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4,400 | If the electron is assumed to orbit in a perfect circle and radiates energy continuously, the electron would rapidly spiral into the nucleus with a fall time of: where a 0 {\displaystyle a_{0}} is the Bohr radius and r 0 {\displaystyle r_{0}} is the classical electron radius. If this were true, all atoms would instantl... | Hydrogen atoms | 0.828321 |
4,401 | Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary (diatomic) hydrogen gas, H2. "Atomic hydrogen" and "hydrogen atom" in ordinary English use have overlapping, yet distinct, meanings. For example, a water molecule contains two hydrogen atoms, but does... | Hydrogen atoms | 0.82832 |
4,402 | In physics, a kinetic term is the part of the Lagrangian that is bilinear in the fields (and for nonlinear sigma models, they are not even bilinear), and usually contains two derivatives with respect to time (or space); in the case of fermions, the kinetic term usually has one derivative only. The equation of motion de... | Kinetic term | 0.82832 |
4,403 | As a discipline, computer science spans a range of topics from theoretical studies of algorithms and the limits of computation to the practical issues of implementing computing systems in hardware and software.CSAB, formerly called Computing Sciences Accreditation Board—which is made up of representatives of the Associ... | Computer science | 0.828313 |
4,404 | This field plays important role in information theory, telecommunications, information engineering and has applications in medical image computing and speech synthesis, among others. What is the lower bound on the complexity of fast Fourier transform algorithms? is one of unsolved problems in theoretical computer scien... | Computer science | 0.828313 |
4,405 | Software engineering is the study of designing, implementing, and modifying the software in order to ensure it is of high quality, affordable, maintainable, and fast to build. It is a systematic approach to software design, involving the application of engineering practices to software. Software engineering deals with ... | Computer science | 0.828313 |
4,406 | Scientific computing (or computational science) is the field of study concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems. A major usage of scientific computing is simulation of various processes, including computational fluid... | Computer science | 0.828313 |
4,407 | A description will have two parts: The first part describes another description language. The second part is a description of the object in that language.In more technical terms, the first part of a description is a computer program (specifically: a compiler for the object's language, written in the description languag... | Kolmogorov Complexity | 0.828312 |
4,408 | Theorem: If K1 and K2 are the complexity functions relative to Turing complete description languages L1 and L2, then there is a constant c – which depends only on the languages L1 and L2 chosen – such that ∀s. −c ≤ K1(s) − K2(s) ≤ c.Proof: By symmetry, it suffices to prove that there is some constant c such that for al... | Kolmogorov Complexity | 0.828312 |
4,409 | The minimum message length principle of statistical and inductive inference and machine learning was developed by C.S. Wallace and D.M. Boulton in 1968. MML is Bayesian (i.e. it incorporates prior beliefs) and information-theoretic. | Kolmogorov Complexity | 0.828312 |
4,410 | In the following discussion, let K(s) be the complexity of the string s. It is not hard to see that the minimal description of a string cannot be too much larger than the string itself — the program GenerateString2 above that outputs s is a fixed amount larger than s. Theorem: There is a constant c such that ∀s. K(s) ≤... | Kolmogorov Complexity | 0.828312 |
4,411 | In this article, an informal approach is discussed. Any string s has at least one description. For example, the second string above is output by the pseudo-code: function GenerateString2() return "4c1j5b2p0cv4w1x8rx2y39umgw5q85s7" whereas the first string is output by the (much shorter) pseudo-code: function GenerateSt... | Kolmogorov Complexity | 0.828312 |
4,412 | In physical chemistry, the Faraday constant (symbol F, sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge (q) by the amount (n) of elementary charge carriers in any given sample of matter: F=q/n; it is expressed in units of coulombs per mole (C/mol). As such, it represe... | Faraday's constant | 0.828309 |
4,413 | In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operat... | Simplex algorithm | 0.828306 |
4,414 | If the values of the nonbasic variables are set to 0, then the values of the basic variables are easily obtained as entries in b and this solution is a basic feasible solution. The algebraic interpretation here is that the coefficients of the linear equation represented by each row are either 0 {\displaystyle 0} , 1 {\... | Simplex algorithm | 0.828306 |
