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14,700 | {\displaystyle x=0.} In the above example, one can take a nonzero x {\displaystyle x} from the kernel of f . {\displaystyle f.} Consequently, the resulting topology need not be Hausdorff. | Minkowski gauge | 0.814981 |
14,701 | Therefore, p K {\displaystyle p_{K}} is a seminorm on X , {\displaystyle X,} with an induced topology. This is characteristic of Minkowski functionals defined via "nice" sets. | Minkowski gauge | 0.814981 |
14,702 | Thus the Minkowski functional p U {\displaystyle p_{U}} is just the norm on X . {\displaystyle X.} Example 2 Let X {\displaystyle X} be a vector space without topology with underlying scalar field K . | Minkowski gauge | 0.814981 |
14,703 | In this next theorem, which follows immediately from the statements above, K {\displaystyle K} is not assumed to be absorbing in X {\displaystyle X} and instead, it is deduced that ( 0 , 1 ) K {\displaystyle (0,1)K} is absorbing when p K {\displaystyle p_{K}} is a seminorm. It is also not assumed that K {\displaystyle ... | Minkowski gauge | 0.814981 |
14,704 | More generally, if K {\displaystyle K} is convex and the origin belongs to the algebraic interior of K , {\displaystyle K,} then p K {\displaystyle p_{K}} is a nonnegative sublinear functional on X , {\displaystyle X,} which implies in particular that it is subadditive and positive homogeneous. If K {\displaystyle K} i... | Minkowski gauge | 0.81498 |
14,705 | The data for pathway analysis come from high throughput biology. This includes high throughput sequencing data and microarray data. Before pathway analysis can be done, each gene's alteration should be evaluated using the omics dataset in either quantitative (differential expression analysis) or qualitative (detection ... | Pathway analysis | 0.81498 |
14,706 | Computational analyses employ special formats of pathway representation. In the simplest form, however, a pathway might be represented as a list of member molecules with order and relations unspecified. Such a representation, generally called Functional Gene Set (FGS), can also refer to other functionally characterised... | Pathway analysis | 0.81498 |
14,707 | Application of pathway analysis methods depends on annotations found in existing databases, such as gene set membership in pathways, pathway topology, presence of genes in the global network etc. These annotations, however, are far from being complete and have highly variable degrees of confidence. In addition, such in... | Pathway analysis | 0.81498 |
14,708 | Pathway is the term from molecular biology for a curated schematic representation of a well characterized segment of the molecular physiological machinery, such as a metabolic pathway describing an enzymatic process within a cell or tissue or a signaling pathway model representing a regulatory process that might, in it... | Pathway analysis | 0.81498 |
14,709 | Latin squares and quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraic. The listing below will consider the examples of some very small orders, which is the side length of the square, or the number of elements in the equivalent quasigroup. | Small Latin squares and quasigroups | 0.814976 |
14,710 | In some cases, it is the logarithm of the dose that is plotted on the X axis. The curve is typically sigmoidal, with the steepest portion in the middle. Biologically based models using dose are preferred over the use of log(dose) because the latter can visually imply a threshold dose when in fact there is none.Statisti... | Dose–response relationship | 0.81497 |
14,711 | An alternative option for coordinates in the complex plane is the polar coordinate system that uses the distance of the point z from the origin (O), and the angle subtended between the positive real axis and the line segment Oz in a counterclockwise sense. This leads to the polar form z = r e i φ = r ( cos φ + i sin ... | Complex Numbers | 0.81497 |
14,712 | The complex numbers of absolute value one form the unit circle. The addition of a complex number is a translation in the complex plane, and the multiplication by a complex number is a similarity centered at the origin. The complex conjugation is the reflection symmetry with respect to the real axis. The complex absolut... | Complex Numbers | 0.81497 |
14,713 | More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number. For example, the equation ( x + 1 ) 2 = − 9 {\displaystyle (x+1)^{2}=-9} has no real solution, since the square of a real number cannot be ne... | Complex Numbers | 0.81497 |
14,714 | The UK Molecular R-Matrix codes are a set of software routines used to calculate the effects of collision of electrons with atoms and molecules. The R-matrix method is used in computational quantum mechanics to study scattering of positrons and electrons by atomic and molecular targets. The fundamental idea was origina... | UK Molecular R-matrix Codes | 0.814968 |
