{"text": "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,\u2026, 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic and type theory, the \u03bb-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 \u03bb-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 \u03bb-cube correspond to: x-axis ( \u2192 {\\displaystyle \\rightarrow } ): types that can bind terms, corresponding to dependent types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Geometrically this is the problem of computing the lengths of the sides of a rectangle whose area A and side-length difference b\u2212a 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 \u2212 2A = c2 \u2212 2ab = (b \u2212 a)2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"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.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 L\u00e9vy alpha-stable distribution, after Paul L\u00e9vy, the first mathematician to have studied it.Of the four parameters defining the family, most attention has been focused on the stability parameter, \u03b1 {\\displaystyle \\alpha } (see panel). Stable distributions have 0 < \u03b1 \u2264 2 {\\displaystyle 0<\\alpha \\leq 2} , with the upper bound corresponding to the normal distribution, and \u03b1 = 1 {\\displaystyle \\alpha =1} to the Cauchy distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u00a7 Dual Leaky Bucket Controller.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems using a command line interface, the user types short commands often followed by various parameters and options.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, the Hardy\u2013Littlewood 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 \u222b R n f ( x ) g ( x ) d x \u2264 \u222b R n f \u2217 ( x ) g \u2217 ( 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 \u2217 {\\displaystyle f^{*}} and g \u2217 {\\displaystyle g^{*}} are the symmetric decreasing rearrangements of f {\\displaystyle f} and g {\\displaystyle g} , respectively.The decreasing rearrangement f \u2217 {\\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 \u2208 X: f ( x ) > r } {\\displaystyle E_{f}(r)=\\left\\{x\\in X:f(x)>r\\right\\}\\quad } and E f \u2217 ( r ) = { x \u2208 X: f \u2217 ( 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 \u2217 ( 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to apply the moment distribution method to analyse a structure, the following things must be considered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u2212 1 . {\\displaystyle f^{-1}.} For a function f: X \u2192 Y {\\displaystyle f\\colon X\\to Y} , its inverse f \u2212 1: Y \u2192 X {\\displaystyle f^{-1}\\colon Y\\to X} admits an explicit description: it sends each element y \u2208 Y {\\displaystyle y\\in Y} to the unique element x \u2208 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 \u2212 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u2061 ( . , . ) {\\displaystyle \\operatorname {adj} (.,.)}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the do ... while loop, the test is done after each iteration. Consequently, the code is always executed at least once.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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) M\u00f6ssbauer 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 ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 W\u00fcstholz 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a residuated lattice is an algebraic structure L = (L, \u2264, \u2022, I) such that (i) (L, \u2264) is a lattice. (ii) (L, \u2022, 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\u2022y \u2264 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 \u2264 x\\z \u21d4 x\u2022y \u2264 z \u21d4 x \u2264 z/y. As suggested by the notation, the residuals are a form of quotient.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u00a7 Criticism, Financial economics \u00a7 Challenges and criticism and Financial engineering \u00a7 Criticisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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: \u2200 ( { g n } n = 1 N \u2208 G N ) ( \u2203 { n k } k = 1 K: \u2211 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\\}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, \u2217) in which there exists at least one pair of elements a and b of G, such that a \u2217 b \u2260 b \u2217 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Information distribution \u2013 This involves dissemination of information needed by the stakeholders and other members of the organization. Performance reporting \u2013 This includes status reporting, progress measurement, and forecasting for the future of the organization. Administrative closure \u2013 This involves generating, gathering, and disseminating information to formalize phase or project completion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Wasserstein distance or Kantorovich\u2013Rubinstein metric is a distance function defined between probability distributions on a given metric space M {\\displaystyle M} . It is named after Leonid Vaser\u0161te\u012dn. 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To satisfy the constraints \u03c3 k ( t + \u0394 t ) {\\displaystyle \\sigma _{k}(t+\\Delta t)} in the next timestep, the Lagrange multipliers should be determined as the following equation, \u03c3 k ( t + \u0394 t ) := \u2016 x k \u03b1 ( t + \u0394 t ) \u2212 x k \u03b2 ( t + \u0394 t ) \u2016 2 \u2212 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 \u03c3 j ( t + \u0394 t ) := \u2016 x ^ j \u03b1 ( t + \u0394 t ) \u2212 x ^ j \u03b2 ( t + \u0394 t ) + \u2211 k = 1 n \u03bb k ( \u0394 t ) 2  \u2016 2 \u2212 d j 2 = 0 , j = 1 \u2026 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 \u03bb k {\\displaystyle \\lambda _{k}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alice sends | \u03c8 \u27e9 {\\displaystyle |\\psi \\rangle } over a public quantum channel to Bob. Bob receives a state \u03b5 \u03c1 = \u03b5 | \u03c8 \u27e9 \u27e8 \u03c8 | {\\displaystyle \\varepsilon \\rho =\\varepsilon |\\psi \\rangle \\langle \\psi |} , where \u03b5 {\\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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Vantieghems theorem is a primality criterion. It states that a natural number n\u22653 is prime if and only if \u220f 1 \u2264 k \u2264 n \u2212 1 ( 2 k \u2212 1 ) \u2261 n mod ( 2 n \u2212 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: \u220f 1 \u2264 k \u2264 n \u2212 1 ( X k \u2212 1 ) \u2261 n \u2212 ( X n \u2212 1 ) / ( X \u2212 1 ) mod ( X n \u2212 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: \u220f 1 \u2264 k \u2264 n \u2212 1 ( X k \u2212 1 ) \u2261 n mod ( X n \u2212 1 ) / ( X \u2212 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).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2003 version, the Vyso\u010dina Region was coded CZ061, and the South Moravian Region was coded CZ062.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u03c0(x) (unrelated to the number \u03c0).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 Erd\u0151s, 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Mathematically, if the coordinate system undergoes a transformation described by an n \u00d7 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 \u2212 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or \u2013 as here \u2013 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, competitors are divided into groups by age. The eight age groups are: 12 and under, 13\u201315, 16\u201317, 18\u201319, Junior (elite 15\u201318), 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "71). To every name or designating expression 'X', there corresponds a cluster of properties, namely the family of those properties \u03c6 such that A believes '\u03c6X'. One of the properties, or some conjointly, are believed by A to pick out some individual uniquely.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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\u2014not the information itself. In today's age of big data, organizations have more information under their control than ever before.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 ( \u03c0 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the Krohn\u2013Rhodes 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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, \u2026, 0x3000 + 4(n \u2212 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u2212 E ) {\\displaystyle (D-E)} F = Actual Excess Losses ( H \u2212 I ) {\\displaystyle (H-I)}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consistent language. Using simple, consistent definitions for requirements described in natural language and use the business terminology that is prevalent in the enterprise. Guidelines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If n {\\textstyle n} is one less than a power of two, then this is always the case. Otherwise, the search may perform \u230a log 2 \u2061 ( n ) + 1 \u230b {\\textstyle \\lfloor \\log _{2}(n)+1\\rfloor } iterations if the search reaches the deepest level of the tree. However, it may make \u230a log 2 \u2061 ( n ) \u230b {\\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 \u230a log 2 \u2061 ( n ) \u230b + 1 \u2212 ( 2 \u230a log 2 \u2061 ( n ) \u230b + 1 \u2212 \u230a log 2 \u2061 ( n ) \u230b \u2212 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "y j \u2208 { 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 \u2208 { 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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\u20139, and of place value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Mathematically, R 0 {\\displaystyle R_{0}} is a threshold for stability of a disease-free equilibrium such that: R 0 \u2264 1 \u21d2 lim t \u2192 \u221e ( C 1 ( t ) , C 2 ( t ) , \u22ef , 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 \u21d2 lim t \u2192 \u221e ( C 1 ( t ) , C 2 ( t ) , \u22ef , 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An interface called \"Stack\" might define two methods: push() and pop(). It can be implemented in different ways, for example, FastStack and GenericStack\u2014the 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The crawl method is an extension of aforementioned discovery method. Except Most search engines use sophisticated scheduling algorithms to \u201cdecide\u201d 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 , \u03b2 ) = \u03b2 0 + \u03b2 1 X i {\\displaystyle f(X_{i},\\beta )=\\beta _{0}+\\beta _{1}X_{i}} , suggesting that the researcher believes Y i = \u03b2 0 + \u03b2 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Breusch\u2013Godfrey 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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\u2019 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical finite group theory, the Dempwolff group is a finite group of order 319979520 = 215\u00b732\u00b75\u00b77\u00b731, 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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\u2013Witten 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 ( \u03c0 {\\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 \u2208 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).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u03b1 (alpha).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u201cright enabling framework based on a set of guiding principles\u201d 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , x k {\\displaystyle x_{1},...,x_{k}} , and two propositional formulas are logically equivalent if and only if they express the same Boolean function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Backus\u2013Gilbert 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\u2013Gilbert 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical statistics, the Kullback\u2013Leibler divergence (also called relative entropy and I-divergence), denoted D KL ( P \u2225 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "are a sheik\u201d e.n.f\u00f3r, \u201che flees\u201dAnother example can be found from Ket: f\u00e8mba.di, \u201cI am a Tungus\u201d d\u0268.fen, \u201cI am standing\u201dIn 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: ko\u015f.u.yor.sun \u201cyou are running\u201d \u00e7avu\u015f.sun \u201cyou are a sergeant\u201dUnder negation, that becomes (negative affixes in bold): ko\u015f.mu.yor.sun \u201cyou are not running\u201d \u00e7avu\u015f de\u011fil.sin \u201cyou are not a sergeant\u201dTherefore, 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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-L\u00f6f\u2019s informal semantics of meaning explanation. This act of \u2018introspection\u2019 is an attempt to become aware of the conceptions which have governed our constructions in the past. It gives rise to a \u201creflection principle which roughly speaking says whatever we are used to doing with types can be done inside a universe\u201d (Martin-L\u00f6f 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u00a7 Maximum entropy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 ) \u2261 f p ( x ) = ( x \u2212 n p ) ( x \u2212 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)\\}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u039b U \u2217 {\\displaystyle A=U\\Lambda U^{*}} . Therefore, A \u2217 A = U \u039b \u2217 \u039b U \u2217 = U | \u039b | U \u2217 {\\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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u2212 \u03a9 ( n 3 / 2 ) {\\displaystyle {\\tbinom {n}{2}}/2-\\Omega (n^{3/2})} , and some tournaments require size ( n 2 ) / 2 \u2212 O ( n 3 / 2 ) {\\displaystyle {\\tbinom {n}{2}}/2-O(n^{3/2})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u2264 j \u2264 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Often a distinction is made between the suffixes /-ak/ ('you', masc.) and /-ik/ ('you', fem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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\u2013Sachs disease.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics (linear algebra), the Faddeev\u2013LeVerrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial p A ( \u03bb ) = det ( \u03bb I n \u2212 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\u2013Hamilton theorem. Computing the characteristic polynomial directly from the definition of the determinant is computationally cumbersome insofar as it introduces a new symbolic quantity \u03bb {\\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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the intersection type discipline is a branch of type theory encompassing type systems that use the intersection type constructor ( \u2229 ) {\\displaystyle (\\cap )} to assign multiple types to a single term. In particular, if a term M {\\displaystyle M} can be assigned both the type \u03c6 1 {\\displaystyle \\varphi _{1}} and the type \u03c6 2 {\\displaystyle \\varphi _{2}} , then M {\\displaystyle M} can be assigned the intersection type \u03c6 1 \u2229 \u03c6 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 \u03bb-term \u03bb x .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 R\u00e9mi Despr\u00e9s as \"virtual circuits\" in the French RCP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Carmichael's totient function conjecture concerns the multiplicity of values of Euler's totient function \u03c6(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 \u2260 n such that \u03c6(m) = \u03c6(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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u2212 10 9 10 10 = 1 \u2212 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 \u2013 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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: ( \u22c1 i f i ) \u2218 ( \u22c1 j g j ) = \u22c1 i , j ( f i \u2218 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 ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u2212 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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 \u2061 ( 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The undesired components are filtered out using regularization: If \u03c3 \u226b \u03bb n {\\displaystyle \\sigma \\gg \\lambda n} , then 1 \u03c3 i + n \u03bb \u223c 1 \u03c3 i {\\displaystyle {\\frac {1}{\\sigma _{i}+n\\lambda }}\\sim {\\frac {1}{\\sigma _{i}}}} . If \u03c3 \u226a \u03bb n {\\displaystyle \\sigma \\ll \\lambda n} , then 1 \u03c3 i + n \u03bb \u223c 1 \u03bb n {\\displaystyle {\\frac {1}{\\sigma _{i}+n\\lambda }}\\sim {\\frac {1}{\\lambda n}}} .The filter function for Tikhonov regularization is therefore defined as: G \u03bb ( \u03c3 ) = 1 \u03c3 + n \u03bb . {\\displaystyle G_{\\lambda }(\\sigma )={\\frac {1}{\\sigma +n\\lambda }}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, consider a study where researchers compare a drug with a placebo. If the patients who are given the drug get better than the patients given the placebo by chance, it may appear that the drug is effective, but in fact the conclusion is incorrect. In reverse, type II errors are errors of omission.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In process improvement efforts, quality costs or cost of quality is a means to quantify the total cost of quality-related efforts and deficiencies. It was first described by Armand V. Feigenbaum in a 1956 Harvard Business Review article.Prior to its introduction, the general perception was that higher quality requires higher costs, either by buying better materials or machines or by hiring more labor. Furthermore, while cost accounting had evolved to categorize financial transactions into revenues, expenses, and changes in shareholder equity, it had not attempted to categorize costs relevant to quality, which is especially important given that most people involved in manufacturing never set hands on the product. By classifying quality-related entries from a company's general ledger, management and quality practitioners can evaluate investments in quality based on cost improvement and profit enhancement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The number of colors required to color unit distance graphs is also unknown (the Hadwiger\u2013Nelson problem): some unit distance graphs require five colors, and every unit distance graph can be colored with seven colors. For every algebraic number there is a unit distance graph with two vertices that must be that distance apart. According to the Beckman\u2013Quarles theorem, the only plane transformations that preserve all unit distance graphs are the isometries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 238, 1238, 2348, and 12348 are the patterns related to Braille pattern dots-126, since the two additional dots of kantenji patterns 0126, 1267, and 01267 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Members of the class of Brandt semigroups are required to satisfy not just one condition but a set of additional properties. A large collection of special classes of semigroups have been defined though not all of them have been studied equally intensively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to demonstrate the use of some of the indicative verb tenses in Louisiana French, take the example of manger, meaning \"to eat\": Some minor simplification of tenses is exhibited in the conjugation of the verb manger, namely of the plural first and second person conjugations which are inflected identically to the third person singular. Not only this, but the inflection of the third person plural verb form has diverged between the form identical to Standard French and the use of -ont in for all verbs. The elision that is common in many aspects of French is accelerated in Louisiana French with the schwa in je often omitted regardless of the presence of a following vowel as well as the regular use of t'es (tu es) and t'as (tu as) as opposed to such avoidance in Standard French. The present progressive tense of Louisiana French initially appears alien as compared to Standard French but apr\u00e8s/ap\u00e9 possesses the same function signified by en train de.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is commonly stated as: In a given instance of the stable-roommates problem (SRP), each of 2n participants ranks the others in strict order of preference. A matching is a set of n disjoint pairs of participants. A matching M in an instance of SRP is stable if there are no two participants x and y, each of whom prefers the other to their partner in M. Such a pair is said to block M, or to be a blocking pair with respect to M.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Dart language, used in the Flutter SDK, the conventions are similar to those of Java, except that constants are written in lowerCamelCase. Dart imposes the syntactic rule that non-local identifiers beginning with an underscore (_) are treated as private (since the language does not have explicit keywords for public or private access). Additionally, source file names do not follow Java's \"one public class per source file, name must match\" rule, instead using snake_case for filenames.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the BitTorrent file distribution system, a torrent file or meta-info file is a computer file that contains metadata about files and folders to be distributed, and usually also a list of the network locations of trackers, which are computers that help participants in the system find each other and form efficient distribution groups called swarms. A torrent file does not contain the content to be distributed; it only contains information about those files, such as their names, folder structure, sizes, and cryptographic hash values for verifying file integrity. Torrent files are normally named with the extension \".torrent\". A torrent file acts like a table of contents (index) that allows computers to find information through the use of a BitTorrent client.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In planar graphs, colorings with k {\\displaystyle k} distinct colors are dual to nowhere-zero flows over the ring Z k {\\displaystyle \\mathbb {Z} _{k}} of integers modulo k {\\displaystyle k} . In this duality, the difference between the colors of two adjacent regions is represented by a flow value across the edge separating the regions. In particular, the existence of nowhere-zero 4-flows is equivalent to the four color theorem. The snark theorem generalizes this result to nonplanar graphs. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first half of the 20th century, various formalisms were proposed to capture the informal concept of a computable function, with \u03bc-recursive functions, Turing machines and the lambda calculus possibly being the best-known examples today. The surprising fact that they are essentially equivalent, in the sense that they are all encodable into each other, supports the Church-Turing thesis. Another shared feature is more rarely commented on: they all are most readily understood as models of sequential computation. The subsequent consolidation of computer science required a more subtle formulation of the notion of computation, in particular explicit representations of concurrency and communication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Apple Darwin operating system, and in the macOS and iOS operating systems built on top of it, the path of the dynamic linker that should be used is embedded at link time into one of the Mach-O load commands in the executable image. In those systems, dynamically loaded shared libraries can be identified either by the filename suffix .dylib or by their placement inside the bundle for a framework. The dynamic linker not only links the target executable to the shared libraries but also places machine code functions at specific address points in memory that the target executable knows about at link time. When an executable wishes to interact with the dynamic linker, it simply executes the machine-specific call or jump instruction to one of those well-known address points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "which is equivalent to \u2200 F \u2203 A \u2200 x  \u21d2 x \u2208 A ] . {\\displaystyle \\forall {\\mathcal {F}}\\,\\exists A\\forall x\\Rightarrow x\\in A].} Compared to the axiom stated at the top of this section, this variation asserts only one direction of the implication, rather than both directions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more advanced mathematics, the partial sums of the harmonic series 1 + 1 2 + 1 3 + 1 4 + 1 5 + \u22ef {\\displaystyle 1+{\\frac {1}{2}}+{\\frac {1}{3}}+{\\frac {1}{4}}+{\\frac {1}{5}}+\\cdots } grow logarithmically. In the design of computer algorithms, logarithmic growth, and related variants, such as log-linear, or linearithmic, growth are very desirable indications of efficiency, and occur in the time complexity analysis of algorithms such as binary search.Logarithmic growth can lead to apparent paradoxes, as in the martingale roulette system, where the potential winnings before bankruptcy grow as the logarithm of the gambler's bankroll. It also plays a role in the St.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Notationally: \u2200 x , x \u2032 \u2208 X , f ( x ) = f ( x \u2032 ) \u27f9 x = x \u2032 , {\\displaystyle \\forall x,x'\\in X,f(x)=f(x')\\implies x=x',} or, equivalently (using logical transposition), \u2200 x , x \u2032 \u2208 X , x \u2260 x \u2032 \u27f9 f ( x ) \u2260 f ( x \u2032 ) . {\\displaystyle \\forall x,x'\\in X,x\\neq x'\\implies f(x)\\neq f(x').} The function is surjective, or onto, if each element of the codomain is mapped to by at least one element of the domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, semantic compression is a process of compacting a lexicon used to build a textual document (or a set of documents) by reducing language heterogeneity, while maintaining text semantics. As a result, the same ideas can be represented using a smaller set of words. In most applications, semantic compression is a lossy compression, that is, increased prolixity does not compensate for the lexical compression, and an original document cannot be reconstructed in a reverse process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\\ matches any single character surrounded by \"\" since the brackets are escaped, for example: \"\", \"\", \"\", \"\", \"]\", and \"\" (bracket space bracket). s. * matches s followed by zero or more characters, for example: \"s\", \"saw\", \"seed\", \"s3w96.7\", and \"s6#h%(>>>m n mQ\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In population dynamics the growth of human population is sometimes supposed to be double exponential. Varfolomeyev and Gurevich experimentally fit N ( y ) = 375.6 \u22c5 1.00185 1.00737 y \u2212 1000 {\\displaystyle N(y)=375.6\\cdot 1.00185^{1.00737^{y-1000}}\\,} where N(y) is the population in millions in year y.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The GDP Deflator Index, or real GDP, measures the level of prices of all-new, domestically produced, final goods and services in an economy. Market performance indices include the labour market index/job index and proprietary stock market index investment instruments offered by brokerage houses. Some indices display market variations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself.An example of a reflexive relation is the relation \"is equal to\" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development has been motivated by descriptive complexity theory and their relationship to database query languages, in particular to Datalog.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other references are given in the References below. The basic definitions in this article are contained within the first few chapters of any of these books. Any monoid can be understood as a special sort of category (with a single object whose self-morphisms are represented by the elements of the monoid), and so can any preorder.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The complement is a determiner phrase (or noun phrase, depending on analytical scheme followed).Determiner Phrase: the head of a determiner phrase (DP) is a determiner. DPs were proposed under generative syntax; not all theories of syntax agree that they exist.Complementizer Phrase: the head of a complementizer phrase (CP) is a complementizer, like that in English. In some cases the C head is covert (not overtly present). The complement of C is generally agreed to be a tense phrase (TP).Tense Phrase: the head of a tense phrase (TP) is tense; these are phrases in which the head is an abstract category representing tense; the complement is a verb phrase.Aspect Phrase: the head of an aspect phrase (AspP) is aspect; these are phrases in which the head is an abstract syntactic category representing aspect. In more traditional analysis the entire phrase (including any elements denoting tense or aspect) is considered to be simply a verb phrase.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a femtocell is a small, low-power cellular base station, typically designed for use in a home or small business. A broader term which is more widespread in the industry is small cell, with femtocell as a subset. It connects to the service provider's network via broadband (such as DSL or cable); current designs typically support four to eight simultaneously active mobile phones in a residential setting depending on version number and femtocell hardware, and eight to sixteen mobile phones in enterprise settings. A femtocell allows service providers to extend service coverage indoors or at the cell edge, especially where access would otherwise be limited or unavailable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Marking a causal process modifies it, a mark not transmitted by a pseudo process. Meanwhile, causal forks are \"the means by which causal structure is generated and modified\". Others have found Salmon's theory of mark transmission to have shortcomings, however, whereby it can fail to discern causal processes from pseudo processes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The need for information sharing has led to the need to depart from the rigidity of MAC in favor of balancing need to protect with need to share. When the \u2018balance\u2019 is decided at the discretion of users, the access control is called discretionary access control (DAC) that is more tolerant of actions that manage risk where MAC requires risk avoidance. Allowing users and systems to manage the risk of sharing information is in some way contrary to the original motivation for MAC.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In query by example, the element used to search is a multimedia content (image, audio, video). In other words, the query is a media. Often, it's used audiovisual indexing. It will be necessary to choose the criteria we are going to use for creating metadata.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of free and open-source software, proprietary software only available as a binary executable is referred to as a blob or binary blob. The term usually refers to a device driver module loaded into the kernel of an open-source operating system, and is sometimes also applied to code running outside the kernel, such as system firmware images, microcode updates, or userland programs. The term blob was first used in database management systems to describe a collection of binary data stored as a single entity. When computer hardware vendors provide complete technical documentation for their products, operating system developers are able to write hardware device drivers to be included in the operating system kernels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Scheinerman also conjectured that segments with only three directions would be sufficient to represent 3-colorable graphs, and West (1991) conjectured that analogously every planar graph could be represented using four directions. If a graph is represented with segments having only k directions and no two segments belong to the same line, then the graph can be colored using k colors, one color for each direction. Therefore, if every planar graph can be represented in this way with only four directions, then the four color theorem follows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following pseudocode algorithm, dist is an array that contains the current distances from the source to other vertices, i.e. dist is the current distance from the source to the vertex u. The prev array contains pointers to previous-hop nodes on the shortest path from source to the given vertex (equivalently, it is the next-hop on the path from the given vertex to the source). The code u \u2190 vertex in Q with min dist, searches for the vertex u in the vertex set Q that has the least dist value. Graph.Edges(u, v) returns the length of the edge joining (i.e. the distance between) the two neighbor-nodes u and v. The variable alt on line 14 is the length of the path from the root node to the neighbor node v if it were to go through u. If this path is shorter than the current shortest path recorded for v, that current path is replaced with this alt path. 1 function Dijkstra(Graph, source): 2 3 for each vertex v in Graph.Vertices: 4 dist \u2190 INFINITY 5 prev \u2190 UNDEFINED 6 add v to Q 7 dist \u2190 0 8 9 while Q is not empty: 10 u \u2190 vertex in Q with min dist 11 remove u from Q 12 13 for each neighbor v of u still in Q: 14 alt \u2190 dist + Graph.Edges(u, v) 15 if alt < dist: 16 dist \u2190 alt 17 prev \u2190 u 18 19 return dist, prev If we are only interested in a shortest path between vertices source and target, we can terminate the search after line 10 if u = target.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Prominent intersection type systems include the Coppo\u2013Dezani type assignment system, the Barendregt-Coppo\u2013Dezani type assignment system, and the essential intersection type assignment system. Most strikingly, intersection type systems are closely related to (and often exactly characterize) normalization properties of \u03bb-terms under \u03b2-reduction. In programming languages, such as TypeScript and Scala, intersection types are used to express ad hoc polymorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the field of group theory, a metanilpotent group is a group that is nilpotent by nilpotent. In other words, it has a normal nilpotent subgroup such that the quotient group is also nilpotent. In symbols, G {\\displaystyle G} is metanilpotent if there is a normal subgroup N {\\displaystyle N} such that both N {\\displaystyle N} and G / N {\\displaystyle G/N} are nilpotent. The following are clear: Every metanilpotent group is a solvable group. Every subgroup and every quotient of a metanilpotent group is metanilpotent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, a dynamical system evolving in time may be described in a phase space, that is by the evolution in time of some variables. If this variables are bounded, that is having a minimum and a maximum, for a theorem due to Liouville, a measure can be defined in the space, having a measure space where the lemma applies. As a consequence, given a configuration of the system (a point in the phase space) the average return period close to this configuration (in the neighbourhood of the point) is inversely proportional to the considered size of volume surrounding the configuration. Normalizing the measure space to 1, it becomes a probability space and the measure P ( A ) {\\displaystyle P(A)} of its set A {\\displaystyle A} represents the probability of finding the system in the states represented by the points of that set. In this case the lemma implies that the smaller is the probability to be in a certain state (or close to it), the longer is the time of return near that state.In formulas, if A {\\displaystyle A} is the region close to the starting point and T R {\\displaystyle T_{R}} is the return period, its average value is: \u27e8 T R \u27e9 = \u03c4 / P ( A ) {\\displaystyle \\langle T_{R}\\rangle =\\tau /P(A)} Where \u03c4 {\\displaystyle \\tau } is a characteristic time of the system in question. Note that since the volume of A {\\displaystyle A} , therefore P ( A ) {\\displaystyle P(A)} , depends exponentially on the n {\\displaystyle n} variables in the system ( A = \u03f5 n {\\displaystyle A=\\epsilon ^{n}} , with \u03f5 {\\displaystyle \\epsilon } infinitesimal side, therefore less than 1, of the volume in n {\\displaystyle n} dimensions), P ( A ) {\\displaystyle P(A)} decreases very rapidly as the variables of the system increase and consequently the return period increases exponentially.In practice, as the variables needed to describe the system increase, the return period increases rapidly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Removing stop words and punctuation Some tokens are less important than others. For instance, common words such as \"the\" might not be very helpful for revealing the essential characteristics of a text. So usually it is a good idea to eliminate stop words and punctuation marks before doing further analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separation of the set into disjoint pairs (\"roommates\"). The matching is stable if there are no two elements which are not roommates and which both prefer each other to their roommate under the matching. This is distinct from the stable-marriage problem in that the stable-roommates problem allows matches between any two elements, not just between classes of \"men\" and \"women\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle c.} Also, recall that a Hermitian (or real symmetric) matrix has real eigenvalues. It can be shown that, for a given matrix, the Rayleigh quotient reaches its minimum value \u03bb min {\\displaystyle \\lambda _{\\min }} (the smallest eigenvalue of M) when x {\\displaystyle \\mathbf {x} } is v min {\\displaystyle \\mathbf {v} _{\\min }} (the corresponding eigenvector).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, code coverage is a percentage measure of the degree to which the source code of a program is executed when a particular test suite is run. A program with high test coverage has more of its source code executed during testing, which suggests it has a lower chance of containing undetected software bugs compared to a program with low test coverage. Many different metrics can be used to calculate test coverage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physical geography, a channel is a type of landform consisting of the outline of a path of relatively shallow and narrow body of water or of other fluids (e.g., lava), most commonly the confine of a river, river delta or strait. The word often refers to a natural body of water, while the cognate term canal denotes a similar artificial structure. Channels are important for the functionality of ports and other bodies of water used for navigability for shipping.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Much of the system's core, including the LWKT subsystem, the IPI messaging subsystem and the new kernel memory allocator, are lockless, meaning that they work without using mutexes, with each process operating on a single CPU. Critical sections are used to protect against local interrupts, individually for each CPU, guaranteeing that a thread currently being executed will not be preempted.Serializing tokens are used to prevent concurrent accesses from other CPUs and may be held simultaneously by multiple threads, ensuring that only one of those threads is running at any given time. Blocked or sleeping threads therefore do not prevent other threads from accessing the shared resource unlike a thread that is holding a mutex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, the grammatical expression of past tense is combined with the expression of other categories such as grammatical aspect (see tense\u2013aspect). Thus a language may have several types of past tense form, their use depending on what aspectual or other additional information is to be encoded. French, for example, has a compound past (pass\u00e9 compos\u00e9) for expressing completed events, and imperfect for continuous or repetitive events. Some languages that grammaticalise for past tense do so by inflecting the verb, while others do so periphrastically using auxiliary verbs, also known as \"verbal operators\" (and some do both, as in the example of French given above).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an addition chain for computing a positive integer n can be given by a sequence of natural numbers starting with 1 and ending with n, such that each number in the sequence is the sum of two previous numbers. The length of an addition chain is the number of sums needed to express all its numbers, which is one less than the cardinality of the sequence of numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion\u2013exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same number of elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions. DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling). Directed acyclic graphs are sometimes instead called acyclic directed graphs or acyclic digraphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The pps sampling results in a fixed sample size n (as opposed to Poisson sampling which is similar but results in a random sample size with expectancy of n). When selecting items with replacement the selection procedure is to just draw one item at a time (like getting n draws from a multinomial distribution with N elements, each with their own p i {\\displaystyle p_{i}} selection probability). If doing a without-replacement sampling, the schema can become more complex. : 93", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory, flow-sensitive typing (also called flow typing or occurrence typing) is a type system where the type of an expression depends on its position in the control flow. In statically typed languages, a type of an expression is determined by the types of the sub-expressions that compose it. However, in flow-sensitive typing, an expression's type may be updated to a more specific type if it follows an operation that validates its type. Validating operations can include type predicates, imperative updates, and control flow.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This automorphism group permutes the three 8-dimensional irreducible representations of Spin(8); these being the vector representation and two chiral spin representations. These automorphisms do not project to automorphisms of SO(8). The vector representation\u2014the natural action of SO(8) (hence Spin(8)) on F8\u2014consists over the real numbers of Euclidean 8-vectors and is generally known as the \"defining module\", while the chiral spin representations are also known as \"half-spin representations\", and all three of these are fundamental representations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most common choice is the initial ordinal in that class. This is usually taken as the definition of cardinal number in axiomatic set theory.Assuming the axiom of choice, the cardinalities of the infinite sets are denoted \u2135 0 < \u2135 1 < \u2135 2 < \u2026 . {\\displaystyle \\aleph _{0}<\\aleph _{1}<\\aleph _{2}<\\ldots .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consider a segment that begins at n = kL + M, for any integer k, and define: x k  \u225c { x  , 1 \u2264 n \u2264 L + M \u2212 1 0 , otherwise . {\\displaystyle x_{k}\\ \\triangleq {\\begin{cases}x,&1\\leq n\\leq L+M-1\\\\0,&{\\textrm {otherwise}}.\\end{cases}}} y k  \u225c x k  \u2217 h  = \u2211 m = 1 M h  \u22c5 x k  . {\\displaystyle y_{k}\\ \\triangleq \\ x_{k}*h=\\sum _{m=1}^{M}h\\cdot x_{k}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The challenge remains to search large indices or popular query lists in under a few milliseconds so that the user sees results pop up while typing. Autocomplete can have an adverse effect on individuals and businesses when negative search terms are suggested when a search takes place. Autocomplete has now become a part of reputation management as companies linked to negative search terms such as scam, complaints and fraud seek to alter the results. Google in particular have listed some of the aspects that affect how their algorithm works, but this is an area that is open to manipulation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "&& for short-circuit logical AND. (4 && 2) is true.In C, C++, and Go, a prefix & is a unary operator denoting the address in memory of the argument, e.g. &x, &func, &a. In C++ and PHP, unary prefix & before a formal parameter of a function denotes pass-by-reference.In Pascal, the & as the first character of an identifier prevents the compiler from treating it as a keyword, thus escaping it. In Fortran, the ampersand forces the compiler to treat two lines as one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some of the most basic are the percentage of program subroutines and the percentage of program statements called during execution of the test suite. Test coverage was among the first methods invented for systematic software testing. The first published reference was by Miller and Maloney in Communications of the ACM, in 1963.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similar definitions exist for digraphs, in terms of directed cycles. Finding a vertex-disjoint cycle cover of a directed graph can also be performed in polynomial time by a similar reduction to perfect matching. However, adding the condition that each cycle should have length at least 3 makes the problem NP-hard.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Later Macs could also read and write 1.44 MB HD disks in PC format with fixed rotation speed. Higher capacities were similarly achieved by Acorn's RISC OS (800 KB for DD, 1,600 KB for HD) and AmigaOS (880 KB for DD, 1,760 KB for HD). All 3\u00bd-inch disks have a rectangular hole in one corner which, if obstructed, write-enables the disk.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They >completely< forgot me! I had _nothing_ to do with it. (Commonly interpreted as underlining, which is an alternative to italics.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"The theorem appears in a 1922 publication of Ernst Steinitz, after whom it is named. It can be proven by mathematical induction (as Steinitz did), by finding the minimum-energy state of a two-dimensional spring system and lifting the result into three dimensions, or by using the circle packing theorem. Several extensions of the theorem are known, in which the polyhedron that realizes a given graph has additional constraints; for instance, every polyhedral graph is the graph of a convex polyhedron with integer coordinates, or the graph of a convex polyhedron all of whose edges are tangent to a common midsphere.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In machine learning, specifically empirical risk minimization, MSE may refer to the empirical risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The MSE is a measure of the quality of an estimator. As it is derived from the square of Euclidean distance, it is always a positive value that decreases as the error approaches zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The algorithm takes its name from the fact that, when this rewriting is done and the resulting proof is displayed as a DAG (directed acyclic graph), the unit node \u03b7 {\\displaystyle \\eta } appears lower (i.e., closer to the root) than it used to appear in the original proof. A naive implementation exploiting theorem would require the proof to be traversed and fixed after each unit node is lowered. It is possible, however, to do better by first collecting and removing all the unit nodes in a single traversal, and afterwards fixing the whole proof in a single second traversal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Brief instructional blocks can be recorded for review by students \u2014 they will see the exact presentation that occurred in the classroom with the teacher's audio input. This can help transform learning and instruction. Many companies and projects now focus on creating supplemental instructional materials specifically designed for interactive whiteboards. One recent use of the IWB is in shared reading lessons. Mimic books, for instance, allow teachers to project children's books onto the interactive whiteboard with book-like interactivity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by Dickson (1904) that for a finite set of linear forms a1 + b1n, a2 + b2n, ..., ak + bkn with bi \u2265 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this (Ribenboim 1996, 6.I). The case k = 1 is Dirichlet's theorem. Two other special cases are well-known conjectures: there are infinitely many twin primes (n and 2 + n are primes), and there are infinitely many Sophie Germain primes (n and 1 + 2n are primes). Dickson's conjecture is further extended by Schinzel's hypothesis H.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In several studies, participants read a list of high or low frequency words along with nonwords (or pseudowords). They were tasked with pronouncing the words or nonwords as fast as possible. High frequency words were read aloud faster than low frequency words. Participants read the nonwords the slowest. More errors were made when pronouncing the low frequency words than the high frequency words.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In fact, all square roots of natural numbers, other than of perfect squares, are irrational.Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence. For example, the decimal representation of \u03c0 starts with 3.14159, but no finite number of digits can represent \u03c0 exactly, nor does it repeat.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For general closed convex sets, the limit point need not be the projection. Classical work on the case of two closed convex sets shows that the rate of convergence of the iterates is linear. There are now extensions that consider cases when there are more than two sets, or when the sets are not convex, or that give faster convergence rates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This chain of extensions canonically embeds the natural numbers in the other number systems. Properties of the natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term Cone of Uncertainty is used in software development where the technical and business environments change very rapidly. However, the concept, under different names, is a well-established basic principle of cost engineering. Most environments change so slowly that they can be considered static for the duration of a typical project, and traditional project management methods therefore focus on achieving a full understanding of the environment through careful analysis and planning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring (described below) of a triangulation of an n {\\displaystyle n} -dimensional simplex contains a cell whose vertices all have different colors. The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain. Sperner colorings have been used for effective computation of fixed points and in root-finding algorithms, and are applied in fair division (cake cutting) algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, the dyadic product is linear in both of its operands. In general, two dyadics can be added to get another dyadic, and multiplied by numbers to scale the dyadic. However, the product is not commutative; changing the order of the vectors results in a different dyadic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The HID descriptor is a hard coded array of bytes that describes the device's data packets. This includes: how many packets the device supports, the size of the packets, and the purpose of each byte and bit in the packet. For example, a keyboard with a calculator program button can tell the host that the button's pressed/released state is stored as the 2nd bit in the 6th byte in data packet number 4 (note: these locations are only illustrative and are device-specific).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the plethystic exponential is a certain operator defined on (formal) power series which, like the usual exponential function, translates addition into multiplication. This exponential operator appears naturally in the theory of symmetric functions, as a concise relation between the generating series for elementary, complete and power sums homogeneous symmetric polynomials in many variables. Its name comes from the operation called plethysm, defined in the context of so-called lambda rings. In combinatorics, the plethystic exponential is a generating function for many well studied sequences of integers, polynomials or power series, such as the number of integer partitions. It is also an important technique in the enumerative combinatorics of unlabelled graphs, and many other combinatorial objects.In geometry and topology, the plethystic exponential of a certain geometric/topologic invariant of a space, determines the corresponding invariant of its symmetric products.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the Paris\u2013Harrington theorem states that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in Peano arithmetic, is not provable in this system. The combinatorial principle is however provable in slightly stronger systems. This result has been described by some (such as the editor of the Handbook of Mathematical Logic in the references below) as the first \"natural\" example of a true statement about the integers that could be stated in the language of arithmetic, but not proved in Peano arithmetic; it was already known that such statements existed by G\u00f6del's first incompleteness theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the CPU guesses wrong, all of these instructions and their context need to be flushed and the correct ones loaded, which takes time. This has led to increasingly complex instruction-dispatch logic that attempts to guess correctly, and the simplicity of the original reduced instruction set computing (RISC) designs has been eroded. VLIW lacks this logic, and thus lacks its energy use, possible design defects, and other negative aspects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where the compact set K {\\displaystyle K} is also convex, the above theorem has as a corollary the first part of the next theorem, which is also often called the Krein\u2013Milman theorem. The convex hull of the extreme points of K {\\displaystyle K} forms a convex subset of K {\\displaystyle K} so the main burden of the proof is to show that there are enough extreme points so that their convex hull covers all of K . {\\displaystyle K.} For this reason, the following corollary to the above theorem is also often called the Krein\u2013Milman theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the International Phonetic Alphabet (IPA), aspirated consonants are written using the symbols for voiceless consonants followed by the aspiration modifier letter \u27e8\u25cc\u02b0\u27e9, a superscript form of the symbol for the voiceless glottal fricative \u27e8h\u27e9. For instance, \u27e8p\u27e9 represents the voiceless bilabial stop, and \u27e8p\u02b0\u27e9 represents the aspirated bilabial stop. Voiced consonants are seldom actually aspirated. Symbols for voiced consonants followed by \u27e8\u25cc\u02b0\u27e9, such as \u27e8b\u02b0\u27e9, typically represent consonants with murmured voiced release (see below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On the other hand, genuine quantifiers (e.g., 'every professor') bear scope. An 'every-NP' triggers the introduction of a complex condition of the form K1 \u2192 K2, where K1 and K2 are sub-DRSs representing the restriction and the scope of the quantification respectively. Unlike true quantifiers, indefinite noun phrases just contribute a new DR (together with some descriptive material in terms of conditions on the DR), which is placed in a larger structure. This larger structure can be the top-level DRS or some sub-DRS according to the sentence-internal environment of the analyzed noun phrase\u2014in other words, a level that is accessible to an anaphor that comes later.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some machine translation and natural language processing systems, written texts in human languages are parsed by computer programs. Human sentences are not easily parsed by programs, as there is substantial ambiguity in the structure of human language, whose usage is to convey meaning (or semantics) amongst a potentially unlimited range of possibilities but only some of which are germane to the particular case. So an utterance \"Man bites dog\" versus \"Dog bites man\" is definite on one detail but in another language might appear as \"Man dog bites\" with a reliance on the larger context to distinguish between those two possibilities, if indeed that difference was of concern. It is difficult to prepare formal rules to describe informal behaviour even though it is clear that some rules are being followed.In order to parse natural language data, researchers must first agree on the grammar to be used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some explosives, e.g. ANFO, show reduced sensitivity under pressure. A transient pressure wave from a nearby detonation may compress the explosive sufficiently to make its initiation fail. This can be prevented by introducing sufficient delays into the firing sequence.A sympathetic detonation during mine blasting may influence the seismic signature of the blast, by boosting the P-wave amplitude without significantly amplifying the surface wave.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Under a Montagovian approach, the indefinite a donkey, which is assumed to be inherently an existential quantifier, ends up becoming a universal quantifier, an unwelcome result because the change in quantificational force cannot be accounted for in any principled way. DRT avoids this problem by assuming that indefinites introduce discourse referents (DRs), which are stored in the mental representation and are accessible (or not, depending on the conditions) to expressions like pronouns and other anaphoric elements. Furthermore, they are inherently non-quantificational, and pick up quantificational force depending upon the context.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Minnan also has words consisting of a consonant followed by a syllabic nasal, such as pn\u0304g \"cooked rice\". So far, all of these syllabic consonants, at least in the lexical words, have been sonorants, such as , , , and , which have a voiced quality similar to vowels. (They can carry tone, for example.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "P(A|B) (the conditional probability of A given B) typically differs from P(B|A). For example, if a person has dengue fever, the person might have a 90% chance of being tested as positive for the disease. In this case, what is being measured is that if event B (having dengue) has occurred, the probability of A (tested as positive) given that B occurred is 90%, simply writing P(A|B) = 90%.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operations on numerical values, problems can arise that result in unexpected output, slowing of a process, or crashing. These can be from a lack of awareness of the qualities of the data storage such as a loss of precision due to rounding, numerically unstable algorithms, arithmetic overflow and underflow, or from lack of awareness of how calculations are handled by different software coding languages such as division by zero which in some languages may throw an exception, and in others may return a special value such as NaN or infinity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some consider \"inter-city\" service to be that which operates as an express service between two main city stations, bypassing intermediate stations. However, this term is used in Australia (Sydney for example) to describe the regional trains operating beyond the boundaries of the suburban services, even though some of these \"inter-city\" services stop all stations similar to German regional services. In this regard, the German service delineations and naming conventions are clearer and better used for academic purposes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the concept discovery step, terms are grouped to meaning bearing units, which correspond to an abstraction of the world and therefore to concepts. The grouped terms are these domain-specific terms and their synonyms, which were identified in the domain terminology extraction step.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following the Majority Judgment winner for the normal ballots is determined. The sorted ratings would be as follows: Result: The median of A is between \"Good\" and \"Poor\" and thus is rounded down to \"Poor\". The median of B is \"Fair\". Thus, B is elected Majority Judgment winner.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This phenomenon is closely related to the coupon collector's problem: in order to be connected, a random graph needs enough edges for each vertex to be incident to at least one edge. More precisely, if random edges are added one by one to a graph, then with high probability the first edge whose addition connects the whole graph touches the last isolated vertex.For different models including the random subgraphs of grid graphs, the connected components are described by percolation theory. A key question in this theory is the existence of a percolation threshold, a critical probability above which a giant component (or infinite component) exists and below which it does not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recursion theory, the Kleene\u2013Brouwer order may be applied to the computation trees of implementations of total recursive functionals. A computation tree is well-founded if and only if the computation performed by it is total recursive. Each state x {\\displaystyle x} in a computation tree may be assigned an ordinal number | | x | | {\\displaystyle ||x||} , the supremum of the ordinal numbers 1 + | | y | | {\\displaystyle 1+||y||} where y {\\displaystyle y} ranges over the children of x {\\displaystyle x} in the tree. In this way, the total recursive functionals themselves can be classified into a hierarchy, according to the minimum value of the ordinal at the root of a computation tree, minimized over all computation trees that implement the functional. The Kleene\u2013Brouwer order of a well-founded computation tree is itself a recursive well-ordering, and at least as large as the ordinal assigned to the tree, from which it follows that the levels of this hierarchy are indexed by recursive ordinals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is no penalty for incorrect answers. The final song of each round is designated as the \"Fast Track\" and is played at double value. During the season finale, this song is played as a \"Fast Track Challenge,\" in which the teams must respond within the time needed for Shazam to identify it. No multiple-choice answers are offered, and only the first team to buzz in is given a chance to name the song and win the money for it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When compared to shipping boxes and printing user manuals, the pace and efficiency provided by the App Store is profound and has changed software distribution forever. During the early development of the Electronic AppWrapper, it became the first commercial software distribution catalog to allow digital data encryption and provide digital rights management for apps, music and data. This was a tremendous advance for the independent developers who could not possibly access the financial resources to publish software boxes across the country and the world, in order to reach their audience.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the U.S. and Canada, dissemination of flood warnings is covered by Specific Area Message Encoding (SAME) code FLW, which is used by the U.S. Emergency Alert System and NOAA Weather Radio network and in Canada's Weatheradio Canada network. \"Flood statements\" are issued by the National Weather Service to inform the public of flooding along major streams in which there is not a serious threat to life or property. They may also follow a flood warning to give later information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For our example key matrix: | 6 24 1 13 16 10 20 17 15 | = 6 ( 16 \u22c5 15 \u2212 10 \u22c5 17 ) \u2212 24 ( 13 \u22c5 15 \u2212 10 \u22c5 20 ) + 1 ( 13 \u22c5 17 \u2212 16 \u22c5 20 ) = 441 \u2261 25 ( mod 26 ) {\\displaystyle {\\begin{vmatrix}6&24&1\\\\13&16&10\\\\20&17&15\\end{vmatrix}}=6(16\\cdot 15-10\\cdot 17)-24(13\\cdot 15-10\\cdot 20)+1(13\\cdot 17-16\\cdot 20)=441\\equiv 25{\\pmod {26}}} So, modulo 26, the determinant is 25. Since 25 = 5 2 {\\displaystyle 25=5^{2}} and 26 = 2 \u00d7 13 {\\displaystyle 26=2\\times 13} , 25 has no common factors with 26, and this matrix can be used for the Hill cipher. The risk of the determinant having common factors with the modulus can be eliminated by making the modulus prime. Consequently, a useful variant of the Hill cipher adds 3 extra symbols (such as a space, a period and a question mark) to increase the modulus to 29.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In standard truth-functional propositional logic, association, or associativity are two valid rules of replacement. The rules allow one to move parentheses in logical expressions in logical proofs. The rules (using logical connectives notation) are: and where \" \u21d4 {\\displaystyle \\Leftrightarrow } \" is a metalogical symbol representing \"can be replaced in a proof with\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The time it takes to organise teams and have them cooperate can be time-consuming. Additionally, there is a potential risk of having a free-rider problem, where individuals within a team can get away with no contribution to the work and still be compensated the same amount as their peers.However, free-riding can be eliminated by organising set protocols. This allows for easier communication and decision-making, giving each member of the team responsibilities and requirements that are agreed upon.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject used in most modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In register machines, a common subexpression (a subexpression which is used multiple times with the same result value) can be evaluated just once and its result saved in a fast register. The subsequent reuses have no time or code cost, just a register reference. This optimization speeds simple expressions (for example, loading variable X or pointer P) as well as less-common complex expressions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By isolating the kernel from concurrency, many parts of the kernel no longer need to be modified to support SMP. However, as in giant-lock SMP systems only one processor can run the kernel code at a time, performance for applications spending significant amounts of time in the kernel is not much improved. Accordingly, the giant-lock approach is commonly seen as a preliminary means of bringing SMP support to an operating system, yielding benefits only in user space. Most modern operating systems use a fine-grained locking approach.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Every job j {\\displaystyle j} consists of m {\\displaystyle m} operations O i j {\\displaystyle O_{ij}} for i = 1 , \u2026 , m {\\displaystyle i=1,\\ldots ,m} , to be scheduled in the given order. Operation O i j {\\displaystyle O_{ij}} must be processed for p i j {\\displaystyle p_{ij}} units on machine i {\\displaystyle i} . J: Job-shop problem. Every job j {\\displaystyle j} consists of n j {\\displaystyle n_{j}} operations O k j {\\displaystyle O_{kj}} for k = 1 , \u2026 , n j {\\displaystyle k=1,\\ldots ,n_{j}} , to be scheduled in that order. Operation O k j {\\displaystyle O_{kj}} must be processed for p k j {\\displaystyle p_{kj}} units on a dedicated machine \u03bc k j {\\displaystyle \\mu _{kj}} with \u03bc k j \u2260 \u03bc k \u2032 j {\\displaystyle \\mu _{kj}\\neq \\mu _{k'j}} for k \u2260 k \u2032 {\\displaystyle k\\neq k'} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In strongly typed programming languages, each parameter's type must be specified in the procedure declaration. Languages using type inference attempt to discover the types automatically from the function's body and usage. Dynamically typed programming languages defer type resolution until run-time. Weakly typed languages perform little to no type resolution, relying instead on the programmer for correctness. Some languages use a special keyword (e.g. void) to indicate that the subroutine has no parameters; in formal type theory, such functions take an empty parameter list (whose type is not void, but rather unit).