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24,100 | A karyotype is the characteristic chromosome complement of a eukaryote species. The preparation and study of karyotypes is part of cytology and, more specifically, cytogenetics. Although the replication and transcription of DNA is highly standardized in eukaryotes, the same cannot be said for their karyotypes, which ar... | Genome duplication | 0.808417 |
24,101 | In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube. There are 6 unique cantellation for the 5-cube, including truncations. Half of them are more easily constructed from the dual 5-orthoplex | Cantitruncated 5-cube | 0.808415 |
24,102 | Topics covered by the chapters in the book include the Leibniz formula for π, configurations of points and lines with equally many points on each line and equally many lines through each point, curvature and non-Euclidean geometry, mechanical linkages, the classification of manifolds by their Euler characteristic, and ... | Geometry and the Imagination | 0.808415 |
24,103 | Geometry and the Imagination is the English translation of the 1932 book Anschauliche Geometrie by David Hilbert and Stefan Cohn-Vossen.The book was based on a series of lectures Hilbert made in the winter of 1920–21. The book is an attempt to present some then-current mathematical thought to "contribute to a more just... | Geometry and the Imagination | 0.808415 |
24,104 | The Mathematical Association of America said about the book, "this book is a masterpiece — a delightful classic that should never go out of print". Physics Today called it "a readable exposition of modern geometry and its relation to other branches of mathematics". The Scientific Monthly said about it "has been a class... | Geometry and the Imagination | 0.808415 |
24,105 | In the original article, k objects (studies) are combined k-1 at a time (jackknife estimation), resulting in k estimates. It is observed that this is a special case of the more general approach of CMA which computes results for k studies taken 1, 2, 3 ... k − 1, k at a time. Where it is computationally feasible to obta... | Combinatorial meta-analysis | 0.808415 |
24,106 | Independent research conducted by Antibody Solutions and published or presented at scientific conferences include the following: Generation of Neutralizing Human Monoclonal Antibodies Against a Therapeutic Target from the Alloy Therapeutics Mouse Generation Using a Molecular Modeling Platform to Guide Therapeutic Antib... | Antibody Solutions | 0.808411 |
24,107 | In population genetics, the four-gamete test is a method for detecting historical recombination events. | Four-gamete test | 0.80841 |
24,108 | Religion: the Four Noble Truths in Buddhism. Biology: 7 ± 2, in cognitive science, George A. Miller's estimate of the number of objects that can be simultaneously held in human working memory. Music: 7 notes in a major or minor scale. | Orders of magnitude (numbers) | 0.808406 |
24,109 | Linguistics: Estimates for the linguistic diversity of living human languages or dialects range between 5,000 and 10,000. (SIL Ethnologue in 2009 listed 6,909 known living languages.) Astronomy – Catalogues: There are 7,840 deep-sky objects in the NGC Catalogue from 1888. Lexicography: 8,674 unique words in the Hebrew ... | Orders of magnitude (numbers) | 0.808406 |
24,110 | Terrorism: 2,996 persons (including 19 terrorists) died in the terrorist attacks of September 11, 2001. Biology: the DNA of the simplest viruses has 3,000 base pairs. Military history: 4,200 (Republic) or 5,200 (Empire) was the standard size of a Roman legion. | Orders of magnitude (numbers) | 0.808406 |
24,111 | Language: There are 20,000–40,000 distinct Chinese characters in more than occasional use. Biology: Each human being is estimated to have 20,000 coding genes. Grammar: Each regular verb in Cherokee can have 21,262 inflected forms. | Orders of magnitude (numbers) | 0.808406 |
24,112 | (10000; ten thousand or a myriad) Biology: Each neuron in the human brain is estimated to connect to 10,000 others. Demography: The population of Tuvalu was 10,544 in 2007. Lexicography: 14,500 unique English words occur in the King James Version of the Bible. Zoology: There are approximately 17,500 distinct butterfly ... | Orders of magnitude (numbers) | 0.808406 |