14,715 | Since the early 1970s, all of the problems in the KöMaL journal have been translated into English; published solutions, however, are not typically translated. In addition to problems in mathematics, physics and more recently, informatics, the journal contains articles on those subjects. A 100-year archive of issues is ... | Középiskolai Matematikai és Fizikai Lapok | 0.814966 |
14,716 | Középiskolai Matematikai és Fizikai Lapok (KöMaL) is a Hungarian mathematics and physics journal for high school students. It was founded by Dániel Arany, a high school teacher from Győr, Hungary and has been continually published since 1894. KöMaL has been organizing various renowned correspondence competitions for h... | Középiskolai Matematikai és Fizikai Lapok | 0.814966 |
14,717 | The notion of "correctness" may not be meaningful when making policy decisions, which are based on values or preferences, rather than just on facts. Some defenders of the theorem hold that it is applicable when voting is aimed at determining which policy best promotes the public good, rather than at merely expressing i... | Jury theorem | 0.814962 |
14,718 | Therefore, a decision may be accepted even if only 6 voters support it. Boland, Proschan and Tong prove that, when the voters are independent and p>1/2, a direct majority system - as in Condorcet's theorem - always has a higher chance of accepting the correct decision than any indirect majority system. | Jury theorem | 0.814962 |
14,719 | Condorcet's theorem considers a direct majority system, in which all votes are counted directly towards the final outcome. Many countries use an indirect majority system, in which the voters are divided into groups. The voters in each group decide on an outcome by an internal majority vote; then, the groups decide on t... | Jury theorem | 0.814962 |
14,720 | Condorcet's jury theorem makes the following three assumptions: Unconditional Independence: the voters make up their minds independently. In other words, their opinions are independent random variables. Unconditional Competence: the probability that the opinion of a single voter coincides with the objective truth is la... | Jury theorem | 0.814962 |
14,721 | Jury theorems are interested in the probability of correctness - the probability that the majority decision coincides with the objective truth. Typical jury theorems make two kinds of claims on this probability: Growing Reliability: the probability of correctness is larger when the group is larger. Crowd Infallibility:... | Jury theorem | 0.814962 |
14,722 | The premise of all jury theorems is that there is an objective truth, which is unknown to the voters. Most theorems focus on binary issues (issues with two possible states), for example, whether a certain defendant is guilty or innocent, whether a certain stock is going to rise or fall, etc. There are n {\displaystyle ... | Jury theorem | 0.814962 |
14,723 | Another cause of correlation between voters is the existence of an opinion leader. Suppose each voter makes an independent decision, but then each voter, with some fixed probability, changes his opinion to match that of the opinion leader. Jury theorems by Boland and Boland, Proschan and Tong shows that, if (and only i... | Jury theorem | 0.814962 |
14,724 | instead of assuming that the voter identity is fixed, one can assume that there is a large pool of potential voters with different competence levels, and the actual voters are selected at random from this pool (as in sortition). A jury theorem by Ben Yashar and Paroush shows that, under certain conditions, the correctn... | Jury theorem | 0.814962 |
14,725 | Epistemic Monotonicity is not sufficient for computing the threshold itself; the threshold can be computed by assuming expected-utility maximization and prior probabilities. A general problem with the weighted majority rules is that they require to know the competence levels of the different voters, which is usually ha... | Jury theorem | 0.814962 |
14,726 | Uniformity can be dismissed if the Competence assumption is strengthened. There are several ways to strengthen it: Strong Competence: for each voter i, the probability of correctness pi is at least 1/2+e, where e>0 is fixed for all voters. In other words: the competence is bounded away from a fair coin toss. A jury the... | Jury theorem | 0.814962 |
14,727 | The weakened assumption is: Tendency to Competence: for each voter, and for each r>0, the probability that p(x) = 1/2+r is at least as large as the probability that p(x) = 1/2-r.A jury theorem by Dietrich and Spiekerman says that Conditional Independence, Tendency to Competence, and Conditional Uniformity, together imp... | Jury theorem | 0.814962 |
