In model theory and related areas of mathematics, a type is an object that describes how a (real or possible) element or finite collection of elements in a mathematical structure might behave. More precisely, it is a set of first-order formulas in a language L with free variables x1, x2,…, xn that are true of a set of n-tuples of an L-structure M {\displaystyle {\mathcal {M}}} . Depending on the context, types can be complete or partial and they may use a fixed set of constants, A, from the structure M {\displaystyle {\mathcal {M}}} . The question of which types represent actual elements of M {\displaystyle {\mathcal {M}}} leads to the ideas of saturated models and omitting types.


In mathematical logic and type theory, the λ-cube (also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds to a new kind of dependency between terms and types. Here, "dependency" refers to the capacity of a term or type to bind a term or type. The respective dimensions of the λ-cube correspond to: x-axis ( → {\displaystyle \rightarrow } ): types that can bind terms, corresponding to dependent types.


In mathematics, and more specifically in graph theory, a polytree (also called directed tree, oriented tree or singly connected network) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is both connected and acyclic. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest.


In some European countries, and especially in France, Minitel data transmitting services were popular before the Internet. Minitel had many consumer-level communication services, including chatting, email, railway and broadcast timetables and travel and hotel booking. Minitel used little terminals rented from telephone companies or computers with modems that accept Minitel transmission protocol speed. Amiga Minitel communication programs were written in France, Germany and Italy (Amiga Videotel). AmigaTel (CEPT2 standard, for Minitel) BTX (CEPT1 standard, for the German BTX service) MtA (CEPT2 and CEPT3 standards, for Italian Videotex which supported both) Ruby View (CEPT3, for UK's Prestel)


Geometrically this is the problem of computing the lengths of the sides of a rectangle whose area A and side-length difference b−a are known, which was a recurring problem in Old Babylonian mathematics. In this case it is found that b = 1 and a = 0.75. The solution method suggests that whoever devised the solution was using the property c2 − 2A = c2 − 2ab = (b − a)2.


In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.). Multinomial logistic regression is known by a variety of other names, including polytomous LR, multiclass LR, softmax regression, multinomial logit (mlogit), the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model.


"The acoustic evidence of dialects revealed the clan to be the largest vocal, and probably matrilineal, unit. Because the Southern Resident community is only a single clan, the nature of the larger, community level of social grouping is clearer in the multi-clan Northern Resident community. Unlike the clan, the community is "defined by travel patterns and not on genealogy or acoustics."


In most computers, individual instructions are stored as machine code with each instruction being given a unique number (its operation code or opcode for short). The command to add two numbers together would have one opcode; the command to multiply them would have a different opcode, and so on. The simplest computers are able to perform any of a handful of different instructions; the more complex computers have several hundred to choose from, each with a unique numerical code. Since the computer's memory is able to store numbers, it can also store the instruction codes.


In object-oriented programming, a covariant return type of a method is one that can be replaced by a "narrower" type when the method is overridden in a subclass. A notable language in which this is a fairly common paradigm is C++. C# supports return type covariance as of version 9.0. Covariant return types have been (partially) allowed in the Java language since the release of JDK5.0, so the following example wouldn't compile on a previous release: More specifically, covariant (wide to narrower) or contravariant (narrow to wider) return type refers to a situation where the return type of the overriding method is changed to a type related to (but different from) the return type of the original overridden method.


In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it.Of the four parameters defining the family, most attention has been focused on the stability parameter, α {\displaystyle \alpha } (see panel). Stable distributions have 0 < α ≤ 2 {\displaystyle 0<\alpha \leq 2} , with the upper bound corresponding to the normal distribution, and α = 1 {\displaystyle \alpha =1} to the Cauchy distribution.


In the case of the leaky bucket algorithm as a meter, the limits on the traffic can be bandwidth and a burstiness of the output.The bandwidth limit and burstiness limit for the connection may be specified in a traffic contract. A bandwidth limit may be specified as a packet or frame rate, a byte or bit rate, or as an emission interval between the packets. A limit on burstiness may be specified as a jitter or delay variation tolerance, or as a maximum burst size (MBS). Multiple sets of contract parameters can be applied concurrently to a connection using multiple instances of the leaky bucket algorithm, each of which may take a bandwidth and a burstiness limit: see Generic cell rate algorithm § Dual Leaky Bucket Controller.


In science, adversarial collaboration is a term used when two or more scientists with opposing views work together in order to jointly advance knowledge of the area under dispute. This can take the form of a scientific experiment conducted by two groups of experimenters with competing hypotheses, with the aim of constructing and implementing an experimental design in a way that satisfies both groups that there are no obvious biases or weaknesses in the experimental design. Adversarial collaboration can involve a neutral moderator and lead to a co-designed experiment and joint publishing of findings in order to resolve differences. With its emphasis on transparency throughout the research process, Adversarial collaboration has been described as sitting within the open science framework.


Buffers are widespread in operating system (OS) code, so it is possible to make attacks that perform privilege escalation and gain unlimited access to the computer's resources. The famed Morris worm in 1988 used this as one of its attack techniques.


Again, this allows data accesses to access physical memory regions beyond the 32-bit range. The entries in the page directory have an additional flag in bit 7, named PS (for page size). If the system has set this bit to 1, the page directory entry does not point to a page table but to a single, large 2 MB page (Page Size Extension).


In operating systems using a command line interface, the user types short commands often followed by various parameters and options.


In mathematical analysis, the Hardy–Littlewood inequality, named after G. H. Hardy and John Edensor Littlewood, states that if f {\displaystyle f} and g {\displaystyle g} are nonnegative measurable real functions vanishing at infinity that are defined on n {\displaystyle n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , then ∫ R n f ( x ) g ( x ) d x ≤ ∫ R n f ∗ ( x ) g ∗ ( x ) d x {\displaystyle \int _{\mathbb {R} ^{n}}f(x)g(x)\,dx\leq \int _{\mathbb {R} ^{n}}f^{*}(x)g^{*}(x)\,dx} where f ∗ {\displaystyle f^{*}} and g ∗ {\displaystyle g^{*}} are the symmetric decreasing rearrangements of f {\displaystyle f} and g {\displaystyle g} , respectively.The decreasing rearrangement f ∗ {\displaystyle f^{*}} of f {\displaystyle f} is defined via the property that for all r > 0 {\displaystyle r>0} the two super-level sets E f ( r ) = { x ∈ X: f ( x ) > r } {\displaystyle E_{f}(r)=\left\{x\in X:f(x)>r\right\}\quad } and E f ∗ ( r ) = { x ∈ X: f ∗ ( x ) > r } {\displaystyle \quad E_{f^{*}}(r)=\left\{x\in X:f^{*}(x)>r\right\}} have the same volume ( n {\displaystyle n} -dimensional Lebesgue measure) and E f ∗ ( r ) {\displaystyle E_{f^{*}}(r)} is a ball in R n {\displaystyle \mathbb {R} ^{n}} centered at x = 0 {\displaystyle x=0} , i.e. it has maximal symmetry.


In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text. Such proofs can be considered more elegant than formal or mathematically rigorous proofs due to their self-evident nature. When the diagram demonstrates a particular case of a general statement, to be a proof, it must be generalisable.A proof without words is not the same as a mathematical proof, because it omits the details of the logical argument it illustrates. However, it can provide valuable intuitions to the viewer that can help them formulate or better understand a true proof.


In object oriented languages type safety is usually intrinsic in the fact that a type system is in place. This is expressed in terms of class definitions. A class essentially defines the structure of the objects derived from it and an API as a contract for handling these objects. Each time a new object is created it will comply with that contract. Each function that exchanges objects derived from a specific class, or implementing a specific interface, will adhere to that contract: hence in that function the operations permitted on that object will be only those defined by the methods of the class the object implements. This will guarantee that the object integrity will be preserved.Exceptions to this are object oriented languages that allow dynamic modification of the object structure, or the use of reflection to modify the content of an object to overcome the constraints imposed by the class methods definitions.


In number theory, the integer complexity of an integer is the smallest number of ones that can be used to represent it using ones and any number of additions, multiplications, and parentheses. It is always within a constant factor of the logarithm of the given integer.


In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence.


In mathematics, a (left) coherent ring is a ring in which every finitely generated left ideal is finitely presented. Many theorems about finitely generated modules over Noetherian rings can be extended to finitely presented modules over coherent rings. Every left Noetherian ring is left coherent.


In order to apply the moment distribution method to analyse a structure, the following things must be considered.


Together these form the science of metrology. Measurement accuracy, repeatability, reproducibility, bias, data shifts, and data drifts are only a few common issues identified in measurement, and any useful system must be evaluated from the technical point of view to assure that it addresses these criteria. It is essential that measurement error is quantified so that managers react to changes in conditions, but not changes due to measurement variation.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 3, 13, 34, and 134 are the patterns related to Braille pattern dots-2, since the two additional dots of kantenji patterns 02, 27, and 027 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In the field of evaluation, and in particular educational evaluation, the Joint Committee on Standards for Educational Evaluation has published three sets of standards for evaluations. The Personnel Evaluation Standards was published in 1988, The Program Evaluation Standards (2nd edition) was published in 1994, and The Student Evaluation Standards was published in 2003. Each publication presents and elaborates a set of standards for use in a variety of educational settings. The standards provide guidelines for designing, implementing, assessing, and improving the identified form of evaluation.


