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29,300 | On the voyage of the Beagle the young Charles Darwin took a break between graduating and starting his career as a clergyman to study the natural history of South America, an interest he had developed at the University of Edinburgh and the University of Cambridge. Influenced by Charles Lyell's Principles of Geology, he ... | On the Tendency of Species to form Varieties; and on the Perpetuation of Varieties and Species by Natural Means of Selection | 0.80555 |
29,301 | In cryptography, electromagnetic attacks are side-channel attacks performed by measuring the electromagnetic radiation emitted from a device and performing signal analysis on it. These attacks are a more specific type of what is sometimes referred to as Van Eck phreaking, with the intention to capture encryption keys. ... | Electromagnetic attack | 0.805549 |
29,302 | In some cases, simple electromagnetic analysis is not possible or does not provide enough information. Differential electromagnetic analysis (DEMA) attacks are more complex, but are effective against symmetric cryptography implementation, against which SEMA attacks are not. Additionally unlike SEMA, DEMA attacks do not... | Electromagnetic attack | 0.805549 |
29,303 | In simple electromagnetic analysis (SEMA) attacks, the attacker deduces the key directly by observing the trace. It is very effective against asymmetric cryptography implementations. Typically, only a few traces are needed, though the attacker needs to have a strong understanding of the cryptographic device and of the ... | Electromagnetic attack | 0.805549 |
29,304 | The Bloch spectrum is a concept in quantum mechanics in the field of theoretical physics; this concept addresses certain energy spectrum considerations. Let H be the one-dimensional Schrödinger equation operator H = − d 2 d x 2 + U α , {\displaystyle H=-{\frac {d^{2}}{dx^{2}}}+U_{\alpha },} where Uα is a periodic funct... | Bloch spectrum | 0.805547 |
29,305 | A deductive system is called complete if every logically valid formula is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense. Thus, in a sense, there is a different completeness theorem for each deductive system. A con... | Gödel's completeness theorem | 0.805546 |
29,306 | The definition of a deduction is such that it is finite and that it is possible to verify algorithmically (by a computer, for example, or by hand) that a given sequence (or tree) of formulae is indeed a deduction. A first-order formula is called logically valid if it is true in every structure for the language of the f... | Gödel's completeness theorem | 0.805546 |
29,307 | The theorem can be expressed more generally in terms of logical consequence. We say that a sentence s is a syntactic consequence of a theory T, denoted T ⊢ s {\displaystyle T\vdash s} , if s is provable from T in our deductive system. We say that s is a semantic consequence of T, denoted T ⊨ s {\displaystyle T\models s... | Gödel's completeness theorem | 0.805546 |
29,308 | Gödel's original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ad hoc argument. In modern logic texts, Gödel's completeness theorem is usually proved with Henkin's proof, rather than with Gödel's original proof. Hen... | Gödel's completeness theorem | 0.805546 |
29,309 | The completeness theorem says that if a formula is logically valid then there is a finite deduction (a formal proof) of the formula. Thus, the deductive system is "complete" in the sense that no additional inference rules are required to prove all the logically valid formulae. A converse to completeness is soundness, t... | Gödel's completeness theorem | 0.805546 |
29,310 | Weak Kőnig's lemma is provable in ZF, the system of Zermelo–Fraenkel set theory without axiom of choice, and thus the completeness and compactness theorems for countable languages are provable in ZF. However the situation is different when the language is of arbitrary large cardinality since then, though the completene... | Gödel's completeness theorem | 0.805546 |
29,311 | Conversely, for many deductive systems, it is possible to prove the completeness theorem as an effective consequence of the compactness theorem. The ineffectiveness of the completeness theorem can be measured along the lines of reverse mathematics. When considered over a countable language, the completeness and compact... | Gödel's completeness theorem | 0.805546 |
29,312 | The completeness theorem and the compactness theorem are two cornerstones of first-order logic. While neither of these theorems can be proven in a completely effective manner, each one can be effectively obtained from the other. The compactness theorem says that if a formula φ is a logical consequence of a (possibly in... | Gödel's completeness theorem | 0.805546 |
