Such a combination of proteins is also called a light-harvesting complex.Although all cells in the green parts of a plant have chloroplasts, the majority of those are found in specially adapted structures called leaves. Certain species adapted to conditions of strong sunlight and aridity, such as many Euphorbia and cactus species, have their main photosynthetic organs in their stems. The cells in the interior tissues of a leaf, called the mesophyll, can contain between 450,000 and 800,000 chloroplasts for every square millimeter of leaf. The surface of the leaf is coated with a water-resistant waxy cuticle that protects the leaf from excessive evaporation of water and decreases the absorption of ultraviolet or blue light to minimize heating. The transparent epidermis layer allows light to pass through to the palisade mesophyll cells where most of the photosynthesis takes place.


In mathematical logic, the Scott–Curry theorem is a result in lambda calculus stating that if two non-empty sets of lambda terms A and B are closed under beta-convertibility then they are recursively inseparable.


In the 1990s, Noam Elkies, followed by A. O. L. Atkin, devised improvements to Schoof's basic algorithm by restricting the set of primes S = { l 1 , … , l s } {\displaystyle S=\{l_{1},\ldots ,l_{s}\}} considered before to primes of a certain kind. These came to be called Elkies primes and Atkin primes respectively. A prime l {\displaystyle l} is called an Elkies prime if the characteristic equation: ϕ 2 − t ϕ + q = 0 {\displaystyle \phi ^{2}-t\phi +q=0} splits over F l {\displaystyle \mathbb {F} _{l}} , while an Atkin prime is a prime that is not an Elkies prime. Atkin showed how to combine information obtained from the Atkin primes with the information obtained from Elkies primes to produce an efficient algorithm, which came to be known as the Schoof–Elkies–Atkin algorithm.


In mathematics — specifically, in Riemannian geometry — geodesic convexity is a natural generalization of convexity for sets and functions to Riemannian manifolds. It is common to drop the prefix "geodesic" and refer simply to "convexity" of a set or function.


Finally, supervenience claims typically involve some modal force, however, the way that modal force is specified depends on which more specific variety of supervenience one decides upon (see below). (1) and (2) are sometimes called "schemata" because they do not correspond to actual supervenience relations until the sets of properties A and B, the domain of entities to which those properties apply, and a modal force have been specified. For modal forms of supervenience, the modal strength of the relation is usually taken to be a parameter (that is, the possible worlds appealed to may be physically possible, logically possible, etc.). Also, note that in the early literature properties were not always central, and there remain some who prefer to frame the relation in terms of predicates, facts, or entities instead, for example.


This was the beginning of a new field of mathematics now called analysis. Though not itself a branch of geometry, it is applicable to geometry, and it solved two families of problems that had long been almost intractable: finding tangent lines to odd curves, and finding areas enclosed by those curves. The methods of calculus reduced these problems mostly to straightforward matters of computation.


In the United States, there are five levels of flooding.


In some cultures of the South Pacific, life is believed to leave a person's body when they are sick or asleep, making for multiple "deaths" in the span of one lifetime.


In media where italicization is not possible, alternatives are used as substitutes: In typewritten or handwritten text, underlining is typically used. In plain-text computer files, including e-mail communication, italicised words are often indicated by surrounding them with slashes or other matched delimiters. For example: I was /really/ annoyed.


In particular, it must be relatively prime to the order of the group, if the group is finite. If the group is abelian, any powering index works. If the powering index 2 or -1 works, then the group is abelian.The group of power automorphisms commutes with the group of inner automorphisms when viewed as subgroups of the automorphism group. Thus, in particular, power automorphisms that are also inner must arise as conjugations by elements in the second group of the upper central series.


In statistics, mean absolute error (MAE) is a measure of errors between paired observations expressing the same phenomenon. Examples of Y versus X include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. MAE is calculated as the sum of absolute errors divided by the sample size:It is thus an arithmetic average of the absolute errors | e i | = | y i − x i | {\displaystyle |e_{i}|=|y_{i}-x_{i}|} , where y i {\displaystyle y_{i}} is the prediction and x i {\displaystyle x_{i}} the true value.


Many X10 protocol charts represent this start code as "1110", but it is important to realize that is in terms of zero crossings, not data bits. Immediately after the start code, a 4-bit house code (normally represented by the letters A to P on interface units) appears, and after the house code comes a 5-bit function code. Function codes may specify a unit number code (1–16) or a command code.


Finally, eight registers (g0 through g7) are globally visible to all procedure levels. The AMD 29000 improved the design by allowing the windows to be of variable size, which helps utilization in the common case where fewer than eight registers are needed for a call. It also separated the registers into a global set of 64, and an additional 128 for the windows.


In the fields of science and engineering, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's true value. The precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. Although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method. The field of statistics, where the interpretation of measurements plays a central role, prefers to use the terms bias and variability instead of accuracy and precision: bias is the amount of inaccuracy and variability is the amount of imprecision.


For two groups with general monotone valuations, there always exists a 1/2-democratic envy-free-except-1 allocation, and it can be found by an efficient algorithm. For three or more groups with binary additive valuations, there always exists a 1/k-democratic envy-free-except-1 allocation; with general monotone valuations, there always exists a 1/k-democratic envy-free-except-2 allocation. The factor 1/k is tight for envy-free-except-c allocation for any constant c. If envy-freeness is relaxed to proportionality or maximin-share, then similar guarantees can be attained using a polynomial-time algorithm. For groups with additive valuations, a variant of round-robin item allocation can be used to find a 1/3-democratic 1-out-of-best-k allocation.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 7, 17, 47, and 147 are the patterns related to Braille pattern dots-3, since the two additional dots of kantenji patterns 03, 37, and 037 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete set of convex uniform 6-polytopes has not been determined, but most can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations of rings of the Coxeter-Dynkin diagrams. Each combination of at least one ring on every connected group of nodes in the diagram produces a uniform 6-polytope. The simplest uniform polypeta are regular polytopes: the 6-simplex {3,3,3,3,3}, the 6-cube (hexeract) {4,3,3,3,3}, and the 6-orthoplex (hexacross) {3,3,3,3,4}.


More precisely, if you start at any node in the network and form the set of all nodes at distance d {\displaystyle d} or less from that starting node, the set will, with probability tending to 1 as n → ∞, take the form of a tree. In tree-like structures, the number of second neighbors averaged over the whole network, c 2 {\displaystyle c_{2}} , is: c 2 = ⟨ k 2 ⟩ − ⟨ k ⟩ . {\displaystyle c_{2}=\langle k^{2}\rangle -\langle k\rangle .}


In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals.


In the context of coding theory, D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} can be constructed by measuring the expected number of extra bits required to code samples from P {\displaystyle P} using a code optimized for Q {\displaystyle Q} rather than the code optimized for P {\displaystyle P} .


In supervised learning, one is given a set of training examples X 1 … X n {\displaystyle X_{1}\ldots X_{n}} with labels y 1 … y n {\displaystyle y_{1}\ldots y_{n}} , and wishes to predict y n + 1 {\displaystyle y_{n+1}} given X n + 1 {\displaystyle X_{n+1}} . To do so one forms a hypothesis, f {\displaystyle f} , such that f ( X n + 1 ) {\displaystyle f(X_{n+1})} is a "good" approximation of y n + 1 {\displaystyle y_{n+1}} . A "good" approximation is usually defined with the help of a loss function, ℓ ( y , z ) {\displaystyle \ell (y,z)} , which characterizes how bad z {\displaystyle z} is as a prediction of y {\displaystyle y} .


In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the (null) hypothesis that two populations have equal means. It is named for its creator, Bernard Lewis Welch, is an adaptation of Student's t-test, and is more reliable when the two samples have unequal variances and possibly unequal sample sizes. These tests are often referred to as "unpaired" or "independent samples" t-tests, as they are typically applied when the statistical units underlying the two samples being compared are non-overlapping. Given that Welch's t-test has been less popular than Student's t-test and may be less familiar to readers, a more informative name is "Welch's unequal variances t-test" — or "unequal variances t-test" for brevity.


In robotics, the manipulability ellipsoid is the geometric interpretation of the scaled eigenvectors resulting from the singular value decomposition of the jacobian that describes a robot's motion.


In programming, instrumentation means: Profiling: measuring dynamic program behaviors during a training run with a representative input. This is useful for properties of a program that cannot be analyzed statically with sufficient precision, such as alias analysis. Inserting timers into functions. Logging major events such as crashes.


In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem in the Euclidean plane. These polynomials are named after Eugène Ehrhart who studied them in the 1960s.


Remote call forwarding is also a means for a suburban business to obtain a city-centre local number (with its full large-city coverage area) for inbound calls; while cheaper than a foreign exchange line, this can reduce long-distance telephony costs in markets where local calls are flat-rated but trunk calls are expensive. One alternative to RCF is Caller Redirect whereby callers simply hear an intercept message notifying them that the number has changed. Another alternative is to port the existing number to a voice over IP carrier, which is not tied to a single physical location as the subscriber may be anywhere on broadband Internet. However, not all phone numbers can be ported.


For example, on the System/370 Model 158, the keyboard sequence 0-7-X (zero, seven and X, in that order) results in an IPL from the device address which was keyed into the input area. The Amdahl 470V/6 and related CPUs supported four hexadecimal digits on those CPUs which had the optional second channel unit installed, for a total of 32 channels.