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and data compression. The rank constraint is related to a constraint on the complexity of a model that fits the data. In applications, often there are other constraints on the approximating matrix apart from the rank constraint, e.g., non-negativity and Hankel structure. Low-rank approximation is closely related to numerous other techniques, including principal component analysis, factor analysis, total least squares, latent semantic analysis, orthogonal regression, and dynamic mode decomposition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of machine learning and pattern classification, the labels of a set of random observations can be divided into 2 or more classes. Each observation is called an instance and the class it belongs to is the label. The Bayes error rate of the data distribution is the probability an instance is misclassified by a classifier that knows the true class probabilities given the predictors. For a multiclass classifier, the expected prediction error may be calculated as follows: E P E = E x  {\\displaystyle EPE=E_{x}} where x is the instance, E  {\\displaystyle E} the expectation value, Ck is a class into which an instance is classified, P(Ck|x) is the conditional probability of label k for instance x, and L() is the 0\u20131 loss function: L ( x , y ) = 1 \u2212 \u03b4 x , y = { 0 if x = y 1 if x \u2260 y , {\\displaystyle L(x,y)=1-\\delta _{x,y}={\\begin{cases}0&{\\text{if }}x=y\\\\1&{\\text{if }}x\\neq y\\end{cases}},} where \u03b4 x , y {\\displaystyle \\delta _{x,y}} is the Kronecker delta.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set  as a subspace of R {\\displaystyle \\mathbb {R} } is both open and closed, whereas as a subset of R {\\displaystyle \\mathbb {R} } it is only closed. As a subspace of R {\\displaystyle \\mathbb {R} } ,  \u222a  is composed of two disjoint open subsets (which happen also to be closed), and is therefore a disconnected space. Let S = [0, 1) be a subspace of the real line R {\\displaystyle \\mathbb {R} } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, secure coding aims to guard against the accidental introduction of security vulnerabilities. It is also possible to create software designed from the ground up to be secure. Such systems are secure by design. Beyond this, formal verification aims to prove the correctness of the algorithms underlying a system; important for cryptographic protocols for example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the domain of logical frameworks, the term higher-order abstract syntax is usually used to refer to a specific representation that uses the binders of the meta-language to encode the binding structure of the object language. For instance, the logical framework LF has a \u03bb-construct, which has arrow (\u2192) type. As an example, consider we wanted to formalize a very primitive language with untyped expressions, a built-in set of variables, and a let construct (let = in ), which allows to bind variables var with definition exp in expressions exp'. In Twelf syntax, we could do as follows: Here, exp is the type of all expressions and var the type of all built-in variables (implemented perhaps as natural numbers, which is not shown).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Boxes present the advantage of being very easily manipulated by computers, as they form the heart of interval analysis. Many interval algorithms naturally provide solutions that are regular subpavings.In computation, a well-known application of subpaving in R\u00b2 is the Quadtree data structure. In image tracing context and other applications is important to see X\u207b as topological interior, as illustrated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2010s, as social media gained prominence, Russia then began to use platforms such as Facebook, Twitter, and YouTube to spread disinformation. Russian web brigades and bots, typically operated by Russia's Internet Research Agency (IRA), were commonly used to disseminate disinformation throughout these social media channels. As of late 2017, Facebook believed that as many as 126 million of its users had seen content from Russian disinformation campaigns on its platform. Twitter stated that it had found 36,000 Russian bots spreading tweets related to the 2016 U.S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All ten rotors were interchangeable in any part of either maze. Using rotors to control the stepping of other rotors was a feature of an earlier cipher machine, the US ECM Mark II. Mercury also used double-wired rotors, consisting of \"Inside and Outside Scrambled Wheels\", the Outer wheels being settable in a number of positions with respect to the Inner wheels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Euclidean distance matrix is an n\u00d7n matrix representing the spacing of a set of n points in Euclidean space. For points x 1 , x 2 , \u2026 , x n {\\displaystyle x_{1},x_{2},\\ldots ,x_{n}} in k-dimensional space \u211dk, the elements of their Euclidean distance matrix A are given by squares of distances between them. That is A = ( a i j ) ; a i j = d i j 2 = \u2016 x i \u2212 x j \u2016 2 {\\displaystyle {\\begin{aligned}A&=(a_{ij});\\\\a_{ij}&=d_{ij}^{2}\\;=\\;\\lVert x_{i}-x_{j}\\rVert ^{2}\\end{aligned}}} where \u2016 \u22c5 \u2016 {\\displaystyle \\|\\cdot \\|} denotes the Euclidean norm on \u211dk. A =  {\\displaystyle A={\\begin{bmatrix}0&d_{12}^{2}&d_{13}^{2}&\\dots &d_{1n}^{2}\\\\d_{21}^{2}&0&d_{23}^{2}&\\dots &d_{2n}^{2}\\\\d_{31}^{2}&d_{32}^{2}&0&\\dots &d_{3n}^{2}\\\\\\vdots &\\vdots &\\vdots &\\ddots &\\vdots &\\\\d_{n1}^{2}&d_{n2}^{2}&d_{n3}^{2}&\\dots &0\\\\\\end{bmatrix}}} In the context of (not necessarily Euclidean) distance matrices, the entries are usually defined directly as distances, not their squares.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network theory, a giant component is a connected component of a given random graph that contains a significant fraction of the entire graph's vertices. More precisely, in graphs drawn randomly from a probability distribution over arbitrarily large graphs, a giant component is a connected component whose fraction of the overall number of vertices is bounded away from zero. In sufficiently dense graphs distributed according to the Erd\u0151s\u2013R\u00e9nyi model, a giant component exists with high probability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, it demonstrates a general technique that has since been used in a wide range of proofs, including the first of G\u00f6del's incompleteness theorems and Turing's answer to the Entscheidungsproblem. Diagonalization arguments are often also the source of contradictions like Russell's paradox and Richard's paradox. : 27", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sekiro: Shadows Die Twice as the sword wielded by the Divine Dragon. Elden Ring as a spear greatly resembling the Seven-Branced Sword called the Death Ritual Spear. Monster Hunter series as a Greatsword crafted from electric monster Kirin, King Thundersword.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The conjecture was significant, because if true, it would have implied the four color theorem: as Tait described, the four-color problem is equivalent to the problem of finding 3-edge-colorings of bridgeless cubic planar graphs. In a Hamiltonian cubic planar graph, such an edge coloring is easy to find: use two colors alternately on the cycle, and a third color for all remaining edges. Alternatively, a 4-coloring of the faces of a Hamiltonian cubic planar graph may be constructed directly, using two colors for the faces inside the cycle and two more colors for the faces outside.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the buffer layer, between 5 wall units and 30 wall units, neither law holds, such that: For 5 < y + < 30 {\\displaystyle 5", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, in-band signaling is the sending of control information within the same band or channel used for data such as voice or video. This is in contrast to out-of-band signaling which is sent over a different channel, or even over a separate network. In-band signals may often be heard by telephony participants, while out-of-band signals are inaccessible to the user. The term is also used more generally, for example of computer data files that include both literal data, and metadata and/or instructions for how to process the literal data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is most conspicuous in uppercase and lowercase characters: uppercase characters are in columns 4 (100) and 5 (101), while the corresponding lowercase characters are in columns 6 (110) and 7 (111), requiring only toggling the 6th bit (2nd high bit) to switch case; as there are only 26 letters, the remaining 6 points in each column were occupied by symbols or, in one case, a control character (DEL, in 127). This is also present, but less precisely, in the organization of digits and symbols in columns 2 (010) and 3 (011) \u2013 this discrepancy is the source of bit-paired layouts. Ideally the characters would have been ordered so that unshifted and shifted values of a typewriter key were in adjacent columns, allowing shifting to be implemented by toggling the 5th bit (1st high bit).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics, the Gibbs algorithm, introduced by J. Willard Gibbs in 1902, is a criterion for choosing a probability distribution for the statistical ensemble of microstates of a thermodynamic system by minimizing the average log probability \u27e8 ln \u2061 p i \u27e9 = \u2211 i p i ln \u2061 p i {\\displaystyle \\langle \\ln p_{i}\\rangle =\\sum _{i}p_{i}\\ln p_{i}\\,} subject to the probability distribution pi satisfying a set of constraints (usually expectation values) corresponding to the known macroscopic quantities. in 1948, Claude Shannon interpreted the negative of this quantity, which he called information entropy, as a measure of the uncertainty in a probability distribution. In 1957, E.T. Jaynes realized that this quantity could be interpreted as missing information about anything, and generalized the Gibbs algorithm to non-equilibrium systems with the principle of maximum entropy and maximum entropy thermodynamics.Physicists call the result of applying the Gibbs algorithm the Gibbs distribution for the given constraints, most notably Gibbs's grand canonical ensemble for open systems when the average energy and the average number of particles are given.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The other constraints are that the measurements of the function are given constants up to order n {\\displaystyle n} . The entropy attains an extremum when the functional derivative is equal to zero: \u03b4 J \u03b4 p ( p ) = ln \u2061 p ( x ) + 1 \u2212 \u03b7 0 \u2212 \u2211 j = 1 n \u03bb j f j ( x ) = 0 {\\displaystyle {\\frac {\\delta J}{\\delta p}}\\left(p\\right)=\\ln {p(x)}+1-\\eta _{0}-\\sum _{j=1}^{n}\\lambda _{j}f_{j}(x)=0} Therefore, the extremal entropy probability distribution in this case must be of the form ( \u03bb 0 := \u03b7 0 \u2212 1 {\\displaystyle \\lambda _{0}:=\\eta _{0}-1} ), p ( x ) = e \u2212 1 + \u03b7 0 \u22c5 e \u2211 j = 1 n \u03bb j f j ( x ) = exp \u2061 ( \u2211 j = 0 n \u03bb j f j ( x ) ) , {\\displaystyle p(x)=e^{-1+\\eta _{0}}\\cdot e^{\\sum _{j=1}^{n}\\lambda _{j}f_{j}(x)}=\\exp \\left(\\sum _{j=0}^{n}\\lambda _{j}f_{j}(x)\\right)\\;,} remembering that f 0 ( x ) = 1 {\\displaystyle f_{0}(x)=1} . It can be verified that this is the maximal solution by checking that the variation around this solution is always negative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural time domain each event is characterized by two terms, the \"natural time\" \u03c7, and the energy Qk. \u03c7 is defined as k/N, where k is a natural number (the k-th event) and N is the total number of events in the time sequence of data. A related term, pk, is the ratio Qk / Qtotal, which describes the fractional energy released. The term \u03ba1 is the variance in natural time: \u03ba 1 = \u2211 k = 1 N p k ( \u03c7 k ) 2 \u2212 ( \u2211 k = 1 N p k \u03c7 k ) 2 {\\displaystyle \\kappa _{1}=\\sum _{k=1}^{N}p_{k}(\\chi _{k})^{2}-{\\bigl (}\\sum _{k=1}^{N}p_{k}\\chi _{k}{\\bigr )}^{2}} where \u03c7 k = k / N {\\displaystyle \\textstyle \\chi _{k}=k/N} and p k = Q k \u2211 n = 1 N Q n {\\displaystyle \\textstyle \\ p_{k}={\\frac {Q_{k}}{\\sum _{n=1}^{N}Q_{n}}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, the minimum degree algorithm is an algorithm used to permute the rows and columns of a symmetric sparse matrix before applying the Cholesky decomposition, to reduce the number of non-zeros in the Cholesky factor. This results in reduced storage requirements and means that the Cholesky factor can be applied with fewer arithmetic operations. (Sometimes it may also pertain to an incomplete Cholesky factor used as a preconditioner\u2014for example, in the preconditioned conjugate gradient algorithm.) Minimum degree algorithms are often used in the finite element method where the reordering of nodes can be carried out depending only on the topology of the mesh, rather than on the coefficients in the partial differential equation, resulting in efficiency savings when the same mesh is used for a variety of coefficient values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In simple conditions, F can be easily computed in terms of population size or of genealogical information. F is often denoted using lowercase (f), but should not be confused with the coancestry coefficient. However, the above prediction for the fitness decline rarely applies, since it was derived assuming no selection, and fitness is precisely the target trait of natural selection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the L\u00e9vy\u2013Prokhorov metric (sometimes known just as the Prokhorov metric) is a metric (i.e., a definition of distance) on the collection of probability measures on a given metric space. It is named after the French mathematician Paul L\u00e9vy and the Soviet mathematician Yuri Vasilyevich Prokhorov; Prokhorov introduced it in 1956 as a generalization of the earlier L\u00e9vy metric.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the calculation of low energy states the term proportional to n 2 U {\\displaystyle n^{2}U} means that large occupation of a single site is improbable, allowing for truncation of local Hilbert space to states containing at most d < \u221e {\\displaystyle d<\\infty } particles. Then the local Hilbert space dimension is d + 1. {\\displaystyle d+1.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the De Bruijn notation is a syntax for terms in the \u03bb calculus invented by the Dutch mathematician Nicolaas Govert de Bruijn. It can be seen as a reversal of the usual syntax for the \u03bb calculus where the argument in an application is placed next to its corresponding binder in the function instead of after the latter's body.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1970, electronic parts were introduced, and the current black-coloured plates were changed to blue. The range of sets was reduced by one with the deletion of the old No. 9 set and the renumbering of the old No. 0 to 8 sets to No. 1 to 9. The No. 10 set remained unchanged.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, not every total recursive function is a primitive recursive function\u2014the most famous example is the Ackermann function. Other equivalent classes of functions are the functions of lambda calculus and the functions that can be computed by Markov algorithms. The subset of all total recursive functions with values in {0,1} is known in computational complexity theory as the complexity class R.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So how does a state machine move an arbitrarily large constant directly into a register, e.g. MOVE (k, r) (Move constant k to register r)? If huge constants are necessary they must either start out in the registers themselves or be created by the state machine using a finite number of instructions e.g. multiply and add subroutines using INC and DEC (but not a quasi-infinite number of these! ).Sometimes the constant k will be created by use of CLR ( r ) followed by INC ( r ) repeated k times \u2013 e.g. to put the constant k=3 into register r, i.e. 3 \u2192 r, so at the end of the instruction =3: CLR (r), INC (r), INC (r), INC (r).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the 100-year flood provides the risk basis for flood insurance rates. Complete information on the National Flood Insurance Program (NFIP) is available here. A regulatory flood or base flood is routinely established for river reaches through a science-based rule-making process targeted to a 100-year flood at the historical average recurrence interval. In addition to historical flood data, the process accounts for previously established regulatory values, the effects of flood-control reservoirs, and changes in land use in the watershed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The difference of two Moser\u2013de Bruijn numbers, multiplied by two, is never square. Every natural number can be formed in a unique way as the sum of a Moser\u2013de Bruijn number and twice a Moser\u2013de Bruijn number. This representation as a sum defines a one-to-one correspondence between integers and pairs of integers, listed in order of their positions on a Z-order curve. The Moser\u2013de Bruijn sequence can be used to construct pairs of transcendental numbers that are multiplicative inverses of each other and both have simple decimal representations. A simple recurrence relation allows values of the Moser\u2013de Bruijn sequence to be calculated from earlier values, and can be used to prove that the Moser\u2013de Bruijn sequence is a 2-regular sequence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set of k-almost primes is usually denoted by Pk. The smallest k-almost prime is 2k. The first few k-almost primes are: The number \u03c0k(n) of positive integers less than or equal to n with exactly k prime divisors (not necessarily distinct) is asymptotic to: \u03c0 k ( n ) \u223c ( n log \u2061 n ) ( log \u2061 log \u2061 n ) k \u2212 1 ( k \u2212 1 ) !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let Kp be a boolean variable which indicates whether p is a corner, then the entropy of Kp is used to measure the information of p being a corner. For a set of pixels Q, the total entropy of KQ (not normalized) is: H(Q) = ( c + n ) log2( c + n ) - clog2c - nlog2n where c = |{ i \u2208 Q: Ki is true}| (number of corners) where n = |{ i \u2208 Q: Ki is false}| (number of non-corners)The information gain can then be represented as: Hg= H(P) - H(Pb) - H(Ps) - H(Pd)A recursive process is applied to each subsets in order to select each x that could maximize the information gain. For example, at first an x is selected to partition P into Pd, Ps, Pb with the most information; then for each subset Pd, Ps, Pb, another y is selected to yield the most information gain (notice that the y could be the same as x ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 \u00d7 11 + 1 = 23 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The frame received on port B is then forwarded to ports A and C, the frame received on port C to ports A and B. So, the node on port A receives two copies of its own broadcast frame while the other two copies produced by the loop continue to cycle. Likewise, each broadcast frame entering the system continues to cycle through the loop in both directions, rebroadcasting back to the network in each loop, and broadcasts accumulate. Eventually, the accumulated broadcasts exhaust the egress capacity of the links, the switch begins dropping frames, and communication across the switch becomes unreliable or even impossible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a strong prime is a prime number that is greater than the arithmetic mean of the nearest prime above and below (in other words, it's closer to the following than to the preceding prime). Or to put it algebraically, writing the sequence of prime numbers as (p1, p2, p3, ...) = (2, 3, 5, ...), pn is a strong prime if pn > pn \u2212 1 + pn + 1/2. For example, 17 is the seventh prime: the sixth and eighth primes, 13 and 19, add up to 32, and half that is 16; 17 is greater than 16, so 17 is a strong prime. The first few strong primes are 11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499 (sequence A051634 in the OEIS).In a twin prime pair (p, p + 2) with p > 5, p is always a strong prime, since 3 must divide p \u2212 2, which cannot be prime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data. SID does not require that the user parametrizes the system matrices before solving a parametric optimization problem and, as a consequence, SID methods do not suffer from problems related to local minima that often lead to unsatisfactory identification results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the R5RS standard and also in later reports, the syntax of Scheme can easily be extended via the macro system. The R5RS standard introduced a powerful hygienic macro system that allows the programmer to add new syntactic constructs to the language using a simple pattern matching sublanguage (R5RS sec 4.3). Prior to this, the hygienic macro system had been relegated to an appendix of the R4RS standard, as a \"high level\" system alongside a \"low level\" macro system, both of which were treated as extensions to Scheme rather than an essential part of the language.Implementations of the hygienic macro system, also called syntax-rules, are required to respect the lexical scoping of the rest of the language. This is assured by special naming and scoping rules for macro expansion and avoids common programming errors that can occur in the macro systems of other programming languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of computer science, semantics refers to the meaning behind programming language constructs, distinguishing it from their mere syntax, which is the arrangement of symbols and keywords. This concept is crucial for ensuring that code is not only correctly written in terms of syntax but also logically meaningful and functional. According to Euzenat, semantics \"provides the rules for interpreting the syntax which do not provide the meaning directly but constrains the possible interpretations of what is declared\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In server/client architectures, the program at the other side may not be an authorised client and the client's server may not be an authorised server. Even when they are, a man-in-the-middle attack could compromise communications. Often the easiest way to break the security of a client/server system is not to go head on to the security mechanisms, but instead to go around them. A man in the middle attack is a simple example of this, because you can use it to collect details to impersonate a user.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of information science, an ontology is a formal representation of knowledge within a domain, using hierarchies of terms including their definitions, attributes, and relations. Ontologies provide a common terminology in a machine-readable framework that facilitates sharing and discovery of data. Having an established ontology for nanoparticles is important for cancer nanomedicine due to the need of researchers to search, access, and analyze large amounts of data.The NanoParticle Ontology is an ontology for the preparation, chemical composition, and characterization of nanomaterials involved in cancer research.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public-key cryptography and computer security, a root key ceremony is a procedure during which a unique pair of public and private root keys gets generated. Depending on the certificate policy, the generation of the root keys may require notarization, legal representation, witnesses, and \"key holders\" to be present, as the information on the system is the responsibility of the parties. A commonly recognized practice is to follow the SAS 70 standard for root key ceremonies.At the heart of every certificate authority (CA) is at least one root key or root certificate and usually at least one intermediate root certificate. \"Root key\" is the term for a unique passcode that must be generated for secure server interaction with a protective network, usually called the root zone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1967 Black Power, Stokely Carmichael introduces black nationalism. He illustrates the prosperity of the black race in the United States as being dependent on the implementation of black sovereignty. Under his theory, black nationalism in the United States would allow Blacks to socially, economically and politically be empowered in a manner that has never been plausible in American history. A Black nation would work to reverse the exploitation of the Black race in America, as Blacks would intrinsically work to benefit their own state of affairs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is the class of functions from A {\\displaystyle A} to C {\\displaystyle C} in a pure set theory. Below the notation x \u2192 y {\\displaystyle x\\to y} is also used for y x {\\displaystyle y^{x}} , for the sake of distinguishing it from ordinal exponentiation. When functions are understood as just function graphs as above, the membership proposition f \u2208 C A {\\displaystyle f\\in C^{A}} is also written f: A \u2192 C {\\displaystyle f\\colon A\\to C} . The boolean-valued \u03c7 B: A \u2192 { 0 , 1 } {\\displaystyle \\chi _{B}\\colon A\\to \\{0,1\\}} are among the classes discussed next.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The trace 1 condition means \u2211 j a j \u2217 a j = 1. {\\displaystyle \\sum _{j}a_{j}^{*}a_{j}=1.} Let p i = a i \u2217 a i , {\\displaystyle p_{i}=a_{i}^{*}a_{i},} and vi be the normalized ai. We see that { p i , v i } {\\displaystyle \\left\\{p_{i},v_{i}\\right\\}} gives the mixed state \u03c1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. It is a method which relies on the well-ordering principle, and is often used to show that a given equation, such as a Diophantine equation, has no solutions.Typically, one shows that if a solution to a problem existed, which in some sense was related to one or more natural numbers, it would necessarily imply that a second solution existed, which was related to one or more 'smaller' natural numbers. This in turn would imply a third solution related to smaller natural numbers, implying a fourth solution, therefore a fifth solution, and so on. However, there cannot be an infinity of ever-smaller natural numbers, and therefore by mathematical induction, the original premise\u2014that any solution exists\u2014is incorrect: its correctness produces a contradiction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication networks, the transmission time is the amount of time from the beginning until the end of a message transmission. In the case of a digital message, it is the time from the first bit until the last bit of a message has left the transmitting node. The packet transmission time in seconds can be obtained from the packet size in bit and the bit rate in bit/s as: Packet transmission time = Packet size / Bit rateExample: Assuming 100 Mbit/s Ethernet, and the maximum packet size of 1526 bytes, results in Maximum packet transmission time = 1526\u00d78 bit / (100 \u00d7 106 bit/s) \u2248 122 \u03bcs", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In single-ended signalling, the transmitter generates a single voltage that the receiver compares with a fixed reference voltage, both relative to a common ground connection shared by both ends. In many instances, single-ended designs are not feasible. Another difficulty is the electromagnetic interference that can be generated by a single-ended signalling system that attempts to operate at high speed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming, there is also the concept of a static member variable, which is a \"class variable\" of a statically defined class, i.e., a member variable of a given class which is shared across all instances (objects), and is accessible as a member variable of these objects. A class variable of a dynamically defined class, in languages where classes can be defined at run time, is allocated when the class is defined and is not static. Object constants known at compile-time, such as string literals, are usually allocated statically. In object-oriented programming, the virtual method tables of classes are usually allocated statically. A statically defined value can also be global in its scope ensuring the same immutable value is used throughout a run for consistency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a proof calculus or a proof system is built to prove statements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the third quarter of 2006, at least 12 billion text messages were sent on AT&T's network, up almost 15% from the preceding quarter. In the U.S., while texting is mainly popular among people from 13\u201322 years old, it is also increasing among adults and business users. The age that a child receives his/her first cell phone has also decreased, making text messaging a popular way of communicating.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The largest component has logarithmic size. The graph is a pseudoforest. Most of its components are trees: the number of vertices in components that have cycles grows more slowly than any unbounded function of the number of vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Traversing this Eulerian trail generates an orientation D of G such that every point has indegree and outdegree = k. Next, replace every vertex v \u03f5 V(D) by two vertices v\u2019 and v\u201d, and replace every directed edge uv of the oriented graph by an undirected edge from u\u2019 to v\u201d. Since D has in- and outdegrees equal to k the resulting bipartite graph G\u2019 is k-regular. The edges of G\u2019 can be partitioned into k perfect matchings by a theorem of K\u0151nig. Now merging v\u2019 with v\u201d for every v recovers the graph G, and maps the k perfect matchings of G\u2019 onto k 2-factors of G which partition its edges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics. These codes are named in honor of Marcel J. E. Golay whose 1949 paper introducing them has been called, by E. R. Berlekamp, the \"best single published page\" in coding theory.There are two closely related binary Golay codes. The extended binary Golay code, G24 (sometimes just called the \"Golay code\" in finite group theory) encodes 12 bits of data in a 24-bit word in such a way that any 3-bit errors can be corrected or any 7-bit errors can be detected. The other, the perfect binary Golay code, G23, has codewords of length 23 and is obtained from the extended binary Golay code by deleting one coordinate position (conversely, the extended binary Golay code is obtained from the perfect binary Golay code by adding a parity bit). In standard coding notation, the codes have parameters  and , corresponding to the length of the codewords, the dimension of the code, and the minimum Hamming distance between two codewords, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The model makes the assumption that customers have some idea of what they want and what the standard of the good or service should be. Models of sequential search have been used in many disciplines, including finance and labour economics. Sequential search models are used in labour economics to examine how employees look for work and how employers hire new employees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The symbol ( n k ) {\\displaystyle {\\tbinom {n}{k}}} is usually read as \"n choose k\" because there are ( n k ) {\\displaystyle {\\tbinom {n}{k}}} ways to choose an (unordered) subset of k elements from a fixed set of n elements. For example, there are ( 4 2 ) = 6 {\\displaystyle {\\tbinom {4}{2}}=6} ways to choose 2 elements from { 1 , 2 , 3 , 4 } , {\\displaystyle \\{1,2,3,4\\},} namely { 1 , 2 } , { 1 , 3 } , { 1 , 4 } , { 2 , 3 } , { 2 , 4 } , {\\displaystyle \\{1,2\\},\\,\\{1,3\\},\\,\\{1,4\\},\\,\\{2,3\\},\\,\\{2,4\\},} and { 3 , 4 } . {\\displaystyle \\{3,4\\}.} The binomial coefficients can be generalized to ( z k ) {\\displaystyle {\\tbinom {z}{k}}} for any complex number z and integer k \u2265 0, and many of their properties continue to hold in this more general form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Flat addressing is possible by applying multiple instructions, which however leads to slower programs. The memory model concept derives from the setup of the segment registers. For example, in the tiny model CS=DS=SS, that is the program's code, data, and stack are all contained within a single 64 KB segment. In the small memory model DS=SS, so both data and stack reside in the same segment; CS points to a different code segment of up to 64 KB.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It will also not be perfectly aligned with the directions of the document, causing aliasing. Features smaller than the resolution will also not be reproduced. In addition, human vision is sensitive to luminance contrast ratio.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "...  point is that one or two degrees is about the experience that we have had in the last 10,000 years, the era of human civilization. There haven't been\u2014globally averaged, we're talking\u2014fluctuations of more than a degree or so. So we're actually getting into uncharted territory from the point of view of the relatively benign climate of the last 10,000 years, if we warm up more than a degree or two.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In simple electromagnetic analysis (SEMA) attacks, the attacker deduces the key directly by observing the trace. It is very effective against asymmetric cryptography implementations. Typically, only a few traces are needed, though the attacker needs to have a strong understanding of the cryptographic device and of the implementation of the cryptographic algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then for any function f: A \u2192 B {\\displaystyle f:A\\to B} , the restriction f | S: S \u2192 B {\\displaystyle f|_{S}:S\\to B} of a function f {\\displaystyle f} onto S {\\displaystyle S} can be defined as the composition f | S = f \u2218 i S {\\displaystyle f|_{S}=f\\circ i_{S}} . Analogously, for an inclusion i T: T \u21aa B {\\displaystyle i_{T}:T\\hookrightarrow B} the corestriction f | T: A \u2192 T {\\displaystyle f|^{T}:A\\to T} of f {\\displaystyle f} onto T {\\displaystyle T} is the unique function f | T {\\displaystyle f|^{T}} such that there is a decomposition f = i T \u2218 f | T {\\displaystyle f=i_{T}\\circ f|^{T}} . The corestriction exists if and only if T {\\displaystyle T} contains the image of f {\\displaystyle f} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to apply control theory tools to the analysis of behavior trees, they can be defined as three-tuple. T i = { f i , r i , \u0394 t } , {\\displaystyle T_{i}=\\{f_{i},r_{i},\\Delta t\\},} where i \u2208 N {\\displaystyle i\\in \\mathbb {N} } is the index of the tree, f i: R n \u2192 R n {\\displaystyle f_{i}:\\mathbb {R} ^{n}\\rightarrow \\mathbb {R} ^{n}} is a vector field representing the right hand side of an ordinary difference equation, \u0394 t {\\displaystyle \\Delta t} is a time step and r i: R n \u2192 { R i , S i , F i } {\\displaystyle r_{i}:\\mathbb {R} ^{n}\\rightarrow \\{R_{i},S_{i},F_{i}\\}} is the return status, that can be equal to either Running R i {\\displaystyle R_{i}} , Success S i {\\displaystyle S_{i}} , or Failure F i {\\displaystyle F_{i}} . Note: A task is a degenerate behavior tree with no parent and no child.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Variants of the functional predicate definition using apartness relations on setoids have been defined as well. It is a metatheorem for theories containing B C S T {\\displaystyle {\\mathsf {BCST}}} that adding a function symbol for a provenly total class function is a conservative extension, despite this changing the scope of bounded Separation. Some notational conveniences involving function application will only work when a set has indeed been established to be a function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, economics, and computer science, the stable matching polytope or stable marriage polytope is a convex polytope derived from the solutions to an instance of the stable matching problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a divisor of an integer n {\\displaystyle n} , also called a factor of n {\\displaystyle n} , is an integer m {\\displaystyle m} that may be multiplied by some integer to produce n {\\displaystyle n} . In this case, one also says that n {\\displaystyle n} is a multiple of m . {\\displaystyle m.} An integer n {\\displaystyle n} is divisible or evenly divisible by another integer m {\\displaystyle m} if m {\\displaystyle m} is a divisor of n {\\displaystyle n} ; this implies dividing n {\\displaystyle n} by m {\\displaystyle m} leaves no remainder.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We can further define a programming language in which we can ensure that even more sophisticated functions always halt. For example, the Ackermann function, which is not primitive recursive, nevertheless is a total computable function computable by a term rewriting system with a reduction ordering on its arguments (Ohlebusch, 2002, pp. 67). Despite the above examples of programming languages which guarantee termination of the programs, there exists no programming language which captures exactly the total recursive functions, i.e. the functions which can be computed by a Turing machine that always halts. This is because existence of such a programming language would be a contradiction to the non-semi-decidability of the problem whether a Turing machine halts on every input.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "}{\\prod _{j=0}^{k}n_{j}!}}} If any q i = 0 {\\displaystyle q_{i}=0} , then the vector q \u2192 {\\displaystyle {\\vec {q}}} is shared in common between orthants. Because of this, the multiplying factor on the permutation must be adjusted from 2 N {\\displaystyle 2^{N}} to be 2 N \u2212 n 0 {\\displaystyle 2^{N-n_{0}}} Multiplying the number of amount of permutations by the adjusted amount of orthants yields, E = N !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "n 2 ! \u22c5 ( N \u2212 n 1 \u2212 n 2 ) ! ( N \u2212 n 1 \u2212 n 2 \u2212 n 3 ) !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If a = b, then b = a (symmetric). If a = b and b = c, then a = c (transitive). Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The original Highway Network paper not only introduced the basic principle for very deep feedforward networks, but also included experimental results with 20, 50, and 100 layers networks, and mentioned ongoing experiments with up to 900 layers. Networks with 50 or 100 layers had lower training error than their plain network counterparts, but no lower training error than their 20 layers counterpart (on the MNIST dataset, Figure 1 in ). No improvement on test accuracy was reported with networks deeper than 19 layers (on the CIFAR-10 dataset; Table 1 in ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. A G\u00f6del numbering is a precomplete numbering on the set of computable functions so the generalized theorem yields the Kleene recursion theorem as a special case.Given a precomplete numbering \u03bd {\\displaystyle \\nu } , then for any partial computable function f {\\displaystyle f} with two parameters there exists a total computable function t {\\displaystyle t} with one parameter such that \u2200 n \u2208 N: \u03bd \u2218 f ( n , t ( n ) ) = \u03bd \u2218 t ( n ) . {\\displaystyle \\forall n\\in \\mathbb {N} :\\nu \\circ f(n,t(n))=\\nu \\circ t(n).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Apple's Garage Band even purveys digital music lessons using the very same iTunes account as used for the iOS App Store, they are all part of the same App Store. Electronic bookstores such as Kindle, Barnes and Noble or Kobo are further examples of successful electronic distribution using the App Store concept. For the Electronic AppWrapper distribution, encryption and the digital rights of the software were universally managed for all participating developers much like stores participating in a shopping mall.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for consistency in data to be maintained and to attain scalable processor systems where every processor has its own memory, the processor consistency model was derived. All processors need to be consistent in the order in which they see writes done by one processor and in the way they see writes by different processors to the same location (coherence is maintained). However, they do not need to be consistent when the writes are by different processors to different locations. Every write operation can be divided into several sub-writes to all memories.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Under the assumption of stationary statistics, at a given position, the normalized correlation function is g ( 2 ) = \u27e8 E ^ \u2212 ( 0 ) E ^ \u2212 ( \u03c4 ) E ^ + ( \u03c4 ) E ^ + ( 0 ) \u27e9 \u27e8 E ^ \u2212 ( 0 ) E ^ + ( 0 ) \u27e9 \u27e8 E ^ \u2212 ( \u03c4 ) E ^ + ( \u03c4 ) \u27e9 {\\displaystyle g^{(2)}={\\frac {\\langle {\\hat {E}}^{-}(0){\\hat {E}}^{-}(\\tau ){\\hat {E}}^{+}(\\tau ){\\hat {E}}^{+}(0)\\rangle }{\\langle {\\hat {E}}^{-}(0){\\hat {E}}^{+}(0)\\rangle \\langle {\\hat {E}}^{-}(\\tau ){\\hat {E}}^{+}(\\tau )\\rangle }}} g ( 2 ) {\\displaystyle g^{(2)}} here measures the probability of coincidence of two photons being detected with a time difference \u03c4 {\\displaystyle \\tau } .For all varieties of chaotic light, the following relationship between the first order and second-order coherences holds: g ( 2 ) ( \u03c4 ) = 1 + | g ( 1 ) ( \u03c4 ) | 2 {\\displaystyle g^{(2)}(\\tau )=1+|g^{(1)}(\\tau )|^{2}} . This relationship is true for both the classical and quantum correlation functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "332, 149 S.E. 541 (1929). \"In assessing statutory language, unless words have acquired a peculiar meaning, by virtue of statutory definition or judicial construction, they are to be construed in accordance with their common usage.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", {\\displaystyle I(r,\\lambda )=\\sum _{y=r}^{\\infty }{\\frac {e^{-\\lambda }\\lambda ^{y}}{y! }},} where s is the integral part of r. The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution (that is P ( X = n ) / P ( X = n \u2212 1 ) {\\displaystyle P(X=n)/P(X=n-1)} ) is given by \u03bb / n {\\displaystyle \\lambda /n} for n > 0 {\\displaystyle n>0} and the displaced Poisson generalizes this ratio to \u03bb / ( n + r ) {\\displaystyle \\lambda /\\left(n+r\\right)} . == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This evolution has resulted in more complex and more flexible ICs being created. The newer circuits are programmable and thus allow a single hardware IC design to undertake a number of different functions, where the appropriate software is installed. Network processors are used in the manufacture of many different types of network equipment such as: Routers, software routers and switches (Inter-network processors) Firewalls Session border controllers Intrusion detection devices Intrusion prevention devices Network monitoring systems Network security (secure cryptoprocessors)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that the mask constraint relates to the effects and not the causes like the other constraints. The graph's direction is as follows: Causes --> intermediate nodes --> Effects The graph can always be rearranged so there is only one node between any input and any output. See conjunctive normal form and disjunctive normal form. A cause\u2013effect graph is useful for generating a reduced decision table.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as a AB = pI, where A and B are square matrices and I is the identity matrix. Given the polynomial p, the matrices A and B can be found by elementary methods. Example:The polynomial x2 + y2 is irreducible over R, but can be written as   = ( x 2 + y 2 )  {\\displaystyle \\left\\left=(x^{2}+y^{2})\\left}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regression, mean response (or expected response) and predicted response, also known as mean outcome (or expected outcome) and predicted outcome, are values of the dependent variable calculated from the regression parameters and a given value of the independent variable. The values of these two responses are the same, but their calculated variances are different. The concept is a generalization of the distinction between the standard error of the mean and the sample standard deviation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic and computer science, a general recursive function, partial recursive function, or \u03bc-recursive function is a partial function from natural numbers to natural numbers that is \"computable\" in an intuitive sense \u2013 as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the \u03bc-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church\u2013Turing thesis). The \u03bc-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a nowhere commutative semigroup is a semigroup S such that, for all a and b in S, if ab = ba then a = b. A semigroup S is nowhere commutative if and only if any two elements of S are inverses of each other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some writers on probability call this the \"conditional covariance formula\" or use other names. Note: The conditional expected values E( X | Z ) and E( Y | Z ) are random variables whose values depend on the value of Z. Note that the conditional expected value of X given the event Z = z is a function of z. If we write E( X | Z = z) = g(z) then the random variable E( X | Z ) is g(Z). Similar comments apply to the conditional covariance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, in particular the subfields of convex analysis and optimization, a proper convex function is an extended real-valued convex function with a non-empty domain, that never takes on the value \u2212 \u221e {\\displaystyle -\\infty } and also is not identically equal to + \u221e . {\\displaystyle +\\infty .} In convex analysis and variational analysis, a point (in the domain) at which some given function f {\\displaystyle f} is minimized is typically sought, where f {\\displaystyle f} is valued in the extended real number line  = R \u222a { \u00b1 \u221e } . {\\displaystyle =\\mathbb {R} \\cup \\{\\pm \\infty \\}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a subset R of the integers is called a reduced residue system modulo n if: gcd(r, n) = 1 for each r in R, R contains \u03c6(n) elements, no two elements of R are congruent modulo n.Here \u03c6 denotes Euler's totient function. A reduced residue system modulo n can be formed from a complete residue system modulo n by removing all integers not relatively prime to n. For example, a complete residue system modulo 12 is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. The so-called totatives 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is {1, 5, 7, 11}. The cardinality of this set can be calculated with the totient function: \u03c6(12) = 4. Some other reduced residue systems modulo 12 are: {13,17,19,23} {\u221211,\u22127,\u22125,\u22121} {\u22127,\u221213,13,31} {35,43,53,61}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, when the code is inserted into a compiler, the compiler may ignore the Bidi char and process the characters in a different order than visually displayed. When the compiler is finished, it could potentially execute code that visually appeared to be non-executable. Formatting marks can be combined multiple times to create complex attacks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The ordinal series are based on ordinal numbers such as the English first, second, third (for numbers higher than 2, the ordinal forms are also used for fractions; only the fraction 1\u20442 has special forms). For the hundreds, there are competing forms: those in -gent-, from the original Latin, and those in -cent-, derived from centi-, etc. plus the prefixes for 1\u20139. Many of the items in the following tables are not in general use, but may rather be regarded as coinages by individuals. In scientific contexts, either scientific notation or SI prefixes are used to express very large or very small numbers, and not unwieldy prefixes. The same suffix may be used with more than one series: Examples", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In memory errors, the faulting program accesses memory that it should not access. Examples include: Attempting to write to a read-only portion of memory Attempting to execute bytes in memory which are not designated as instructions Attempting to read as data bytes in memory which are designated as instructions Other miscellaneous conflicts between the designation of a part of memory and its useHowever, many modern operating systems implement their memory access-control schemes via paging instead of segmentation, so it is often the case that invalid memory references in operating systems such as Windows are reported via page faults instead of general protection faults. Operating systems typically provide an abstraction layer (such as exception handling or signals) that hides whatever internal processor mechanism was used to raise a memory access error from a program, for the purposes of providing a standard interface for handling many different types of processor-generated error conditions. In terms of the x86 architecture, general protection faults are specific to segmentation-based protection when it comes to memory accesses. However, general protection faults are still used to report other protection violations (aside from memory access violations) when paging is used, such as the use of instructions not accessible from the current privilege level (CPL). While it is theoretically possible for an operating system to utilize both paging and segmentation, for the most part, common operating systems typically rely on paging for the bulk of their memory access control needs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In packed BCD (or simply packed decimal), each nibble represent a decimal digit. Packed BCD has been in use since at least the 1960s and is implemented in all IBM mainframe hardware since then. Most implementations are big endian, i.e. with the more significant digit in the upper half of each byte, and with the leftmost byte (residing at the lowest memory address) containing the most significant digits of the packed decimal value. The lower nibble of the rightmost byte is usually used as the sign flag, although some unsigned representations lack a sign flag.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of the copies. It is a time-reversed dual to the no-cloning theorem, which states that arbitrary states cannot be copied. This theorem seems remarkable, because, in many senses, quantum states are fragile; the theorem asserts that, in a particular case, they are also robust.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The idea originated with the Scottish physicist Alexander Crichton Mitchell, who was helped by the Royal Navy at HMS Tarlair. He had shown that the passage of a submarine past a cable formed an induction loop which induced a voltage of approximately a millivolt, detectable by a sensitive galvanometer. Voltages were also induced in the cable by random fluctuations in the Earth's magnetic field and electrical noise from the Glasgow tram lines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, while the word representation properly designates a group homomorphism from a group G to GL(V), where V is a vector space, it is common to call V \"a representation of G\". Another common abuse of language consists in identifying two mathematical objects that are different, but canonically isomorphic. Other examples include identifying a constant function with its value, identifying a group with a binary operation with the name of its underlying set, or identifying to R 3 {\\displaystyle \\mathbb {R} ^{3}} the Euclidean space of dimension three equipped with a Cartesian coordinate system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are the with-carry analog of m-sequences or maximum length sequences. There are efficient algorithms for FCSR synthesis. This is the problem: given a prefix of a sequence, construct a minimal length FCSR that outputs the sequence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Littlewood\u2013Richardson rule is a combinatorial description of the coefficients that arise when decomposing a product of two Schur functions as a linear combination of other Schur functions. These coefficients are natural numbers, which the Littlewood\u2013Richardson rule describes as counting certain skew tableaux. They occur in many other mathematical contexts, for instance as multiplicity in the decomposition of tensor products of finite-dimensional representations of general linear groups, or in the decomposition of certain induced representations in the representation theory of the symmetric group, or in the area of algebraic combinatorics dealing with Young tableaux and symmetric polynomials. Littlewood\u2013Richardson coefficients depend on three partitions, say \u03bb , \u03bc , \u03bd {\\displaystyle \\lambda ,\\mu ,\\nu } , of which \u03bb {\\displaystyle \\lambda } and \u03bc {\\displaystyle \\mu } describe the Schur functions being multiplied, and \u03bd {\\displaystyle \\nu } gives the Schur function of which this is the coefficient in the linear combination; in other words they are the coefficients c \u03bb , \u03bc \u03bd {\\displaystyle c_{\\lambda ,\\mu }^{\\nu }} such that s \u03bb s \u03bc = \u2211 \u03bd c \u03bb , \u03bc \u03bd s \u03bd . {\\displaystyle s_{\\lambda }s_{\\mu }=\\sum _{\\nu }c_{\\lambda ,\\mu }^{\\nu }s_{\\nu }.} The Littlewood\u2013Richardson rule states that c \u03bb , \u03bc \u03bd {\\displaystyle c_{\\lambda ,\\mu }^{\\nu }} is equal to the number of Littlewood\u2013Richardson tableaux of skew shape \u03bd / \u03bb {\\displaystyle \\nu /\\lambda } and of weight \u03bc {\\displaystyle \\mu } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Dudley's theorem is a result relating the expected upper bound and regularity properties of a Gaussian process to its entropy and covariance structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, including a number of Chinese varieties, many of the words that serve as prepositions can also be used as verbs. For instance, in Standard Chinese, \u5230 d\u00e0o can be used in either a prepositional or a verbal sense: \u6211\u5230\u5317\u4eac\u53bb w\u01d2 d\u00e0o B\u011bij\u012bng q\u00f9 (\"I go to Beijing\"; q\u00f9, meaning \"to go\", is the main verb, d\u00e0o is prepositional meaning \"to\") \u6211\u5230\u4e86 w\u01d2 d\u00e0o le (\"I have arrived\"; d\u00e0o is the main verb, meaning \"to arrive\")Because of this overlap, and the fact that a sequence of prepositional phrases and verb phrases often resembles a serial verb construction, Chinese prepositions (and those of other languages with similar grammatical structures) are often referred to as coverbs. As noted in previous sections, Chinese can also be said to have postpositions, although these can be analyzed as nominal (noun) elements. For more information, see the article on Chinese grammar, particularly the sections on coverbs and locative phrases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although the general principles underlying binomial nomenclature are common to these two codes, there are some differences in the terminology they use and their particular rules. In modern usage, the first letter of the generic name is always capitalized in writing, while that of the specific epithet is not, even when derived from a proper noun such as the name of a person or place. Similarly, both parts are italicized in normal text (or underlined in handwriting).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These kinds of contemporary features help gain citizen a new level of technology. Majority of space in the chip has been made available for the private sector to use for their products and services. It might appear expensive for the private sector to use this card initially but once the number of citizens having critical mass is reached, it will be more profitable for the private sector to use this secure and universal platform.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multitasking computing an operating system can handle several programs, both native applications or emulated software, that are running independent, parallel, together in the same time in the same device, using separated or shared resources and/or data, executing their tasks separately or together, while a user can switch on the fly between them or groups of them to use obtained effects or supervise purposes, without waste of time or waste of performance. In operating systems using GUI very often it is done by switching from an active window (or an object playing similar role) of a particular software piece to another one but of another software. A computer can compute results on the fly, or retrieve a previously stored result.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the value of a large quantity of items has a Zipf's law distribution, the total value of the n most-valuable items is proportional to the n-th harmonic number. This leads to a variety of surprising conclusions regarding the long tail and the theory of network value. The Bertrand-Chebyshev theorem implies that, except for the case n = 1, the harmonic numbers are never integers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Fr\u00e9chet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. It is named after Maurice Fr\u00e9chet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, integer factorization is the decomposition, of a positive integer into a product of integers. If the factors are further restricted to be prime numbers, the process is called prime factorization, and includes the test whether the given integer is prime (in this case, one has a \"product\" of a single factor). When the numbers are sufficiently large, no efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The newly created package provided a standard collection of common numerical operations on top of the Numeric array data structure. Shortly thereafter, Fernando P\u00e9rez released IPython, an enhanced interactive shell widely used in the technical computing community, and John Hunter released the first version of Matplotlib, the 2D plotting library for technical computing. Since then the SciPy environment has continued to grow with more packages and tools for technical computing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociology a social rule refers to any social convention commonly adhered to in a society. These rules are not written in law or otherwise formalized. In social constructionism there is a great focus on social rules. It is argued that these rules are socially constructed, that these rules act upon every member of a society, but at the same time, are re-produced by the individuals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers \"wrap around\" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The coefficient field is called the base field. If constructive and algorithmic methods are the main issue it is Q ( x , y ) {\\displaystyle \\mathbb {Q} (x,y)} . The respective ring of differential operators is denoted by D = Q ( x , y )  {\\displaystyle {\\mathcal {D}}=\\mathbb {Q} (x,y)} or D = F  {\\displaystyle {\\mathcal {D}}={\\mathcal {F}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The conditioning event is interpreted as evidence for the conditioned event. That is, P(A) is the probability of A before accounting for evidence E, and P(A|E) is the probability of A after having accounted for evidence E or after having updated P(A). This is consistent with the frequentist interpretation, which is the first definition given above.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such strings may be translated into English by using \"and\", \"while\", \"(in order) to\" or other connectives, but some may have a more compact translation, as in the following example (from Hayao Miyazaki's Mononoke Hime) in which the actions of \"following\" and \"coming\" are simultaneous: The following sentence from Mandarin Chinese can be considered to contain four verb phrases in sequence: In Chinese, however, there is often no clear distinction between serial verb phrases and prepositional phrases. The first three \"verbs\" in the above sentence may alternatively be regarded as prepositions (this applies particularly to words like c\u00f3ng which do not normally appear as independent verbs). Words used in that way in Chinese and in some other languages are commonly referred to as coverbs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the category of algebraic varieties, the product is given by the Segre embedding. In the category of semi-abelian monoids, the product is given by the history monoid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the Hilbert\u2013Bernays provability conditions, named after David Hilbert and Paul Bernays, are a set of requirements for formalized provability predicates in formal theories of arithmetic (Smith 2007:224). These conditions are used in many proofs of Kurt G\u00f6del's second incompleteness theorem. They are also closely related to axioms of provability logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In several interesting cases, the functor G {\\displaystyle G} is an inclusion of a full subcategory not admitting a left adjoint. For example, the codensity monad of the inclusion of FinSet into Set is the ultrafilter monad associating to any set M {\\displaystyle M} the set of ultrafilters on M . {\\displaystyle M.} This was proven by Kennison and Gildenhuys, though without using the term \"codensity\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics and in many other fields of science.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The solution of eq. 108 has the form where la, ma, \u03c1, are arbitrary functions of coordinates x, y bound by condition eq. 110 derived from eq. 107. To find higher terms of this decomposition, it is convenient to write the matrix of required quantities \u03b3ab in the form where the symbol ~ means matrix transposition. Matrix H is symmetric and its trace is zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most major handicapping systems, a golfer does not use their exact handicap (or handicap index) directly, but use it to produce their playing or course handicap. For some systems, this means simply rounding the exact handicap to the nearest whole number; however, systems that use slope ratings require a more complex calculation to produce a course handicap with some also factoring in the course rating: Course handicap = ( handicap index \u00d7 slope rating ) 113 {\\displaystyle {\\mbox{Course handicap}}={\\frac {({\\mbox{handicap index}}\\times {\\mbox{slope rating}})}{\\mbox{113}}}} or Course handicap = ( handicap index \u00d7 slope rating ) 113 + ( course rating \u2212 par ) {\\displaystyle {\\mbox{Course handicap}}={\\frac {({\\mbox{handicap index}}\\times {\\mbox{slope rating}})}{\\mbox{113}}}+({\\mbox{course rating}}-{\\mbox{par}})} The USGA and Golf Australia systems use the first calculation; the WHS, EGA, and Golf RSA systems use the second. Under CONGU's Unified Handicapping System the exact handicap is rounded to the nearest whole number to produce the playing handicap, and in the Argentinian system the exact handicap is used directly. A playing handicap may also refer to the stroke allowance for a given competition dependent on playing format, and is generally calculated as a percentage of the course handicap.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If tests are developed without an understanding of what the business considers to be an acceptable level of risk, it is possible to have a release candidate that passes all the available tests, but which the business leaders would not consider to be ready for release. For the test results to accurately indicate whether each release candidate meets business expectations, the approach to designing tests must be based on the business's tolerance for risks related to security, performance, reliability, and compliance. In addition to having unit tests that check code at a very granular bottom-up level, there is a need for a broader suite of tests to provide a top-down assessment of the release candidate's business risk.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of statistical learning theory, matrix regularization generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the more common vector framework, Tikhonov regularization optimizes over min x \u2016 A x \u2212 y \u2016 2 + \u03bb \u2016 x \u2016 2 {\\displaystyle \\min _{x}\\|Ax-y\\|^{2}+\\lambda \\|x\\|^{2}} to find a vector x {\\displaystyle x} that is a stable solution to the regression problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the NFS games Underground 2 to Carbon, the network (as Cingular) was shown as the mobile internet provider in the ingame voice/text message.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is the girth of its dual matroid. Matroid girth generalizes the notion of the shortest cycle in a graph, the edge connectivity of a graph, Hall sets in bipartite graphs, even sets in families of sets, and general position of point sets. It is hard to compute, but fixed-parameter tractable for linear matroids when parameterized both by the matroid rank and the field size of a linear representation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most mobile phone operators had charged for such calls previously, with Orange being the final major network to introduce such charges during December 2005. Certain helplines, such as those in the 0808 80x xxxx series had remained free from most networks on a voluntary basis and some niche operators, such as Giffgaff always offered freephone calls at no charge.The UK mobile operators offer an alternative product to organisations who wish to provide toll-free services - 5-digit voice short codes which are sold through mobile aggregators. 0500 numbers, introduced by Mercury Communications (later known as Cable & Wireless, now Vodafone) in 1982, were also freephone numbers (known as \"FreeCall\"), but were officially withdrawn by Ofcom on 3 June 2017.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mechanical typewriters, the shift key functions by mechanically shifting some component so an alternate row of characters on typebars hits the paper. In an electronic system, by contrast, there is no necessary connection between the code points of unshifted and shifted values, though implementation is simpler if the code points of unshifted and shifted keys are related, most simply by a single bit differing. In electromechanical systems, this makes a significant difference in ease of implementation, as shifting must be accomplished by some physical linkage. For this reason, among others (such as ease of collation), the ASCII standard strove to organize the code points so that shifting could be implemented by simply toggling a bit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, implementations of Optimality Theory often make use of many concepts of phonological theories of representations, such as the syllable, the mora, or feature geometry. Completely distinct from these, there are sub-theories which have been proposed entirely within Optimality Theory, such as positional faithfulness theory, correspondence theory (McCarthy & Prince 1995), sympathy theory, stratal OT, and a number of theories of learnability, most notably by Bruce Tesar. Other theories within Optimality Theory are concerned with issues like the need for derivational levels within the phonological domain, the possible formulations of constraints, and constraint interactions other than strict domination.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the tactic is applied to the second case, then the resulting partition can be considered as the standard partition for that operator. Stocks and Carrington in (Stocks & Carrington 1996) illustrate this situation with R \u2295 G = ( dom G \u22ea R ) \u222a G {\\displaystyle R\\oplus G=({\\text{dom }}G\\ntriangleleft R)\\cup G} , where \u22ea {\\displaystyle \\ntriangleleft } means domain anti-restriction, by giving standard partitions for \u22ea {\\displaystyle \\ntriangleleft } and \u222a {\\displaystyle \\cup } and propagating them to calculate a partition for \u2295 {\\displaystyle \\oplus } . Specification Mutation (SM).