14,728 | A jury theorem is a mathematical theorem proving that, under certain assumptions, a decision attained using majority voting in a large group is more likely to be correct than a decision attained by a single expert. It serves as a formal argument for the idea of wisdom of the crowd, for decision of questions of fact by ... | Jury theorem | 0.814962 |
14,729 | A jury theorem by Pivato shows that, if the average covariance between voters becomes small as the population becomes large, then Crowd Infallibility holds (for some voting rule). There are other jury theorems that take into account the degree to which votes may be correlated. | Jury theorem | 0.814962 |
14,730 | The applicability of jury theorems, in particular, Condorcet's Jury Theorem (CJT) to democratic processes is debated, as it can prove majority rule to be a perfect mechanism or a disaster depending on individual competence. Recent studies show that, in a non-homogeneous case, the theorem's thesis does not hold almost s... | Jury theorem | 0.814962 |
14,731 | With three or more options, Conditional Competence can be generalized as follows: Multioption Conditional Competence: for any two options x and y, if x is correct and y is not, then any voter is more likely to vote for x than for y.A jury theorem by List and Goodin shows that Multioption Conditional Competence and Cond... | Jury theorem | 0.814962 |
14,732 | Often, decision problems involve three or more options. This critical limitation was in fact recognized by Condorcet (see Condorcet's paradox), and in general it is very difficult to reconcile individual decisions between three or more outcomes (see Arrow's theorem). This limitation may also be overcome by means of a s... | Jury theorem | 0.814962 |
14,733 | For n = 5 {\displaystyle n=5} and p = 0.55 {\displaystyle p=0.55} , the maximum admissible second-order correlation coefficient equals ≈ 0.43 {\displaystyle \approx 0.43} . The above example shows that when the individual competence is low but the correlation is high: The collective competence under simple majority may... | Jury theorem | 0.814962 |
14,734 | In game-theoretic terms, truthful voting might not be a Nash equilibrium. This problem has been termed the swing voter's curse, as it is analogous to the winner's curse in auction theory. A jury theorem by Peleg and Zamir shows sufficient and necessary conditions for the existence of a Bayesian-Nash equilibrium that sa... | Jury theorem | 0.814962 |
14,735 | The first scientific paper on using neural networks in machine translation appeared in 2014 when Bahdanau et al. and Sutskever et al. proposed end-to-end neural network translation models and formally used the phrase "neural machine translation" in their research. The first large-scale NMT system was launched by Baidu ... | Neural machine translation | 0.814961 |
14,736 | Neural machine translation (NMT) is an approach to machine translation that uses an artificial neural network to predict the likelihood of a sequence of words, typically modeling and then translating entire sentences in a single integrated model. | Neural machine translation | 0.814961 |
14,737 | Further Coverage Models address the issues in these attention mechanisms, such as ignoring past alignment information leading to over-translation and under-translation.Convolutional Neural Networks (CNNs) are, in principle, somewhat better for long continuous sequences but were initially not used due to several weaknes... | Neural machine translation | 0.814961 |
14,738 | A bidirectional recurrent neural network, known as an encoder, is used by the neural network to encode a source sentence for a second RNN, known as a decoder, that is used to predict words in the target language. RNNs struggle to encode long inputs into a single vector. This can be addressed by using an attention mecha... | Neural machine translation | 0.814961 |
14,739 | There is no separate language model, translation model, and reordering model, but just a single sequence model that predicts one word at a time. However, this sequence prediction is conditioned on the entire source sentence and the already-produced target sequence. Word sequence modeling in NMT systems was, at first, t... | Neural machine translation | 0.814961 |
14,740 | NMT systems use deep learning and representation learning and depart from phrase-based statistical approaches that use separately engineered subcomponents by taking the whole sentence into account. Neural machine translation (NMT) is similar to what has been traditionally done in statistical machine translation (SMT). ... | Neural machine translation | 0.814961 |
14,741 | The Center for Molecular and Biomolecular Informatics (CMBI) is an academic computational biology (bioinformatics) research department based in Nijmegen (the Netherlands), and is part of the Radboudumc University Medical Center. Most of the research topics at the CMBI focus strongly on (in silico) biomedical data analy... | Center for Molecular and Biomolecular Informatics | 0.814957 |