29,313 | The model existence theorem and its proof can be formalized in the framework of Peano arithmetic. Precisely, we can systematically define a model of any consistent effective first-order theory T in Peano arithmetic by interpreting each symbol of T by an arithmetical formula whose free variables are the arguments of the... | Gödel's completeness theorem | 0.805546 |
29,314 | Metabolomics is a peer-reviewed scientific journal covering topics including whole metabolome analysis of organisms, metabolite target analysis, with applications within animals, plants and microbes, pharmacometabolomics for precision medicine, as well as systems biology. It is published by Springer Science+Business Me... | Metabolomics (journal) | 0.805545 |
29,315 | Michał Gryziński (29 September 1930 - 1 June 2004) was a Polish nuclear physicist, plasma physics specialist and the founder of the free-fall atomic model, an alternative theoretical formulation, a classical approximation asking for trajectories of electron averaging to probability densities described by quantum mechan... | Free-fall atomic model | 0.805544 |
29,316 | "Double ionization of atoms by electrons". Journal of Physics B. 32 (24): 5789–5804. | Free-fall atomic model | 0.805544 |
29,317 | "Dynamical model of the molecular bond". Chemical Physics Letters. 217 (5–6): 481–485. | Free-fall atomic model | 0.805544 |
29,318 | International Journal of Theoretical Physics. 26 (10): 967–980. Bibcode:1987IJTP...26..967G. | Free-fall atomic model | 0.805544 |
29,319 | Journal of Chemical Physics. 62 (7): 2620–2628. Bibcode:1975JChPh..62.2620G. | Free-fall atomic model | 0.805544 |
29,320 | Journal of Physics B. 6 (11): 2292–2302. Bibcode:1973JPhB....6.2292G. | Free-fall atomic model | 0.805544 |
29,321 | Physics Letters A. 38 (1): 35–36. Bibcode:1972PhLA...38...35G. | Free-fall atomic model | 0.805544 |
29,322 | In molecular biology, translation initiation factor IF-3 (gene infC) is one of the three factors required for the initiation of protein biosynthesis in bacteria. IF-3 is thought to function as a fidelity factor during the assembly of the ternary initiation complex which consists of the 30S ribosomal subunit, the initia... | Translation initiation factor IF-3 | 0.805543 |
29,323 | In numerical linear algebra, the Bartels–Stewart algorithm is used to numerically solve the Sylvester matrix equation A X − X B = C {\displaystyle AX-XB=C} . Developed by R.H. Bartels and G.W. | Bartels–Stewart algorithm | 0.805538 |
29,324 | Thomas H. Lowry & Kathleen Schueller Richardson, 1987, Mechanism and Theory in Organic Chemistry, 3rd Edn., New York, NY, US: Harper & Row, ISBN 0060440848, see , accessed 20 June 2015. Francis A. Carey & Richard J. Sundberg, 2006, "Title Advanced Organic Chemistry: Part A: Structure and Mechanisms," 4th Edn., New York... | Rho value | 0.805537 |
29,325 | Roberto Todeschini, Viviana Consonni, Raimund Mannhold, Hugo Kubinyi & Hendrik Timmerman, 2008, "Entry: Electronic substituent constants (Hammet substituent constants, σ electronic constants)," in Handbook of Molecular Descriptors, Vol. 11 of Methods and Principles in Medicinal Chemistry (book series), pp. 144–157, New... | Rho value | 0.805537 |
29,326 | L.P. Hammett, 1970, Physical Organic Chemistry, 2nd Edn., New York, NY, US: McGraw-Hill. John Shorter, 1982, Correlation Analysis of Organic Reactivity, Chichester 1982. Otto Exner, 1988, Correlation Analysis of Chemical Data, New York, NY, US: Plenum. | Rho value | 0.805537 |
29,327 | Systems Modeling Language (SysML), a modeling language used for systems engineering applications, supports the specification, analysis, design, verification and validation of a broad range of complex systems. | Engineered systems | 0.805537 |
29,328 | For example, the performance of a packet-switched network is characterized by the end-to-end packet transit delay, or the number of packets switched in an hour. The design of high-performance systems uses analytical or simulation modeling, whereas the delivery of high-performance implementation involves thorough perfor... | Engineered systems | 0.805537 |
29,329 | Ac for the acetyl group (Ac is also the symbol for the element actinium. However, actinium is almost never encountered in organic chemistry, so the use of Ac to represent the acetyl group never causes confusion); Bz for the benzoyl group; OBz is the benzoate group Piv for the pivalyl (t-butylcarbonyl) group; OPiv is th... | Pseudoelement symbol | 0.805535 |
29,330 | Several other ways of depicting chemical structures are also commonly used in organic chemistry (though less frequently than skeletal formulae). For example, conformational structures look similar to skeletal formulae and are used to depict the approximate positions of atoms in 3D space, as a perspective drawing. Other... | Pseudoelement symbol | 0.805535 |