In parallel to the Concurrent DOS 68K effort, Digital Research also previewed Concurrent DOS 286 in cooperation with Intel in January 1985. This was based on MP/M-286 and Concurrent CP/M-286, on which Digital Research had worked since 1982.Concurrent DOS 286 was a complete rewrite in the C language based on a new system architecture with dynamically loadable device drivers instead of a static BIOS or XIOS. One of its main architects was Francis "Frank" R. Holsworth. The operating system would function strictly in 80286 native mode, allowing protected mode multi-user, multitasking operation while running 8086 emulation.


In telecommunication and computer engineering, the queuing delay or queueing delay is the time a job waits in a queue until it can be executed. It is a key component of network delay. In a switched network, queuing delay is the time between the completion of signaling by the call originator and the arrival of a ringing signal at the call receiver. Queuing delay may be caused by delays at the originating switch, intermediate switches, or the call receiver servicing switch. In a data network, queuing delay is the sum of the delays between the request for service and the establishment of a circuit to the called data terminal equipment (DTE). In a packet-switched network, queuing delay is the sum of the delays encountered by a packet between the time of insertion into the network and the time of delivery to the address.


In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.} For a function f: X → Y {\displaystyle f\colon X\to Y} , its inverse f − 1: Y → X {\displaystyle f^{-1}\colon Y\to X} admits an explicit description: it sends each element y ∈ Y {\displaystyle y\in Y} to the unique element x ∈ X {\displaystyle x\in X} such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result.


In one variation of monadic second-order graph logic known as MSO1, the graph is described by a set of vertices and a binary adjacency relation adj  ( . , . ) {\displaystyle \operatorname {adj} (.,.)}


In the do ... while loop, the test is done after each iteration. Consequently, the code is always executed at least once.


In nuclear physics these methods are used to study properties of the nucleus itself. Methods for studies of the nucleus: Gamma spectroscopy Hypernuclear spectroscopyMethods for condensed matter studies: Nuclear magnetic resonance (NMR) Mössbauer spectroscopy Perturbed angular correlation (PAC, TDPAC, PAC spectroscopy) Muon spin spectroscopy Nuclear orientation Channeling Nuclear reaction analysis Nuclear quadrupole resonance (NQR)Methods for trace element analysis: Neutron activation analysis (NAA) == References ==


In mathematics, the analytic subgroup theorem is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's theorem on linear forms in logarithms. Gisbert Wüstholz proved it in the 1980s. It marked a breakthrough in the theory of transcendental numbers. Many longstanding open problems can be deduced as direct consequences.


In mathematics, a residuated lattice is an algebraic structure L = (L, ≤, •, I) such that (i) (L, ≤) is a lattice. (ii) (L, •, I) is a monoid. (iii) For all z there exists for every x a greatest y, and for every y a greatest x, such that x•y ≤ z (the residuation properties).In (iii), the "greatest y", being a function of z and x, is denoted x\z and called the right residual of z by x. Think of it as what remains of z on the right after "dividing" z on the left by x. Dually, the "greatest x" is denoted z/y and called the left residual of z by y. An equivalent, more formal statement of (iii) that uses these operations to name these greatest values is (iii)' for all x, y, z in L, y ≤ x\z ⇔ x•y ≤ z ⇔ x ≤ z/y. As suggested by the notation, the residuals are a form of quotient.


For those processors that have only one pipeline per core, interleaved multithreading is the only possible way, because it can issue at most one instruction per cycle. Simultaneous multithreading (SMT): Issue multiple instructions from multiple threads in one cycle. The processor must be superscalar to do so.


In fact, these may go so far as to question the "empirical and scientific validity... of modern financial theory". Notable here are Nassim Taleb and Benoit Mandelbrot. See also Mathematical finance § Criticism, Financial economics § Challenges and criticism and Financial engineering § Criticisms.


In object-oriented programming theory, abstraction involves the facility to define objects that represent abstract "actors" that can perform work, report on and change their state, and "communicate" with other objects in the system. The term encapsulation refers to the hiding of state details, but extending the concept of data type from earlier programming languages to associate behavior most strongly with the data, and standardizing the way that different data types interact, is the beginning of abstraction. When abstraction proceeds into the operations defined, enabling objects of different types to be substituted, it is called polymorphism. When it proceeds in the opposite direction, inside the types or classes, structuring them to simplify a complex set of relationships, it is called delegation or inheritance.


In mathematics, the Davenport constant D(G ) is an invariant of a group studied in additive combinatorics, quantifying the size of nonunique factorizations. Given a finite abelian group G, D(G ) is defined as the smallest number such that every sequence of elements of that length contains a non-empty subsequence adding up to 0. In symbols, this is D ( G ) = min { N: ∀ ( { g n } n = 1 N ∈ G N ) ( ∃ { n k } k = 1 K: ∑ k = 1 K g n k = 0 ) } . {\displaystyle D(G)=\min \left\{N:\forall \left(\{g_{n}\}_{n=1}^{N}\in G^{N}\right)\left(\exists \{n_{k}\}_{k=1}^{K}:\sum _{k=1}^{K}{g_{n_{k}}}=0\right)\right\}.}


In modern parallel computing systems, memory consistency must be maintained to avoid undesirable outcomes. Strict consistency models like sequential consistency are intuitively composed but can be quite restrictive in terms of performance as they would disable instruction level parallelism which is widely applied in sequential programming. To achieve better performance, some relaxed models are explored and release consistency is an aggressive relaxing attempt.


In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists at least one pair of elements a and b of G, such that a ∗ b ≠ b ∗ a. This class of groups contrasts with the abelian groups. (In an abelian group, all pairs of group elements commute). Non-abelian groups are pervasive in mathematics and physics. One of the simplest examples of a non-abelian group is the dihedral group of order 6.


It is licensed under the GNU Lesser General Public License. MapReduce-MPI Library is an implementation of MapReduce for distributed-memory parallel machines, utilizing the Message Passing Interface (MPI) for communication. It is developed under a modified Berkeley Software Distribution license.


Information distribution – This involves dissemination of information needed by the stakeholders and other members of the organization. Performance reporting – This includes status reporting, progress measurement, and forecasting for the future of the organization. Administrative closure – This involves generating, gathering, and disseminating information to formalize phase or project completion.


In mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space M {\displaystyle M} . It is named after Leonid Vaseršteĭn. Intuitively, if each distribution is viewed as a unit amount of earth (soil) piled on M {\displaystyle M} , the metric is the minimum "cost" of turning one pile into the other, which is assumed to be the amount of earth that needs to be moved times the mean distance it has to be moved. This problem was first formalised by Gaspard Monge in 1781.


To satisfy the constraints σ k ( t + Δ t ) {\displaystyle \sigma _{k}(t+\Delta t)} in the next timestep, the Lagrange multipliers should be determined as the following equation, σ k ( t + Δ t ) := ‖ x k α ( t + Δ t ) − x k β ( t + Δ t ) ‖ 2 − d k 2 = 0. {\displaystyle \sigma _{k}(t+\Delta t):=\left\|\mathbf {x} _{k\alpha }(t+\Delta t)-\mathbf {x} _{k\beta }(t+\Delta t)\right\|^{2}-d_{k}^{2}=0.} This implies solving a system of n {\displaystyle n} non-linear equations σ j ( t + Δ t ) := ‖ x ^ j α ( t + Δ t ) − x ^ j β ( t + Δ t ) + ∑ k = 1 n λ k ( Δ t ) 2  ‖ 2 − d j 2 = 0 , j = 1 … n {\displaystyle \sigma _{j}(t+\Delta t):=\left\|{\hat {\mathbf {x} }}_{j\alpha }(t+\Delta t)-{\hat {\mathbf {x} }}_{j\beta }(t+\Delta t)+\sum _{k=1}^{n}\lambda _{k}\left(\Delta t\right)^{2}\left\right\|^{2}-d_{j}^{2}=0,\quad j=1\ldots n} simultaneously for the n {\displaystyle n} unknown Lagrange multipliers λ k {\displaystyle \lambda _{k}} .


Therefore, the distribution is often abbreviated U ( a , b ) , {\displaystyle U(a,b),} where U {\displaystyle U} stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable X {\displaystyle X} under no constraint other than that it is contained in the distribution's support.


Alice sends | ψ ⟩ {\displaystyle |\psi \rangle } over a public quantum channel to Bob. Bob receives a state ε ρ = ε | ψ ⟩ ⟨ ψ | {\displaystyle \varepsilon \rho =\varepsilon |\psi \rangle \langle \psi |} , where ε {\displaystyle \varepsilon } represents the effects of noise in the channel as well as eavesdropping by a third party we'll call Eve. After Bob receives the string of qubits, all three parties, namely Alice, Bob and Eve, have their own states.


It is still a popular language for high-performance computing and is used for programs that benchmark and rank the world's TOP500 fastest supercomputers.Another early programming language was devised by Grace Hopper in the US, named FLOW-MATIC. It was developed for the UNIVAC I at Remington Rand during the period from 1955 until 1959. Hopper found that business data processing customers were uncomfortable with mathematical notation, and in early 1955, she and her team wrote a specification for an English language programming language and implemented a prototype.


Values for parameters of the receiver method are stored in the command. The receiver object to execute these methods is also stored in the command object by aggregation. The receiver then does the work when the execute() method in command is called.