14,742 | If opposite sides in a convex quadrilateral ABCD intersect at E and F, then | A B | + | B C | = | A D | + | D C | ⇔ | A E | + | E C | = | A F | + | F C | . {\displaystyle |AB|+|BC|=|AD|+|DC|\quad \Leftrightarrow \quad |AE|+|EC|=|AF|+|FC|.} The implication to the right is named after L. M. Urquhart (1902–1966) although ... | Ex-tangential quadrilateral | 0.814951 |
14,743 | In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral. It has also been called an exscriptible quadrilateral. The circle is called its excircle, its radius the exradius and its center the excenter (E in th... | Ex-tangential quadrilateral | 0.814951 |
14,744 | If an ex-tangential quadrilateral also has a circumcircle, it is called an ex-bicentric quadrilateral. Then, since it has two opposite supplementary angles, its area is given by K = a b c d {\displaystyle \displaystyle K={\sqrt {abcd}}} which is the same as for a bicentric quadrilateral. If x is the distance between th... | Ex-tangential quadrilateral | 0.814951 |
14,745 | A way of combining these characterizations regarding the sides is that the absolute values of the differences between opposite sides are equal for the two pairs of opposite sides, | a − c | = | b − d | . {\displaystyle |a-c|=|b-d|.} These equations are closely related to the Pitot theorem for tangential quadrilaterals,... | Ex-tangential quadrilateral | 0.814951 |
14,746 | N-version programming (NVP), also known as multiversion programming or multiple-version dissimilar software, is a method or process in software engineering where multiple functionally equivalent programs are independently generated from the same initial specifications. The concept of N-version programming was introduce... | N-version programming | 0.814949 |
14,747 | The journal is abstracted and indexed in Scopus and the Science Citation Index. According to the Journal Citation Reports, Neural Networks has a 2021 impact factor of 9.657. | Neural Networks (journal) | 0.814946 |
14,748 | Neural Networks was established in 1988 and is published by Elsevier. The journal covers all aspects of research on artificial neural networks. The founding editor-in-chief was Stephen Grossberg (Boston University). The current editors-in-chief are DeLiang Wang (Ohio State University) and Taro Toyoizumi (RIKEN Center f... | Neural Networks (journal) | 0.814946 |
14,749 | Neural Networks is a monthly, peer-reviewed, scientific journal and an official journal of the International Neural Network Society, European Neural Network Society, and Japanese Neural Network Society. | Neural Networks (journal) | 0.814946 |
14,750 | Instrument mechanics are required to study a large body of knowledge. This includes information on: Process Control Measurement Instrumentation Final Control Elements Motors Electronics Industrial networks Signalling standards Chemistry Fluid Dynamics == References == | Instrument mechanic | 0.814932 |
14,751 | MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and started developing MATLAB for his students as a hobby. He developed MATLAB's initial linear algebra programming in 1967 with ... | MATLAB | 0.814924 |
14,752 | The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks. Many of the toolboxes were developed as a result of Stanford students that used MATLAB in academia, then brought the software with them to the private sector.Over time, MATLAB was... | MATLAB | 0.814924 |
14,753 | MATLAB supports elements of lambda calculus by introducing function handles, or function references, which are implemented either in .m files or anonymous/nested functions. | MATLAB | 0.814924 |
14,754 | In the Northern Hemisphere, rough alignment can be done by visually aligning the axis of the telescope mount with Polaris. In the Southern hemisphere or places where Polaris is not visible, a rough alignment can be performed by ensuring the mount is level, adjusting the latitude adjustment pointer to match the observer... | Polar alignment | 0.81492 |
14,755 | Sony Research Center published the first Japan Patent application for S.P.I.N.O.R. (Spin Polarized Injection Non-Volatile Orthogonal Read/Write RAM), a forerunner of STT RAM, in 1997. Subsequently, at IEDM 2005, Sony researchers reported the first working 4kb STT memory, dubbed Spin-RAM, with replacement of the paramag... | Spin torque transfer | 0.814903 |
14,756 | The above treatment for an incident wave accounts for the radiation pressure experienced by a black (totally absorbing) body. If the wave is specularly reflected, then the recoil due to the reflected wave will further contribute to the radiation pressure. In the case of a perfect reflector, this pressure will be identi... | Radiation Pressure | 0.814903 |
