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24,000 | For example, a rule may produce the special symbol δ, in which case the membrane that contains it is dissolved and all its contents move up in the region hierarchy. The variety of suggestions from biology and the range of possibilities to define the architecture and the functioning of a membrane-based multiset processi... | Membrane computing | 0.808473 |
24,001 | The intuition behind the notion of a membrane is a three-dimensional vesicle from biology. However the concept itself is more general, and a membrane is seen as a separator of two regions. The membrane provides for selective communication between the two regions. | Membrane computing | 0.808473 |
24,002 | Membrane computing (or MC) is an area within computer science that seeks to discover new computational models from the study of biological cells, particularly of the cellular membranes. It is a sub-task of creating a cellular model. Membrane computing deals with distributed and parallel computing models, processing mul... | Membrane computing | 0.808473 |
24,003 | This example is extremely simple, although complications are already apparent. More likely it will be a case of many procedures, having a variety of deducible or programmer-declared properties that may enable the compiler's optimizations to find some advantage. Any parameter to a procedure might be read only, be writte... | Link-time optimization | 0.808471 |
24,004 | GCC and Clang perform IPO by default at optimization level 2. However, the degree of optimization is limited when LTO is disabled, as IPO can only happen within an object file and non-static functions can never be eliminated. The latter problem has a non-LTO solution: the -fwhole-program switch can be used to assume th... | Link-time optimization | 0.808471 |
24,005 | The Intel C/C++ compilers allow whole-program IPO. The flag to enable interprocedural optimizations for a single file is -ip, the flag to enable interprocedural optimization across all files in the program is -ipo.The MSVC compiler, integrated into Visual Studio, also supports interprocedural optimization on the whole ... | Link-time optimization | 0.808471 |
24,006 | For example, suppose one started with 0 and added 0.3 to that one hundred times while rounding the running total between every addition. The result would be 0 with regular rounding, but with stochastic rounding, the expected result would be 30, which is the same value obtained without rounding. This can be useful in ma... | Nearest integer function | 0.808471 |
24,007 | Positron plasmas are also used in atomic physics experiments that study the interaction of antimatter with neutral atoms and molecules. Cryogenic pure ion plasmas have been used in studies of strongly coupled plasmas and quantum entanglement. More prosaically, pure electron plasmas are used to produce the microwaves in... | Non-neutral plasma | 0.808466 |
24,008 | Simplex algorithm of George Dantzig, designed for linear programming Extensions of the simplex algorithm, designed for quadratic programming and for linear-fractional programming Variants of the simplex algorithm that are especially suited for network optimization Combinatorial algorithms Quantum optimization algorithm... | Optimization theory | 0.808465 |
24,009 | One of Fermat's theorems states that optima of unconstrained problems are found at stationary points, where the first derivative or the gradient of the objective function is zero (see first derivative test). More generally, they may be found at critical points, where the first derivative or gradient of the objective fu... | Optimization theory | 0.808465 |
24,010 | 685–698, 1940 (in Italian). Darlington, Sidney, "Synthesis of reactance 4-poles which produce prescribed insertion loss characteristics: Including special applications to filter design", MIT Journal of Mathematics and Physics, vol. 18, pp. | Foster synthesis | 0.808464 |
24,011 | Brune, Otto, "Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency", MIT Journal of Mathematics and Physics, vol. 10, pp. 191–236, April 1931. | Foster synthesis | 0.808464 |
24,012 | Bott, Raoul; Duffin, Richard, "Impedance synthesis without use of transformers", Journal of Applied Physics, vol. 20, iss. 8, p. | Foster synthesis | 0.808464 |
24,013 | Network synthesis has historically been concerned with synthesising passive networks, but is not limited to such circuits. The field was founded by Wilhelm Cauer after reading Ronald M. Foster's 1924 paper A reactance theorem. Foster's theorem provided a method of synthesising LC circuits with arbitrary number of eleme... | Foster synthesis | 0.808464 |