29,331 | An early form of this representation was first developed by organic chemist August Kekulé, while the modern form is closely related to and influenced by the Lewis structure of molecules and their valence electrons. Hence they are sometimes termed Kekulé structures or Lewis–Kekulé structures. Skeletal formulae have beco... | Pseudoelement symbol | 0.805535 |
29,332 | The skeletal formula, or line-angle formula or shorthand formula, of an organic compound is a type of molecular structural formula that serves as a shorthand representation of a molecule's bonding and some details of its molecular geometry. A skeletal formula shows the skeletal structure or skeleton of a molecule, whic... | Pseudoelement symbol | 0.805535 |
29,333 | An alternate representation that emphasizes this delocalization uses a circle, drawn inside the hexagon of single bonds, to represent the delocalized pi orbital. This style, based on one proposed by Johannes Thiele, used to be very common in introductory organic chemistry textbooks and is still frequently used in infor... | Pseudoelement symbol | 0.805535 |
29,334 | They suggested that physical organs and also personality is a product of natural selection.With the advent of genomic sequencing, it has become possible to search for and identify specific gene polymorphisms that affect traits such as IQ and personality. These techniques work by tracking the association of differences ... | Nature versus nurture | 0.805532 |
29,335 | For example, it is hypothesized that a given behavioral disorder may represent an extreme of a continuous distribution of a normal behavior and hence an extreme of a continuous distribution of genetic and environmental variation. Depression, phobias, and reading disabilities have been examined in this context.For a few... | Nature versus nurture | 0.805532 |
29,336 | As both "nature" and "nurture" factors were found to contribute substantially, often in an inextricable manner, such views were seen as naive or outdated by most scholars of human development by the 21st century.The strong dichotomy of nature versus nurture has thus been claimed to have limited relevance in some fields... | Nature versus nurture | 0.805532 |
29,337 | The phrase in its modern sense was popularized by the Victorian polymath Francis Galton, the modern founder of eugenics and behavioral genetics when he was discussing the influence of heredity and environment on social advancement. Galton was influenced by On the Origin of Species written by his half-cousin, the evolut... | Nature versus nurture | 0.805532 |
29,338 | Nature versus nurture is a long-standing debate in biology and society about the relative influence on human beings of their genetic inheritance (nature) and the environmental conditions of their development (nurture). The alliterative expression "nature and nurture" in English has been in use since at least the Elizab... | Nature versus nurture | 0.805532 |
29,339 | Close feedback loops have been found in which nature and nurture influence one another constantly, as seen in self-domestication. In ecology and behavioral genetics, researchers think nurture has an essential influence on nature. Similarly in other fields, the dividing line between an inherited and an acquired trait be... | Nature versus nurture | 0.805532 |
29,340 | Nature is what people think of as pre-wiring and is influenced by genetic inheritance and other biological factors. Nurture is generally taken as the influence of external factors after conception e.g. the product of exposure, experience and learning on an individual. The phrase in its modern sense was popularized by t... | Nature versus nurture | 0.805532 |
29,341 | Nature versus nurture is a long-standing debate in biology and society about the relative influence on human beings of their genetic inheritance (nature) and the environmental conditions of their development (nurture). The alliterative expression "nature and nurture" in English has been in use since at least the Elizab... | Nature versus nurture | 0.805532 |
29,342 | "The situation as it presented itself by the end of the 20th century was summarized in The Blank Slate: The Modern Denial of Human Nature (2002) by Steven Pinker. The book became a best-seller, and was instrumental in bringing to the attention of a wider public the paradigm shift away from the behaviourist purism of th... | Nature versus nurture | 0.805532 |
29,343 | Cognitive functions have a significant genetic component. A 2015 meta-analysis of over 14 million twin pairs found that genetics explained 57% of the variability in cognitive functions. Evidence from behavioral genetic research suggests that family environmental factors may have an effect upon childhood IQ, accounting ... | Nature versus nurture | 0.805532 |
29,344 | At the height of the controversy, during the 1970s to 1980s, the debate was highly ideologised. In Not in Our Genes: Biology, Ideology and Human Nature (1984), Richard Lewontin, Steven Rose and Leon Kamin criticise "genetic determinism" from a Marxist framework, arguing that "Science is the ultimate legitimator of bour... | Nature versus nurture | 0.805532 |