4,415 | However the complexity of problems related to structure prediction and analysis, as well as the desire for perfection, compactness and consistency, led to the program's expansion into neighboring areas such as graphics, chemistry, sequence analysis and database searches, mathematics, statistics and plotting. The origin... | Internal Coordinate Mechanics | 0.828291 |
4,416 | ICM also is a programming environment for various tasks in computational chemistry and computational structural biology, sequence analysis and rational drug design. The original goal was to develop algorithms for energy optimization of several biopolymers with respect to an arbitrary subset of internal coordinates such... | Internal Coordinate Mechanics | 0.828291 |
4,417 | Internal Coordinate Mechanics (ICM) is a software program and algorithm to predict low-energy conformations of molecules by sampling the space of internal coordinates (bond lengths, bond angles and dihedral angles) defining molecular geometry. In ICM each molecule is constructed as a tree from an entry atom where each ... | Internal Coordinate Mechanics | 0.828291 |
4,418 | Morgan Chase also run internal contests involving large numbers of employees.Examples of data science competition platforms include Bitgrit, Correlation One, Kaggle, InnoCentive, Microprediction, AIcrowd, and Alibaba Tianchi. Alibaba's competition platform was used in KDD 2017. == References == | Data science competition platform | 0.828279 |
4,419 | A data science competition platform is used by businesses to host data science challenges that are hard to solve for one group. Historically, crowdsourcing challenges have been known to solve very complex problems. The Netflix Prize is one such competition. Since then there have been several platforms developed on the ... | Data science competition platform | 0.828279 |
4,420 | In molecular biology and genetics, DNA annotation or genome annotation is the process of describing the structure and function of the components of a genome, by analyzing and interpreting them in order to extract their biological significance and understand the biological processes in which they participate. Among othe... | Genome annotation | 0.828272 |
4,421 | A module is called a simple module if it does not contain a nontrivial submodule. An algebra is called a simple algebra if it does not contain a nontrivial two sided ideal.The general pattern is that the structure admits no non-trivial congruence relations. | Simple (abstract algebra) | 0.828269 |
4,422 | In mathematics, the term simple is used to describe an algebraic structure which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if the kernel of every homomorphism is either the whole structure or a single element. Some examples are: A group is... | Simple (abstract algebra) | 0.828269 |
4,423 | In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity, independent of the sys... | Sommerfeld constant | 0.828263 |
4,424 | Many problems can be framed as a form of the shortest path for some suitably substituted notions of addition along a path and taking the minimum. The general approach to these is to consider the two operations to be those of a semiring. Semiring multiplication is done along the path, and the addition is between paths. ... | Shortest path problems | 0.828259 |
4,425 | The concepts of size homotopy group and size functor are strictly related to the concept of persistent homology group studied in persistent homology. It is worth to point out that the size function is the rank of the 0 {\displaystyle 0} -th persistent homology group, while the relation between the persistent homology g... | Measuring function | 0.82825 |
4,426 | An extension of the concept of size function to algebraic topology was made in where the concept of size homotopy group was introduced. Here measuring functions taking values in R k {\displaystyle \mathbb {R} ^{k}} are allowed. An extension to homology theory (the size functor) was introduced in . | Measuring function | 0.82825 |
4,427 | Size functions were introduced in for the particular case of M {\displaystyle M} equal to the topological space of all piecewise C 1 {\displaystyle C^{1}} closed paths in a C ∞ {\displaystyle C^{\infty }} closed manifold embedded in a Euclidean space. Here the topology on M {\displaystyle M} is induced by the C 0 {\dis... | Measuring function | 0.82825 |
4,428 | In mathematics, the spectrum of a matrix is the multiset of the eigenvalues of the matrix. In functional analysis, the concept of the spectrum of a bounded operator is a generalization of the eigenvalue concept for matrices. In algebraic topology, a spectrum is an object representing a generalized cohomology theory. | Energy spectrum | 0.82822 |