24,014 | The first example of this kind of synthesis is due to Stephen Butterworth in 1930. The Butterworth filter he produced became a classic of filter design, but more frequently implemented with purely passive rather than active components. More generally applicable designs of this kind include the Sallen–Key topology due t... | Foster synthesis | 0.808464 |
24,015 | Then we have a ring isomorphism, σ: F q / ( f ( x ) ) → ∏ i F q / ( f i ( x ) ) {\textstyle \sigma :\mathbb {F} _{q}/(f(x))\to \prod _{i}\mathbb {F} _{q}/(f_{i}(x))} , given by the Chinese remainder theorem. The crucial observation is that the Frobenius automorphism x → x p {\textstyle x\to x^{p}} commutes with σ {\t... | Berlekamp's algorithm | 0.808459 |
24,016 | With some abstract algebra, the idea behind Berlekamp's algorithm becomes conceptually clear. We represent a finite field F q {\textstyle \mathbb {F} _{q}} , where q = p m {\textstyle q=p^{m}} for some prime p {\textstyle p} , as F p / ( g ( y ) ) {\textstyle \mathbb {F} _{p}/(g(y))} . We can assume that f ( x ) ∈ F q... | Berlekamp's algorithm | 0.808459 |
24,017 | By computing the matrix Q − I {\displaystyle {\mathcal {Q}}-I} and reducing it to reduced row echelon form and then easily reading off a basis for the null space, we may find a basis for the Berlekamp subalgebra and hence construct polynomials g ( x ) {\displaystyle g(x)} in it. We then need to successively compute GCD... | Berlekamp's algorithm | 0.808459 |
24,018 | {\displaystyle x^{iq}\equiv q_{i,n-1}x^{n-1}+q_{i,n-2}x^{n-2}+\ldots +q_{i,0}{\pmod {f(x)}}.\,} With a certain polynomial g ( x ) ∈ R {\displaystyle g(x)\in R} , say: g ( x ) = g n − 1 x n − 1 + g n − 2 x n − 2 + … + g 0 , {\displaystyle g(x)=g_{n-1}x^{n-1}+g_{n-2}x^{n-2}+\ldots +g_{0},\,} we may associate the row vect... | Berlekamp's algorithm | 0.808459 |
24,019 | Berlekamp's algorithm finds polynomials g ( x ) {\displaystyle g(x)} suitable for use with the above result by computing a basis for the Berlekamp subalgebra. This is achieved via the observation that Berlekamp subalgebra is in fact the kernel of a certain n × n {\displaystyle n\times n} matrix over F q {\displaystyle ... | Berlekamp's algorithm | 0.808459 |
24,020 | The Berlekamp subalgebra is of interest because the polynomials g ( x ) {\displaystyle g(x)} it contains satisfy f ( x ) = ∏ s ∈ F q gcd ( f ( x ) , g ( x ) − s ) . {\displaystyle f(x)=\prod _{s\in \mathbb {F} _{q}}\gcd(f(x),g(x)-s).} In general, not every GCD in the above product will be a non-trivial factor of f ( x ... | Berlekamp's algorithm | 0.808459 |
24,021 | {\displaystyle R={\frac {\mathbb {F} _{q}}{\langle f(x)\rangle }}.} The algorithm focuses on polynomials g ( x ) ∈ R {\displaystyle g(x)\in R} which satisfy the congruence: g ( x ) q ≡ g ( x ) ( mod f ( x ) ) . {\displaystyle g(x)^{q}\equiv g(x){\pmod {f(x)}}.\,} These polynomials form a subalgebra of R (which can be c... | Berlekamp's algorithm | 0.808459 |
24,022 | One important application of Berlekamp's algorithm is in computing discrete logarithms over finite fields F p n {\displaystyle \mathbb {F} _{p^{n}}} , where p {\displaystyle p} is prime and n ≥ 2 {\displaystyle n\geq 2} . Computing discrete logarithms is an important problem in public key cryptography and error-control... | Berlekamp's algorithm | 0.808459 |
24,023 | In mathematics, particularly computational algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields). The algorithm consists mainly of matrix reduction and polynomial GCD computations. It was invented by Elwyn Berlekamp in 1967. It was the dominant ... | Berlekamp's algorithm | 0.808459 |
24,024 | The following is known as Bing's metrization theorem: A space X is metrizable iff it is regular and has a basis that is countably locally discrete. 5. A countable collection of sets is necessarily countably locally discrete. Therefore, if X is a metrizable space with a countable basis, one implication of Bing's metriza... | Locally discrete collection | 0.808459 |
24,025 | In mathematics, particularly topology, collections of subsets are said to be locally discrete if they look like they have precisely one element from a local point of view. The study of locally discrete collections is worthwhile as Bing's metrization theorem shows. | Locally discrete collection | 0.808459 |
24,026 | That includes, but is not limited to, biomicroscopy (where light is used to irradiate and observe microbes, cells, and molecules), quantum optics, and optomechanics (where light is used to probe and control objects like atoms, qubits and macroscopic quantum objects). Direct applications of the radiation pressure force ... | Light pressure | 0.808453 |