24,113 | Mathematics: 360,000 – The approximate number of entries in The On-Line Encyclopedia of Integer Sequences as of January 2023. Biology – Plants: There are approximately 390,000 distinct plant species known, of which approximately 20% (or 78,000) are in risk of extinction. Biology – Flowers: There are approximately 400,0... | Orders of magnitude (numbers) | 0.808406 |
24,114 | (100000; one hundred thousand or a lakh). Demography: The population of Saint Vincent and the Grenadines was 100,982 in 2009. Biology – Strands of hair on a head: The average human head has about 100,000–150,000 strands of hair. | Orders of magnitude (numbers) | 0.808406 |
24,115 | Demography: The population of the United States was 328,239,523 in 2019. Mathematics: 358,833,097 stellations of the rhombic triacontahedron. Info – Web sites: As of November 2011, the Netcraft web survey estimates that there are 525,998,433 (526 million) distinct websites. Astronomy – Cataloged stars: The Guide Star C... | Orders of magnitude (numbers) | 0.808406 |
24,116 | (10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard) Mathematics: There are 157 152 858 401 024 063 281 013 959 519 483 771 508 510 790 313 968 742 344 694 684 829 502 629 88... | Orders of magnitude (numbers) | 0.808406 |
24,117 | (0.000000000001; 1000−4; short scale: one trillionth; long scale: one billionth) ISO: pico- (p) Mathematics: The probability in a game of bridge of one player getting a complete suit is approximately 2.52×10−11 (0.00000000252%). Biology: Human visual sensitivity to 1000 nm light is approximately 1.0×10−10 of its peak s... | Orders of magnitude (numbers) | 0.808406 |
24,118 | Astronomy: 8 planets in the Solar System. Religion: the Noble Eightfold Path in Buddhism. Literature: 9 circles of Hell in the Inferno by Dante Alighieri. | Orders of magnitude (numbers) | 0.808406 |
24,119 | (10000000000; short scale: ten billion; long scale: ten thousand million, or ten milliard) Biology – bacteria in the human body: There are roughly 1010 bacteria in the human mouth. Computing – web pages: approximately 5.6×1010 web pages indexed by Google as of 2010. | Orders of magnitude (numbers) | 0.808406 |
24,120 | Science Fiction: In Isaac Asimov's Galactic Empire, in what we call 22,500 CE, there are 25,000,000 different inhabited planets in the Galactic Empire, all inhabited by humans in Asimov's "human galaxy" scenario, each with an average population of 2,000,000,000, thus yielding a total Galactic Empire population of appro... | Orders of magnitude (numbers) | 0.808406 |
24,121 | (1000000000000000; 10005; short scale: one quadrillion; long scale: one thousand billion, or one billiard) ISO: peta- (P) Biology – Insects: 1,000,000,000,000,000 to 10,000,000,000,000,000 (1015 to 1016) – The estimated total number of ants on Earth alive at any one time (their biomass is approximately equal to the tot... | Orders of magnitude (numbers) | 0.808406 |
24,122 | Mathematics – NCAA basketball tournament: There are 9,223,372,036,854,775,808 (263) possible ways to enter the bracket. Mathematics – Bases: 9,439,829,801,208,141,318 (≈9.44×1018) is the 10th and (by conjecture) largest number with more than one digit that can be written from base 2 to base 18 using only the digits 0 t... | Orders of magnitude (numbers) | 0.808406 |
24,123 | Astronomy – Stars: 70 sextillion = 7×1022, the estimated number of stars within range of telescopes (as of 2003). Astronomy – Stars: in the range of 1023 to 1024 stars in the observable universe. Mathematics: 146,361,946,186,458,562,560,000 (≈1.5×1023) is the fifth unitary perfect number. Mathematics: 357,686,312,646,2... | Orders of magnitude (numbers) | 0.808406 |
24,124 | (1000000000000000000000000000000; 100010; short scale: one nonillion; long scale: one quintillion) ISO: quetta- (Q) Biology – Bacterial cells on Earth: The number of bacterial cells on Earth is estimated at 5,000,000,000,000,000,000,000,000,000,000, or 5 × 1030. Mathematics: 5,000,000,000,000,000,000,000,000,000,027 is... | Orders of magnitude (numbers) | 0.808406 |