4,429 | The Library of Efficient Data types and Algorithms (LEDA) is a proprietarily-licensed software library providing C++ implementations of a broad variety of algorithms for graph theory and computational geometry. It was originally developed by the Max Planck Institute for Informatics Saarbrücken. Since 2001, LEDA is furt... | Library of Efficient Data types and Algorithms | 0.828213 |
4,430 | LEDA is useful in the field of computational geometry due to its support for exact representations of real numbers via the leda_real datatype. This provides an advantage in accuracy over floating-point arithmetic. For example, calculations involving radicals are considerably more accurate when computed using leda_real.... | Library of Efficient Data types and Algorithms | 0.828213 |
4,431 | The zeroth algebraic K group K 0 ( R ) {\displaystyle K_{0}(R)} of a (not necessarily commutative) ring R is the Grothendieck group of the monoid consisting of isomorphism classes of finitely generated projective modules over R, with the monoid operation given by the direct sum. Then K 0 {\displaystyle K_{0}} is a cova... | Group completion | 0.828211 |
4,432 | Another construction that carries the name Grothendieck group is the following: Let R be a finite-dimensional algebra over some field k or more generally an artinian ring. Then define the Grothendieck group G 0 ( R ) {\displaystyle G_{0}(R)} as the abelian group generated by the set { ∣ X ∈ R -mod } {\displaystyle \{\... | Group completion | 0.828211 |
4,433 | G 0 {\displaystyle G_{0}} is not a functor, but nevertheless it carries important information.Since the (bounded) derived category is triangulated, there is a Grothendieck group for derived categories too. This has applications in representation theory for example. For the unbounded category the Grothendieck group howe... | Group completion | 0.828211 |
4,434 | For a ringed space ( X , O X ) {\displaystyle (X,{\mathcal {O}}_{X})} , one can consider the category A {\displaystyle {\mathcal {A}}} of all locally free sheaves over X. K 0 ( X ) {\displaystyle K_{0}(X)} is then defined as the Grothendieck group of this exact category and again this gives a functor.For a ringed space... | Group completion | 0.828211 |
4,435 | In the Euclidean plane, two circles that are concentric necessarily have different radii from each other. However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different meridians of a terrestrial globe are concentr... | Concentric objects | 0.828197 |
4,436 | The components of the pixels (primary colors red, green and blue) in an image sensor or display can be ordered in different patterns, called pixel geometry. The geometric arrangement of the primary colors within a pixel varies depending on usage (see figure 1). In monitors, such as LCDs or CRTs, that typically display ... | Pixel geometry | 0.828184 |
4,437 | Several algorithms could be used in this estimation process, including maximum likelihood, neural networks, and the hierarchical Bayes model. The Hierarchical Bayes model is beneficial because it allows for borrowing across the data, although since BWS often allows the estimation of individual level models, the benefit... | Best–worst scaling | 0.828174 |
4,438 | Louviere attributes the idea to the early work of Anthony A. J. Marley in his PhD thesis, who together with Duncan Luce in the 1960s produced much of the ground-breaking research in mathematical psychology and psychophysics to axiomatise utility theory. Marley had encountered problems axiomatising certain types of rank... | Best–worst scaling | 0.828174 |
4,439 | They successfully identified eight putative SCEs in the murine (mouse) embryonic stem (meS) cell line with resolution up to 23 bp. This methodology has also been shown to hold great utility in discerning patterns of non-random chromatid segregation, especially in stem cell lineages. Furthermore, SCEs have been implicat... | Single-cell DNA template strand sequencing | 0.828167 |
4,440 | The Bioinformatic Analysis of Inherited Templates (BAIT) was the first bioinformatic software to exclusively analyze reads generated from the Strand-seq methodology. It begins by aligning the reads to a reference sequence, binning the genome into sections, and finally counting the number of Watson and Crick reads falli... | Single-cell DNA template strand sequencing | 0.828167 |
4,441 | If a hole associates itself with a neutral atom, that atom loses an electron and becomes positive. Therefore, the hole is taken to have positive charge of +e, precisely the opposite of the electron charge. In reality, due to the uncertainty principle of quantum mechanics, combined with the energy levels available in th... | Electron hole | 0.82816 |
4,442 | The analogy above is quite simplified, and cannot explain why holes create an opposite effect to electrons in the Hall effect and Seebeck effect. A more precise and detailed explanation follows. A dispersion relation is the relationship between wavevector (k-vector) and energy in a band, part of the electronic band str... | Electron hole | 0.82816 |