29,345 | Malnutrition in early childhood has been linked to lower IQ scores later in life, while supplementation with certain nutrients such as iron and iodine has been shown to improve IQ scores. Social support is also an important environmental factor that positively affects IQ, with one study indicating that children who rec... | Nature versus nurture | 0.805532 |
29,346 | But even for intermediate heritabilities, a trait is always shaped by both genetic dispositions and the environments in which people develop, merely with greater and lesser plasticities associated with these heritability measures. Heritability measures always refer to the degree of variation between individuals in a po... | Nature versus nurture | 0.805532 |
29,347 | In the early 20th century, there was an increased interest in the role of the environment, as a reaction to the strong focus on pure heredity in the wake of the triumphal success of Darwin's theory of evolution. During this time, the social sciences developed as the project of studying the influence of culture in clean... | Nature versus nurture | 0.805532 |
29,348 | In numerical analysis to handle contributions of geometry where it is difficult to obtain discretizations, the moving least squares methods have also been used and generalized to solve PDEs on curved surfaces and other geometries. This includes numerical methods developed for curved surfaces for solving scalar paraboli... | Moving least squares | 0.805528 |
29,349 | jMetrik is free and open source software for conducting a comprehensive psychometric analysis. It was developed by J. Patrick Meyer at the University of Virginia. Current methods include classical item analysis, differential item functioning (DIF) analysis, item response theory, IRT equating, and nonparametric item res... | Psychometric software | 0.805526 |
29,350 | IRT equating methods include mean/mean, mean/sigma, Haebara, and Stocking-Lord procedures. jMetrik also includes IRT illustrator, a basic descriptive statistics and a graphics facility that produces bar charts, pie chart, histograms, kernel density estimates, and line plots. jMetrik is a pure Java application that runs... | Psychometric software | 0.805526 |
29,351 | Confirmatory factor analysis is limited to the common factor model for congeneric, tau-equivalent, and parallel measures. Fit statistics are reported along with factor loadings and error variances. IRT methods include the Rasch, partial credit, and rating scale models. | Psychometric software | 0.805526 |
29,352 | IRT equating methods include mean/mean, mean/sigma, Haebara, and Stocking-Lord procedures. jMetrik also include basic descriptive statistics and a graphics facility that produces bar charts, pie chart, histograms, kernel density estimates, and line plots. jMetrik is a pure Java application that runs on 32-bit and 64-bi... | Psychometric software | 0.805526 |
29,353 | jMetrik is free and open source software for conducting a comprehensive psychometric analysis. It was developed by J. Patrick Meyer at the University of Virginia. Current methods include classical item analysis, differential item functioning (DIF) analysis, confirmatory factor analysis, item response theory, IRT equati... | Psychometric software | 0.805526 |
29,354 | WINMIRA 2001 is a program for analyses with the Rasch model for dichotomous and polytomous ordinal responses, with the latent class analysis, and with the Mixture Distribution Rasch model for dichotomous and polytomous item responses. The software provides conditional maximum likelihood (CML) estimation of item paramet... | Psychometric software | 0.805526 |
29,355 | ViSta-CITA (Classical Item and Test Analysis) is a module included in the Visual Statistics System (ViSta) that focuses on graphical-oriented methods applied to psychometric analysis. It was developed by Ruben Ledesma, J. Gabriel Molina, Pedro M. Valero-Mora, and Forrest W. Young. ViSta has not been updated since 2014 | Psychometric software | 0.805526 |
29,356 | Testfact features - Marginal maximum likelihood (MML) exploratory factor analysis and classical item analysis of binary data - Computes tetrachoric correlations, principal factor solution, classical item descriptive statistics, fractile tables and plots - Handles up to 10 factors using numerical quadrature: up to 5 for... | Psychometric software | 0.805526 |
29,357 | TAP (the Test Analysis Program) is free a Windows 9x/NT/2000/XP/7 program written in Delphi Pascal that performs test analyses and item analyses based on classical test theory. TAP is a classical test and item analysis program. It provides reports for examinee total scores, item statistics ('e.g.' item difficulty, item... | Psychometric software | 0.805526 |