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a common weighting scheme consists in giving each neighbor a weight of 1/d, where d is the distance to the neighbor.The neighbors are taken from a set of objects for which the class (for k-NN classification) or the object property value (for k-NN regression) is known. This can be thought of as the training set for the algorithm, though no explicit training step is required. A peculiarity of the k-NN algorithm is that it is sensitive to the local structure of the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir \u2061 ( \u03b1 ) {\\displaystyle \\operatorname {Dir} ({\\boldsymbol {\\alpha }})} , is a family of continuous multivariate probability distributions parameterized by a vector \u03b1 {\\displaystyle {\\boldsymbol {\\alpha }}} of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution. The infinite-dimensional generalization of the Dirichlet distribution is the Dirichlet process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Its powers have poles of order 4 , 6 {\\displaystyle 4,6} and so on. Therefore, such a P {\\displaystyle P} has the gap sequence 1 , 3 , 5 , \u2026 , 2 g \u2212 1. {\\displaystyle 1,3,5,\\dots ,2g-1.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In project management, risk assessment is an integral part of the risk management plan, studying the probability, the impact, and the effect of every known risk on the project, as well as the corrective action to take should an incident be implied by a risk occur. Of special consideration in this area are the relevant codes of practice that are enforced in the specific jurisdiction. Understanding the regime of regulations that risk management must abide by is integral to formulating safe and compliant risk assessment practices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative; however, the usual representative is the least positive residue, the smallest non-negative integer that belongs to that class (i.e., the remainder of the Euclidean division). However, other conventions are possible. Computers and calculators have various ways of storing and representing numbers; thus their definition of the modulo operation depends on the programming language or the underlying hardware. In nearly all computing systems, the quotient q and the remainder r of a divided by n satisfy the following conditions: This still leaves a sign ambiguity if the remainder is non-zero: two possible choices for the remainder occur, one negative and the other positive, and two possible choices for the quotient occur.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of fast Fourier transform algorithms, a butterfly is a portion of the computation that combines the results of smaller discrete Fourier transforms (DFTs) into a larger DFT, or vice versa (breaking a larger DFT up into subtransforms). The name \"butterfly\" comes from the shape of the data-flow diagram in the radix-2 case, as described below. The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states. The butterfly diagram show a data-flow diagram connecting the inputs x (left) to the outputs y that depend on them (right) for a \"butterfly\" step of a radix-2 Cooley\u2013Tukey FFT algorithm. This diagram resembles a butterfly as in the Morpho butterfly shown for comparison, hence the name.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the univariate polynomial \u03a8 \u2113 ( X , j ( E ) ) {\\displaystyle \\Psi _{\\ell }(X,j(E))} has a root in F q {\\displaystyle \\mathbb {F} _{q}} , where j ( E ) {\\displaystyle j(E)} denotes the j-invariant of E {\\displaystyle E} , then \u2113 {\\displaystyle \\ell } is an Elkies prime, and otherwise it is an Atkin prime. In the Elkies case, further computations involving modular polynomials are used to obtain a proper factor of the division polynomial \u03c8 \u2113 {\\displaystyle \\psi _{\\ell }} . The degree of this factor is O ( \u2113 ) {\\displaystyle O(\\ell )} , whereas \u03c8 \u2113 {\\displaystyle \\psi _{\\ell }} has degree O ( \u2113 2 ) {\\displaystyle O(\\ell ^{2})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the definition of NP-complete given above, the term reduction was used in the technical meaning of a polynomial-time many-one reduction. Another type of reduction is polynomial-time Turing reduction. A problem X {\\displaystyle \\scriptstyle X} is polynomial-time Turing-reducible to a problem Y {\\displaystyle \\scriptstyle Y} if, given a subroutine that solves Y {\\displaystyle \\scriptstyle Y} in polynomial time, one could write a program that calls this subroutine and solves X {\\displaystyle \\scriptstyle X} in polynomial time. This contrasts with many-one reducibility, which has the restriction that the program can only call the subroutine once, and the return value of the subroutine must be the return value of the program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, GXL was developed to enable interoperability between software reengineering tools and components, such as code extractors (parsers), analyzers and visualizers. GXL allows software reengineers to combine single-purpose tools especially for parsing, source code extraction, architecture recovery, data flow analysis, pointer analysis, program slicing, query techniques, source code visualization, object recovery, restructuring, refactoring, remodularization, etc., into a single powerful reengineering workbench. There are two innovative features in GXL that make it well-suited to an exchange format for software data. The conceptual data model is a typed, attributed, directed graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The purpose of the test theory is to allow a(v) and b(v) to be measured by experiment, and to see how close the experimental values come to the values predicted by special relativity. (Notice that Newtonian physics, which has been conclusively excluded by experiment, results from a ( v ) = b ( v ) = d ( v ) = 1 , and e ( v ) = 0 . {\\displaystyle a(v)=b(v)=d(v)=1,{\\text{ and }}e(v)=0\\,.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some economic models, the role of social networks in job searching often use exogenous job networks. Using this framework, Calvo-Armegnol and Jackson were able to point out some network related labor market issues.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early seventies Stephen Wiesner introduced a primitive called multiplexing in his seminal paper \"Conjugate Coding\", which was the starting point of quantum cryptography. Unfortunately it took more than ten years to be published. Even though this primitive was equivalent to what was later called 1\u20132 oblivious transfer, Wiesner did not see its application to cryptography.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These evolutionary lineages can thereby be portrayed through a phylogenetic tree, or cladogram, where varying relatedness amongst species is evidently depicted. Through this tree, organisms can be categorized by divergence from the common ancestor, and primitive characters, to clades of organisms with shared derived character states. Furthermore, cladograms allow researchers to view the changes and evolutionary alterations occurring in a species over time as they move from primitive characters to varying derived character states.Cladograms are important for scientists as they allow them to classify and hypothesize the origin and future of organisms. Cladograms allow scientists to propose their evolutionary scenarios about the lineage from a primitive trait to a derived one. By understanding how the trait came to be, scientists can hypothesize the environment that specific organism was in and how that affected the evolutionary adaptations of the trait that came to be.Other, more technical, terms for these two conditions\u2014for example, \"plesiomorphic\" and \"synapomorphic\"\u2014are frequently encountered; see the table below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. No such formula which is efficiently computable is known. A number of constraints are known, showing what such a \"formula\" can and cannot be.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two moves in: At this point, the requirement that the graph be proper comes into effect, as a red area must be made which does not touch the existing one: Once the third region is coloured: Note that areas only count as touching if they share edges, not if they only share vertices, so this move is legal. The game continues, players moving alternately, until one player cannot make a move. This player loses. A possible continuation of the game is as follows (with each move numbered for clarity): Game over: In this outcome, the blue player has lost.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Scheme theory also unifies algebraic geometry with much of number theory, which eventually led to Wiles's proof of Fermat's Last Theorem. Formally, a scheme is a topological space together with commutative rings for all of its open sets, which arises from gluing together spectra (spaces of prime ideals) of commutative rings along their open subsets. In other words, it is a ringed space which is locally a spectrum of a commutative ring.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, several students of Jean-Paul Benz\u00e9cri have refined MCA and incorporated it into a more general framework of data analysis known as geometric data analysis. This involves the development of direct connections between simple correspondence analysis, principal component analysis and MCA with a form of cluster analysis known as Euclidean classification.Two extensions have great practical use. It is possible to include, as active elements in the MCA, several quantitative variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If an industry uses little of a factor of production, a small increase in the output of that industry will not bid the price of that factor up. To a first-order approximation, firms in the industry will experience constant costs, and the industry supply curves will not slope up. If an industry uses an appreciable amount of that factor of production, an increase in the output of that industry will exhibit increasing costs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The SQL standard defines the following properties: Language - defines the programming language in which the user-defined function is implemented; examples include SQL, C, C# and Java. Parameter style - defines the conventions that are used to pass the function parameters and results between the implementation of the function and the database system (only applicable if language is not SQL). Specific name - a name for the function that is unique within the database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Links not in the MCF are paid nothing. This routing problem is one of the cases for which VCG is strategyproof and minimum. In 2004, it was shown that the expected VCG overpayment of an Erd\u0151s\u2013R\u00e9nyi random graph with n nodes and edge probability p, G \u2208 G ( n , p ) {\\displaystyle \\scriptstyle G\\in G(n,p)} approaches p 2 \u2212 p {\\displaystyle {\\frac {p}{2-p}}} as n, approaches \u221e {\\displaystyle \\scriptstyle \\infty } , for n p = \u03c9 ( n log \u2061 n ) {\\displaystyle np=\\omega ({\\sqrt {n\\log n}})} . Prior to this result, it was known that VCG overpayment in G(n, p) is \u03a9 ( 1 n p ) {\\displaystyle \\Omega \\left({\\frac {1}{np}}\\right)} and O ( 1 ) {\\displaystyle O(1)\\,} with high probability given n p = \u03c9 ( log \u2061 n ) . {\\displaystyle np=\\omega (\\log n).\\,}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to effectively aid marketers in fully understanding customers and subsequently developing a strategic marketing plan, marketing automation platforms (MAPs) are designed to perform eight key tasks: Development and analysis of marketing campaigns and customers Management of marketing campaigns Appropriate customer data organization and storage Moving contacts from leads (marketing prospects) to customers Lead scoring to qualify leads by measuring their engagement level Integration of multiple touch-points such as email and social media Lead management Campaign performance analytics (i.e. open rate or click-through rates on emails, conversion rates on landing pages)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, mathematical optimization (or optimization or mathematical programming) refers to the selection of a best element from some set of available alternatives. In the simplest case, an optimization problem involves maximizing or minimizing a real function by selecting input values of the function and computing the corresponding values of the function. The solution process includes satisfying general necessary and sufficient conditions for optimality. For optimization problems, specialized notation may be used as to the function and its input(s).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The negation of an event in probability theory: Pr(A\u2032) = 1 \u2212 Pr(A) (other notation also exists). The result of a transformation: Tx = x\u2032 The transpose of a matrix (other notation also exists) The dual of a vector spaceThe prime is said to \"decorate\" the letter to which it applies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, the impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of a potential field U(r) created by an object that the projectile is approaching (see diagram). It is often referred to in nuclear physics (see Rutherford scattering) and in classical mechanics. The impact parameter is related to the scattering angle \u03b8 by \u03b8 = \u03c0 \u2212 2 b \u222b r min \u221e d r r 2 1 \u2212 ( b / r ) 2 \u2212 2 U / ( m v \u221e 2 ) , {\\displaystyle \\theta =\\pi -2b\\int _{r_{\\text{min}}}^{\\infty }{\\frac {dr}{r^{2}{\\sqrt {1-(b/r)^{2}-2U/(mv_{\\infty }^{2})}}}},} where v\u221e is the velocity of the projectile when it is far from the center, and rmin is its closest distance from the center.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as {0, 1}, or B . {\\displaystyle \\mathbb {B} .} The algebraic structure that naturally builds on a Boolean domain is the Boolean algebra with two elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"The text also states that, \"... over most of the area affected by the EMP the electric field strength on the ground would exceed 0.5Emax. For yields of less than a few hundred kilotons, this would not necessarily be true because the field strength at the Earth's tangent could be substantially less than 0.5Emax.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Supposing that the Kempe chain is connecting the green and yellow neighbors, red and blue must then necessarily not have a Kempe chain between them. So, when placing the original vertex v back into the graph, we can simply reverse the colors of the red vertex and its neighbors (including the red vertex, making it blue) and color vertex v as red. This results in a four-colored graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such a formula can be made either true or false based on the values assigned to its propositional variables. The double turnstile notation \u22a8 S {\\displaystyle \\vDash S} is used to indicate that S is a tautology. Tautology is sometimes symbolized by \"Vpq\", and contradiction by \"Opq\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Ingleton's inequality is an inequality that is satisfied by the rank function of any representable matroid. In this sense it is a necessary condition for representability of a matroid over a finite field. Let M be a matroid and let \u03c1 be its rank function, Ingleton's inequality states that for any subsets X1, X2, X3 and X4 in the support of M, the inequality \u03c1(X1)+\u03c1(X2)+\u03c1(X1\u222aX2\u222aX3)+\u03c1(X1\u222aX2\u222aX4)+\u03c1(X3\u222aX4) \u2264 \u03c1(X1\u222aX2)+\u03c1(X1\u222aX3)+\u03c1(X1\u222aX4)+\u03c1(X2\u222aX3)+\u03c1(X2\u222aX4) is satisfied.Aubrey William Ingleton, an English mathematician, wrote an important paper in 1969 in which he surveyed the representability problem in matroids. Although the article is mainly expository, in this paper Ingleton stated and proved Ingleton's inequality, which has found interesting applications in information theory, matroid theory, and network coding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some states, grand theft of a vehicle may be charged as \"grand theft auto\" (see motor vehicle theft for more information). Repeat offenders who continue to steal may become subject to life imprisonment in certain states.Sometimes the federal anti-theft-of-government-property law 18 U.S.C. \u00a7 640 is used to prosecute cases where the Espionage Act would otherwise be involved; the theory being that by retaining sensitive information, the defendant has taken a 'thing of value' from the government. For examples, see the Amerasia case and United States v. Manning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Areas most at risk for flooding could be put to valuable uses that could be abandoned temporarily as people retreat to safer areas when a flood is imminent. Planning for flood safety involves many aspects of analysis and engineering, including: observation of previous and present flood heights and inundated areas, statistical, hydrologic, and hydraulic model analyses, mapping inundated areas and flood heights for future flood scenarios, long-term land use planning and regulation, engineering design and construction of structures to control or withstand flooding, intermediate-term monitoring, forecasting, and emergency-response planning, and short-term monitoring, warning, and response operations.Each topic presents distinct yet related questions with varying scope and scale in time, space, and the people involved. Attempts to understand and manage the mechanisms at work in floodplains have been made for at least six millennia.In the United States, the Association of State Floodplain Managers works to promote education, policies, and activities that mitigate current and future losses, costs, and human suffering caused by flooding and to protect the natural and beneficial functions of floodplains \u2013 all without causing adverse impacts. A portfolio of best practice examples for disaster mitigation in the United States is available from the Federal Emergency Management Agency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In simple type theory objects are elements of various disjoint \"types\". Types are implicitly built up as follows. If \u03c41,...,\u03c4m are types then there is a type (\u03c41,...,\u03c4m) that can be thought of as the class of propositional functions of \u03c41,...,\u03c4m (which in set theory is essentially the set of subsets of \u03c41\u00d7...\u00d7\u03c4m). In particular there is a type () of propositions, and there may be a type \u03b9 (iota) of \"individuals\" from which other types are built.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If it is consistent with either state, Bob announces that the bit is invalid, since he cannot distinguish which state was transmitted based on the measurement. If on the other hand, one of the two candidate states was inconsistent with the observed measurement, Bob announces that the bit is valid since he can deduce the state (and therefore the secret bit). Consider for example the scenario that Alice transmits | \u03c8 00 \u27e9 {\\displaystyle |\\psi _{00}\\rangle } and announces the two states | \u03c8 00 \u27e9 {\\displaystyle |\\psi _{00}\\rangle } and | \u03c8 01 \u27e9 {\\displaystyle |\\psi _{01}\\rangle } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution. If X has a Laplace distribution with parameters \u03bc and b, then Y = eX has a log-Laplace distribution. The distributional properties can be derived from the Laplace distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The linear form \u27e8 \u03d5 | {\\displaystyle \\langle \\phi |} is a covector to | \u03d5 \u27e9 {\\displaystyle |\\phi \\rangle } , and the set of all covectors form a subspace of the dual vector space V \u2228 {\\displaystyle V^{\\vee }} , to the initial vector space V {\\displaystyle V} . The purpose of this linear form \u27e8 \u03d5 | {\\displaystyle \\langle \\phi |} can now be understood in terms of making projections on the state \u03d5 {\\displaystyle {\\boldsymbol {\\phi }}} , to find how linearly dependent two states are, etc. For the vector space C n {\\displaystyle \\mathbb {C} ^{n}} , kets can be identified with column vectors, and bras with row vectors. Combinations of bras, kets, and linear operators are interpreted using matrix multiplication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since you and your opponent are each infinitely wealthy, there is no limit to how long the game can last. This means the sample space \u03a9 must consist of all possible infinite sequences of H {\\displaystyle H} or T: {\\displaystyle T:} However, after n {\\displaystyle n} flips of the coin, you may want to determine or revise your betting strategy in advance of the next flip. The observed information at that point can be described in terms of the 2n possibilities for the first n {\\displaystyle n} flips. Formally, since you need to use subsets of \u03a9, this is codified as the \u03c3-algebra Observe that then where G \u221e {\\displaystyle {\\mathcal {G}}_{\\infty }} is the smallest \u03c3-algebra containing all the others.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Now we are taking balls randomly in such a way that the probability of taking a particular ball is proportional to its weight, but independent of what happens to the other balls. The number of balls taken of a particular color follows the binomial distribution. If the total number n of balls taken is known then the conditional distribution of the number of taken red balls for given n is Fisher's noncentral hypergeometric distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some types of computer video displays, the related technique of double buffering may be used to improve video performance. In this case, while the processor is updating the contents of one set of physical memory locations, the video generation hardware is accessing and displaying the contents of a second set. When the processor has completed its update, it can signal to the video display hardware to swap active banks, so that the transition visible on screen is free of artifacts or distortion. In this case, the processor may have access to all the memory at once, but the video display hardware is bank-switched between parts of the video memory. If the two (or more) banks of video memory contain slightly different images, rapidly cycling (page-flipping) between them can create animation or other visual effects that the processor might otherwise be too slow to carry out directly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This always includes the content of general-purpose CPU registers, the CPU process status word, stack and frame pointers, etc. During context switch, the running process is stopped and another process runs. The kernel must stop the execution of the running process, copy out the values in hardware registers to its PCB, and update the hardware registers with the values from the PCB of the new process. Process control information is used by the OS to manage the process itself. This includes: Process scheduling state \u2013 The state of the process in terms of \"ready\", \"suspended\", etc., and other scheduling information as well, such as priority value, the amount of time elapsed since the process gained control of the CPU or since it was suspended. Also, in case of a suspended process, event identification data must be recorded for the event the process is waiting for; Process structuring information \u2013 the process's children id's, or the id's of other processes related to the current one in some functional way, which may be represented as a queue, a ring or other data structures; Interprocess communication information \u2013 flags, signals and messages associated with the communication among independent processes; Process Privileges \u2013 allowed/disallowed access to system resources; Process State \u2013 new, ready, running, waiting, dead; Process Number (PID) \u2013 unique identification number for each process (also known as Process ID); Program Counter (PC) \u2013 a pointer to the address of the next instruction to be executed for this process; CPU Registers \u2013 register set where process needs to be stored for execution for running state; CPU Scheduling Information \u2013 information scheduling CPU time; Memory Management Information \u2013 page table, memory limits, segment table; Accounting Information \u2013 amount of CPU used for process execution, time limits, execution ID etc.; I/O Status Information \u2013 list of I/O devices allocated to the process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in particular number theory, an odd composite number N is a Somer\u2013Lucas d-pseudoprime (with given d \u2265 1) if there exists a nondegenerate Lucas sequence U ( P , Q ) {\\displaystyle U(P,Q)} with the discriminant D = P 2 \u2212 4 Q , {\\displaystyle D=P^{2}-4Q,} such that gcd ( N , D ) = 1 {\\displaystyle \\gcd(N,D)=1} and the rank appearance of N in the sequence U(P, Q) is 1 d ( N \u2212 ( D N ) ) , {\\displaystyle {\\frac {1}{d}}\\left(N-\\left({\\frac {D}{N}}\\right)\\right),} where ( D N ) {\\displaystyle \\left({\\frac {D}{N}}\\right)} is the Jacobi symbol.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, there are many different writings on mathematics and mathematics methodology that date back to 1800 BCE. These were mostly located in Mesopotamia, where the Sumerians were practicing multiplication and division. There are also artifacts demonstrating their methodology for solving equations like the quadratic equation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "SQL query is tightly coupled and rigidly constrained by datatype within the specific database and can join tables and extract data from tables, and the result is generally a table, and a query can join tables by any columns which match by datatype. SPARQL query is the standard query language and protocol for Linked Open Data on the web and loosely coupled with the database so that it facilitates the reusability and can extract data through the relations free from the datatype, and not only extract but also generate additional knowledge graph with more sophisticated operations(logic: transitive/symmetric/inverseOf/functional). The inference based query (query on the existing asserted facts without the generation of new facts by logic) can be fast comparing to the reasoning based query (query on the existing plus the generated/discovered facts based on logic).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(TCP's sister protocol, UDP, does not do this. UDP simply sends data packets over the network in a best effort manner and assumes the packets are well-received.) An early problem noted with TCP's ACK mechanism was it did not work well in large multicast group communications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first of these is that the context changes functional interpretations of the same behaviors, such as the way \u201cwright, right, right, rite, and write\u201d are interpreted based on the context of the sentence. \u201cRight\u201d can be interpreted as a direction or as something good depending on the context. A second line of evidence says that errors are involved in human behavior as hierarchical organization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 258, 1258, 2458, and 12458 are the patterns related to Braille pattern dots-146, since the two additional dots of kantenji patterns 0146, 1467, and 01467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the quasi-commutative property is an extension or generalization of the general commutative property. This property is used in specific applications with various definitions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The main reason for the design of this format is that it fits the maximum amount of data on a standard 80-character-wide screen or printer, while still being very easy to read and skim visually. Here the leftmost column represents the address at which the bytes represented by the following columns are located. CP/M and various DOS systems ran in real mode on the x86 CPUs, where addresses are composed of two parts (base and offset). In the above examples the final 00s are non-existent bytes beyond the end of the file. Some dump tools display other characters so that it is clear they are beyond the end of the file, typically using spaces or asterisks, e.g.: or", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages that support recursive data types, it is possible to type the Y combinator by appropriately accounting for the recursion at the type level. The need to self-apply the variable x can be managed using a type (Rec a), which is defined so as to be isomorphic to (Rec a -> a). For example, in the following Haskell code, we have In and out being the names of the two directions of the isomorphism, with types: which lets us write: Or equivalently in OCaml: Alternatively:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Philippines, The Data Privacy Act of 2012 mandated the creation of the National Privacy Commission that would monitor and maintain policies that involve information privacy and personal data protection in the country. Modeled after the EU Data Protection Directive and the Asia-Pacific Economic Cooperation (APEC) Privacy Framework, the independent body would ensure compliance of the country with international standards set for data protection. The law requires government and private organizations composed of at least 250 employees or those which have access to the personal and identifiable information of at least 1000 people to appoint a Data Protection Officer that would assist in regulating the management of personal information in such entities.In summary, the law identifies important points regarding the handling of personal information as follows: Personal information must be collected for reasons that are specified, legitimate, and reasonable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a supercommutative (associative) algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y we have y x = ( \u2212 1 ) | x | | y | x y , {\\displaystyle yx=(-1)^{|x||y|}xy,} where |x| denotes the grade of the element and is 0 or 1 (in Z2) according to whether the grade is even or odd, respectively. Equivalently, it is a superalgebra where the supercommutator  = x y \u2212 ( \u2212 1 ) | x | | y | y x {\\displaystyle =xy-(-1)^{|x||y|}yx} always vanishes. Algebraic structures which supercommute in the above sense are sometimes referred to as skew-commutative associative algebras to emphasize the anti-commutation, or, to emphasize the grading, graded-commutative or, if the supercommutativity is understood, simply commutative. Any commutative algebra is a supercommutative algebra if given the trivial gradation (i.e. all elements are even).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word \"permutation\" also refers to the act or process of changing the linear order of an ordered set.Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is possible because the logarithm of a product is the sum of the logarithms of the factors: provided that b, x and y are all positive and b \u2260 1. The slide rule, also based on logarithms, allows quick calculations without tables, but at lower precision. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century, and who also introduced the letter e as the base of natural logarithms.Logarithmic scales reduce wide-ranging quantities to smaller scopes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In USAID, the use of a program cycle, \"codified in the Automated Directive Systems (ADS) 201, is USAID's operational model for planning, delivering, assessing, and adapting development programming in a given region or country to achieve more effective and sustainable results in order to advance U.S. foreign policy\". Relatedly, within the agency there exists resources regarding adaptive management decision cycles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As properties of permutations do not depend on the nature of the set elements, it is often the permutations of the set { 1 , 2 , \u2026 , n } {\\displaystyle \\{1,2,\\ldots ,n\\}} that are considered for studying permutations. In elementary combinatorics, the k-permutations, or partial permutations, are the ordered arrangements of k distinct elements selected from a set. When k is equal to the size of the set, these are the permutations of the set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In meteorology a ridge or barometric ridge is an elongated area of relatively high atmospheric pressure compared to the surrounding environment, without being a closed circulation. It is associated with an area of maximum anticyclonic curvature of wind flow. The ridge originates in the center of an anticyclone and sandwiched between two low-pressure areas, and the locus of the maximum curvature is called the ridge line. This phenomenon is the opposite of a trough.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6. Nicolaas Govert de Bruijn coined the word multiset in the 1970s, according to Donald Knuth. : 694 However, the concept of multisets predates the coinage of the word multiset by many centuries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the SVP, a basis of a vector space V and a norm N (often L2) are given for a lattice L and one must find the shortest non-zero vector in V, as measured by N, in L. In other words, the algorithm should output a non-zero vector v such that \u2016 v \u2016 N = \u03bb ( L ) {\\displaystyle \\|v\\|_{N}=\\lambda (L)} . In the \u03b3-approximation version SVP\u03b3, one must find a non-zero lattice vector of length at most \u03b3 \u22c5 \u03bb ( L ) {\\displaystyle \\gamma \\cdot \\lambda (L)} for given \u03b3 \u2265 1 {\\displaystyle \\gamma \\geq 1} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Error correction does not seem to have a direct influence on learning a second language. Instruction may affect the rate of learning, but the stages remain the same.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value \u2013 the value it would take \"on average\" over an arbitrarily large number of occurrences \u2013 given that a certain set of \"conditions\" is known to occur. If the random variable can take on only a finite number of values, the \"conditions\" are that the variable can only take on a subset of those values. More formally, in the case when the random variable is defined over a discrete probability space, the \"conditions\" are a partition of this probability space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function with n = 0), and continues with the binary operations of addition (n = 1), multiplication (n = 2), exponentiation (n = 3), tetration (n = 4), pentation (n = 5), etc. Various notations have been used to represent hyperoperations. One such notation is H n ( a , b ) {\\displaystyle H_{n}(a,b)} . Knuth's up-arrow notation \u2191 {\\displaystyle \\uparrow } is another. For example: the single arrow \u2191 {\\displaystyle \\uparrow } represents exponentiation (iterated multiplication) the double arrow \u2191\u2191 {\\displaystyle \\uparrow \\uparrow } represents tetration (iterated exponentiation) the triple arrow \u2191\u2191\u2191 {\\displaystyle \\uparrow \\uparrow \\uparrow } represents pentation (iterated tetration) The general definition of the up-arrow notation is as follows (for a \u2265 0 , n \u2265 1 , b \u2265 0 {\\displaystyle a\\geq 0,n\\geq 1,b\\geq 0} ): Here, \u2191 n {\\displaystyle \\uparrow ^{n}} stands for n arrows, so for example The square brackets are another notation for hyperoperations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is a PBE - it is a best-response for both sender and receiver. The sender's strategy is: never give. Suppose the receiver's beliefs when receiving a gift is that the sender is a friend with probability q {\\displaystyle q} , where q {\\displaystyle q} is any number in  {\\displaystyle } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions and to systems of equations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one special case two covariates, say j and k, are identical for each observation, so that x ( j ) = x ( k ) {\\displaystyle x_{(j)}=x_{(k)}} , where x ( j ) , i = x ( k ) , i {\\displaystyle x_{(j),i}=x_{(k),i}} . Then the values of \u03b2 j {\\displaystyle \\beta _{j}} and \u03b2 k {\\displaystyle \\beta _{k}} that minimize the lasso objective function are not uniquely determined. In fact, if some \u03b2 ^ {\\displaystyle {\\hat {\\beta }}} in which \u03b2 ^ j \u03b2 ^ k \u2265 0 {\\displaystyle {\\hat {\\beta }}_{j}{\\hat {\\beta }}_{k}\\geq 0} , then if s \u2208  {\\displaystyle s\\in } replacing \u03b2 ^ j {\\displaystyle {\\hat {\\beta }}_{j}} by s ( \u03b2 ^ j + \u03b2 ^ k ) {\\displaystyle s({\\hat {\\beta }}_{j}+{\\hat {\\beta }}_{k})} and \u03b2 ^ k {\\displaystyle {\\hat {\\beta }}_{k}} by ( 1 \u2212 s ) ( \u03b2 ^ j + \u03b2 ^ k ) {\\displaystyle (1-s)({\\hat {\\beta }}_{j}+{\\hat {\\beta }}_{k})} , while keeping all the other \u03b2 ^ i {\\displaystyle {\\hat {\\beta }}_{i}} fixed, gives a new solution, so the lasso objective function then has a continuum of valid minimizers. Several variants of the lasso, including the Elastic net regularization, have been designed to address this shortcoming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Whatever we may say something 'is' obviously is not the 'something' on the silent levels.\" By making it a 'mental' habit to find and keep one's bearings among the ordered stages, general semantics training seeks to sharpen internal orientation much as a GPS device may sharpen external orientation. Once trained, general semanticists affirm, a person will act, respond, and make decisions more appropriate to any given set of happenings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Given a data array X, the basic Backus-Gilbert inverse is: H \u03b8 = C \u2212 1 G \u03b8 G \u03b8 T C \u2212 1 G \u03b8 {\\displaystyle \\mathbf {H} _{\\theta }={\\frac {\\mathbf {C} ^{-1}\\mathbf {G} _{\\theta }}{\\mathbf {G} _{\\theta }^{T}\\mathbf {C} ^{-1}\\mathbf {G} _{\\theta }}}} where C is the covariance matrix of the data, and G\u03b8 is an a priori constraint representing the source \u03b8 for which a solution is sought. Regularization is implemented by \"whitening\" the covariance matrix: C \u2032 = C + \u03bb I {\\displaystyle \\mathbf {C} '=\\mathbf {C} +\\lambda \\mathbf {I} } with C\u2032 replacing C in the equation for H\u03b8. Then, H \u03b8 T X {\\displaystyle \\mathbf {H} _{\\theta }^{T}\\mathbf {X} } is an estimate of the activity of the source \u03b8.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some countries such as Germany, the above multiplication is depicted similarly but with the original product kept horizontal and computation starting with the first digit of the multiplier: 23958233 \u00b7 5830 \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014 119791165 191665864 71874699 00000000 \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014 139676498390 Below pseudocode describes the process of above multiplication. It keeps only one row to maintain the sum which finally becomes the result. Note that the '+=' operator is used to denote sum to existing value and store operation (akin to languages such as Java and C) for compactness.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\cdot }\\,} _{i\\in I}A_{i}} ). A standard way for building the disjoint union is to define A {\\displaystyle A} as the set of ordered pairs ( x , i ) {\\displaystyle (x,i)} such that x \u2208 A i , {\\displaystyle x\\in A_{i},} and the injection A i \u2192 A {\\displaystyle A_{i}\\to A} as x \u21a6 ( x , i ) . {\\displaystyle x\\mapsto (x,i).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories using sample data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We can show that c = 2 \u2135 0 {\\displaystyle {\\mathfrak {c}}=2^{\\aleph _{0}}} , this also being the cardinality of the set of all subsets of the natural numbers. The continuum hypothesis says that \u2135 1 = 2 \u2135 0 {\\displaystyle \\aleph _{1}=2^{\\aleph _{0}}} , i.e. 2 \u2135 0 {\\displaystyle 2^{\\aleph _{0}}} is the smallest cardinal number bigger than \u2135 0 {\\displaystyle \\aleph _{0}} , i.e. there is no set whose cardinality is strictly between that of the integers and that of the real numbers. The continuum hypothesis is independent of ZFC, a standard axiomatization of set theory; that is, it is impossible to prove the continuum hypothesis or its negation from ZFC\u2014provided that ZFC is consistent. For more detail, see \u00a7 Cardinality of the continuum below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, the set of all integers (including negative numbers) can be brought into bijection with the set of natural numbers, and even seemingly much larger sets like that of all finite sequences of rational numbers are still (only) countably infinite. Nevertheless, there are sets, such as the set of real numbers, that can be shown to be \"too large\" to admit a bijection with the natural numbers, and these sets are called \"uncountable.\" Sets for which there exists a bijection between them are said to have the same cardinality, and in the most general sense counting a set can be taken to mean determining its cardinality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. It cannot be untrue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A line l in a projective plane \u03a0 is a translation line if the group of all elations with axis l acts transitively on the points of the affine plane obtained by removing l from the plane \u03a0, \u03a0l (the affine derivative of \u03a0). A projective plane with a translation line is called a translation plane. The affine plane obtained by removing the translation line is called an affine translation plane. While it is often easier to work with projective planes, in this context several authors use the term translation plane to mean affine translation plane.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The LRN removes the need for the public telephone number to identify the local exchange carrier. If a subscriber changes to another telephone service provider, the current telephone number can be retained, and only the LRN needs to be changed. In addition to supporting service provider telephone number portability, an LRN also supports the possibility of two other types of number portability: service portability (for example, ordinary service to ISDN) and geographic portability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to define a custom structure type using Oracle Database one could use statements such as these:Such structure type can be then used to create a table that would also hold all columns defined in Person_Type:Custom structure types support inheritance, which means that one can create another type that inherits from previous. NOT FINAL statement must be however included in a base structure type definition in order to allow for creation of any other subtypes.Student_Type then could be used in order to create a Student_Table which will include all columns defined in Person_Type as well. Primary Key and Constraints should be defined during or after creation of table and cannot be defined inside structure type itself.Each custom structure type can also contain other types in order to support more complex structures:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 19th century, Sir William Thomson made a hypothesis that the chemical elements were based upon knotted vortices in the aether. In an attempt to make a periodic table of the elements, P. G. Tait, C. N. Little and others started to attempt to count all possible knots. Because their work predated the invention of the digital computer, all work had to be done by hand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "VoIP systems are based on Internet standards and technology which have not previously attempted to satisfy such complex and demanding requirements as those that specify call control. An alternative name often used is call processing.In a VoIP network, call control is one of three major categories of communications traffic, the other two being call signaling and media communications. Call control uses Q.931, a connection protocol for digital networks, especially VoIP systems. Messages are transmitted as octets as specified in ITU H.245, which resolves the type of call media to be used (for example, conventional call, videoconferencing, or VoIP), and then manages the connection after it has been established. Call control functions include, but are not limited to, the determination of master/slave status for the endpoints, monitoring of the status of the endpoints, modification of the parameters of a connection, termination of a connection, and restarting a terminated or failed connection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These critics suggest that direct parameters would be better placed on the operational uses of data in general. Opponents of regulatory reform say this would, perhaps unintentionally, drastically inhibit businesses ability to utilize the data for positive measures. Furthermore, because singular data points may be used across a large array of industries, sector-specific legislation may prove fruitless.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode the algorithm can be stated as: Begin 1) Objective function: f ( x ) , x = ( x 1 , x 2 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An example is the assignment of the code EUR to the euro. ISO 4217 amendment 94, which created this code, states \"The code element 'EU' has been reserved by the ISO 3166 Maintenance Agency for use within ISO 4217 where 'R' has been appended to make an acceptable mnemonic code.\" Here the R comes from the third letter in the word \"euro\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, who programmed it on the Z4, and extensively researched it.The biconjugate gradient method provides a generalization to non-symmetric matrices. Various nonlinear conjugate gradient methods seek minima of nonlinear optimization problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When an item in the left column is related to an item across the top, a mark is placed in the intersecting cell. The number of relationships are added up for each row and each column.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, metaheuristics usually allow to meet the resolution delays imposed in the industrial field as well as they allow to study general problem classes instead that particular problem instances. In general, many of the best performing techniques in precision and effort to solve complex and real-world problems are metaheuristics. Their fields of application range from combinatorial optimization, bioinformatics, and telecommunications to economics, software engineering, etc. These fields are full of many tasks needing fast solutions of high quality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or by allocating resources to the choice. This is a classic reinforcement learning problem that exemplifies the exploration\u2013exploitation tradeoff dilemma. The name comes from imagining a gambler at a row of slot machines (sometimes known as \"one-armed bandits\"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. The multi-armed bandit problem also falls into the broad category of stochastic scheduling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In test-driven development (TDD), which is frequently used in both extreme programming and scrum, unit tests are created before the code itself is written. When the tests pass, that code is considered complete. The same unit tests are run against that function frequently as the larger code base is developed either as the code is changed or via an automated process with the build. If the unit tests fail, it is considered to be a bug either in the changed code or the tests themselves. The unit tests then allow the location of the fault or failure to be easily traced. Since the unit tests alert the development team of the problem before handing the code off to testers or clients, potential problems are caught early in the development process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s, there was a two-player game made by Tri-ang Toys & Games called Check Lines, in which the board consisted of eleven holes arranged in a geometrical pattern of twelve straight lines each containing three of the holes. Each player had exactly five tokens and played in turn placing one token in any of the holes. The winner was the first player whose tokens were arranged in two lines of three (which by definition were intersecting lines). If neither player had won by the tenth turn, subsequent turns consisted of moving one of one's own tokens to the remaining empty hole, with the constraint that this move could only be from an adjacent hole.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimal control theory, the evolution of n state variables through time depends at any time on their own values and on the values of k control variables. With linear evolution, matrices of coefficients appear in the state equation (equation of evolution). In some problems the values of the parameters in these matrices are not known with certainty, in which case there are random matrices in the state equation and the problem is known as one of stochastic control. : ch. 13 A key result in the case of linear-quadratic control with stochastic matrices is that the certainty equivalence principle does not apply: while in the absence of multiplier uncertainty (that is, with only additive uncertainty) the optimal policy with a quadratic loss function coincides with what would be decided if the uncertainty were ignored, the optimal policy may differ if the state equation contains random coefficients.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The position of an element in a sequence is its rank or index; it is the natural number for which the element is the image. The first element has index 0 or 1, depending on the context or a specific convention. In mathematical analysis, a sequence is often denoted by letters in the form of a n {\\displaystyle a_{n}} , b n {\\displaystyle b_{n}} and c n {\\displaystyle c_{n}} , where the subscript n refers to the nth element of the sequence; for example, the nth element of the Fibonacci sequence F {\\displaystyle F} is generally denoted as F n {\\displaystyle F_{n}} . In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them in computer memory; infinite sequences are called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most languages that provide this feature, a procedural parameter f of a subroutine P can be called inside the body of P as if it were an ordinary procedure: procedure P(f): return f(6,3) * f(2,1) When calling the subroutine P, one must give it one argument, that must be some previously defined function compatible with the way P uses its parameter f. For example, if we define procedure plus(x, y): return x + y then we may call P (plus), and the result will be plus(6,3) * plus(2,1) = (6 + 3)*(2 + 1) = 27. On the other hand, if we define procedure quot(u, v): return u/v then the call P (quot) will return quot(6,3)*quot(2,1) = (6/3)*(2/1) = 4. Finally, if we define procedure evil(z) return z + 100 then the call P (evil) will not make much sense, and may be flagged as an error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a branch of mathematics, a Mirimanoff's congruence is one of a collection of expressions in modular arithmetic which, if they hold, entail the truth of Fermat's Last Theorem. Since the theorem has now been proven, these are now of mainly historical significance, though the Mirimanoff polynomials are interesting in their own right. The theorem is due to Dmitry Mirimanoff.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity element is often shortened to identity (as in the case of additive identity and multiplicative identity) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count data with more than one parameter. This distribution is flexible in terms of its ability to allow a moderate over-dispersion in the data. The authors Kemp and Kemp have called it \"Hermite distribution\" from the fact its probability function and the moment generating function can be expressed in terms of the coefficients of (modified) Hermite polynomials.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The typical metric used in this case the Lee distance. There exist a Gray isometry between Z 2 2 m {\\displaystyle \\mathbb {Z} _{2}^{2m}} (i.e. GF(22m)) with the Hamming distance and Z 4 m {\\displaystyle \\mathbb {Z} _{4}^{m}} (also denoted as GR(4,m)) with the Lee distance. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, proof compression by splitting is an algorithm that operates as a post-process on resolution proofs. It was proposed by Scott Cotton in his paper \"Two Techniques for Minimizing Resolution Proof\".The Splitting algorithm is based on the following observation: Given a proof of unsatisfiability \u03c0 {\\displaystyle \\pi } and a variable x {\\displaystyle x} , it is easy to re-arrange (split) the proof in a proof of x {\\displaystyle x} and a proof of \u00ac x {\\displaystyle \\neg x} and the recombination of these two proofs (by an additional resolution step) may result in a proof smaller than the original. Note that applying Splitting in a proof \u03c0 {\\displaystyle \\pi } using a variable x {\\displaystyle x} does not invalidates a latter application of the algorithm using a differente variable y {\\displaystyle y} . Actually, the method proposed by Cotton generates a sequence of proofs \u03c0 1 \u03c0 2 \u2026 {\\displaystyle \\pi _{1}\\pi _{2}\\ldots } , where each proof \u03c0 i + 1 {\\displaystyle \\pi _{i+1}} is the result of applying Splitting to \u03c0 i {\\displaystyle \\pi _{i}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In political science, the policy cycle is a tool used for analyzing the development of a policy. It can also be referred to as a \"stages model\" or \"stages heuristic\". It is thus a rule of thumb rather than the actual reality of how policy is created, but has been influential in how political scientists looked at policy in general. It was developed as a theory from Harold Lasswell's work.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is primarily because adding another Opteron processor increases memory bandwidth, while that is not always the case for Xeon systems, and the fact that the Opterons use a switched fabric, rather than a shared bus. In particular, the Opteron's integrated memory controller allows the CPU to access local RAM very quickly. In contrast, multiprocessor Xeon system CPUs share only two common buses for both processor-processor and processor-memory communication. As the number of CPUs increases in a typical Xeon system, contention for the shared bus causes computing efficiency to drop. Intel migrated to a memory architecture similar to the Opteron's for the Intel Core i7 family of processors and their Xeon derivatives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, they consider the above LP with one additional constraint:The additional constraint guarantees that the \"vacant space\" in the bins can be filled by the small items. The dual of this LP is more complex and cannot be solved by a simple knapsack-problem separation oracle. Csirik, Johnson and Kenyon present a different method to solve it approximately in time exponential in 1/epsilon. Jansen and Solis-Oba present an improved method to solve it approximately in time exponential in 1/epsilon.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially group theory, the centralizer (also called commutant) of a subset S in a group G is the set C G \u2061 ( S ) {\\displaystyle \\operatorname {C} _{G}(S)} of elements of G that commute with every element of S, or equivalently, such that conjugation by g {\\displaystyle g} leaves each element of S fixed. The normalizer of S in G is the set of elements N G ( S ) {\\displaystyle \\mathrm {N} _{G}(S)} of G that satisfy the weaker condition of leaving the set S \u2286 G {\\displaystyle S\\subseteq G} fixed under conjugation. The centralizer and normalizer of S are subgroups of G. Many techniques in group theory are based on studying the centralizers and normalizers of suitable subsets S. Suitably formulated, the definitions also apply to semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Mertens conjecture is the statement that the Mertens function M ( n ) {\\displaystyle M(n)} is bounded by \u00b1 n {\\displaystyle \\pm {\\sqrt {n}}} . Although now disproven, it had been shown to imply the Riemann hypothesis. It was conjectured by Thomas Joannes Stieltjes, in an 1885 letter to Charles Hermite (reprinted in Stieltjes (1905)), and again in print by Franz Mertens (1897), and disproved by Andrew Odlyzko and Herman te Riele (1985). It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in its favor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": " relation algebra to specify information systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 58, 158, 458, and 1458 are the patterns related to Braille pattern dots-46, since the two additional dots of kantenji patterns 046, 467, and 0467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let \u2113 {\\displaystyle \\ell } be the single literal of the unit clause of \u03b7 \u2032 {\\displaystyle \\eta ^{\\prime }} . Then any occurrence of \u2113 \u00af {\\displaystyle {\\overline {\\ell }}} in the subproof above \u03b7 {\\displaystyle \\eta } will not be cancelled by resolution inferences with \u03b7 \u2032 {\\displaystyle \\eta ^{\\prime }} anymore. Consequently, \u2113 \u00af {\\displaystyle {\\overline {\\ell }}} will be propagated downwards when the proof is fixed and will appear in the clause of \u03b7 {\\displaystyle \\eta } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some texts, especially in random matrix theory, authors have found it more convenient to use a matrix argument in the Jack function. The connection is simple. If X {\\displaystyle X} is a matrix with eigenvalues x 1 , x 2 , \u2026 , x m {\\displaystyle x_{1},x_{2},\\ldots ,x_{m}} , then J \u03ba ( \u03b1 ) ( X ) = J \u03ba ( \u03b1 ) ( x 1 , x 2 , \u2026 , x m ) . {\\displaystyle J_{\\kappa }^{(\\alpha )}(X)=J_{\\kappa }^{(\\alpha )}(x_{1},x_{2},\\ldots ,x_{m}).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, FPUs may be specialized, and divided between simpler floating-point operations (mainly addition and multiplication) and more complicated operations, like division. In some cases, only the simple operations may be implemented in hardware or microcode, while the more complex operations are implemented as software. In some current architectures, the FPU functionality is combined with SIMD units to perform SIMD computation; an example of this is the augmentation of the x87 instructions set with SSE instruction set in the x86-64 architecture used in newer Intel and AMD processors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some older virtual memory operating systems, space in swap backing store is reserved when programs allocate memory for runtime data. Operating system vendors typically issue guidelines about how much swap space should be allocated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most legal proceedings, one party has a burden of proof, which requires it to present prima facie evidence for all of the essential facts in its case. If it cannot, its claim may be dismissed without any need for a response by other parties. A prima facie case might not stand or fall on its own; if an opposing party introduces other evidence or asserts an affirmative defense, it can be reconciled only with a full trial.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "and by Stanley P. Frankel in 1950 for the purpose of automatically solving linear systems on digital computers. Over-relaxation methods had been used before the work of Young and Frankel. An example is the method of Lewis Fry Richardson, and the methods developed by R. V. Southwell. However, these methods were designed for computation by human calculators, requiring some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. These aspects are discussed in the thesis of David M. Young Jr.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle, or extended ideal) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1993 book \"Information Coordination: The Management of Information Models, Systems, and Organizations\" Veryard gives a snapshot of the state of the art around these subjects. \"Maximizing the value of corporate data depends upon being able to manage information models both within and between businesses. A centralized information model is not appropriate for many organizations,\" Veryard explains.His book \"takes the approach that multiple information models exist and the differences and links between them have to be managed. Coordination is currently an area of both intensive theoretical speculation and of practical research and development. Information Coordination explains practical guidelines for information management, both from on-going research and from recent field experience with CASE tools and methods\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Only call packets from or destined to a phone serviced by the concentrator actually are processed by the concentrator \u2014 nonlocal phones' time slots just pass through the concentrator unchanged. If the concentrator malfunctions, a fail-safe relay connects the \"in\" wires to the \"out\" wires, and nonlocal phones detect no difference. The central switch periodically counts concentrators, and schedules maintenance, probably before users notice the failure. Concentrators for several hundred customers can be threaded on this loop like pearls. The interface between remote concentrators and their parent telephone switches has been standardised by ETSI as the V5 interface.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Considering even the simple case of exponentiation as a primitive recursive function, and that the composition of primitive recursive functions is primitive recursive, one can begin to see how quickly a primitive recursive function can grow. And any function that can be computed by a Turing machine in a running time bounded by a primitive recursive function is itself primitive recursive. So it is difficult to imagine a practical use for full \u03bc-recursion where primitive recursion will not do, especially since the former can be simulated by the latter up to exceedingly long running times. And in any case, Kurt G\u00f6del's first incompleteness theorem and the halting problem imply that there are while loops that always terminate but cannot be proven to do so; thus it is unavoidable that any requirement for a formal proof of termination must reduce the expressive power of a programming language. While we have shown that every loop that terminates has a variant, this does not mean that the well-foundedness of the loop iteration can be proven.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Abstract datatypes are structures of concrete datatypes, with a new name assigned. For example, a list of integers could be called integer_list. In object-oriented jargon, abstract datatypes are called classes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Even if they are uncorrelated, we cannot tell which factor corresponds to verbal intelligence and which corresponds to mathematical intelligence without an outside argument. The values of the loadings L {\\displaystyle L} , the averages \u03bc {\\displaystyle \\mu } , and the variances of the \"errors\" \u03b5 {\\displaystyle \\varepsilon } must be estimated given the observed data X {\\displaystyle X} and F {\\displaystyle F} (the assumption about the levels of the factors is fixed for a given F {\\displaystyle F} ). The \"fundamental theorem\" may be derived from the above conditions: \u2211 i z a i z b i = \u2211 j \u2113 a j \u2113 b j + \u2211 i \u03b5 a i \u03b5 b i {\\displaystyle \\sum _{i}z_{ai}z_{bi}=\\sum _{j}\\ell _{aj}\\ell _{bj}+\\sum _{i}\\varepsilon _{ai}\\varepsilon _{bi}} The term on the left is the ( a , b ) {\\displaystyle (a,b)} -term of the correlation matrix (a p \u00d7 p {\\displaystyle p\\times p} matrix derived as the product of the p \u00d7 N {\\displaystyle p\\times N} matrix of standardized observations with its transpose) of the observed data, and its p {\\displaystyle p} diagonal elements will be 1 {\\displaystyle 1} s. The second term on the right will be a diagonal matrix with terms less than unity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The equivalence class of a set A under this relation, then, consists of all those sets which have the same cardinality as A. There are two ways to define the \"cardinality of a set\": The cardinality of a set A is defined as its equivalence class under equinumerosity. A representative set is designated for each equivalence class.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible. A bottleneck edge is the highest weighted edge in a spanning tree. A spanning tree is a minimum bottleneck spanning tree if the graph does not contain a spanning tree with a smaller bottleneck edge weight. For a directed graph, a similar problem is known as Minimum Bottleneck Spanning Arborescence (MBSA).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, a service switching point (SSP) is the telephone exchange that initially responds, when a telephone caller dials a number, by sending a query to a central database called a service control point (SCP) so that the call can be handled. The service switching point uses the Signalling System No. 7 (SS7) protocols which are responsible for the call setup, management, and termination with other service switching points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and statistics, the arithmetic mean ( arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context is clear) is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a survey. The term \"arithmetic mean\" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic. In addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology, history, and almost every academic field to some extent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Clustering of machines and parts is one of the most popular production flow analysis methods. The algorithms for machine part grouping include Rank Order Clustering, Modified Rank Order Clustering, and Similarity coefficients. There are also a number of mathematical models and algorithms to aid in planning a cellular manufacturing center, which take into account a variety of important variables such as, \"multiple plant locations, multi-market allocations with production planning and various part mix.\" Once these variables are determined with a given level of uncertainty, optimizations can be performed to minimize factors such as, \"total cost of holding, inter-cell material handling, external transportation, fixed cost for producing each part in each plant, machine and labor salaries.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some data exfiltration scenarios, a large amount of aggregated data may be exfiltrated. However, in these and other scenarios, it is likely that certain types of data may be targeted. Types of data that are targeted includes: Usernames, associated passwords, and other system authentication related information Information associated with strategic decisions Cryptographic keys Personal financial information Social security numbers and other personally identifiable information (PII) Mailing addresses United States National Security Agency hacking tools", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s, theoretical research in computer science on regular expressions and finite automata led to the discovery that context-free grammars are equivalent to nondeterministic pushdown automata. These grammars were thought to capture the syntax of computer programming languages. The first high-level computer programming languages were under development at the time (see History of programming languages) and writing compilers was difficult. But using context-free grammars to help automate the parsing part of the compiler simplified the task.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example is the subgroup of invertible 2 \u00d7 2 integer matrices of determinant 1 in which the off-diagonal entries are even. More generally, the notion of congruence subgroup can be defined for arithmetic subgroups of algebraic groups; that is, those for which we have a notion of 'integral structure' and can define reduction maps modulo an integer. The existence of congruence subgroups in an arithmetic group provides it with a wealth of subgroups, in particular it shows that the group is residually finite. An important question regarding the algebraic structure of arithmetic groups is the congruence subgroup problem, which asks whether all subgroups of finite index are essentially congruence subgroups. Congruence subgroups of 2\u00d72 matrices are fundamental objects in the classical theory of modular forms; the modern theory of automorphic forms makes a similar use of congruence subgroups in more general arithmetic groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a self-descriptive number is an integer m that in a given base b is b digits long in which each digit d at position n (the most significant digit being at position 0 and the least significant at position b\u22121) counts how many instances of digit n are in m.