In a laboratory setting, each one of these prepped systems might be used as input for one subsequent testing procedure. Again, the testing procedure involves a physical apparatus and some protocols; as a result of the testing procedure we obtain a yes or no answer. Given a testing procedure E applied to each prepared system, we obtain a sequence of values Meas (E, X1), Meas (E, X2), ...., Meas (E, Xk).


In number theory, Vantieghems theorem is a primality criterion. It states that a natural number n≥3 is prime if and only if ∏ 1 ≤ k ≤ n − 1 ( 2 k − 1 ) ≡ n mod ( 2 n − 1 ) . {\displaystyle \prod _{1\leq k\leq n-1}\left(2^{k}-1\right)\equiv n\mod \left(2^{n}-1\right).} Similarly, n is prime, if and only if the following congruence for polynomials in X holds: ∏ 1 ≤ k ≤ n − 1 ( X k − 1 ) ≡ n − ( X n − 1 ) / ( X − 1 ) mod ( X n − 1 ) {\displaystyle \prod _{1\leq k\leq n-1}\left(X^{k}-1\right)\equiv n-\left(X^{n}-1\right)/\left(X-1\right)\mod \left(X^{n}-1\right)} or: ∏ 1 ≤ k ≤ n − 1 ( X k − 1 ) ≡ n mod ( X n − 1 ) / ( X − 1 ) . {\displaystyle \prod _{1\leq k\leq n-1}\left(X^{k}-1\right)\equiv n\mod \left(X^{n}-1\right)/\left(X-1\right).}


In some concurrent computing systems, communication between the concurrent components is hidden from the programmer (e.g., by using futures), while in others it must be handled explicitly. Explicit communication can be divided into two classes: Shared memory communication Concurrent components communicate by altering the contents of shared memory locations (exemplified by Java and C#). This style of concurrent programming usually needs the use of some form of locking (e.g., mutexes, semaphores, or monitors) to coordinate between threads. A program that properly implements any of these is said to be thread-safe.Message passing communication Concurrent components communicate by exchanging messages (exemplified by MPI, Go, Scala, Erlang and occam).


In the 2003 version, the Vysočina Region was coded CZ061, and the South Moravian Region was coded CZ062.


They are closely related to reputation systems. Simple forms of binary trust metrics can be found e.g. in PGP. The first commercial forms of trust metrics in computer software were in applications like eBay's Feedback Rating. Slashdot introduced its notion of karma, earned for activities perceived to promote group effectiveness, an approach that has been very influential in later virtual communities.


In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points. A distance between populations can be interpreted as measuring the distance between two probability distributions and hence they are essentially measures of distances between probability measures. Where statistical distance measures relate to the differences between random variables, these may have statistical dependence, and hence these distances are not directly related to measures of distances between probability measures.


If each item is associated to some features (e.g. author, year, publisher, actors) it is possible to define an embedding function, which given the item features estimates the corresponding item latent factors. The embedding function can be designed in many ways and it is trained with the data already available from warm items. Alternatively, one could apply a group-specific method.


In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by π(x) (unrelated to the number π).


This approach (often referred to as the probabilistic method) proved highly effective in applications to extremal combinatorics and graph theory. A closely related area is the study of finite Markov chains, especially on combinatorial objects. Here again probabilistic tools are used to estimate the mixing time.Often associated with Paul Erdős, who did the pioneering work on the subject, probabilistic combinatorics was traditionally viewed as a set of tools to study problems in other parts of combinatorics. The area recently grew to become an independent field of combinatorics.


Mathematically, if the coordinate system undergoes a transformation described by an n × n {\displaystyle n\times n} invertible matrix M, so that the basis vectors transform according to  =  M {\displaystyle {\begin{bmatrix}\mathbf {e} _{1}^{\prime }\ \mathbf {e} _{2}^{\prime }\ ...\ \mathbf {e} _{n}^{\prime }\end{bmatrix}}={\begin{bmatrix}\mathbf {e} _{1}\ \mathbf {e} _{2}\ ...\ \mathbf {e} _{n}\end{bmatrix}}M} , then the components of a vector v in the original basis ( v i {\displaystyle v^{i}} ) must be similarly transformed via  = M − 1  {\displaystyle {\begin{bmatrix}v^{1}{^{\prime }}\\v^{2}{^{\prime }}\\...\\v^{n}{^{\prime }}\end{bmatrix}}=M^{-1}{\begin{bmatrix}v^{1}\\v^{2}\\...\\v^{n}\end{bmatrix}}} . The components of a vector are often represented arranged in a column.


In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or – as here – simply a vector) is a geometric object that has both a magnitude (or length) and direction. A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "one who carries". The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity.


In psychological literature on memory, long-term memory (LTM) is commonly divided into two types: semantic and episodic. Semantic memories are memories that are stored in LTM without specific encoding information linked to them, and thus represent general knowledge about the world that a person has acquired across the lifespan. Episodic memories are memories that are stored in long-term memory as specific "episodes" and that, therefore, have some sort of specific context information associated with them, such as where or when they were encoded. At retrieval, episodic memories are often divided into two different categories based on how much information is available about the "episode."


right) ideal of R is an intersection of maximal left (resp. right) ideals of RA commutative ring is a V-ring if and only if it is Von Neumann regular. == References ==


In statistics, jackknife variance estimates for random forest are a way to estimate the variance in random forest models, in order to eliminate the bootstrap effects.


In the United States, competitors are divided into groups by age. The eight age groups are: 12 and under, 13–15, 16–17, 18–19, Junior (elite 15–18), Senior (elite 15+), Collegiate, and Master. In addition to these groups, younger swimmers may be divided by ability into 3 levels: Novice, Intermediate, and age group.


71). To every name or designating expression 'X', there corresponds a cluster of properties, namely the family of those properties φ such that A believes 'φX'. One of the properties, or some conjointly, are believed by A to pick out some individual uniquely.


In the default mode, where Extended Channel Interpretation is not in effect, the interface between the reader and the host is said to be in "Basic Channel Mode". In this mode, each octet of transmitted data is defined (by the corresponding bar code symbology standard) to correspond directly to a single data character code point in some default character set, normally ISO/IEC 8859-1 (Latin-1). However, when ECI is in effect, the data interface is said to be in "Extended Channel Mode". In this mode the interpretation of the transmitted data is defined by the current ECI modes that are enabled, which are activated and deactivated by "ECI indicators" included in the transmitted data.


In more traditional processor architectures, a processor is usually programmed by defining the executed operations and their operands. For example, an addition instruction in a RISC architecture could look like the following. add r3, r1, r2 This example operation adds the values of general-purpose registers r1 and r2 and stores the result in register r3. Coarsely, the execution of the instruction in the processor probably results in translating the instruction to control signals which control the interconnection network connections and function units.


In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. Unlike the Euclidean definition, this does not presume that the objects under consideration lie in a common space.


In past decades, information governance responsibilities might have fallen under the purview of the chief information officer (CIO). But somewhere along the line, the CIO job description changed to focus solely on the information systems and associated technology that power a company—not the information itself. In today's age of big data, organizations have more information under their control than ever before.


In mathematics, nonlinear modelling is empirical or semi-empirical modelling which takes at least some nonlinearities into account. Nonlinear modelling in practice therefore means modelling of phenomena in which independent variables affecting the system can show complex and synergetic nonlinear effects. Contrary to traditional modelling methods, such as linear regression and basic statistical methods, nonlinear modelling can be utilized efficiently in a vast number of situations where traditional modelling is impractical or impossible. The newer nonlinear modelling approaches include non-parametric methods, such as feedforward neural networks, kernel regression, multivariate splines, etc., which do not require a priori knowledge of the nonlinearities in the relations.


For each possible value of the theoretical mean, the Z-test statistic has a different probability distribution. In these circumstances (the case of a so-called composite null hypothesis) the p-value is defined by taking the least favourable null-hypothesis case, which is typically on the border between null and alternative. This definition ensures the complementarity of p-values and alpha-levels.


This realization consists of geometric simplices, glued together according to the rules of the simplicial set. Indeed, one may view a simplicial set as a purely combinatorial construction designed to capture the essence of a "well-behaved" topological space for the purposes of homotopy theory. Specifically, the category of simplicial sets carries a natural model structure, and the corresponding homotopy category is equivalent to the familiar homotopy category of topological spaces. Simplicial sets are used to define quasi-categories, a basic notion of higher category theory. A construction analogous to that of simplicial sets can be carried out in any category, not just in the category of sets, yielding the notion of simplicial objects.


In survey methodology, Poisson sampling (sometimes denoted as PO sampling: 61 ) is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample. : 85 Each element of the population may have a different probability of being included in the sample ( π i {\displaystyle \pi _{i}} ). The probability of being included in a sample during the drawing of a single sample is denoted as the first-order inclusion probability of that element ( p i {\displaystyle p_{i}} ). If all first-order inclusion probabilities are equal, Poisson sampling becomes equivalent to Bernoulli sampling, which can therefore be considered to be a special case of Poisson sampling.


In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and finite simple groups that are combined in a feedback-free manner (called a "wreath product" or "cascade"). Krohn and Rhodes found a general decomposition for finite automata. The authors discovered and proved an unexpected major result in finite semigroup theory, revealing a deep connection between finite automata and semigroups.


In several programming languages, index notation is a way of addressing elements of an array. This method is used since it is closest to how it is implemented in assembly language whereby the address of the first element is used as a base, and a multiple (the index) of the element size is used to address inside the array. For example, if an array of integers is stored in a region of the computer's memory starting at the memory cell with address 3000 (the base address), and each integer occupies four cells (bytes), then the elements of this array are at memory locations 0x3000, 0x3004, 0x3008, …, 0x3000 + 4(n − 1) (note the zero-based numbering). In general, the address of the ith element of an array with base address b and element size s is b + is.