4,443 | Therefore, if the laws of physics do not change with time, then the conservation of energy follows. For energy conservation to be violated to allow perpetual motion would require that the foundations of physics would change.Scientific investigations as to whether the laws of physics are invariant over time use telescop... | Perpetual motion machines | 0.828156 |
4,444 | "Epistemic impossibility" describes things which absolutely cannot occur within our current formulation of the physical laws. This interpretation of the word "impossible" is what is intended in discussions of the impossibility of perpetual motion in a closed system.The conservation laws are particularly robust from a m... | Perpetual motion machines | 0.828156 |
4,445 | Any proposed perpetual motion design offers a potentially instructive challenge to physicists: one is certain that it cannot work, so one must explain how it fails to work. The difficulty (and the value) of such an exercise depends on the subtlety of the proposal; the best ones tend to arise from physicists' own though... | Perpetual motion machines | 0.828156 |
4,446 | In statistics, the terms "mathematical elimination" and "mathematically eliminated" mean to be excluded in a decision, based on numerical counts, due to insufficient total numbers, even if all remaining events were 100% in favor. The excluded outcome is considered to be eliminated due to the mathematical probability be... | Mathematical elimination | 0.82815 |
4,447 | In computational matrix algebra, iterative methods are generally needed for large problems.Iterative methods are more common than direct methods in numerical analysis. Some methods are direct in principle but are usually used as though they were not, e.g. GMRES and the conjugate gradient method. For these methods the n... | Numerical algorithm | 0.828143 |
4,448 | Numerical analysis is also concerned with computing (in an approximate way) the solution of differential equations, both ordinary differential equations and partial differential equations.Partial differential equations are solved by first discretizing the equation, bringing it into a finite-dimensional subspace. This c... | Numerical algorithm | 0.828143 |
4,449 | A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences. The problem of computing l... | Longest common subsequence problem | 0.828138 |
4,450 | The third drawback is that of collisions. Since the checksum or hash is not guaranteed to be unique, there is a small chance that two different items could be reduced to the same hash. This is unlikely in source code, but it is possible. A cryptographic hash would therefore be far better suited for this optimization, a... | Longest common subsequence problem | 0.828138 |
4,451 | A hash function or checksum can be used to reduce the size of the strings in the sequences. That is, for source code where the average line is 60 or more characters long, the hash or checksum for that line might be only 8 to 40 characters long. Additionally, the randomized nature of hashes and checksums would guarantee... | Longest common subsequence problem | 0.828138 |
4,452 | Most of the time taken by the naive algorithm is spent performing comparisons between items in the sequences. For textual sequences such as source code, you want to view lines as the sequence elements instead of single characters. This can mean comparisons of relatively long strings for each step in the algorithm. Two ... | Longest common subsequence problem | 0.828138 |
4,453 | bar chart Bayes' theorem Bayes estimator Bayes factor Bayesian inference bias 1. Any feature of a sample that is not representative of the larger population. 2. The difference between the expected value of an estimator and the true value. | Glossary of probability and statistics | 0.828131 |
4,454 | admissible decision rule algebra of random variables alternative hypothesis analysis of variance atomic event Another name for elementary event. | Glossary of probability and statistics | 0.828131 |
4,455 | statistical dispersion A measure of the diversity within a set of data, expressed by the variance or the standard deviation. statistical parameter A parameter that indexes a family of probability distributions. statistical significance statistics Student's t-test stem-and-leaf display stratified sampling survey methodo... | Glossary of probability and statistics | 0.828131 |
4,456 | Response variables are those that change or respond to some phenomenon under study. The term is often used interchangeably with dependent variable. restricted randomization robust statistics round-off error | Glossary of probability and statistics | 0.828131 |
4,457 | nonparametric regression nonparametric statistics non-sampling error normal distribution normal probability plot null hypothesis (H0) The statement being tested in a test of statistical significance; usually a statement of 'no effect' or 'no difference'. For example, in a test of whether light has an effect on sleep, t... | Glossary of probability and statistics | 0.828131 |