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music theory, an inversion is a type of change to intervals, chords, voices (in counterpoint), and melodies. In each of these cases, \"inversion\" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is not a cogent and simple way. It is claimed to be precise, but precise for what purpose?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a software development process is a process of planning and managing software development. It typically involves dividing software development work into smaller, parallel, or sequential steps or sub-processes to improve design and/or product management. It is also known as a software development life cycle (SDLC).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software, a stack buffer overflow or stack buffer overrun occurs when a program writes to a memory address on the program's call stack outside of the intended data structure, which is usually a fixed-length buffer. Stack buffer overflow bugs are caused when a program writes more data to a buffer located on the stack than what is actually allocated for that buffer. This almost always results in corruption of adjacent data on the stack, and in cases where the overflow was triggered by mistake, will often cause the program to crash or operate incorrectly. Stack buffer overflow is a type of the more general programming malfunction known as buffer overflow (or buffer overrun).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to formulate a classical field theory, the following structures are needed:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The classes in a class diagram represent both the main elements, interactions in the application, and the classes to be programmed. In the diagram, classes are represented with boxes that contain three compartments: The top compartment contains the name of the class. It is printed in bold and centered, and the first letter is capitalized.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The algorithm performs a series of iterations, each consisting of two basic steps: Authority update: Update each node's authority score to be equal to the sum of the hub scores of each node that points to it. That is, a node is given a high authority score by being linked from pages that are recognized as Hubs for information. Hub update: Update each node's hub score to be equal to the sum of the authority scores of each node that it points to.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term generalized inverse is sometimes used as a synonym for pseudoinverse. A common use of the pseudoinverse is to compute a \"best fit\" (least squares) solution to a system of linear equations that lacks a solution (see below under \u00a7 Applications). Another use is to find the minimum (Euclidean) norm solution to a system of linear equations with multiple solutions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the absence of interference, there are two factors at play when recalling a list of items: the recency and the primacy effects. The recency effect occurs when the short-term memory is used to remember the most recent items, and the primacy effect occurs when the long-term memory has encoded the earlier items. The recency effect can be eliminated if there is a period of interference between the input and the output of information extending longer than the holding time of short-term memory (15\u201330 seconds). This occurs when a person is given subsequent information to recall preceding the recall of the initial information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The trade secret law varies from country to country, unlike the case for patents, trademarks and copyright for which there are formal conventions through which subscribing countries grant the same protection to the property as the others; examples of which are the Paris Convention for the Protection of Industrial Property and the World Intellectual Property Organization (WIPO), under United Nations, a supportive organization designed \"to encourage creative activity,  to promote the protection of intellectual property throughout the world\". The World Trade Organization defined a trade secret by the following criteria: Natural and legal persons shall have the possibility of preventing information lawfully within their control from being disclosed to, acquired by, or used by others without their consent in a manner contrary to honest commercial practices (10) so long as such information: (a) is secret in the sense that it is not, as a body or in the precise configuration and assembly of its components, generally known among or readily accessible to persons within the circles that normally deal with the kind of information in question; (b) has commercial value because it is secret; and (c) has been subject to reasonable steps under the circumstances, by the person lawfully in control of the information, to keep it secret. For purposes of illustration, the following may be a provision in a license agreement serving to define know-how:- Know-how shall mean technical data, formulas, standards, technical information, specifications, processes, methods, codebooks, raw materials, as well as all information, knowledge, assistance, trade practices and secrets, and improvements thereto, divulged, disclosed, or in any way communicated to the Licensee under this Agreement, unless such information was, at the time of disclosure, or thereafter becomes part of the general knowledge or literature which is generally available for public use from other lawful sources. The burden of proving that any information disclosed hereunder is not confidential information shall rest on the licensee.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, many authors qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them. In this context, statements become well-formed formulas of some formal language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Rack (1984 and 2013), for the case n = 3, the explicit values of the optimal (unique and zero-symmetric) 4 interpolation nodes and the explicit value of the minimal Lebesgue constant are known. All arbitrary optimal sets of 4 interpolation nodes in  when n = 3 have been explicitly determined, in two different but equivalent fashions, by H.-J. Rack and R. Vajda (2015). The Padua points provide another set of nodes with slow growth (although not as slow as the Chebyshev nodes) and with the additional property of being a unisolvent point set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While Principles of Operation discusses the TLB in general terms, the details are not part of the architecture and vary from model to model. Starting with the 3031, 3032, and 3033 processor complexes, IBM offered a feature called Dual-address Space: 5-13\u20135-17, Dual-Address-Space Control: 5-17\u20135-20, DAS Authorization Mechanisms: 5-21\u20135-24, PC-Number Translation (DAS), which allows a program to switch between the translation tables for two address spaces, referred to as primary address space (CR1) and secondary address space (CR7), and to move data between the address spaces subject to protection key. DAS supports a translation table to convert a 16-bit address space number (ASN) to an STD, with privileged instructions to load the STD into CR1 (primary) or CR7 (secondary).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "10 consecutive 0 bits followed by a 1 bit provide frame synchronization.One frame is sent at the desired sample rate, for a bit rate of 256\u00d748 kHz = 12.288 Mbit/s. This is twice the baud rate used by S/PDIF (3.072 Mbit/s, doubled by biphase coding to 6.144 MBd), but still within the specified 15 Mbaud capacity of the popular TOTX147 /TORX147  TOSLINK transceivers. User data bit allocations: User bit 0 is designated for Timecode transport User bit 1 is designated for MIDI data transport User bit 2 is designated for S/Mux indication (96 kHz sample rate mode) User bit 3 is reserved and set to 0The transmission speed of the user bits is equal to the sampling rate (e.g. 48,000 bits per second)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics texts it is customary to denote permutations using lowercase Greek letters. Commonly, either \u03b1 {\\displaystyle \\alpha } and \u03b2 , {\\displaystyle \\beta ,} or \u03c3 , \u03c4 {\\displaystyle \\sigma ,\\tau } and \u03c0 {\\displaystyle \\pi } are used.Permutations can be defined as bijections from a set S onto itself. All permutations of a set with n elements form a symmetric group, denoted S n {\\displaystyle S_{n}} , where the group operation is function composition. Thus for two permutations, \u03c0 {\\displaystyle \\pi } and \u03c3 {\\displaystyle \\sigma } in the group S n {\\displaystyle S_{n}} , the four group axioms hold: Closure: If \u03c0 {\\displaystyle \\pi } and \u03c3 {\\displaystyle \\sigma } are in S n {\\displaystyle S_{n}} then so is \u03c0 \u03c3 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example, the vector p does not escape into g, so it can be allocated on the stack and then removed from the stack before calling g. If, however, we had then either p would need to be allocated on the heap or (if g is known to the compiler when f is compiled, and behaves well) allocated on the stack in such a fashion that it can remain in place when g is called. If continuations are used to implement exception-like control structures, escape analysis can often detect this to avoid having to actually allocate a continuation and copy the call stack into it. For example, in escape analysis will determine that the continuation captured by call/cc doesn't escape, so no continuation structure needs to be allocated, and invoking the continuation by calling continuation can be implemented by unwinding the stack.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In subtyping systems, the bottom type is a subtype of all types. It is dual to the top type, which spans all possible values in a system. If a type system is sound, the bottom type is uninhabited and a term of bottom type represents a logical contradiction. In such systems, typically no distinction is drawn between the bottom type and the empty type, and the terms may be used interchangeably.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite value known as Brun's constant, usually denoted by B2 (sequence A065421 in the OEIS). Brun's theorem was proved by Viggo Brun in 1919, and it has historical importance in the introduction of sieve methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That provides a clear and structured approach to the description of shared data and the coordination and communication between concurrent processes. This method is flexible in its ability to express timing, and can be used in different ways. In addition, path expressions are useful for process synchronization for two reasons: first, the close relationship between stream expressions and regular expressions that simplify the task of writing and reasoning about programs that use this synchronization mechanism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Bantu languages, attributive verbs are formed by the addition of the \"pre-prefix\" (or \"initial vowel\"). For example, in Luganda: Abasajja batambula \"The men walk\" (predicative) Abasajja abatambula \"The men who walk\" (attributive)This is similar to the behaviour of attributive adjectives: Abasajja bagagga \"The men are rich\" (predicative) Abasajja abagagga \"The men who are rich\" (i.e \"the rich men\") (attributive)The attributive verb formation is the usual way of forming relatives in Luganda when the antecedent is the subject of the subordinate verb, and is sometimes called the \"subject relative\". Relative pronouns do exist, but they are only used for \"object relatives\", i.e. relative clauses where the antecedent is the object of the subordinate verb.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, a synonym ring or synset, is a group of data elements that are considered semantically equivalent for the purposes of information retrieval. These data elements are frequently found in different metadata registries. Although a group of terms can be considered equivalent, metadata registries store the synonyms at a central location called the preferred data element. According to WordNet, a synset or synonym set is defined as a set of one or more synonyms that are interchangeable in some context without changing the truth value of the proposition in which they are embedded.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function f: R d \u2192 R {\\displaystyle f:\\mathbb {R} ^{d}\\rightarrow \\mathbb {R} } that for all x , y \u2208 R d {\\displaystyle x,y\\in \\mathbb {R} ^{d}} such that x {\\displaystyle x} is majorized by y {\\displaystyle y} , one has that f ( x ) \u2264 f ( y ) {\\displaystyle f(x)\\leq f(y)} . Named after Issai Schur, Schur-convex functions are used in the study of majorization. Every function that is convex and symmetric is also Schur-convex. The opposite implication is not true, but all Schur-convex functions are symmetric (under permutations of the arguments).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In UPSR, the data is transmitted in both directions, clock and counter clock wise, at the source ADM. At the destination then, both signals are compared and the best one of the two is selected. If a failure occurs then the destination just needs to switch to the unaffected path.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a basic exchange telecommunications radio service (BETRS) is a commercial service that can extend telephone service to rural areas by replacing the local loop with radio communications. In the BETRS, non-government ultra high frequency (UHF) and very high frequency (VHF) common carrier and the private radio service frequencies are shared.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Convergence is usually non-monotone, that is, neither the objective function nor the residual or gradient magnitude necessarily decrease with each iteration along a successful convergence toward the solution. If f {\\displaystyle f} is a quadratic function with Hessian A {\\displaystyle A} , 1 / \u03b1 L O N G {\\displaystyle 1/\\alpha ^{LONG}} is the Rayleigh quotient of A {\\displaystyle A} by vector \u0394 x {\\displaystyle \\Delta x} , and 1 / \u03b1 S H O R T {\\displaystyle 1/\\alpha ^{SHORT}} is the Rayleigh quotient of A {\\displaystyle A} by vector A \u0394 x {\\displaystyle {\\sqrt {A}}\\Delta x} (here taking A {\\displaystyle {\\sqrt {A}}} as a solution to ( A ) T A = A {\\displaystyle ({\\sqrt {A}})^{T}{\\sqrt {A}}=A} , more at Definite matrix). Fletcher compared its computational performance to conjugate gradient (CG) methods, finding CG tending faster for linear problems, but BB often faster for non-linear problems versus applicable CG-based methods. BB has low storage requirements, suitable for large systems with millions of elements in x {\\displaystyle x} . \u03b1 S H O R T \u03b1 L O N G = c o s 2 ( {\\displaystyle {\\frac {\\alpha ^{SHORT}}{\\alpha ^{LONG}}}=cos^{2}(} angle between \u0394 x {\\displaystyle \\Delta x} and \u0394 g ) {\\displaystyle \\Delta g)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The CP decomposition has found some applications in linguistics and chemometrics. The CP rank was introduced by Frank Lauren Hitchcock in 1927 and later rediscovered several times, notably in psychometrics. The CP decomposition is referred to as CANDECOMP, PARAFAC, or CANDECOMP/PARAFAC (CP). PARAFAC2 rank decomposition is yet to explore. Another popular generalization of the matrix SVD known as the higher-order singular value decomposition computes orthonormal mode matrices and has found applications in econometrics, signal processing, computer vision, computer graphics, psychometrics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\left(\\pm a^{\\frac {p+1}{4}}\\right)^{2}=a^{\\frac {p+1}{2}}=a\\cdot a^{\\frac {p-1}{2}}\\equiv a\\left({\\frac {a}{p}}\\right)=a{\\bmod {p}}.} This formula only works if it is known in advance that a {\\displaystyle a} is a quadratic residue, which can be checked using the law of quadratic reciprocity. The quadratic reciprocity theorem was conjectured by Euler and Legendre and first proved by Gauss, who referred to it as the \"fundamental theorem\" in his Disquisitiones Arithmeticae and his papers, writing The fundamental theorem must certainly be regarded as one of the most elegant of its type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical mathematics, artificial precision is a source of error that occurs when a numerical value or semantic is expressed with more precision than was initially provided from measurement or user input. For example, a person enters their birthday as the date 1984-01-01 but it is stored in a database as 1984-01-01T00:00:00Z which introduces the artificial precision of the hour, minute, and second they were born, and may even affect the date, depending on the user's actual place of birth. This is also an example of false precision, which is artificial precision specifically of numerical quantities or measures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bob proceeds to generate a string of random bits b \u2032 {\\displaystyle b'} of the same length as b {\\displaystyle b} and then measures the qubits he has received from Alice, obtaining a bit string a \u2032 {\\displaystyle a'} . At this point, Bob announces publicly that he has received Alice's transmission. Alice then knows she can now safely announce b {\\displaystyle b} , i.e., the bases in which the qubits were prepared.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, we can construct one specific rank factorization as follows: we can compute B {\\textstyle B} , the reduced row echelon form of A {\\textstyle A} . Then C {\\textstyle C} is obtained by removing from A {\\textstyle A} all non-pivot columns (which can be determined by looking for columns in B {\\textstyle B} which do not contain a pivot), and F {\\textstyle F} is obtained by eliminating any all-zero rows of B {\\textstyle B} . Note: For a full-rank square matrix (i.e. when n = m = r {\\textstyle n=m=r} ), this procedure will yield the trivial result C = A {\\textstyle C=A} and F = B = I n {\\textstyle F=B=I_{n}} (the n \u00d7 n {\\textstyle n\\times n} identity matrix).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Unicode standard, a plane is a continuous group of 65,536 (216) code points. There are 17 planes, identified by the numbers 0 to 16, which corresponds with the possible values 00\u20131016 of the first two positions in six position hexadecimal format (U+hhhhhh). Plane 0 is the Basic Multilingual Plane (BMP), which contains most commonly used characters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The network does this by utilising the Authentication Center and is accomplished without transmitting the key directly. Every GSM phone contains a unique identifier (different from the phone number), called the International Mobile Equipment Identity (IMEI). This can be found by dialing *#06#. When a phone contacts the network, its IMEI may be checked against the Equipment Identity Register to locate stolen phones and facilitate monitoring.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Concretely, in a linear regression where the errors are identically distributed, the variability of residuals of inputs in the middle of the domain will be higher than the variability of residuals at the ends of the domain: linear regressions fit endpoints better than the middle. This is also reflected in the influence functions of various data points on the regression coefficients: endpoints have more influence. Thus to compare residuals at different inputs, one needs to adjust the residuals by the expected variability of residuals, which is called studentizing. This is particularly important in the case of detecting outliers, where the case in question is somehow different from the others in a dataset. For example, a large residual may be expected in the middle of the domain, but considered an outlier at the end of the domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These are set on objects by the higher-level storage systems that use the OSD for persistent storage. For example, attributes might be used to classify objects, or to capture relationships among different objects stored on different OSDs. A list command returns a list of identifiers for objects within a partition, optionally filtered by matches against their attribute values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, we have n kinds of items, a 1 {\\displaystyle a_{1}} through a n {\\displaystyle a_{n}} and m kinds of bins b 1 {\\displaystyle b_{1}} through b m {\\displaystyle b_{m}} . Each bin b i {\\displaystyle b_{i}} is associated with a budget t i {\\displaystyle t_{i}} . For a bin b i {\\displaystyle b_{i}} , each item a j {\\displaystyle a_{j}} has a profit p i j {\\displaystyle p_{ij}} and a weight w i j {\\displaystyle w_{ij}} . A solution is an assignment from items to bins.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "OpenSocial Markup Language (OSML Markup) is a new set of standardized tags to accomplish common tasks or safely perform normally unsafe operations within templates. OSML is extensible. Developers can create a library of their own custom tags.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are two ways to give consent: explicit consent or implied consent. Explicit consent is when a patient clearly communicates to a healthcare worker, verbally or in writing or in some other way, that relevant confidential information can be shared. Implied consent, means that a patient's consent to share personal confidential information is assumed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Subsequences can contain consecutive elements which were not consecutive in the original sequence. A subsequence which consists of a consecutive run of elements from the original sequence, such as \u27e8 B , C , D \u27e9 , {\\displaystyle \\langle B,C,D\\rangle ,} from \u27e8 A , B , C , D , E , F \u27e9 , {\\displaystyle \\langle A,B,C,D,E,F\\rangle ,} is a substring. The substring is a refinement of the subsequence. The list of all subsequences for the word \"apple\" would be \"a\", \"ap\", \"al\", \"ae\", \"app\", \"apl\", \"ape\", \"ale\", \"appl\", \"appe\", \"aple\", \"apple\", \"p\", \"pp\", \"pl\", \"pe\", \"ppl\", \"ppe\", \"ple\", \"pple\", \"l\", \"le\", \"e\", \"\" (empty string).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of integrating supplemental data source, KG(Knowledge graph) formally represents the meaning involved in information by describing concepts, relationships between things, and categories of things. These embedded semantics with the data offer significant advantages such as reasoning over data and dealing with heterogeneous data sources. The rules can be applied on KG more efficiently using graph query.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Chinese hypothesis is a disproven conjecture stating that an integer n is prime if and only if it satisfies the condition that 2 n \u2212 2 {\\displaystyle 2^{n}-2} is divisible by n\u2014in other words, that an integer n is prime if and only if 2 n \u2261 2 mod n {\\displaystyle 2^{n}\\equiv 2{\\bmod {n}}} . It is true that if n is prime, then 2 n \u2261 2 mod n {\\displaystyle 2^{n}\\equiv 2{\\bmod {n}}} (this is a special case of Fermat's little theorem), however the converse (if 2 n \u2261 2 mod n {\\displaystyle 2^{n}\\equiv 2{\\bmod {n}}} then n is prime) is false, and therefore the hypothesis as a whole is false. The smallest counterexample is n = 341 = 11\u00d731. Composite numbers n for which 2 n \u2212 2 {\\displaystyle 2^{n}-2} is divisible by n are called Poulet numbers. They are a special class of Fermat pseudoprimes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Now if the domain is a set, the function comprehension principle, also called axiom of unique choice or non-choice, says that a function as a set, with some codomain, exists well. (And this principle is valid in a theory like C Z F {\\displaystyle {\\mathsf {CZF}}} . Also compare with the Replacement axiom.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1912, British engineer Arthur Pollen developed the first electrically powered mechanical analogue computer (called at the time the Argo Clock). It was used by the Imperial Russian Navy in World War I. The alternative Dreyer Table fire control system was fitted to British capital ships by mid-1916. Mechanical devices were also used to aid the accuracy of aerial bombing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In robot motion planning, a Pfaffian constraint is a set of k linearly independent constraints linear in velocity, i.e., of the form One source of Pfaffian constraints is rolling without slipping in wheeled robots. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a relative scalar (of weight w) is a scalar-valued function whose transform under a coordinate transform, on an n-dimensional manifold obeys the following equation where that is, the determinant of the Jacobian of the transformation. A scalar density refers to the w = 1 {\\displaystyle w=1} case. Relative scalars are an important special case of the more general concept of a relative tensor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1969 Frank DeRemer invented the LALR and Simple LR parsers, both based on the LR parser and having greatly reduced memory requirements at the cost of less language recognition power. The LALR parser was the stronger alternative. These two parsers have since been widely used in compilers of many computer languages. Recent research has identified methods by which canonical LR parsers may be implemented with dramatically reduced table requirements over Knuth's table-building algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Branching processes can also be used to model other systems with similar dynamics, e.g., the spread of surnames in genealogy or the propagation of neutrons in a nuclear reactor. A central question in the theory of branching processes is the probability of ultimate extinction, where no individuals exist after some finite number of generations. Using Wald's equation, it can be shown that starting with one individual in generation zero, the expected size of generation n equals \u03bcn where \u03bc is the expected number of children of each individual.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a translation plane is a projective plane which admits a certain group of symmetries (described below). Along with the Hughes planes and the Figueroa planes, translation planes are among the most well-studied of the known non-Desarguesian planes, and the vast majority of known non-Desarguesian planes are either translation planes, or can be obtained from a translation plane via successive iterations of dualization and/or derivation.In a projective plane, let P represent a point, and l represent a line. A central collineation with center P and axis l is a collineation fixing every point on l and every line through P. It is called an elation if P is on l, otherwise it is called a homology. The central collineations with center P and axis l form a group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments into evaluating a sequence of functions, each with a single argument. For example, currying a function f {\\displaystyle f} that takes three arguments creates a nested unary function g {\\displaystyle g} , so that the code let x = f ( a , b , c ) {\\displaystyle {\\text{let }}x=f(a,b,c)} gives x {\\displaystyle x} the same value as the code let h = g ( a ) let i = h ( b ) let x = i ( c ) , {\\displaystyle {\\begin{aligned}{\\text{let }}h=g(a)\\\\{\\text{let }}i=h(b)\\\\{\\text{let }}x=i(c),\\end{aligned}}} or called in sequence, let x = g ( a ) ( b ) ( c ) . {\\displaystyle {\\text{let }}x=g(a)(b)(c).} In a more mathematical language, a function that takes two arguments, one from X {\\displaystyle X} and one from Y {\\displaystyle Y} , and produces outputs in Z , {\\displaystyle Z,} by currying is translated into a function that takes a single argument from X {\\displaystyle X} and produces as outputs functions from Y {\\displaystyle Y} to Z .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In socio-hydrology, it is often assumed that societies build flood memory after extreme events. Flood memory is considered as a primary mechanism explaining the emergence of levee effects. It is hyphosised to be built after flooding and proportional to associated losses. Flood memory does decay over time. It is very difficult to observe, so proxy variable such as flood insurance coverage are used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". , k \u2212 1 {\\displaystyle 1,2,...,k-1} , find the best cover that does not violate the budget. Call this cover H 1 {\\displaystyle H_{1}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum mechanics, different possibilities can cancel. In probability theory with a finite number of states, the probabilities can always be multiplied by a positive number to make their sum equal to one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Germanic languages, a strong verb is a verb that marks its past tense by means of changes to the stem vowel. The majority of the remaining verbs form the past tense by means of a dental suffix, and are known as weak verbs. In modern English, strong verbs include sing (present I sing, past I sang, past participle I have sung) and drive (present I drive, past I drove, past participle I have driven), as opposed to weak verbs such as open (present I open, past I opened, past participle I have opened). Not all verbs with a change in the stem vowel are strong verbs, however; they may also be irregular weak verbs such as bring, brought, brought or keep, kept, kept.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Next is that the errors in behavior suggest internal plans for what will be done later. Also, the time to initiate a movement sequence can increase with the length or complexity of the sequence. The next line is the properties of movements occurring early in a sequence can anticipate later features.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in order theory, a maximal element of a subset S of some preordered set is an element of S that is not smaller than any other element in S. A minimal element of a subset S of some preordered set is defined dually as an element of S that is not greater than any other element in S. The notions of maximal and minimal elements are weaker than those of greatest element and least element which are also known, respectively, as maximum and minimum. The maximum of a subset S {\\displaystyle S} of a preordered set is an element of S {\\displaystyle S} which is greater than or equal to any other element of S , {\\displaystyle S,} and the minimum of S {\\displaystyle S} is again defined dually. In the particular case of a partially ordered set, while there can be at most one maximum and at most one minimum there may be multiple maximal or minimal elements. Specializing further to totally ordered sets, the notions of maximal element and maximum coincide, and the notions of minimal element and minimum coincide.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music theory, the scale degree is the position of a particular note on a scale relative to the tonic\u2014the first and main note of the scale from which each octave is assumed to begin. Degrees are useful for indicating the size of intervals and chords and whether an interval is major or minor. In the most general sense, the scale degree is the number given to each step of the scale, usually starting with 1 for tonic. Defining it like this implies that a tonic is specified.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, informally speaking, Euclid's orchard is an array of one-dimensional \"trees\" of unit height planted at the lattice points in one quadrant of a square lattice. More formally, Euclid's orchard is the set of line segments from (x, y, 0) to (x, y, 1), where x and y are positive integers. The trees visible from the origin are those at lattice points (x, y, 0), where x and y are coprime, i.e., where the fraction x/y is in reduced form. The name Euclid's orchard is derived from the Euclidean algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For this problem: Auletta, De Prisco, Penna and Persiano presented a 4-approximation monotone algorithm, which runs in polytime when the number of machines is fixed. Ambrosio and Auletta proved that the Longest Processing Time algorithm is monotone whenever the machine speeds are powers of some c \u2265 2, but not when c \u2264 1.78. In contrast, List scheduling is not monotone for c > 2. Andelman, Azar and Sorani presented a 5-approximation monotone algorithm, which runs in polytime even when the number of machines is variable. Kovacz presented a 3-approximation monotone algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first and second editions of A Dictionary of Modern English Usage Fowler uses the heading false scent to explain writing that causes the reader to second-guess: because the writer knows what is coming ahead, he may forget that his reader does not, and unwittingly \"lay false scent\" by writing something ambiguous that can only be disambiguated later in the text (for example \"I looked at the man with the telescope, and watched him put the telescope away\"). The reader, once he realises he has been distracted, must go back and rescan the sentence or paragraph to understand the writer's intended meaning. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can be compared with the classical discrete Fourier transform, which takes O ( n 2 n ) {\\displaystyle O(n2^{n})} gates (where n {\\displaystyle n} is the number of bits), which is exponentially more than O ( n 2 ) {\\displaystyle O(n^{2})} . The quantum Fourier transform acts on a quantum state vector (a quantum register), and the classical Fourier transform acts on a vector. Both types of vectors can be written as lists of complex numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for the conditions for atomic broadcast to be satisfied, the participants must effectively \"agree\" on the order of receipt of the messages. Participants recovering from failure, after the other participants have \"agreed\" an order and started to receive the messages, must be able to learn and comply with the agreed order. Such considerations indicate that in systems with crash failures, atomic broadcast and consensus are equivalent problems.A value can be proposed by a process for consensus by atomically broadcasting it, and a process can decide a value by selecting the value of the first message which it atomically receives. Thus, consensus can be reduced to atomic broadcast.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical finite group theory, a group of GF(2)-type is a group with an involution centralizer whose generalized Fitting subgroup is a group of symplectic type (Gorenstein 1982, definition 1.45). As the name suggests, many of the groups of Lie type over the field with 2 elements are groups of GF(2)-type. Also 16 of the 26 sporadic groups are of GF(2)-type, suggesting that in some sense sporadic groups are somehow related to special properties of the field with 2 elements. Timmesfeld (1978) showed roughly that groups of GF(2)-type can be subdivided into 8 types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory. Cutting plane methods for MILP work by solving a non-integer linear program, the linear relaxation of the given integer program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. Conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability without. If A {\\displaystyle A} is the hypothesis, and B {\\displaystyle B} and C {\\displaystyle C} are observations, conditional independence can be stated as an equality: P ( A \u2223 B , C ) = P ( A \u2223 C ) {\\displaystyle P(A\\mid B,C)=P(A\\mid C)} where P ( A \u2223 B , C ) {\\displaystyle P(A\\mid B,C)} is the probability of A {\\displaystyle A} given both B {\\displaystyle B} and C {\\displaystyle C} . Since the probability of A {\\displaystyle A} given C {\\displaystyle C} is the same as the probability of A {\\displaystyle A} given both B {\\displaystyle B} and C {\\displaystyle C} , this equality expresses that B {\\displaystyle B} contributes nothing to the certainty of A {\\displaystyle A} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a heavy traffic approximation (sometimes heavy traffic limit theorem or diffusion approximation) is the matching of a queueing model with a diffusion process under some limiting conditions on the model's parameters. The first such result was published by John Kingman who showed that when the utilisation parameter of an M/M/1 queue is near 1 a scaled version of the queue length process can be accurately approximated by a reflected Brownian motion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the basic SIP specification, only requests and final responses (i.e. 2XX response codes) are transmitted reliably, this is, they are retransmitted by the sender until the acknowledge message arrives (i.e. the corresponding response code to a request, or the ACK request corresponding to a 2XX response code). This mechanism is necessary since SIP can run not only over reliable transport protocols (TCP) that assure that the message is delivered, but also over unreliable ones (UDP) that offer no delivery guarantees, and it is even possible that both kinds of protocols are present in different parts of the transport network. However, in such an scenario as the IMS framework, it is necessary to extend this reliability to provisional responses to INVITE requests (for session establishment, this is, to start a call). The reliability of provisional responses extension provides a mechanism to confirm that provisional responses such as the 180 Ringing response code, that lets the caller know that the callee is being alerted, are successfully received.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two regularization parameters are used in this framework: \u03bb {\\displaystyle \\lambda } for the estimation of C ^ Y X \u03c0 , C ^ X X \u03c0 = \u03a5 D \u03a5 T {\\displaystyle {\\widehat {\\mathcal {C}}}_{YX}^{\\pi },{\\widehat {\\mathcal {C}}}_{XX}^{\\pi }={\\boldsymbol {\\Upsilon }}\\mathbf {D} {\\boldsymbol {\\Upsilon }}^{T}} and \u03bb ~ {\\displaystyle {\\widetilde {\\lambda }}} for the estimation of the final conditional embedding operator C ^ Y \u2223 X \u03c0 = C ^ Y X \u03c0 ( ( C ^ X X \u03c0 ) 2 + \u03bb ~ I ) \u2212 1 C ^ X X \u03c0 . {\\displaystyle {\\widehat {\\mathcal {C}}}_{Y\\mid X}^{\\pi }={\\widehat {\\mathcal {C}}}_{YX}^{\\pi }\\left(\\left({\\widehat {\\mathcal {C}}}_{XX}^{\\pi }\\right)^{2}+{\\widetilde {\\lambda }}\\mathbf {I} \\right)^{-1}{\\widehat {\\mathcal {C}}}_{XX}^{\\pi }.} The latter regularization is done on square of C ^ X X \u03c0 {\\displaystyle {\\widehat {\\mathcal {C}}}_{XX}^{\\pi }} because D {\\displaystyle D} may not be positive definite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in the opposite direction. These functors, and certain variants of them, are essential parts of sheaf theory. Due to their general nature and versatility, sheaves have several applications in topology and especially in algebraic and differential geometry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As an example, the greatest common divisor of 15 and 69 is 3, and 3 can be written as a combination of 15 and 69 as 3 = 15 \u00d7 (\u22129) + 69 \u00d7 2, with B\u00e9zout coefficients \u22129 and 2. Many other theorems in elementary number theory, such as Euclid's lemma or the Chinese remainder theorem, result from B\u00e9zout's identity. A B\u00e9zout domain is an integral domain in which B\u00e9zout's identity holds. In particular, B\u00e9zout's identity holds in principal ideal domains. Every theorem that results from B\u00e9zout's identity is thus true in all principal ideal domains.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other words, each quantifier is a family of properties on dom(A), so each is called a monadic quantifier. Any quantifier defined as an n > 0-ary relation between properties on dom(A) is called monadic. Lindstr\u00f6m introduced polyadic ones that are n > 0-ary relations between relations on domains of structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics in general, a characterization theorem says that a particular object \u2013 a function, a space, etc. \u2013 is the only one that possesses properties specified in the theorem. A characterization of a probability distribution accordingly states that it is the only probability distribution that satisfies specified conditions. More precisely, the model of characterization of probability distribution was described by V.M. Zolotarev in such manner.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While this allows non-standard interpretations of symbols such as + {\\displaystyle +} , one can restrict their meaning by providing additional axioms. The satisfiability modulo theories problem considers satisfiability of a formula with respect to a formal theory, which is a (finite or infinite) set of axioms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-relational systems, hierarchical databases, the distant counterpart of a table is a structured file, representing the rows of a table in each row of the file and each column in a row. This structure implies that a row can have repeating information, generally in the child data segments. Data are stored in sequence of physical records.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of retrieval systems, established approaches include: Data retrieval systems, such as database management systems, are well suitable for the storage and retrieval of structured data. Information retrieval systems, such as web search engines, are very effective in finding the relevant documents or web pages.Both approaches require a user to read and analyze often long lists of data sets or documents in order to extract meaning. The goal of knowledge retrieval systems is to reduce the burden of those processes by improved search and representation. This improvement is needed to leverage the increasing data volumes available on the Internet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most such devices include a tiny postage-stamp-sized LCD screen for viewing simplified ladder logic (only a very small portion of the program being visible at a given time) and status of I/O points, and typically these screens are accompanied by a 4-way rocker push-button plus four more separate push-buttons, similar to the key buttons on a VCR remote control, and used to navigate and edit the logic. Most have a small plug for connecting via RS-232 or RS-485 to a personal computer so that programmers can use simple applications in general-purpose OS like MS Windows, macOS or Linux, that have user-friendly (G)UIs, for programming instead of being forced to use the tiny LCD and push-button set for this purpose. Unlike regular PLCs that are usually modular and greatly expandable, the PLRs are usually not modular or expandable, but their price can be two orders of magnitude less than a PLC, and they still offer robust design and deterministic execution of the logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and geographic information science, a shortest-path graph is an undirected graph defined from a set of points in the Euclidean plane. The shortest-path graph is proposed with the idea of inferring edges between a point set such that the shortest path taken over the inferred edges will roughly align with the shortest path taken over the imprecise region represented by the point set. The edge set of the shortest-path graph varies based on a single parameter t \u2265 1. When the weight of an edge is defined as its Euclidean length raised to the power of the parameter t \u2265 1, the edge is present in the shortest-path graph if and only if it is the least weight path between its endpoints.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are also examples for which the minimal number of cells is doubly exponential, showing that every general algorithm for cylindrical algebraic decomposition has a double exponential complexity. CAD provides an effective version of quantifier elimination over the reals that has a much better computational complexity than that resulting from the original proof of Tarski\u2013Seidenberg theorem. It is efficient enough to be implemented on a computer. It is one of the most important algorithms of computational real algebraic geometry. Searching to improve Collins' algorithm, or to provide algorithms that have a better complexity for subproblems of general interest, is an active field of research.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\textstyle {\\frac {n!}{k!(n-k)!}}} whenever k \u2264 n {\\displaystyle k\\leq n} , and which is zero when k > n {\\displaystyle k>n} . This formula can be derived from the fact that each k-combination of a set S of n members has k !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, Wilson's theorem is useless as a primality test because computing (n \u2212 1)! modulo n for large n is computationally complex, and much faster primality tests are known (indeed, even trial division is considerably more efficient).Used in the other direction, to determine the primality of the successors of large factorials, it is indeed a very fast and effective method. This is of limited utility, however.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and in particular game theory, Sion's minimax theorem is a generalization of John von Neumann's minimax theorem, named after Maurice Sion. It states: Let X {\\displaystyle X} be a compact convex subset of a linear topological space and Y {\\displaystyle Y} a convex subset of a linear topological space. If f {\\displaystyle f} is a real-valued function on X \u00d7 Y {\\displaystyle X\\times Y} with f ( x , \u22c5 ) {\\displaystyle f(x,\\cdot )} upper semicontinuous and quasi-concave on Y {\\displaystyle Y} , \u2200 x \u2208 X {\\displaystyle \\forall x\\in X} , and f ( \u22c5 , y ) {\\displaystyle f(\\cdot ,y)} lower semicontinuous and quasi-convex on X {\\displaystyle X} , \u2200 y \u2208 Y {\\displaystyle \\forall y\\in Y} then, min x \u2208 X sup y \u2208 Y f ( x , y ) = sup y \u2208 Y min x \u2208 X f ( x , y ) . {\\displaystyle \\min _{x\\in X}\\sup _{y\\in Y}f(x,y)=\\sup _{y\\in Y}\\min _{x\\in X}f(x,y).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, #S is one possible notation for the cardinality or size of the set S, instead of | S | {\\displaystyle |S|} . That is, for a set S = { s 1 , s 2 , s 3 , \u2026 , s n } {\\displaystyle S=\\{s_{1},s_{2},s_{3},\\dots ,s_{n}\\}} , in which all s i {\\displaystyle s_{i}} are mutually distinct, # S = n = | S | . {\\displaystyle \\#S=n=|S|.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The same argument repeated (by symmetry of the problem) is valid when \u03c9 {\\displaystyle \\omega } starts with a negative rotation about the z axis, or a rotation about the x axis. This shows that if \u03c9 {\\displaystyle \\omega } is given by a non-trivial word in A and B, then \u03c9 \u2260 e {\\displaystyle \\omega \\neq e} . Therefore, the group H is a free group, isomorphic to F2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations A x = b {\\displaystyle A\\mathbf {x} =\\mathbf {b} } , the matrix A can be decomposed via the LU decomposition. The LU decomposition factorizes a matrix into a lower triangular matrix L and an upper triangular matrix U. The systems L ( U x ) = b {\\displaystyle L(U\\mathbf {x} )=\\mathbf {b} } and U x = L \u2212 1 b {\\displaystyle U\\mathbf {x} =L^{-1}\\mathbf {b} } require fewer additions and multiplications to solve, compared with the original system A x = b {\\displaystyle A\\mathbf {x} =\\mathbf {b} } , though one might require significantly more digits in inexact arithmetic such as floating point. Similarly, the QR decomposition expresses A as QR with Q an orthogonal matrix and R an upper triangular matrix. The system Q(Rx) = b is solved by Rx = QTb = c, and the system Rx = c is solved by 'back substitution'. The number of additions and multiplications required is about twice that of using the LU solver, but no more digits are required in inexact arithmetic because the QR decomposition is numerically stable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of network theory a scale-free ideal network is a random network with a degree distribution following the scale-free ideal gas density distribution. These networks are able to reproduce city-size distributions and electoral results by unraveling the size distribution of social groups with information theory on complex networks when a competitive cluster growth process is applied to the network. In models of scale-free ideal networks it is possible to demonstrate that Dunbar's number is the cause of the phenomenon known as the 'six degrees of separation'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Due to this superposition, measurement of the qubit will \"collapse\" it into one of its basis states with a given probability. Because of the entanglement, measurement of one qubit will \"collapse\" the other qubit to a state whose measurement will yield one of two possible values, where the value depends on which Bell's state the two qubits are in initially. Bell's states can be generalized to certain quantum states of multi-qubit systems, such as the GHZ state for 3 or more subsystems. Understanding of Bell's states is useful in analysis of quantum communication, such as superdense coding and quantum teleportation. The no-communication theorem prevents this behavior from transmitting information faster than the speed of light.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In contrast to the steady incremental improvements of the past few decades, the application of deep learning decreased word error rate by 30%. This innovation was quickly adopted across the field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metric graph theory, a convex subgraph of an undirected graph G is a subgraph that includes every shortest path in G between two of its vertices. Thus, it is analogous to the definition of a convex set in geometry, a set that contains the line segment between every pair of its points. Convex subgraphs play an important role in the theory of partial cubes and median graphs. In particular, in median graphs, the convex subgraphs have the Helly property: if a family of convex subgraphs has the property that all pairwise intersections are nonempty, then the whole family has a nonempty intersection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, a 64-bit microprocessor can address 16 EiB (16 \u00d7 10246 = 264 = 18,446,744,073,709,551,616 bytes, or about 18.4 exabytes) of memory. However, not all instruction sets, and not all processors implementing those instruction sets, support a full 64-bit virtual or physical address space. The x86-64 architecture (as of 2016) allows 48 bits for virtual memory and, for any given processor, up to 52 bits for physical memory. These limits allow memory sizes of 256 TiB (256 \u00d7 10244 bytes) and 4 PiB (4 \u00d7 10245 bytes), respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, pentation (or hyper-5) is the next hyperoperation after tetration and before hexation. It is defined as iterated (repeated) tetration (assuming right-associativity), just as tetration is iterated right-associative exponentiation. It is a binary operation defined with two numbers a and b, where a is tetrated to itself b-1 times. For instance, using hyperoperation notation for pentation and tetration, 2  3 {\\displaystyle 23} means tetrating 2 to itself 2 times, or 2  ( 2  2 ) {\\displaystyle 2(22)} . This can then be reduced to 2  ( 2 2 ) = 2  4 = 2 2 2 2 = 2 2 4 = 2 16 = 65 , 536. {\\displaystyle 2(2^{2})=24=2^{2^{2^{2}}}=2^{2^{4}}=2^{16}=65,536.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociology, command hierarchy is seen as the most visible element of a \"power network.\" In this model, social capital is viewed as being mobilized in response to orders that move through the hierarchy leading to the phrase \"command and control\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Later it was demonstrated that all basic mathematical structures either are some kinds of named sets or are built of named sets. According to Anellis, Burgin & Kaloujnine introduced set-theoretical named sets in 1983 and Burgin introduced named sets in the most general form in 1990. Since then Burgin continued to develop this theory in a series of papers and a book. In 2011, Zellweger applied the theory of named sets to model data relations in the relational database for an end-user interface.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this agrees with the intuitive notion of number of elements. In the case of infinite sets, the behavior is more complex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of modern algebra known as group theory, the Suzuki groups, denoted by Sz(22n+1), 2B2(22n+1), Suz(22n+1), or G(22n+1), form an infinite family of groups of Lie type found by Suzuki (1960), that are simple for n \u2265 1. These simple groups are the only finite non-abelian ones with orders not divisible by 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This eliminates noncredible threats, which are threats that a player would not carry out if they were ever called upon to do so. For example, consider a dynamic game with an incumbent firm and a potential entrant to the industry. The incumbent has a monopoly and wants to maintain its market share.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nonstandard analysis, a branch of mathematics, overspill (referred to as overflow by Goldblatt (1998, p. 129)) is a widely used proof technique. It is based on the fact that the set of standard natural numbers N is not an internal subset of the internal set *N of hypernatural numbers. By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction: For any internal subset A of *N, if 1 is an element of A, and for every element n of A, n + 1 also belongs to A,then A = *NIf N were an internal set, then instantiating the internal induction principle with N, it would follow N = *N which is known not to be the case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this case, the voting circuit can output the correct result, and discard the erroneous version. After this, the internal state of the erroneous replication is assumed to be different from that of the other two, and the voting circuit can switch to a DMR mode. This model can be applied to any larger number of replications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, binary data is a statistical data type consisting of categorical data that can take exactly two possible values, such as \"A\" and \"B\", or \"heads\" and \"tails\". It is also called dichotomous data, and an older term is quantal data. The two values are often referred to generically as \"success\" and \"failure\". As a form of categorical data, binary data is nominal data, meaning the values are qualitatively different and cannot be compared numerically.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network theory, the Wiener connector is a means of maximizing efficiency in connecting specified \"query vertices\" in a network. Given a connected, undirected graph and a set of query vertices in a graph, the minimum Wiener connector is an induced subgraph that connects the query vertices and minimizes the sum of shortest path distances among all pairs of vertices in the subgraph. In combinatorial optimization, the minimum Wiener connector problem is the problem of finding the minimum Wiener connector. It can be thought of as a version of the classic Steiner tree problem (one of Karp's 21 NP-complete problems), where instead of minimizing the size of the tree, the objective is to minimize the distances in the subgraph.The minimum Wiener connector was first presented by Ruchansky et al. in 2015.The minimum Wiener connector has applications in many domains where there is a graph structure and an interest in learning about connections between sets of individuals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Early scrambling or encryption methods required a hard line for authorization of receive sites. Today, a digital cellular telephone is sufficient for most situations. C-Band transportable service remains a prevalent source of long-haul transmission because of its immunity to the \"rain fade\" that Ku band experiences in significant rainstorms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, there can be more than one such code for a given word length, but the term Gray code was first applied to a particular binary code for non-negative integers, the binary-reflected Gray code, or BRGC. Bell Labs researcher George R. Stibitz described such a code in a 1941 patent application, granted in 1943. Frank Gray introduced the term reflected binary code in his 1947 patent application, remarking that the code had \"as yet no recognized name\". He derived the name from the fact that it \"may be built up from the conventional binary code by a sort of reflection process\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a surjective function (also known as surjection, or onto function ) is a function f such that every element y can be mapped from some element x such that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y. The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The French word sur means over or above, and relates to the fact that the image of the domain of a surjective function completely covers the function's codomain. Any function induces a surjection by restricting its codomain to the image of its domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , n } \u2192 { 0 , 1 } {\\displaystyle f:\\{0,1,...,n\\}\\rightarrow \\{0,1\\}} . Symmetric Boolean functions are used to classify Boolean satisfiability problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the areas of group theory and combinatorics, Hall words provide a unique monoid factorisation of the free monoid. They are also totally ordered, and thus provide a total order on the monoid. This is analogous to the better-known case of Lyndon words; in fact, the Lyndon words are a special case, and almost all properties possessed by Lyndon words carry over to Hall words. Hall words are in one-to-one correspondence with Hall trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As told by Hardy: I remember once going to see him  when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. \"No,\" he replied, \"it is a very interesting number; it is the smallest number expressible as the sum of two  cubes in two different ways.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system. The concept of a test particle often simplifies problems, and can provide a good approximation for physical phenomena. In addition to its uses in the simplification of the dynamics of a system in particular limits, it is also used as a diagnostic in computer simulations of physical processes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Kernel adaptive filters implement a nonlinear transfer function using kernel methods. In these methods, the signal is mapped to a high-dimensional linear feature space and a nonlinear function is approximated as a sum over kernels, whose domain is the feature space. If this is done in a reproducing kernel Hilbert space, a kernel method can be a universal approximator for a nonlinear function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A semigroup without an identity element can be easily turned into a monoid by just adding an identity element. Consequently, monoids are studied in the theory of semigroups rather than in group theory. Semigroups should not be confused with quasigroups, which are a generalization of groups in a different direction; the operation in a quasigroup need not be associative but quasigroups preserve from groups a notion of division.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, probabilistic metric spaces are a generalization of metric spaces where the distance no longer takes values in the non-negative real numbers R \u2265 0, but in distribution functions.Let D+ be the set of all probability distribution functions F such that F(0) = 0 (F is a nondecreasing, left continuous mapping from R into  such that max(F) = 1). Then given a non-empty set S and a function F: S \u00d7 S \u2192 D+ where we denote F(p, q) by Fp,q for every (p, q) \u2208 S \u00d7 S, the ordered pair (S, F) is said to be a probabilistic metric space if: For all u and v in S, u = v if and only if Fu,v(x) = 1 for all x > 0. For all u and v in S, Fu,v = Fv,u. For all u, v and w in S, Fu,v(x) = 1 and Fv,w(y) = 1 \u21d2 Fu,w(x + y) = 1 for x, y > 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern news, social media has become a major source of amateur reporting. The Arab Spring is believed to have been aided by citizen journalism that was reported using and disseminated by Facebook and Twitter. The Top 15 Most Popular Social Media Sites range from 15 million users to 900 million users, and as their user base grows stronger, amateur reporting's base expands as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, this problem arises when we attempt to build a so-called RASP, a \"universal machine\" (see more at Universal Turing machine) that uses its finite-state machine to interpret a \"program of instructions\" located in its registers \u2013 i.e. we are building what is nowadays called a computer with the von Neumann architecture.Observe that the counter machine's finite state machine must call out a register explicitly (directly) by its name/number: INC (65,356) calls out register number \"65,365\" explicitly. If the number of registers exceeds the capability of the finite state machine to address them, then registers outside the bounds will be unreachable. For example, if the finite state machine can only reach 65,536 = 216 registers then how can it reach the 65,537th?So how do we address a register beyond the bounds of the finite state machine?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to achieve a precise and effective typestate analysis, it is necessary to address the problem of aliasing. Aliasing occurs when an object has more than one reference or pointer that points to it. For the analysis to be correct, state changes to a given object must be reflected in all references that point to that object, but in general it is a difficult problem to track all such references. This becomes especially hard if the analysis needs to be modular, that is, applicable to each part of a large program separately without taking the rest of the program into account.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Coordinating Committee admitted that they \"wrestled with articulating a business case for implementing RDA\", nevertheless the report recommended that RDA be adopted by the three national libraries, contingent on several improvements being made. The earliest possible date for implementation was given as January 2013, as the consensus emerging from the analysis of the test data showed that while there were discernible benefits to implementing RDA, these benefits would not be realized without further changes to current cataloging practices, including developing a successor to the MARC format.Several other institutions were involved in the RDA test. Many of these institutions documented their findings in a special issue of Cataloging & Classification Quarterly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In supervised learning, a random sub-sample of all records is taken and manually classified as either 'fraudulent' or 'non-fraudulent' (task can be decomposed on more classes to meet algorithm requirements). Relatively rare events such as fraud may need to be over sampled to get a big enough sample size. These manually classified records are then used to train a supervised machine learning algorithm. After building a model using this training data, the algorithm should be able to classify new records as either fraudulent or non-fraudulent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the cellular phone industry, mobile phones and their networks sometimes support concatenated short message service (or concatenated SMS) to overcome the limitation on the number of characters that can be sent in a single SMS text message transmission (which is usually 160). Using this method, long messages are split into smaller messages by the sending device and recombined at the receiving end. Each message is then billed separately.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, functions are identified with their function graphs. Using set builder notation, a collection of pairs may be characterized, f := { \u27e8 x , y \u27e9 \u2223 x \u2208 A \u2227 \u03c8 ( x , y ) } . {\\displaystyle f:={\\big \\{}\\langle x,y\\rangle \\mid x\\in A\\land \\psi (x,y){\\big \\}}.} The axiom of replacement in Zermelo\u2013Fraenkel set theory implies that this is actually a set and a function in the above sense.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This notation has been retained in operating systems that were directly or indirectly derived from CP/M, including DR-DOS, MS-DOS, OS/2 and Windows. On Linux systems, the command hexcat produces this classic output format too.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fields of databases and transaction processing (transaction management), a schedule (or history) of a system is an abstract model to describe execution of transactions running in the system. Often it is a list of operations (actions) ordered by time, performed by a set of transactions that are executed together in the system. If the order in time between certain operations is not determined by the system, then a partial order is used. Examples of such operations are requesting a read operation, reading, writing, aborting, committing, requesting a lock, locking, etc. Not all transaction operation types should be included in a schedule, and typically only selected operation types (e.g., data access operations) are included, as needed to reason about and describe certain phenomena. Schedules and schedule properties are fundamental concepts in database concurrency control theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order of increasing strength, i.e., decreasing sets of pairs, three of the possible partial orders on the Cartesian product of two partially ordered sets are (see Fig.4): the lexicographical order: (a, b) \u2264 (c, d) if a < c or (a = c and b \u2264 d); the product order: (a, b) \u2264 (c, d) if a \u2264 c and b \u2264 d; the reflexive closure of the direct product of the corresponding strict orders: (a, b) \u2264 (c, d) if (a < c and b < d) or (a = c and b = d).All three can similarly be defined for the Cartesian product of more than two sets. Applied to ordered vector spaces over the same field, the result is in each case also an ordered vector space. See also orders on the Cartesian product of totally ordered sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in functional analysis and topology, closed graph is a property of functions. A function f: X \u2192 Y between topological spaces has a closed graph if its graph is a closed subset of the product space X \u00d7 Y. A related property is open graph.This property is studied because there are many theorems, known as closed graph theorems, giving conditions under which a function with a closed graph is necessarily continuous. One particularly well-known class of closed graph theorems are the closed graph theorems in functional analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Attack - An attempt by a player to win a point by hitting the ball over the net. Attack line - In indoor volleyball, a line three metres from the net which marks the limit for where a back-row player may advance to hit a ball from above the net. Back-row player - In indoor volleyball, any of three players positioned at the back of the court.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Army used in for tactical group messaging in its Force Battle Command Brigade and Below (FBCB2) system.Several other approaches to reliable multicast were being developed at approximately the same time, and in April 1999, the IETF chartered the Reliable Multicast Transport Working Group (RMTWG) to standardize reliable multicast transport.The RMTWG pursued the strategy of developing building blocks and protocol instantiations. This strategy avoided a \"one size fits all\" protocol, which in turn could accommodate the large number of applications and types of applications that reliable multicast could support. Building blocks were defined as \u201ca set of easily-separable coarse-grained modular components that are common to multiple protocols along with abstract APIs that define a building block's access methods and their arguments.\u201d Initial building blocks included negative acknowledgments, forward error correction, a generic signaling mechanism for router assist, and transport protection Protocol instantiations were defined as \u201cspecifications that define the necessary gluing logic and minimal additional functionality required to realize a working protocol from one or more building blocks.