24,125 | Physics: 7×10245, approximate spacetime volume of the history of the observable universe in Planck units. Computing: 1.797 693 134 862 315 807×10308 is approximately equal to the largest value that can be represented in the IEEE double precision floating-point format. Computing: (10 – 10−15)×10384 is equal to the large... | Orders of magnitude (numbers) | 0.808406 |
24,126 | Board games: 3.457×10181, number of ways to arrange the tiles in English Scrabble on a standard 15-by-15 Scrabble board. Physics: 10186, approximate number of Planck volumes in the observable universe. Shogi: 10226, an estimation of the game-tree complexity of shogi. | Orders of magnitude (numbers) | 0.808406 |
24,127 | (0.001; 1000−1; one thousandth) ISO: milli- (m) Mathematics – Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10−3 (0.14%). Mathematics – Poker: The odds of being dealt a flush in poker are 507.8 to 1 against, for a probability of 1.9 × 10−3 (0.19%). Mathematics – P... | Orders of magnitude (numbers) | 0.808406 |
24,128 | Vertex normals can also be computed for polygonal approximations to surfaces such as NURBS, or specified explicitly for artistic purposes. Vertex normals are used in Gouraud shading, Phong shading and other lighting models. Using vertex normals, much smoother shading than flat shading can be achieved; however, without ... | Vertex normal | 0.808402 |
24,129 | In the geometry of computer graphics, a vertex normal at a vertex of a polyhedron is a directional vector associated with a vertex, intended as a replacement to the true geometric normal of the surface. Commonly, it is computed as the normalized average of the surface normals of the faces that contain that vertex. The ... | Vertex normal | 0.808402 |
24,130 | They further examine the product for suitability to package as capsules, tablets, aerosol, intramuscular injectable, subcutaneous injectable, or intravenous formulations. Together, these processes are known in preclinical and clinical development as chemistry, manufacturing, and control (CMC). Many aspects of drug deve... | Drug development | 0.808401 |
24,131 | This section describes the propositional and predicate calculus, and gives the basic properties of classes, relations, and types. | Principia Mathematica | 0.808399 |
24,132 | Indeed, PM was in part brought about by an interest in logicism, the view on which all mathematical truths are logical truths. It was in part thanks to the advances made in PM that, despite its defects, numerous advances in meta-logic were made, including Gödel's incompleteness theorems. | Principia Mathematica | 0.808399 |
24,133 | The National Center for Integrative Biomedical Informatics (NCIBI) is one of seven National Centers for Biomedical Computing funded by the National Institutes of Health's (NIH) Roadmap for Medical Research. The center is based at the University of Michigan and is part of the Center for Computational Medicine and Bioinf... | National Center for Integrative Biomedical Informatics | 0.808397 |
24,134 | This perfect correlation at a distance is special: maybe the two particles "agreed" in advance, when the pair was created (before the qubits were separated), which outcome they would show in case of a measurement. Hence, following Einstein, Podolsky, and Rosen in their famous 1935 "EPR paper", there is something missin... | EPR pair | 0.808394 |
24,135 | In organic chemistry, an alicyclic compound contains one or more all-carbon rings which may be either saturated or unsaturated, but do not have aromatic character. Alicyclic compounds may have one or more aliphatic side chains attached. The simplest alicyclic compounds are the monocyclic cycloalkanes: cyclopropane, cyc... | Alicyclic compounds | 0.808393 |
24,136 | Polycyclic alkanes include cubane, basketane, and tetrahedrane. Spiro compounds have two or more rings that are connected through only one carbon atom. The mode of ring-closing in the formation of many alicyclic compounds can be predicted by Baldwin's rules. Otto Wallach, a German chemist, received the 1910 Nobel Prize... | Alicyclic compounds | 0.808393 |