29,358 | R package. The package includes marginal and joint maximum likelihood estimation of uni- and multidimensional item response models (Rasch, 2PL, Generalized Partial Credit, Rating Scale, Multi Facets), fit statistics, standard error estimation, as well as plausible value imputation and weighted likelihood estimation of ... | Psychometric software | 0.805526 |
29,359 | R package. A number of routines for personality, psychometrics and experimental psychology. Functions are primarily for scale construction using factor analysis, cluster analysis and reliability analysis, although others provide basic descriptive statistics. Item Response Theory is done using factor analysis of tetrach... | Psychometric software | 0.805526 |
29,360 | PACER (Psychometric Analysis and Computing Environment for Researchers) is a psychometric ecosystem and cloud-based application for psychometricians and data scientists developed by Harold Doran. The software offers IRT parameter and person estimation (MLE, MAP, EAP, TCC, and bifactor models), parameter and person esti... | Psychometric software | 0.805526 |
29,361 | Lertap5 (the 5th version of the Laboratory of Educational Research Test Analysis Program) is a comprehensive software package for test and survey analyses, developed for use on Windows and Macintosh computers with Microsoft Excel. It includes test, item, and option statistics, classification consistency and mastery tes... | Psychometric software | 0.805526 |
29,362 | Lertap calculates several statistics related to decision and classification consistency, including Livingston's coefficient, the Brennan-Kane dependability index, kappa, and an estimate of p(0), number of correct classifications as a proportion, derived by using the Peng-Subkoviac adaptation of Huynh's method. More det... | Psychometric software | 0.805526 |
29,363 | Iteman is a commercial Windows program specifically designed for classical test analysis. It is unique in that it produces tech reports ub Microsoft Word rather than ASCII output, with graphics, narratives, and embedded tables. It calculates the proportion and point biserial of each item, as well as high/low subgroup p... | Psychometric software | 0.805526 |
29,364 | Peierls' theorem states that a one-dimensional equally spaced chain with one electron per ion is unstable. This theorem was first espoused in the 1930s by Rudolf Peierls. It can be proven using a simple model of the potential for an electron in a 1-D crystal with lattice spacing a {\displaystyle a} . The periodicity of... | Peierls distortion | 0.805525 |
29,365 | Other models that move beyond the GTR model in specific ways were also developed and refined by several researchers.Almost all DNA substitution models are mechanistic models (as described above). The small number of parameters that one needs to estimate for these models makes it feasible to estimate those parameters fr... | Substitution model | 0.80552 |
29,366 | Thus, substitution models are central to maximum likelihood estimation of phylogeny as well as Bayesian inference in phylogeny. Estimates of evolutionary distances (numbers of substitutions that have occurred since a pair of sequences diverged from a common ancestor) are typically calculated using substitution models (... | Substitution model | 0.80552 |
29,367 | In biology, a substitution model, also called models of DNA sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules (e.g., DNA sequences) represented as sequence of symbols (A, C, G, and T in the case of DNA). Substitution models a... | Substitution model | 0.80552 |
29,368 | However, it is possible to specify the expected site pattern frequencies using five degrees of freedom if using the Jukes-Cantor model of DNA evolution, which is a simple substitution model that allows one to calculate the expected site pattern frequencies only the tree topology and the branch lengths (given four taxa ... | Substitution model | 0.80552 |
29,369 | In 1997, Tuffley and Steel described a model that they named the no common mechanism (NCM) model. The topology of the maximum likelihood tree for a specific dataset given the NCM model is identical to the topology of the optimal tree for the same data given the maximum parsimony criterion. The NCM model assumes all of ... | Substitution model | 0.80552 |
29,370 | Log-odds matrices based on the Dayhoff PAM model were commonly used to assess the significance of homology search results, although the BLOSUM matrices have superseded the PAM log-odds matrices in this context because the BLOSUM matrices appear to be more sensitive across a variety of evolutionary distances, unlike the... | Substitution model | 0.80552 |
29,371 | The practice of expressing the exchangeability parameters in relative terms is not problematic because the Q {\displaystyle Q} matrix is normalized. Normalization allows t {\displaystyle t} (time) in the matrix exponentiation P ( t ) = e Q t {\displaystyle P(t)=e^{Qt}} to be expressed in units of expected substitutions... | Substitution model | 0.80552 |