\u201d Those specifications would also include an abstract API that defined the interface between the protocol implementation and an application. Two protocol instantiations were chosen: A NACK-based protocol An Asynchronous Layered Coding protocolIn July 2005 the NACK-based protocol building blocks and protocol instantiation were submitted as \u201cExperimental\u201d in RFC 3940, and in November 2009 \u201cNACK-Oriented Reliable Multicast (NORM) Transport Protocol\u201d was approved in RFC 5740.The RMTWG was disestablished in September 2013.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, Student's t-distribution (or simply the t-distribution) t \u03bd {\\displaystyle t_{\\nu }} is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, t \u03bd {\\displaystyle t_{\\nu }} has heavier tails and the amount of probability mass in the tails is controlled by the parameter \u03bd {\\displaystyle \\nu } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Fermat quotient of an integer a with respect to an odd prime p is defined as q p ( a ) = a p \u2212 1 \u2212 1 p , {\\displaystyle q_{p}(a)={\\frac {a^{p-1}-1}{p}},} or \u03b4 p ( a ) = a \u2212 a p p {\\displaystyle \\delta _{p}(a)={\\frac {a-a^{p}}{p}}} .This article is about the former; for the latter see p-derivation. The quotient is named after Pierre de Fermat. If the base a is coprime to the exponent p then Fermat's little theorem says that qp(a) will be an integer. If the base a is also a generator of the multiplicative group of integers modulo p, then qp(a) will be a cyclic number, and p will be a full reptend prime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The challenge is to reduce the number of colors from n to, e.g., \u0394 + 1. The more colors are employed, e.g. O(\u0394) instead of \u0394 + 1, the fewer communication rounds are required.A straightforward distributed version of the greedy algorithm for (\u0394 + 1)-coloring requires \u0398(n) communication rounds in the worst case \u2212 information may need to be propagated from one side of the network to another side. The simplest interesting case is an n-cycle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1993 film Jurassic Park, Connection Machines (non-functioning dummies) are visible in the park's control room, programmer Dennis Nedry mentions \"eight Connection Machines\" and a video about dinosaur cloning mentions \"Thinking Machines supercomputers\". In the 1996 film Mission Impossible, Luther Stickell asks Franz Krieger for \"Thinking Machine laptops\" to help hack into the CIA's Langley supercomputer.Tom Clancy's novel Rainbow Six speaks of the NSA's \"star machine from a company gone bankrupt, the Super-Connector from Thinking Machines, Inc., of Cambridge, Massachusetts\" in the NSA's basement. In addition, in The Bear and the Dragon says the National Security Agency could crack nearly any book or cipher with one of three custom operating systems designed for a Thinking Machines supercomputer. In the 2008 video game Fallout 3, it is mentioned that the pre-war firm that made the computer systems for Vaults is called Think Machine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, the cardinality of the continuum is the cardinality or \"size\" of the set of real numbers R {\\displaystyle \\mathbb {R} } , sometimes called the continuum. It is an infinite cardinal number and is denoted by c {\\displaystyle {\\mathfrak {c}}} (lowercase Fraktur \"c\") or | R | {\\displaystyle |\\mathbb {R} |} .The real numbers R {\\displaystyle \\mathbb {R} } are more numerous than the natural numbers N {\\displaystyle \\mathbb {N} } . Moreover, R {\\displaystyle \\mathbb {R} } has the same number of elements as the power set of N . {\\displaystyle \\mathbb {N} .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a G\u00f6del numbering for sequences provides an effective way to represent each finite sequence of natural numbers as a single natural number. While a set theoretical embedding is surely possible, the emphasis is on the effectiveness of the functions manipulating such representations of sequences: the operations on sequences (accessing individual members, concatenation) can be \"implemented\" using total recursive functions, and in fact by primitive recursive functions. It is usually used to build sequential \u201cdata types\u201d in arithmetic-based formalizations of some fundamental notions of mathematics. It is a specific case of the more general idea of G\u00f6del numbering. For example, recursive function theory can be regarded as a formalization of the notion of an algorithm, and can be regarded as a programming language to mimic lists by encoding a sequence of natural numbers in a single natural number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical finite group theory, the uniqueness case is one of the three possibilities for groups of characteristic 2 type given by the trichotomy theorem. The uniqueness case covers groups G of characteristic 2 type with e(G) \u2265 3 that have an almost strongly p-embedded maximal 2-local subgroup for all primes p whose 2-local p-rank is sufficiently large (usually at least 3). Aschbacher (1983a, 1983b) proved that there are no finite simple groups in the uniqueness case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, since only Alice knows b {\\displaystyle b} , it makes it virtually impossible for either Bob or Eve to distinguish the states of the qubits. Also, after Bob has received the qubits, we know that Eve cannot be in possession of a copy of the qubits sent to Bob, by the no-cloning theorem, unless she has made measurements. Her measurements, however, risk disturbing a particular qubit with probability \u00bd if she guesses the wrong basis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regards to issues with connectivity, it is important to consider the musical score of composite films. Much like visual repetition or thematic similarities, the score offers another medium through which stories can be linked. Rather than leaving viewers with content to process, decode, intellectualize and then react to, the film score can produce emotional reactions immediately, before viewers have a chance to analyze their own responses. There are three main categories of composite film scores:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other words, a \"sum\" s 1 {\\displaystyle s_{1}} with only one term evaluates to that one term, while a \"sum\" s 0 {\\displaystyle s_{0}} with no terms evaluates to 0. Allowing a \"sum\" with only 1 or 0 terms reduces the number of cases to be considered in many mathematical formulas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a weighing matrix of order n {\\displaystyle n} and weight w {\\displaystyle w} is a matrix W {\\displaystyle W} with entries from the set { 0 , 1 , \u2212 1 } {\\displaystyle \\{0,1,-1\\}} such that: W W T = w I n {\\displaystyle WW^{\\mathsf {T}}=wI_{n}} Where W T {\\displaystyle W^{\\mathsf {T}}} is the transpose of W {\\displaystyle W} and I n {\\displaystyle I_{n}} is the identity matrix of order n {\\displaystyle n} . The weight w {\\displaystyle w} is also called the degree of the matrix. For convenience, a weighing matrix of order n {\\displaystyle n} and weight w {\\displaystyle w} is often denoted by W ( n , w ) {\\displaystyle W(n,w)} .Weighing matrices are so called because of their use in optimally measuring the individual weights of multiple objects. When the weighing device is a balance scale, the statistical variance of the measurement can be minimized by weighing multiple objects at once, including some objects in the opposite pan of the scale where they subtract from the measurement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a model might be selected by maximizing its performance on some set of training data, and yet its suitability might be determined by its ability to perform well on unseen data; then over-fitting occurs when a model begins to \"memorize\" training data rather than \"learning\" to generalize from a trend. As an extreme example, if the number of parameters is the same as or greater than the number of observations, then a model can perfectly predict the training data simply by memorizing the data in its entirety. (For an illustration, see Figure 2.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Carmichael's theorem, named after the American mathematician R. D. Carmichael, states that, for any nondegenerate Lucas sequence of the first kind Un(P, Q) with relatively prime parameters P, Q and positive discriminant, an element Un with n \u2260 1, 2, 6 has at least one prime divisor that does not divide any earlier one except the 12th Fibonacci number F(12) = U12(1, \u22121) = 144 and its equivalent U12(\u22121, \u22121) = \u2212144. In particular, for n greater than 12, the nth Fibonacci number F(n) has at least one prime divisor that does not divide any earlier Fibonacci number. Carmichael (1913, Theorem 21) proved this theorem. Recently, Yabuta (2001) gave a simple proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of primitive recursive functions, it is convenient to have a means to represent finite sequences of natural numbers as single natural numbers. One such method, G\u00f6del's encoding, represents a sequence of positive integers \u27e8 n 0 , n 1 , n 2 , \u2026 , n k \u27e9 {\\displaystyle \\langle n_{0},n_{1},n_{2},\\ldots ,n_{k}\\rangle } as \u220f i = 0 k p i n i {\\displaystyle \\prod _{i=0}^{k}p_{i}^{n_{i}}} ,where pi represent the ith prime. It can be shown that, with this representation, the ordinary operations on sequences are all primitive recursive. These operations include Determining the length of a sequence, Extracting an element from a sequence given its index, Concatenating two sequences.Using this representation of sequences, it can be seen that if h(m) is primitive recursive then the function f ( n ) = h ( \u27e8 f ( 0 ) , f ( 1 ) , f ( 2 ) , \u2026 , f ( n \u2212 1 ) \u27e9 ) {\\displaystyle f(n)=h(\\langle f(0),f(1),f(2),\\ldots ,f(n-1)\\rangle )} .is also primitive recursive. When the sequence \u27e8 n 0 , n 1 , n 2 , \u2026 , n k \u27e9 {\\displaystyle \\langle n_{0},n_{1},n_{2},\\ldots ,n_{k}\\rangle } is allowed to include zeros, it is instead represented as \u220f i = 0 k p i ( n i + 1 ) {\\displaystyle \\prod _{i=0}^{k}p_{i}^{(n_{i}+1)}} ,which makes it possible to distinguish the codes for the sequences \u27e8 0 \u27e9 {\\displaystyle \\langle 0\\rangle } and \u27e8 0 , 0 \u27e9 {\\displaystyle \\langle 0,0\\rangle } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example, statement b explicitly negates statement a: Statements can also be mutually exclusive, without explicitly negating each other as in the following example:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the classic problem the fuel in the jeep and at fuel dumps is treated as a continuous quantity. More complex variations on the problem have been proposed in which the fuel can only be left or collected in discrete amounts.In the camel and bananas problem, the merchant has n units of bananas. The camel can carry at most 1 unit of bananas at any time, and can travel 1 unit of distance on 1 unit of bananas. The market is at m units of distance away.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another square-difference-free set is obtained by doubling the Moser\u2013de Bruijn sequence. The best known upper bound on the size of a square-difference-free set of numbers up to n {\\displaystyle n} is only slightly sublinear, but the largest known sets of this form are significantly smaller, of size \u2248 n 0.733412 {\\displaystyle \\approx n^{0.733412}} . Closing the gap between these upper and lower bounds remains an open problem. The sublinear size bounds on square-difference-free sets can be generalized to sets where certain other polynomials are forbidden as differences between pairs of elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, pre-emphasis is a technique to protect against anticipated noise. The idea is to boost (and hence distort) the frequency range that is most susceptible to noise beforehand, so that after a noisy process (transmission over cable, tape recording...) more information can be recovered from that frequency range. Removal of the distortion caused by pre-emphasis is called de-emphasis, making the output accurately reproduce the original input. Emphasis is commonly used in FM broadcasting (preemphasis improvement) and vinyl (e.g. LP) records. For example, high-frequency signal components may be emphasized to produce a more equal modulation index for a transmitted frequency spectrum, and therefore a better signal-to-noise ratio for the entire frequency range.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In protected mode, the segment_part is replaced by a 16-bit selector, in which the 13 upper bits (bit 3 to bit 15) contain the index of an entry inside a descriptor table. The next bit (bit 2) specifies whether the operation is used with the GDT or the LDT. The lowest two bits (bit 1 and bit 0) of the selector are combined to define the privilege of the request, where the values of 0 and 3 represent the highest and the lowest privilege, respectively. This means that the byte offset of descriptors in the descriptor table is the same as the 16-bit selector, provided the lower three bits are zeroed. The descriptor table entry defines the real linear address of the segment, a limit value for the segment size, and some attribute bits (flags).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle x|(y\\mid (x\\mid z))=((z\\mid y)\\mid y)\\mid x.} In 1973, Padmanabhan and Quackenbush demonstrated a method that, in principle, would yield a 1-basis for Boolean algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the rational sieve is a general algorithm for factoring integers into prime factors. It is a special case of the general number field sieve. While it is less efficient than the general algorithm, it is conceptually simpler. It serves as a helpful first step in understanding how the general number field sieve works.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. A coarse problem with one or few unknowns per subdomain is used to further coordinate the solution between the subdomains globally. The problems on the subdomains are independent, which makes domain decomposition methods suitable for parallel computing. Domain decomposition methods are typically used as preconditioners for Krylov space iterative methods, such as the conjugate gradient method, GMRES, and LOBPCG.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In neural networks, each neuron receives input from some number of locations in the previous layer. In a convolutional layer, each neuron receives input from only a restricted area of the previous layer called the neuron's receptive field. Typically the area is a square (e.g. 5 by 5 neurons). Whereas, in a fully connected layer, the receptive field is the entire previous layer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "According to Kunegis, Blattner, and Moser several online networks follow a non-linear preferential attachment model. Communication networks and online contact networks are sub-linear while interaction networks are super-linear. The co-author network among scientists also shows the signs of sub-linear preferential attachment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social systems, deterministic chaos is infrequent, because the elements of the system include individuals whose values, awareness, will, foresight, and fallibility, affect the dynamic behavior of the system. However, this does not completely exclude any notional possibility of deterministic chaos in social systems. In fact some authorities argue an increase in the development of nonlinear dynamics and instabilities of social systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The classification efficiency is usually indicated by Receiver operating characteristics. In the original SIMCA method, the ends of the hyper-plane of each class are closed off by setting statistical control limits along the retained principal components axes (i.e., score value between plus and minus 0.5 times score standard deviation). More recent adaptations of the SIMCA method close off the hyper-plane by construction of ellipsoids (e.g. Hotelling's T2 or Mahalanobis distance). With such modified SIMCA methods, classification of an object requires both that its orthogonal distance from the model and its projection within the model (i.e. score value within the region defined by the ellipsoid) are not significant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is not to say that all software data ought to be manipulated as graphs, but rather that they can be exchanged as graphs. It can be used to represent instance data as well as schemas for describing the structure of the data. Moreover, the schema can be explicitly stated along with instance data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Hindley\u2013Milner type system, expressions can be given multiple types through parametric polymorphism. But naively giving multiple types to references breaks type safety. The following are typing rules for references and related operators in ML-like languages. r e f: \u2200 \u03b1 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In markup languages and the digital humanities, overlap occurs when a document has two or more structures that interact in a non-hierarchical manner. A document with overlapping markup cannot be represented as a tree. This is also known as concurrent markup. Overlap happens, for instance, in poetry, where there may be a metrical structure of feet and lines; a linguistic structure of sentences and quotations; and a physical structure of volumes and pages and editorial annotations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a kth root of unity modulo n for positive integers k, n \u2265 2, is a root of unity in the ring of integers modulo n; that is, a solution x to the equation (or congruence) x k \u2261 1 ( mod n ) {\\displaystyle x^{k}\\equiv 1{\\pmod {n}}} . If k is the smallest such exponent for x, then x is called a primitive kth root of unity modulo n. See modular arithmetic for notation and terminology. The roots of unity modulo n are exactly the integers that are coprime with n. In fact, these integers are roots of unity modulo n by Euler's theorem, and the other integers cannot be roots of unity modulo n, because they are zero divisors modulo n. A primitive root modulo n, is a generator of the group of units of the ring of integers modulo n. There exist primitive roots modulo n if and only if \u03bb ( n ) = \u03c6 ( n ) , {\\displaystyle \\lambda (n)=\\varphi (n),} where \u03bb {\\displaystyle \\lambda } and \u03c6 {\\displaystyle \\varphi } are respectively the Carmichael function and Euler's totient function. A root of unity modulo n is a primitive kth root of unity modulo n for some divisor k of \u03bb ( n ) , {\\displaystyle \\lambda (n),} and, conversely, there are primitive kth roots of unity modulo n if and only if k is a divisor of \u03bb ( n ) . {\\displaystyle \\lambda (n).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Wieferich prime is a prime number p such that p2 divides 2p \u2212 1 \u2212 1, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides 2p \u2212 1 \u2212 1. Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's Last Theorem, at which time both of Fermat's theorems were already well known to mathematicians.Since then, connections between Wieferich primes and various other topics in mathematics have been discovered, including other types of numbers and primes, such as Mersenne and Fermat numbers, specific types of pseudoprimes and some types of numbers generalized from the original definition of a Wieferich prime. Over time, those connections discovered have extended to cover more properties of certain prime numbers as well as more general subjects such as number fields and the abc conjecture. As of April 2023, the only known Wieferich primes are 1093 and 3511 (sequence A001220 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Very often, and in this article, the coefficients of the equations are real or complex numbers and the solutions are searched in the same set of numbers, but the theory and the algorithms apply for coefficients and solutions in any field. For solutions in an integral domain like the ring of the integers, or in other algebraic structures, other theories have been developed, see Linear equation over a ring. Integer linear programming is a collection of methods for finding the \"best\" integer solution (when there are many). Gr\u00f6bner basis theory provides algorithms when coefficients and unknowns are polynomials. Also tropical geometry is an example of linear algebra in a more exotic structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In simple terms, software verification is: \"Assuming we should build X, does our software achieve its goals without any bugs or gaps?\" On the other hand, software validation is: \"Was X what we should have built? Does X meet the high-level requirements?\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A bijective proof. Two sets are shown to have the same number of members by exhibiting a bijection, i.e. a one-to-one correspondence, between them.The term \"combinatorial proof\" may also be used more broadly to refer to any kind of elementary proof in combinatorics. However, as Glass (2003) writes in his review of Benjamin & Quinn (2003) (a book about combinatorial proofs), these two simple techniques are enough to prove many theorems in combinatorics and number theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Supercritical p > ( 1 + \u03b5 ) / n {\\displaystyle p>(1+\\varepsilon )/n} There is a single giant component containing a linear number of vertices. For large values of p {\\displaystyle p} its size approaches the whole graph: | C 1 | \u2248 y n {\\displaystyle |C_{1}|\\approx yn} where y {\\displaystyle y} is the positive solution to the equation e \u2212 p n y = 1 \u2212 y {\\displaystyle e^{-pny}=1-y} . The remaining components are small, with logarithmic size.In the same model of random graphs, there will exist multiple connected components with high probability for values of p {\\displaystyle p} below a significantly higher threshold, p < ( 1 \u2212 \u03b5 ) ( log \u2061 n ) / n {\\displaystyle p<(1-\\varepsilon )(\\log n)/n} , and a single connected component for values above the threshold, p > ( 1 + \u03b5 ) ( log \u2061 n ) / n {\\displaystyle p>(1+\\varepsilon )(\\log n)/n} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, if x 5 {\\displaystyle x_{5}} is non-basic and its coefficient in r {\\displaystyle r} is positive, then increasing it above 0 may make z {\\displaystyle z} larger. If it is possible to do so without violating other constraints, then the increased variable becomes basic (it \"enters the basis\"), while some basic variable is decreased to 0 to keep the equality constraints and thus becomes non-basic (it \"exits the basis\"). If this process is done carefully, then it is possible to guarantee that z {\\displaystyle z} increases until it reaches an optimal BFS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The concept is not unlike the limited licensing approach for computer software, which places rigid restrictions on resale and reproduction. The intent is to make users understand that the content of any textbook is the intellectual property of the author and/or the publisher, and that as such, subject to copyright. Obviously, this idea is completely opposed to the millennia-old tradition of the sale of used books, and would make that entire industry illegal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle M^{\\text{T}}\\Omega M=\\Omega .} Under a change of basis, represented by a matrix A, we have \u03a9 \u21a6 A T \u03a9 A {\\displaystyle \\Omega \\mapsto A^{\\text{T}}\\Omega A} M \u21a6 A \u2212 1 M A . {\\displaystyle M\\mapsto A^{-1}MA.} One can always bring \u03a9 {\\displaystyle \\Omega } to either the standard form given in the introduction or the block diagonal form described below by a suitable choice of A.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In personality pathology, dimensional models of personality disorders (also known as the dimensional approach to personality disorders, dimensional classification, and dimensional assessments) conceptualize personality disorders as quantitatively rather than qualitatively different from normal personality. They consist of extreme, maladaptive levels of certain personality characteristics (these characteristics are commonly described as facets within broader personality factors or traits). Within the context of personality psychology, a \"dimension\" refers to a continuum on which an individual can have various levels of a characteristic, in contrast to the dichotomous categorical approach in which an individual does or does not possess a characteristic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Euclid numbers are integers of the form En = pn # + 1, where pn # is the nth primorial, i.e. the product of the first n prime numbers. They are named after the ancient Greek mathematician Euclid, in connection with Euclid's theorem that there are infinitely many prime numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese encodings ISO 646-JP (a 7-bit code based on ASCII), JIS X 0201 (an 8-bit code), and Shift JIS (a multi-byte encoding which is 8-bit for ASCII), the code point 0x5C that would be used for backslash in ASCII is instead rendered as a yen sign \u00a5. Due to extensive use of the 005C code point to represent the yen sign, even today some fonts such as MS Mincho render the backslash character as a \u00a5, so the characters at Unicode code points 00A5 (\u00a5) and 005C (\\) both render as \u00a5 when these fonts are selected. Computer programs still treat 005C as a backslash in these environments but display it as a yen sign, causing confusion, especially in MS-DOS filenames.Several other ISO 646 versions also replace backslash with other characters, including \u20a9 (Korean), \u00d6 (German, Swedish), \u00d8 (Danish, Norwegian), \u00e7 (French) and \u00d1 (Spanish), leading to similar problems, though with less lasting impact compared to the yen sign. In 1991, RFC 1345 suggested // as a unique two-character mnemonic that might be used in internet standards as \"a practical way of identifying  character, without reference to a coded character set and its code in  coded character set\". Consequently, this style may be seen in early Internet Engineering Task Force documents.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most computer programming languages a do while loop is a control flow statement that executes a block of code and then either repeats the block or exits the loop depending on a given boolean condition. The do while construct consists of a process symbol and a condition. First the code within the block is executed. Then the condition is evaluated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s, the Graphical Kernel System (GKS) library, based on a 1970s specification with a similar basic geometry and command structure to NAPLPS, was widely implemented on microcomputers, and became the basis of Digital Research's GSX graphics system used in their GEM GUI. GKS was later extended into a 3D version, and additions to this resulted in PHIGS (Programmer's Hierarchical Interactive Graphics System), a competitor to OpenGL.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result, it is often considered to be a more intuitive, but a less systematic approach to divisions \u2013 where the efficiency is highly dependent upon one's numeracy skills. To calculate the whole number quotient of dividing a large number by a small number, the student repeatedly takes away \"chunks\" of the large number, where each \"chunk\" is an easy multiple (for example 100\u00d7, 10\u00d7, 5\u00d7 2\u00d7, etc.) of the small number, until the large number has been reduced to zero \u2013 or the remainder is less than the small number itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "And symmetrically (when Xk is a sub-martingale): P ( X N \u2212 X 0 \u2264 \u2212 \u03f5 ) \u2264 exp \u2061 ( \u2212 \u03f5 2 2 \u2211 k = 1 N c k 2 ) . {\\displaystyle {\\text{P}}(X_{N}-X_{0}\\leq -\\epsilon )\\leq \\exp \\left({-\\epsilon ^{2} \\over 2\\sum _{k=1}^{N}c_{k}^{2}}\\right).} If X is a martingale, using both inequalities above and applying the union bound allows one to obtain a two-sided bound: P ( | X N \u2212 X 0 | \u2265 \u03f5 ) \u2264 2 exp \u2061 ( \u2212 \u03f5 2 2 \u2211 k = 1 N c k 2 ) . {\\displaystyle {\\text{P}}(|X_{N}-X_{0}|\\geq \\epsilon )\\leq 2\\exp \\left({-\\epsilon ^{2} \\over 2\\sum _{k=1}^{N}c_{k}^{2}}\\right).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As in discrete percolation, a common research focus of continuum percolation is studying the conditions of occurrence for infinite or giant components. Other shared concepts and analysis techniques exist in these two types of percolation theory as well as the study of random graphs and random geometric graphs. Continuum percolation arose from an early mathematical model for wireless networks, which, with the rise of several wireless network technologies in recent years, has been generalized and studied in order to determine the theoretical bounds of information capacity and performance in wireless networks. In addition to this setting, continuum percolation has gained application in other disciplines including biology, geology, and physics, such as the study of porous material and semiconductors, while becoming a subject of mathematical interest in its own right.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Light's associativity test is a procedure invented by F. W. Light for testing whether a binary operation defined in a finite set by a Cayley multiplication table is associative. The naive procedure for verification of the associativity of a binary operation specified by a Cayley table, which compares the two products that can be formed from each triple of elements, is cumbersome. Light's associativity test simplifies the task in some instances (although it does not improve the worst-case runtime of the naive algorithm, namely O ( n 3 ) {\\displaystyle {\\mathcal {O}}\\left(n^{3}\\right)} for sets of size n {\\displaystyle n} ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the proton spin puzzle, the EMC effect, the distributions of electric charges inside the nucleons, as found by Hofstadter in 1956, and the ad hoc CKM matrix elements. When the term \"preon\" was coined, it was primarily to explain the two families of spin-1/2 fermions: quarks and leptons. More recent preon models also account for spin-1 bosons, and are still called \"preons\". Each of the preon models postulates a set of fewer fundamental particles than those of the Standard Model, together with the rules governing how those fundamental particles combine and interact. Based on these rules, the preon models try to explain the Standard Model, often predicting small discrepancies with this model and generating new particles and certain phenomena which do not belong to the Standard Model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 20th century, following the development of formal logic, the ampersand became a commonly used logical notation for the binary operator or sentential connective AND. This usage was adopted in computing. Many languages with syntax derived from C, including C++, Perl, and more differentiate between: & for bitwise AND. (4 & 2) is zero, (4 & 5) is 4.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the US, the CDC recommends essential components of AMS programs (ASP) for acute care hospitals, small and critical access hospitals, resource-limited facilities, long-term care facilities, and outpatient facilities.As of 2014, thirteen internet-based institutional ASP resources in US academic medical centers had been published. An ASP has the following tasks, in line with quality improvement theory:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An arrow from the node representing a candidate X to the one representing a candidate Y is labelled with d. To avoid cluttering the diagram, an arrow has only been drawn from X to Y when d > d (i.e. the table cells with light green background), omitting the one in the opposite direction (the table cells with light red background). One example of computing the strongest path strength is p = 33: the strongest path from B to D is the direct path (B, D) which has strength 33. But when computing p, the strongest path from A to C is not the direct path (A, C) of strength 26, rather the strongest path is the indirect path (A, D, C) which has strength min(30, 28) = 28.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a formal theory is a set of sentences expressed in a formal language. A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules, which may be interpreted as valid rules of inference, or a set of axioms, or have both.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These directories contain files with names such as \"ABCD1234.JPG\" that consist of four alphanumeric characters (often \"100_\", \"DSC0\", \"DSCF\", \"IMG_\", \"MOV_\", or \"P000\"), followed by a number. Handling of directories with possibly user-created duplicate numbers may vary among camera firmwares. DCF 2.0 adds support for DCF optional files recorded in an optional color space (that is, Adobe RGB rather than sRGB). Such files must be indicated by a leading \"_\" (as in \"_DSC\" instead of \"100_\" or \"DSC0\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In structure mining, a graph kernel is a kernel function that computes an inner product on graphs. Graph kernels can be intuitively understood as functions measuring the similarity of pairs of graphs. They allow kernelized learning algorithms such as support vector machines to work directly on graphs, without having to do feature extraction to transform them to fixed-length, real-valued feature vectors. They find applications in bioinformatics, in chemoinformatics (as a type of molecule kernels), and in social network analysis.Concepts of graph kernels have been around since the 1999, when D. Haussler introduced convolutional kernels on discrete structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical analysis of binary classification, the F-score or F-measure is a measure of a test's accuracy. It is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the number of all positive results, including those not identified correctly, and the recall is the number of true positive results divided by the number of all samples that should have been identified as positive. Precision is also known as positive predictive value, and recall is also known as sensitivity in diagnostic binary classification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to measure the information of a string relative to another there is the need to rely on relative semi-distances (NRC). These are measures that do not need to respect symmetry and triangle inequality distance properties. Although the NCD and the NRC seem very similar, they address different questions. The NCD measures how similar both strings are, mostly using the information content, while the NRC indicates the fraction of a target string that cannot be constructed using information from another string. For a comparison, with application to the evolution of primate genomes, see.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "According to the Curry\u2013Howard isomorphism, lambda calculus on its own can express theorems in intuitionistic logic only, and several classical logical theorems can't be written at all. However with these new operators one is able to write terms that have the type of, for example, Peirce's law. Semantically these operators correspond to continuations, found in some functional programming languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. A binary relation over sets X and Y is a new set of ordered pairs (x, y) consisting of elements x in X and y in Y. It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element x is related to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation. A binary relation is the most studied special case n = 2 of an n-ary relation over sets X1, ..., Xn, which is a subset of the Cartesian product X 1 \u00d7 \u22ef \u00d7 X n .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Unlike Schoof's algorithm, the SEA algorithm is typically implemented as a probabilistic algorithm (of the Las Vegas type), so that root-finding and other operations can be performed more efficiently. Its computational complexity is dominated by the cost of computing the modular polynomials \u03a8 \u2113 ( X , Y ) {\\displaystyle \\Psi _{\\ell }(X,Y)} , but as these do not depend on E {\\displaystyle E} , they may be computed once and reused. Under the heuristic assumption that there are sufficiently many small Elkies primes, and excluding the cost of computing modular polynomials, the asymptotic running time of the SEA algorithm is O ( n 2 M ( n 2 ) / log \u2061 n ) = O ( n 4 + o ( 1 ) ) {\\displaystyle O(n^{2}M(n^{2})/\\log {n})=O(n^{4+o(1)})} , where n = log \u2061 q {\\displaystyle n=\\log {q}} . Its space complexity is O ( n 3 log \u2061 n ) {\\displaystyle O(n^{3}\\log {n})} , but when precomputed modular polynomials are used this increases to O ( n 4 ) {\\displaystyle O(n^{4})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to test plastic welds, there are several requirements for both the inspector as well as the test method. Furthermore, there are two different types of testing weld quality. These two types are destructive and non-destructive testing. Destructive testing serves to qualify and quantify the weld joint whereas nondestructive testing serves to identify anomalies, discontinuities, cracks, and/or crevices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most of these cases the OEMs are open about their use of such software and fulfil the requirements of their Free software licenses, such as the GNU General Public License (GPL), but in a small number of cases this use is masked, either deliberately or through professed ignorance or misunderstanding. Violators are usually found through public records, where they may be forced to declare their implementations, or through their own advertising, for example \"Embedded Software Engineers with Mandatory Linux Experience Required\" on their careers pages, and yet their site or product documentation offers no source download or offer to supply the software source as required by the license GPL. Organizations such as gpl-violations.org, the Free Software Foundation (FSF) and the Software Freedom Law Center (SFLC) are now more organized at pursuing such violators and obtaining compliance. Usually, they seek voluntary compliance as a first step and only enter legal proceedings when blocked. When notified of violations they confirm them by asking the supplier, examining available product samples, or even going so far as to make blind purchases of the product through front companies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The interpretation commonly taken, however, is that an underlying morpheme |-i| palatalizes the consonant and is subsequently deleted. Palatalization may also occur as a morphological feature. For example, although Russian makes phonemic contrasts between palatalized and unpalatalized consonants, alternations across morpheme boundaries are normal: \u043e\u0442\u0432\u0435\u0442 ('answer') vs. \u043e\u0442\u0432\u0435\u0442\u0438\u0442\u044c ('to answer') \u043d\u0435\u0441\u0443 (' carry') vs. \u043d\u0435\u0441\u0451\u0442 ('carries') \u0433\u043e\u043b\u043e\u0434 ('hunger') vs. \u0433\u043e\u043b\u043e\u0434\u0435\u043d  ('hungry' masc.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When p = 1 / 2 {\\displaystyle p=1/2} , the uncertainty is at a maximum; if one were to place a fair bet on the outcome in this case, there is no advantage to be gained with prior knowledge of the probabilities. In this case, the entropy is maximum at a value of 1 bit. Intermediate values fall between these cases; for instance, if p = 1 / 4 {\\displaystyle p=1/4} , there is still a measure of uncertainty on the outcome, but one can still predict the outcome correctly more often than not, so the uncertainty measure, or entropy, is less than 1 full bit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and sufficient condition for an object to exist: The combinatorial formulation answers whether a finite collection of sets has a transversal\u2014that is, whether an element can be chosen from each set without repetition. Hall's condition is that for any group of sets from the collection, the total unique elements they contain is at least as large as the number of sets in the group. The graph theoretic formulation answers whether a finite bipartite graph has a perfect matching\u2014that is, a way to match each vertex from one group uniquely to an adjacent vertex from the other group. Hall's condition is that any subset of vertices from one group has a neighbourhood of equal or greater size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, language identification or language guessing is the problem of determining which natural language given content is in. Computational approaches to this problem view it as a special case of text categorization, solved with various statistical methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, the Peano kernel theorem is a general result on error bounds for a wide class of numerical approximations (such as numerical quadratures), defined in terms of linear functionals. It is attributed to Giuseppe Peano.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the interval chromatic number X<(H) of an ordered graph H is the minimum number of intervals the (linearly ordered) vertex set of H can be partitioned into so that no two vertices belonging to the same interval are adjacent in H.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical combinatorics, the Transylvania lottery is a lottery where players selected three numbers from 1-14 for each ticket, and then three numbers are chosen randomly. A ticket wins if two of the numbers match the random ones. The problem asks how many tickets the player must buy in order to be certain of winning. (Javier Mart\u00ednez, Gloria Guti\u00e9rrez & Pablo Cordero et al. 2008, p.85)(Mazur 2010, p.280 problem 15) An upper bound can be given using the Fano plane with a collection of 14 tickets in two sets of seven.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The question is: how should we choose the prior parameters ( s , G 0 ) {\\displaystyle \\left(s,G_{0}\\right)} of the DP, in particular the infinite dimensional one G 0 {\\displaystyle G_{0}} , in case of lack of prior information? To address this issue, the only prior that has been proposed so far is the limiting DP obtained for s \u2192 0 {\\displaystyle s\\rightarrow 0} , which has been introduced under the name of Bayesian bootstrap by Rubin; in fact it can be proven that the Bayesian bootstrap is asymptotically equivalent to the frequentist bootstrap introduced by Bradley Efron. The limiting Dirichlet process s \u2192 0 {\\displaystyle s\\rightarrow 0} has been criticized on diverse grounds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, syntactic methods are techniques for developing correct software programs. The techniques attempt to detect, and thus prevent, certain kinds of defects (bugs) by examining the structure of the code being produced at its syntactic rather than semantic level.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis ( H 0 {\\displaystyle H_{0}} ) when a specific alternative hypothesis ( H 1 {\\displaystyle H_{1}} ) is true. It is commonly denoted by 1 \u2212 \u03b2 {\\displaystyle 1-\\beta } , and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability \u03b2 {\\displaystyle \\beta } of making a type II error by wrongly failing to reject the null hypothesis decreases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to speed up web server responses by lowering average HTTP response times and hardware resources used, many popular web servers implement one or more content caches, each one specialized in a content category.Content is usually cached by its origin, e.g.: static content: file cache; dynamic content: dynamic cache (module / program output).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", FN), and let Q {\\displaystyle \\mathbb {Q} } denote an equivalent martingale measure. Let U = (U0, U1, . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Defining Child-Related OperationsThere are two design variants for defining and implementing child-related operations like adding/removing a child component to/from the container (add(child)/remove(child)) and accessing a child component (getChild()): Design for uniformity: Child-related operations are defined in the Component interface. This enables clients to treat Leaf and Composite objects uniformly. But type safety is lost because clients can perform child-related operations on Leaf objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical cryptography, a Kleinian integer is a complex number of the form m + n 1 + \u2212 7 2 {\\displaystyle m+n{\\frac {1+{\\sqrt {-7}}}{2}}} , with m and n rational integers. They are named after Felix Klein. The Kleinian integers form a ring called the Kleinian ring, which is the ring of integers in the imaginary quadratic field Q ( \u2212 7 ) {\\displaystyle \\mathbb {Q} ({\\sqrt {-7}})} . This ring is a unique factorization domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some jurisdictions, false statement is a crime similar to perjury.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each array contains 140 (one for each priority level) pointers to doubly linked lists, which in turn reference all processes with the given priority. The scheduler selects the next process from the active array with highest priority. When a process' quantum expires, it is placed into the expired array with some priority.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of electrical modeling of transformers and transmission lines, shunt components that provide paths of least resistance in certain models are generally specified in terms of their admittance. Each side of most transformer models contains shunt components which model magnetizing current and core losses. These shunt components can be referenced to the primary or secondary side. For simplified transformer analysis, admittance from shunt elements can be neglected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The problem with this LP is that, in the bin-covering problem, handling small items is problematic, since small items may be essential for the optimal solution. With small items allowed, the number of configurations may be too large even for the technique of Karmarkar and Karp. Csirik, Johnson and Kenyon present an alternative LP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This in turn permits a somewhat unified analysis of arithmetic objects through their automorphic functions. Simply put, the Langlands philosophy allows a general analysis of structuring the abstractions of numbers. Naturally, this description is at once a reduction and over-generalization of the program's proper theorems, but these mathematical analogues provide the basis of its conceptualization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although such evidence is not seen as conclusive, researchers may sometimes regard it as an invitation to more rigorous scientific study of the phenomenon in question. For instance, one study found that 35 of 47 anecdotal reports of drug side-effects were later sustained as \"clearly correct. \"Anecdotal evidence is considered the least certain type of scientific information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most promising solution is the decoy states in which Alice randomly sends some of her laser pulses with a lower average photon number. These decoy states can be used to detect a PNS attack, as Eve has no way to tell which pulses are signal and which decoy. Using this idea the secure key rate scales as t {\\displaystyle t} , the same as for a single photon source. This idea has been implemented successfully first at the University of Toronto, and in several follow-up QKD experiments, allowing for high key rates secure against all known attacks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the grammatical tradition of Sanskrit, aspirated consonants are called voiceless aspirated, and breathy-voiced consonants are called voiced aspirated. There are no dedicated IPA symbols for degrees of aspiration and typically only two degrees are marked: unaspirated \u27e8k\u27e9 and aspirated \u27e8k\u02b0\u27e9. An old symbol for light aspiration was \u27e8\u02bb\u27e9, but this is now obsolete.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These relations will need to be slowly and consistently established in order to truly unify any kind of information policy and decision-making. If information policy can be established and guided on a semi-national level, the degree of communication and cooperation throughout the world will increase dramatically. As information policy continues to shape many aspects of society, these international relations will become vital (Harpham, 2011).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, sufficient dimension reduction (SDR) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency. Dimension reduction has long been a primary goal of regression analysis. Given a response variable y and a p-dimensional predictor vector x {\\displaystyle {\\textbf {x}}} , regression analysis aims to study the distribution of y \u2223 x {\\displaystyle y\\mid {\\textbf {x}}} , the conditional distribution of y {\\displaystyle y} given x {\\displaystyle {\\textbf {x}}} . A dimension reduction is a function R ( x ) {\\displaystyle R({\\textbf {x}})} that maps x {\\displaystyle {\\textbf {x}}} to a subset of R k {\\displaystyle \\mathbb {R} ^{k}} , k < p, thereby reducing the dimension of x {\\displaystyle {\\textbf {x}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When using dilated layers, the number of pixels in the receptive field remains constant, but the field is more sparsely populated as its dimensions grow when combining the effect of several layers. To manipulate the receptive field size as desired, there are some alternatives to the standard convolutional layer. For example, atrous or dilated convolution expands the receptive field size without increasing the number of parameters by interleaving visible and blind regions. Moreover, a single dilated convolutional layer can comprise filters with multiple dilation ratios, thus having a variable receptive field size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The code rate of a convolutional code is commonly modified via symbol puncturing. For example, a convolutional code with a 'mother' code rate n / k = 1 / 2 {\\displaystyle n/k=1/2} may be punctured to a higher rate of, for example, 7 / 8 {\\displaystyle 7/8} simply by not transmitting a portion of code symbols. The performance of a punctured convolutional code generally scales well with the amount of parity transmitted. The ability to perform economical soft decision decoding on convolutional codes, as well as the block length and code rate flexibility of convolutional codes, makes them very popular for digital communications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. Various kinds of reliability coefficients, with values ranging between 0.00 (much error) and 1.00 (no error), are usually used to indicate the amount of error in the scores.\" For example, measurements of people's height and weight are often extremely reliable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus for some rational number \u03b2 . {\\displaystyle \\beta .} The uniqueness of the decomposition over 1 and c {\\displaystyle {\\sqrt {c}}} implies thus that the considered equation is equivalent with It follows by Vieta's formulas that x and y must be roots of the quadratic equation its \u0394 = a 2 \u2212 c = d 2 > 0 {\\displaystyle ~\\Delta =a^{2}-c=d^{2}>0~} (\u2260 0, otherwise c would be the square of a), hence x and y must be and a \u2212 a 2 \u2212 c 2 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, \"push to talk\" services offer the instant connectivity of SMS and are typically unlimited. The integration between competing providers and technologies necessary for cross-network text messaging was not initially available. Some providers originally charged extra for texting, reducing its appeal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sweep and prune exploits temporal coherence as it is likely that solids do not move significantly between two simulation steps. Because of that, at each step, the sorted lists of bounding volume starts and ends can be updated with relatively few computational operations. Sorting algorithms which are fast at sorting almost-sorted lists, such as insertion sort, are particularly good for this purpose.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, however, a quadratic nonresidue of p is found via a modified Euclid's algorithm and taken as the value of a, since if a is a quadratic nonresidue modulo p then the converse is also true, and the test is conclusive. For such an a the Legendre symbol is ( a p ) = \u2212 1. {\\displaystyle \\left({\\frac {a}{p}}\\right)=-1.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the BIT predicate, sometimes written BIT ( i , j ) {\\displaystyle {\\text{BIT}}(i,j)} , is a predicate that tests whether the j {\\displaystyle j} th bit of the number i {\\displaystyle i} (starting from the least significant digit) is 1, when i {\\displaystyle i} is written as a binary number. Its mathematical applications include modeling the membership relation of hereditarily finite sets, and defining the adjacency relation of the Rado graph. In computer science, it is used for efficient representations of set data structures using bit vectors, in defining the private information retrieval problem from communication complexity, and in descriptive complexity theory to formulate logical descriptions of complexity classes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It could thus be thought of as a Boolean, i.e., a truth value represented as the numerical value 0 or 1 (as is sometimes done in computer programming). Dummy variables may be extended to more complex cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, the idea of a typical subspace plays an important role in the proofs of many coding theorems (the most prominent example being Schumacher compression). Its role is analogous to that of the typical set in classical information theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Vector processors use this technique with one additional trick. Because the data layout is in a known format \u2014 a set of numbers arranged sequentially in memory \u2014 the pipelines can be tuned to improve the performance of fetches. On the receipt of a vector instruction, special hardware sets up the memory access for the arrays and stuffs the data into the processor as fast as possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It became the basis of a modern international system that divides clouds into five physical forms which can be further divided or classified into altitude levels to derive ten basic genera. The main representative cloud types for each of these forms are stratiform, cumuliform, stratocumuliform, cumulonimbiform, and cirriform.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Also it is sufficient to assume P is a polynomial over Q {\\displaystyle \\mathbb {Q} } and multiply P by the appropriate denominators to yield integer coefficients. However, whether quantification over rationals can also be substituted for quantification over the integers is a notoriously hard open problem.The MRDP theorem (so named for the initials of the four principal contributors to its solution) states that a set of integers is Diophantine if and only if it is computably enumerable. A set of integers S is computably enumerable if and only if there is an algorithm that, when given an integer, halts if that integer is a member of S and runs forever otherwise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The addition of virtual memory into the Atlas also eliminated a looming programming problem: planning and scheduling data transfers between main and secondary memory and recompiling programs for each change of size of main memory. The first Atlas was commissioned in 1962 but working prototypes of paging had been developed by 1959.: 2 In 1961, the Burroughs Corporation independently released the first commercial computer with virtual memory, the B5000, with segmentation rather than paging.IBM developed the concept of hypervisors in their CP-40 and CP-67, and in 1972 provided it for the S/370 as Virtual Machine Facility/370. IBM introduced the Start Interpretive Execution (SIE) instruction as part of 370-XA on the 3081, and VM/XA versions of VM to exploit it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Because fuzzy clustering allows genes to belong to more than one cluster, it allows for the identification of genes that are conditionally co-regulated or co-expressed. For example, one gene may be acted on by more than one transcription factor, and one gene may encode a protein that has more than one function. Thus, fuzzy clustering is more appropriate than hard clustering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution. The probability mass function is P ( X = n ) = { e \u2212 \u03bb \u03bb n + r ( n + r ) ! \u22c5 1 I ( r , \u03bb ) , n = 0 , 1 , 2 , \u2026 if r \u2265 0 e \u2212 \u03bb \u03bb n + r ( n + r ) ! \u22c5 1 I ( r + s , \u03bb ) , n = s , s + 1 , s + 2 , \u2026 otherwise {\\displaystyle P(X=n)={\\begin{cases}e^{-\\lambda }{\\dfrac {\\lambda ^{n+r}}{\\left(n+r\\right)!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In surveying, an initial point is a datum (a specific point on the surface of the earth) that marks the beginning point for a cadastral survey. The initial point establishes a local geographic coordinate system for the surveys that refer to that point. An initial point is defined by the intersection of a principal meridian and a base line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Unix operating system, most types of input and output operations are considered to be streams of bytes read from a device or written to a device. This stream of bytes model is used for file I/O, socket I/O, and terminal I/O in order to provide device independence. In order to read and write to a device at the application level, the program calls a function to open the device, which may be a real device such as a terminal or a virtual device such as a network port or a file in a file system. The device's physical characteristics are mediated by the operating system which in turn presents an abstract interface that allows the programmer to read and write bytes from/to the device. The operating system then performs the actual transformation needed to read and write the stream of bytes to the device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the language of ordered abelian groups has one constant symbol 0, one unary function symbol \u2212, one binary function symbol +, and one binary relation symbol \u2264. Then: The expressions +(x, y) and +(x, +(y, \u2212(z))) are terms. These are usually written as x + y and x + y \u2212 z. The expressions +(x, y) = 0 and \u2264(+(x, +(y, \u2212(z))), +(x, y)) are atomic formulas. These are usually written as x + y = 0 and x + y \u2212 z \u2264 x + y. The expression ( \u2200 x \u2200 y  {\\displaystyle (\\forall x\\forall y\\,} is a formula, which is usually written as \u2200 x \u2200 y ( x + y \u2264 z ) \u2192 \u2200 x \u2200 y ( x + y = 0 ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One sampling unit from each set is then selected (based on the observed ranks) for subsequent measurement using a more accurate and reliable (hence, more expensive) method for the contaminant of interest. Relative to simple random sampling, this design results in more representative samples and so leads to more precise estimates of the population parameters. Ranked set sampling is useful when the cost of locating and ranking locations in the field is low compared to laboratory measurements. It is also appropriate when an inexpensive auxiliary variable (based on expert knowledge or measurement) is available to rank population units with respect to the variable of interest. To use this design effectively, it is important that the ranking method and analytical method are strongly correlated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, an entity\u2013relationship model (ERM) is an abstract and conceptual representation of data. Entity\u2013relationship modeling is a database modeling method, used to produce a type of conceptual schema or semantic data model of a system, often a relational database, and its requirements in a top-down fashion. Diagrams created by this process are called entity-relationship diagrams, ER diagrams, or ERDs. Entity\u2013relationship models have had wide application in the building of information systems intended to support activities involving objects and events in the real world. In these cases they are models that are conceptual. However, this modeling method can be used to build computer games or a family tree of the Greek Gods, in these cases it would be used to model concepts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Army began issuing an improved STANAG magazine in March 2009.According to the Army, the M4 only suffered 296 stoppages and said that the high number reported could be attributed to discrepancies in the scoring process. The Army testing command stated that, if the number of stoppages caused by a broken part met some threshold, they would be eliminated from the final report pending redesign of the part. The methodology of the test has been debated, as many of the M4s in the test had already seen use, whereas the other rifles were brand new, and that the wide variance in results between summer and fall showed that the test was not accurate, as it was not repeatable with consistent results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One type is a subtype of another if and only if it contains all the features of the base type, or subtypes thereof. The subtype may contain added features, such as members not present in the base type, or stronger invariants. A distinction exists between structural substitution for inferred and non-inferred polymorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Java programming language, the try...catch block is used often to catch exceptions. All potentially dangerous code is placed inside the block and, if an exception occurred, is stopped, or caught.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At the end of the process, the approximate best cover will be either H 1 {\\displaystyle H_{1}} or H 2 {\\displaystyle H_{2}} . This algorithm achieves an approximation ratio of 1 \u2212 1 e {\\displaystyle 1-{1 \\over e}} for values of k \u2265 3 {\\displaystyle k\\geq 3} . This is the best possible approximation ratio unless N P \u2286 D T I M E ( n O ( log \u2061 log \u2061 n ) ) {\\displaystyle NP\\subseteq DTIME(n^{O(\\log \\log n)})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, two square matrices A and B over a field are called congruent if there exists an invertible matrix P over the same field such that PTAP = Bwhere \"T\" denotes the matrix transpose. Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space: two matrices are congruent if and only if they represent the same bilinear form with respect to different bases. Note that Halmos defines congruence in terms of conjugate transpose (with respect to a complex inner product space) rather than transpose, but this definition has not been adopted by most other authors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". {\\displaystyle \\exp ^{*}(x)=\\delta _{0}+\\sum _{n=1}^{\\infty }{\\frac {x^{*n}}{n!}}.} It is not generally possible to extend this definition to arbitrary distributions, although a class of distributions on which this series still converges in an appropriate weak sense is identified by Ben Chrouda, El Oued & Ouerdiane (2002).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In rendezvous hashing, also called highest random weight (HRW) hashing, all clients use the same hash function h ( ) {\\displaystyle h()} (chosen ahead of time) to associate a key to one of the n available servers. Each client has the same list of identifiers {S1, S2, ..., Sn }, one for each server. Given some key k, a client computes n hash weights w1 = h(S1, k), w2 = h(S2, k), ..., wn = h(Sn, k). The client associates that key with the server corresponding to the highest hash weight for that key. A server with ID S x {\\displaystyle S_{x}} owns all the keys k m {\\displaystyle k_{m}} for which the hash weight h ( S x , k m ) {\\displaystyle h(S_{x},k_{m})} is higher than the hash weight of any other node for that key.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of computing, computer applications directly communicated to the hardware and there was no operating system. As applications grew larger encompassing various domains, OSes were invented. They served as middleware providing hardware abstractions to applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the bin packing problem, the size of the bins is fixed and their number can be enlarged (but should be as small as possible). In contrast, in the multiway number partitioning problem, the number of bins is fixed and their size can be enlarged. The objective is to find a partition in which the bin sizes are as nearly equal is possible (in the variant called multiprocessor scheduling problem or minimum makespan problem, the goal is specifically to minimize the size of the largest bin). In the inverse bin packing problem, both the number of bins and their sizes are fixed, but the item sizes can be changed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phrase structure grammars, such as generalised phrase structure grammar, head-driven phrase structure grammar and lexical functional grammar, a feature structure is essentially a set of attribute\u2013value pairs. For example, the attribute named number might have the value singular. The value of an attribute may be either atomic, e.g. the symbol singular, or complex (most commonly a feature structure, but also a list or a set). A feature structure can be represented as a directed acyclic graph (DAG), with the nodes corresponding to the variable values and the paths to the variable names.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the \"size\" of the field extension. The concept plays an important role in many parts of mathematics, including algebra and number theory \u2014 indeed in any area where fields appear prominently.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vall\u00e9e Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is \u03c0(N) ~ N/log(N), where \u03c0(N) is the prime-counting function (the number of primes less than or equal to N) and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After the primary finishes its update, the update is forwarded to other replicas and all perform the update locally. This non-blocking approach can lead to an improvement. The diagram of the local-write protocol depicts the local-write approach in primary-based protocols. A process requests a write operation in a data item x. The current server is considered as the new primary for a data item x. The write operation is performed and when the request is finished, the primary sends an update request to other backup servers. Each backup sends an acknowledgment to the primary after finishing the update operation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Yet G\u00f6del proved that, for any consistent recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) true propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally undecidable propositions. For example, the continuum hypothesis is undecidable in the Zermelo\u2013Fraenkel set theory as shown by Cohen.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Calculate an \u2212 1 modulo n. If the result is not 1, then n is composite. If the result is 1, then n is likely to be prime; n is then called a probable prime to base a. A weak probable prime to base a is an integer that is a probable prime to base a, but which is not a strong probable prime to base a (see below). For a fixed base a, it is unusual for a composite number to be a probable prime (that is, a pseudoprime) to that base. For example, up to 25 \u00d7 109, there are 11,408,012,595 odd composite numbers, but only 21,853 pseudoprimes base 2.: 1005 The number of odd primes in the same interval is 1,091,987,404.