4,458 | elementary event An event which contains only a single outcome in the sample space; in a set of possibilities, a possibility that can occur in precisely one way. For example, when pulling a card from a standard deck of playing cards, 'pulling the jack of spades' is an elementary event (because there is only one jack of... | Glossary of probability and statistics | 0.828131 |
4,459 | data data analysis data set A sample and the associated data points. data point A typed measurement — it can be a Boolean value, a real number, a vector (in which case it is also called a data vector), etc. decision rule decision theory degrees of freedom density estimation dependence dependent variable descriptive sta... | Glossary of probability and statistics | 0.828131 |
4,460 | conditional probability The probability of some event A, assuming the occurrence of event B. In mathematical notation, conditional probability is written P(A|B), and is read "the probability of A, given B". conditional probability distribution confidence interval (CI) In inferential statistics, a range of plausible val... | Glossary of probability and statistics | 0.828131 |
4,461 | central limit theorem central moment characteristic function chi-squared distribution chi-squared test cluster analysis cluster sampling complementary event completely randomized design computational statistics The study of statistical methods that are enabled by using computational methods, at the interface of statist... | Glossary of probability and statistics | 0.828131 |
4,462 | This glossary of statistics and probability is a list of definitions of terms and concepts used in the mathematical sciences of statistics and probability, their sub-disciplines, and related fields. For additional related terms, see Glossary of mathematics and Glossary of experimental design. | Glossary of probability and statistics | 0.828131 |
4,463 | Markov chain Monte Carlo mathematical statistics maximum likelihood estimation mean 1. The expected value of a random variable. 2. | Glossary of probability and statistics | 0.828131 |
4,464 | L-moment law of large numbers (LLN) A theorem according to which the average of the results obtained from performing the same experiment a large number of times should be close to the experiment's expected value, and tends to become closer to the expected value as more trials are performed. The law suggests that a suff... | Glossary of probability and statistics | 0.828131 |
4,465 | Spaced learning is a learning method in which highly condensed learning content is repeated three times, with two 10-minute breaks during which distractor activities such as physical activities are performed by the students. It is based on the temporal pattern of stimuli for creating long-term memories reported by R. D... | Spaced learning | 0.828124 |
4,466 | The use of the term 'spaced' reflects the distinction in other research between 'spaced training' and 'massed training' where there have been conflicting results reported (for example, see spaced repetition). Spaced retrieval practice – trying to recover long-term memories quickly and accurately – is the subject of a d... | Spaced learning | 0.828124 |
4,467 | The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned into triplets that all have the same sum. More precisely: The input to the problem is a multiset S of n = 3 m positive integers. The sum of all integers is m T ... | 3-partition problem | 0.82812 |
4,468 | Pseudo amino acid composition, or PseAAC, in molecular biology, was originally introduced by Kuo-Chen Chou in 2001 to represent protein samples for improving protein subcellular localization prediction and membrane protein type prediction. Like the vanilla amino acid composition (AAC) method, it characterizes the prote... | Pseudo amino acid composition | 0.828102 |
4,469 | To do this we first observe that the atoms of a finite Boolean algebra correspond to its ultrafilters and that an atom is below an element of a finite Boolean algebra if and only if that element is contained in the ultrafilter corresponding to the atom. This leads us to construct a representation of a Boolean algebra b... | Complex algebra (set theory) | 0.828087 |
4,470 | It is the basis of Stone's representation theorem for Boolean algebras and an example of a completion procedure in order theory based on ideals or filters, similar to Dedekind cuts. Alternatively one can consider the set of homomorphisms onto the two element Boolean algebra and form complexes by associating each elemen... | Complex algebra (set theory) | 0.828087 |
4,471 | Similarly, every finite Boolean algebra can be represented as a power set – the power set of its set of atoms; each element of the Boolean algebra corresponds to the set of atoms below it (the join of which is the element). This power set representation can be constructed more generally for any complete atomic Boolean ... | Complex algebra (set theory) | 0.828087 |