14,757 | Using this information can further a priori knowledge of a pathway and thus help to choose the most likely candidate gene involved. Topp Gene is another useful database that allows users to prioritize candidate genes using functional annotations or network analysis. ToppGene aids researchers in selecting a subset of li... | Candidate gene | 0.814902 |
14,758 | Suitable candidate genes are generally selected based on known biological, physiological, or functional relevance to the disease in question. This approach is limited by its reliance on existing knowledge about known or theoretical biology of disease. However, molecular tools are allowing insight into disease mechanism... | Candidate gene | 0.814902 |
14,759 | Inorganic chemistry, a unified approach. Reading Massachusetts, USA: Addison Wesley Publishing Co. ISBN 0-201-05660-7. | Atomic radii of the elements (data page) | 0.814892 |
14,760 | Keiter (1993). Inorganic Chemistry: Principles of Structure and Reactivity (4th ed.). New York, USA: HarperCollins. | Atomic radii of the elements (data page) | 0.814892 |
14,761 | The full title of the first edition was The doctrine of chances: or, a method for calculating the probabilities of events in play; it was published in 1718, by W. Pearson, and ran for 175 pages. Published in 1738 by Woodfall and running for 258 pages, the second edition of de Moivre's book introduced the concept of nor... | The Doctrine of Chances | 0.814892 |
14,762 | The Doctrine of Chances was the first textbook on probability theory, written by 18th-century French mathematician Abraham de Moivre and first published in 1718. De Moivre wrote in English because he resided in England at the time, having fled France to escape the persecution of Huguenots. The book's title came to be s... | The Doctrine of Chances | 0.814892 |
14,763 | In the ring Z obtained by adjoining the quadratic integer √3 to Z, one has (2 + √3)(2 − √3) = 1, so 2 + √3 is a unit, and so are its powers, so Z has infinitely many units. More generally, for the ring of integers R in a number field F, Dirichlet's unit theorem states that R× is isomorphic to the group where μ R {\disp... | Unit element | 0.814888 |
14,764 | The numerical uncertainty of the energies and the wave functions found in this way is far smaller than the uncertainty stemming from using the Schrödinger equation (which does not incorporate all relevant physics), rather than fundamentally more accurate equations, such as the Dirac equation or a non-relativistic quant... | Hydrogen molecule-ion | 0.814883 |
14,765 | Negation normal form Conjunctive normal form Disjunctive normal form Algebraic normal form Prenex normal form Skolem normal form Blake canonical form, also known as the complete sum of prime implicants, the complete sum, or the disjunctive prime form | Normal form (mathematics) | 0.814883 |
14,766 | Therefore, in computer algebra, normal form is a weaker notion: A normal form is a representation such that zero is uniquely represented. This allows testing for equality by putting the difference of two objects in normal form. Canonical form can also mean a differential form that is defined in a natural (canonical) wa... | Normal form (mathematics) | 0.814883 |
14,767 | More generally, for a class of objects on which an equivalence relation is defined, a canonical form consists in the choice of a specific object in each class. For example: Jordan normal form is a canonical form for matrix similarity. The row echelon form is a canonical form, when one considers as equivalent a matrix a... | Normal form (mathematics) | 0.814883 |
14,768 | In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way. The distinction between "... | Normal form (mathematics) | 0.814883 |
14,769 | According to OED and LSJ, the term canonical stems from the Ancient Greek word kanonikós (κανονικός, "regular, according to rule") from kanṓn (κᾰνών, "rod, rule"). The sense of norm, standard, or archetype has been used in many disciplines. Mathematical usage is attested in a 1738 letter from Logan. The German term kan... | Normal form (mathematics) | 0.814883 |
14,770 | The Löwenheim–Skolem theorem shows that if a first-order theory has any infinite model, then it has infinite models of every cardinality. In particular, no first-order theory with an infinite model can be categorical. Thus there is no first-order theory whose only model has the set of natural numbers as its domain, or ... | First Order Logic | 0.814883 |
14,771 | The earliest fossils of multicellular organisms include the contested Grypania spiralis and the fossils of the black shales of the Palaeoproterozoic Francevillian Group Fossil B Formation in Gabon (Gabonionta). The Doushantuo Formation has yielded 600 million year old microfossils with evidence of multicellular traits.... | Evolution of complex life | 0.814882 |