A formal language begins with different types of symbols. These types can include variables, operators, function symbols, predicate (or relation) symbols, quantifiers, and propositional constants. (Grouping symbols such as delimiters are often added for convenience in using the language, but do not play a logical role.)


In prose writing, twelve, being the last single-syllable numeral, is sometimes taken as the last number to be written as a word, and 13 the first to be written using digits. This is not a binding rule, and in English language tradition, it is sometimes recommended to spell out numbers up to and including either nine, ten or twelve, or even ninety-nine or one hundred. Another system spells out all numbers written in one or two words (sixteen, twenty-seven, fifteen thousand, but 372 or 15,001). In German orthography, there used to be the widely followed (but unofficial) rule of spelling out numbers up to twelve (zwölf). The Duden (the German standard dictionary) mentions this rule as outdated.


This random tree has several equivalent definitions and constructions: using sub-trees generated by finitely many leaves, using a Brownian excursion, Poisson separating a straight line or as a limit of Galton-Watson trees. Intuitively, the Brownian tree is a binary tree whose nodes (or branching points) are dense in the tree; which is to say that for any distinct two points of the tree, there will always exist a node between them. It is a fractal object which can be approximated with computers or by physical processes with dendritic structures.


Researchers note that a password based protocol with mutual authentication is important because user identities and passwords are still protected, as the messages are only readable to the two parties involved.However, a negative aspect about password-based authentication is that password tables can take up a lot of memory space. One way around using a lot of memory during a password-based authentication scheme is to implement one-time passwords (OTP), which is a password sent to the user via SMS or email. OTPs are time-sensitive, which means that they will expire after a certain amount of time and that memory does not need to be stored.


This would give a model perplexity of 2190 per sentence. However, it is more common to normalize for sentence length. Thus, if the test sample's sentences comprised a total of 1,000 words, and could be coded using 7.95 bits per word, one could report a model perplexity of 27.95 = 247 per word. In other words, the model is as confused on test data as if it had to choose uniformly and independently among 247 possibilities for each word.


In the case of deconvolution of seismic data, the original unknown signal is made of spikes hence is possible to characterize with sparsity constraints or regularizations such as l1 norm/l2 norm norm ratios, suggested by W. C. Gray in 1978.


The spectral characteristics of these areas are used to train the remote sensing software using decision rules for classifying the rest of the image. These decision rules such as Maximum Likelihood Classification, Parallelopiped Classification, and Minimum Distance Classification offer different techniques to classify an image. Additional ground truth sites allow the remote sensor to establish an error matrix that validates the accuracy of the classification method used.


The general linear groups PGL(2,q) are imperfect for q an odd prime power. For any group H, the wreath product H wr Sym2 of H with the symmetric group on two points is imperfect. In particular, every group can be embedded as a two-step subnormal subgroup of an imperfect group of roughly the same cardinality (2|H|2).


In order to substantiate an athlete's or team's improvements, progress must be monitored. During the monitoring step feedback is provided and the necessary adjustments follow thereafter. It is important to remember this is a feedback loop and operates in a manner that the feedback feeds into adjustments made and vice versa.


Due to the nature of our value function’s different slopes for gains and losses, our utility is maximized in different ways, depending on how we code the four kinds of transactions x {\displaystyle x} and y {\displaystyle y} (as gains or as losses):1) Multiple gains: x {\displaystyle x} and y {\displaystyle y} are both considered gains. Here, we see that V a l u e ( x ) + V a l u e ( y ) > V a l u e ( x + y ) {\displaystyle Value(x)+Value(y)>Value(x+y)} . Thus, we want to segregate multiple gains.


In one sense, DRT offers a variation of first-order predicate calculus—its forms are pairs of first-order formulae and the free variables that occur in them. In traditional natural language semantics, only individual sentences are examined, but the context of a dialogue plays a role in meaning as well. For example, anaphoric pronouns such as he and she rely upon previously introduced individual constants in order to have meaning. DRT uses variables for every individual constant in order to account for this problem.


In mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "yes" or "no" according to whether the statement is universally valid, i.e., valid in every structure satisfying the axioms.


Subscribing organisations are expected to provide relevant data to maintain the common data pool.Credit reference agencies are bound by the Data Protection Act 2018, which requires that data relating to identifiable individuals must be accurate, relevant, held for a proper purpose and not out-of-date, and gives individuals the legal right to access data held on them. Credit agencies are therefore required under law to provide an individual with a copy of their consumer credit report upon request. Most agencies also provide online services for ongoing access to reports.


This is one case where they go beyond merely ensuring integrity, and with some reactive security mechanisms, may actually prevent the malicious activity, e.g. by dropping all packets containing the honeytoken at the router. However, such mechanisms have pitfalls because it might cause serious problems if the honeytoken was poorly chosen and appeared in otherwise legitimate network traffic, which was then dropped. The term was first coined by Augusto Paes de Barros in 2003.


The "topics" produced by topic modeling techniques are clusters of similar words. A topic model captures this intuition in a mathematical framework, which allows examining a set of documents and discovering, based on the statistics of the words in each, what the topics might be and what each document's balance of topics is. Topic models are also referred to as probabilistic topic models, which refers to statistical algorithms for discovering the latent semantic structures of an extensive text body.


In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group. It is a central tool in combinatorial and geometric group theory. The structure and symmetry of Cayley graphs makes them particularly good candidates for constructing families of expander graphs.


In mathematics, a closure operator on a set S is a function cl: P ( S ) → P ( S ) {\displaystyle \operatorname {cl} :{\mathcal {P}}(S)\rightarrow {\mathcal {P}}(S)} from the power set of S to itself that satisfies the following conditions for all sets X , Y ⊆ S {\displaystyle X,Y\subseteq S} Closure operators are determined by their closed sets, i.e., by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set containing X. Such families of "closed sets" are sometimes called closure systems or "Moore families". A set together with a closure operator on it is sometimes called a closure space. Closure operators are also called "hull operators", which prevents confusion with the "closure operators" studied in topology.


Numerous methods exist to compute descent directions, all with differing merits, such as gradient descent or the conjugate gradient method. More generally, if P {\displaystyle P} is a positive definite matrix, then p k = − P ∇ f ( x k ) {\displaystyle p_{k}=-P\nabla f(x_{k})} is a descent direction at x k {\displaystyle x_{k}} . This generality is used in preconditioned gradient descent methods.


In scrum, the term developer or team member refers to anyone who plays a role in the development and support of the product and can include researchers, architects, designers, programmers, etc.


For example, a realizer for the proposition "A implies B" is a computable function that takes a realizer for A, and uses it to compute a realizer for B. Realizability models characterize realizers for propositions in terms of their visible behavior, and not in terms of their internal structure. Girard shows that for second-order affine linear logic, given a computational system with nontermination and error stops as effects, realizability and focalization give the same meaning to types. Ludics was proposed by the logician Jean-Yves Girard.


In the efforts-expended method, the share of effort consumed to date is compared to the total effort expected for the project. For example, the completion percentage may be established on direct work hours, machine hours, or quantities of material.


, which at least chooses a minimum-expected-loss action δ ( x ) {\displaystyle \delta (x)\!\,} for those x {\displaystyle x\,\!} for which a finite-expected-loss action does exist. In addition, a generalized Bayes rule may be desirable because it must choose a minimum-expected-loss action δ ( x ) {\displaystyle \delta (x)\,\!}


However, descriptions of the elements of a smart television can be found in public discourse from the beginning of the 1980s, if not earlier, with the introduction of videotex services, particularly teletext information for reception by television sets, leading commentators to consider that televisions and accessories would evolve to encompass a range of related activities. In the words of one commentator: "In the long run, this machine is likely to develop into a multi-purpose receiver, for electronic mail, dealing with the bank, calculations, remote information - and 'Not the nine o'clock news' or 'Casablanca' on video. "The mass acceptance of digital television in the mid-late 2000s and early 2010s greatly improved Smart TVs.


In modern Gaelic, person inflections have almost disappeared, but the negative and interrogative are marked by distinctive forms. In Irish, particularly in the south, person inflections are still very common for the tá/bhí series.


A similar system, known as Emergency Alert, is used in Australia to notify the public of impending disasters through both SMS and landline phone calls. These messages can be sent based on either the location of the phone or the address to which the handset is registered. In the early 2020s, device manufacturers have begun to integrate satellite messaging connectivity and satellite emergency services into conventional mobile phones for use in remote regions, where there is no reliable terrestrial cellular network.


The purpose of this directive is to prevent the production of waste electronics and also to encourage reuse and recycling of such waste. The directive requires the Member States to encourage design and production methods that take into account the future dismantling and recovery of their products. These take-back programs have been adopted in nearly every OECD country. In the United States, most of these policies have been implemented at the state level.


The motive behind the project was to provide the utility of a smartphone in a simplistic and less dynamic delivery. Moreover, other projects have focused on building second phones with less functionality, or putting human nature and design above technology. Some critics disagree with Google's approach to the digital detox phenomenon, however, and instead argue that harmony between technology use and well-being can be achieved. Additionally, these critics suggest that the best way to digitally detox is to be mindful of the amount of time that is being spent on a digital device.


In order to prove the HSW coding theorem, we really just need a few basic things from quantum mechanics. First, a quantum state is a unit trace, positive operator known as a density operator. Usually, we denote it by ρ {\displaystyle \rho } , σ {\displaystyle \sigma } , ω {\displaystyle \omega } , etc. The simplest model for a quantum channel is known as a classical-quantum channel: The meaning of the above notation is that inputting the classical letter x {\displaystyle x} at the transmitting end leads to a quantum state ρ x {\displaystyle \rho _{x}} at the receiving end. It is the task of the receiver to perform a measurement to determine the input of the sender.