24,137 | In one study, physicians were asked to give the chances of malignancy with a 1% prior probability of occurring. A test can detect 80% of malignancies and has a 10% false positive rate. What is the probability of malignancy given a positive test result? Approximately 95 out of 100 physicians responded the probability of... | Confusion of the inverse | 0.80839 |
24,138 | R.T. Sanderson has also noted the relationship between Mulliken electronegativity and atomic size, and has proposed a method of calculation based on the reciprocal of the atomic volume. With a knowledge of bond lengths, Sanderson's model allows the estimation of bond energies in a wide range of compounds. Sanderson's m... | Electronegativity | 0.808389 |
24,139 | The theory of stationary iterative methods was solidly established with the work of D.M. Young starting in the 1950s. The conjugate gradient method was also invented in the 1950s, with independent developments by Cornelius Lanczos, Magnus Hestenes and Eduard Stiefel, but its nature and applicability were misunderstood ... | Iterative algorithm | 0.808389 |
24,140 | Several machine learning models can be used in conjunction with conformal prediction. Studies have shown that it can be applied to for example convolutional neural networks, support-vector machines and others. | Conformal prediction | 0.808388 |
24,141 | In MICP, the alpha values are class-dependent (Mondrian) and the underlying model does not follow the original online setting introduced in 2005.Training algorithm: Train a machine learning model (MLM) Run a calibration set through the MLM, save output from the chosen stage In deep learning, the softmax values are ofte... | Conformal prediction | 0.808388 |
24,142 | Conformal prediction is used in a variety of fields and is an active area of research. For example, in biotechnology it has been used to predict uncertainties in breast cancer and stroke risks. Within language technology, conformal prediction papers are routinely presented at COPA. | Conformal prediction | 0.808388 |
24,143 | For example, a significance level of 0.1 means that the algorithm can make at most 10% erroneous predictions. To meet this requirement, the output is a set prediction, instead of a point prediction produced by standard supervised machine learning models. | Conformal prediction | 0.808388 |
24,144 | Conformal prediction (CP) is a machine learning framework for uncertainty quantification that can produce prediction regions for any underlying point predictor (where statistical, machine or deep learning) only assuming exchangeability of the data. CP works by computing nonconformity scores on previously labeled data, ... | Conformal prediction | 0.808388 |
24,145 | The data has to conform to some standards, such as data being exchangeable (a slightly weaker assumption than the standard IID imposed in standard machine learning). For conformal prediction, a n% prediction region is said to be valid if the truth is in the output n% of the time. The efficiency is the size of the outpu... | Conformal prediction | 0.808388 |
24,146 | Inductive Conformal Prediction was first known as inductive confidence machines, but was later re-introduced as ICP. It has gained popularity in practical settings because the underlying model does not need to be retrained for every new test example. This makes it interesting for any model that is heavy to train, such ... | Conformal prediction | 0.808388 |
24,147 | In 2009, Foodomics was defined as "a discipline that studies the Food and Nutrition domains through the application and integration of advanced -omics technologies to improve consumer's well-being, health, and knowledge". Foodomics requires the combination of food chemistry, biological sciences, and data analysis. Food... | Food science | 0.808388 |
24,148 | Food technology incorporates concepts from chemical engineering, for example. Activities of food scientists include the development of new food products, design of processes to produce these foods, choice of packaging materials, shelf-life studies, sensory evaluation of products using survey panels or potential consume... | Food science | 0.808388 |
24,149 | Food science is the basic science and applied science of food; its scope starts at overlap with agricultural science and nutritional science and leads through the scientific aspects of food safety and food processing, informing the development of food technology. Food science brings together multiple scientific discipl... | Food science | 0.808388 |