However, callers typically pay a higher rate when calling mobile phones. Special prefixes are used to designate mobile numbers so that callers are aware they are calling a mobile phone and therefore will be charged a higher rate. From the caller's point of view, it does not matter where the mobile subscriber is, as the technical process of connecting the call is the same. If a subscriber is roaming on a different company's network, the subscriber, instead of the caller, may pay a surcharge for the connection time. International roaming calls are often quite expensive, and as a result some companies require subscribers to grant explicit permission to receive calls while roaming to certain countries.


In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics. In computational mechanics, a characteristic length is defined to force localization of a stress softening constitutive equation. The length is associated with an integration point. For 2D analysis, it is calculated by taking the square root of the area. For 3D analysis, it is calculated by taking the cubic root of the volume associated to the integration point.


In mathematics, the Grothendieck existence theorem, introduced by Grothendieck (1961, section 5), gives conditions that enable one to lift infinitesimal deformations of a scheme to a deformation, and to lift schemes over infinitesimal neighborhoods over a subscheme of a scheme S to schemes over S. The theorem can be viewed as an instance of (Grothendieck's) formal GAGA.


Repeated application of distributivity may exponentially increase the size of a formula. In the classical propositional logic, transformation to negation normal form does not impact computational properties: the satisfiability problem continues to be NP-complete, and the validity problem continues to be co-NP-complete. For formulas in conjunctive normal form, the validity problem is solvable in polynomial time, and for formulas in disjunctive normal form, the satisfiability problem is solvable in polynomial time.


In the EMR calculation there are 4 fundamental losses that are necessary for the calculation, they are: D = Expected Incurred Losses E = Expected Primary Losses H = Actual Incurred Losses Claims under $2,000. I = Actual Primary Losses All claims including Actual Incurred LossesThe losses that are not part of this fundamental 4 are, C = Expected Excess Losses ( D − E ) {\displaystyle (D-E)} F = Actual Excess Losses ( H − I ) {\displaystyle (H-I)}


Consistent language. Using simple, consistent definitions for requirements described in natural language and use the business terminology that is prevalent in the enterprise. Guidelines.


In the early 2020s, manufacturers began to integrate satellite connectivity into smartphone devices for use in remote areas, out of the cellular network range. The satellite-to-phone services use L band frequencies, which are compatible with most modern handsets. However, due to the antenna limitations in the conventional phones, in the early stages of implementation satellite connectivity would be limited to the satellite messaging and satellite emergency services.The Apple iPhone 14 can send emergency text messages via Globalstar satellites.


In some languages that have verb serialization, the verbs must appear consecutively with nothing intervening. In other languages, however, it is possible for arguments, normally the object of one of the verbs, to come in between the serialized verbs. The resulting construction is a sequence of verb phrases rather than of plain verbs. The following example is from the Nigerian Yoruba: The object of the first verb intervenes between the verbs, resulting in two consecutive verb phrases, the first meaning "took the book", the second "came".


It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from A to B. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space.


If n {\textstyle n} is one less than a power of two, then this is always the case. Otherwise, the search may perform ⌊ log 2  ( n ) + 1 ⌋ {\textstyle \lfloor \log _{2}(n)+1\rfloor } iterations if the search reaches the deepest level of the tree. However, it may make ⌊ log 2  ( n ) ⌋ {\textstyle \lfloor \log _{2}(n)\rfloor } iterations, which is one less than the worst case, if the search ends at the second-deepest level of the tree.On average, assuming that each element is equally likely to be searched, binary search makes ⌊ log 2  ( n ) ⌋ + 1 − ( 2 ⌊ log 2  ( n ) ⌋ + 1 − ⌊ log 2  ( n ) ⌋ − 2 ) / n {\displaystyle \lfloor \log _{2}(n)\rfloor +1-(2^{\lfloor \log _{2}(n)\rfloor +1}-\lfloor \log _{2}(n)\rfloor -2)/n} iterations when the target element is in the array.


In supercomputers tracked by TOP500, the appearance of 64-bit extensions for the x86 architecture enabled 64-bit x86 processors by AMD and Intel to replace most RISC processor architectures previously used in such systems (including PA-RISC, SPARC, Alpha and others), as well as 32-bit x86, even though Intel itself initially tried unsuccessfully to replace x86 with a new incompatible 64-bit architecture in the Itanium processor. As of 2020, a Fujitsu A64FX-based supercomputer called Fugaku is number one. The first ARM-based supercomputer appeared on the list in 2018 and, in recent years, non-CPU architecture co-processors (GPGPU) have also played a big role in performance. Intel's Xeon Phi "Knights Corner" coprocessors, which implement a subset of x86-64 with some vector extensions, are also used, along with x86-64 processors, in the Tianhe-2 supercomputer.


y j ∈ { 0 , 1 } {\displaystyle y_{j}\in \{0,1\}} ; (if y j = 1 {\displaystyle y_{j}=1} then e j {\displaystyle e_{j}} is covered) x i ∈ { 0 , 1 } {\displaystyle x_{i}\in \{0,1\}} (if x i = 1 {\displaystyle x_{i}=1} then S i {\displaystyle S_{i}} is selected for the cover).A greedy algorithm will no longer produce solutions with a performance guarantee. Namely, the worst case behavior of this algorithm might be very far from the optimal solution. The approximation algorithm is extended by the following way.


Occupying the adjacent squares of an opposing token (e.g. tafl), also known as a custodian capture, custodianship or interception. Occupying one immediately adjacent square to an opposing token, also known as approach. The reverse of approach: capturing an adjacent opposing token by moving away from it in a straight line (e.g. fanorona), also known as withdrawal.


A topic is a discrete piece of content that: focuses on one subject has an identifiable purpose does not require external context to understandTopics can be written to be independent of one another and reused wherever needed. The Darwin Information Typing Architecture is a standard designed to help authors create topic-based structured content. The standard is managed by the Organization for the Advancement of Structured Information Standards DITA Technical Committee.


If binary code compatibility is required in future releases, the constant interface must remain forever an interface (it cannot be converted into a class), even though it has not been used as an interface in the conventional sense. Without an IDE that resolves where the constant are coming from, tracking it back to its containing class or interface can be time consuming. An instance of the interface is syntactically no more useful than the interface name itself (since it has no methods). Unless a developer checks any implemented interfaces when adding a constant to a class, or does so but makes a typo in the name of the added constant, the value of a constant can be silently changed. Consider Example 2 below.Note that the Java libraries use constant interface pattern themselves, showing that it may be a reasonable choice in some situations.


But this, on the whole, the algorithm and even the Pythagorean arcs, I still reckoned almost an error compared to the Indian method. Therefore strictly embracing the Indian method, and attentive to the study of it, from mine own sense adding some, and some more still from the subtle Euclidean geometric art, applying the sum that I was able to perceive to this book, I worked to put it together in xv distinct chapters, showing certain proof for almost everything that I put in, so that further, this method perfected above the rest, this science is instructed to the eager, and to the Italian people above all others, who up to now are found without a minimum. If, by chance, something less or more proper or necessary I omitted, your indulgence for me is entreated, as there is no one who is without fault, and in all things is altogether circumspect.The nine Indian figures are: 9 8 7 6 5 4 3 2 1 With these nine figures, and with the sign 0 which the Arabs call zephir any number whatsoever is written...In other words, in his book he advocated the use of the digits 0–9, and of place value.


Mathematically, R 0 {\displaystyle R_{0}} is a threshold for stability of a disease-free equilibrium such that: R 0 ≤ 1 ⇒ lim t → ∞ ( C 1 ( t ) , C 2 ( t ) , ⋯ , C n ( t ) ) = DFE {\displaystyle R_{0}\leq 1\Rightarrow \lim _{t\to \infty }(C_{1}(t),C_{2}(t),\cdots ,C_{n}(t))={\textrm {DFE}}} R 0 > 1 , I ( 0 ) > 0 ⇒ lim t → ∞ ( C 1 ( t ) , C 2 ( t ) , ⋯ , C n ( t ) ) = EE . {\displaystyle R_{0}>1,I(0)>0\Rightarrow \lim _{t\to \infty }(C_{1}(t),C_{2}(t),\cdots ,C_{n}(t))={\textrm {EE}}.} To calculate R 0 {\displaystyle R_{0}} , the first step is to linearise around the disease-free equilibrium (DFE), but for the infected subsystem of non-linear ODEs which describe the production of new infections and changes in state among infected individuals.


An interface called "Stack" might define two methods: push() and pop(). It can be implemented in different ways, for example, FastStack and GenericStack—the first being fast, working with a data structure of fixed size, and the second using a data structure that can be resized, but at the cost of somewhat lower speed. Though interfaces can contain many methods they may contain only one or even none at all. For example, the Java language defines the interface Readable that has the single read() method; various implementations are used for different purposes, including BufferedReader, FileReader, InputStreamReader, PipedReader, and StringReader. Marker interfaces like Serializable contain no methods at all and serve to provide run-time information to generic processing using Reflection.