In mathematics, more precisely in formal language theory, the profinite words are a generalization of the notion of finite words into a complete topological space. This notion allows the use of topology to study languages and finite semigroups. For example, profinite words are used to give an alternative characterization of the algebraic notion of a variety of finite semigroups.


In mathematical statistics, a random variable X is standardized by subtracting its expected value E   {\displaystyle \operatorname {E} } and dividing the difference by its standard deviation σ ( X ) = Var  ( X ): {\displaystyle \sigma (X)={\sqrt {\operatorname {Var} (X)}}:} Z = X − E   σ ( X ) {\displaystyle Z={X-\operatorname {E}  \over \sigma (X)}} If the random variable under consideration is the sample mean of a random sample X 1 , … , X n {\displaystyle \ X_{1},\dots ,X_{n}} of X: X ¯ = 1 n ∑ i = 1 n X i {\displaystyle {\bar {X}}={1 \over n}\sum _{i=1}^{n}X_{i}} then the standardized version is Z = X ¯ − E   σ ( X ) / n . {\displaystyle Z={\frac {{\bar {X}}-\operatorname {E} }{\sigma (X)/{\sqrt {n}}}}.}


Sometimes it is enough to prove negligence, while in other cases a more serious fault is required. Thus, anyone who unlawfully interferes, intentionally or through recklessness, with the life, body, health, freedom or property of others is liable to others to repair the resulting damage. On the other hand, less protection is granted in the event of damage to purely intangible interests, nicht-gegenständliche Interessen, that is to say when the victim only suffers purely economic or moral damage.


When the learner knows the conditional probability, then one solution is: C ^ B ( x ) = arg  max k ∈ { 1... K } P ( C k | X = x ) {\displaystyle {\hat {C}}_{B}(x)=\arg \max _{k\in \{1...K\}}P(C_{k}|X=x)} This solution is known as the Bayes classifier. The corresponding expected Prediction Error is called the Bayes error rate: B E = E x  = E x  = E x  {\displaystyle BE=E_{x}=E_{x}=E_{x}} ,where the sum can be omitted in the last step due to considering the counter event. By the definition of the Bayes classifier, it maximizes P ( C ^ B ( x ) | x ) {\displaystyle P({\hat {C}}_{B}(x)|x)} and, therefore, minimizes the Bayes error BE. The Bayes error is non-zero if the classification labels are not deterministic, i.e., there is a non-zero probability of a given instance belonging to more than one class.. In a regression context with squared error, the Bayes error is equal to the noise variance.


In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–Kochen–Specker theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved by Kochen and Specker also gave an explicit example for this constraint in terms of a finite number of state vectors. The theorem is a complement to Bell's theorem (to be distinguished from the (Bell–)Kochen–Specker theorem of this article).


In number theory, an equidigital number is a natural number in a given number base that has the same number of digits as the number of digits in its prime factorization in the given number base, including exponents but excluding exponents equal to 1. For example, in base 10, 1, 2, 3, 5, 7, and 10 (2 × 5) are equidigital numbers (sequence A046758 in the OEIS). All prime numbers are equidigital numbers in any base. A number that is either equidigital or frugal is said to be economical.


Some versions of coordinate descent randomly pick a different coordinate direction each iteration. Random-restart hill climbing is a meta-algorithm built on top of the hill climbing algorithm. It is also known as Shotgun hill climbing.


In social network analysis and mathematical sociology, interpersonal ties are defined as information-carrying connections between people. Interpersonal ties, generally, come in three varieties: strong, weak or absent. Weak social ties, it is argued, are responsible for the majority of the embeddedness and structure of social networks in society as well as the transmission of information through these networks. Specifically, more novel information flows to individuals through weak rather than strong ties.


In political/economic theory, notably socialist, Marxist, and many anarchist philosophies, the distinction between private and personal property is an important one. In capitalism private and personal property are considered to be of equal importance and significance without the need for making a distinction. Personal property, or possessions, includes "items intended for personal use" (e.g., one's toothbrush, clothes, and vehicles, and rarely money). It must be gained in a "fair" manner according to socialist doctrine.


In number theory, Bonse's inequality, named after H. Bonse, relates the size of a primorial to the smallest prime that does not appear in its prime factorization. It states that if p1, ..., pn, pn+1 are the smallest n + 1 prime numbers and n ≥ 4, then p n # = p 1 ⋯ p n > p n + 1 2 . {\displaystyle p_{n}\#=p_{1}\cdots p_{n}>p_{n+1}^{2}.} (the middle product is short-hand for the primorial p n # {\displaystyle p_{n}\#} of pn) Mathematician Denis Hanson showed an upper bound where n # ≤ 3 n {\displaystyle n\#\leq 3^{n}} .


It is an example of an algorithm, a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.


In mathematics, particularly linear algebra, a zero matrix is a matrix with all its entries being zero. It is alternately denoted by the symbol O {\displaystyle O} . Some examples of zero matrices are 0 1 , 1 =  , 0 2 , 2 =  , 0 2 , 3 =  , {\displaystyle 0_{1,1}={\begin{bmatrix}0\end{bmatrix}},\ 0_{2,2}={\begin{bmatrix}0&0\\0&0\end{bmatrix}},\ 0_{2,3}={\begin{bmatrix}0&0&0\\0&0&0\end{bmatrix}},\ } The set of m × n matrices with entries in a ring K forms a module K m , n {\displaystyle K_{m,n}} . The zero matrix 0 K m , n {\displaystyle 0_{K_{m,n}}} in K m , n {\displaystyle K_{m,n}} is the matrix with all entries equal to 0 K {\displaystyle 0_{K}} , where 0 K {\displaystyle 0_{K}} is the additive identity in K.


In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of a pointwise convergent sequence of random variables defined on a common probability space. It is named for the Soviet mathematician A. V. Skorokhod.


Neumann (1935), G.A. Miller (1935), and J.A. de Séguier (1904).


In either case, the PC would display an error message and halt. Some later PC clones used an NMI to conceal the hardware differences from that of a standard PC. On such computers, an NMI would be generated when a program attempted to access incompatible hardware.


In practice, the tests are run once or twice per week during the entire development cycle, using three to five test subjects per round, and with the results delivered within 24 hours to the designers. The number of users actually tested over the course of the project can thus easily reach 50 to 100 people. Research shows that user testing conducted by organisations most commonly involves the recruitment of 5-10 participants.In the early stage, when users are most likely to immediately encounter problems that stop them in their tracks, almost anyone of normal intelligence can be used as a test subject.


In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of the elements of a set J, then J is an index set. The indexing consists of a surjective function from J onto A, and the indexed collection is typically called an indexed family, often written as {Aj}j∈J.


Some examples of algorithms used are Filterbank, adjacent orientation vector (AOV) system, and correlation-filter. Filterbank requires whole fingerprints and cannot identify just the tips of the finger since it uses both the local and overall structure. The algorithm works by selecting a region of interest and dividing it into sectors.


In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies.


Categorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data. More specifically, categorical data may derive from observations made of qualitative data that are summarised as counts or cross tabulations, or from observations of quantitative data grouped within given intervals. Often, purely categorical data are summarised in the form of a contingency table.


"Surveys in the academic community have shown NLP to be widely discredited among scientists. Among the reasons for considering NLP a pseudoscience are that evidence in favor of it is limited to anecdotes and personal testimony, that it is not informed by scientific understanding of neuroscience and linguistics, and that the name "neuro-linguistic programming" uses jargon words to impress readers and obfuscate ideas, whereas NLP itself does not relate any phenomena to neural structures and has nothing in common with linguistics or programming. In fact, in education, NLP has been used as a key example of pseudoscience.


The two codes C 1 {\displaystyle \mathbf {C_{1}} } and C 2 {\displaystyle \mathbf {C_{2}} } can be constructed as subcodes of the ( 7 , 4 , 3 ) {\displaystyle (7,4,3)} Hamming code and thus has minimum distance of 3 {\displaystyle 3} . Given the generator matrix G {\displaystyle \mathbf {G} } of the original Hamming code, the generator matrix G 1 {\displaystyle \mathbf {G_{1}} } for C 1 {\displaystyle \mathbf {C_{1}} } is constructed by taking any two rows from G {\displaystyle \mathbf {G} } , and G 2 {\displaystyle \mathbf {G_{2}} } is constructed by the remaining two rows of G {\displaystyle \mathbf {G} } . The corresponding ( 5 × 7 ) {\displaystyle (5\times 7)} parity-check matrix for each sub-code can be generated according to the generator matrix and used to generate syndrome bits.


In some languages, a pointer can reference executable code, i.e., it can point to a function, method, or procedure. A function pointer will store the address of a function to be invoked. While this facility can be used to call functions dynamically, it is often a favorite technique of virus and other malicious software writers.


Unlike other Indo-European languages, in Slavic languages tense is independent of aspect, with imperfective and perfective aspects being indicated instead by means of prefixes, stem changes, or suppletion. In many West Slavic and East Slavic languages, the early Slavic past tenses have largely merged into a single past tense. In both West and East Slavic, verbs in the past tense are conjugated for gender (masculine, feminine, neuter) and number (singular, plural).