24,150 | Food physical chemistry is the study of both physical and chemical interactions in foods in terms of physical and chemical principles applied to food systems, as well as the application of physicochemical techniques and instrumentation for the study and analysis of foods. | Food science | 0.808388 |
24,151 | Food microbiology is the study of the microorganisms that inhabit, create, or contaminate food, including the study of microorganisms causing food spoilage. "Good" bacteria, however, such as probiotics, are becoming increasingly important in food science. In addition, microorganisms are essential for the production of ... | Food science | 0.808388 |
24,152 | Food chemistry is the study of chemical processes and interactions of all biological and non-biological components of foods. The biological substances include such items as meat, poultry, lettuce, beer, and milk. It is similar to biochemistry in its main components such as carbohydrates, lipids, and protein, but it als... | Food science | 0.808388 |
24,153 | In the United States, food science is typically studied at land-grant universities. Some of the country's pioneering food scientists were women who had attended chemistry programs at land-grant universities (which were state-run and largely under state mandates to allow for sex-blind admission), but then graduated and ... | Food science | 0.808388 |
24,154 | The five most common college degrees leading to a career in food science are: Food science/technology (66%), biological sciences (12%), business/marketing (10%), nutrition (9%), and chemistry (8%). Careers available to food scientists include food technologists, research and development (R&D), quality control, flavor c... | Food science | 0.808388 |
24,155 | Molecular gastronomy is a subdiscipline of food science that seeks to investigate the physical and chemical transformations of ingredients that occur in cooking. Its program includes three axes, as cooking was recognized to have three components, which are social, artistic, and technical. | Food science | 0.808388 |
24,156 | A carbonate is a salt of carbonic acid (H2CO3), characterized by the presence of the carbonate ion, a polyatomic ion with the formula CO2−3. The word carbonate may also refer to a carbonate ester, an organic compound containing the carbonate group O=C(−O−)2. The term is also used as a verb, to describe carbonation: the... | (CO3)2- | 0.808388 |
24,157 | In organic chemistry a carbonate can also refer to a functional group within a larger molecule that contains a carbon atom bound to three oxygen atoms, one of which is double bonded. These compounds are also known as organocarbonates or carbonate esters, and have the general formula ROCOOR′, or RR′CO3. Important organo... | (CO3)2- | 0.808388 |
24,158 | A Pharmaceutical Physician is a healthcare professional, usually a medical physician, who performs actions related to pharmacology. They work in biotechnology companies, Clinical Research Organisations (CROs), Regulatory Authorities, and pharmaceutical companies. | Pharmaceutical physician | 0.808387 |
24,159 | According to Dirichlet's unit theorem, the torsion-free unit rank r of an algebraic number field K with r1 real embeddings and r2 pairs of conjugate complex embeddings is determined by the formula r = r1 + r2 − 1. Hence a totally real cubic field K with r1 = 3, r2 = 0 has two independent units ε1, ε2 and a complex cubi... | Cyclic cubic field | 0.808387 |
24,160 | In mathematics, specifically the area of algebraic number theory, a cubic field is an algebraic number field of degree three. | Cyclic cubic field | 0.808387 |
24,161 | Creating stable algorithms for ill-conditioned problems is a central concern in numerical linear algebra. One example is that the stability of householder triangularization makes it a particularly robust solution method for linear systems, whereas the instability of the normal equations method for solving least squares... | Matrix computation | 0.808385 |