The crawl method is an extension of aforementioned discovery method. Except Most search engines use sophisticated scheduling algorithms to “decide” when to revisit a particular page, to appeal to its relevance. These algorithms range from constant visit-interval with higher priority for more frequently changing pages to adaptive visit-interval based on several criteria such as frequency of change, popularity, and overall quality of site. The speed of the web server running the page as well as resource constraints like amount of hardware or bandwidth also figure in.


In neural network applications, the number K of possible outcomes is often large, e.g. in case of neural language models that predict the most likely outcome out of a vocabulary which might contain millions of possible words. This can make the calculations for the softmax layer (i.e. the matrix multiplications to determine the z i {\displaystyle z_{i}} , followed by the application of the softmax function itself) computationally expensive. What's more, the gradient descent backpropagation method for training such a neural network involves calculating the softmax for every training example, and the number of training examples can also become large. The computational effort for the softmax became a major limiting factor in the development of larger neural language models, motivating various remedies to reduce training times.Approaches that reorganize the softmax layer for more efficient calculation include the hierarchical softmax and the differentiated softmax.


A feasible solution is a solution in which for each bin b i {\displaystyle b_{i}} the total weight of assigned items is at most t i {\displaystyle t_{i}} . The solution's profit is the sum of profits for each item-bin assignment.


In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation. Other operations, e.g., the set-theoretic operations union and intersection, are also often iterated, but the iterations are not given separate names.


Sometimes the form of this function is based on knowledge about the relationship between Y i {\displaystyle Y_{i}} and X i {\displaystyle X_{i}} that does not rely on the data. If no such knowledge is available, a flexible or convenient form for f {\displaystyle f} is chosen. For example, a simple univariate regression may propose f ( X i , β ) = β 0 + β 1 X i {\displaystyle f(X_{i},\beta )=\beta _{0}+\beta _{1}X_{i}} , suggesting that the researcher believes Y i = β 0 + β 1 X i + e i {\displaystyle Y_{i}=\beta _{0}+\beta _{1}X_{i}+e_{i}} to be a reasonable approximation for the statistical process generating the data.


In statistics, the Breusch–Godfrey test is used to assess the validity of some of the modelling assumptions inherent in applying regression-like models to observed data series. In particular, it tests for the presence of serial correlation that has not been included in a proposed model structure and which, if present, would mean that incorrect conclusions would be drawn from other tests or that sub-optimal estimates of model parameters would be obtained. The regression models to which the test can be applied include cases where lagged values of the dependent variables are used as independent variables in the model's representation for later observations. This type of structure is common in econometric models. The test is named after Trevor S. Breusch and Leslie G. Godfrey.


In order for indicators to be considered valid for accountability, they must meet a few minimum requirements. They need to measure marketing outcomes from the consumers’ point of view, they need to include all marketing activities, they must be repeated over time, and they must meet statistical and technical criteria required of all measurement systems. The measurements need to be true outcome indicators. Unlike sales where the outcome is easily quantifiable, marketing is more difficult to define: there is not a direct, fast-acting relationship between marketing activities and sales.


In most formalisms that use syntactic predicates, the syntax of the predicate is noncommutative, which is to say that the operation of predication is ordered. For instance, using the above example, consider the following pseudo-grammar, where X ::= Y PRED Z is understood to mean: "Y produces X if and only if Y also satisfies predicate Z": S ::= a X X ::= Y PRED Z Y ::= a+ BNCN Z ::= ANBN c+ BNCN ::= b  c ANBN ::= a  b Given the string aaaabbbccc, in the case where Y must be satisfied first (and assuming a greedy implementation), S will generate aX and X in turn will generate aaabbbccc, thereby generating aaaabbbccc. In the case where Z must be satisfied first, ANBN will fail to generate aaaabbb, and thus aaaabbbccc is not generated by the grammar. Moreover, if either Y or Z (or both) specify any action to be taken upon reduction (as would be the case in many parsers), the order that these productions match determines the order in which those side-effects occur. Formalisms that vary over time (such as adaptive grammars) may rely on these side effects.


In the fair cake-cutting problem, classic allocation rules such as divide and choose are not PM. Several rules are known to be PM: When the pieces may be disconnected, any function that maximizes a concave welfare function (a monotonically-increasing function of the utilities) is PM. This holds whether the welfare function operates on the absolute utilities or on the relative utilities. In particular, the Nash-optimal rule, absolute-leximin and relative-leximin rules, absolute-utilitarian and relative utilitarian rules are all PM.


In mathematical finite group theory, the Dempwolff group is a finite group of order 319979520 = 215·32·5·7·31, that is the unique nonsplit extension 2 5 . G L 5 ( F 2 ) {\displaystyle 2^{5\,. }\mathrm {GL} _{5}(\mathbb {F} _{2})} of G L 5 ( F 2 ) {\displaystyle \mathrm {GL} _{5}(\mathbb {F} _{2})} by its natural module of order 2 5 {\displaystyle 2^{5}} . The uniqueness of such a nonsplit extension was shown by Dempwolff (1972), and the existence by Thompson (1976), who showed using some computer calculations of Smith (1976) that the Dempwolff group is contained in the compact Lie group E 8 {\displaystyle E_{8}} as the subgroup fixing a certain lattice in the Lie algebra of E 8 {\displaystyle E_{8}} , and is also contained in the Thompson sporadic group (the full automorphism group of this lattice) as a maximal subgroup.


In political campaigns, an attack ad is an advertisement designed to wage a personal attack against an opposing candidate or political party in order to gain support for the attacking candidate and attract voters. Attack ads often form part of negative campaigning or smear campaigns, and in large or well-financed campaigns, may be disseminated via mass media. An attack ad will generally unfairly criticize an opponent's political platform, usually by pointing out its faults.


Using Michell's schema, Ben Richards (Kyngdon & Richards, 2007) discovered that some instances of the triple cancellation axiom are "incoherent" as they contradict the single cancellation axiom. Moreover, he identified many instances of the triple cancellation which are trivially true if double cancellation is supported. The axioms of the theory of conjoint measurement are not stochastic; and given the ordinal constraints placed on data by the cancellation axioms, order restricted inference methodology must be used (Iverson & Falmagne 1985).


In the 1990s, digital speech recognition technology became a feature of the personal computer with IBM, Philips and Lernout & Hauspie fighting for customers. Much later the market launch of the first smartphone IBM Simon in 1994 laid the foundation for smart virtual assistants as we know them today.In 1997, Dragon's Naturally Speaking software could recognize and transcribe natural human speech without pauses between each word into a document at a rate of 100 words per minute. A version of Naturally Speaking is still available for download and it is still used today, for instance, by many doctors in the US and the UK to document their medical records.In 2001 Colloquis publicly launched SmarterChild, on platforms like AIM and MSN Messenger. While entirely text-based SmarterChild was able to play games, check the weather, look up facts, and converse with users to an extent.The first modern digital virtual assistant installed on a smartphone was Siri, which was introduced as a feature of the iPhone 4S on 4 October 2011.


A high return loss is desirable and results in a lower insertion loss. From a certain perspective 'Return Loss' is a misnomer. The usual function of a transmission line is to convey power from a source to a load with minimal loss.


In mathematics, a stacky curve is an object in algebraic geometry that is roughly an algebraic curve with potentially "fractional points" called stacky points. A stacky curve is a type of stack used in studying Gromov–Witten theory, enumerative geometry, and rings of modular forms. Stacky curves are deeply related to 1-dimensional orbifolds and therefore sometimes called orbifold curves or orbicurves.


In pseudocode, the algorithm will be: function KahanSum(input) var sum = 0.0 // Prepare the accumulator. var c = 0.0 // A running compensation for lost low-order bits. for i = 1 to input.length do // The array input has elements indexed input to input. var y = input - c // c is zero the first time around.


For a vector to represent a geometric object, it must be possible to describe how it looks in any other coordinate system. That is to say, the components of the vectors will transform in a certain way in passing from one coordinate system to another. A vector, which is an example of a contravariant tensor, has components that transform inversely to the transformation of the reference axes, (with example transformations including rotation and dilation).


In some contexts, the value of the loss function itself is a random quantity because it depends on the outcome of a random variable X.


Historically - long before anyone defined nested intervals in a textbook - people implicitly constructed such nestings for concrete calculation purposes. For example, the ancient Babylonians discovered a method for computing square roots of numbers. In contrast, the famed Archimedes constructed sequences of polygons, that inscribed and surcumscribed a unit circle, in order to get a lower and upper bound for the circles circumference - which is the circle number Pi ( π {\displaystyle \pi } ). The central question to be posed is the nature of the intersection over all the natural numbers, or, put differently, the set of numbers, that are found in every Interval I n {\displaystyle I_{n}} (thus, for all n ∈ N {\displaystyle n\in \mathbb {N} } ). In modern mathematics, nested intervals are used as a construction method for the real numbers (in order to complete the field of rational numbers).


In statistics, the size of a test is the probability of falsely rejecting the null hypothesis. That is, it is the probability of making a type I error. It is denoted by the Greek letter α (alpha).


The set of all k-combinations of a set S is often denoted by ( S k ) {\displaystyle \textstyle {\binom {S}{k}}} . A combination is a combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-combination with repetition, k-multiset, or k-selection, are often used.


In order to reap the real benefits of a sharing economy and somehow address some issues that revolve around it, there is a great need for the government and policy-makers to create the “right enabling framework based on a set of guiding principles” proposed by the World Economic Forum. These principles are derived from the analysis of global policymaking and consultation with experts. The following are the seven principles for regulation in the sharing economy. The first principle is creating space for innovation.