24,027 | The result is known as the Gauss–Wantzel theorem: A regular n-gon can be constructed with compass and straightedge if and only if n is a power of 2 or the product of a power of 2 and any number of distinct Fermat primes.A Fermat prime is a prime number of the form 2 ( 2 m ) + 1. {\displaystyle 2^{(2^{m})}+1.} In order ... | Constructible polygon | 0.808452 |
24,028 | In the specific case of a regular n-gon, the question reduces to the question of constructing a length cos 2π/n ,which is a trigonometric number and hence an algebraic number. This number lies in the n-th cyclotomic field — and in fact in its real subfield, which is a totally real field and a rational vector space of d... | Constructible polygon | 0.808452 |
24,029 | In the light of later work on Galois theory, the principles of these proofs have been clarified. It is straightforward to show from analytic geometry that constructible lengths must come from base lengths by the solution of some sequence of quadratic equations. In terms of field theory, such lengths must be contained i... | Constructible polygon | 0.808452 |
24,030 | Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than purposive (quota) sampling.Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of ... | Statistical Sciences | 0.808451 |
24,031 | He also coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation". In his 1930 book The Genetical Theory of Natural Selection, he applied statistics to various biological concepts such as Fisher's principle... | Statistical Sciences | 0.808451 |
24,032 | Galton and Pearson founded Biometrika as the first journal of mathematical statistics and biostatistics (then called biometry), and the latter founded the world's first university statistics department at University College London.The second wave of the 1910s and 20s was initiated by William Sealy Gosset, and reached i... | Statistical Sciences | 0.808451 |
24,033 | The first wave, at the turn of the century, was led by the work of Francis Galton and Karl Pearson, who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well. Galton's contributions included introducing the concepts of standard deviat... | Statistical Sciences | 0.808451 |
24,034 | This was the first book where the realm of games of chance and the realm of the probable (which concerned opinion, evidence, and argument) were combined and submitted to mathematical analysis. The method of least squares was first described by Adrien-Marie Legendre in 1805, though Carl Friedrich Gauss presumably made u... | Statistical Sciences | 0.808451 |
24,035 | Today, statistics is widely employed in government, business, and natural and social sciences. The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens. Although the idea of pro... | Statistical Sciences | 0.808451 |
24,036 | The earliest writing containing statistics in Europe dates back to 1663, with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt. Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its stat- ... | Statistical Sciences | 0.808451 |
24,037 | Either the true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to... | Statistical Sciences | 0.808451 |
24,038 | Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory. | Statistical Sciences | 0.808451 |
24,039 | The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced ... | Zero-one loss function | 0.80845 |
24,040 | In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a ... | Zero-one loss function | 0.80845 |
24,041 | Unparticle physics has been proposed as an explanation for anomalies in superconducting cuprate materials, where the charge measured by ARPES appears to exceed predictions from Luttinger's theorem for the quantity of electrons. | Unparticle physics | 0.808448 |
24,042 | The idea of unparticles comes from conjecturing that there may be "stuff" that does not necessarily have zero mass but is still scale-invariant, with the same physics regardless of a change of length (or equivalently energy). This stuff is unlike particles, and described as unparticle. The unparticle stuff is equivalen... | Unparticle physics | 0.808448 |
24,043 | All particles exist in states that may be characterized by a certain energy, momentum and mass. In most of the Standard Model of particle physics, particles of the same type cannot exist in another state with all these properties scaled up or down by a common factor – electrons, for example, always have the same mass r... | Unparticle physics | 0.808448 |