24,162 | Noting the broad applications of numerical linear algebra, Lloyd N. Trefethen and David Bau, III argue that it is "as fundamental to the mathematical sciences as calculus and differential equations",: x even though it is a comparatively small field. Because many properties of matrices and vectors also apply to function... | Matrix computation | 0.808385 |
24,163 | For many problems in applied linear algebra, it is useful to adopt the perspective of a matrix as being a concatenation of column vectors. For example, when solving the linear system x = A − 1 b {\displaystyle x=A^{-1}b} , rather than understanding x as the product of A − 1 {\displaystyle A^{-1}} with b, it is helpful ... | Matrix computation | 0.808385 |
24,164 | Several programming languages use numerical linear algebra optimisation techniques and are designed to implement numerical linear algebra algorithms. These languages include MATLAB, Analytica, Maple, and Mathematica. Other programming languages which are not explicitly designed for numerical linear algebra have librari... | Matrix computation | 0.808385 |
24,165 | Numerical linear algebra aims to solve problems of continuous mathematics using finite precision computers, so its applications to the natural and social sciences are as vast as the applications of continuous mathematics. It is often a fundamental part of engineering and computational science problems, such as image an... | Matrix computation | 0.808385 |
24,166 | Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Co... | Matrix computation | 0.808385 |
24,167 | Numerical linear algebra was developed by computer pioneers like John von Neumann, Alan Turing, James H. Wilkinson, Alston Scott Householder, George Forsythe, and Heinz Rutishauser, in order to apply the earliest computers to problems in continuous mathematics, such as ballistics problems and the solutions to systems o... | Matrix computation | 0.808385 |
24,168 | The problem of computing the Birkhoff decomposition with the minimum number of terms has been shown to be NP-hard, but some heuristics for computing it are known. This theorem can be extended for the general stochastic matrix with deterministic transition matrices.Budish, Che, Kojima and Milgrom generalize Birkhoff's a... | Birkhoff algorithm | 0.808384 |
24,169 | A perfect matching in a bipartite graph can be found in polynomial time, e.g. using any algorithm for maximum cardinality matching. Kőnig's theorem is equivalent to the following:The positivity graph of any bistochastic matrix admits a perfect matching.A matrix is called scaled-bistochastic if all elements are weakly-p... | Birkhoff algorithm | 0.808384 |
24,170 | A permutation set of an n-by-n matrix X is a set of n entries of X containing exactly one entry from each row and from each column. A theorem by Dénes Kőnig says that:: 35 Every bistochastic matrix has a permutation-set in which all entries are positive.The positivity graph of an n-by-n matrix X is a bipartite graph wi... | Birkhoff algorithm | 0.808384 |
24,171 | Thus the holomorphic extension of the fi has at worst algebraic poles and ordinary algebraic branchings over the critical points. Note that, away from the critical points, we have p ( x , y ) = a n ( x ) ( y − f 1 ( x ) ) ( y − f 2 ( x ) ) ⋯ ( y − f n ( x ) ) {\displaystyle p(x,y)=a_{n}(x)(y-f_{1}(x))(y-f_{2}(x))\cdots... | Algebraic function | 0.808384 |
24,172 | It is normally assumed that p should be an irreducible polynomial. The existence of an algebraic function is then guaranteed by the implicit function theorem. Formally, an algebraic function in m variables over the field K is an element of the algebraic closure of the field of rational functions K(x1, ..., xm). | Algebraic function | 0.808384 |
24,173 | {\displaystyle y^{2}+x^{2}=1.\,} This determines y, except only up to an overall sign; accordingly, it has two branches: y = ± 1 − x 2 . {\displaystyle y=\pm {\sqrt {1-x^{2}}}.\,} An algebraic function in m variables is similarly defined as a function y = f ( x 1 , … , x m ) {\displaystyle y=f(x_{1},\dots ,x_{m})} whic... | Algebraic function | 0.808384 |