At most two Foster processors could be accommodated in a symmetric multiprocessing (SMP) system built with a mainstream chipset, so a second version (Foster MP) was introduced with a 1 MB L3 cache and the Jackson Hyper-Threading capacity. This improved performance slightly, but not enough to lift it out of third place. It was also priced much higher than the dual-processor (DP) versions. The Foster shared the 80528 product code with Willamette.


. . , x k {\displaystyle x_{1},...,x_{k}} , and two propositional formulas are logically equivalent if and only if they express the same Boolean function.


In non-overlapping methods, the subdomains intersect only on their interface. In primal methods, such as Balancing domain decomposition and BDDC, the continuity of the solution across subdomain interface is enforced by representing the value of the solution on all neighboring subdomains by the same unknown. In dual methods, such as FETI, the continuity of the solution across the subdomain interface is enforced by Lagrange multipliers.


In natural language processing, entity linking, also referred to as named-entity linking (NEL), named-entity disambiguation (NED), named-entity recognition and disambiguation (NERD) or named-entity normalization (NEN) is the task of assigning a unique identity to entities (such as famous individuals, locations, or companies) mentioned in text. For example, given the sentence "Paris is the capital of France", the idea is to determine that "Paris" refers to the city of Paris and not to Paris Hilton or any other entity that could be referred to as "Paris". Entity linking is different from named-entity recognition (NER) in that NER identifies the occurrence of a named entity in text but it does not identify which specific entity it is (see Differences from other techniques).


Numerical software execution results or through-put on a network test, for example, provides analytical evidence that the requirement has been met. Inspection of vendor documentation or spec sheets also verifies requirements. Testing or demonstrating the software in a lab environment also verifies the requirements: a test type of verification will occur when test equipment not normally part of the lab (or system under test) is used.


In mathematics, the lower envelope or pointwise minimum of a finite set of functions is the pointwise minimum of the functions, the function whose value at every point is the minimum of the values of the functions in the given set. The concept of a lower envelope can also be extended to partial functions by taking the minimum only among functions that have values at the point. The upper envelope or pointwise maximum is defined symmetrically. For an infinite set of functions, the same notions may be defined using the infimum in place of the minimum, and the supremum in place of the maximum.For continuous functions from a given class, the lower or upper envelope is a piecewise function whose pieces are from the same class.


In mathematics, the Backus–Gilbert method, also known as the optimally localized average (OLA) method is named for its discoverers, geophysicists George E. Backus and James Freeman Gilbert. It is a regularization method for obtaining meaningful solutions to ill-posed inverse problems. Where other regularization methods, such as the frequently used Tikhonov regularization method, seek to impose smoothness constraints on the solution, Backus–Gilbert instead seeks to impose stability constraints, so that the solution would vary as little as possible if the input data were resampled multiple times. In practice, and to the extent that is justified by the data, smoothness results from this.


In mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} , is a type of statistical distance: a measure of how one probability distribution P is different from a second, reference probability distribution Q. A simple interpretation of the KL divergence of P from Q is the expected excess surprise from using Q as a model when the actual distribution is P. While it is a distance, it is not a metric, the most familiar type of distance: it is not symmetric in the two distributions (in contrast to variation of information), and does not satisfy the triangle inequality. Instead, in terms of information geometry, it is a type of divergence, a generalization of squared distance, and for certain classes of distributions (notably an exponential family), it satisfies a generalized Pythagorean theorem (which applies to squared distances).In the simple case, a relative entropy of 0 indicates that the two distributions in question have identical quantities of information. Relative entropy is a nonnegative function of two distributions or measures. It has diverse applications, both theoretical, such as characterizing the relative (Shannon) entropy in information systems, randomness in continuous time-series, and information gain when comparing statistical models of inference; and practical, such as applied statistics, fluid mechanics, neuroscience and bioinformatics.


are a sheik” e.n.fór, “he flees”Another example can be found from Ket: fèmba.di, “I am a Tungus” dɨ.fen, “I am standing”In Turkic, and a few Uralic and Australian Aboriginal languages, predicative adjectives and copular complements take affixes that are identical to those used on predicative verbs, but their negation is different. For example, in Turkish: koş.u.yor.sun “you are running” çavuş.sun “you are a sergeant”Under negation, that becomes (negative affixes in bold): koş.mu.yor.sun “you are not running” çavuş değil.sin “you are not a sergeant”Therefore, the person agreement affixes used with predicative adjectives and nominals in Turkic languages are considered to be nonverbal in character. In some analyses, they are viewed as a form of verbal takeover by a copular strategy.


In the context of building simulation models, error refers to the discrepancy between simulation results and the actual measured performance of the building. There are normally occurring uncertainties in building design and building assessment, which generally stem from approximations in model inputs, such as occupancy behavior. Calibration refers to the process of "tuning" or adjusting assumed simulation model inputs to match observed data from the utilities or Building Management System (BMS).The number of publications dealing with accuracy in building modeling and simulation increased significantly over the past decade. Many papers report large gaps between simulation results and measurements, while other studies show that they can match very well.


During the course of developing a particular formalization of type theory, the type theorist may look back over the rules for types, say C, which have been introduced hitherto and perform the step of recognizing that they are valid according to Martin-Löf’s informal semantics of meaning explanation. This act of ‘introspection’ is an attempt to become aware of the conceptions which have governed our constructions in the past. It gives rise to a “reflection principle which roughly speaking says whatever we are used to doing with types can be done inside a universe” (Martin-Löf 1975, 83). On the formal level, this leads to an extension of the existing formalization of type theory in that the type forming capacities of C become enshrined in a type universe UC mirroring C.


In mathematics, a refinement monoid is a commutative monoid M such that for any elements a0, a1, b0, b1 of M such that a0+a1=b0+b1, there are elements c00, c01, c10, c11 of M such that a0=c00+c01, a1=c10+c11, b0=c00+c10, and b1=c01+c11. A commutative monoid M is said to be conical if x+y=0 implies that x=y=0, for any elements x,y of M.


In the early 2000s, the concept of "disclosure" became increasingly popular in the UFO conspiracy community: that the government had classified and withheld information on alien contact and full disclosure was needed, and was pursued by activist lobbying groups. In 1993, Steven M. Greer founded the Disclosure Project to promote the concept. In May 2001, Greer held a press conference at the National Press Club in Washington, D.C. that demanded Congress hold hearings on "secret U.S.


More abstractly, the logistic function is the natural parameter for the Bernoulli distribution, and in this sense is the "simplest" way to convert a real number to a probability. In particular, it maximizes entropy (minimizes added information), and in this sense makes the fewest assumptions of the data being modeled; see § Maximum entropy.


Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the most general continuous functions, and their definition is the basis of topology.


In mathematics, near sets are either spatially close or descriptively close. Spatially close sets have nonempty intersection. In other words, spatially close sets are not disjoint sets, since they always have at least one element in common. Descriptively close sets contain elements that have matching descriptions.


In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors X = (X1, ..., Xn) and Y = (Y1, ..., Ym) of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of X and Y which have maximum correlation with each other. T. R. Knapp notes that "virtually all of the commonly encountered parametric tests of significance can be treated as special cases of canonical-correlation analysis, which is the general procedure for investigating the relationships between two sets of variables." The method was first introduced by Harold Hotelling in 1936, although in the context of angles between flats the mathematical concept was published by Jordan in 1875.


In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which can only yield integer values may have a non-integer mean). It is a fundamental concept in all areas of quantum physics.


In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f ( x ) {\displaystyle f(x)} with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irreducible polynomial f ( x ) = x 2 + a x + b {\displaystyle f(x)=x^{2}+ax+b} splits into linear terms when reduced mod p {\displaystyle p} . That is, it determines for which prime numbers the relation f ( x ) ≡ f p ( x ) = ( x − n p ) ( x − m p ) ( mod p ) {\displaystyle f(x)\equiv f_{p}(x)=(x-n_{p})(x-m_{p}){\text{ }}({\text{mod }}p)} holds. For a general reciprocity lawpg 3, it is defined as the rule determining which primes p {\displaystyle p} the polynomial f p {\displaystyle f_{p}} splits into linear factors, denoted Spl { f ( x ) } {\displaystyle {\text{Spl}}\{f(x)\}} .


The singular values are the absolute values of the eigenvalues of a normal matrix A, because the spectral theorem can be applied to obtain unitary diagonalization of A {\displaystyle A} as A = U Λ U ∗ {\displaystyle A=U\Lambda U^{*}} . Therefore, A ∗ A = U Λ ∗ Λ U ∗ = U | Λ | U ∗ {\textstyle {\sqrt {A^{*}A}}={\sqrt {U\Lambda ^{*}\Lambda U^{*}}}=U\left|\Lambda \right|U^{*}} . Most norms on Hilbert space operators studied are defined using s-numbers.


It is minimal, because each of its edges belongs to a cycle with the Hamiltonian path edges that is disjoint from all other such cycles. In a tournament, it may be the case that the minimum feedback arc set and maximum acyclic subgraph are both close to half the edges. More precisely, every tournament graph has a feedback arc set of size ( n 2 ) / 2 − Ω ( n 3 / 2 ) {\displaystyle {\tbinom {n}{2}}/2-\Omega (n^{3/2})} , and some tournaments require size ( n 2 ) / 2 − O ( n 3 / 2 ) {\displaystyle {\tbinom {n}{2}}/2-O(n^{3/2})} .