24,044 | In theoretical physics, unparticle physics is a speculative theory that conjectures a form of matter that cannot be explained in terms of particles using the Standard Model of particle physics, because its components are scale invariant. Howard Georgi proposed this theory in two 2007 papers, "Unparticle Physics" and "A... | Unparticle physics | 0.808448 |
24,045 | Macrocycles are often described as molecules and ions containing a ring of twelve or more atoms. Classical examples include the crown ethers, calixarenes, porphyrins, and cyclodextrins. Macrocycles describe a large, mature area of chemistry. | Macrocyclic compounds | 0.808448 |
24,046 | Experience shows that anything on a smaller scale (such as 'millimeter' paper) is practically worthless in the hands of beginners. "The term "graph paper" did not catch on quickly in American usage. A School Arithmetic (1919) by H. S. Hall and F. H. Stevens had a chapter on graphing with "squared paper". Analytic Geome... | Coordinate paper | 0.808447 |
24,047 | The Metropolitan Museum of Art owns a pattern book dated to around 1596 in which each page bears a grid printed with a woodblock. The owner has used these grids to create block pictures in black and white and in colour.The first commercially published "coordinate paper" is usually attributed to a Dr. Buxton of England,... | Coordinate paper | 0.808447 |
24,048 | Health physics is also known as radiation safety or radiation protection. Health physics is the applied physics of radiation protection for health and health care purposes. It is the science concerned with the recognition, evaluation, and control of health hazards to permit the safe use and application of ionizing radi... | Medical physics | 0.808446 |
24,049 | The International Organization for Medical Physics (IOMP) recognizes main areas of medical physics employment and focus. | Medical physics | 0.808446 |
24,050 | Some education institutions house departments or programs bearing the title "medical biophysics" or "biomedical physics" or "applied physics in medicine". Generally, these fall into one of two categories: interdisciplinary departments that house biophysics, radiobiology, and medical physics under a single umbrella; and... | Medical physics | 0.808446 |
24,051 | Some aspects of non-ionising radiation physics may be considered under radiation protection or diagnostic imaging physics. Imaging modalities include MRI, optical imaging and ultrasound. Safety considerations include these areas and lasers Lasers and applications in medicine | Medical physics | 0.808446 |
24,052 | Expert consultancy: Provision of expert advice to outside clients (e.g., clinics with no in-house medical physics expertise). Education of healthcare professionals (including medical physics trainees: Contributing to quality healthcare professional education through knowledge transfer activities concerning the technica... | Medical physics | 0.808446 |
24,053 | Testing to be based on current recommended techniques and protocols. Clinical involvement: Carrying out, participating in and supervising everyday radiation protection and quality control procedures to ensure ongoing effective and optimised use of medical radiological devices and including patient specific optimization... | Medical physics | 0.808446 |
24,054 | In hospital medical physics departments, the mission statement for medical physicists as adopted by the European Federation of Organisations for Medical Physics (EFOMP) is the following: "Medical Physicists will contribute to maintaining and improving the quality, safety and cost-effectiveness of healthcare services th... | Medical physics | 0.808446 |
24,055 | Medical imaging physics is also known as diagnostic and interventional radiology physics. Clinical (both "in-house" and "consulting") physicists typically deal with areas of testing, optimization, and quality assurance of diagnostic radiology physics areas such as radiographic X-rays, fluoroscopy, mammography, angiogra... | Medical physics | 0.808446 |
24,056 | ICRU: International Commission on Radiation Units and Measurements ICRP: International Commission on Radiological Protection NCRP: National Council on Radiation Protection & Measurements NRC: Nuclear Regulatory Commission FDA: Food and Drug Administration IAEA: International Atomic Energy Agency AMPI: Association of Me... | Medical physics | 0.808446 |
24,057 | In the more fundamental field the organisms are studied as the subject itself on a deeper (theoretical) level. Applied microbiology refers to the fields where the micro-organisms are applied in certain processes such as brewing or fermentation. The organisms itself are often not studied as such, but applied to sustain ... | Branches of microbiology | 0.808446 |