In the Bayesian network below, X {\displaystyle X\,\!} and Y {\displaystyle Y\,\!} are parent variables and Z {\displaystyle Z\,\!} is the child variable.


In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element. More precisely, if A is a finite set of generators for G then the word problem is the membership problem for the formal language of all words in A and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on A to the group G. If B is another finite generating set for G, then the word problem over the generating set B is equivalent to the word problem over the generating set A. Thus one can speak unambiguously of the decidability of the word problem for the finitely generated group G. The related but different uniform word problem for a class K of recursively presented groups is the algorithmic problem of deciding, given as input a presentation P for a group G in the class K and two words in the generators of G, whether the words represent the same element of G. Some authors require the class K to be definable by a recursively enumerable set of presentations.


The theorems are those formulae B {\displaystyle B} such that ⊢ B {\displaystyle \vdash B} (with an empty left-hand side) is the conclusion of a valid proof. (In some presentations of natural deduction, the A i {\displaystyle A_{i}} s and the turnstile are not written down explicitly; instead a two-dimensional notation from which they can be inferred is used.) The standard semantics of a judgment in natural deduction is that it asserts that whenever A 1 {\displaystyle A_{1}} , A 2 {\displaystyle A_{2}} , etc., are all true, B {\displaystyle B} will also be true. The judgments A 1 , … , A n ⊢ B {\displaystyle A_{1},\ldots ,A_{n}\vdash B} and ⊢ ( A 1 ∧ ⋯ ∧ A n ) → B {\displaystyle \vdash (A_{1}\land \cdots \land A_{n})\rightarrow B} are equivalent in the strong sense that a proof of either one may be extended to a proof of the other.


In the field of telephony, quality of service was defined by the ITU in 1994. Quality of service comprises requirements on all the aspects of a connection, such as service response time, loss, signal-to-noise ratio, crosstalk, echo, interrupts, frequency response, loudness levels, and so on. A subset of telephony QoS is grade of service (GoS) requirements, which comprises aspects of a connection relating to capacity and coverage of a network, for example guaranteed maximum blocking probability and outage probability.In the field of computer networking and other packet-switched telecommunication networks, teletraffic engineering refers to traffic prioritization and resource reservation control mechanisms rather than the achieved service quality. Quality of service is the ability to provide different priorities to different applications, users, or data flows, or to guarantee a certain level of performance to a data flow.


In the area of modern algebra known as group theory, the McLaughlin group McL is a sporadic simple group of order 27 ⋅ 36 ⋅ 53 ⋅ 7 ⋅ 11 = 898,128,000 ≈ 9×108.


In the Bayesian version of binary hypothesis testing one is interested in minimizing the average error probability under both hypothesis, assuming a prior probability of occurrence on each hypothesis. Let π 0 {\displaystyle \pi _{0}} denote the prior probability of hypothesis H 0 {\displaystyle H_{0}} . In this case the average error probability is given by P ave = π 0 P ( error ∣ H 0 ) + ( 1 − π 0 ) P ( error ∣ H 1 ) {\displaystyle P_{\text{ave}}=\pi _{0}P({\text{error}}\mid H_{0})+(1-\pi _{0})P({\text{error}}\mid H_{1})} . In this setting again a likelihood ratio test is optimal and the optimal error decays as lim n → ∞ − ln  P ave n = C ( f 0 , f 1 ) {\displaystyle \lim _{n\to \infty }{\frac {-\ln P_{\text{ave}}}{n}}=C(f_{0},f_{1})} where C ( f 0 , f 1 ) {\displaystyle C(f_{0},f_{1})} represents the Chernoff-information between the two distributions defined as C ( f 0 , f 1 ) = max λ ∈   {\displaystyle C(f_{0},f_{1})=\max _{\lambda \in }\left} . == References ==


In these examples, the (negative) least absolute remainder is obtained from the least positive remainder by subtracting 5, which is d. This holds in general. When dividing by d, either both remainders are positive and therefore equal, or they have opposite signs. If the positive remainder is r1, and the negative one is r2, then r1 = r2 + d.


The set of positive matrices is a subset of all non-negative matrices. While such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive-definite matrices, which are different. A matrix which is both non-negative and is positive semidefinite is called a doubly non-negative matrix. A rectangular non-negative matrix can be approximated by a decomposition with two other non-negative matrices via non-negative matrix factorization. Eigenvalues and eigenvectors of square positive matrices are described by the Perron–Frobenius theorem.


Since its initial sound is aspirated, it can be represented as , and the word's phonetic representation would then be . (The precise features shown in a phonetic representation depend on whether a narrow or broad transcription is used and which features the writer wishes to draw attention to in a particular context.) When phones are considered to be realizations of the same phoneme, they are called allophones of that phoneme (more information on the methods of making such assignments can be found under phoneme). In English, for example,  and  are considered allophones of a single phoneme, which is written /p/. The phonemic transcriptions of those two words is thus /spɪn/ and /pɪn/, and aspiration is then no longer shown since it is not distinctive.


In number theory, the parity problem refers to a limitation in sieve theory that prevents sieves from giving good estimates in many kinds of prime-counting problems. The problem was identified and named by Atle Selberg in 1949. Beginning around 1996, John Friedlander and Henryk Iwaniec developed some parity-sensitive sieves that make the parity problem less of an obstacle.


Pure type systems may obscure the distinction between types and terms and collapse the type hierarchy, as is the case with the calculus of constructions, but this is not generally the case, e.g. the simply typed lambda calculus allows only terms to depend on terms. Pure type systems were independently introduced by Stefano Berardi (1988) and Jan Terlouw (1989). Barendregt discussed them at length in his subsequent papers.


This can make the distribution a useful overdispersed alternative to the Poisson distribution, for example for a robust modification of Poisson regression. In epidemiology, it has been used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. More generally, it may be appropriate where events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term. The term "negative binomial" is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability mass function of the distribution can be written more simply with negative numbers.


They must be fitted with a speedometer and may not be used by children under 14.All three classes may be used on footways and cycle paths. Class 2 and 3 may be used on dual carriageways with a flashing amber beacon, and otherwise must comply with most other regulations pertaining to use of vehicles on the carriageway (e.g. lights and reflectors), though they are specifically excluded from the definition of "motor vehicle". All are banned from motorways. None of them cover the types described in the section above, which are ordinary motor vehicles subject to all regulations applicable to such.


In software development, obfuscation is the act of creating source or machine code that is difficult for humans or computers to understand. Like obfuscation in natural language, it may use needlessly roundabout expressions to compose statements. Programmers may deliberately obfuscate code to conceal its purpose (security through obscurity) or its logic or implicit values embedded in it, primarily, in order to prevent tampering, deter reverse engineering, or even to create a puzzle or recreational challenge for someone reading the source code. This can be done manually or by using an automated tool, the latter being the preferred technique in industry.


In particle physics, preons are hypothetical point particles, conceived of as sub-components of quarks and leptons. The word was coined by Jogesh Pati and Abdus Salam, in 1974. Interest in preon models peaked in the 1980s but has slowed, as the Standard Model of particle physics continues to describe physics mostly successfully, and no direct experimental evidence for lepton and quark compositeness has been found.


In bra–ket notation, this is typically denoted as ψ + = | + ⟩ {\displaystyle {\boldsymbol {\psi }}_{+}=|+\rangle } , and ψ − = | − ⟩ {\displaystyle {\boldsymbol {\psi }}_{-}=|-\rangle } . As above, kets and bras with the same label are interpreted as kets and bras corresponding to each other using the inner product. In particular, when also identified with row and column vectors, kets and bras with the same label are identified with Hermitian conjugate column and row vectors. Bra–ket notation was effectively established in 1939 by Paul Dirac; it is thus also known as Dirac notation, despite the notation having a precursor in Hermann Grassmann's use of  {\displaystyle } for inner products nearly 100 years earlier.


In number theory, the ideal class group (or class group) of an algebraic number field K is the quotient group JK /PK where JK is the group of fractional ideals of the ring of integers of K, and PK is its subgroup of principal ideals. The class group is a measure of the extent to which unique factorization fails in the ring of integers of K. The order of the group, which is finite, is called the class number of K. The theory extends to Dedekind domains and their fields of fractions, for which the multiplicative properties are intimately tied to the structure of the class group. For example, the class group of a Dedekind domain is trivial if and only if the ring is a unique factorization domain.


One approach would be to modify the program-instructions (the ones stored in the registers) so that they contain more than one command. But this too can be exhausted unless an instruction is of (potentially) unbounded size. So why not use just one "über-instruction" – one really really big number – that contains all the program instructions encoded into it!


(The above properties relating to rows may be replaced by the corresponding statements with respect to columns.) Determinants occur throughout mathematics.


In queueing theory, a discipline within the mathematical theory of probability, the flow-equivalent server method (also known as flow-equivalent aggregation technique, Norton's theorem for queueing networks or the Chandy–Herzog–Woo method) is a divide-and-conquer method to solve product form queueing networks inspired by Norton's theorem for electrical circuits. The network is successively split into two, one portion is reconfigured to a closed network and evaluated. Marie's algorithm is a similar method where analysis of the sub-network are performed with state-dependent Poisson process arrivals. == References ==


The technique was extended to unit disk graphs by Schneider et al. The fastest deterministic algorithms for (Δ + 1)-coloring for small Δ are due to Leonid Barenboim, Michael Elkin and Fabian Kuhn. The algorithm by Barenboim et al. runs in time O(Δ) + log*(n)/2, which is optimal in terms of n since the constant factor 1/2 cannot be improved due to Linial's lower bound. Panconesi & Srinivasan (1996) use network decompositions to compute a Δ+1 coloring in time 2 O ( log  n ) {\displaystyle 2^{O\left({\sqrt {\log n}}\right)}} .