29,372 | When the physics of nuclear fusion was first put on a firm footing during the early 1950s, a string of proposed devices to harness that energy was quickly created. These all aimed to solve the problem of containing a plasma fuel that was heated to at least 50 million Kelvin, which would melt any substance. The trick us... | Princeton Large Torus | 0.80552 |
29,373 | The Princeton Large Torus (or PLT), was an early tokamak built at the Princeton Plasma Physics Laboratory (PPPL). It was one of the first large scale tokamak machines, and among the most powerful in terms of current and magnetic fields. Originally built to demonstrate that larger devices would have better confinement t... | Princeton Large Torus | 0.80552 |
29,374 | On the night of July 24, they pushed the system further to 5.5 kV, hitting 60 million degrees. This was a milestone in the fusion program; PLT demonstrated that one could make a tokamak that could confine its plasma long enough to heat it to the temperatures needed in a practical reactor. The density of the plasma woul... | Princeton Large Torus | 0.80552 |
29,375 | Their machine was complete by late 1970, but bringing it into operation took most of 1971 and the first physics results were not being returned until early 1972. By 1973 the machine was operating sufficiently well that the lab began plans to turn on the NBI injectors.PPPL was not willing to give up its leadership posit... | Princeton Large Torus | 0.80552 |
29,376 | Lastly, when your goal is to study cellular progression through differentiation, average expression profiles can only order cells by time rather than by developmental stage. Consequently, they cannot show trends in gene expression levels specific to certain stages.Recent advances in biotechnology allow the measurement ... | Single-cell transcriptomics | 0.805517 |
29,377 | Knowledge Discovery Metamodel (KDM) is a publicly available specification from the Object Management Group (OMG). KDM is a common intermediate representation for existing software systems and their operating environments, that defines common metadata required for deep semantic integration of Application Lifecycle Manag... | Knowledge Discovery Metamodel | 0.805514 |
29,378 | ISBN 0-521-20515-8. MR 0394604. V. V. Fedorchuk, The Fundamentals of Dimension Theory, appearing in Encyclopaedia of Mathematical Sciences, Volume 17, General Topology I, (1993) A. V. Arkhangel'skii and L. S. Pontryagin (Eds. ), Springer-Verlag, Berlin ISBN 3-540-18178-4. | Topological dimension | 0.805514 |
29,379 | Given a flux according to the electromagnetism definition, the corresponding flux density, if that term is used, refers to its derivative along the surface that was integrated. By the Fundamental theorem of calculus, the corresponding flux density is a flux according to the transport definition. Given a current such as... | Flux of a vector field | 0.805513 |
29,380 | The word flux comes from Latin: fluxus means "flow", and fluere is "to flow". As fluxion, this term was introduced into differential calculus by Isaac Newton. The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena. | Flux of a vector field | 0.805513 |
29,381 | In quantum mechanics, particles of mass m in the quantum state ψ(r, t) have a probability density defined as So the probability of finding a particle in a differential volume element d3r is Then the number of particles passing perpendicularly through unit area of a cross-section per unit time is the probability flux; T... | Flux of a vector field | 0.805513 |
29,382 | However, every planar drawing of a complete graph with five or more vertices must contain a crossing, and the nonplanar complete graph K5 plays a key role in the characterizations of planar graphs: by Kuratowski's theorem, a graph is planar if and only if it contains neither K5 nor the complete bipartite graph K3,3 as ... | Complete graph | 0.805511 |
29,383 | A complete graph with n nodes represents the edges of an (n – 1)-simplex. Geometrically K3 forms the edge set of a triangle, K4 a tetrahedron, etc. The Császár polyhedron, a nonconvex polyhedron with the topology of a torus, has the complete graph K7 as its skeleton. Every neighborly polytope in four or more dimensions... | Complete graph | 0.805511 |
29,384 | In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction).Graph theory its... | Complete graph | 0.805511 |
29,385 | Manifold System was first sold in January 1998 as Release 3.00. Releases 3.00 and 4.00 were heavily weighted to analytics, with many tools for abstract graph theory analysis but a very limited GIS toolset. Release 4.50 emphasized general GIS features of broader interest and emerged as Manifold's first commercial GIS, a... | Manifold System | 0.805511 |