24,058 | Aeromicrobiology (or air microbiology): The study of airborne microorganisms. Biotechnology: related to recombinant DNA technology or genetic engineering. == References == | Branches of microbiology | 0.808446 |
24,059 | This involves the characterization of key bacterial habitats such as the rhizosphere and phyllosphere, soil and groundwater ecosystems, open oceans or extreme environments (extremophiles). This field includes other branches of microbiology such as: Microbial ecology Microbially mediated nutrient cycling Geomicrobiology... | Branches of microbiology | 0.808446 |
24,060 | Soil microbiology: the study of those microorganisms that are found in soil. Veterinary microbiology: the study of the role of microbes in veterinary medicine or animal taxonomy. Environmental microbiology: the study of the function and diversity of microbes in their natural environments. | Branches of microbiology | 0.808446 |
24,061 | Using microorganisms to produce foods, for example by fermentation. Agricultural microbiology: the study of agriculturally relevant microorganisms. This field can be further classified into the following: Plant microbiology and Plant pathology: The study of the interactions between microorganisms and plants and plant p... | Branches of microbiology | 0.808446 |
24,062 | This field also includes brewing, an important application of microbiology. Microbial biotechnology: the manipulation of microorganisms at the genetic and molecular level to generate useful products. Food microbiology: the study of microorganisms causing food spoilage and foodborne illness. | Branches of microbiology | 0.808446 |
24,063 | Industrial microbiology: the exploitation of microbes for use in industrial processes. Examples include industrial fermentation and wastewater treatment. Closely linked to the biotechnology industry. | Branches of microbiology | 0.808446 |
24,064 | Medical microbiology: the study of the pathogenic microbes and the role of microbes in human illness. Includes the study of microbial pathogenesis and epidemiology and is related to the study of disease pathology and immunology. This area of microbiology also covers the study of human microbiota, cancer, and the tumor ... | Branches of microbiology | 0.808446 |
24,065 | Astro microbiology: the study of microorganisms in outer space Biological agent: the study of those microorganisms which are being used in weapon industries. Nano microbiology: the study of those microscopic organisms on nano level. Predictive microbiology: the quantification of relations between controlling factors in... | Branches of microbiology | 0.808445 |
24,066 | The branches of microbiology can be classified into pure and applied sciences. Microbiology can be also classified based on taxonomy, in the cases of bacteriology, mycology, protozoology, and phycology. There is considerable overlap between the specific branches of microbiology with each other and with other discipline... | Branches of microbiology | 0.808445 |
24,067 | In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as the gravitational force field excerted on another massive body. It has dimens... | Newtonian gravitational field | 0.808445 |
24,068 | As noted above, the Lie bracket of two Killing fields is still a Killing field. The Killing fields on a manifold M {\displaystyle M} thus form a Lie subalgebra g {\displaystyle {\mathfrak {g}}} of all vector fields on M . {\displaystyle M.} Selecting a point p ∈ M , {\displaystyle p\in M~,} the algebra g {\displaystyle... | Killing vectors | 0.808439 |
24,069 | Killing fields are used to discuss isometries in general relativity (in which the geometry of spacetime as distorted by gravitational fields is viewed as a 4-dimensional pseudo-Riemannian manifold). In a static configuration, in which nothing changes with time, the time vector will be a Killing vector, and thus the Kil... | Killing vectors | 0.808439 |
24,070 | In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product: The radical plays a central role in the statement of the abc conjecture. | Radical of an integer | 0.808436 |
24,071 | An alternative definition based on the notion of a metric space aimed at its subspace was described by Holsztyński (1968), who proved that the injective envelope of a Banach space, in the category of Banach spaces, coincides (after forgetting the linear structure) with the tight span. This theorem allows to reduce cert... | Hyperconvex hull | 0.808434 |
24,072 | {\displaystyle f=e_{a}.} ) (X,d) is hyperbolic if and only if (T(X),δ) is hyperbolic. : Theorem 5.3 | Hyperconvex hull | 0.808434 |