4,472 | T ( X ) {\displaystyle T(\mathbf {X} )} is a compact space with compact open sets F {\displaystyle {\mathcal {F}}} if and only if X {\displaystyle \mathbf {X} } is compact. T ( X ) {\displaystyle T(\mathbf {X} )} is a Boolean space with clopen sets F {\displaystyle {\mathcal {F}}} if and only if X {\displaystyle \mathb... | Complex algebra (set theory) | 0.828087 |
4,473 | We denote by T ( X ) {\displaystyle T(\mathbf {X} )} the corresponding topological space, ( X , T ) {\displaystyle (X,{\mathcal {T}})} where T {\displaystyle {\mathcal {T}}} is the topology formed by taking arbitrary unions of complexes. Then T ( X ) {\displaystyle T(\mathbf {X} )} is always a zero-dimensional space. T... | Complex algebra (set theory) | 0.828087 |
4,474 | A field of sets is called separative (or differentiated) if and only if for every pair of distinct points there is a complex containing one and not the other. A field of sets is called compact if and only if for every proper filter over X {\displaystyle X} the intersection of all the complexes contained in the filter i... | Complex algebra (set theory) | 0.828087 |
4,475 | Graphical models, including electron density are a commonly employed tool in chemistry education. Note in the left-most image of aniline, high electron densities are associated with the carbons and nitrogen, but the hydrogens with only one proton in their nuclei, are not visible. This is the reason that X-ray diffracti... | Electronic density | 0.828082 |
4,476 | Poset games are impartial games, meaning that every move available to Alice would also be available to Bob if Alice were allowed to pass, and vice versa. Therefore, by the Sprague–Grundy theorem, every position in a poset game has a Grundy value, a number describing an equivalent position in the game of Nim. The Grundy... | Poset game | 0.828076 |
4,477 | David R. Lide (ed), CRC Handbook of Chemistry and Physics, 85th Edition, online version. CRC Press. Boca Raton, Florida, 2003; Section 6, Fluid Properties; Critical Constants. Also agrees with Celsius values from Section 4: Properties of the Elements and Inorganic Compounds, Melting, Boiling, Triple, and Critical Point... | Critical points of the elements (data page) | 0.828073 |
4,478 | J.A. Dean (ed), Lange's Handbook of Chemistry (15th Edition), McGraw-Hill, 1999; Section 6; Table 6.5 Critical Properties | Critical points of the elements (data page) | 0.828073 |
4,479 | Molecular phylogenetics () is the branch of phylogeny that analyzes genetic, hereditary molecular differences, predominantly in DNA sequences, to gain information on an organism's evolutionary relationships. From these analyses, it is possible to determine the processes by which diversity among species has been achieve... | Molecular phylogenetics | 0.828073 |
4,480 | There are many problems related to the satisfiability of conjunctive normal form Boolean formulas. Decision problems: 2SAT 3SAT Optimization problems, where the goal is to maximize the number of clauses satisfied: MAX-SAT, and the corresponded weighted version Weighted MAX-SAT MAX-kSAT, where each clause has exactly k ... | Maximum satisfiability problem | 0.828048 |
4,481 | MAX-SAT is one of the optimization extensions of the boolean satisfiability problem, which is the problem of determining whether the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to TRUE. If the clauses are restricted to have at most 2 literals, as in 2-satisfiabilit... | Maximum satisfiability problem | 0.828048 |
4,482 | Canada's food regulatory system differs from those of most other countries, and its procedures already accommodate products from any breeding technique, including NBTs. This is because its 1993 'Biotechnology Regulatory Framework' is based upon a concept of regulatory triggering based upon "Plants with Novel Traits". I... | New Breeding Techniques | 0.828041 |
4,483 | The United States Department of Agriculture is responsible for determining whether food products derived from NBTs should be regulated, and this is undertaken on a case-by-case manner under the US Plant Protection Act. As of 2015 there was no specific policy towards NBTs, although in the summer of that year the White H... | New Breeding Techniques | 0.828041 |
4,484 | The Organization for Economic Cooperation and Development (OECD) has its own 'Working Group on Harmonization of Regulatory Oversight in Biotechnology' but, as at 2015, there had been virtually no progress in addressing issues around NBTs, and this includes many major food-producing countries like Russia, South Africa, ... | New Breeding Techniques | 0.828041 |
4,485 | Algebraic K-theory is related to the group of invertible matrices with coefficients the given field. For example, the process of taking the determinant of an invertible matrix leads to an isomorphism K1(F) = F×. Matsumoto's theorem shows that K2(F) agrees with K2M(F). In higher degrees, K-theory diverges from Milnor K-... | Field (algebra) | 0.828035 |