14,772 | Let t p = { S ⊆ X ∣ p ∈ S } {\displaystyle t_{p}=\{S\subseteq X\mid p\in S\}} and t q = { S ⊆ X ∣ q ∈ S } {\displaystyle t_{q}=\{S\subseteq X\mid q\in S\}} . That is tq is the particular point topology on X with q being the distinguished point. Then (X,tp) and (X,tq) are homeomorphic incomparable topologies on the same... | Connected two-point set | 0.814879 |
14,773 | Separability {p} is dense and hence X is a separable space. However if X is uncountable then X \ {p} is not separable. This is an example of a subspace of a separable space not being separable.Countability (first but not second) If X is uncountable then X is first countable but not second countable.Alexandrov-discrete ... | Connected two-point set | 0.814879 |
14,774 | If X is uncountable, the topology on X is called the uncountable particular point topology.A generalization of the particular point topology is the closed extension topology. In the case when X \ {p} has the discrete topology, the closed extension topology is the same as the particular point topology. This topology is ... | Connected two-point set | 0.814879 |
14,775 | In mathematics, the particular point topology (or included point topology) is a topology where a set is open if it contains a particular point of the topological space. Formally, let X be any non-empty set and p ∈ X. The collection T = { S ⊆ X ∣ p ∈ S } ∪ { ∅ } {\displaystyle T=\{S\subseteq X\mid p\in S\}\cup \{\emptys... | Connected two-point set | 0.814879 |
14,776 | In mechanical engineering, a jaw coupling is a type of general purpose power transmission coupling that also can be used in motion control (servo) applications. It is designed to transmit torque (by connecting two shafts) while damping system vibrations and accommodating misalignment, which protects other components fr... | Jaw coupling | 0.814878 |
14,777 | In logic, the parameters passed to (or operated on by) an open predicate are called parameters by some authors (e.g., Prawitz, "Natural Deduction"; Paulson, "Designing a theorem prover"). Parameters locally defined within the predicate are called variables. This extra distinction pays off when defining substitution (wi... | Parameter | 0.814877 |
14,778 | In environmental science and particularly in chemistry and microbiology, a parameter is used to describe a discrete chemical or microbiological entity that can be assigned a value: commonly a concentration, but may also be a logical entity (present or absent), a statistical result such as a 95 percentile value or in so... | Parameter | 0.814877 |
14,779 | (In casual usage the terms parameter and argument might inadvertently be interchanged, and thereby used incorrectly.) These concepts are discussed in a more precise way in functional programming and its foundational disciplines, lambda calculus and combinatory logic. Terminology varies between languages; some computer ... | Parameter | 0.814877 |
14,780 | In artificial intelligence, a model describes the probability that something will occur. Parameters in a model are the weight of the various probabilities. Tiernan Ray, in an article on GPT-3, described parameters this way: A parameter is a calculation in a neural network that applies a great or lesser weighting to som... | Parameter | 0.814877 |
14,781 | In analytic geometry, a curve can be described as the image of a function whose argument, typically called the parameter, lies in a real interval. For example, the unit circle can be specified in the following two ways: implicit form, the curve is the locus of points (x, y) in the Cartesian plane that satisfy the relat... | Parameter | 0.814877 |
14,782 | A parameter (from Ancient Greek παρά (pará) 'beside, subsidiary', and μέτρον (métron) 'measure'), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical... | Parameter | 0.814877 |
14,783 | Indeed, in the latter case, it is only defined for non-negative integer arguments. More formal presentations of such situations typically start out with a function of several variables (including all those that might sometimes be called "parameters") such as ( n , k ) ↦ n k _ {\displaystyle (n,k)\mapsto n^{\underline {... | Parameter | 0.814877 |
14,784 | It is possible to make statistical inferences without assuming a particular parametric family of probability distributions. In that case, one speaks of non-parametric statistics as opposed to the parametric statistics just described. For example, a test based on Spearman's rank correlation coefficient would be called n... | Parameter | 0.814877 |
14,785 | In statistics and econometrics, the probability framework above still holds, but attention shifts to estimating the parameters of a distribution based on observed data, or testing hypotheses about them. In frequentist estimation parameters are considered "fixed but unknown", whereas in Bayesian estimation they are trea... | Parameter | 0.814877 |