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In microeconomics, value added may be defined as the market value of aggregate output of a transformation process, minus the market value of aggregate input (or aggregate inputs) of a transformation process. One may describe value added with the help of Ulbo de Sitter's design theory for production synergies. He divides transformation processes into two categories, parts and aspects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical linear algebra, the Gauss\u2013Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobi method. Though it can be applied to any matrix with non-zero elements on the diagonals, convergence is only guaranteed if the matrix is either strictly diagonally dominant, or symmetric and positive definite. It was only mentioned in a private letter from Gauss to his student Gerling in 1823. A publication was not delivered before 1874 by Seidel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the Hilbert symbol, Hilbert's reciprocity law for an algebraic number field states that \u220f v ( a , b ) v = 1 {\\displaystyle \\prod _{v}(a,b)_{v}=1} where the product is over all finite and infinite places. Over the rational numbers this is equivalent to the law of quadratic reciprocity. To see this take a and b to be distinct odd primes. Then Hilbert's law becomes ( p , q ) \u221e ( p , q ) 2 ( p , q ) p ( p , q ) q = 1 {\\displaystyle (p,q)_{\\infty }(p,q)_{2}(p,q)_{p}(p,q)_{q}=1} But (p,q)p is equal to the Legendre symbol, (p,q)\u221e is 1 if one of p and q is positive and \u20131 otherwise, and (p,q)2 is (\u20131)(p\u20131)(q\u20131)/4. So for p and q positive odd primes Hilbert's law is the law of quadratic reciprocity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Scientific technologies, similarly, often require the development of a full experimental system to go from a viable concept to a technique that works in practice on a usefully consistent basis. For example, the invention of the polymerase chain reaction (PCR) is generally attributed to Kary Mullis, who came up with the concept in 1983, but the process of development of PCR into the revolutionary technology it became by the early 1990s took years of work by others at Cetus Corporation\u2014and the basic components of the system had been known since the 1960s DNA synthesis work of Har Gobind Khorana\u2014making \"who invented PCR?\" a complicated question.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above formulation, if the bit rate constraint is neglected by setting \u03bb {\\displaystyle \\lambda } equal to 0, or equivalently if it is assumed that a fixed-length code (FLC) will be used to represent the quantized data instead of a variable-length code (or some other entropy coding technology such as arithmetic coding that is better than an FLC in the rate\u2013distortion sense), the optimization problem reduces to minimization of distortion D {\\displaystyle D} alone. The indices produced by an M {\\displaystyle M} -level quantizer can be coded using a fixed-length code using R = \u2308 log 2 \u2061 M \u2309 {\\displaystyle R=\\lceil \\log _{2}M\\rceil } bits/symbol. For example, when M = {\\displaystyle M=} 256 levels, the FLC bit rate R {\\displaystyle R} is 8 bits/symbol. For this reason, such a quantizer has sometimes been called an 8-bit quantizer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The processor could still address 4 GB in this mode, but could not execute anything above address 0x3FFFFFC (64 MB). This mode was used by RISC OS running on the Acorn Risc PC to utilise the new processors while retaining compatibility with existing software. ARM architecture version 4 made the support of the 26-bit addressing modes optional, and ARM architecture version 5 onwards has removed them entirely.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Mind Doesn't Work That Way, a reaction to Steven Pinker's How the Mind Works, is devoted to this subject. Fodor (1983) states that modular systems must\u2014at least to \"some interesting extent\"\u2014fulfill certain properties: Domain specificity: modules only operate on certain kinds of inputs\u2014they are specialised Obligatory firing: modules process in a mandatory manner Limited accessibility: what central processing can access from input system representations is limited Fast speed: probably due to the fact that they are encapsulated (thereby needing only to consult a restricted database) and mandatory (time need not be wasted in determining whether or not to process incoming input) Informational encapsulation: modules need not refer to other psychological systems in order to operate Shallow outputs: the output of modules is very simple Specific breakdown patterns Characteristic ontogeny: there is a regularity of development Fixed neural architecture.Pylyshyn (1999) has argued that while these properties tend to occur with modules, one\u2014information encapsulation\u2014stands out as being the real signature of a module; that is the encapsulation of the processes inside the module from both cognitive influence and from cognitive access. One example is that conscious awareness that the M\u00fcller-Lyer illusion is an illusion does not correct visual processing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle P^{-1}(a')={\\begin{cases}MN-1&{\\text{if }}a'=MN-1,\\\\Ma'{\\bmod {(}}MN-1)&{\\text{otherwise}}.\\end{cases}}} (This is just a consequence of the fact that the inverse of an N\u00d7M transpose is an M\u00d7N transpose, although it is also easy to show explicitly that P\u22121 composed with P gives the identity.) As proved by Cate & Twigg (1977), the number of fixed points (cycles of length 1) of the permutation is precisely 1 + gcd(N\u22121,M\u22121), where gcd is the greatest common divisor. For example, with N = M the number of fixed points is simply N (the diagonal of the matrix).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "What protection level is implemented and does it adhere to compliance regulations?When implemented it provides a bridge between IT professionals and process or application owners. IT staff are informed about the data value and management (usually application owners) understands better which part of the data centre needs to be invested in to keep operations running effectively. This can be of particular importance in risk management, legal discovery, and compliance with government regulations. Data classification is typically a manual process; however, there are many tools from different vendors that can help gather information about the data. Data classification needs to take into account the following: Regulatory requirements Strategic or proprietary worth Organization specific policies Ethical and privacy considerations Contractual agreements", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A group-specific method further decomposes each latent factor into two additive parts: One part corresponds to each item (and/or each user), while the other part is shared among items within each item group (e.g., a group of movies could be movies of the same genre). Then once a new item arrives, we can assign a group label to it, and approximates its latent factor by the group-specific part (of the corresponding item group). Therefore, although the individual part of the new item is not available, the group-specific part provides an immediate and effective solution. The same applies for a new user, as if some information is available for them (e.g. age, nationality, gender) then his/her latent factors can be estimated via an embedding function or a group-specific latent factor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of distributed algorithms, graph coloring is closely related to the problem of symmetry breaking. The current state-of-the-art randomized algorithms are faster for sufficiently large maximum degree \u0394 than deterministic algorithms. The fastest randomized algorithms employ the multi-trials technique by Schneider et al.In a symmetric graph, a deterministic distributed algorithm cannot find a proper vertex coloring.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a message Base station is a predetermined or prescribed spatial or time-sequential arrangement of the parts of a message that is recorded in or on a data storage medium. At one time, messages prepared for electrical transmission were composed on a printed blank form with spaces for each part of the message and for administrative entries. This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Galois rings were studied by Krull (1924), and independently by Janusz (1966) and by Raghavendran (1969), who both introduced the name Galois ring. They are named after \u00c9variste Galois, similar to Galois fields, which is another name for finite fields. Galois rings have found applications in coding theory, where certain codes are best understood as linear codes over Z / 4 Z {\\displaystyle \\mathbb {Z} /4\\mathbb {Z} } using Galois rings GR(4, r).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These machines placed the operands on a push-down (last-in, first out) stack. The instruction set was supplemented with a few instructions to fetch and store memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Constraints may be added to the causes and effects. These are represented as edges labeled with the constraint symbol using a dashed line. For causes, valid constraint symbols are E (exclusive), O (one and only one), I (at least one), and R (Requires).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, giving the structure of the simply-typed \u03bb-calculus at the type level requires binding, or higher-order, type operators. These binding type operators correspond to the 2nd axis of the \u03bb-cube, and type theories such as the simply-typed \u03bb-calculus with type operators, \u03bb\u03c9. Combining type operators with the polymorphic \u03bb-calculus (System F) yields System F\u03c9.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the failure to read a company's privacy policy regarding communications on their platform could lead one to assume that their communication is protected when it is in fact not. Additionally, companies frequently have been known to lack transparency in how they use information, which can be both intentional and unintentional. Discussion of communication privacy necessarily requires consideration of technological methods of protecting information/communication in digital mediums, the effectiveness and ineffectiveness of such methods/systems, and the development/advancement of new and current technologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Kolmogorov's two-series theorem is a result about the convergence of random series. It follows from Kolmogorov's inequality and is used in one proof of the strong law of large numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This amounts to choosing, uniformly at random, an edge of the graph (representing a pair of friends) and an endpoint of that edge (one of the friends), and again calculating the degree of the selected endpoint. The probability of a certain vertex v {\\displaystyle v} to be chosen is d ( v ) | E | 1 2 . {\\displaystyle {\\frac {d(v)}{|E|}}{\\frac {1}{2}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a liquid medium with few or no expected organisms, from an area that is normally sterile (such as CSF, blood inside the circulatory system) centrifugation, decanting the supernatant and using only the sediment will increase the chance to grow and isolate bacteria or the usually cell-associated viruses. If one expects or looks for a particularly fastidious organism, the microbiological culture and isolation techniques will have to be geared towards that microbe. For example, a bacterium that dies when exposed to air, can only be isolated if the sample is carried and processed under airless or anaerobic conditions. A bacterium that dies when exposed to room temperature (thermophilic) requires a pre-warmed transport container, and a microbe that dries and dies when carried on a cotton swab will need a viral transport medium before it can be cultured successfully.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases the computer may not be able to programatically (via programmed I/O) acquire position information with adequate timing precision. For example, the computer may be unable to demand samples on a timely periodic schedule (e.g., for speed measurement) due to software timing variability. Also, in some applications it is necessary to demand samples upon the occurrence of external events, and the computer may be unable to do so in a timely manner. At higher encoder speeds and resolutions, position measurement errors can occur even when interrupts are used to demand samples, because the encoder may move between the time the IRQ is signaled and the sample demand is issued by the interrupt handler.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Eight registers (L0 through L7) are local to the current procedure level, and eight registers (o0 through o7) are the outputs from the current procedure level to the next level called. When a procedure is called, the register window shifts by sixteen registers, hiding the old input registers and old local registers and making the old output registers the new input registers. The common registers (old output registers and new input registers) are used for parameter passing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the finite element method may be recast as a multigrid method. In these cases, multigrid methods are among the fastest solution techniques known today.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On the other hand equation (4) introduces a way of weighting the movement from the previous step in the iteration. Note that if this term was not present in (5) then the algorithm would output a movement in the estimation even if m = E ( x ^ o l d ) {\\displaystyle \\mathbf {m} =E({\\hat {\\mathbf {x} }}_{old})} . It's worth noting that the only strategy used here is to maximize the likelihood at all cost, so artifacts on the image can be introduced. It is worth noting that no prior knowledge on the shape of the ground truth x {\\displaystyle \\mathbf {x} } is used in this derivation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example, the lexical entry is associated with a lemma clergyman and two inflected forms clergyman and clergymen. The language coding is set for the whole lexical resource. The language value is set for the whole lexicon as shown in the following UML instance diagram. The elements Lexical Resource, Global Information, Lexicon, Lexical Entry, Lemma, and Word Form define the structure of the lexicon.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Germanic languages, weak verbs are by far the largest group of verbs, and are therefore often regarded as the norm (the regular verbs). They are distinguished from the Germanic strong verbs by the fact that their past tense form is marked by an inflection containing a /t/, /d/, or /\u00f0/ sound (as in English I walk~I walked) rather than by changing the verb's root vowel (as in English I rise~I rose). Whereas the strong verbs are the oldest group of verbs in Germanic, originating in Indo-European, the weak verbs arose as an innovation in proto-Germanic. Originally the weak verbs consisted of new verbs coined from pre-existing nouns (for example the noun name was turned into the verb to name), or coined from strong verbs to express the sense of causing the action denoted by that strong verb (for example the strong verb to rise was turned into the weak verb to raise).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Second, is a more complex model better? Third, what contribution do individual predictors make to the model? In order to assess models, different model fit statistics would be examined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of simply typed lambda calculus, a type has an inhabitant if and only if its corresponding proposition is a tautology of minimal implicative logic. Similarly, a System F type has an inhabitant if and only if its corresponding proposition is a tautology of intuitionistic second-order logic. Girard's paradox shows that type inhabitation is strongly related to the consistency of a type system with Curry\u2013Howard correspondence. To be sound, such a system must have uninhabited types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The UNIVAC 418 (aka 1219) was an 18-bit word core memory machine. Over the three different models, more than 392 systems were manufactured. The UNIVAC 490 was a 30-bit word core memory machine with 16K or 32K words; 4.8 microsecond cycle time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, minimize the maximal load of all remaining links, but now without the bottleneck links of the first layer. This second iteration further refines the path diversity. Next, we determine the bottleneck links of the 2nd network layer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", x 1 ) {\\displaystyle x^{i}=(x_{i},x_{i-1},x_{i-2},...,x_{1})} and the channel become P ( y i | x i , y i \u2212 1 ) . {\\displaystyle P(y_{i}|x^{i},y^{i-1}).} . In such a case the capacity is given by the mutual information rate when there is no feedback available and the Directed information rate in the case that either there is feedback or not (if there is no feedback the directed information equals the mutual information).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics invariant theory, the bracket ring is the subring of the ring of polynomials k generated by the d-by-d minors of a generic d-by-n matrix (xij). The bracket ring may be regarded as the ring of polynomials on the image of a Grassmannian under the Pl\u00fccker embedding.For given d \u2264 n we define as formal variables the brackets  with the \u03bb taken from {1,...,n}, subject to  = \u2212  and similarly for other transpositions. The set \u039b(n,d) of size ( n d ) {\\displaystyle {\\binom {n}{d}}} generates a polynomial ring K over a field K. There is a homomorphism \u03a6(n,d) from K to the polynomial ring K in nd indeterminates given by mapping  to the determinant of the d by d matrix consisting of the columns of the xi,j indexed by the \u03bb. The bracket ring B(n,d) is the image of \u03a6. The kernel I(n,d) of \u03a6 encodes the relations or syzygies that exist between the minors of a generic n by d matrix. The projective variety defined by the ideal I is the (n\u2212d)d dimensional Grassmann variety whose points correspond to d-dimensional subspaces of an n-dimensional space.To compute with brackets it is necessary to determine when an expression lies in the ideal I(n,d). This is achieved by a straightening law due to Young (1928).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The following week, \"Gangnam Style\" descended to number 18 on the chart but achieved the milestone of 3 million downloads sold in the country, becoming the first and only K-pop song to reach the mark. For the week of January 12, 2013, powered by consumers purchasing some of 2012's most buzzworthy hits and radio airplay recounting the same in year-end retrospectives, the song resurged from number 19 to number six with its best weekly total 400,000 downloads sold, returning to the Hot 100's top ten after three weeks out of the top ten. The track dropped to number 14 in its 18th week, ending a 12-week in the top 10, and number 22 in its 19th week, despite staying in the top ten of Digital Songs chart with 192,000 and 105,000 copies sold, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predictive coding, optimising model parameters through a gradient descent on the time integral of free energy (free action) reduces to associative or Hebbian plasticity and is associated with synaptic plasticity in the brain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It should be apparent now that falsely equating the two probabilities can lead to various errors of reasoning, which is commonly seen through base rate fallacies. While conditional probabilities can provide extremely useful information, limited information is often supplied or at hand. Therefore, it can be useful to reverse or convert a conditional probability using Bayes' theorem: P ( A \u2223 B ) = P ( B \u2223 A ) P ( A ) P ( B ) {\\displaystyle P(A\\mid B)={{P(B\\mid A)P(A)} \\over {P(B)}}} . Another option is to display conditional probabilities in a conditional probability table to illuminate the relationship between events.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to overcome the limits of basic boolean searches, information systems have attempted to classify case laws and statutes into more computer friendly structures. Usually, this results in the creation of an ontology to classify the texts, based on the way a legal professional might think about them. These attempt to link texts on the basis of their type, their value, and/or their topic areas. Most major legal search providers now implement some sort of classification search, such as Westlaw's \u201cNatural Language\u201d or LexisNexis' Headnote searches.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the infinite cardinal numbers have been introduced, which are often denoted with the Hebrew letter \u2135 {\\displaystyle \\aleph } (aleph) marked with subscript indicating their rank among the infinite cardinals. Cardinality is defined in terms of bijective functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software, telemetry is used to gather data on the use and performance of applications and application components, e.g. how often certain features are used, measurements of start-up time and processing time, hardware, application crashes, and general usage statistics and/or user behavior. In some cases, very detailed data is reported like individual window metrics, counts of used features, and individual function timings. This kind of telemetry can be essential to software developers to receive data from a wide variety of endpoints that can't possibly all be tested in-house, as well as getting data on the popularity of certain features and whether they should be given priority or be considered for removal. Due to concerns about privacy since software telemetry can easily be used to profile users, telemetry in user software is often user choice, commonly presented as an opt-in feature (requiring explicit user action to enable it) or user choice during the software installation process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The applications of model theory to algebraic and Diophantine geometry reflect this proximity to classical mathematics, as they often involve an integration of algebraic and model-theoretic results and techniques. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. The most prominent scholarly organization in the field of model theory is the Association for Symbolic Logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a square is the result of multiplying a number by itself. The verb \"to square\" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x^2 (caret) or x**2 may be used in place of x2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for any concept to have meaning, it must be related to sense perception. The 12 categories, or a priori concepts, are related to phenomenal appearances through schemata. Each category has a schema. It is a connection through time between the category, which is an a priori concept of the understanding, and a phenomenal a posteriori appearance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the term analysis may refer to any method used for data analysis. Among the many such methods, some are: Analysis of variance (ANOVA) \u2013 a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts Boolean analysis \u2013 a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis Cluster analysis \u2013 techniques for finding groups (called clusters), based on some measure of proximity or similarity Factor analysis \u2013 a method to construct models describing a data set of observed variables in terms of a smaller set of unobserved variables (called factors) Meta-analysis \u2013 combines the results of several studies that address a set of related research hypotheses Multivariate analysis \u2013 analysis of data involving several variables, such as by factor analysis, regression analysis, or principal component analysis Principal component analysis \u2013 transformation of a sample of correlated variables into uncorrelated variables (called principal components), mostly used in exploratory data analysis Regression analysis \u2013 techniques for analysing the relationships between several predictive variables and one or more outcomes in the data Scale analysis (statistics) \u2013 methods to analyse survey data by scoring responses on a numeric scale Sensitivity analysis \u2013 the study of how the variation in the output of a model depends on variations in the inputs Sequential analysis \u2013 evaluation of sampled data as it is collected, until the criterion of a stopping rule is met Spatial analysis \u2013 the study of entities using geometric or geographic properties Time-series analysis \u2013 methods that attempt to understand a sequence of data points spaced apart at uniform time intervals", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some phonological theories use 'doubling' as a synonym for gemination, while others describe two distinct phenomena.Consonant length is a distinctive feature in certain languages, such as Arabic, Berber, Danish, Estonian, Finnish, Hindi, Hungarian, Italian, Japanese, Kannada, Malayalam, Punjabi, Polish and Turkish. Other languages, such as English, do not have word-internal phonemic consonant geminates. Consonant gemination and vowel length are independent in languages like Arabic, Japanese, Finnish and Estonian; however, in languages like Italian, Norwegian and Swedish, vowel length and consonant length are interdependent. For example, in Norwegian and Swedish, a geminated consonant is always preceded by a short vowel, while an ungeminated consonant is preceded by a long vowel. A clear example are the Norwegian words tak  ('ceiling or roof' of a building), and takk  ('thanks').", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software applications that modify information stored on disk, this generally involves flushing any outstanding writes; see buffering. With telecom applications, this generally involves allowing existing callers to finish their call but preventing new calls from initiating.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another example, in C++, uses the \"angle bracket\" characters < and > in the syntax for template specialization, but two consecutive > characters are interpreted as the right-shift operator >>. Prior to C++11, the following code would produce a parse error, because the right-shift operator token is encountered instead of two right-angle-bracket tokens: The C++11 standard adopted in August 2011 amended the grammar so that a right-shift token is accepted as synonymous with a pair of right angle brackets (as in Java), which complicates the grammar but allows the continued use of the maximal munch principle. An exception to the maximal munch rule had to be added anyway to deal with the sequence <:: which can appear in templates. In that case, unless the sequence is followed by: or > the character < is interpreted as its own token instead of part of the token <:.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Semantic Web and in knowledge representation, a metaclass is a class whose instances can themselves be classes. Similar to their role in programming languages, metaclasses in Semantic Web languages can have properties otherwise applicable only to individuals, while retaining the same class's ability to be classified in a concept hierarchy. This enables knowledge about instances of those metaclasses to be inferred by semantic reasoners using statements made in the metaclass. Metaclasses thus enhance the expressivity of knowledge representations in a way that can be intuitive for users.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the assessment and prediction of software reliability, we use the reliability growth model. During operation of the software, any data about its failure is stored in statistical form and is given as input to the reliability growth model. Using this data, the reliability growth model can evaluate the reliability of software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The operations can be scheduled in any order. Operation O i j {\\displaystyle O_{ij}} must be processed for p i j {\\displaystyle p_{ij}} units on machine i {\\displaystyle i} . F: Flow-shop problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The ability of a mobile phone to connect to a base station depends on the strength of the signal. That may be boosted by higher power transmissions, better antennas, taller antenna masts or alternative solutions like in-building picocells. Normal Macro-Cell signals need to be boosted to pass through buildings, which is a particular problem designing networks for large metropolitan areas with modern skyscrapers, hence the current drive for small cells and micro and pico cells. Signals also do not travel deep underground, so specialized transmission solutions are used to deliver mobile phone coverage into areas such as underground parking garages and subway trains.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class (or group) it belongs to. A linear classifier achieves this by making a classification decision based on the value of a linear combination of the characteristics. An object's characteristics are also known as feature values and are typically presented to the machine in a vector called a feature vector. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, the method derandomizes the proof. The basic idea is to replace each random choice in a random experiment by a deterministic choice, so as to keep the conditional probability of failure, given the choices so far, below 1. The method is particularly relevant in the context of randomized rounding (which uses the probabilistic method to design approximation algorithms). When applying the method of conditional probabilities, the technical term pessimistic estimator refers to a quantity used in place of the true conditional probability (or conditional expectation) underlying the proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This results in a faster comparison loop, as one comparison is eliminated per iteration, while it requires only one more iteration on average.Hermann Bottenbruch published the first implementation to leave out this check in 1962. Set L {\\displaystyle L} to 0 {\\displaystyle 0} and R {\\displaystyle R} to n \u2212 1 {\\displaystyle n-1} . While L \u2260 R {\\displaystyle L\\neq R} , Set m {\\displaystyle m} (the position of the middle element) to the ceiling of L + R 2 {\\displaystyle {\\frac {L+R}{2}}} , which is the least integer greater than or equal to L + R 2 {\\displaystyle {\\frac {L+R}{2}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimal LS SPCA (USPCA, uncorrelated SPCA) the orthogonality constraints require that the cardinality of the solutions is not smaller than the order of the component, These constraints may also create numerical problems when computing components of order larger than two. Correlated SPCA (CSPCA, correlated SPCA) is a variant of LS SPCA in which the orthogonality constraints are relaxed and the solutions are obtained iteratively by minimizing the norm of the approximation error from residuals orthogonal to the previously computed SPCs. Even though the resulting components are correlated (usually very mildly) , they have lower cardinality and in many cases explain more variance than the corresponding USPCA solutions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Exactly where the boundary is drawn between proper values and data structures masquerading as such is often hard to predict. In C, an array (of which strings are special cases) is a data structure but the name of an array is treated as (has as value) the reference to the first element of the array, while a struct variable's name refers to a value even if it has fields that are vectors. In Maple, a vector is a special case of a table and therefore a data structure, but a list (which gets rendered and can be indexed in exactly the same way) is a value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The UML sequence diagram shows the run-time interactions. In this example, a Mediator1 object mediates (controls and coordinates) the interaction between Colleague1 and Colleague2 objects. Assuming that Colleague1 wants to interact with Colleague2 (to update/synchronize its state, for example), Colleague1 calls mediate(this) on the Mediator1 object, which gets the changed data from Colleague1 and performs an action2() on Colleague2. Thereafter, Colleague2 calls mediate(this) on the Mediator1 object, which gets the changed data from Colleague2 and performs an action1() on Colleague1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On the week of September 12, 2012, the song debuted at number seven on the Top 20 Digital Tracks chart, based on Nielsen SoundScan data. The following week it topped the chart and spent four weeks at the top spot before giving the summit to \"I Knew You Were Trouble\" by Taylor Swift. \"Gangnam Style,\" however, was back on top of the chart for the week of October 24, and grabbed the number one position for another four straight weeks, tallying a total of eight nonconsecutive weeks atop the chart. On November 16, 2012, the track was certified 4\u00d7 Platinum by Music Canada, and as of January 2013 had sold more than 476,000 copies in the country.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Bulgarian language the vowels \u0430 , \u044a , \u043e  and \u0435  can be partially or fully reduced, depending on the dialect, when unstressed to , ,  and , respectively. The most prevalent is  > ,  >  and  > , which, in its partial form, is considered correct in literary speech. The reduction  >  is prevalent in the eastern dialects of the language and is not considered formally correct.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of information security, and especially network security, a spoofing attack is a situation in which a person or program successfully identifies as another by falsifying data, to gain an illegitimate advantage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let G = Per ( 3 ) {\\displaystyle G={\\text{Per}}(3)} be the permutation groups in three elements. Let \u03c1: Per ( 3 ) \u2192 GL 5 ( C ) {\\displaystyle \\rho :{\\text{Per}}(3)\\to {\\text{GL}}_{5}(\\mathbb {C} )} be a linear representation of Per ( 3 ) {\\displaystyle {\\text{Per}}(3)} defined on the generating elements as follows: \u03c1 ( 1 , 2 ) = ( \u2212 1 2 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 ) , \u03c1 ( 1 , 3 ) = ( 1 2 1 2 0 0 0 1 2 \u2212 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 ) , \u03c1 ( 2 , 3 ) = ( 0 \u2212 2 0 0 0 \u2212 1 2 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 ) . {\\displaystyle \\rho (1,2)={\\begin{pmatrix}-1&2&0&0&0\\\\0&1&0&0&0\\\\0&0&0&1&0\\\\0&0&1&0&0\\\\0&0&0&0&1\\end{pmatrix}},\\quad \\rho (1,3)={\\begin{pmatrix}{\\frac {1}{2}}&{\\frac {1}{2}}&0&0&0\\\\{\\frac {1}{2}}&-1&0&0&0\\\\0&0&0&0&1\\\\0&0&0&1&0\\\\0&0&1&0&0\\end{pmatrix}},\\quad \\rho (2,3)={\\begin{pmatrix}0&-2&0&0&0\\\\-{\\frac {1}{2}}&0&0&0&0\\\\", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, A \u27f6 {\\displaystyle {\\stackrel {\\,\\longrightarrow }{A}}} \u22c5 B \u27f6 {\\displaystyle {\\stackrel {\\,\\longrightarrow }{B}}} = | A \u27f6 {\\displaystyle {\\stackrel {\\,\\longrightarrow }{A}}} | | B \u27f6 {\\displaystyle {\\stackrel {\\,\\longrightarrow }{B}}} | cos \u03b8More generally, a bilinear product in an algebra over a field. Cross product \u2013 also known as the \"vector product\", a binary operation on two vectors that results in another vector. The cross product of two vectors in 3-space is defined as the vector perpendicular to the plane determined by the two vectors whose magnitude is the product of the magnitudes of the two vectors and the sine of the angle between the two vectors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "2) Multiple losses: x {\\displaystyle x} and y {\\displaystyle y} are both considered losses. Here, we see that V a l u e ( \u2212 x ) + V a l u e ( \u2212 y ) < V a l u e ( \u2212 ( x + y ) ) {\\displaystyle Value(-x)+Value(-y) V a l u e ( x \u2212 y ) {\\displaystyle Value(x)+Value(-y)>Value(x-y)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But one really requires average numbers. These average numbers can be obtained by the Darwin\u2013Fowler method. Of course, for systems in the thermodynamic limit (large number of particles), as in statistical mechanics, the results are the same as with maximization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Principle 3: An audit trail or other record of all processes applied to digital evidence should be created and preserved. An independent third party should be able to examine those processes and achieve the same result. Principle 4: The person in charge of the investigation has overall responsibility for ensuring that the law and these principles are adhered to. These guidelines are widely accepted in courts of England and Scotland, but they do not constitute a legal requirement and their use is voluntary. It is arguable that whilst voluntary, non adherence is almost certain to lead to the exclusion of evidence that does not comply subject to the provisions of s 78 Police and Criminal Evidence Act 1984 (Power to exclude evidence obtained unfairly)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This division requires quotient digit estimation and correction. The Montgomery form, in contrast, depends on a constant R > N which is coprime to N, and the only division necessary in Montgomery multiplication is division by R. The constant R can be chosen so that division by R is easy, significantly improving the speed of the algorithm. In practice, R is always a power of two, since division by powers of two can be implemented by bit shifting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matroid theory, a Sylvester matroid is a matroid in which every pair of elements belongs to a three-element circuit (a triangle) of the matroid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The equipment would descramble the signal so that it can be viewed by the subscriber. It also is addressable, meaning that it can be remotely controlled by the company's technical staff. The first major case covered by the media was when 317 subscribers were caught in 1991 when the company they subscribed sent a \"bullet\" (a video signal that turns off the equipment) to their cable boxes. The boxes were modified, but possibly belonged to the cable company.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, the use of production means is scheduled in advance in order to respond to load profiles. The load corresponds to the total electricity consumption over the area of interest. Load profiles are usually given by load forecasts which are of high accuracy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Accordingly, the subclass relation makes the collection of all classes into a Boolean lattice, which the subset relation does not do for the collection of all sets. Instead, the collection of all sets is an ideal in the collection of all classes. (Of course, the collection of all classes is something larger than even a class!) == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of mathematics known as semigroup theory, an E-semigroup is a semigroup in which the idempotents form a subsemigroup.Certain classes of E-semigroups have been studied long before the more general class, in particular, a regular semigroup that is also an E-semigroup is known as an orthodox semigroup. Weipoltshammer proved that the notion of weak inverse (the existence of which is one way to define E-inversive semigroups) can also be used to define/characterize E-semigroups as follows: a semigroup S is an E-semigroup if and only if, for all a and b \u2208 S, W(ab) = W(b)W(a), where W(a) \u225d {x \u2208 S | xax = x} is the set of weak inverses of a. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Russell and Whitehead's notation for building up types from other types is rather cumbersome, and the notation here is due to Church. In the ramified type theory of PM all objects are elements of various disjoint ramified types. Ramified types are implicitly built up as follows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each agent, in turn, claims any item that was not allocated to an agent with a higher priority (\"claims\" means that the agent assigns \"1\" to the corresponding variable). After an agent has assigned all its variables (either 1 or 0), it sends the resulting assignment to the next agent in the lexicographic order. The agents send to each other messages with their envy evaluation of the current assignment. After receiving envy evaluations from other agents, the agent may decide to backtrack on a variable; if there are no more variables to backtrack, the agent may backtrack to a previous agent. Once the first agent backtracks its first variable, the search has ended and the optimal allocation has been found.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Among other things, this may permit a single variable to refer to values of different types at different points in the program execution. However, type errors cannot be automatically detected until a piece of code is actually executed, potentially making debugging more difficult. Lisp, Smalltalk, Perl, Python, JavaScript, and Ruby are all examples of dynamically-typed languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a library supporting data structures, for example, a class modeling linear structures effects universal quantification with a function for_all of type BOOLEAN that accepts an agent, an instance of FUNCTION, as an argument. So, in the following example, my_action is executed only if all members of my_list contain the character '!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Pillai prime is a prime number p for which there is an integer n > 0 such that the factorial of n is one less than a multiple of the prime, but the prime is not one more than a multiple of n. To put it algebraically, n ! \u2261 \u2212 1 mod p {\\displaystyle n!\\equiv -1\\mod p} but p \u2262 1 mod n {\\displaystyle p\\not \\equiv 1\\mod n} . The first few Pillai primes are 23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, ... (sequence A063980 in the OEIS)Pillai primes are named after the mathematician Subbayya Sivasankaranarayana Pillai, who studied these numbers. Their infinitude has been proved several times, by Subbarao, Erd\u0151s, and Hardy & Subbarao.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of f is the function f \u2212 1: R \u2192 R {\\displaystyle f^{-1}\\colon \\mathbb {R} \\to \\mathbb {R} } defined by f \u2212 1 ( y ) = y + 7 5 . {\\displaystyle f^{-1}(y)={\\frac {y+7}{5}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above example, the result of applying the Schensted insertion to successively insert 1,3,3,2,2,1,2 into an initially empty tableau results in a tableau P, and an additional standard tableau Q0 recoding the successive shapes, given by P = 1 1 2 2 2 3 3 , Q 0 = 1 2 3 7 4 5 6 , {\\displaystyle P\\quad =\\quad {\\begin{matrix}1&1&2&2\\\\2&3\\\\3\\end{matrix}},\\qquad Q_{0}\\quad =\\quad {\\begin{matrix}1&2&3&7\\\\4&5\\\\6\\end{matrix}},} and after replacing the entries 1,2,3,4,5,6,7 in Q0 successively by 1,1,1,2,2,3,3 one obtains the pair of semistandard tableaux P = 1 1 2 2 2 3 3 , Q = 1 1 1 3 2 2 3 . {\\displaystyle P\\quad =\\quad {\\begin{matrix}1&1&2&2\\\\2&3\\\\3\\end{matrix}},\\qquad Q\\quad =\\quad {\\begin{matrix}1&1&1&3\\\\2&2\\\\3\\end{matrix}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Quantitative PCR, however, offers an accurate and rapid alternative to traditional PCR. Quantitative PCR offers the researcher the opportunity to amplify and analyze the product in a single tube using fluorescent dyes. This is known as homogeneous PCR.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Traditional approaches in statistical physics studied the limit of intensive properties as the size of a finite system approaches infinity (the thermodynamic limit). When the energy function can be written as a sum of terms that each involve only variables from a finite subsystem, the notion of a Gibbs measure provides an alternative approach. Gibbs measures were proposed by probability theorists such as Dobrushin, Lanford, and Ruelle and provided a framework to directly study infinite systems, instead of taking the limit of finite systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, for example in the study of statistical properties of graphs, a null model is a type of random object that matches one specific object in some of its features, or more generally satisfies a collection of constraints, but which is otherwise taken to be an unbiasedly random structure. The null model is used as a term of comparison, to verify whether the object in question displays some non-trivial features (properties that wouldn't be expected on the basis of chance alone or as a consequence of the constraints), such as community structure in graphs. An appropriate null model behaves in accordance with a reasonable null hypothesis for the behavior of the system under investigation. One null model of utility in the study of complex networks is that proposed by Newman and Girvan, consisting of a randomized version of an original graph G {\\displaystyle G} , produced through edges being rewired at random, under the constraint that the expected degree of each vertex matches the degree of the vertex in the original graph.The null model is the basic concept behind the definition of modularity, a function which evaluates the goodness of partitions of a graph into clusters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most jurisdictions, prison inmates are forbidden from possessing mobile phones due to their ability to communicate with the outside world and other security issues. Mobile phones are one of the most smuggled items into prisons. They provide inmates the ability to make and receive unauthorized phone calls, send email and text messages, use social media, and follow news pertaining to their case, among other forbidden uses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The generic algorithm has a strongly polynomial O(V 2E) time complexity, which is asymptotically more efficient than the O(VE 2) Edmonds\u2013Karp algorithm. Specific variants of the algorithms achieve even lower time complexities. The variant based on the highest label node selection rule has O(V 2\u221aE) time complexity and is generally regarded as the benchmark for maximum flow algorithms. Subcubic O(VElog(V 2/E)) time complexity can be achieved using dynamic trees, although in practice it is less efficient.The push\u2013relabel algorithm has been extended to compute minimum cost flows. The idea of distance labels has led to a more efficient augmenting path algorithm, which in turn can be incorporated back into the push\u2013relabel algorithm to create a variant with even higher empirical performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are several different ways to express reciprocity laws. The early reciprocity laws found in the 19th century were usually expressed in terms of a power residue symbol (p/q) generalizing the quadratic reciprocity symbol, that describes when a prime number is an nth power residue modulo another prime, and gave a relation between (p/q) and (q/p). Hilbert reformulated the reciprocity laws as saying that a product over p of Hilbert norm residue symbols (a,b/p), taking values in roots of unity, is equal to 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first five examples are in fact birationally equivalent. That is, for example, a cubic surface has a function field isomorphic to that of the projective plane, being the rational functions in two indeterminates. The Cartesian product of two curves also provides examples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some computers, the machine code of the architecture is implemented by an even more fundamental underlying layer called microcode, providing a common machine language interface across a line or family of different models of computer with widely different underlying dataflows. This is done to facilitate porting of machine language programs between different models. An example of this use is the IBM System/360 family of computers and their successors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead, virtual memory pages in both processes may refer to the same pages of physical memory until one of them writes to such a page: then it is copied. This optimization is important in the common case where fork is used in conjunction with exec to execute a new program: typically, the child process performs only a small set of actions before it ceases execution of its program in favour of the program to be started, and it requires very few, if any, of its parent's data structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Files (or links to files) can be located in directories. However, more generally, a directory can contain either a list of files or a list of links to files. Within this definition, it is of paramount importance that the term \"file\" includes directories.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But notice that if we are given a particular subset, we can efficiently verify whether the subset sum is zero, by summing the integers of the subset. If the sum is zero, that subset is a proof or witness for the answer is \"yes\". An algorithm that verifies whether a given subset has sum zero is a verifier.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\sum _{k=0}^{\\infty }\\left|\\Pr(S_{n}=k)-{\\lambda _{n}^{k}e^{-\\lambda _{n}} \\over k! }\\right|<2\\left(1\\wedge {\\frac {1}{\\lambda }}_{n}\\right)\\left(\\sum _{i=1}^{n}p_{i}^{2}\\right).} , where \u2227 {\\displaystyle \\wedge } represents the min {\\displaystyle \\min } operator. It is also possible to weaken the independence requirement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such as a set of coin flips) or conditional probabilities (such as drawing cards from a deck, without replacing the cards). Each node on the diagram represents an event and is associated with the probability of that event. The root node represents the certain event and therefore has probability 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, structured cabling is building or campus cabling infrastructure that consists of a number of standardized smaller elements (hence structured) called subsystems. Structured cabling components include twisted pair and optical cabling, patch panels and patch cables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is a decentralized, distributed, self-organizing network of individual fusion centers and their respective partners within each center's area of responsibility. The process is a method of managing the flow of information and intelligence across levels and sectors of government to integrate information for analysis. Fusion centers rely on the active involvement of state, local, tribal, and federal law enforcement agencies\u2014and sometimes on non\u2013law enforcement agencies\u2014to provide intelligence for their analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The function SSCG(k) denotes that length for simple subcubic graphs. The function SCG(k) denotes that length for (general) subcubic graphs. The SCG sequence begins SCG(0) = 6, but then explodes to a value equivalent to f\u03b52*2 in the fast-growing hierarchy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pure mathematics, there are several notational methods for representing large numbers by which the magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth's up-arrow notation, Steinhaus\u2013Moser notation, or Conway chained arrow notation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, we can see how important guard digits can be. An example of the error caused by floating point roundoff is illustrated in the following C code. It appears that the program should not terminate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To \"measure\" is to place a shorter measuring length s successively (q times) along longer length l until the remaining portion r is less than the shorter length s. In modern words, remainder r = l \u2212 q\u00d7s, q being the quotient, or remainder r is the \"modulus\", the integer-fractional part left over after the division.For Euclid's method to succeed, the starting lengths must satisfy two requirements: (i) the lengths must not be zero, AND (ii) the subtraction must be \"proper\"; i.e., a test must guarantee that the smaller of the two numbers is subtracted from the larger (or the two can be equal so their subtraction yields zero). Euclid's original proof adds a third requirement: the two lengths must not be prime to one another. Euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers' common measure is in fact the greatest. While Nicomachus' algorithm is the same as Euclid's, when the numbers are prime to one another, it yields the number \"1\" for their common measure. So, to be precise, the following is really Nicomachus' algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the Klee\u2013Minty cube is an example that shows the worst-case computational complexity of many algorithms of linear optimization. It is a deformed cube with exactly 2D corners in dimension D. Klee and Minty showed that Dantzig's simplex algorithm visits all corners of a (perturbed) cube in dimension D in the worst case.Modifications of the Klee\u2013Minty construction showed similar exponential time complexity for other pivoting rules of simplex type, which maintain primal feasibility, such as Bland's rule. Another modification showed that the criss-cross algorithm, which does not maintain primal feasibility, also visits all the corners of a modified Klee\u2013Minty cube. Like the simplex algorithm, the criss-cross algorithm visits all 8 corners of the three-dimensional cube in the worst case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development XRX is a web application architecture based on XForms, REST and XQuery. XRX applications store data on both the web client and on the web server in XML format and do not require a translation between data formats. XRX is considered a simple and elegant application architecture due to the minimal number of translations needed to transport data between client and server systems. The XRX architecture is also tightly coupled to W3C standards (CSS, XHTML 2.0, XPath, XML Schema) to ensure XRX applications will be robust in the future. Because XRX applications leverage modern declarative languages on the client and functional languages on the server they are designed to empower non-developers who are not familiar with traditional imperative languages such as JavaScript, Java or .Net.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, in 2003, Alexander Ol'shanskii and Mark Sapir exhibited a collection of finitely-presented groups which do not satisfy the conjecture. In 2013, Nicolas Monod found an easy counterexample to the conjecture. Given by piecewise projective homeomorphisms of the line, the group is remarkably simple to understand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern X11 systems (or utilities such as WinCompose on Windows systems), the double acute can be typed by pressing the Compose key followed by = (the equal sign) and desired letter (o or u).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, profiling (\"program profiling\", \"software profiling\") is a form of dynamic program analysis that measures, for example, the space (memory) or time complexity of a program, the usage of particular instructions, or the frequency and duration of function calls. Most commonly, profiling information serves to aid program optimization, and more specifically, performance engineering. Profiling is achieved by instrumenting either the program source code or its binary executable form using a tool called a profiler (or code profiler). Profilers may use a number of different techniques, such as event-based, statistical, instrumented, and simulation methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of digital and interactive television, Nested Context Language (NCL) is a declarative authoring language for hypermedia documents. NCL documents do not contain multimedia elements such as audio or video content; rather they function as a \"glue\" language that specifies how multimedia components are related. In particular, NCL documents specify how these components are synchronized relative to each other and how the components are composed together into a unified document. Among its main facilities, it treats hypermedia relations as first-class entities through the definition of hypermedia connectors, and it can specify arbitrary semantics for a hypermedia composition using the concept of composite templates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consider a sequence { A k } {\\displaystyle \\{\\mathbf {A} _{k}\\}} of fixed self-adjoint matrices that satisfy ( H ( z 1 , \u2026 , z k , \u2026 , z n ) \u2212 H ( z 1 , \u2026 , z k \u2032 , \u2026 , z n ) ) 2 \u2aaf A k 2 , {\\displaystyle \\left(\\mathbf {H} (z_{1},\\ldots ,z_{k},\\ldots ,z_{n})-\\mathbf {H} (z_{1},\\ldots ,z'_{k},\\ldots ,z_{n})\\right)^{2}\\preceq \\mathbf {A} _{k}^{2},} where z i {\\displaystyle z_{i}} and z i \u2032 {\\displaystyle z'_{i}} range over all possible values of Z i {\\displaystyle Z_{i}} for each index i {\\displaystyle i} . Compute the variance parameter \u03c3 2 = \u2016 \u2211 k A k 2 \u2016 . {\\displaystyle \\sigma ^{2}={\\bigg \\Vert }\\sum _{k}\\mathbf {A} _{k}^{2}{\\bigg \\Vert }.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As indicated by the accent marks, the stress is always on the last syllable, which is unlike the dative-case forms with the same spelling. A few feminine nouns that end with the soft sign, such as \u0434\u0432\u0435\u0440\u044c and \u043f\u044b\u043b\u044c, also have a locative form that differs from the prepositional in that the stress shifts to the final syllable: \"\u043d\u0430 \u0434\u0432\u0435\u0440\u0438\u0301\", na dver\u00ed (\"on the door\"), but \"\u043f\u0440\u0438 \u0434\u0432\u0435\u0301\u0440\u0438\", pri dv\u00e9ri (\"by the door\"). These distinct feminine forms are sometimes referenced as \"second locative\" or \"new locative\", because they developed independently from the true locative case, which existed in Old Russian.With some words, such as \u0434\u043e\u043c, dom (house), the second locative form is used only in certain idiomatic expressions, while the prepositional is used elsewhere. For example, \"\u043d\u0430 \u0434\u043e\u043c\u0443\u0301\", na domu (\"at the house\" or \"at home\") would be used to describe activity that is performed at home, while \"\u043d\u0430 \u0434\u043e\u0301\u043c\u0435\" (\"on the house\") would be used to specify the location of the roof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From this principle the error rules of summation, multiplication etc. are derived, e.g.: That is to say, in multiplication, the total relative error is the sum of the relative errors of the parameters. To illustrate how this depends on the function considered, consider the case where the function is f ( a , b ) = a ln \u2061 b {\\displaystyle f(a,b)=a\\ln b} instead. Then, it can be computed that the error estimate is with an extra 'ln b' factor not found in the case of a simple product. This additional factor tends to make the error smaller, as ln b is not as large as a bare b.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other scenarios, a dispatched object immediately loses its full or partial value, if a certain number of consumers Ca have already received the object. In a function, the ordinate value takes on zero, if value x representing cn, has received the value. It draws a dramatic knee on the function's graph. This scenario is prevalent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a probable prime (PRP) is an integer that satisfies a specific condition that is satisfied by all prime numbers, but which is not satisfied by most composite numbers. Different types of probable primes have different specific conditions. While there may be probable primes that are composite (called pseudoprimes), the condition is generally chosen in order to make such exceptions rare. Fermat's test for compositeness, which is based on Fermat's little theorem, works as follows: given an integer n, choose some integer a that is not a multiple of n; (typically, we choose a in the range 1 < a < n \u2212 1).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean. Given a sample x = ( x 1 , x 2 \u2026 , x n ) {\\displaystyle x=(x_{1},x_{2}\\dots ,x_{n})} and weights w = ( w 1 , w 2 , \u2026 , w n ) {\\displaystyle w=(w_{1},w_{2},\\dots ,w_{n})} , it is calculated as: x \u00af = ( \u220f i = 1 n x i w i ) 1 / \u2211 i = 1 n w i = exp \u2061 ( \u2211 i = 1 n w i ln \u2061 x i \u2211 i = 1 n w i ) {\\displaystyle {\\bar {x}}=\\left(\\prod _{i=1}^{n}x_{i}^{w_{i}}\\right)^{1/\\sum _{i=1}^{n}w_{i}}=\\quad \\exp \\left({\\frac {\\sum _{i=1}^{n}w_{i}\\ln x_{i}}{\\sum _{i=1}^{n}w_{i}\\quad }}\\right)} The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. If all the weights are equal, the weighted geometric mean simplifies to the ordinary unweighted geometric mean.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Without knowledge of the pepper, other passwords in the database will be far more difficult to extract from their hashed values, as the attacker would need to guess the password as well as the pepper. A pepper adds security to a database of salts and hashes because unless the attacker is able to obtain the pepper, cracking even a single hash is intractable, no matter how weak the original password. Even with a list of (salt, hash) pairs, an attacker must also guess the secret pepper in order to find the password which produces the hash. The NIST specification for a secret salt suggests using a Password-Based Key Derivation Function (PBKDF) with an approved Pseudorandom Function such as HMAC with SHA-3 as the hash function of the HMAC. The NIST recommendation is also to perform at least 1000 iterations of the PBKDF, and a further minimum 1000 iterations using the secret salt in place of the non-secret salt.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formally, a vertex conflict happens when \u03c0 i  = \u03c0 j  {\\displaystyle \\pi _{i}=\\pi _{j}} . Edge conflict: an edge conflict occurs whenever two agents cross the same edge in the same direction at the same time, that is \u03c0 i  = \u03c0 j  {\\displaystyle \\pi _{i}=\\pi _{j}} and \u03c0 i  = \u03c0 j  {\\displaystyle \\pi _{i}=\\pi _{j}} . If vertex conflicts are not allowed, then edge conflicts cannot exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The HITS computation is performed only on this focused subgraph. According to Kleinberg the reason for constructing a base set is to ensure that most (or many) of the strongest authorities are included. Authority and hub values are defined in terms of one another in a mutual recursion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A stochastic process { Z n , n = 1 , 2 , \u2026 } {\\displaystyle \\{Z_{n},n=1,2,\\ldots \\}} is said to be a threshold geometric process (threshold GP), if there exists real numbers a i > 0 , i = 1 , 2 , \u2026 , k {\\displaystyle a_{i}>0,i=1,2,\\ldots ,k} and integers { 1 = M 1 < M 2 < \u22ef < M k < M k + 1 = \u221e } {\\displaystyle \\{1=M_{1} 0 {\\displaystyle h(k)>0} for natural number k {\\displaystyle k} , then { X k , k = 1 , 2 , \u2026 } {\\displaystyle \\{X_{k},k=1,2,\\ldots \\}} is called a doubly geometric process (DGP). The semi-geometric process. Given a sequence of non-negative random variables { X k , k = 1 , 2 , \u2026 } {\\displaystyle \\{X_{k},k=1,2,\\dots \\}} , if P { X k < x | X k \u2212 1 = x k \u2212 1 , \u2026 , X 1 = x 1 } = P { X k < x | X k \u2212 1 = x k \u2212 1 } {\\displaystyle P\\{X_{k}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "0 7 2 9 4 11 6 1 8 3 10 5 (0 + 0 5 10 3 8 1 6 11 4 9 2 7 (0 ________________________________________ = 0 0 0 0 0 0 0 0 0 0 0 0 (0 The two cycles may also be aligned as pairs of sum 7 or sum 5 dyads. All together these pairs of cycles form a set complex, \"any cyclic set of the set complex may be uniquely identified by its two adjacency sums,\" and as such the example above shows p0p7 and i5i0. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In neuroscience, predictive coding (also known as predictive processing) is a theory of brain function which postulates that the brain is constantly generating and updating a \"mental model\" of the environment. According to the theory, such a mental model is used to predict input signals from the senses that are then compared with the actual input signals from those senses. With the rising popularity of representation learning, the theory is being actively pursued and applied in machine learning and related fields.The phrase 'predictive coding' is also used in several other disciplines such as signal-processing technologies and law in loosely-related or unrelated senses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(reflexivity). (Here, id {\\displaystyle \\operatorname {id} } denotes the identity function on X {\\displaystyle X} .) R = R \u2212 1 {\\displaystyle R=R^{-1}} (symmetry). R R \u2286 R {\\displaystyle RR\\subseteq R} (transitivity).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relation to audiovisual content, according to the meaning given by the Canadian Radio-television and Telecommunications Commission (CRTC) for the purpose of its 2016 Discoverability Summit, discoverability can be summed up to the intrinsic ability of given content to \"stand out of the lot\", or to position itself so as to be easily found and discovered. A piece of audiovisual content can be a movie, a TV series, music, a book (eBook), an audio book or podcast. When audiovisual content such as a digital file for a TV show, movie, or song, is made available online, if the content is \"tagged\" with identifying information such as the names of the key artists (e.g., actors, directors and screenwriters for TV shows and movies; singers, musicians and record producers for songs) and the genres (for movies genres, music genres, etc.). When users interact with online content, algorithms typically determine what types of content the user is interested in, and then a computer program suggests \"more like this\", which is other content that the user may be interested in.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In standard NMF, matrix factor W \u2208 R+m \u00d7 k\uff0c i.e., W can be anything in that space. Convex NMF restricts the columns of W to convex combinations of the input data vectors ( v 1 , \u2026 , v n ) {\\displaystyle (v_{1},\\dots ,v_{n})} . This greatly improves the quality of data representation of W. Furthermore, the resulting matrix factor H becomes more sparse and orthogonal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the computer era, spacing between sentences is handled in several different ways by various software packages. Some systems accept whatever the user types, while others attempt to alter the spacing or use the user input as a method of detecting sentences. Computer-based word processors and typesetting software such as troff and TeX allow users to arrange text in a manner previously only available to professional typesetters.The text-editing environment in Emacs uses a double space following a period to identify the end of sentences unambiguously; the double-space convention prevents confusion with periods within sentences that signify abbreviations. How Emacs recognizes the end of a sentence is controlled by the settings sentence-end-double-space and sentence-end.The Unix typesetter program Troff uses two spaces to mark the end of a sentence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics there is a close link between map coloring and graph coloring, since every map showing different areas has a corresponding graph. By far the most famous result in this area is the four color theorem, which states that any planar map can be colored with at most four colors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to preserve the precise meaning and enable accurate parsing of complex UDC expressions, a number of connecting symbols are made available to relate and extend UDC numbers. These are:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The item-and-process and word-and-paradigm approaches usually address fusional languages. As there is very little fusion involved in word formation, classical typology mostly applies to inflectional morphology. Depending on the preferred way of expressing non-inflectional notions, languages may be classified as synthetic (using word formation) or analytic (using syntactic phrases).