A significant invention, which later had a profound effect on electronic music, was the audion in 1906. This was the first thermionic valve, or vacuum tube and which led to the generation and amplification of electrical signals, radio broadcasting, and electronic computation, among other things. Other early synthesizers included the Telharmonium (1897), the Theremin (1919), Jörg Mager's Spharophon (1924) and Partiturophone, Taubmann's similar Electronde (1933), Maurice Martenot's ondes Martenot ("Martenot waves", 1928), Trautwein's Trautonium (1930).


In mathematical optimization, oracle complexity is a standard theoretical framework to study the computational requirements for solving classes of optimization problems. It is suitable for analyzing iterative algorithms which proceed by computing local information about the objective function at various points (such as the function's value, gradient, Hessian etc.). The framework has been used to provide tight worst-case guarantees on the number of required iterations, for several important classes of optimization problems.


The distinction between BYOD and school-issued devices became blurred when many schools started recommending devices for parents to buy (examples for both iPads and Chromebooks being used 1:1 in schools, but being paid for by parents exist, there may be similar evidence for other devices). The term 1:1 computing in education is now redefined to a situation where students have access to a device per individual that is used in the teaching as a tool for learning. Historically, the programs have centered around the following devices: Laptops (Windows and Mac) 1990s-2010. iPads (with some competing Android and Windows devices) 2010-2014 Chromebooks (2015–present) (with iPad+keyboard and other laptop & tablet-computers competing).


Tuple may be formally defined from ordered pairs by recurrence by starting from ordered pairs; indeed, a n-tuple can be identified with the ordered pair of its (n − 1) first elements and its nth element. Tuples are usually written by listing the elements within parentheses "( )", separated by a comma and a space; for example, (2, 7, 4, 1, 7) denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets "" or angle brackets "⟨ ⟩".


In the Netherlands, there is coverage on all the lines and the old system called Telerail was abandoned in favour of GSM-R in 2006.


In order to ensure replica convergence, a system must reconcile differences between multiple copies of distributed data. This consists of two parts: exchanging versions or updates of data between servers (often known as anti-entropy); and choosing an appropriate final state when concurrent updates have occurred, called reconciliation.The most appropriate approach to reconciliation depends on the application. A widespread approach is "last writer wins". Another is to invoke a user-specified conflict handler.


Be aware that roundoff errors can accumulate. If M decimal places are used in the intermediate calculation, we say there are M−N guard digits. Guard digits are also used in floating point operations in most computer systems.


In mathematical logic the theory of pure equality is a first-order theory. It has a signature consisting of only the equality relation symbol, and includes no non-logical axioms at all.This theory is consistent but incomplete, as a non-empty set with the usual equality relation provides an interpretation making certain sentences true. It is an example of a decidable theory and is a fragment of more expressive decidable theories, including monadic class of first-order logic (which also admits unary predicates and is, via Skolem normal form, related to set constraints in program analysis) and monadic second-order theory of a pure set (which additionally permits quantification over predicates and whose signature extends to monadic second-order logic of k successors).


Hence, it cannot account for the correct or incorrect application of a name. He claimed that there was a natural correctness to names. To do this, he pointed out that compound words and phrases have a range of correctness.


C libraries complying to POSIX or the Single Unix Specification (SUSv3) provided such routines as getcontext, setcontext, makecontext and swapcontext, but these functions were declared obsolete in POSIX 1.2008.Once a second call stack has been obtained with one of the methods listed above, the setjmp and longjmp functions in the standard C library can then be used to implement the switches between coroutines. These functions save and restore, respectively, the stack pointer, program counter, callee-saved registers, and any other internal state as required by the ABI, such that returning to a coroutine after having yielded restores all the state that would be restored upon returning from a function call. Minimalist implementations, which do not piggyback off the setjmp and longjmp functions, may achieve the same result via a small block of inline assembly which swaps merely the stack pointer and program counter, and clobbers all other registers.


In the distributed environment, one might have difficulties in keeping track of everyone's workload and contribution towards the deliverable. Through adoption of agile principles and practices, the visibility is made clearer as there are multiple iterations where one can visualize the issues or criticalities on the initial stages of the project. Continuous integration of programming code, which is one of the focal pieces of agile software development, additionally serves to reduce setup of the executive issues. Adopting of agile principles appears to positively affect correspondence between groups as advancement in cycles makes it simpler for members to see the short-term objectives.


In mathematics, two non-empty subsets A and B of a given metric space (X, d) are said to be positively separated if the infimum inf a ∈ A , b ∈ B d ( a , b ) > 0. {\displaystyle \inf _{a\in A,b\in B}d(a,b)>0.} (Some authors also specify that A and B should be disjoint sets; however, this adds nothing to the definition, since if A and B have some common point p, then d(p, p) = 0, and so the infimum above is clearly 0 in that case.) For example, on the real line with the usual distance, the open intervals (0, 2) and (3, 4) are positively separated, while (3, 4) and (4, 5) are not. In two dimensions, the graph of y = 1/x for x > 0 and the x-axis are not positively separated.


Formally, given a set of data points x, the k centers ci are to be chosen so as to minimize the sum of the distances from each x to the nearest ci. The criterion function formulated in this way is sometimes a better criterion than that used in the k-means clustering algorithm, in which the sum of the squared distances is used.


The programmer would change the one-word BR to the two-word JMP instruction from the next group. As JMP has no conditional forms, the programmer would change BEQ to a BNE that branched around a JMP. SOB (Subtract One and Branch) is another conditional branch instruction. The specified register is decremented by 1, and if the result is not zero, a reverse branch is taken based on the 6 bit word offset.


In modern operating systems, non-system (i.e. user-mode) applications are prevented from accessing any memory locations not explicitly authorized by the virtual memory controller (called memory management unit (MMU)). In addition to containing damage that may be caused by software flaws and allowing more efficient use of physical memory, this architecture forms an integral part of the security of the operating system. However, kernel-mode drivers, many hardware devices, and user-mode vulnerabilities allow direct, unimpeded access of the physical memory address space. The physical address space includes all of the main system memory, as well as memory-mapped buses and hardware devices (which are controlled by the operating system through reads and writes as if they were ordinary RAM).


In mathematics, a nonnegative matrix, written X ≥ 0 , {\displaystyle \mathbf {X} \geq 0,} is a matrix in which all the elements are equal to or greater than zero, that is, x i j ≥ 0 ∀ i , j . {\displaystyle x_{ij}\geq 0\qquad \forall {i,j}.} A positive matrix is a matrix in which all the elements are strictly greater than zero.


In the EAV table itself, this is just an attribute ID, a foreign key into an Attribute Definitions table, as stated above. However, there are usually multiple metadata tables that contain attribute-related information, and these are discussed shortly.


In the 1880s Herman Hollerith invented the recording of data on a medium that could then be read by a machine. Prior uses of machine readable media had been for lists of instructions (not data) to drive programmed machines such as Jacquard looms and mechanized musical instruments. "After some initial trials with paper tape, he settled on punched cards ".


Therefore, equation (5) applied successively, provides an algorithm to estimate our ground truth x n e w {\displaystyle \mathbf {x} _{new}} by ascending (since it moves in the direction of the gradient of the likelihood) in the likelihood landscape. It has not been demonstrated in this derivation that it converges and no dependence on the initial choice is shown. Note that equation (2) provides a way of following the direction that increases the likelihood but the choice of the log-derivative is arbitrary.


More precisely, letting X = X(t,m) be the minimal number of cuts required to split the necklace. The following holds as m tends to infinity. For any s < ( t + 1 ) / 2 {\displaystyle s<(t+1)/2} P ( X = s ) = Θ ( m s − ( t + 1 ) / 2 ) . {\displaystyle \mathbb {P} (X=s)=\Theta {\big (}m^{s-(t+1)/2}{\big )}.} For any ( t + 1 ) / 2 < s ≤ t {\displaystyle (t+1)/2


Instead of repeating step two to convergence, it may be formulated and solved as a set of linear equations. These equations are merely obtained by making s = s ′ {\displaystyle s=s'} in the step two equation. Thus, repeating step two to convergence can be interpreted as solving the linear equations by relaxation. This variant has the advantage that there is a definite stopping condition: when the array π {\displaystyle \pi } does not change in the course of applying step 1 to all states, the algorithm is completed. Policy iteration is usually slower than value iteration for a large number of possible states.


In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. : 20– Such sets are now known as uncountable sets, and the size of infinite sets is now treated by the theory of cardinal numbers which Cantor began. The diagonal argument was not Cantor's first proof of the uncountability of the real numbers, which appeared in 1874.


The discrepancy (irregularity) measures how far a given distribution deviates from an ideal one. Discrepancy theory can be described as the study of inevitable irregularities of distributions, in measure-theoretic and combinatorial settings. Just as Ramsey theory elucidates the impossibility of total disorder, discrepancy theory studies the deviations from total uniformity. A significant event in the history of discrepancy theory was the 1916 paper of Weyl on the uniform distribution of sequences in the unit interval.