24,174 | A composition of transcendental functions can give an algebraic function: f ( x ) = cos arcsin x = 1 − x 2 {\displaystyle f(x)=\cos \arcsin x={\sqrt {1-x^{2}}}} . As a polynomial equation of degree n has up to n roots (and exactly n roots over an algebraically closed field, such as the complex numbers), a polynomia... | Algebraic function | 0.808384 |
24,175 | Sometimes, coefficients a i ( x ) {\displaystyle a_{i}(x)} that are polynomial over a ring R are considered, and one then talks about "functions algebraic over R". A function which is not algebraic is called a transcendental function, as it is for example the case of exp x , tan x , ln x , Γ ( x ) {\displaystyle ... | Algebraic function | 0.808384 |
24,176 | It can be shown that the same class of functions is obtained if algebraic numbers are accepted for the coefficients of the ai(x)'s. If transcendental numbers occur in the coefficients the function is, in general, not algebraic, but it is algebraic over the field generated by these coefficients. The value of an algebrai... | Algebraic function | 0.808384 |
24,177 | In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation. Quite often algebraic functions are algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional pow... | Algebraic function | 0.808383 |
24,178 | Discretization in the space produces a system of ordinary differential equations for unsteady problems and algebraic equations for steady problems. Implicit or semi-implicit methods are generally used to integrate the ordinary differential equations, producing a system of (usually) nonlinear algebraic equations. Applyi... | Computer simulations of fluids | 0.808381 |
24,179 | Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of ... | Computer simulations of fluids | 0.808381 |
24,180 | Smith of Douglas Aircraft in 1967. This method discretized the surface of the geometry with panels, giving rise to this class of programs being called Panel Methods. Their method itself was simplified, in that it did not include lifting flows and hence was mainly applied to ship hulls and aircraft fuselages. | Computer simulations of fluids | 0.808381 |
24,181 | There is nothing inherent in Reynolds averaging to preclude this, but the turbulence models used to close the equations are valid only as long as the time over which these changes in the mean occur is large compared to the time scales of the turbulent motion containing most of the energy. RANS models can be divided int... | Computer simulations of fluids | 0.808381 |
24,182 | Restricting our attention to this case, we can imagine that the first n-1 votes cancel out and that the deciding vote is cast by the n-th voter. In this case the probability of getting a correct majority is just p. Now suppose we send in the two extra voters. The probability that they change an incorrect majority to a ... | Condorcet's jury theorem | 0.808381 |
24,183 | The result depends on whether p is greater than or less than 1/2: If p is greater than 1/2 (each voter is more likely to vote correctly), then adding more voters increases the probability that the majority decision is correct. In the limit, the probability that the majority votes correctly approaches 1 as the number of... | Condorcet's jury theorem | 0.808381 |
24,184 | Condorcet's jury theorem is a political science theorem about the relative probability of a given group of individuals arriving at a correct decision. The theorem was first expressed by the Marquis de Condorcet in his 1785 work Essay on the Application of Analysis to the Probability of Majority Decisions.The assumption... | Condorcet's jury theorem | 0.808381 |
24,185 | The Condorcet jury theorem has recently been used to conceptualize score integration when several physician readers (radiologists, endoscopists, etc.) independently evaluate images for disease activity. This task arises in central reading performed during clinical trials and has similarities to voting. According to the... | Condorcet's jury theorem | 0.808381 |
24,186 | Current generations of experiments are designed to be sensitive to the supersymmetry range of EDMs, providing complementary experiments to those done at the LHC.Indeed, many theories are inconsistent with the current limits and have effectively been ruled out, and established theory permits a much larger value than the... | Dipole moments of molecules | 0.808379 |