In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications. Using the form of the shortest addition chain, with multiplication instead of addition, computes the desired exponent (instead of multiple) of the base. (This corresponds to OEIS sequence A003313 (Length of shortest addition chain for n).) Each exponentiation in the chain can be evaluated by multiplying two of the earlier exponentiation results.


Such a procedure adds a link from every sink, dangling state a {\displaystyle a} to every other node. Now by the construction the sum of all elements in any column of matrix S is equal to unity. In this way the matrix S is mathematically well defined and it belongs to the class of Markov chains and the class of Perron-Frobenius operators. That makes S suitable for the PageRank algorithm.


During this operation, each column is transformed using a fixed matrix (matrix left-multiplied by column gives new value of column in the state):  =   0 ≤ j ≤ 3 {\displaystyle {\begin{bmatrix}b_{0,j}\\b_{1,j}\\b_{2,j}\\b_{3,j}\end{bmatrix}}={\begin{bmatrix}2&3&1&1\\1&2&3&1\\1&1&2&3\\3&1&1&2\end{bmatrix}}{\begin{bmatrix}a_{0,j}\\a_{1,j}\\a_{2,j}\\a_{3,j}\end{bmatrix}}\qquad 0\leq j\leq 3} Matrix multiplication is composed of multiplication and addition of the entries. Entries are bytes treated as coefficients of polynomial of order x 7 {\displaystyle x^{7}} . Addition is simply XOR.


Often a distinction is made between the suffixes /-ak/ ('you', masc.) and /-ik/ ('you', fem.


In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants".


If the original curve is a line then the inverse curve will pass through the center of inversion. If the original curve passes through the center of inversion then the inverted curve will be a line. The inverted curve will be the same as the original exactly when the curve intersects the circle of inversion at right angles.


In the beginning linkers gave users very limited control over the arrangement of generated output object files. As the target systems became complex with different memory requirements such as embedded systems, it became necessary to give users control to generate output object files with their specific requirements such as defining base addresses' of segments. Linkers control scripts were used for this.


In organic chemistry, GM2 is a type of ganglioside. G refers to ganglioside, the M is for monosialic (as in it has one sialic acid), and 2 refers to the fact that it was the second monosialic ganglioside discovered. It is associated with GM2 gangliosidoses such as Tay–Sachs disease.


"Grade of Service" sometimes means a measure of inbound call center traffic to verify adherence to conditions to measure the success of customers served. On the other hand, the quality of service which a single circuit is designed or conditioned to provide, e.g. voice grade or program grade is called the quality of service. Quality criteria for such circuits may include equalization for amplitude over a specified band of frequencies, or in the case of digital data transported via analogue circuits, may include equalization for phase. Criteria for mobile quality of service in cellular telephone circuits include the probability of abnormal termination of the call.


In mathematics (linear algebra), the Faddeev–LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial p A ( λ ) = det ( λ I n − A ) {\displaystyle p_{A}(\lambda )=\det(\lambda I_{n}-A)} of a square matrix, A, named after Dmitry Konstantinovich Faddeev and Urbain Le Verrier. Calculation of this polynomial yields the eigenvalues of A as its roots; as a matrix polynomial in the matrix A itself, it vanishes by the Cayley–Hamilton theorem. Computing the characteristic polynomial directly from the definition of the determinant is computationally cumbersome insofar as it introduces a new symbolic quantity λ {\displaystyle \lambda } ; by contrast, the Faddeev-Le Verrier algorithm works directly with coefficients of matrix A {\displaystyle A} . The algorithm has been independently rediscovered several times in different forms.


In phonology, a natural class is a set of phonemes in a language that share certain distinctive features. A natural class is determined by participation in shared phonological processes, described using the minimum number of features necessary for descriptive adequacy.


In instruction pipelines, this technique is called out-of-order execution. Guess and backtrack: One important example of item-to-item dependency is the handling of a conditional branch instruction X by an instruction pipeline. The first stage A of the pipeline, that fetches the next instruction Y to be executed, cannot perform its task until X has fetched its operand and determined whether the branch is to be taken or not.


In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist.


In mathematical logic, the intersection type discipline is a branch of type theory encompassing type systems that use the intersection type constructor ( ∩ ) {\displaystyle (\cap )} to assign multiple types to a single term. In particular, if a term M {\displaystyle M} can be assigned both the type φ 1 {\displaystyle \varphi _{1}} and the type φ 2 {\displaystyle \varphi _{2}} , then M {\displaystyle M} can be assigned the intersection type φ 1 ∩ φ 2 {\displaystyle \varphi _{1}\cap \varphi _{2}} (and vice versa). Therefore, the intersection type constructor can be used to express finite heterogeneous ad hoc polymorphism (as opposed to parametric polymorphism). For example, the λ-term λ x .


Standard examples of each, all of which are linear classifiers, are: generative classifiers: naive Bayes classifier and linear discriminant analysis discriminative model: logistic regressionIn application to classification, one wishes to go from an observation x to a label y (or probability distribution on labels). One can compute this directly, without using a probability distribution (distribution-free classifier); one can estimate the probability of a label given an observation, P ( Y | X = x ) {\displaystyle P(Y|X=x)} (discriminative model), and base classification on that; or one can estimate the joint distribution P ( X , Y ) {\displaystyle P(X,Y)} (generative model), from that compute the conditional probability P ( Y | X = x ) {\displaystyle P(Y|X=x)} , and then base classification on that. These are increasingly indirect, but increasingly probabilistic, allowing more domain knowledge and probability theory to be applied. In practice different approaches are used, depending on the particular problem, and hybrids can combine strengths of multiple approaches.


In telecommunication, a virtual call capability, sometimes called a virtual call facility, is a service feature in which: a call set-up procedure and a call disengagement procedure determine the period of communication between two DTEs in which user data are transferred by a packet switched network end-to-end transfer control of packets within the network is required data may be delivered to the network by the call originator before the call access phase is completed, but the data are not delivered to the call receiver if the call attempt is unsuccessful the network delivers all the user data to the call receiver in the same sequence in which the data are received by the network multi-access DTEs may have several virtual calls in progress at the same time.An alternative approach to virtual calls is connectionless communication using datagrams.In the 1970s, the "virtual call" concept was used in the British EPSS and enhanced by Rémi Després as "virtual circuits" in the French RCP.


In the C and C++ programming languages, an #include guard, sometimes called a macro guard, header guard or file guard, is a particular construct used to avoid the problem of double inclusion when dealing with the include directive. The C preprocessor processes directives of the form #include in a source file by locating the associated file on disk and transcluding ("including") its contents into a copy of the source file known as the translation unit, replacing the include directive in the process. The files included in this regard are generally header files, which typically contain declarations of functions and classes or structs. If certain C or C++ language constructs are defined twice, the resulting translation unit is invalid.


In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration.


These threads sit on a run queue in the operating system until processor time is available for them to perform processing for the interrupt. SLIHs may have a long-lived execution time, and thus are typically scheduled similarly to threads and processes. In Linux, FLIHs are called upper half, and SLIHs are called lower half or bottom half. This is different from naming used in other Unix-like systems, where both are a part of bottom half.


These include its relationship to ridge regression and best subset selection and the connections between lasso coefficient estimates and so-called soft thresholding. It also reveals that (like standard linear regression) the coefficient estimates do not need to be unique if covariates are collinear. Though originally defined for linear regression, lasso regularization is easily extended to other statistical models including generalized linear models, generalized estimating equations, proportional hazards models, and M-estimators. Lasso's ability to perform subset selection relies on the form of the constraint and has a variety of interpretations including in terms of geometry, Bayesian statistics and convex analysis. The LASSO is closely related to basis pursuit denoising.


In mathematics, Carmichael's totient function conjecture concerns the multiplicity of values of Euler's totient function φ(n), which counts the number of integers less than and coprime to n. It states that, for every n there is at least one other integer m ≠ n such that φ(m) = φ(n). Robert Carmichael first stated this conjecture in 1907, but as a theorem rather than as a conjecture. However, his proof was faulty, and in 1922, he retracted his claim and stated the conjecture as an open problem.


In the event that a study requires the shoreline position from before aerial photographs, or if the location has poor photographic coverage, historical maps provide an alternative. Many errors are associated with early maps and charts. Such errors may be associated with scale, datum changes, distortions from uneven shrinkage, stretching, creases, tears and folds, different surveying standards, different publication standards and projection errors. The severity of these errors depends on the accuracy of the map and the physical changes that occurred after it was made.


Tables of logarithms prepared by John Napier in 1614 and 1619 used the period (full stop) as the decimal separator, which was then adopted by Henry Briggs in his influential 17th century work. In France, the full stop was already in use in printing to make Roman numerals more readable, so the comma was chosen.Many other countries, such as Italy, also chose to use the comma to mark the decimal units position. It has been made standard by the ISO for international blueprints. However, English-speaking countries took the comma to separate sequences of three digits. In some countries, a raised dot or dash (upper comma) may be used for grouping or decimal separator; this is particularly common in handwriting.