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also, a version of Goldbach's conjecture has been extended to them. There are infinitely many lucky numbers. Twin lucky numbers and twin primes also appear to occur with similar frequency. However, if Ln denotes the n-th lucky number, and pn the n-th prime, then Ln > pn for all sufficiently large n.Because of their apparent similarities with the prime numbers, some mathematicians have suggested that some of their common properties may also be found in other sets of numbers generated by sieves of a certain unknown form, but there is little theoretical basis for this conjecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the binary tree representation, a successful search can be represented by a path from the root to the target node, called an internal path. The length of a path is the number of edges (connections between nodes) that the path passes through. The number of iterations performed by a search, given that the corresponding path has length l {\\displaystyle l} , is l + 1 {\\displaystyle l+1} counting the initial iteration. The internal path length is the sum of the lengths of all unique internal paths.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval  {\\displaystyle } is about log \u2061 log x \u2061 y {\\displaystyle \\log \\log _{x}y} .Several computer searches have been done in the hope of finding new Wilson primes. The Ibercivis distributed computing project includes a search for Wilson primes. Another search was coordinated at the Great Internet Mersenne Prime Search forum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical physics, a large diffeomorphism is an equivalence class of diffeomorphisms under the equivalence relation where diffeomorphisms that can be continuously connected to each other are in the same equivalence class. For example, a two-dimensional real torus has a SL(2,Z) group of large diffeomorphisms by which the one-cycles a , b {\\displaystyle a,b} of the torus are transformed into their integer linear combinations. This group of large diffeomorphisms is called the modular group. More generally, for a surface S, the structure of self-homeomorphisms up to homotopy is known as the mapping class group. It is known (for compact, orientable S) that this is isomorphic with the automorphism group of the fundamental group of S. This is consistent with the genus 1 case, stated above, if one takes into account that then the fundamental group is Z2, on which the modular group acts as automorphisms (as a subgroup of index 2 in all automorphisms, since the orientation may also be reverse, by a transformation with determinant \u22121).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The book The Art of the Metaobject Protocol explains the implementation and use of CLOS generic functions in detail. One of the early object-oriented programming extensions to Lisp is Flavors. It used the usual message sending paradigm influenced by Smalltalk.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The analysis, which is written in the experimental protocol before the experiment is conducted, is examined in grant applications and administrative review boards. Besides the power analysis, there are less formal methods for selecting the number of experimental units. These include graphical methods based on limiting the probability of false negative errors, graphical methods based on an expected variation increase (above the residuals) and methods based on achieving a desired confidence interval.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems as Multiprocessor system, multi-core and NUMA system, where a dedicated cache for each processor, core or node is used, a consistency problem may occur when a same data is stored in more than one cache. This problem arises when a data is modified in one cache. This problem can be solved in two ways: Invalidate all the copies on other caches (broadcast-invalidate) Update all the copies on other caches (write-broadcasting), while the memory may be updated (write through) or not updated (write-back).Note: Coherency generally applies only to data (as operands) and not to instructions (see Self-Modifying Code). The schemes can be classified based on: Snoopy scheme vs Directory scheme and vs Shared caches Write through vs Write-back (ownership-based) protocol Update vs Invalidation protocol Intervention vs not Intervention Dirty-sharing vs not-dirty-sharing protocol (MOESI vs MESI)Three approaches are adopted to maintain the coherency of data. Bus watching or Snooping \u2013 generally used for bus-based SMP \u2013 Symmetric Multiprocessor System/multi-core systems Directory-based \u2013 Message-passing \u2013 may be used in all systems but typically in NUMA system and in large multi-core systems Shared cache \u2013 generally used in multi-core systems", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Ramanujan\u2013Hardy number, is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103. The name is derived from a conversation in about 1919 involving mathematicians G. H. Hardy and Srinivasa Ramanujan.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Invertibility: For every permutation \u03c0 \u2208 S n {\\displaystyle \\pi \\in S_{n}} , there exists an inverse permutation \u03c0 \u2212 1 \u2208 S n {\\displaystyle \\pi ^{-1}\\in S_{n}} , so that \u03c0 \u03c0 \u2212 1 = \u03c0 \u2212 1 \u03c0 = id . {\\displaystyle \\pi \\pi ^{-1}=\\pi ^{-1}\\pi =\\operatorname {id} .} In general, composition of two permutations is not commutative, that is, \u03c0 \u03c3 \u2260 \u03c3 \u03c0 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It relies on K-mer graphs, which performs well with vast quantities of short reads. Greedy graph-based approach, which may also use one of the OLC or DBG approaches.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of the development of K-triviality, attention was paid to separation of K-trivial sets and computable sets. Chaitin in his 1976 paper mainly studied sets such that there exists b \u2208 N {\\displaystyle \\mathbb {N} } with \u2200 n C ( A \u21be n ) \u2264 C ( n ) + b {\\displaystyle \\forall nC(A\\upharpoonright n)\\leq C(n)+b} where C denotes the plain Kolmogorov complexity. These sets are known as C-trivial sets. Chaitin showed they coincide with the computable sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ": 201-202: 1-2 Several reasons were given for the choice of 31 bits instead of 32 bits: The desire to retain the high-order bit as a \"control or escape bit. \": 201 In particular, the standard subroutine calling convention marked the final parameter word by setting its high bit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1940 Alonzo Church (re)formulated it as simply typed lambda calculus. and examined by G\u00f6del in 1944. A survey of these developments is found in Collins (2012).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sweep and prune is also known as sort and sweep, referred to this way in David Baraff's Ph.D. thesis in 1992. Later works like the 1995 paper about I-COLLIDE by Jonathan D. Cohen et al. refer to the algorithm as sweep and prune.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If a group is finite, then its coset enumeration must terminate eventually, although it may take arbitrarily long and use an arbitrary amount of memory, even if the group is trivial. Depending on the algorithm used, it may happen that making small changes to the presentation that do not change the group nevertheless have a large impact on the amount of time or memory needed to complete the enumeration. These behaviours are a consequence of the unsolvability of the word problem for groups. A gentle introduction to coset enumeration is given in Rotman's text on group theory. More detailed information on correctness, efficiency, and practical implementation can be found in the books by Sims and Holt et al. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the days of text mode computing, Western characters were normally laid out in a grid on the screen, often 80 columns by 24 or 25 lines. Each character was displayed as a small dot matrix, often about 8 pixels wide, and a SBCS (single-byte character set) was generally used to encode characters of Western languages. For aesthetic reasons and readability, it is preferable for Chinese characters to be approximately square-shaped, therefore twice as wide as these fixed-width SBCS characters. As these were typically encoded in a DBCS (double-byte character set), this also meant that their width on screen in a duospaced font was proportional to their byte length.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Their work, known at the time as the IBM 801, eventually led to the RISC (Reduced Instruction Set Computing) concept. Microcode was removed, and only the most basic versions of any given instruction were put into the CPU. Any more complex code was left to the compiler. The removal of so much circuitry, about 1\u20443 of the transistors in the Motorola 68000 for instance, allowed the CPU to include more registers, which had a direct impact on performance. By the mid-1980s, further developed versions of these basic concepts were delivering performance as much as 10 times that of the fastest CISC designs, in spite of using less-developed fabrication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software, an XML pipeline is formed when XML (Extensible Markup Language) processes, especially XML transformations and XML validations, are connected. For instance, given two transformations T1 and T2, the two can be connected so that an input XML document is transformed by T1 and then the output of T1 is fed as input document to T2. Simple pipelines like the one described above are called linear; a single input document always goes through the same sequence of transformations to produce a single output document.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hutchinson metric otherwise known as Kantorovich metric is a function which measures \"the discrepancy between two images for use in fractal image processing\" and \"can also be applied to describe the similarity between DNA sequences expressed as real or complex genomic signals\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the GSM cellular mobile phone standard, timing advance (TA) value corresponds to the length of time a signal takes to reach the base station from a mobile phone. GSM uses TDMA technology in the radio interface to share a single frequency between several users, assigning sequential timeslots to the individual users sharing a frequency. Each user transmits periodically for less than one-eighth of the time within one of the eight timeslots. Since the users are at various distances from the base station and radio waves travel at the finite speed of light, the precise arrival-time within the slot can be used by the base station to determine the distance to the mobile phone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, a common newspaper column measurement is about 11 picas wide \u2014about 1.83 inches (46 mm)\u2014though this measure varies from paper to paper and in other countries. The examples in this article follow this assumption for illustrative purposes only.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of this article, all graphs will be simple and undirected, unless stated otherwise. This means that the edges of the graph form a set (and not a multiset) and each edge is a pair of distinct vertices. Graphs are assumed to have an implicit representation in which each vertex has a unique identifier or label and in which it is possible to test the adjacency of any two vertices, but for which adjacency testing is the only allowed primitive operation. Informally, a graph property is a property of a graph that is independent of labeling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, the kernel of a function f {\\displaystyle f} (or equivalence kernel) may be taken to be either the equivalence relation on the function's domain that roughly expresses the idea of \"equivalent as far as the function f {\\displaystyle f} can tell\", or the corresponding partition of the domain.An unrelated notion is that of the kernel of a non-empty family of sets B , {\\displaystyle {\\mathcal {B}},} which by definition is the intersection of all its elements: This definition is used in the theory of filters to classify them as being free or principal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example: the roots of numbers such as 10, 15, 20 which are not squares, the sides of numbers which are not cubes etc.\" In contrast to Euclid's concept of magnitudes as lines, Al-Mahani considered integers and fractions as rational magnitudes, and square roots and cube roots as irrational magnitudes. He also introduced an arithmetical approach to the concept of irrationality, as he attributes the following to irrational magnitudes: \"their sums or differences, or results of their addition to a rational magnitude, or results of subtracting a magnitude of this kind from an irrational one, or of a rational magnitude from it.\" The Egyptian mathematician Ab\u016b K\u0101mil Shuj\u0101 ibn Aslam (c.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory, the associativity of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses. If an operand is both preceded and followed by operators (for example, ^ 3 ^), and those operators have equal precedence, then the operand may be used as input to two different operations (i.e. the two operations indicated by the two operators). The choice of which operations to apply the operand to, is determined by the associativity of the operators. Operators may be associative (meaning the operations can be grouped arbitrarily), left-associative (meaning the operations are grouped from the left), right-associative (meaning the operations are grouped from the right) or non-associative (meaning operations cannot be chained, often because the output type is incompatible with the input types).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While the continuity assumption is usually met, the compactness assumption about the parameter space is often not, as the bounds of the true parameter values might be unknown. In that case, concavity of the likelihood function plays a key role. More specifically, if the likelihood function is twice continuously differentiable on the k-dimensional parameter space \u0398 {\\displaystyle \\Theta } assumed to be an open connected subset of R k , {\\displaystyle \\mathbb {R} ^{k}\\,,} there exists a unique maximum \u03b8 ^ \u2208 \u0398 {\\displaystyle {\\hat {\\theta }}\\in \\Theta } if the matrix of second partials is negative definite for every \u03b8 \u2208 \u0398 {\\displaystyle \\,\\theta \\in \\Theta \\,} at which the gradient \u2207 L \u2261  i = 1 n i {\\displaystyle \\;\\nabla L\\equiv \\left_{i=1}^{n_{\\mathrm {i} }}\\;} vanishes, and if the likelihood function approaches a constant on the boundary of the parameter space, \u2202 \u0398 , {\\displaystyle \\;\\partial \\Theta \\;,} i.e., which may include the points at infinity if \u0398 {\\displaystyle \\,\\Theta \\,} is unbounded.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the bandwidth-limited regime ( \u03c1 > 2 b / 2 D {\\displaystyle \\rho >2~b/2D} , i.e. the domain of non-binary signaling), the effective coding gain \u03b3 e f f ( A ) {\\displaystyle \\gamma _{\\mathrm {eff} }(A)} of a signal set A {\\displaystyle A} at a given target error rate P s ( E ) {\\displaystyle P_{s}(E)} is defined as the difference in dB between the S N R n o r m {\\displaystyle SNR_{\\mathrm {norm} }} required to achieve the target P s ( E ) {\\displaystyle P_{s}(E)} with A {\\displaystyle A} and the S N R n o r m {\\displaystyle SNR_{\\mathrm {norm} }} required to achieve the target P s ( E ) {\\displaystyle P_{s}(E)} with M-PAM or (M\u00d7M)-QAM (i.e. no coding). The nominal coding gain \u03b3 c ( A ) {\\displaystyle \\gamma _{c}(A)} is defined as \u03b3 c ( A ) = ( 2 \u03c1 \u2212 1 ) d min 2 ( A ) 6 E s . {\\displaystyle \\gamma _{c}(A)={(2^{\\rho }-1)d_{\\min }^{2}(A) \\over 6E_{s}}.} This definition is normalized so that \u03b3 c ( A ) = 1 {\\displaystyle \\gamma _{c}(A)=1} for M-PAM or (M\u00d7M)-QAM. The UBE becomes P s ( E ) \u2248 K s ( A ) Q 3 \u03b3 c ( A ) S N R n o r m , {\\displaystyle P_{s}(E)\\approx K_{s}(A)Q{\\sqrt {3\\gamma _{c}(A)SNR_{\\mathrm {norm} }}},} where K s ( A ) {\\displaystyle K_{s}(A)} is the average number of nearest neighbors per two dimensions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It follows from ZFC alone that \u03a0 1 1 {\\displaystyle {\\boldsymbol {\\Pi }}_{1}^{1}} and \u03a3 2 1 {\\displaystyle {\\boldsymbol {\\Sigma }}_{2}^{1}} have the uniformization property. It follows from the existence of sufficient large cardinals that \u03a0 2 n + 1 1 {\\displaystyle {\\boldsymbol {\\Pi }}_{2n+1}^{1}} and \u03a3 2 n + 2 1 {\\displaystyle {\\boldsymbol {\\Sigma }}_{2n+2}^{1}} have the uniformization property for every natural number n {\\displaystyle n} . Therefore, the collection of projective sets has the uniformization property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multiple criteria decision aiding (MCDA), multicriteria classification (or sorting) involves problems where a finite set of alternative actions should be assigned into a predefined set of preferentially ordered categories (classes). For example, credit analysts classify loan applications into risk categories (e.g., acceptable/unacceptable applicants), customers rate products and classify them into attractiveness groups, candidates for a job position are evaluated and their applications are approved or rejected, technical systems are prioritized for inspection on the basis of their failure risk, clinicians classify patients according to the extent to which they have a complex disease or not, etc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some n-ary groups there exists an element e (called an n-ary identity or neutral element) such that any string of n-elements consisting of all e's, apart from one place, is mapped to the element at that place. E.g., in a quaternary group with identity e, eeae = a for every a. An n-ary group containing a neutral element is reducible. Thus, an n-ary group that is not reducible does not contain such elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, ringdown is a method of signaling an operator in which telephone ringing current is sent over the line to operate a lamp or cause the operation of a self-locking relay known as a drop. Ringdown is used in manual operation, and is distinguished from automatic signaling by dialing a number. The signal consists of a continuous or pulsed alternating current (AC) signal transmitted over the line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The process also involves taking geographic coordinates of the ground resolution cell with GPS technology and comparing those with the coordinates of the \"pixel\" being studied provided by the remote sensing software to understand and analyze the location errors and how it may affect a particular study. Ground truth is important in the initial supervised classification of an image. When the identity and location of land cover types are known through a combination of field work, maps, and personal experience these areas are known as training sites.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In superscalar designs, the number of execution units is invisible to the instruction set. Each instruction encodes one operation only. For most superscalar designs, the instruction width is 32 bits or fewer. In contrast, one VLIW instruction encodes multiple operations, at least one operation for each execution unit of a device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field (Artin 1966), usually the field of complex numbers. If G is any group, then the set Ch(G) of these morphisms forms an abelian group under pointwise multiplication. This group is referred to as the character group of G. Sometimes only unitary characters are considered (characters whose image is in the unit circle); other such homomorphisms are then called quasi-characters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, dimension theory is the study in terms of commutative algebra of the notion dimension of an algebraic variety (and by extension that of a scheme). The need of a theory for such an apparently simple notion results from the existence of many definitions of dimension that are equivalent only in the most regular cases (see Dimension of an algebraic variety). A large part of dimension theory consists in studying the conditions under which several dimensions are equal, and many important classes of commutative rings may be defined as the rings such that two dimensions are equal; for example, a regular ring is a commutative ring such that the homological dimension is equal to the Krull dimension. The theory is simpler for commutative rings that are finitely generated algebras over a field, which are also quotient rings of polynomial rings in a finite number of indeterminates over a field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, \"the conditional probability of A given B\", or \"the probability of A under the condition B\", is usually written as P(A|B) or occasionally PB(A). This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the \"given\" one happening (how many times A occurs rather than not assuming B has occurred): P ( A \u2223 B ) = P ( A \u2229 B ) P ( B ) {\\displaystyle P(A\\mid B)={\\frac {P(A\\cap B)}{P(B)}}} .For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages and type theory, a product of types is another, compounded, type in a structure. The \"operands\" of the product are types, and the structure of a product type is determined by the fixed order of the operands in the product. An instance of a product type retains the fixed order, but otherwise may contain all possible instances of its primitive data types. The expression of an instance of a product type will be a tuple, and is called a \"tuple type\" of expression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a function between topological spaces is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of the Release 8 of 3GPP standards, VCC was replaced by a wider concept that covers all services provided by IMS. This work resulted in the specification of IMS Service Continuity and IMS Centralized Services (ICS), which are meant to be used in particular to provide the continuity of voice calls between LTE and legacy 2G/3G networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, signal subspace methods are empirical linear methods for dimensionality reduction and noise reduction. These approaches have attracted significant interest and investigation recently in the context of speech enhancement, speech modeling, and speech classification research. The signal subspace is also used in radio direction finding using the MUSIC (algorithm).Essentially the methods represent the application of a principal components analysis (PCA) approach to ensembles of observed time-series obtained by sampling, for example sampling an audio signal. Such samples can be viewed as vectors in a high-dimensional vector space over the real numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Multiplication is modulo irreducible polynomial x 8 + x 4 + x 3 + x + 1 {\\displaystyle x^{8}+x^{4}+x^{3}+x+1} . If processed bit by bit, then, after shifting, a conditional XOR with 1B16 should be performed if the shifted value is larger than FF16 (overflow must be corrected by subtraction of generating polynomial). These are special cases of the usual multiplication in GF \u2061 ( 2 8 ) {\\displaystyle \\operatorname {GF} (2^{8})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Baire space is defined to be the Cartesian product of countably infinitely many copies of the set of natural numbers, and is given the product topology (where each copy of the set of natural numbers is given the discrete topology). The Baire space is often represented using the tree of finite sequences of natural numbers. The Baire space can be contrasted with Cantor space, the set of infinite sequences of binary digits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The buffer pointer is a proxy for the memory address 0xB8000000. Functional programming languages based on lambda-calculus reify the concept of a procedure abstraction and procedure application in the form of the Lambda expression. The Scheme programming language reifies continuations (approximately, the call stack).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On the song's third week on the chart it reached its peak position of 16, where it remained for three weeks. It has since been certified gold by the Australian Recording Industry Association (ARIA) for sales of 35,000 units.In New Zealand the single entered at number 38 on the New Zealand Singles Chart. The following week, it rose to position 21 and then proceeded to fall off the charts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One purpose of XML Metadata Interchange (XMI) is to enable easy interchange of metadata between UML-based modeling tools and MOF-based metadata repositories in distributed heterogeneous environments. XMI is also commonly used as the medium by which models are passed from modeling tools to software generation tools as part of model-driven engineering. Examples of XMI, and lists of the XML tags that make up XMI-formatted files, are available in the version 2.5.1 specification document.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A stronger notion is that of strongly exposed point of C {\\displaystyle C} which is an exposed point x \u2208 C {\\displaystyle x\\in C} such that some exposing functional f {\\displaystyle f} of x {\\displaystyle x} attains its strong maximum over C {\\displaystyle C} at x {\\displaystyle x} , i.e. for each sequence ( x n ) \u2282 C {\\displaystyle (x_{n})\\subset C} we have the following implication: f ( x n ) \u2192 max f ( C ) \u27f9 \u2016 x n \u2212 x \u2016 \u2192 0 {\\displaystyle f(x_{n})\\to \\max f(C)\\Longrightarrow \\|x_{n}-x\\|\\to 0} . The set of all strongly exposed points of C {\\displaystyle C} is usually denoted str \u2061 exp \u2061 ( C ) {\\displaystyle \\operatorname {str} \\exp(C)} . There are two weaker notions, that of extreme point and that of support point of C {\\displaystyle C} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social network theory, social relationships are viewed in terms of nodes and ties. Nodes are the individual actors within the networks, and ties are the relationships between the actors. There can be many kinds of ties between the nodes. In its simplest form, a social network is a map of all of the relevant ties between the nodes being studied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 37, 137, 347, and 1347 are the patterns related to Braille pattern dots-23, since the two additional dots of kantenji patterns 023, 237, and 0237 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "During batch processing, several different programs were loaded in the computer memory, and the first one began to run. When the first program reached an instruction waiting for a peripheral, the context of this program was stored away, and the second program in memory was given a chance to run. The process continued until all programs finished running.The use of multiprogramming was enhanced by the arrival of virtual memory and virtual machine technology, which enabled individual programs to make use of memory and operating system resources as if other concurrently running programs were, for all practical purposes, nonexistent.Multiprogramming gives no guarantee that a program will run in a timely manner.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Internet protocol suite, the application layer contains the communications protocols and interface methods used in process-to-process communications across an Internet Protocol (IP) computer network. The application layer only standardizes communication and depends upon the underlying transport layer protocols to establish host-to-host data transfer channels and manage the data exchange in a client\u2013server or peer-to-peer networking model. Though the TCP/IP application layer does not describe specific rules or data formats that applications must consider when communicating, the original specification (in RFC 1123) does rely on and recommend the robustness principle for application design.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and data mining, affinity propagation (AP) is a clustering algorithm based on the concept of \"message passing\" between data points. Unlike clustering algorithms such as k-means or k-medoids, affinity propagation does not require the number of clusters to be determined or estimated before running the algorithm. Similar to k-medoids, affinity propagation finds \"exemplars,\" members of the input set that are representative of clusters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The C programming language uses an integer type, where relational expressions like i > j and logical expressions connected by && and || are defined to have value 1 if true and 0 if false, whereas the test parts of if, while, for, etc., treat any non-zero value as true. Indeed, a Boolean variable may be regarded (and implemented) as a numerical variable with one binary digit (bit), or as a bit string of length one, which can store only two values. The implementation of Booleans in computers are most likely represented as a full word, rather than a bit; this is usually due to the ways computers transfer blocks of information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More generally, | Z: n Z | = n {\\displaystyle |\\mathbb {Z} :n\\mathbb {Z} |=n} for any positive integer n. When G is finite, the formula may be written as | G: H | = | G | / | H | {\\displaystyle |G:H|=|G|/|H|} , and it implies Lagrange's theorem that | H | {\\displaystyle |H|} divides | G | {\\displaystyle |G|} . When G is infinite, | G: H | {\\displaystyle |G:H|} is a nonzero cardinal number that may be finite or infinite. For example, | Z: 2 Z | = 2 {\\displaystyle |\\mathbb {Z} :2\\mathbb {Z} |=2} , but | R: Z | {\\displaystyle |\\mathbb {R} :\\mathbb {Z} |} is infinite. If N is a normal subgroup of G, then | G: N | {\\displaystyle |G:N|} is equal to the order of the quotient group G / N {\\displaystyle G/N} , since the underlying set of G / N {\\displaystyle G/N} is the set of cosets of N in G.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Intermediate angles give intermediate correlations in a way that, on careful analysis, proves inconsistent with the idea that each particle has a definite, independent probability of producing the observed measurements (the correlations violate Bell's inequality). This subtle dependence of one measurement on the other holds even when measurements are made simultaneously and a great distance apart, which gives the appearance of a superluminal communication taking place between the two electrons. Put simply, how can Bob's electron \"know\" what Alice measured on hers, so that it can adjust its own behavior accordingly?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Comprehensive test procedures which outline the steps, and their expected results clearly identify what is to be seen as a result of performing the step. After the step or set of steps is completed the last step's expected result will call out what has been seen and then identify what requirement or requirements have been verified (identified by number). The requirement number, title and verbiage are tied together in another location in the test document.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, the problem may also be simplified by subtracting a point from both sides of the equation and taking the norm of the result. For example, to solvefor \u03be 3 {\\textstyle \\xi _{3}} , where \u03be 1 {\\textstyle \\xi _{1}} and \u03be 2 {\\textstyle \\xi _{2}} intersect at the point q {\\textstyle q} , both sides of the equation may be applied to a point p {\\textstyle p} that is not on the axis of \u03be 3 {\\textstyle \\xi _{3}} . Subtracting q {\\textstyle q} and taking the norm of both sides yields This may be solved using Subproblem 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, in the case of drawing a red card or a king, drawing any of a red king, a red non-king, or a black king is considered a success. In a standard 52-card deck, there are twenty-six red cards and four kings, two of which are red, so the probability of drawing a red or a king is 26/52 + 4/52 \u2013 2/52 = 28/52. Events are collectively exhaustive if all the possibilities for outcomes are exhausted by those possible events, so at least one of those outcomes must occur.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0. Laurence Kirby and Jeff Paris showed that it is unprovable in Peano arithmetic (but it can be proven in stronger systems, such as second-order arithmetic). This was the third example of a true statement that is unprovable in Peano arithmetic, after the examples provided by G\u00f6del's incompleteness theorem and Gerhard Gentzen's 1943 direct proof of the unprovability of \u03b50-induction in Peano arithmetic. The Paris\u2013Harrington theorem gave another example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the torus is different from the sphere: the torus has a \"hole\"; the sphere doesn't. However, since continuity (the basic notion of topology) only deals with the local structure, it can be difficult to formally define the obvious global difference. The homotopy groups, however, carry information about the global structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example program only normal calls are used, so all the information will be on a single stack. For asynchronous calls, a separate stack is initiated for each asynchronous process so that the processes share data but run asynchronously.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for virtual memory compression to provide measurable performance improvements, the throughput of the virtual memory system must be improved when compared to the uncompressed equivalent. Thus, the additional amount of processing introduced by the compression must not increase the overall latency. However, in I/O-bound systems or applications with highly compressible data sets, the gains can be substantial.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plumbing fittings, the \"M\" or \"F\" usually comes at the beginning rather than the end of the abbreviated designation. For example: MIPT denotes male iron pipe thread; FIPT denotes female iron pipe thread.A short length of pipe having an MIP thread at both ends is sometimes called a nipple. A short pipe fitting having an FIP thread at both ends is sometimes called a coupling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem. Therefore, the solution to the primal is an upper bound to the solution of the dual, and the solution of the dual is a lower bound to the solution of the primal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following code, neither f nor g functions is reentrant. In the above, f() depends on a non-constant global variable v; thus, if f() is interrupted during execution by an ISR which modifies v, then reentry into f() will return the wrong value of v. The value of v and, therefore, the return value of f, cannot be predicted with confidence: they will vary depending on whether an interrupt modified v during f's execution. Hence, f is not reentrant. Neither is g, because it calls f, which is not reentrant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In linear algebra, the n \u00d7 n {\\displaystyle n\\times n} identity matrix I {\\displaystyle \\mathbf {I} } has entries equal to the Kronecker delta: where i {\\displaystyle i} and j {\\displaystyle j} take the values 1 , 2 , \u22ef , n {\\displaystyle 1,2,\\cdots ,n} , and the inner product of vectors can be written as Here the Euclidean vectors are defined as n-tuples: a = ( a 1 , a 2 , \u2026 , a n ) {\\displaystyle \\mathbf {a} =(a_{1},a_{2},\\dots ,a_{n})} and b = ( b 1 , b 2 , . . . , b n ) {\\displaystyle \\mathbf {b} =(b_{1},b_{2},...,b_{n})} and the last step is obtained by using the values of the Kronecker delta to reduce the summation over j {\\displaystyle j} . It is common for i and j to be restricted to a set of the form {1, 2, ..., n} or {0, 1, ..., n \u2212 1}, but the Kronecker delta can be defined on an arbitrary set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In many less-developed countries, such as Spain, Mexico, Brazil, and Egypt, calls were placed at a central office the caller went to, filled out a paper slip, sometimes paid in advance for the call, and then waited for it to be connected. In Spain these were known as locutorios, literally \"a place to talk\". In towns too small to support a phone office, placing long-distance calls was a sideline for some businesses with telephones, such as pharmacies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Internally, the CPU of the computer is built up from a number of separate parts dedicated to a single task, for instance, adding a number, or fetching from memory. Normally, as the instruction flows through the machine, only one part is active at any given time. This means that each sequential step of the entire process must complete before a result can be saved.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A bijective function is also called a bijection. That is, combining the definitions of injective and surjective, \u2200 y \u2208 Y , \u2203 ! x \u2208 X such that y = f ( x ) , {\\displaystyle \\forall y\\in Y,\\exists !x\\in X{\\text{ such that }}y=f(x),} where \u2203 !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly abstract algebra, a binary operation \u2022 on a set is flexible if it satisfies the flexible identity: a \u2219 ( b \u2219 a ) = ( a \u2219 b ) \u2219 a {\\displaystyle a\\bullet \\left(b\\bullet a\\right)=\\left(a\\bullet b\\right)\\bullet a} for any two elements a and b of the set. A magma (that is, a set equipped with a binary operation) is flexible if the binary operation with which it is equipped is flexible. Similarly, a nonassociative algebra is flexible if its multiplication operator is flexible. Every commutative or associative operation is flexible, so flexibility becomes important for binary operations that are neither commutative nor associative, e.g. for the multiplication of sedenions, which are not even alternative. In 1954, Richard D. Schafer examined the algebras generated by the Cayley\u2013Dickson process over a field and showed that they satisfy the flexible identity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the monotone likelihood ratio property is a property of the ratio of two probability density functions (PDFs). Formally, distributions \u0192(x) and g(x) bear the property if for every x 1 > x 0 , f ( x 1 ) g ( x 1 ) \u2265 f ( x 0 ) g ( x 0 ) {\\displaystyle {\\text{for every }}x_{1}>x_{0},\\quad {\\frac {f(x_{1})}{g(x_{1})}}\\geq {\\frac {f(x_{0})}{g(x_{0})}}} that is, if the ratio is nondecreasing in the argument x {\\displaystyle x} . If the functions are first-differentiable, the property may sometimes be stated \u2202 \u2202 x ( f ( x ) g ( x ) ) \u2265 0 {\\displaystyle {\\frac {\\partial }{\\partial x}}\\left({\\frac {f(x)}{g(x)}}\\right)\\geq 0} For two distributions that satisfy the definition with respect to some argument x, we say they \"have the MLRP in x.\" For a family of distributions that all satisfy the definition with respect to some statistic T(X), we say they \"have the MLR in T(X).\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). For example, if we know that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, then without knowing the value of n, we can determine that the remainder of n divided by 105 (the product of 3, 5, and 7) is 23. Importantly, this tells us that if n is a natural number less than 105, then 23 is the only possible value of n. The earliest known statement of the theorem is by the Chinese mathematician Sunzi in the Sunzi Suanjing in the 3rd century CE.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Job j {\\displaystyle j} on machine i {\\displaystyle i} takes time p j / s i {\\displaystyle p_{j}/s_{i}} . R: Unrelated-machines scheduling. There are m {\\displaystyle m} parallel machines, and they are unrelated \u2013 Job j {\\displaystyle j} on machine i {\\displaystyle i} takes time p i j {\\displaystyle p_{ij}} .These letters might be followed by the number of machines, which is then fixed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Their specific use as metadata is left to the developer and can cover a wide range of types of information about any given application, classes and members that is not instance-specific. The decision to expose any given attribute as a property is also left to the developer as is the decision to use them as part of a larger application framework. Attributes are implemented as classes that are derived from System.Attribute.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Unlike Peano arithmetic, Skolem arithmetic is a decidable theory. This means it is possible to effectively determine, for any sentence in the language of Skolem arithmetic, whether that sentence is provable from the axioms of Skolem arithmetic. The asymptotic running-time computational complexity of this decision problem is triply exponential.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The process responds at the next time step by randomly moving into a new state s \u2032 {\\displaystyle s'} , and giving the decision maker a corresponding reward R a ( s , s \u2032 ) {\\displaystyle R_{a}(s,s')} . The probability that the process moves into its new state s \u2032 {\\displaystyle s'} is influenced by the chosen action. Specifically, it is given by the state transition function P a ( s , s \u2032 ) {\\displaystyle P_{a}(s,s')} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the SQUOZE encoding, identifiers in the symbol table were represented in a 50-character alphabet, allowing a 36-bit machine word to represent six alphanumeric characters plus two flag bits, thus saving two bits per six characters, because the six bits normally allocated for each character could store up to 64 states rather than only the 50 states needed to represent the 50 letters of the alphabet, and 506 < 234. Using base 50 already saves a single bit every three characters, so it was used in two three-character chunks. The manual has a formula for encoding six characters ABCDEF: ( A \u2217 50 2 + B \u2217 50 + C ) \u2217 2 17 + ( D \u2217 50 2 + E \u2217 50 + F ) {\\displaystyle (A*50^{2}+B*50+C)*2^{17}+(D*50^{2}+E*50+F)} For example \"SQUOZE\", normally 36 bits: 35 33 37 31 44 17(base 8) would be encoded in two 17-bit pieces to fit in the 34 bits as ( 0o220231 << 17 ) | 0o175473 == 0o110114575473. A simpler example of the same logic would be how a three-digit BCD number would take up 12 bits, such as 987: 9 8 7(base 16) 1001 1000 0111(base 2), but any such value could be stored in 10 bits directly, saving two bits, such as 987: 3db(base 16) 11 1101 1011(base 2).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to state the hypergraph regularity and counting lemmas formally, we need to define several rather technical terms to formalize appropriate notions of pseudo-randomness (random-likeness) and boundedness, as well as to describe the random-like blocks and partitions. Notation K j ( k ) {\\displaystyle K_{j}^{(k)}} denotes a k {\\displaystyle k} -uniform clique on j {\\displaystyle j} vertices. G ( j ) {\\displaystyle {\\mathcal {G}}^{(j)}} is an l {\\displaystyle l} -partite j {\\displaystyle j} -graph on vertex partition G ( 1 ) = V 1 \u2294 \u2026 \u2294 V l {\\displaystyle {\\mathcal {G}}^{(1)}=V_{1}\\sqcup \\ldots \\sqcup V_{l}} . K j ( G ( i ) ) {\\displaystyle {\\mathcal {K}}_{j}({\\mathcal {G}}^{(i)})} is the family of all j {\\displaystyle j} -element vertex sets that span the clique K j ( i ) {\\displaystyle K_{j}^{(i)}} in G ( i ) {\\displaystyle {\\mathcal {G}}^{(i)}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most cases, we want to find out the relationships between social data and another event or we want to get interesting results from social data analyses to predict some events. There are some outstanding articles in this field, including Twitter Mood Predicts The Stock Market, Predicting The Present With Google Trends etc. In order to accomplish these goals, we need the appropriate methods to do the analyses. Usually, we use statistic methods, methods of machine learning or methods of data mining to do the analyses. Universities all over the world are opening graduate program in Social Data Analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The client decides which commands to execute at which points. To execute a command, it passes the command object to the invoker object.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", y 1 ) . {\\displaystyle P(y_{i}|x_{i},x_{i-1},x_{i-2},...,x_{1},y_{i-1},y_{i-2},...,y_{1}).} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is true. Furthermore, the distribution of p-values departs from a uniform distribution and becomes a right-skewed unimodal distribution, especially for small p-values. This leads to a large Type I error rate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, the notation Y X {\\displaystyle Y^{X}} is used to denote the set of functions from the set X {\\displaystyle X} to the set Y {\\displaystyle Y} . Currying is the natural bijection between the set A B \u00d7 C {\\displaystyle A^{B\\times C}} of functions from B \u00d7 C {\\displaystyle B\\times C} to A {\\displaystyle A} , and the set ( A C ) B {\\displaystyle (A^{C})^{B}} of functions from B {\\displaystyle B} to the set of functions from C {\\displaystyle C} to A {\\displaystyle A} . In symbols: A B \u00d7 C \u2245 ( A C ) B {\\displaystyle A^{B\\times C}\\cong (A^{C})^{B}} Indeed, it is this natural bijection that justifies the exponential notation for the set of functions. As is the case in all instances of currying, the formula above describes an adjoint pair of functors: for every fixed set C {\\displaystyle C} , the functor B \u21a6 B \u00d7 C {\\displaystyle B\\mapsto B\\times C} is left adjoint to the functor A \u21a6 A C {\\displaystyle A\\mapsto A^{C}} . In the category of sets, the object Y X {\\displaystyle Y^{X}} is called the exponential object.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The various problems, algorithms, and tools of cost distance analysis operate over an unconstrained two-dimensional space, meaning that a path could be of any shape. Similar cost optimization problems can also arise in a constrained space, especially a one-dimensional linear network such as a road or telecommunications network. Although they are similar in principle, the problems in network space require very different (usually simpler) algorithms to solve, largely adopted from graph theory. The collection of GIS tools for solving these problems are called network analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modulus 12, one can assert that: 38 \u2261 14 ( mod 12 ) {\\displaystyle 38\\equiv 14{\\pmod {12}}} because 38 \u2212 14 = 24, which is a multiple of 12. Another way to express this is to say that both 38 and 14 have the same remainder 2, when divided by 12. The definition of congruence also applies to negative values. For example: 2 \u2261 \u2212 3 ( mod 5 ) \u2212 8 \u2261 7 ( mod 5 ) \u2212 3 \u2261 \u2212 8 ( mod 5 ) . {\\displaystyle {\\begin{aligned}2&\\equiv -3{\\pmod {5}}\\\\-8&\\equiv 7{\\pmod {5}}\\\\-3&\\equiv -8{\\pmod {5}}.\\end{aligned}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch\u2013Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after mathematicians Bryan John Birch and Peter Swinnerton-Dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. As of 2023, only special cases of the conjecture have been proven.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "gxf5 14. Nxf7 Kxf7 15. Bd2 Nd7 16.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Renaming truth as a product of the will cannot help it solve the problems of the intellect, according to Bittle. Bittle cited what he saw as contradictions in pragmatism, such as using objective facts to prove that truth does not emerge from objective fact; this reveals that pragmatists do recognize truth as objective fact, and not, as they claim, what is useful. Bittle argued there are also some statements that cannot be judged on human welfare at all.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2, 12, 24, and 124 are the 8-dot braille patterns related to Braille pattern dots-1, since the two additional dots of kantenji patterns 01, 17, and 017 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, quantales are certain partially ordered algebraic structures that generalize locales (point free topologies) as well as various multiplicative lattices of ideals from ring theory and functional analysis (C*-algebras, von Neumann algebras). Quantales are sometimes referred to as complete residuated semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can be significantly faster, as setjmp and longjmp must conservatively store all registers which may be in use according to the ABI, whereas the clobber method allows the compiler to store (by spilling to the stack) only what it knows is actually in use. Due to the lack of direct language support, many authors have written their own libraries for coroutines which hide the above details.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, 29/30 could be written as 1 2 4 2 3 5 {\\displaystyle {\\tfrac {1\\,\\,2\\,\\,4}{2\\,\\,3\\,\\,5}}} , representing the value 4 5 + 2 3 \u00d7 5 + 1 2 \u00d7 3 \u00d7 5 {\\displaystyle {\\tfrac {4}{5}}+{\\tfrac {2}{3\\times 5}}+{\\tfrac {1}{2\\times 3\\times 5}}} . This can be viewed as a form of mixed radix notation, and was very convenient for dealing with traditional systems of weights, measures, and currency. For instance, for units of length, a foot is 1/3 of a yard, and an inch is 1/12 of a foot, so a quantity of 5 yards, 2 feet, and 7 3 4 {\\displaystyle 7{\\tfrac {3}{4}}} inches could be represented as a composite fraction: 3 7 2 4 12 3 5 {\\displaystyle {\\tfrac {3\\ \\,7\\,\\,2}{4\\,\\,12\\,\\,3}}\\,5} yards.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, factor analysis of mixed data or factorial analysis of mixed data (FAMD, in the French original: AFDM or Analyse Factorielle de Donn\u00e9es Mixtes), is the factorial method devoted to data tables in which a group of individuals is described both by quantitative and qualitative variables. It belongs to the exploratory methods developed by the French school called Analyse des donn\u00e9es (data analysis) founded by Jean-Paul Benz\u00e9cri. The term mixed refers to the use of both quantitative and qualitative variables. Roughly, we can say that FAMD works as a principal components analysis (PCA) for quantitative variables and as a multiple correspondence analysis (MCA) for qualitative variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With stack machines, in contrast, results can be stored in one of two ways. Firstly, results can be stored using a temporary variable in memory. Storing and subsequent retrievals cost additional instructions and additional data cache cycles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Around 2007, LSTM trained by Connectionist Temporal Classification (CTC) started to outperform traditional speech recognition in certain applications. In 2015, Google's speech recognition reportedly experienced a dramatic performance jump of 49% through CTC-trained LSTM, which is now available through Google Voice to all smartphone users. Transformers, a type of neural network based on solely on attention, have been widely adopted in computer vision and language modeling, sparking the interest of adapting such models to new domains, including speech recognition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages that have non-hygienic macro systems, it is possible for existing variable bindings to be hidden from a macro by variable bindings that are created during its expansion. In C, this problem can be illustrated by the following fragment: Running the above through the C preprocessor produces: The variable a declared in the top scope is shadowed by the a variable in the macro, which introduces a new scope. As a result, a is never altered by the execution of the program, as the output of the compiled program shows: a is now 4, b is now 9", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel France and Germany signed a joint development agreement in 1984 and were joined by Italy and the UK in 1986. In 1986, the MTS and European Commission proposed reserving the 900 MHz spectrum band for GSM. It was long believed that the former Finnish prime minister Harri Holkeri made the world's first GSM call on 1 July 1991, MTS calling Kaarina Suonio (deputy mayor of the city of Tampere) using a network built by Nokia and Siemens and operated by Radiolinja. In 2021 a former Nokia engineer Pekka Lonka revealed to Helsingin Sanomat making a test call just a couple of hours earlier.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mutual authentication schemes that require a user's input password as part of the verification process, there is a higher vulnerability to hackers because the password is human-made rather than a computer-generated certificate. While applications could simply require users to use a computer-generated password, it is inconvenient for people to remember. User-made passwords and the ability to change one's password are important for making an application user-friendly, so many schemes work to accommodate the characteristic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that occurs naturally in a human community by a process of use, repetition, and change without conscious planning or premeditation. It can take different forms, namely either a spoken language or a sign language. Natural languages are distinguished from constructed and formal languages such as those used to program computers or to study logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Second, synchronization in many concurrent programs in a finite state, and therefore can be adequately described by regular expressions. For precisely the same reasons, path expressions are useful for controlling the behavior of complicated asynchronous circuits. In fact, the finite state assumption may be even more reasonable at the hardware level than at the monitor level. Path expressions provide a high level of descriptive synchronization that aids in the prevention and detection of design errors in complex systems and overcomes some of the dangers, such as certain forms of coding errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In paging the memory address space or segment is divided into equal-sized blocks called pages. Using virtual memory hardware, each page can reside in any location at a suitable boundary of the computer's physical memory, or be flagged as being protected. Virtual memory makes it possible to have a linear virtual memory address space and to use it to access blocks fragmented over physical memory address space. Most computer architectures which support paging also use pages as the basis for memory protection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above example, the RLI mark (right-to-left isolate) forces the following text to be interpreted in the reverse order: the triple-quote is first (ending the string), followed by a semicolon (starting a new line), and finally with the premature return (returning None and ignoring any code below it). The new line terminates the RLI mark, preventing it from flowing into the below code. Because of the Bidi character, some source code editors and IDEs rearrange the code for display without any visual indication that the code has been rearranged, so a human code reviewer would not normally detect them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If we remove the vertex v, we can four-color the remaining vertices. We can set the colors as (in clockwise order) red, yellow, blue, and green. In this situation, there can be a Kempe chain joining the red and blue neighbors or a Kempe chain joining the green and yellow neighbors, but not both, since these two paths would necessarily intersect, and the vertex where they intersect cannot be colored.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a regular semigroup is a semigroup S in which every element is regular, i.e., for each element a in S there exists an element x in S such that axa = a. Regular semigroups are one of the most-studied classes of semigroups, and their structure is particularly amenable to study via Green's relations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Infinity can also be used to describe infinite series, as follows: \u2211 i = 0 \u221e f ( i ) = a {\\displaystyle \\sum _{i=0}^{\\infty }f(i)=a} means that the sum of the infinite series converges to some real value a . {\\displaystyle a.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although languages that are described as having imperfective and perfective aspects agree in most cases in their use of these aspects, they may not agree in every situation. For example: Some languages have additional grammatical aspects. Spanish and Ancient Greek, for example, have a perfect (not the same as the perfective), which refers to a state resulting from a previous action (also described as a previous action with relevance to a particular time, or a previous action viewed from the perspective of a later time).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to get 128 bits of security for hash based signatures to sign 1 million messages using the fractal Merkle tree method of Naor Shenhav and Wool the public and private key sizes are roughly 36,000 bits in length.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "y-axis ( \u2191 {\\displaystyle \\uparrow } ): terms that can bind types, corresponding to polymorphism. z-axis ( \u2197 {\\displaystyle \\nearrow } ): types that can bind types, corresponding to (binding) type operators.The different ways to combine these three dimensions yield the 8 vertices of the cube, each corresponding to a different kind of typed system. The \u03bb-cube can be generalized into the concept of a pure type system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(This bound is tight, as a sequence of m \u2212 1 {\\displaystyle m-1} zeroes and m \u2212 1 {\\displaystyle m-1} ones cannot have any subset of size m {\\displaystyle m} summing to zero.) There are known proofs of this result using the Cauchy-Davenport theorem, Fermat's little theorem, or the Chevalley\u2013Warning theorem.Generalizing this result, one can define for any abelian group G the minimum quantity E G Z ( G ) {\\displaystyle EGZ(G)} of elements of G such that there must be a subsequence of o ( G ) {\\displaystyle o(G)} elements (where o ( G ) {\\displaystyle o(G)} is the order of the group) which adds to zero. It is known that E G Z ( G ) \u2264 2 o ( G ) \u2212 1 {\\displaystyle EGZ(G)\\leq 2o(G)-1} , and that this bound is strict if and only if G = Z m {\\displaystyle G=\\mathbb {Z} _{m}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the regula falsi, method of false position, or false position method is a very old method for solving an equation with one unknown; this method, in modified form, is still in use. In simple terms, the method is the trial and error technique of using test (\"false\") values for the variable and then adjusting the test value according to the outcome. This is sometimes also referred to as \"guess and check\". Versions of the method predate the advent of algebra and the use of equations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, common telephone lines are designed to transmit frequencies between 300 and 3400 Hz. Since electric power in the United States is distributed at 60 Hz, it normally does not interfere with telephone communications because its frequency is too low.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be logically contingent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In marketing, contact center telephony is the communication and collaboration system used by businesses to either manage high volumes of inbound queries or outbound telephone calls keeping their workforce or agents productive and in control to serve or acquire customers. This business communication system is an extension of computer telephony integration (CTI).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle f\\circ g_{1}=f\\circ g_{2}\\implies g_{1}=g_{2}.} Monomorphisms are a categorical generalization of injective functions (also called \"one-to-one functions\"); in some categories the notions coincide, but monomorphisms are more general, as in the examples below. In the setting of posets intersections are idempotent: the intersection of anything with itself is itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mistrustful cryptography the participating parties do not trust each other. For example, Alice and Bob collaborate to perform some computation where both parties enter some private inputs. But Alice does not trust Bob and Bob does not trust Alice. Thus, a secure implementation of a cryptographic task requires that after completing the computation, Alice can be guaranteed that Bob has not cheated and Bob can be guaranteed that Alice has not cheated either.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Derived from the causal order is the differential structure and the conformal metric of a manifold. A probability is assigned to a causal set becoming embedded in a manifold; thus there can be a transition from a discrete Planck scale fundamental unit of volume to a classical large scale continuous space.Random graphs by Antonsen Spacetime is described by dynamical graphs with points (associated with vertices) and links (of unit length) that are created or annihilated according to probability calculations. The parameterization of graphs in a metaspace gives rise to time.Bootstrap universe by Cahill and Klinger An iterative map composed of monads and the relations between them becomes a tree-graph of nodes and links.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The same cannot be done with the other two deductions systems: as context is changed in some of their rules of inferences, they cannot be formalized so that hypothetical judgments could be avoided\u2014not even if we want to use them just for proving derivability of tautologies. This basic diversity among the various calculi allows such difference, that the same basic thought (e.g. deduction theorem) must be proven as a metatheorem in Hilbert-style deduction system, while it can be declared explicitly as a rule of inference in natural deduction. In type theory, some analogous notions are used as in mathematical logic (giving rise to connections between the two fields, e.g. Curry\u2013Howard correspondence). The abstraction in the notion of judgment in mathematical logic can be exploited also in foundation of type theory as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s, analysis of high-level languages indicated compilers produced some complex corresponding machine language. It was determined that new instructions could improve performance. Some instructions were added that were never intended to be used in assembly language but fit well with compiled high-level languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for the trivial group and G itself. The classification theorem states that the list of finite simple groups consists of 18 countably infinite families plus 26 exceptions that do not follow such a systematic pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In neutral prosody, Turkish verb phrases are primarily head-final, as the verb comes after its complement. Variation in object-verb ordering is not strictly rigid. However, constructions where the verb precedes the object are less common. ]", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In these cases it can happen that ab \u2260 ba; then \"inverse\" typically implies that an element is both a left and right inverse. The notation f \u22121 is sometimes also used for the inverse function of the function f, which is for most functions not equal to the multiplicative inverse. For example, the multiplicative inverse 1/(sin x) = (sin x)\u22121 is the cosecant of x, and not the inverse sine of x denoted by sin\u22121 x or arcsin x. The terminology difference reciprocal versus inverse is not sufficient to make this distinction, since many authors prefer the opposite naming convention, probably for historical reasons (for example in French, the inverse function is preferably called the bijection r\u00e9ciproque).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It affects the choice of comparable data for use in the analysis. It can also affect the method used to value the property. For example, tree value can contribute up to 27% of property value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, cycle time is a software metric which estimates development speed in agile software projects. The cycle time measures how long it takes to process a given job - whether it's a client request, an order, or a defined production process stage. The crucial aspect of measuring the cycle time is considering only the active, operating processing time and discarding any idle, waiting, or service times occurring mid-process. According to the PMBOK (7th edition) by the Project Management Institute (PMI), cycle time is the \"total elapsed time from the start of a particular activity or work item to its completion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a base-orderable matroid is a matroid that has the following additional property, related to the bases of the matroid. For any two bases A {\\displaystyle A} and B {\\displaystyle B} there exists a feasible exchange bijection, defined as a bijection f {\\displaystyle f} from A {\\displaystyle A} to B {\\displaystyle B} , such that for every a \u2208 A \u2216 B {\\displaystyle a\\in A\\setminus B} , both ( A \u2216 { a } ) \u222a { f ( a ) } {\\displaystyle (A\\setminus \\{a\\})\\cup \\{f(a)\\}} and ( B \u2216 { f ( a ) } ) \u222a { a } {\\displaystyle (B\\setminus \\{f(a)\\})\\cup \\{a\\}} are bases.The property was introduced by Brualdi and Scrimger. A strongly-base-orderable matroid has the following stronger property:For any two bases A {\\displaystyle A} and B {\\displaystyle B} , there is a strong feasible exchange bijection, defined as a bijection f {\\displaystyle f} from A {\\displaystyle A} to B {\\displaystyle B} , such that for every X \u2286 A {\\displaystyle X\\subseteq A} , both ( A \u2216 X ) \u222a f ( X ) {\\displaystyle (A\\setminus X)\\cup f(X)} and ( B \u2216 f ( X ) ) \u222a X {\\displaystyle (B\\setminus f(X))\\cup X} are bases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some implementations of software development processes, issues are investigated by quality assurance analysts a system is verified for correctness, and then assigned back to a member of the development team to resolve the identified issue. They can also be identified by system users during the User Acceptance Testing (UAT) phase. Issues can be recorded and communicated using Issue or Defect Tracking Systems. In the absence of a formal Issue or Defect Tracking system, it is commonplace to simply use any form of written communication such as emails or instant messages to communicate the existence of a found issue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one version of airline scheduling the goal is to produce a feasible schedule with at most k crews. To solve this problem one uses a variation of the circulation problem called bounded circulation which is the generalization of network flow problems, with the added constraint of a lower bound on edge flows. Let G = (V, E) be a network with s,t \u2208 V as the source and the sink nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Differential variational inequalities were first formally introduced by Pang and Stewart, whose definition should not be confused with the differential variational inequality used in Aubin and Cellina (1984). Differential variational inequalities have the form to find u ( t ) \u2208 K {\\displaystyle u(t)\\in K} such that \u27e8 v \u2212 u ( t ) , F ( t , x ( t ) , u ( t ) ) \u27e9 \u2265 0 {\\displaystyle \\langle v-u(t),F(t,x(t),u(t))\\rangle \\geq 0} for every v \u2208 K {\\displaystyle v\\in K} and almost all t; K a closed convex set, where d x d t = f ( t , x ( t ) , u ( t ) ) , x ( t 0 ) = x 0 . {\\displaystyle {\\frac {dx}{dt}}=f(t,x(t),u(t)),\\quad x(t_{0})=x_{0}.} Closely associated with DVIs are dynamic/differential complementarity problems: if K is a closed convex cone, then the variational inequality is equivalent to the complementarity problem: K \u220b u ( t ) \u22a5 F ( t , x ( t ) , u ( t ) ) \u2208 K \u2217 . {\\displaystyle K\\ni u(t)\\quad \\perp \\quad F(t,x(t),u(t))\\in K^{*}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic (a subtopic within the field of formal logic), two formulae are equisatisfiable if the first formula is satisfiable whenever the second is and vice versa; in other words, either both formulae are satisfiable or both are not. Equisatisfiable formulae may disagree, however, for a particular choice of variables. As a result, equisatisfiability is different from logical equivalence, as two equivalent formulae always have the same models.