29,386 | The development team for Manifold was created in 1993 to optimize mathematics libraries for a massively-parallel supercomputer created in a joint venture between Intel Corporation and the US Department of Defense. The team subsequently embarked on a plan to create and sell mathematics libraries, including the General G... | Manifold System | 0.805511 |
29,387 | Conditionally safe: Different threads can access different objects simultaneously, and access to shared data is protected from race conditions. Not thread safe: Data structures should not be accessed simultaneously by different threads.Thread safety guarantees usually also include design steps to prevent or limit the r... | Thread safety | 0.805509 |
29,388 | The mapping class group is generated by the subset of Dehn twists about all simple closed curves on the surface. The Dehn–Lickorish theorem states that it is sufficient to select a finite number of those to generate the mapping class group. This generalises the fact that SL 2 ( Z ) {\displaystyle \operatorname {SL} _... | Dehn-Nielsen theorem | 0.805508 |
29,389 | This comes from the fact that the intersection number of closed curves induces a symplectic form on the first homology, which is preserved by the action of the mapping class group. The surjectivity is proven by showing that the images of Dehn twists generate Sp 2 g ( Z ) {\displaystyle \operatorname {Sp} _{2g}(\mathb... | Dehn-Nielsen theorem | 0.805508 |
29,390 | It is possible to prove that all relations between the Dehn twists in a generating set for the mapping class group can be written as combinations of a finite number among them. This means that the mapping class group of a surface is a finitely presented group. One way to prove this theorem is to deduce it from the prop... | Dehn-Nielsen theorem | 0.805508 |
29,391 | In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up to continuous (in the compact-open topology) deformation. It is of fundamental importance for the study of 3-mani... | Dehn-Nielsen theorem | 0.805508 |
29,392 | Scalar may refer to: Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers Scalar (physics), a physical quantity that can be described by a single element of a number field such as a real number Lorentz scalar, a quantity in the theory of relativity which... | Scalar quantity | 0.805496 |
29,393 | Similarly, foliations correspond to G-structures coming from block matrices, together with integrability conditions so that the Frobenius theorem applies. A flat G-structure is a G-structure P having a global section (V1,...,Vn) consisting of commuting vector fields. A G-structure is integrable (or locally flat) if it ... | Reduction of the structure group | 0.805495 |
29,394 | In particle physics, underlying event (UE) refers to the additional interactions of two particle beams at a collision point beyond the main collision under study. Specifically, the term is used for hadron collider events which do not originate from the primary hard scattering (high energy, high momentum impact) process... | Underlying event | 0.805494 |
29,395 | Simula, invented in the late 1960s by Nygaard and Dahl as a superset of ALGOL 60, was the first language designed to support object-oriented programming. FORTH, the earliest concatenative programming language was designed by Charles Moore in 1969 as a personal development system while at the National Radio Astronomy Ob... | History of programming languages | 0.805494 |
29,396 | The period from the late 1960s to the late 1970s brought a major flowering of programming languages. Most of the major language paradigms now in use were invented in this period: Speakeasy, developed in 1964 at Argonne National Laboratory (ANL) by Stanley Cohen, is an object-oriented programming system (OOPS), much lik... | History of programming languages | 0.805494 |
29,397 | During 1842–1849, Ada Lovelace translated the memoir of Italian mathematician Luigi Menabrea about Charles Babbage's newest proposed machine: the Analytical Engine; she supplemented the memoir with notes that specified in detail a method for calculating Bernoulli numbers with the engine, recognized by most of historian... | History of programming languages | 0.805494 |
29,398 | John Backus, inventor of Fortran, cooperated in designing ALGOL 58 and ALGOL 60. John C. Reynolds, co-inventor of the polymorphic lambda calculus (System F). John McCarthy, inventor of LISP, design committee of ALGOL 60. | History of programming languages | 0.805494 |
29,399 | The version for the EDSAC 2 was devised by Douglas Hartree of University of Cambridge Mathematical Laboratory in 1961. Known as EDSAC 2 Autocode, it was a straight development from Mercury Autocode adapted for local circumstances and was noted for its object code optimization and source-language diagnostics which were ... | History of programming languages | 0.805494 |
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