4,486 | Milnor K-theory is defined as K n M ( F ) = F × ⊗ ⋯ ⊗ F × / ⟨ x ⊗ ( 1 − x ) ∣ x ∈ F ∖ { 0 , 1 } ⟩ . {\displaystyle K_{n}^{M}(F)=F^{\times }\otimes \cdots \otimes F^{\times }/\left\langle x\otimes (1-x)\mid x\in F\setminus \{0,1\}\right\rangle .} The norm residue isomorphism theorem, proved around 2000 by Vladimir Voevo... | Field (algebra) | 0.828035 |
4,487 | Among other results, this theory shows that angle trisection and squaring the circle cannot be done with a compass and straightedge. Moreover, it shows that quintic equations are, in general, algebraically unsolvable. Fields serve as foundational notions in several mathematical domains. | Field (algebra) | 0.828035 |
4,488 | In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The... | Field (algebra) | 0.828035 |
4,489 | This includes different branches of mathematical analysis, which are based on fields with additional structure. Basic theorems in analysis hinge on the structural properties of the field of real numbers. Most importantly for algebraic purposes, any field may be used as the scalars for a vector space, which is the stand... | Field (algebra) | 0.828035 |
4,490 | It was launched on 2 November 2009, with the Rockot launch system together with ESA's SMOS mission. The platform was launched in a sun-synchronous low Earth orbit (altitude of 725 km).PROBA-2 contains five scientific instruments. Two of them are designated to observe the Sun: "The Sun Watcher using APS and Image Proces... | PROBA-2 | 0.828018 |
4,491 | Probability amplitude Statistical physics Boltzmann factor Feynman–Kac formula Fluctuation theorem Information entropy Vacuum expectation value Cosmic variance Negative probability Gibbs state Master equation Partition function (mathematics) Quantum probability | List of statistical mechanics articles | 0.828012 |
4,492 | Quantum electrodynamics (QED) is perhaps the most stringently tested theory in physics, with highly nontrivial predictions verified to an accuracy better than 10 parts per billion: See precision tests of QED. Since Maxwell's equations can be derived as the classical limit of the equations of QED, it follows that if QED... | Weber electrodynamics | 0.828008 |
4,493 | A partition of a set X is any collection of mutually disjoint non-empty sets whose union is X. Every partition can equivalently be described by an equivalence relation, a binary relation that describes whether two elements belong to the same set in the partition.Disjoint-set data structures and partition refinement are... | Disjoint sets | 0.828004 |
4,494 | In physics, the field effect refers to the modulation of the electrical conductivity of a material by the application of an external electric field. In a metal, the electron density that responds to applied fields is so large that an external electric field can penetrate only a very short distance into the material. Ho... | Field effect (semiconductor) | 0.827983 |
4,495 | Little further research in machine translation was conducted in America (though some research continued elsewhere, such as Japan and Europe) until the late 1980s when the first statistical machine translation systems were developed. 1960s: Some notably successful natural language processing systems developed in the 196... | Natural language recognition | 0.827974 |
4,496 | Symbolic approach, i.e., the hand-coding of a set of rules for manipulating symbols, coupled with a dictionary lookup, was historically the first approach used both by AI in general and by NLP in particular: such as by writing grammars or devising heuristic rules for stemming. Machine learning approaches, which include... | Natural language recognition | 0.827974 |
4,497 | In physics, a dynamical system is said to be mixing if the phase space of the system becomes strongly intertwined, according to at least one of several mathematical definitions. For example, a measure-preserving transformation T is said to be strong mixing if lim k → ∞ μ ( T − k A ∩ B ) = μ ( A ) ⋅ μ ( B ) {\displaysty... | Mixing (physics) | 0.827972 |
4,498 | If the points are obstacles, then the edges of the graph will be the routes furthest from obstacles (and theoretically any collisions). In machine learning, Voronoi diagrams are used to do 1-NN classifications. In global scene reconstruction, including with random sensor sites and unsteady wake flow, geophysical data, ... | Voronoi diagrams | 0.827965 |
4,499 | In networking, Voronoi diagrams can be used in derivations of the capacity of a wireless network. In computer graphics, Voronoi diagrams are used to calculate 3D shattering / fracturing geometry patterns. It is also used to procedurally generate organic or lava-looking textures. In autonomous robot navigation, Voronoi ... | Voronoi diagrams | 0.827965 |
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