24,073 | : Proposition 4.6.3 (Proof: The extreme-value theorem implies that d, being continuous as a function X × X → R , {\displaystyle X\times X\to \mathbb {R} ,} is bounded, so (see previous bullet) T ( X ) ⊆ { f ∈ C ( X ): ‖ f ‖ ∞ ≤ ‖ d ‖ ∞ } {\displaystyle T(X)\subseteq \{f\in C(X):\|f\|_{\infty }\leq \|d\|_{\infty }\}} is... | Hyperconvex hull | 0.808434 |
24,074 | In metric geometry, the metric envelope or tight span of a metric space M is an injective metric space into which M can be embedded. In some sense it consists of all points "between" the points of M, analogous to the convex hull of a point set in a Euclidean space. The tight span is also sometimes known as the injectiv... | Hyperconvex hull | 0.808434 |
24,075 | Neoglycorandomization is a chemoselective glycodiversification method inspired by the alkoxyamine-based ‘neoglycosylation’ reaction first described Peri and Dumy. This reaction proceeds via an oxy-iminium intermediate to ultimately provide the more thermodynamically-favored closed ring neoglycoside. The neoglycosylatio... | Glycorandomization | 0.808434 |
24,076 | Both chemoenzymatic glycorandomization and neoglycorandomization use free reducing sugars and unprotected aglycons and are thereby a notable advance over classical glycosylation methods. A notable advantage of the enzymatic approach is the use of the corresponding genes encoding for the permissive kinases, nucleotidylt... | Glycorandomization | 0.808434 |
24,077 | Population genetics models are used to infer which genes are undergoing selection. One common approach is to look for regions of high linkage disequilibrium and low genetic variance along the chromosome, to detect recent selective sweeps. A second common approach is the McDonald–Kreitman test which compares the amount ... | Population biologist | 0.808431 |
24,078 | Linear programming problems are optimization problems in which the objective function and the constraints are all linear. In the primal problem, the objective function is a linear combination of n variables. There are m constraints, each of which places an upper bound on a linear combination of the n variables. The goa... | Primal problem | 0.80843 |
24,079 | The duality gap is the difference between the values of any primal solutions and any dual solutions. If d ∗ {\displaystyle d^{*}} is the optimal dual value and p ∗ {\displaystyle p^{*}} is the optimal primal value, then the duality gap is equal to p ∗ − d ∗ {\displaystyle p^{*}-d^{*}} . This value is always greater tha... | Primal problem | 0.80843 |
24,080 | Modern evidence suggests that early cellular evolution occurred in a biological realm radically distinct from modern biology. It is thought that in this ancient realm, the current genetic role of DNA was largely filled by RNA, and catalysis was also largely mediated by RNA (that is, by ribozyme counterparts of enzymes)... | Evolution of cells | 0.808427 |
24,081 | Steiner tree problems in graphs are applied to various problems in research and industry, including multicast routing and bioinformatics.A special case of this problem is when G is a complete graph, each vertex v ∈ V corresponds to a point in a metric space, and the edge weights w(e) for each e ∈ E correspond to distan... | Steiner tree problem | 0.808426 |
24,082 | Steiner trees have been extensively studied in the context of weighted graphs. The prototype is, arguably, the Steiner tree problem in graphs. Let G = (V, E) be an undirected graph with non-negative edge weights c and let S ⊆ V be a subset of vertices, called terminals. A Steiner tree is a tree in G that spans S. There... | Steiner tree problem | 0.808426 |
24,083 | A race, in the biology sense, is a less clearly distinguishable wild population within a species or subspecies, separated by environment, geography, or genetics. Landraces, and mongrel (including most feral) populations, are never capitalized except where a proper name occurs. | Wikipedia:Manual of Style/Organisms | 0.808426 |
24,084 | This taxonomic authority string –as in Felis catus Linnaeus, 1758 – is almost never needed outside of biology articles, and need not be repeated within one. Cases where this information is useful include: At first occurrence in the biological article about that taxon; this is usually done in the taxobox, for the accept... | Wikipedia:Manual of Style/Organisms | 0.808426 |
24,085 | Although findings from traditional ethnologic studies have been used to buttress DIT arguments, thus far there have been little ethnographic fieldwork designed to explicitly test these hypotheses.Herb Gintis has named DIT one of the two major conceptual theories with potential for unifying the behavioral sciences, incl... | Gene–culture coevolution | 0.808425 |