In most dialects of American English, speakers have a process known as intervocalic alveolar flapping that changes the consonants /t/ and /d/ into a quick flap consonant () in words such as "butter" () and "notable" (). The stop consonants /t/ and /d/ only become a flap in between two vowels, where the first vowel is stressed and the second is stressless. It is common to represent phonological rules using formal rewrite rules in the most general way possible. Thus, the intervocalic alveolar flapping described above can be formalized as


A rainbow set is a conflict-free set in the special case in which GO is made of disjoint cliques, where each clique represents a color.Conflict-free set cover is the problem of finding a conflict-free subset of O that is a covering of P. Banik, Panolan, Raman, Sahlot and Saurabh prove the following for the special case in which the conflict-graph has bounded arboricity: If the geometric cover problem is fixed-parameter tractable (FPT), then the conflict-free geometric cover problem is FPT. If the geometric cover problem admits an r-approximation algorithm, then the conflict-free geometric cover problem admits a similar approximation algorithm in FPT time. == References ==


In mathematical logic, the Friedberg–Muchnik theorem is a theorem about Turing reductions that was proven independently by Albert Muchnik and Richard Friedberg in the middle of the 1950s. It is a more general view of the Kleene–Post theorem. The Kleene–Post theorem states that there exist incomparable languages A and B below K. The Friedberg–Muchnik theorem states that there exist incomparable, computably enumerable languages A and B. Incomparable meaning that there does not exist a Turing reduction from A to B or a Turing reduction from B to A. It is notable for its use of the priority finite injury approach.


In probability theory and statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions with probability density function f ( x ) = ( a / b ) p / 2 2 K p ( a b ) x ( p − 1 ) e − ( a x + b / x ) / 2 , x > 0 , {\displaystyle f(x)={\frac {(a/b)^{p/2}}{2K_{p}({\sqrt {ab}})}}x^{(p-1)}e^{-(ax+b/x)/2},\qquad x>0,} where Kp is a modified Bessel function of the second kind, a > 0, b > 0 and p a real parameter. It is used extensively in geostatistics, statistical linguistics, finance, etc. This distribution was first proposed by Étienne Halphen. It was rediscovered and popularised by Ole Barndorff-Nielsen, who called it the generalized inverse Gaussian distribution. Its statistical properties are discussed in Bent Jørgensen's lecture notes.


In recreational mathematics, many problems concern the properties of numbers under concatenation of their numerals in some base. Examples include home primes (primes obtained by repeatedly factoring the increasing concatenation of prime factors of a given number), Smarandache–Wellin numbers (the concatenations of the first prime numbers), and the Champernowne and Copeland–Erdős constants (the real numbers formed by the decimal representations of the positive integers and the prime numbers, respectively).


Language is not an arbitrary set of conventions but a way of thinking and representing the world to oneself. It is not a conditioning process, but one in which the learner actively organizes his perceptions into linguistics concepts.The series method is a variety of the direct method in that experiences are directly connected to the target language. There are three reasons that Gouin preceded psycholinguistic theory of the 20th century.


In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., m × n for an m × n matrix) is sometimes referred to as the sparsity of the matrix.


In a completely regular semigroup, each Green H-class is a group and the semigroup is the union of these groups. Hence completely regular semigroups are also referred to as "unions of groups". Epigroups generalize this notion and their class includes all completely regular semigroups.


In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x + 3 = y {\displaystyle x+3=y} is satisfiable because it is true when x = 3 {\displaystyle x=3} and y = 6 {\displaystyle y=6} , while the formula x + 1 = x {\displaystyle x+1=x} is not satisfiable over the integers. The dual concept to satisfiability is validity; a formula is valid if every assignment of values to its variables makes the formula true. For example, x + 3 = 3 + x {\displaystyle x+3=3+x} is valid over the integers, but x + 3 = y {\displaystyle x+3=y} is not.


In matroid theory, the dual of a matroid M {\displaystyle M} is another matroid M ∗ {\displaystyle M^{\ast }} that has the same elements as M {\displaystyle M} , and in which a set is independent if and only if M {\displaystyle M} has a basis set disjoint from it.Matroid duals go back to the original paper by Hassler Whitney defining matroids. They generalize to matroids the notions of plane graph duality.


In mathematics, the map segmentation problem is a kind of optimization problem. It involves a certain geographic region that has to be partitioned into smaller sub-regions in order to achieve a certain goal. Typical optimization objectives include: Minimizing the workload of a fleet of vehicles assigned to the sub-regions; Balancing the consumption of a resource, as in fair cake-cutting. Determining the optimal locations of supply depots; Maximizing the surveillance coverage.Fair division of land has been an important issue since ancient times, e.g. in ancient Greece.


If data models are developed on a system by system basis, then not only is the same analysis repeated in overlapping areas, but further analysis must be performed to create the interfaces between them. Most systems within an organization contain the same basic data, redeveloped for a specific purpose. Therefore, an efficiently designed basic data model can minimize rework with minimal modifications for the purposes of different systems within the organization


In the early 1990s Sun-Joo Shin presented an extension of Existential Graphs called Venn-II. Syntax and semantics are given formally, together with a set of Rules of Transformation which are shown to be sound and complete. Proofs proceed by applying the rules (which remove or add syntactic elements to or from diagrams) sequentially. Venn-II is equivalent in expressive power to a first-order monadic language.


To overcome the problems, some applications may simply attempt to replace the decomposed characters with the equivalent precomposed characters. With an incomplete font, however, precomposed characters may also be problematic – especially if they are more exotic, as in the following example (showing the reconstructed Proto-Indo-European word for "dog"): ḱṷṓn (U+1E31 U+1E77 U+1E53 U+006E) ḱṷṓn (U+006B U+0301 U+0075 U+032D U+006F U+0304 U+0301 U+006E)In some situations, the precomposed green k, u and o with diacritics may render as unrecognized characters, or their typographical appearance may be very different from the final letter n with no diacritic. On the second line, the base letters should at least render correctly even if the combining diacritics could not be recognized. OpenType has the ccmp "feature tag" to define glyphs that are compositions or decompositions involving combining characters.


In painting and other visual arts, two-dimensional color wheels or three-dimensional color solids are used to represent the essential relationships between colors. The split-primary palette is a color-wheel model that attempts to explain, and to compensate for, the unsatisfactory results often produced when mixing the traditional primary colors, red, yellow, and blue. Painters have long considered red, yellow, and blue to be primary colors. In practice, however, many of the mixtures produced from these colors lack chromatic intensity.


For instance, the product of type1, ..., typen is written type1*...*typen in ML and (type1,...,typen) in Haskell. In both these languages, tuples are written (v1,...,vn) and the components of a tuple are extracted by pattern-matching. Additionally, many functional programming languages provide more general algebraic data types, which extend both product and sum types. Product types are the dual of sum types.


In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same (in which case they are both that number). The simplest non-trivial case – i.e., with more than one variable – for two non-negative numbers x and y, is the statement that x + y 2 ≥ x y {\displaystyle {\frac {x+y}{2}}\geq {\sqrt {xy}}} with equality if and only if x = y. This case can be seen from the fact that the square of a real number is always non-negative (greater than or equal to zero) and from the elementary case (a ± b)2 = a2 ± 2ab + b2 of the binomial formula: 0 ≤ ( x − y ) 2 = x 2 − 2 x y + y 2 = x 2 + 2 x y + y 2 − 4 x y = ( x + y ) 2 − 4 x y . {\displaystyle {\begin{aligned}0&\leq (x-y)^{2}\\&=x^{2}-2xy+y^{2}\\&=x^{2}+2xy+y^{2}-4xy\\&=(x+y)^{2}-4xy.\end{aligned}}} Hence (x + y)2 ≥ 4xy, with equality precisely when (x − y)2 = 0, i.e. x = y. The AM–GM inequality then follows from taking the positive square root of both sides and then dividing both sides by 2. For a geometrical interpretation, consider a rectangle with sides of length x and y, hence it has perimeter 2x + 2y and area xy.


In public policy a polycentric network is a group of distinct local, regional, or national entities that work co-operatively towards a common goal. Proponents claim that such networks can better adapt to changing issues collectively than individually, thus providing network participants better results from relevant efforts.


In recent years, scientists and audio engineers have been developing smartphone apps to conduct sound measurements, similar to the standalone sound level meters and dosimeters. In 2014, the National Institute for Occupational Safety and Health (NIOSH) within the Centers for Disease Control and Prevention (CDC) published a study examining the efficacy of 192 sound measurement apps on Apple and Android smartphones.The authors found that only 10 apps, all of which were on the App Store, met all acceptability criteria. Of these 10 apps, only 4 apps met accuracy criteria within 2 dB(A) from the reference standard. As a result of this study, they created the NIOSH Sound Level Meter App to increase accessibility and decrease costs of monitoring noise using crowdsourcing data with a tested and highly accurate application.


In practice, signals exhibiting cyclicity with more than one incommensurate period arise and require a generalization of the theory of cyclostationarity. Such signals are called polycyclostationary if they exhibit a finite number of incommensurate periods and almost cyclostationary if they exhibit a countably infinite number. Such signals arise frequently in radio communications due to multiple transmissions with differing sine-wave carrier frequencies and digital symbol rates. The theory was introduced in for stochastic processes and further developed in for non-stochastic time series.


In mobile networks, the terminal adapter is used by the terminal equipment to access the mobile termination, using AT commands (see Hayes command set). In 2G (such as GSM or CDMA), the terminal adapter is a theoretically optional while in 3G (such as W-CDMA), the terminal adapter is mandatory and is part of the mobile termination.