In the case of an approximation of an extremely large number, the relative error may be large, yet there may still be a sense in which one wants to consider the numbers as "close in magnitude". For example, consider 10 10 {\displaystyle 10^{10}} and 10 9 {\displaystyle 10^{9}} The relative error is 1 − 10 9 10 10 = 1 − 1 10 = 90 % {\displaystyle 1-{\frac {10^{9}}{10^{10}}}=1-{\frac {1}{10}}=90\%} a large relative error. However, one can also consider the relative error in the logarithms; in this case, the logarithms (to base 10) are 10 and 9, so the relative error in the logarithms is only 10%. The point is that exponential functions magnify relative errors greatly – if a and b have a small relative error, 10 a {\displaystyle 10^{a}} and 10 b {\displaystyle 10^{b}} the relative error is larger, and 10 10 a {\displaystyle 10^{10^{a}}} and 10 10 b {\displaystyle 10^{10^{b}}} will have an even larger relative error.


For example, there are methods to locate a gene within a sequence, to predict protein structure and/or function, and to cluster protein sequences into families of related sequences.The primary goal of bioinformatics is to increase the understanding of biological processes. What sets it apart from other approaches is its focus on developing and applying computationally intensive techniques to achieve this goal. Examples include: pattern recognition, data mining, machine learning algorithms, and visualization.


For this conclusion to be valid, only very mild assumptions in the theory of computational complexity have to be invoked. In this sense, quantum random sampling schemes can have the potential to show quantum supremacy.A notable property of quantum supremacy is that it can be feasibly achieved by near-term quantum computers, since it does not require a quantum computer to perform any useful task or use high-quality quantum error correction, both of which are long-term goals. Consequently, researchers view quantum supremacy as primarily a scientific goal, with relatively little immediate bearing on the future commercial viability of quantum computing. Due to unpredictable possible improvements in classical computers and algorithms, quantum supremacy may be temporary or unstable, placing possible achievements under significant scrutiny.


For Hockett, morphemes are "meaning elements", not "form elements". For him, there is a morpheme plural using allomorphs such as -s, -en and -ren. Within much morpheme-based morphological theory, the two views are mixed in unsystematic ways so a writer may refer to "the morpheme plural" and "the morpheme -s" in the same sentence.


In mathematics, particularly in algebra, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and the largest essential extension of it. Injective hulls were first described in (Eckmann & Schopf 1953).


In mathematics, a quantaloid is a category enriched over the category Sup of suplattices. In other words, for any objects a and b the morphism object between them is not just a set but a complete lattice, in such a way that composition of morphisms preserves all joins: ( ⋁ i f i ) ∘ ( ⋁ j g j ) = ⋁ i , j ( f i ∘ g j ) {\displaystyle (\bigvee _{i}f_{i})\circ (\bigvee _{j}g_{j})=\bigvee _{i,j}(f_{i}\circ g_{j})} The endomorphism lattice H o m ( X , X ) {\displaystyle \mathrm {Hom} (X,X)} of any object X {\displaystyle X} in a quantaloid is a quantale, whence the name. == References ==


In order to make any use of unlabeled data, some relationship to the underlying distribution of data must exist. Semi-supervised learning algorithms make use of at least one of the following assumptions:


In the double-tap technique, after the first round is fired, the shooter quickly reacquires the sights for a fast second shot. This skill can be practiced by firing two shots at a time, taking time between the shots to reacquire the sights. With practice, the time between shots becomes briefer and briefer until it seems to an observer as if the shooter is just pulling the trigger twice very quickly. According to a U.S.


In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory, and to construct fine moduli stacks when fine moduli spaces do not exist. Descent theory is concerned with generalisations of situations where isomorphic, compatible geometrical objects (such as vector bundles on topological spaces) can be "glued together" within a restriction of the topological basis. In a more general set-up the restrictions are replaced with pullbacks; fibred categories then make a good framework to discuss the possibility of such gluing.


In the United Kingdom, personal data is protected by the Data Protection Act 1998. The Act covers all personal data which an organization may hold, including names, birthday and anniversary dates, addresses, and telephone numbers. Under English law (which extends to Wales but not to Northern Ireland or Scotland), the deception offences under the Theft Act 1968 increasingly contend with identity theft situations.


It is also possible to construct universal graphs for planar graphs that have n1+o(1) vertices.Sumner's conjecture states that tournaments are universal for polytrees, in the sense that every tournament with 2n − 2 vertices contains every polytree with n vertices as a subgraph.A family F of graphs has a universal graph of polynomial size, containing every n-vertex graph as an induced subgraph, if and only if it has an adjacency labelling scheme in which vertices may be labeled by O(log n)-bit bitstrings such that an algorithm can determine whether two vertices are adjacent by examining their labels. For, if a universal graph of this type exists, the vertices of any graph in F may be labeled by the identities of the corresponding vertices in the universal graph, and conversely if a labeling scheme exists then a universal graph may be constructed having a vertex for every possible label.In older mathematical terminology, the phrase "universal graph" was sometimes used to denote a complete graph. The notion of universal graph has been adapted and used for solving mean payoff games.


In mathematics, Burnside's theorem in group theory states that if G is a finite group of order p a q b {\displaystyle p^{a}q^{b}} where p and q are prime numbers, and a and b are non-negative integers, then G is solvable. Hence each non-Abelian finite simple group has order divisible by at least three distinct primes.


At this point, both the parent and offspring rules are returned to . The LCS genetic algorithm is highly elitist since each learning iteration, the vast majority of the population is preserved. Rule discovery may alternatively be performed by some other method, such as an estimation of distribution algorithm, but a GA is by far the most common approach. Evolutionary algorithms like the GA employ a stochastic search, which makes LCS a stochastic algorithm. LCS seeks to cleverly explore the search space, but does not perform an exhaustive search of rule combinations, and is not guaranteed to converge on an optimal solution.


In recent years project management software has moved to Mobile devices. In 2015 there are more cell phones than computers in the world, therefore the move of SaaS applications to the mobile devices makes perfect sense. This migration has had the additional benefit of enabling the users to view and update project details on the go.


In order to evaluate automatic systems on lexical substitution, a task was organized at the Semeval-2007 evaluation competition held in Prague in 2007. A Semeval-2010 task on cross-lingual lexical substitution has also taken place.


Despite the large QA infrastructure most publishers have, many developers retain a small group of testers to provide on-the-spot QA. Now most game developers rely on their highly technical and game savvy testers to find glitches and 'bugs' in either the programming code or graphic layers. Game testers usually have a background playing a variety of different games on a multitude of platforms.


In statistics The optimistic knowledge gradient is a approximation policy proposed by Xi Chen, Qihang Lin and Dengyong Zhou in 2013. This policy is created to solve the challenge of computationally intractable of large size of optimal computing budget allocation problem in binary/multi-class crowd labeling where each label from the crowd has a certain cost.


In mathematics, exponential equivalence of measures is how two sequences or families of probability measures are "the same" from the point of view of large deviations theory.


In telecommunications and data communication systems, an errored second is an interval of a second during which any error whatsoever has occurred, regardless of whether that error was a single bit error or a complete loss of communication for that entire second. The type of error is not important for the purpose of counting errored seconds. In communication systems with very low uncorrected bit error rates, such as modern fiber optic transmission systems, or systems with higher low-level error rates that are corrected using large amounts of forward error correction, errored seconds are often a better measure of the effective user-visible error rate than the raw bit error rate.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 236, 1236, 2346, and 12346 are the patterns related to Braille pattern dots-125, since the two additional dots of kantenji patterns 0125, 1257, and 01257 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Assuming that the required time for each of the tasks is known in advance, an optimal execution order must lead to the minimization of the total execution time. Although this is an NP-hard problem and therefore can be difficult to be solved exactly. There are algorithms, like job scheduler, that calculate optimal task distributions using metaheuristic methods.


In mathematics, a linearised polynomial (or q-polynomial) is a polynomial for which the exponents of all the constituent monomials are powers of q and the coefficients come from some extension field of the finite field of order q. We write a typical example as where each a i {\displaystyle a_{i}} is in F q m ( = GF  ( q m ) ) {\displaystyle F_{q^{m}}(=\operatorname {GF} (q^{m}))} for some fixed positive integer m {\displaystyle m} . This special class of polynomials is important from both a theoretical and an applications viewpoint. The highly structured nature of their roots makes these roots easy to determine.


In the U.S. telephone network, the 12-channel carrier system was an early frequency-division multiplexing system standard, used to carry multiple telephone calls on a single twisted pair of wires, mostly for short to medium distances. In this system twelve voice channels are multiplexed in a high frequency carrier and passed through a balanced pair trunk line similar to those used for individual voice frequency connections. The original system is obsolete today, but the multiplexing of voice channels in units of 12 or 24 channels in modern digital trunk lines such as T-1 is a legacy of the system.


The undesired components are filtered out using regularization: If σ ≫ λ n {\displaystyle \sigma \gg \lambda n} , then 1 σ i + n λ ∼ 1 σ i {\displaystyle {\frac {1}{\sigma _{i}+n\lambda }}\sim {\frac {1}{\sigma _{i}}}} . If σ ≪ λ n {\displaystyle \sigma \ll \lambda n} , then 1 σ i + n λ ∼ 1 λ n {\displaystyle {\frac {1}{\sigma _{i}+n\lambda }}\sim {\frac {1}{\lambda n}}} .The filter function for Tikhonov regularization is therefore defined as: G λ ( σ ) = 1 σ + n λ . {\displaystyle G_{\lambda }(\sigma )={\frac {1}{\sigma +n\lambda }}.}


In natural language processing (NLP), a text graph is a graph representation of a text item (document, passage or sentence). It is typically created as a preprocessing step to support NLP tasks such as text condensationterm disambiguation (topic-based) text summarization, relation extraction and textual entailment.