24,086 | Controversy surrounding Wilson's sociobiological theories may also have decreased the lasting effect of this book.The second 1981 book was Cavalli-Sforza and Feldman's Cultural Transmission and Evolution: A Quantitative Approach. Borrowing heavily from population genetics and epidemiology, this book built a mathematica... | Gene–culture coevolution | 0.808425 |
24,087 | In probability and statistics, a moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positio... | Moment measure | 0.808425 |
24,088 | Atomtronics is a form of computing that involves the use of ultra-cold atoms in coherent matter-wave circuits, which can have components similar to those found in electronic or optical systems. These circuits have potential applications in several fields, including fundamental physics research and the development of pr... | Unconventional computing | 0.808424 |
24,089 | Superconducting computing is a form of cryogenic computing that utilizes the unique properties of superconductors, including zero resistance wires and ultrafast switching, to encode, process, and transport data using single flux quanta. It is often used in quantum computing and requires cooling to cryogenic temperature... | Unconventional computing | 0.808424 |
24,090 | Reservoir computing is a computational framework derived from recurrent neural network theory that involves mapping input signals into higher dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir. The reservoir, which can be virtual or physical, is made up of individual ... | Unconventional computing | 0.808424 |
24,091 | The general theory of computation allows for a variety of models. Computing technology first developed using mechanical systems and then evolved into the use of electronic devices. Other fields of modern physics provide additional avenues for development. | Unconventional computing | 0.808424 |
24,092 | DNA computing is a branch of unconventional computing that uses DNA and molecular biology hardware to perform calculations. It is a form of parallel computing that can solve certain specialized problems faster and more efficiently than traditional electronic computers. While DNA computing does not provide any new capab... | Unconventional computing | 0.808424 |
24,093 | Cellular automata are discrete models of computation consisting of a grid of cells in a finite number of states, such as on and off. The state of each cell is determined by a fixed rule based on the states of the cell and its neighbors. There are four primary classifications of cellular automata, ranging from patterns ... | Unconventional computing | 0.808424 |
24,094 | The notion of quasirandom groups arises when considering subsets of groups for which no two elements in the subset have a product in the subset; such subsets are termed product-free. László Babai and Vera Sós asked about the existence of a constant c {\displaystyle c} for which every finite group G {\displaystyle G} wi... | Quasirandom group | 0.808422 |
24,095 | In mathematics, a quasirandom group is a group that does not contain a large product-free subset. Such groups are precisely those without a small non-trivial irreducible representation. The namesake of these groups stems from their connection to graph theory: bipartite Cayley graphs over any subset of a quasirandom gro... | Quasirandom group | 0.808422 |
24,096 | This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, then factorization into primes would not be unique; for example, 2 = 2 ⋅ 1 = 2 ⋅ 1 ⋅ 1 = … {\displaystyle 2=2\cdot 1=2\cdot 1\cdot 1=\ldots } The theorem generalizes to other algebraic structures that are called unique fact... | Fundamental Theorem of Arithmetic | 0.808422 |
24,097 | In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. For example, 1200 = 2 4 ⋅ 3 1 ⋅ 5 2 = ( 2 ⋅ 2 ⋅ 2 ⋅ 2 )... | Fundamental Theorem of Arithmetic | 0.808422 |
24,098 | The fundamental theorem of arithmetic can also be proved without using Euclid's lemma. The proof that follows is inspired by Euclid's original version of the Euclidean algorithm. Assume that s {\displaystyle s} is the smallest positive integer which is the product of prime numbers in two different ways. | Fundamental Theorem of Arithmetic | 0.808422 |
24,099 | Its molecular geometry is tetrahedral. Its specific heat capacity (Cp) is 38.171 J·mol−1·K−1 at 25 °C. The critical point of fluoromethane is at 44.9 °C (318.1 K) and 6.280 MPa. | CH3F | 0.80842 |
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