, the European Synchrotron Radiation Facility and one of the five branches of the European Molecular Biology Laboratory. In 2006, the complex Minatec specializing in nanotechnology opens on the Polygon and in 2007, the ... | Polygone Scientifique | 0.804524 |
31,282 | Polygon hosts in 1956 the first French Atomic Energy Commission (CEA) outside Paris and created by Professor Louis Néel. In 1962, it hosts a campus CNRS. In 1967, the Laboratoire d'électronique et de technologie de l'information was founded by CEA and became one of the world’s largest organizations for applied research... | Polygone Scientifique | 0.804524 |
31,283 | In mathematics, nonlinear modelling is empirical or semi-empirical modelling which takes at least some nonlinearities into account. Nonlinear modelling in practice therefore means modelling of phenomena in which independent variables affecting the system can show complex and synergetic nonlinear effects. Contrary to tr... | Nonlinear model | 0.804524 |
31,284 | The ex-post tracking error formula is the standard deviation of the active returns, given by: T E = ω = Var ( r p − r b ) = E − ( E ) 2 = ( w p − w b ) T Σ ( w p − w b ) {\displaystyle TE=\omega ={\sqrt {\operatorname {Var} (r_{p}-r_{b})}}={\sqrt {{E}-({E})^{2}}}={\sqrt {(w_{p}-w_{b})^{T}\Sigma (w_{p}-w_{b})}}} whe... | Active risk | 0.804523 |
31,285 | Index funds are expected to minimize the tracking error with respect to the index they are attempting to replicate, and this problem may be solved using standard optimization techniques. To begin, define ω 2 {\displaystyle \omega ^{2}} to be:where w − w b {\displaystyle w-w_{b}} is the vector of active weights for each... | Active risk | 0.804523 |
31,286 | In multiple regression, the omnibus test is an ANOVA F test on all the coefficients, that is equivalent to the multiple correlations R Square F test. The omnibus F test is an overall test that examines model fit, thus failure to reject the null hypothesis implies that the suggested linear model is not significantly sui... | Omnibus test | 0.804521 |
31,287 | It may be considered to use the simple Bonferroni correction or another suitable correction. Another omnibus test we can find in ANOVA is the F test for testing one of the ANOVA assumptions: the equality of variance between groups. In One-Way ANOVA, for example, the hypotheses tested by omnibus F test are: H0: μ1=μ2=..... | Omnibus test | 0.804521 |
31,288 | In statistics, logistic regression is a type of regression analysis used for predicting the outcome of a categorical dependent variable (with a limited number of categories) or dichotomic dependent variable based on one or more predictor variables. The probabilities describing the possible outcome of a single trial are... | Omnibus test | 0.804521 |
31,289 | Runtime predictive analysis (or predictive analysis) is a runtime verification technique in computer science for detecting property violations in program executions inferred from an observed execution. An important class of predictive analysis methods has been developed for detecting concurrency errors (such as data ra... | Runtime predictive analysis | 0.80452 |
31,290 | Given an input trace of size n {\displaystyle n} executed by k {\displaystyle k} threads, general race prediction is NP-complete and even W-hard parameterized by k {\displaystyle k} , but admits a polynomial-time algorithm when the communication topology is acyclic. Happens-before races are detected in O ( n ⋅ k ) {\di... | Runtime predictive analysis | 0.80452 |
31,291 | Protein–protein interaction prediction is a field combining bioinformatics and structural biology in an attempt to identify and catalog physical interactions between pairs or groups of proteins. Understanding protein–protein interactions is important for the investigation of intracellular signaling pathways, modelling ... | Protein-protein interaction prediction | 0.804517 |
31,292 | The American National Standards Institute–Nanotechnology Standards Panel (ANSI-NSP) enables stakeholders in nanotechnology to work together to coordinate the development of voluntary standards. Such standards include terminology and materials properties and measurement procedures to facilitate commercialization of appl... | American National Standards Institute Nanotechnology Panel | 0.804516 |
31,293 | Objectives of the ANSI-NSP include: Providing a forum to define needs, determine work plans and establish priorities for updating standards or creating new standards. Soliciting participation from sectors that have not traditionally participated in the voluntary standards system. Facilitating the development and adopti... | American National Standards Institute Nanotechnology Panel | 0.804516 |
31,294 | The vertex-connectivity of an input graph G can be computed in polynomial time in the following way consider all possible pairs ( s , t ) {\displaystyle (s,t)} of nonadjacent nodes to disconnect, using Menger's theorem to justify that the minimal-size separator for ( s , t ) {\displaystyle (s,t)} is the number of pairw... | K-connected graph | 0.804514 |
31,295 | The 1-skeleton of any k-dimensional convex polytope forms a k-vertex-connected graph (Balinski's theorem). As a partial converse, Steinitz's theorem states that any 3-vertex-connected planar graph forms the skeleton of a convex polyhedron. | K-connected graph | 0.804514 |
31,296 | Quantum mechanics or particle physics When a spinless particle (or even an unpolarized particle with spin) decays, the resulting decay distribution must be isotropic in the rest frame of the decaying particle regardless of the detailed physics of the decay. This follows from rotational invariance of the Hamiltonian, wh... | Isotropic material | 0.804514 |
31,297 | In physics and geometry, isotropy (from Ancient Greek ἴσος (ísos) 'equal', and τρόπος (trópos) 'turn, way') is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix a- or an-, hence anisotropy. Anisotropy is also used to descr... | Isotropic material | 0.804514 |
31,298 | In organic chemistry, an electrophilic addition reaction is an addition reaction where a chemical compound containing a double or triple bond has a π bond broken, with the formation of two new σ bonds.The driving force for this reaction is the formation of an electrophile X+ that forms a covalent bond with an electron-... | Electrophilic addition | 0.804512 |
31,299 | Point plotting is an elementary mathematical skill required in analytic geometry. Invented by René Descartes and originally used to locate positions on military maps, this skill is now assumed of everyone who wants to locate grid 7A on any map. Using point plotting, one associates an ordered pair of real numbers (x, y)... | Point plotting | 0.804511 |
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