14,786 | Without altering the system, we can take multiple samples, which will have a range of values of k, but the system is always characterized by the same λ. For instance, suppose we have a radioactive sample that emits, on average, five particles every ten minutes. We take measurements of how many particles the sample emit... | Parameter | 0.814877 |
14,787 | In probability theory, one may describe the distribution of a random variable as belonging to a family of probability distributions, distinguished from each other by the values of a finite number of parameters. For example, one talks about "a Poisson distribution with mean value λ". The function defining the distributi... | Parameter | 0.814877 |
14,788 | LLVM/Clang provides a "CFI" option that works in the forward edge by checking for errors in virtual tables and type casts. It depends on link-time optimization (LTO) to know what functions are supposed to be called in normal cases. There is a separate "shadow call stack" scheme that defends on the backward edge by chec... | Control-flow integrity | 0.814868 |
14,789 | Some proposed propulsion methods apparently violate currently-understood laws of physics, including: Quantum Vacuum Thruster EM Drive or Cannae Drive | Electrical propulsion | 0.814868 |
14,790 | In physics, the Newtonian limit is a mathematical approximation applicable to physical systems exhibiting (1) weak gravitation, (2) objects moving slowly compared to the speed of light, and (3) slowly changing (or completely static) gravitational fields. Under these conditions, Newton's law of universal gravitation may... | Newtonian approximation | 0.814867 |
14,791 | In the theory of vector measures, Lyapunov's theorem states that the range of a (non-atomic) finite-dimensional vector measure is closed and convex. In fact, the range of a non-atomic vector measure is a zonoid (the closed and convex set that is the limit of a convergent sequence of zonotopes). It is used in economics,... | Vector measure | 0.814867 |
14,792 | The calculation of cube roots can be traced back to Babylonian mathematicians from as early as 1800 BCE. In the fourth century BCE Plato posed the problem of doubling the cube, which required a compass-and-straightedge construction of the edge of a cube with twice the volume of a given cube; this required the construct... | Cube roots | 0.814864 |
14,793 | The main sources of education and professional guidance for pharmaceutical microbiology come from Dr Tim Sandle's Pharmaceutical Microbiology Resources, Dr Scott Sutton's Microbiology Network, and the UK and Ireland Pharmaceutical Microbiology Interest Group (Pharmig). | Pharmaceutical microbiology | 0.814864 |
14,794 | What happens if a microorganism "fell in" whilst the lid was off? There are tests that look at that. The product is "challenged" with a known amount of specific microorganisms, such as E. coli and C. albicans and the anti-microbial activity monitored Pharmaceutical microbiology is additionally involved with the validat... | Pharmaceutical microbiology | 0.814864 |
14,795 | Drug safety is a major focus of pharmaceutical microbiology. Pathogenic bacteria, fungi (yeasts and moulds) and toxins produced by microorganisms are all possible contaminants of medicines- although stringent, regulated processes are in place to ensure the risk is minimal. | Pharmaceutical microbiology | 0.814864 |
14,796 | Another major focus of pharmaceutical microbiology is to determine how a product will react in cases of contamination. For example: You have a bottle of cough medicine. Imagine you take the lid off, pour yourself a dose and forget to replace the lid. You come back to take your next dose and discover that you will indee... | Pharmaceutical microbiology | 0.814864 |
14,797 | Pharmaceutical microbiology is an applied branch of microbiology. It involves the study of microorganisms associated with the manufacture of pharmaceuticals e.g. minimizing the number of microorganisms in a process environment, excluding microorganisms and microbial byproducts like exotoxin and endotoxin from water and... | Pharmaceutical microbiology | 0.814864 |
14,798 | The nonassociative algebra structure of A may be studied by associating it with other associative algebras which are subalgebras of the full algebra of K-endomorphisms of A as a K-vector space. Two such are the derivation algebra and the (associative) enveloping algebra, the latter being in a sense "the smallest associ... | Example of a non-associative algebra | 0.814864 |
14,799 | In other words, "non-associative" means "not necessarily associative", just as "noncommutative" means "not necessarily commutative" for noncommutative rings. An algebra is unital or unitary if it has an identity element e with ex = x = xe for all x in the algebra. For example, the octonions are unital, but Lie algebras... | Example of a non-associative algebra | 0.814864 |
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