In most regions, Google Pay on Android permits the issuing bank to determine whether to allow its payment cards to be able to transmit when the mobile device is locked under a certain monetary amount. Issuers in Argentina, Brazil, Ecuador, Mexico, and the United States of America cannot allow locked-device payments except for select transit transactions.On Wear OS, this option is not available. All transactions for all amounts on wearable devices must be authenticated by opening the Wallet app prior to tapping.


In some programming languages, an implicit declaration is provided the first time such a variable is encountered at compile time. In other languages, such a usage is considered to be an error, which may result in a diagnostic message. Some languages have started out with the implicit declaration behavior, but as they matured they provided an option to disable it (e.g. Perl's "use strict" or Visual Basic's "Option Explicit").


In Flames' next two albums, Soundtrack to Your Escape (2004) and Come Clarity (2006), peaked at numbers 145 and 58 on the Billboard 200, respectively, with the latter album giving In Flames a Swedish Grammy Award. The Black Dahlia Murder, Arch Enemy, Children of Bodom, and Amon Amarth also enter the Billboard 200 during the 2000s decade. In the mid–late 2000s, melodic metalcore became one of the most popular heavy metal genres, with bands like Killswitch Engage, Unearth, Bullet for My Valentine, All That Remains, Shadows Fall and Atreyu achieving success, headlining major festivals and selling a lot of records.


In the algorithm, αk is chosen such that r k + 1 {\displaystyle \mathbf {r} _{k+1}} is orthogonal to r k {\displaystyle \mathbf {r} _{k}} . The denominator is simplified from α k = r k T r k r k T A p k = r k T r k p k T A p k {\displaystyle \alpha _{k}={\frac {\mathbf {r} _{k}^{\mathsf {T}}\mathbf {r} _{k}}{\mathbf {r} _{k}^{\mathsf {T}}\mathbf {A} \mathbf {p} _{k}}}={\frac {\mathbf {r} _{k}^{\mathsf {T}}\mathbf {r} _{k}}{\mathbf {p} _{k}^{\mathsf {T}}\mathbf {Ap} _{k}}}} since r k + 1 = p k + 1 − β k p k {\displaystyle \mathbf {r} _{k+1}=\mathbf {p} _{k+1}-\mathbf {\beta } _{k}\mathbf {p} _{k}} . The βk is chosen such that p k + 1 {\displaystyle \mathbf {p} _{k+1}} is conjugate to p k {\displaystyle \mathbf {p} _{k}} .


In an adaptation of LPT called restricted LPT or RLPT, inputs are assigned in pairs - one to each machine (for m=2 machines). The resulting partition is balanced by design. Coffman, Frederickson and Lueker show that the expected largest sum of RLPT when inputs are uniformly-distributed random variables is exactly n 4 + 1 2 n + 2 {\displaystyle {\frac {n}{4}}+{\frac {1}{2n+2}}} . The expected difference between the largest and smallest sum is Θ ( 1 / n ) {\displaystyle \Theta (1/n)} .


The unit number or command code occupies the first 4 of the 5 bits. The final bit is a 0 for a unit code and a 1 for a command code. Multiple unit codes may be transmitted in sequence before a command code is finally sent.


If the net gain expressed in dB is negative, it is also called the net loss. If the net gain is expressed as a ratio, and the ratio is less than unity, a net loss is indicated. The test signal must be chosen so that its power level is within the usual operating range of the circuit being tested.


Let C A {\displaystyle C^{A}} (also written A C {\displaystyle ^{A}C} ) denote the class of sets that fulfill the function property. This is the class of functions from A {\displaystyle A} to C {\displaystyle C} in a pure set theory. Below the notation x → y {\displaystyle x\to y} is also used for y x {\displaystyle y^{x}} , for the sake of distinguishing it from ordinal exponentiation. When functions are understood as just function graphs as above, the membership proposition f ∈ C A {\displaystyle f\in C^{A}} is also written f: A → C {\displaystyle f\colon A\to C} . The boolean-valued χ B: A → { 0 , 1 } {\displaystyle \chi _{B}\colon A\to \{0,1\}} are among the classes discussed next.


In radio communication systems, information is carried across space using radio waves. At the sending end, the information to be sent is converted by some type of transducer to a time-varying electrical signal called the modulation signal. The modulation signal may be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal consisting of a sequence of bits representing binary data from a computer. The modulation signal is applied to a radio transmitter.


The associativity up to isomorphism is then a way of expressing that different ways of aggregating the same data—such as ( ( a , b ) , c ) {\displaystyle ((a,b),c)} and ( a , ( b , c ) ) {\displaystyle (a,(b,c))} —store the same information even though the aggregate values need not be the same. The aggregate type may be analogous to the operation of addition (type sum) or of multiplication (type product). For type product, the identity object is the unit ( ) {\displaystyle ()} , so there is only one inhabitant of the type, and that is why a product with it is always isomorphic to the other operand.


Its first known appearance in a technical paper was in a 2003 paper by Austrian researcher Leo Sauermann.Many of the existing semantic wiki applications were started in the mid-2000s, including ArtificialMemory (2004), Semantic MediaWiki (2005), Freebase (2005), and OntoWiki (2006). June 2006 saw the first meeting dedicated to semantic wikis, the "SemWiki" workshop, co-located with the European Semantic Web Conference in Montenegro. This workshop ran annually until 2010.The site DBpedia, launched in 2007, though not a semantic wiki, publishes structured data from Wikipedia in RDF form, which enables semantic querying of Wikipedia's data. In March 2008, Wikia, the world's largest wiki farm, made the use of Semantic MediaWiki available for all their wikis on request, thus allowing all the wikis they hosted to function as semantic wikis. However, since upgrading to version 1.19 of MediaWiki in 2013, they have stopped supporting Semantic MediaWiki for new requests on the basis of performance problem.In July 2010, Google purchased Metaweb, the company behind Freebase.In April 2012, work began on Wikidata, a collaborative, multi-language store of data, whose data could then be used within Wikipedia articles, as well as by the outside world.


In the context of classification of groups, there is an essentially unique group containing exactly 2 elements. Similarly, there is also an essentially unique group containing exactly 3 elements: the cyclic group of order three. In fact, regardless of how one chooses to write the three elements and denote the group operation, all such groups can be shown to be isomorphic to each other, and hence are "the same". On the other hand, there does not exist an essentially unique group with exactly 4 elements, as there are in this case two non-isomorphic groups in total: the cyclic group of order 4 and the Klein four group.


In mathematics, mirror descent is an iterative optimization algorithm for finding a local minimum of a differentiable function. It generalizes algorithms such as gradient descent and multiplicative weights.


In the early years, a prepaid mobile phone could only be used within the network of the operator from which the customer purchased the phone. It was not possible to roam onto other GSM networks when using the phone abroad. This was because the operator had no way to bill calls in real time from another network.


In number theory, a Carmichael number is a composite number n {\displaystyle n} , which in modular arithmetic satisfies the congruence relation: b n ≡ b ( mod n ) {\displaystyle b^{n}\equiv b{\pmod {n}}} for all integers b {\displaystyle b} . The relation may also be expressed in the form: b n − 1 ≡ 1 ( mod n ) {\displaystyle b^{n-1}\equiv 1{\pmod {n}}} .for all integers b {\displaystyle b} which are relatively prime to n {\displaystyle n} . Carmichael numbers are named after American mathematician Robert Carmichael, the term having been introduced by Nicolaas Beeger in 1950 (Øystein Ore had referred to them in 1948 as numbers with the "Fermat property", or "F numbers" for short).


In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators. The technique is now commonly applied to problems in physics, but has its origins in attempts to give precise meanings to ill-conditioned sums appearing in number theory.


Some significant work was also done on percolation on random graphs. From a physicist's point of view this would still be a mean-field model, so the justification of the research is often formulated in terms of the robustness of the graph, viewed as a communication network. Given a random graph of n ≫ 1 nodes with an average degree ⟨ k ⟩ {\displaystyle \langle k\rangle } .


Third person singular pronouns in English also have a gender feature: "she" is , "he"  and "it . Different lexical categories realise or are specified for different grammatical features: for example, verbs in English are specified for tense, aspect and mood features, as well as person and number. The features that a category realises can also differ from language to language.There is often a correspondence between morphological and syntactic features, in that certain features, such as person, are relevant to both morphology and syntax; these are known as morphosyntactic features.


In principle, however, this could also signify that a parametric test has been employed in a situation where all parametric assumptions are fully met, but it is in most cases impossible to prove this completely in a real-world situation. Exceptions in which it is certain that parametric tests are exact include tests based on the binomial or Poisson distributions. The term permutation test is sometimes used as a synonym for exact test, but it should be kept in mind that all permutation tests are exact tests, but not all exact tests are permutation tests.


This vector corresponds to the stationary distribution of the Markov chain represented by the row-normalized adjacency matrix; however, the adjacency matrix must first be modified to ensure a stationary distribution exists. The second smallest eigenvector can be used to partition the graph into clusters, via spectral clustering. Other methods are also available for clustering.


This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establish a general framework for these algebras, which culminated in a series of papers on rings of operators. These papers considered a special class of C*-algebras which are now known as von Neumann algebras.


Another is defined the same way, but using split octonions instead of octonions. The final is constructed from the non-split octonions using a different standard involution. Over any algebraically closed field, there is just one Albert algebra, and its automorphism group G is the simple split group of type F4.