24,187 | Not to be confused with spin which refers to the magnetic dipole moments of particles, much experimental work is continuing on measuring the electric dipole moments (EDM; or anomalous electric dipole moment) of fundamental and composite particles, namely those of the electron and neutron, respectively. As EDMs violate ... | Dipole moments of molecules | 0.808379 |
24,188 | {\displaystyle {\tfrac {777480}{8288641}}.} The question of existence of (integer) diophantine quintuples was one of the oldest outstanding unsolved problems in number theory. | Diophantine quintuple | 0.808378 |
24,189 | In number theory, a diophantine m-tuple is a set of m positive integers { a 1 , a 2 , a 3 , a 4 , … , a m } {\displaystyle \{a_{1},a_{2},a_{3},a_{4},\ldots ,a_{m}\}} such that a i a j + 1 {\displaystyle a_{i}a_{j}+1} is a perfect square for any 1 ≤ i < j ≤ m . {\displaystyle 1\leq i | Diophantine quintuple | 0.808378 |
24,190 | The Lie algebra g 2 {\displaystyle {\mathfrak {g}}_{2}} , being the smallest exceptional simple Lie algebra, was the first of these to be discovered in the attempt to classify simple Lie algebras. On May 23, 1887, Wilhelm Killing wrote a letter to Friedrich Engel saying that he had found a 14-dimensional simple Lie alg... | G2 (mathematics) | 0.808378 |
24,191 | The group G2(q) is the points of the algebraic group G2 over the finite field Fq. These finite groups were first introduced by Leonard Eugene Dickson in Dickson (1901) for odd q and Dickson (1905) for even q. The order of G2(q) is q6(q6 − 1)(q2 − 1). When q ≠ 2, the group is simple, and when q = 2, it has a simple subg... | G2 (mathematics) | 0.808377 |
24,192 | G2 is the automorphism group of the following two polynomials in 7 non-commutative variables. C 1 = t 2 + u 2 + v 2 + w 2 + x 2 + y 2 + z 2 {\displaystyle C_{1}=t^{2}+u^{2}+v^{2}+w^{2}+x^{2}+y^{2}+z^{2}} C 2 = t u v + w t x + y w u + z y t + v z w + x v y + u x z {\displaystyle C_{2}=tuv+wtx+ywu+zyt+vzw+xvy+uxz} (± per... | G2 (mathematics) | 0.808377 |
24,193 | These can all be constructed with Clifford algebra using an invertible form 3 e 1234567 ± φ {\displaystyle 3e_{1234567}\pm \varphi } for octonions. For other signed variations of φ {\displaystyle \varphi } , this form has remainders that classify 6 other non-associative algebras that show partial G 2 {\displaystyle G_{... | G2 (mathematics) | 0.808377 |
24,194 | Adding a representation of the 14 generators with coefficients A, ..., N gives the matrix: A λ 1 + ⋯ + N λ 14 = {\displaystyle A\lambda _{1}+\cdots +N\lambda _{14}={\begin{bmatrix}0&C&-B&E&-D&-G&F-M\\-C&0&A&F&-G+N&D-K&-E-L\\B&-A&0&-N&M&L&-K\\-E&-F&N&0&-A+H&-B+I&C-J\\D&G-N&-M&A-H&0&J&I\\G&K-D&-L&B-I&-J&0&-H\\-F+M&E+L&K... | G2 (mathematics) | 0.808377 |
24,195 | The associated simple Lie group has fundamental group of order 2 and its outer automorphism group is the trivial group. Its maximal compact subgroup is SU(2) × SU(2)/(−1,−1). It has a non-algebraic double cover that is simply connected. | G2 (mathematics) | 0.808377 |
24,196 | The associated Lie group has no outer automorphisms, no center, and is simply connected and compact. The Lie algebra of the non-compact (split) form has dimension 14. | G2 (mathematics) | 0.808377 |
24,197 | There are 3 simple real Lie algebras associated with this root system: The underlying real Lie algebra of the complex Lie algebra G2 has dimension 28. It has complex conjugation as an outer automorphism and is simply connected. The maximal compact subgroup of its associated group is the compact form of G2. The Lie alge... | G2 (mathematics) | 0.808377 |
24,198 | The characters of finite-dimensional representations of the real and complex Lie algebras and Lie groups are all given by the Weyl character formula. The dimensions of the smallest irreducible representations are (sequence A104599 in the OEIS): 1, 7, 14, 27, 64, 77 (twice), 182, 189, 273, 286, 378, 448, 714, 729, 748, ... | G2 (mathematics) | 0.808377 |
24,199 | In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras g 2 , {\displaystyle {\mathfrak {g}}_{2},} as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14. It has t... | G2 (mathematics) | 0.808377 |
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