In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix-free Kolmogorov complexity is as low as possible, close to that of a computable set. Solovay proved in 1975 that a set can be K-trivial without being computable. The Schnorr–Levin theorem says that random sets have a high initial segment complexity.


In the United Kingdom and other parts of the Commonwealth of Nations, an equivalent service to direct distance dialing is subscriber trunk dialing (STD), and ISD for international subscriber trunk dialing. Queen Elizabeth II inaugurated STD on 5 December 1958, when she dialed a call from Bristol to Edinburgh and spoke to the Lord Provost.


In the ETen (倚天) Chinese operating system, the following code points are added, to add support for some characters present in the IBM 5550's code page but absent from generic Big5: 0xA3C0–0xA3E0: 33 control characters. 0xC6A1–0xC875: circle 1–10, bracket 1–10, Roman numerals 1–9 (i–ix), CJK radical glyphs, Japanese hiragana, Japanese katakana, Cyrillic characters 0xF9D6–0xF9FE: the characters '碁', '銹', '恒', '裏', '墻', '粧' and '嫺', followed by 34 additional semigraphic symbols.In some versions of ETen, there are extra graphical symbols and simplified Chinese characters.


In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set.


In software engineering, overhead can influence the decision whether or not to include features in new products, or indeed whether to fix bugs. A feature that has a high overhead may not be included – or needs a big financial incentive to do so. Often, even though software providers are well aware of bugs in their products, the payoff of fixing them is not worth the reward, because of the overhead. For example, an implicit data structure or succinct data structure may provide low space overhead, but at the cost of slow performance (space/time tradeoff).


In mathematical optimization, the problem of non-negative least squares (NNLS) is a type of constrained least squares problem where the coefficients are not allowed to become negative. That is, given a matrix A and a (column) vector of response variables y, the goal is to find a r g m i n x  ‖ A x − y ‖ 2 2 {\displaystyle \operatorname {arg\,min} \limits _{\mathbf {x} }\|\mathbf {Ax} -\mathbf {y} \|_{2}^{2}} subject to x ≥ 0.Here x ≥ 0 means that each component of the vector x should be non-negative, and ‖·‖2 denotes the Euclidean norm. Non-negative least squares problems turn up as subproblems in matrix decomposition, e.g. in algorithms for PARAFAC and non-negative matrix/tensor factorization. The latter can be considered a generalization of NNLS.Another generalization of NNLS is bounded-variable least squares (BVLS), with simultaneous upper and lower bounds αi ≤ xi ≤ βi. : 291


Doing this is only a win if the subexpression computation costs more in time than fetching from memory, which in most stack CPUs, almost always is the case. It is never worthwhile for simple variables and pointer fetches, because those already have the same cost of one data cache cycle per access. It is only marginally worthwhile for expressions such as X+1.


In the United States, taxation of sodium has been proposed as a method of decreasing sodium intake and thereby improving health in countries where typical salt consumption is high. Taking an alternative view, the Salt Institute, a salt industry body based in North America, is active in promoting the use of salt, and questioning or opposing the recommended restrictions on salt intake.


In the exhaustive recall method, participants are asked to record all the memories they can access before a specific age. This method, like free recall, relies on participants to come up with memories without cues. Exhaustive recall yields a better understanding than others on the number of memories surviving from early childhood but can be demanding for the subjects who often have to spend many hours trying to remember events from their childhood. No major differences among word cued, interview, focused and exhaustive recall have been found.


This problem is NP-complete, implying that neither it nor the optimization problem are expected to have polynomial time algorithms. It was one of Richard M. Karp's original set of 21 NP-complete problems; its NP-completeness was proved by Karp and Eugene Lawler by showing that inputs for another hard problem, the vertex cover problem, could be transformed ("reduced") into equivalent inputs to the feedback arc set decision problem.Some NP-complete problems can become easier when their inputs are restricted to special cases. But for the most important special case of the feedback arc set problem, the case of tournaments, the problem remains NP-complete.


Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis. Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications.


In the context of a clinical trial, quality typically refers to the absence of errors which can impact decision making, both during the conduct of the trial and in use of the trial results.


The main market for RISC CPUs has been systems that need low power or small size. Even some CISC processors (based on architectures that were created before RISC grew dominant), such as newer x86 processors, translate instructions internally into a RISC-like instruction set.


In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as forecasting.


In the book that was published in 1572, entitled Algebra, Bombelli gave a comprehensive account of the algebra known at the time. He was the first European to write down the way of performing computations with negative numbers. The following is an excerpt from the text: "Plus times plus makes plus Minus times minus makes plus Plus times minus makes minus Minus times plus makes minus Plus 8 times plus 8 makes plus 64 Minus 5 times minus 6 makes plus 30 Minus 4 times plus 5 makes minus 20 Plus 5 times minus 4 makes minus 20" As was intended, Bombelli used simple language as can be seen above so that anybody could understand it. But at the same time, he was thorough.


{\displaystyle \mathbb {Q} ({\sqrt {c}}).} In this field every element may be uniquely written α + β c , {\displaystyle \alpha +\beta {\sqrt {c}},} with α {\displaystyle \alpha } and β {\displaystyle \beta } being rational numbers. This implies that ± 2 x y {\displaystyle \pm 2{\sqrt {xy}}} is not rational (otherwise the right-hand side of the equation would be rational; but the left-hand side is irrational).


In some applications, it is more important to minimize the total length of the cuts (e.g. to minimize the cost of performing the partition, or to minimize the amount of dust). This problem is called minimum edge-length rectangular partitioning. It was first studied by Lingas, Pinter, Rivest and Shamir in 1982. The run-time complexity of this problem crucially depends on whether the raw polygon is allowed to have holes.


The NIHR Quality, Safety and Outcomes Policy Research Unit has focused on measuring and assessing the integration of services. They began by examining whether measures were available to assess processes and outcomes of integration of services. They found a very large number of available measures but the infrequent use of any common set of measures made comparisons between systems very difficult.


In model theory, the notion of an algebraic structure is generalized to structures involving both operations and relations. Let L be a signature consisting of function and relation symbols, and A, B be two L-structures. Then a homomorphism from A to B is a mapping h from the domain of A to the domain of B such that h(FA(a1,…,an)) = FB(h(a1),…,h(an)) for each n-ary function symbol F in L, RA(a1,…,an) implies RB(h(a1),…,h(an)) for each n-ary relation symbol R in L.In the special case with just one binary relation, we obtain the notion of a graph homomorphism.


In the body of a generic unit, the (formal) type parameter is handled like its upper bound (expressed with extends; Object if not constrained). If the return type of a method is the type parameter, the result (e.g. of type ?) can be referenced by a variable of the type of the upper bound (or Object). In the other direction, the wildcard fits no other type, not even Object: If ?


In the case of two enemies sharing a friend, the shared friend is likely to choose one over the other and turn one of his or her friendships into an enemy. Antal, Krapivsky and Reder consider social dynamics as the change in sign on an edge of a signed graph. The social relations with previous friends of a divorcing couple are used to illustrate the evolution of a signed graph in society.


: "addictive * of biblioscopy".) To emulate unordered search of the NEAR operator can be done using a combination of ordered searches. For example, to specify a close co-occurrence of "house" and "dog", the following search-expression could be specified: "house dog" OR "dog house" OR "house * dog" OR "dog * house" OR "house * * dog" OR "dog * * house".


In mathematical optimization, the network simplex algorithm is a graph theoretic specialization of the simplex algorithm. The algorithm is usually formulated in terms of a minimum-cost flow problem. The network simplex method works very well in practice, typically 200 to 300 times faster than the simplex method applied to general linear program of same dimensions.


Recursion though may be achieved by obtaining the same function passed in as an argument, and then using that argument to make the recursive call, instead of using the function's own name, as is done in languages which do support recursion natively. The Y combinator demonstrates this style of programming. An example implementation of Y combinator in two languages is presented below.


The values ISO 639-3, clergyman, clergymen are plain character strings. The value eng is taken from the list of languages as defined by ISO 639-3. With some additional information like dtdVersion and feat, the same data can be expressed by the following XML fragment: This example is rather simple, while LMF can represent much more complex linguistic descriptions the XML tagging is correspondingly complex.


In most cases the same mechanisms must be applied as in the positioning of an image or text content.


These occur when microorganisms only come into contact with disinfectants but are not killed by them. When ascertaining the cleanability of a surface with regard to particles, the analysis can be carried out in correlation with the surface cleanliness classes described in VDI 2083 Part 9.1. Surface roughness can be measured, for example, using profile methods (DIN EN ISO 11562) or AFM (atomic force microscope). However, no norm is currently in existence which describes a standardized AFM procedure.


The request is forwarded to (performed on) all objects downwards the tree structure. The NonTerminalExpression objects (ntExpr1,ntExpr2) forward the request to their child expressions. The TerminalExpression objects (tExpr1,tExpr2,…) perform the interpretation directly.


For example, time may be required to obtain approval of the transaction by government agencies, shareholders, labor unions, lenders, or others. Until the transaction is completed, the companies involved go on about their business and are subject to risks. Contract terms that deal with material adverse changes are carefully negotiated by the parties and take into account the relevant circumstances of each party.


However, as more classes are added to a program, especially during maintenance and/or refactoring, the problem of communication between these classes may become more complex. This makes the program harder to read and maintain. Furthermore, it can become difficult to change the program, since any change may affect code in several other classes.


In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way.