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the beginning of the agglomerative clustering process, each element is in a cluster of its own. The clusters are then sequentially combined into larger clusters, until all elements end up being in the same cluster. At each step, the two clusters separated by the shortest distance are combined. The function used to determine the distance between two clusters, known as the linkage function, is what differentiates the agglomerative clustering methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is particularly common for discrete data. When this happens, the test procedure defined above is usually undefined because there is no way to uniquely rank the data. (The sole exception is if there is a single sample X i {\\displaystyle X_{i}} which is zero and no other zeros or ties.) Because of this, the test statistic needs to be modified.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "( c \u2208 C ) . f ( a ) = c {\\displaystyle \\forall (a\\in A).\\,\\exists ! (c\\in C).f(a)=c} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "PCA is used to identify a set of orthogonal basis vectors (basis signals) which capture as much as possible of the energy in the ensemble of observed samples. The vector space spanned by the basis vectors identified by the analysis is then the signal subspace. The underlying assumption is that information in speech signals is almost completely contained in a small linear subspace of the overall space of possible sample vectors, whereas additive noise is typically distributed through the larger space isotropically (for example when it is white noise).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A utility program (MOVCPM) was provided with system distribution that allowed relocating the object code to different memory areas. The utility program adjusted the addresses in absolute jump and subroutine call instructions to new addresses required by the new location of the operating system in processor memory. This newly patched version could then be saved on a new disk, allowing application programs to access the additional memory made available by moving the system components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "During the construction of the sequence, if a proof \u03c0 j {\\displaystyle \\pi _{j}} happens to be too large, \u03c0 j + 1 {\\displaystyle \\pi _{j+1}} is set to be the smallest proof in { \u03c0 1 , \u03c0 2 , \u2026 , \u03c0 j } {\\displaystyle \\{\\pi _{1},\\pi _{2},\\ldots ,\\pi _{j}\\}} . For achieving a better compression/time ratio, a heuristic for variable selection is desirable. For this purpose, Cotton defines the \"additivity\" of a resolution step (with antecedents p {\\displaystyle p} and n {\\displaystyle n} and resolvent r {\\displaystyle r} ): add \u2061 ( r ) := max ( | r | \u2212 max ( | p | , | n | ) , 0 ) {\\displaystyle \\operatorname {add} (r):=\\max(|r|-\\max(|p|,|n|),0)} Then, for each variable v {\\displaystyle v} , a score is calculated summing the additivity of all the resolution steps in \u03c0 {\\displaystyle \\pi } with pivot v {\\displaystyle v} together with the number of these resolution steps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The binary logarithm has also been written as log n with a prior statement that the default base for the logarithm is 2. Another notation that is often used for the same function (especially in the German scientific literature) is ld n, from Latin logarithmus dualis or logarithmus dyadis. The DIN 1302, ISO 31-11 and ISO 80000-2 standards recommend yet another notation, lb n. According to these standards, lg n should not be used for the binary logarithm, as it is instead reserved for the common logarithm log10 n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a linear equation is an equation that may be put in the form a 1 x 1 + \u2026 + a n x n + b = 0 , {\\displaystyle a_{1}x_{1}+\\ldots +a_{n}x_{n}+b=0,} where x 1 , \u2026 , x n {\\displaystyle x_{1},\\ldots ,x_{n}} are the variables (or unknowns), and b , a 1 , \u2026 , a n {\\displaystyle b,a_{1},\\ldots ,a_{n}} are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients a 1 , \u2026 , a n {\\displaystyle a_{1},\\ldots ,a_{n}} are required to not all be zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an asymmetric relation is a binary relation R {\\displaystyle R} on a set X {\\displaystyle X} where for all a , b \u2208 X , {\\displaystyle a,b\\in X,} if a {\\displaystyle a} is related to b {\\displaystyle b} then b {\\displaystyle b} is not related to a . {\\displaystyle a.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most schema migration tools aim to minimize the impact of schema changes on any existing data in the database. Despite this, preservation of data in general is not guaranteed because schema changes such as the deletion of a database column can destroy data (i.e. all values stored under that column for all rows in that table are deleted). Instead, the tools help to preserve the meaning of the data or to reorganize existing data to meet new requirements. Since meaning of the data often cannot be encoded, the configuration of the tools usually needs manual intervention.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This knowledge comes from repeated examinations over time that show changes from marketing initiatives (from brand and competition) and the evolution of consumers\u2019 needs. Harold Geneen in his groundbreaking book \u201cManaging\u201d explains the role of an effective CEO: to repeatedly evaluate performance numbers on a continuous basis. Only long term observation brings true insight of unanticipated changes and \u201cred flags\u201d in the data.All measurement systems are prone to misinterpretation and error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The SSCG sequence begins slower than SCG, SSCG(0) = 2, SSCG(1) = 5, but then grows rapidly. SSCG(2) = 3 \u00d7 2(3 \u00d7 295) \u2212 8 \u2248 3.241704 \u00d7 1035775080127201286522908640065. Its first and last 20 digits are 32417042291246009846...34057047399148290040.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This allows for forward and reverse branches in code. The limited range of the branch instructions meant that, as code grew, the target addresses of some branches would become unreachable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some time-critical situations, failure to act may entail a continuously increasing cost over time, or a continuously decreasing probability over time of achieving the desired outcome. In real-time computing systems, this may be represented by time-utility functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Minimal-rights: stronger than non-negativity: each claimant should get at least his minimal right, which is what's left if all other agents get their full claims: \u2200 i: x i \u2265 m i , where m i := max ( 0 , E \u2212 \u2211 j \u2260 i c j ) {\\displaystyle \\forall i:x_{i}\\geq m_{i},{\\text{ where }}m_{i}:=\\max(0,E-\\sum _{j\\neq i}c_{j})} . Note that efficiency, non-negativity and claims-boundedness together imply minimal-rights. Equal treatment of equals (ETE): two claimants with identical claims should get identical allocations: c i = c j \u27f9 x i = x j {\\displaystyle c_{i}=c_{j}\\implies x_{i}=x_{j}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With some precomputation, only a single multiplication per sector is required (note that addition in a binary finite field is a simple bitwise addition, also known as xor): F \u2297 I = F \u2297 ( I 0 \u2295 \u03b4 ) = F \u2297 I 0 \u2295 F \u2297 \u03b4 {\\displaystyle F\\otimes I=F\\otimes (I_{0}\\oplus \\delta )=F\\otimes I_{0}\\oplus F\\otimes \\delta } , where F \u2297 \u03b4 {\\displaystyle F\\otimes \\delta } are precomputed for all possible values of \u03b4 {\\displaystyle \\delta } . This mode of operation needs only a single encryption per block and protects against all the above attacks except a minor leak: if the user changes a single plaintext block in a sector then only a single ciphertext block changes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In search of \"Framework for Modeling Space Systems Architectures\" Peter Shames and Joseph Skipper (2006) defined a \"nominal set of views\", Derived from CCSDS RASDS, RM-ODP, ISO 10746 and compliant with IEEE 1471. This \"set of views\", as described below, is a listing of possible modeling viewpoints. Not all of these views may be used for any one project and other views may be defined as necessary. Note that for some analyses elements from multiple viewpoints may be combined into a new view, possibly using a layered representation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are studied in the eight queens puzzle, where eight non-attacking queens are placed on a standard 8 \u00d7 8 {\\displaystyle 8\\times 8} chessboard. Dominating sets represent arrangements of queens where every square is attacked or occupied by a queen; five queens, but no fewer, can dominate the 8 \u00d7 8 {\\displaystyle 8\\times 8} chessboard. Colourings of the graphs represent ways to colour each square so that a queen cannot move between any two squares of the same colour; at least n colours are needed for an n \u00d7 n {\\displaystyle n\\times n} chessboard, but 9 colours are needed for the 8 \u00d7 8 {\\displaystyle 8\\times 8} board.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In actual implementation, that is not two separate steps; the DFT replaces the DTFT. So J.Cooley (pp. 77\u201378) describes the implementation as discrete finite Fourier transform.or another name for the Fourier series coefficients.or another name for one snapshot of a short-time Fourier transform.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more technical terms, roaming refers to the ability for a cellular customer to automatically make and receive voice calls, send and receive data, or access other services, including home data services, when travelling outside the geographical coverage area of the home network, by means of using a visited network. For example: should a subscriber travel beyond their cell phone company's transmitter range, their cell phone would automatically hop onto another phone company's service, if available. The process is supported by the Telecommunication processes of mobility management, authentication, authorization and accounting billing procedures (known as AAA or 'triple A').", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The RNN hierarchy can be \"collapsed\" into a single RNN, by \"distilling\" a higher level \"chunker\" network into a lower level \"automatizer\" network. In 1993, a chunker solved a deep learning task whose CAP depth exceeded 1000. Such history compressors can substantially facilitate downstream supervised deep learning.Geoffrey Hinton et al. (2006) proposed learning a high-level internal representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine to model each layer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(b) \"Instrument\" means a negotiable instrument. (c) An order that meets all of the requirements of subsection (a), except paragraph (1), and otherwise falls within the definition of \"check\" in subsection (f) is a negotiable instrument and a check. (d) A promise or order other than a check is not an instrument if, at the time it is issued or first comes into possession of a holder, it contains a conspicuous statement, however expressed, to the effect that the promise or order is not negotiable or is not an instrument governed by this Article.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most of Europe, LPD433 band is allowed for license-free voice communication in addition to PMR446. Wireless network devices use wavebands as follows: IEEE 802.11/Wi-Fi 2450 MHz and 5800 MHz bands Bluetooth 2450 MHz band falls under WPANIEEE 802.15.4, Zigbee and other personal area networks may use the 915 MHz and 2450 MHz ISM bands because of frequency sharing between different allocations. Wireless LANs and cordless phones can also use bands other than those shared with ISM, but such uses require approval on a country by country basis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The name \"uniform norm\" derives from the fact that a sequence of functions { f n } {\\displaystyle \\left\\{f_{n}\\right\\}} converges to f {\\displaystyle f} under the metric derived from the uniform norm if and only if f n {\\displaystyle f_{n}} converges to f {\\displaystyle f} uniformly.If f {\\displaystyle f} is a continuous function on a closed and bounded interval, or more generally a compact set, then it is bounded and the supremum in the above definition is attained by the Weierstrass extreme value theorem, so we can replace the supremum by the maximum. In this case, the norm is also called the maximum norm. In particular, if x {\\displaystyle x} is some vector such that x = ( x 1 , x 2 , \u2026 , x n ) {\\displaystyle x=\\left(x_{1},x_{2},\\ldots ,x_{n}\\right)} in finite dimensional coordinate space, it takes the form: \u2016 x \u2016 \u221e := max ( | x 1 | , \u2026 , | x n | ) . {\\displaystyle \\|x\\|_{\\infty }:=\\max \\left(\\left|x_{1}\\right|,\\ldots ,\\left|x_{n}\\right|\\right).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\left|S_{n}-\\ell \\right|<\\varepsilon .} If the series is convergent, the (necessarily unique) number \u2113 {\\displaystyle \\ell } is called the sum of the series. The same notation \u2211 k = 1 \u221e a k {\\displaystyle \\sum _{k=1}^{\\infty }a_{k}} is used for the series, and, if it is convergent, to its sum. This convention is similar to that which is used for addition: a + b denotes the operation of adding a and b as well as the result of this addition, which is called the sum of a and b. Any series that is not convergent is said to be divergent or to diverge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UK, Ofcom requires that predictive dialers abandon fewer than 3% of answered calls on a daily basis. Ofcom also requires that if an agent is not available within 2 seconds the call is considered \"abandoned\" and an automated message is played. The automated message must identify the company making the call, the purpose of the call, a free phone or basic rate phone number to call back on and must not contain any form of marketing. A phone call to the return number must not be treated by the company as an opportunity to market, but to be removed from the calling list.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the information word consists of n {\\displaystyle n} bits, then the Berger code needs k = \u2308 log 2 \u2061 ( n + 1 ) \u2309 {\\displaystyle k=\\lceil \\log _{2}(n+1)\\rceil } \"check bits\", giving a Berger code of length k+n. (In other words, the k {\\displaystyle k} check bits are enough to check up to n = 2 k \u2212 1 {\\displaystyle n=2^{k}-1} information bits). Berger codes can detect any number of one-to-zero bit-flip errors, as long as no zero-to-one errors occurred in the same code word.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some places and at some times, the one- and two-stroke variants have been used in the same contexts to distinguish between the U.S. dollar and other local currency, such as the former Portuguese escudo.However, such usage is not standardized, and furthermore the two versions are generally considered mere graphic variants of the same symbol\u2014a typeface design choice. Computer and typewriter keyboards usually have a single key for that sign, and many character encodings (including ASCII and Unicode) reserve a single numeric code for it. Indeed, dollar signs in the same digital document may be rendered with one or two strokes, if different computer fonts are used, but the underlying codepoint U+0024 (ASCII 3610) remains unchanged.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Electronic news gathering, including live via satellite interviews, reporters' live shots, and sporting events are all examples of radio or television content that is backhauled to a station or network before being made available to the public through that station or network. Cable TV channels, particularly public, educational, and government access (PEG) along with (local origination) channels, may also backhauled to cable headends before making their way to the subscriber. Finished network feeds are not considered backhauls, even if local insertion is used to modify the content prior to final transmission.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case p = 2 {\\displaystyle \\textstyle p=2} , the inequality holds with A 2 = B 2 = 1 {\\displaystyle \\textstyle A_{2}=B_{2}=1} , and it reduces to the rule for the sum of variances of independent random variables with zero mean, known from elementary statistics: If E ( X i ) = 0 {\\displaystyle \\textstyle E\\left(X_{i}\\right)=0} and E ( | X i | 2 ) < + \u221e {\\displaystyle \\textstyle E\\left(\\left\\vert X_{i}\\right\\vert ^{2}\\right)<+\\infty } , then V a r ( \u2211 i = 1 n X i ) = E ( | \u2211 i = 1 n X i | 2 ) = \u2211 i = 1 n \u2211 j = 1 n E ( X i X \u00af j ) = \u2211 i = 1 n E ( | X i | 2 ) = \u2211 i = 1 n V a r ( X i ) . {\\displaystyle \\mathrm {Var} \\left(\\sum _{i=1}^{n}X_{i}\\right)=E\\left(\\left\\vert \\sum _{i=1}^{n}X_{i}\\right\\vert ^{2}\\right)=\\sum _{i=1}^{n}\\sum _{j=1}^{n}E\\left(X_{i}{\\overline {X}}_{j}\\right)=\\sum _{i=1}^{n}E\\left(\\left\\vert X_{i}\\right\\vert ^{2}\\right)=\\sum _{i=1}^{n}\\mathrm {Var} \\left(X_{i}\\right).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, an honest leftmost branch of a tree T on \u03c9 \u00d7 \u03b3 is a branch (maximal chain) \u0192 \u2208  such that for each branch g \u2208 , one has \u2200 n \u2208 \u03c9: \u0192(n) \u2264 g(n). Here,  denotes the set of branches of maximal length of T, \u03c9 is the smallest infinite ordinal (represented by the natural numbers N), and \u03b3 is some other ordinal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some countries of Europe, the European Telecommunications Standards Institute (ETSI) standards 200 778-1 and -2 \u2013 replacing 300 778-1 & -2 \u2013 allow 3 physical transport layers (Telcordia Technologies (formerly Bellcore), British Telecom (BT) and Cable Communications Association (CCA)), combined with 2 data formats Multiple Data Message Format (MDMF) & Single Data Message Format (SDMF), plus the Dual-tone multi-frequency (DTMF) system and a no-ring mode for meter-reading and the like. It's more of a recognition that the different types exist than an attempt to define a single \"standard\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "NLRP3, for example, recruits ASC adaptor protein via PYD-PYD interaction. Both pro-caspase-1 and ASC contain a caspase activation and recruitment domain (CARD), and this homotypic CARD-CARD interaction enables autocatalytic cleavage and reassembly of procaspase-1 to form active caspase-1. Alternatively, NLRC4 can directly recruit pro-caspase-1, as it has a CARD instead of a PYD.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, if the original cake is rectangular then each piece is a rectangle. Several years after this algorithm has been published, it was proved that envy-free partitions with connected pieces cannot be found by finite protocols. Hence, an approximation algorithm is the best that we can hope for in finite time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In medical diagnosis, test sensitivity is the ability of a test to correctly identify those with the disease (true positive rate), whereas test specificity is the ability of the test to correctly identify those without the disease (true negative rate). If 100 patients known to have a disease were tested, and 43 test positive, then the test has 43% sensitivity. If 100 with no disease are tested and 96 return a completely negative result, then the test has 96% specificity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some Linux desktop environments a letter with double dots can be produced by pressing AltGr\u21e7 Shift:, then the letter. When the system has a compose key, the same procedure as that described at X-Windows (below) may be used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a variable length buffer or elastic buffer is a buffer into which data may be entered at one rate and removed at another rate without changing the data sequence. Most first-in first-out (FIFO) storage devices are variable-length buffers in that the input rate may be variable while the output rate is constant or the output rate may be variable while the input rate is constant. Various clocking and control systems are used to allow control of underflow or overflow conditions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2568, 12568, 24568, and 124568 are the patterns related to Braille pattern dots-1456, since the two additional dots of kantenji patterns 01456, 14567, and 014567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many sources define an elliptic curve to be simply a curve given by an equation of this form. (When the coefficient field has characteristic 2 or 3, the above equation is not quite general enough to include all non-singular cubic curves; see \u00a7 Elliptic curves over a general field below.) An elliptic curve is an abelian variety \u2013 that is, it has a group law defined algebraically, with respect to which it is an abelian group \u2013 and O serves as the identity element.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Given any ideal I {\\displaystyle I} it may occur that it is properly contained in some larger ideal J {\\displaystyle J} with coefficients in the base field of I {\\displaystyle I} ; then J {\\displaystyle J} is called a divisor of I {\\displaystyle I} . In general, a divisor in a ring of partial differential operators need not be principal. The greatest common right divisor (Gcrd) or sum of two ideals I {\\displaystyle I} and J {\\displaystyle J} is the smallest ideal with the property that both I {\\displaystyle I} and J {\\displaystyle J} are contained in it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Noise exposure and its associated disease burden is likely to increase to a level where the disease burden is similar to that of traffic accidents. The rough estimates do not provide a complete picture of the environmental health burden, because data are uncertain, not all environmental-health relationships are known, not all environmental factors have been included, and it was not possible to assess all potential health effects. The effects of a number of these assumptions were evaluated in an uncertainty analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum teleportation, a sender wishes to transmit an arbitrary quantum state of a particle to a possibly distant receiver. Consequently, the teleportation process is a quantum channel. The apparatus for the process itself requires a quantum channel for the transmission of one particle of an entangled-state to the receiver. Teleportation occurs by a joint measurement of the sent particle and the remaining entangled particle. This measurement results in classical information which must be sent to the receiver to complete the teleportation. Importantly, the classical information can be sent after the quantum channel has ceased to exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In addition to formalizing mathematics, category theory is also used to formalize many other systems in computer science, such as the semantics of programming languages. Two categories are the same if they have the same collection of objects, the same collection of arrows, and the same associative method of composing any pair of arrows. Two different categories may also be considered \"equivalent\" for purposes of category theory, even if they do not have precisely the same structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the arithmetic\u2013geometric mean of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means: Begin the sequences with x and y: Then define the two interdependent sequences (an) and (gn) as These two sequences converge to the same number, the arithmetic\u2013geometric mean of x and y; it is denoted by M(x, y), or sometimes by agm(x, y) or AGM(x, y). The arithmetic\u2013geometric mean is used in fast algorithms for exponential and trigonometric functions, as well as some mathematical constants, in particular, computing \u03c0. The arithmetic\u2013geometric mean can be extended to complex numbers and when the branches of the square root are allowed to be taken inconsistently, it is, in general, a multivalued function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phylogenetics, a single-access key (also called dichotomous key, sequential key, analytical key, or pathway key) is an identification key where the sequence and structure of identification steps is fixed by the author of the key. At each point in the decision process, multiple alternatives are offered, each leading to a result or a further choice. The alternatives are commonly called \"leads\", and the set of leads at a given point a \"couplet\". Single access keys are closely related to decision trees or self-balancing binary search trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s and 1980s, attempts were made to build database systems with integrated hardware and software. The underlying philosophy was that such integration would provide higher performance at a lower cost. Examples were IBM System/38, the early offering of Teradata, and the Britton Lee, Inc. database machine. Another approach to hardware support for database management was ICL's CAFS accelerator, a hardware disk controller with programmable search capabilities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the expression named entity, the word named restricts the task to those entities for which one or many strings, such as words or phrases, stands (fairly) consistently for some referent. This is closely related to rigid designators, as defined by Kripke, although in practice NER deals with many names and referents that are not philosophically \"rigid\". For instance, the automotive company created by Henry Ford in 1903 can be referred to as Ford or Ford Motor Company, although \"Ford\" can refer to many other entities as well (see Ford). Rigid designators include proper names as well as terms for certain biological species and substances, but exclude pronouns (such as \"it\"; see coreference resolution), descriptions that pick out a referent by its properties (see also De dicto and de re), and names for kinds of things as opposed to individuals (for example \"Bank\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs. Its practical applications are found in all areas in which complex networks need to be modeled \u2013 many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. In a mathematical context, random graph refers almost exclusively to the Erd\u0151s\u2013R\u00e9nyi random graph model. In other contexts, any graph model may be referred to as a random graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Disagreements within ontology are often about whether entities belonging to a certain category exist and, if so, how they are related to other entities.When used as a countable noun, the words ontology and ontologies refer not to the science of being but to theories within the science of being. Ontological theories can be divided into various types according to their theoretical commitments. Monocategorical ontologies hold that there is only one basic category, but polycategorical ontologies rejected this view. Hierarchical ontologies assert that some entities exist on a more fundamental level and that other entities depend on them. Flat ontologies, on the other hand, deny such a privileged status to any entity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the objective value may be noisy or even non-numerical, and hence its gradient information may be unreliable or unavailable. This is particularly true when the problem is multi-objective. At present, many designs and refinements are mainly made through a manual trial-and-error process with the help of a CAD simulation package. Usually, such a posteriori learning or adjustments need to be repeated many times until a \u2018satisfactory\u2019 or \u2018optimal\u2019 design emerges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Quango (quasi-autonomous-non-governmental organisation) is a commonly used acronym to refer to a non-departmental public body. The Scottish public bodies is used to indicate all quangos and other organisations in Scotland.N.B. An entity described by the undefined term public body is not inevitably a statutory corporation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Gauss\u2013Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. The errors do not need to be normal, nor do they need to be independent and identically distributed (only uncorrelated with mean zero and homoscedastic with finite variance). The requirement that the estimator be unbiased cannot be dropped, since biased estimators exist with lower variance. See, for example, the James\u2013Stein estimator (which also drops linearity), ridge regression, or simply any degenerate estimator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The kernel is usually denoted ker f (or a variation). In symbols: ker \u2061 f = { a \u2208 A: f ( a ) = e B } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multiprocessing, the processors can be used to execute a single sequence of instructions in multiple contexts (single instruction, multiple data or SIMD, often used in vector processing), multiple sequences of instructions in a single context (multiple instruction, single data or MISD, used for redundancy in fail-safe systems and sometimes applied to describe pipelined processors or hyper-threading), or multiple sequences of instructions in multiple contexts (multiple instruction, multiple data or MIMD).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is important to know which notation is being used when working in different software programs. The respective ISO standard defines both the comma and the small dot as decimal markers, but does not explicitly define universal radix marks for bases other than 10. Fractional numbers are rarely displayed in other number bases, but, when they are, a radix character may be used for the same purpose. When used with the binary (base 2) representation, it may be called \"binary point\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of instruction set, ARM11 builds on the preceding ARM9 generation. It incorporates all ARM926EJ-S features and adds the ARMv6 instructions for media support (SIMD) and accelerating IRQ response. Microarchitecture improvements in ARM11 cores include: SIMD instructions which can double MPEG-4 and audio digital signal processing algorithm speed Cache is physically addressed, solving many cache aliasing problems and reducing context switch overhead. Unaligned and mixed-endian data access is supported.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The leftmost digit '1' of the result is then discarded. Discarding the leftmost '1' is especially convenient on calculators or computers that use a fixed number of digits: there is nowhere for it to go so it is simply lost during the calculation. The nines' complement plus one is known as the ten's complement. The method of complements can be extended to other number bases (radices); in particular, it is used on most digital computers to perform subtraction, represent negative numbers in base 2 or binary arithmetic and test underflow and overflow in calculation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Rather the program's behavior is undefined. To make a fuzzer more sensitive to failures other than crashes, sanitizers can be used to inject assertions that crash the program when a failure is detected. There are different sanitizers for different kinds of bugs: to detect memory related errors, such as buffer overflows and use-after-free (using memory debuggers such as AddressSanitizer), to detect race conditions and deadlocks (ThreadSanitizer), to detect undefined behavior (UndefinedBehaviorSanitizer), to detect memory leaks (LeakSanitizer), or to check control-flow integrity (CFISanitizer).Fuzzing can also be used to detect \"differential\" bugs if a reference implementation is available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, blue\u2013green (also blue/green) deployment is a method of installing changes to a web, app, or database server by swapping alternating production and staging servers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The class separation in a direction w \u2192 {\\displaystyle {\\vec {w}}} in this case will be given by S = w \u2192 T \u03a3 b w \u2192 w \u2192 T \u03a3 w \u2192 {\\displaystyle S={\\frac {{\\vec {w}}^{\\mathrm {T} }\\Sigma _{b}{\\vec {w}}}{{\\vec {w}}^{\\mathrm {T} }\\Sigma {\\vec {w}}}}} This means that when w \u2192 {\\displaystyle {\\vec {w}}} is an eigenvector of \u03a3 \u2212 1 \u03a3 b {\\displaystyle \\Sigma ^{-1}\\Sigma _{b}} the separation will be equal to the corresponding eigenvalue. If \u03a3 \u2212 1 \u03a3 b {\\displaystyle \\Sigma ^{-1}\\Sigma _{b}} is diagonalizable, the variability between features will be contained in the subspace spanned by the eigenvectors corresponding to the C \u2212 1 largest eigenvalues (since \u03a3 b {\\displaystyle \\Sigma _{b}} is of rank C \u2212 1 at most). These eigenvectors are primarily used in feature reduction, as in PCA.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In several mathematical areas, generalized distributivity laws are considered. This may involve the weakening of the above conditions or the extension to infinitary operations. Especially in order theory one finds numerous important variants of distributivity, some of which include infinitary operations, such as the infinite distributive law; others being defined in the presence of only one binary operation, such as the according definitions and their relations are given in the article distributivity (order theory). This also includes the notion of a completely distributive lattice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A tensor may be expressed as a linear sum of the tensor product of vector and covector basis elements. The resulting tensor components are labelled by indices of the basis. Each index has one possible value per dimension of the underlying vector space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are specified within the LMF document. On the contrary, languageCoding, language, partOfSpeech, commonNoun, writtenForm, grammaticalNumber, singular, plural are data categories that are taken from the Data Category Registry. These marks adorn the structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statutory interpretation, it refers to the problem of giving meaning to groups of words where one of the words is ambiguous or inherently unclear. For example, in road traffic law, a statute may require consideration of large vehicles separately from other vehicles. The word large is ambiguous per se, but may be considered heavy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a diffiety () is a geometrical object which plays the same role in the modern theory of partial differential equations that algebraic varieties play for algebraic equations, that is, to encode the space of solutions in a more conceptual way. The term was coined in 1984 by Alexandre Mikhailovich Vinogradov as portmanteau from differential variety.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The JavaScript (E4X) extension explicitly defines two specific objects (XML and XMLList), which support XML document nodes and XML node lists as distinct objects and use a dot-notation specifying parent-child relationships. These data structures represent XML documents as a tree structure. An XML Tree represented graphically can be as simple as an ASCII chart or a more graphically complex hierarchy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Equating the derivative of the Lagrangian with respect to the various probabilities to zero yields a functional form for those probabilities which corresponds to those used in logistic regression.As in the above section on multinomial logistic regression, we will consider M + 1 {\\displaystyle M+1} explanatory variables denoted x m {\\displaystyle x_{m}} and which include x 0 = 1 {\\displaystyle x_{0}=1} . There will be a total of K data points, indexed by k = { 1 , 2 , \u2026 , K } {\\displaystyle k=\\{1,2,\\dots ,K\\}} , and the data points are given by x m k {\\displaystyle x_{mk}} and y k {\\displaystyle y_{k}} . The xmk will also be represented as an ( M + 1 ) {\\displaystyle (M+1)} -dimensional vector x k = { x 0 k , x 1 k , \u2026 , x M k } {\\displaystyle {\\boldsymbol {x}}_{k}=\\{x_{0k},x_{1k},\\dots ,x_{Mk}\\}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle X\\times Y.} A binary relation is called a homogeneous relation when X = Y. A binary relation is also called a heterogeneous relation when it is not necessary that X = Y. Since relations are sets, they can be manipulated using set operations, including union, intersection, and complementation, and satisfying the laws of an algebra of sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the proximal operator is an operator associated with a proper, lower semi-continuous convex function f {\\displaystyle f} from a Hilbert space X {\\displaystyle {\\mathcal {X}}} to  {\\displaystyle } , and is defined by: prox f \u2061 ( v ) = arg \u2061 min x \u2208 X ( f ( x ) + 1 2 \u2016 x \u2212 v \u2016 X 2 ) . {\\displaystyle \\operatorname {prox} _{f}(v)=\\arg \\min _{x\\in {\\mathcal {X}}}\\left(f(x)+{\\frac {1}{2}}\\|x-v\\|_{\\mathcal {X}}^{2}\\right).} For any function in this class, the minimizer of the right-hand side above is unique, hence making the proximal operator well-defined. The proximal operator is used in proximal gradient methods, which is frequently used in optimization algorithms associated with non-differentiable optimization problems such as total variation denoising.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the examples below, bold denotes the primary stress of the measure, and italics denote a secondary stress. Syllables such as \"and\" are frequently used for pulsing in between numbers. Simple: 34 is a simple triple meter time signature that represents three quarter notes (crotchets), usually perceived as three beats. In this case the subdivision would be the eighth note (quaver). It is felt as 34: one and two and three and ...Compound: Most often, 68 is felt as two beats, each being a dotted quarter note (crotchet), and each containing subdivisions of three eighth notes (quavers). It is felt as 68: one two three four five six ... (or, if counting dotted-quarter beats, one and a two and a)The table below shows the characteristics of the most frequently used time signatures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, multi-frequency signaling (MF) is a type of signaling that was introduced by the Bell System after World War II. It uses a combination of audible tones for address (telephone number) transport and supervision signaling on trunk lines between central offices. The signaling is sent in-band over the same channel as the bearer channel used for voice traffic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In microeconomics, quasiconcave utility functions imply that consumers have convex preferences. Quasiconvex functions are important also in game theory, industrial organization, and general equilibrium theory, particularly for applications of Sion's minimax theorem. Generalizing a minimax theorem of John von Neumann, Sion's theorem is also used in the theory of partial differential equations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Rather, the appearance of any given colorant is inherent to its chemical and physical properties, the purity of such a substance being unrelated to whether it conforms to our arbitrary conception of an ideal hue. Moreover, the identity of gamut-optimizing primary colors is determined by the physiology underlying human color vision. Although no set of three primary paints can be mixed to obtain the complete color gamut perceived by humans, red, yellow, and blue are a poor choice if high-chroma mixtures are desired.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The PowerPC model uses a single fence instruction called the SYNC instruction. It is similar to the MB instruction, but with a little exception that reads can occur out of program order even if a SYNC is placed between two reads to the same location.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", A n {\\displaystyle A_{1},A_{2},...,A_{n}} of sentences in its language, if A 1 , A 2 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In visual sensor networks (VSN), sensors are cameras which record images and video sequences. In many applications of VSN, a camera can't give a perfect illustration including all details of the scene. This is because of the limited depth of focus of the optical lens of cameras.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term implies that the hidden complexity is at least in principle understandable, in contrast to black magic and deep magic (see Variants), which describe arcane techniques that are deliberately hidden or extremely difficult to understand. However, the term can also be applied endearingly, suggesting a \"charm\" about the code. The action of such abstractions is described as being done \"automagically\", a portmanteau of \"automatically\" and \"magically\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming and information security, a buffer overflow or buffer overrun is an anomaly whereby a program writes data to a buffer beyond the buffer's allocated memory, overwriting adjacent memory locations. Buffers are areas of memory set aside to hold data, often while moving it from one section of a program to another, or between programs. Buffer overflows can often be triggered by malformed inputs; if one assumes all inputs will be smaller than a certain size and the buffer is created to be that size, then an anomalous transaction that produces more data could cause it to write past the end of the buffer. If this overwrites adjacent data or executable code, this may result in erratic program behavior, including memory access errors, incorrect results, and crashes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The descriptors for degree of substitution, primary, secondary, tertiary, and quaternary, are translated as \u4f2f (b\u00f3), \u4ef2 (zh\u00f2ng), \u53d4 (sh\u016b), \u5b63 (j\u00ec), which refer to the first, second, third, and fourth male siblings in a family. For instance, tert-butyllithium is translated as \u53d4\u4e01\u57fa\u9502 (, , , ). Other commonly used isomeric descriptors normal-, iso-, and neo- are translated as \u6b63 (zh\u00e8ng, 'proper'), \u5f02 (y\u00ec, 'different'), and \u65b0 (x\u012bn, 'new'), respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to fully test that all the requirements of an application are met, there must be at least two test cases for each requirement: one positive test and one negative test. If a requirement has sub-requirements, each sub-requirement must have at least two test cases. Keeping track of the link between the requirement and the test is frequently done using a traceability matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The problem is generally attributed to Harold Davenport in about 1927, though he did not publish it at the time. Davenport did not claim to be its discoverer \"because he could not believe that it had not been stated earlier\". The first publication of a version of the birthday problem was by Richard von Mises in 1939.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then for each \u03b3 \u2208 S , {\\displaystyle \\gamma \\in S,} \u03b3 \u2208 C \u03b2 {\\displaystyle \\gamma \\in C_{\\beta }} for all \u03b2 < \u03b3 . {\\displaystyle \\beta <\\gamma .} Since each C \u03b2 {\\displaystyle C_{\\beta }} is closed, \u03b1 \u2208 C \u03b2 {\\displaystyle \\alpha \\in C_{\\beta }} for all \u03b2 < \u03b1 , {\\displaystyle \\beta <\\alpha ,} so \u03b1 \u2208 C .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In positional voting, voters complete a ranked ballot by expressing their preferences in rank order. The rank position of each voter preference is allotted a specific fixed weighting. Typically, the higher the rank of the preference, the more points it is worth. Occasionally, it may share the same weighting as a lower-ranked preference but it is never worth fewer points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the relational model of databases, a table can be considered a convenient representation of a relation, but the two are not strictly equivalent. For instance, a SQL table can potentially contain duplicate rows, whereas a true relation cannot contain duplicate rows that we call tuples. Similarly, representation as a table implies a particular ordering to the rows and columns, whereas a relation is explicitly unordered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The cumulants of the sum of the grouped variable and the uniform variable are the sums of the cumulants. As odd cumulants of a uniform distribution are zero; only even moments are affected. The second and fourth cumulants of the uniform distribution on (\u22120.5c, 0.5c) are respectively, c2/12 and \u2212c4/120. The correction to moments can be derived from the relation between cumulants and moments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Project planning resource leveling is the process of resolving these conflicts. It can also be used to balance the workload of primary resources over the course of the project, usually at the expense of one of the traditional triple constraints (time, cost, scope). When using specially designed project software, leveling typically means resolving conflicts or over allocations in the project plan by allowing the software to calculate delays and update tasks automatically.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This implies that each element q i \u2208 { 0 , 1 , . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to fall within the obligation for disclosure, the matter must meet three conditions: it must be legal authority, it must be directly adverse, and it must be from a controlling jurisdiction. Legal authority The matter for which disclosure is compelled must be a matter of decided law, rather than a mere opinion rendered by an academic. For example, where an attorney is arguing that a certain transfer of assets should be permitted in a bankruptcy proceeding, that attorney need not disclose a law review article, casebook, or op-ed piece in which the author argues that exactly such a transfer of assets should never be permitted. Such a writing need not be disclosed even if the author of the article is a leading expert on the area of law, and the article contains strong and well-written arguments in support of the position.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes (the others being M\u00f6bius plane and Laguerre plane).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For example, 1234567890 (one billion two hundred thirty four million five hundred sixty seven thousand eight hundred ninety) is a pandigital number in base 10. The first few pandigital base 10 numbers are given by (sequence A171102 in the OEIS): 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689The smallest pandigital number in a given base b is an integer of the form b b \u2212 1 + \u2211 d = 2 b \u2212 1 d b b \u2212 1 \u2212 d = b b \u2212 b ( b \u2212 1 ) 2 + ( b \u2212 1 ) \u00d7 b b \u2212 2 \u2212 1 {\\displaystyle b^{b-1}+\\sum _{d=2}^{b-1}db^{b-1-d}={\\frac {b^{b}-b}{(b-1)^{2}}}+(b-1)\\times b^{b-2}-1} The following table lists the smallest pandigital numbers of a few selected bases. OEIS: A049363 gives the base 10 values for the first 18 bases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, Bhattacharyya angle, also called statistical angle, is a measure of distance between two probability measures defined on a finite probability space. It is defined as \u0394 ( p , q ) = arccos \u2061 BC \u2061 ( p , q ) {\\displaystyle \\Delta (p,q)=\\arccos \\operatorname {BC} (p,q)} where pi, qi are the probabilities assigned to the point i, for i = 1, ..., n, and BC \u2061 ( p , q ) = \u2211 i = 1 n p i q i {\\displaystyle \\operatorname {BC} (p,q)=\\sum _{i=1}^{n}{\\sqrt {p_{i}q_{i}}}} is the Bhattacharya coefficient.The Bhattacharya distance is the geodesic distance in the orthant of the sphere S n \u2212 1 {\\displaystyle S^{n-1}} obtained by projecting the probability simplex on the sphere by the transformation p i \u21a6 p i , i = 1 , \u2026 , n {\\displaystyle p_{i}\\mapsto {\\sqrt {p_{i}}},\\ i=1,\\ldots ,n} . This distance is compatible with Fisher metric. It is also related to Bures distance and fidelity between quantum states as for two diagonal states one has \u0394 ( \u03c1 , \u03c3 ) = arccos \u2061 F ( \u03c1 , \u03c3 ) . {\\displaystyle \\Delta (\\rho ,\\sigma )=\\arccos {\\sqrt {F(\\rho ,\\sigma )}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is a collaborative effort, developed by Sandia National Laboratories, Los Alamos National Laboratories, and the United States Army Research Laboratory, and funded by the Advanced Simulation and Computing Program. It is developed under a BSD license. Pyomo is a python-based optimization Mathematical Programming Language which supports most commercial and open-source solver engines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\{1,2,3,\\ldots \\}.} Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Providers of nomadic VoIP service\u2014those who are unable to determine the location of their users\u2014are exempt from state telecommunications regulation.Another legal issue that the US Congress is debating concerns changes to the Foreign Intelligence Surveillance Act. The issue in question is calls between Americans and foreigners. The NSA is not authorized to tap Americans' conversations without a warrant\u2014but the Internet, and specifically VoIP does not draw as clear a line to the location of a caller or a call's recipient as the traditional phone system does. As VoIP's low cost and flexibility convinces more and more organizations to adopt the technology, surveillance for law enforcement agencies becomes more difficult. VoIP technology has also increased federal security concerns because VoIP and similar technologies have made it more difficult for the government to determine where a target is physically located when communications are being intercepted, and that creates a whole set of new legal challenges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, effective numbers or the computable reals or recursive reals. The concept of a computable real number was introduced by Emile Borel in 1912, using the intuitive notion of computability available at the time.Equivalent definitions can be given using \u03bc-recursive functions, Turing machines, or \u03bb-calculus as the formal representation of algorithms. The computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "), and spruces (Picea spp.). In some areas of this biome, the conifers may be a more important canopy species than the broadleaf species. In the Southern Hemisphere, endemic genera such as Nothofagus and Eucalyptus occupy this biome, and most coniferous trees (members of the Araucariaceae and Podocarpaceae) occur in mixtures with broadleaf species, and are classed as broadleaf and mixed forests.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, projections onto convex sets (POCS), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets. It is a very simple algorithm and has been rediscovered many times. The simplest case, when the sets are affine spaces, was analyzed by John von Neumann. The case when the sets are affine spaces is special, since the iterates not only converge to a point in the intersection (assuming the intersection is non-empty) but to the orthogonal projection of the point onto the intersection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is sometimes denoted RSI-value if the SI units are used. An R-value can be given for a material (e.g. for polyethylene foam), or for an assembly of materials (e.g. a wall or a window). In the case of materials, it is often expressed in terms of R-value per metre.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The researchers estimated that a 1024-bit RSA modulus would take about 500 times as long.Not all numbers of a given length are equally hard to factor. The hardest instances of these problems (for currently known techniques) are semiprimes, the product of two prime numbers. When they are both large, for instance more than two thousand bits long, randomly chosen, and about the same size (but not too close, for example, to avoid efficient factorization by Fermat's factorization method), even the fastest prime factorization algorithms on the fastest computers can take enough time to make the search impractical; that is, as the number of digits of the integer being factored increases, the number of operations required to perform the factorization on any computer increases drastically. Many cryptographic protocols are based on the difficulty of factoring large composite integers or a related problem\u2014for example, the RSA problem. An algorithm that efficiently factors an arbitrary integer would render RSA-based public-key cryptography insecure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the analysis of algorithms, several authors have studied the computation of the volume of high-dimensional convex bodies, a problem that can also be used to model many other problems in combinatorial enumeration. Often these works use a black box model of computation in which the input is given by a subroutine for testing whether a point is inside or outside of the convex body, rather than by an explicit listing of the vertices or faces of a convex polytope. It is known that, in this model, no deterministic algorithm can achieve an accurate approximation, and even for an explicit listing of faces or vertices the problem is #P-hard. However, a joint work by Martin Dyer, Alan M. Frieze and Ravindran Kannan provided a randomized polynomial time approximation scheme for the problem, providing a sharp contrast between the capabilities of randomized and deterministic algorithms.The main result of the paper is a randomized algorithm for finding an \u03b5 {\\displaystyle \\varepsilon } approximation to the volume of a convex body K {\\displaystyle K} in n {\\displaystyle n} -dimensional Euclidean space by assuming the existence of a membership oracle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, preferential attachment means that nodes of a network tend to connect to those nodes which have more links. If the network is growing and new nodes tend to connect to existing ones with linear probability in the degree of the existing nodes then preferential attachment leads to a scale-free network. If this probability is sub-linear then the network\u2019s degree distribution is stretched exponential and hubs are much smaller than in a scale-free network. If this probability is super-linear then almost all nodes are connected to a few hubs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an open set is a generalization of an open interval in the real line. In a metric space (a set along with a distance defined between any two points), an open set is a set that, along with every point P, contains all points that are sufficiently near to P (that is, all points whose distance to P is less than some value depending on P). More generally, an open set is a member of a given collection of subsets of a given set, a collection that has the property of containing every union of its members, every finite intersection of its members, the empty set, and the whole set itself. A set in which such a collection is given is called a topological space, and the collection is called a topology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a balanced boolean function is a boolean function whose output yields as many 0s as 1s over its input set. This means that for a uniformly random input string of bits, the probability of getting a 1 is 1/2. Examples of balanced boolean functions are the function that copies the first bit of its input to the output, and the function that produces the exclusive or of the input bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nature, networks rarely appear in isolation. They are typically elements in larger systems and can have non-trivial effects on one another. For example, infrastructure networks exhibit interdependency to a large degree. The power stations which form the nodes of the power grid require fuel delivered via a network of roads or pipes and are also controlled via the nodes of communications network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Brasch et al. 2012 show how a generalized Fibonacci sequence also can be connected to the field of economics. In particular, it is shown how a generalized Fibonacci sequence enters the control function of finite-horizon dynamic optimisation problems with one state and one control variable. The procedure is illustrated in an example often referred to as the Brock\u2013Mirman economic growth model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Relations of this kind are treated in more detail in the Section \"Types of spaces\". It is not always clear whether a given mathematical object should be considered as a geometric \"space\", or an algebraic \"structure\". A general definition of \"structure\", proposed by Bourbaki, embraces all common types of spaces, provides a general definition of isomorphism, and justifies the transfer of properties between isomorphic structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The state set at input position k is called S(k). The parser is seeded with S(0) consisting of only the top-level rule. The parser then repeatedly executes three operations: prediction, scanning, and completion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Normally, they represent information concerning time (\"@past\", \"@future\", etc.), reference (\"@def\", \"@indef\", etc.), modality (\"@can\", \"@must\", etc.), focus (\"@topic\", \"@focus\", etc.), and so on. Within the UNL Program, the process of representing natural language sentences in UNL graphs is called UNLization, and the process of generating natural language sentences out of UNL graphs is called NLization. UNLization, which involves natural language analysis and understanding, is intended to be carried out semi-automatically (i.e., by humans with computer aids); and NLization is intended to be carried out fully automatically.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network management, fault management is the set of functions that detect, isolate, and correct malfunctions in a telecommunications network, compensate for environmental changes, and include maintaining and examining error logs, accepting and acting on error detection notifications, tracing and identifying faults, carrying out sequences of diagnostics tests, correcting faults, reporting error conditions, and localizing and tracing faults by examining and manipulating database information.When a fault or event occurs, a network component will often send a notification to the network operator using a protocol such as SNMP. An alarm is a persistent indication of a fault that clears only when the triggering condition has been resolved. A current list of problems occurring on the network component is often kept in the form of an active alarm list such as is defined in RFC 3877, the Alarm MIB. A list of cleared faults is also maintained by most network management systems.Fault management systems may use complex filtering systems to assign alarms to severity levels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The natural logarithm has the number e \u2248 2.718 as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base 2 and is frequently used in computer science.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems, a task manager is a system monitor program used to provide information about the processes and applications running on a computer, as well as the general status of the computer. Some implementations can also be used to terminate processes and applications, as well as change the processes' scheduling priority. In some environments, users can access a task manager with the Control-Alt-Delete keyboard shortcut. Task managers can display running services (processes) as well as those that were stopped. They can display information about the services, including their process identifier and group identifier.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The maximum among the conductance of clusters provides a bound which can be used, along with inter-cluster edge weight, to define a measure on the quality of clustering. Intuitively, the conductance of a cluster (which can be seen as a set of vertices in a graph) should be low. Apart from this, the conductance of the subgraph induced by a cluster (called \"internal conductance\") can be used as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\Pr \\left\\geq \\Pr \\left.} While this intuitive-seeming result is true for Gaussian processes, it is not in general true for other random variables\u2014not even those with expectation 0. As a corollary, if ( X t ) t \u2265 0 {\\displaystyle (X_{t})_{t\\geq 0}} is a centered stationary Gaussian process such that E \u2061  \u2265 0 {\\displaystyle \\operatorname {E} \\geq 0} for all t {\\displaystyle t} , it holds for any real number c {\\displaystyle c} that Pr  X t \u2264 c ] \u2265 Pr  X t \u2264 c ] Pr  X t \u2264 c ] , T , S > 0. {\\displaystyle \\Pr \\left}X_{t}\\leq c\\right]\\geq \\Pr \\left}X_{t}\\leq c\\right]\\Pr \\left}X_{t}\\leq c\\right],\\quad T,S>0.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another term, used to denote call attempts that fail during the call setup procedure, is blocked calls. The call setup success rate in conventional (so-called land-line) networks is extremely high and is significantly above 99.9%. In mobile communication systems using radio channels the call setup success rate is lower and may range for commercial networks between 90% and 98% or higher.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orders of different elements may be different powers of p. Abelian p-groups are also called p-primary or simply primary. A finite group is a p-group if and only if its order (the number of its elements) is a power of p. Given a finite group G, the Sylow theorems guarantee the existence of a subgroup of G of order pn for every prime power pn that divides the order of G. Every finite p-group is nilpotent. The remainder of this article deals with finite p-groups. For an example of an infinite abelian p-group, see Pr\u00fcfer group, and for an example of an infinite simple p-group, see Tarski monster group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming and software development, fuzzing or fuzz testing is an automated software testing technique that involves providing invalid, unexpected, or random data as inputs to a computer program. The program is then monitored for exceptions such as crashes, failing built-in code assertions, or potential memory leaks. Typically, fuzzers are used to test programs that take structured inputs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of telephony, a telephone line (the system) typically offers a set of features that include call forwarding and call waiting. Call waiting allows one call to be suspended while a second call is answered, while call forwarding enables a customer to specify a secondary phone number to which additional calls will be forwarded in the event that the customer is already using the phone. To illustrate the example, we consider a telephone line provided to a customer, and we assume that both call forwarding and call waiting are enabled on the line. When a first call arrives on the line, the phone rings and is answered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character-state changes (or minimizes the cost of differentially weighted character-state changes). Under the maximum-parsimony criterion, the optimal tree will minimize the amount of homoplasy (i.e., convergent evolution, parallel evolution, and evolutionary reversals). In other words, under this criterion, the shortest possible tree that explains the data is considered best. Some of the basic ideas behind maximum parsimony were presented by James S. Farris in 1970 and Walter M. Fitch in 1971.Maximum parsimony is an intuitive and simple criterion, and it is popular for this reason.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pattern recognition and machine learning, a feature vector is an n-dimensional vector of numerical features that represent some object. Many algorithms in machine learning require a numerical representation of objects, since such representations facilitate processing and statistical analysis. When representing images, the feature values might correspond to the pixels of an image, while when representing texts the features might be the frequencies of occurrence of textual terms. Feature vectors are equivalent to the vectors of explanatory variables used in statistical procedures such as linear regression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spoken language Yes/no questions will oftentimes differ in their word order from the statement form. For example, in English: English Statement: HE WILL BUY THE SHIRT.English Yes/no Q:WILL HE BUY THE SHIRT?In ASL, yes/no questions are marked by the non-manual grammatical markings (as discussed in section 4.4.1). This eyebrow raise, slight tilt of the head and lean forward are what indicate that a yes/no question is being asked, without any change in word order from the statement form. There is speculation amongst linguists that these non-manual grammatical markings that indicate a yes/no questions are similar to the question intonation of spoken languages.Yes/no questions differ from wh-questions as they do not differ in word order from the original statement form of the sentence, whereas wh-questions do.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The examples we choose should stress simple dutifulness. The first of these methods, argues Kant, is destined to fail because students will not come to understand the unconditional nature of duty. The examples will also not be very inspiring.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Both of these examples use multiple sensors to sample signals and form images based on the manipulation of these multiple signals. Processing in multi-dimension (m-D) requires more complex algorithms, compared to the 1-D case, to handle calculations such as the fast Fourier transform due to more degrees of freedom. In some cases, m-D signals and systems can be simplified into single dimension signal processing methods, if the considered systems are separable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The order of a group G is denoted by ord(G) or |G|, and the order of an element a is denoted by ord(a) or |a|, instead of ord \u2061 ( \u27e8 a \u27e9 ) , {\\displaystyle \\operatorname {ord} (\\langle a\\rangle ),} where the brackets denote the generated group. Lagrange's theorem states that for any subgroup H of a finite group G, the order of the subgroup divides the order of the group; that is, |H| is a divisor of |G|. In particular, the order |a| of any element is a divisor of |G|.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to assess the performance of machine learning models, TensorFlow gives API access to commonly used metrics. Examples include various accuracy metrics (binary, categorical, sparse categorical) along with other metrics such as Precision, Recall, and Intersection-over-Union (IoU).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical programming and polyhedral combinatorics, the Hirsch conjecture is the statement that the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n \u2212 d. That is, any two vertices of the polytope must be connected to each other by a path of length at most n \u2212 d. The conjecture was first put forth in a letter by Warren M. Hirsch to George B. Dantzig in 1957 and was motivated by the analysis of the simplex method in linear programming, as the diameter of a polytope provides a lower bound on the number of steps needed by the simplex method. The conjecture is now known to be false in general. The Hirsch conjecture was proven for d < 4 and for various special cases, while the best known upper bounds on the diameter are only sub-exponential in n and d. After more than fifty years, a counter-example was announced in May 2010 by Francisco Santos Leal, from the University of Cantabria.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The row is then interpreted as a relvar composed of a set of tuples, with each tuple consisting of the two items: the name of the relevant column and the value this row provides for that column. Each column expects a data value of a particular type. For example, one column might require a unique identifier, another might require text representing a person's name, another might require an integer representing hourly pay in dollars.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Catalan language, sentences consist of a collection of noun phrases grouped around a verb. One of these noun phrases has the syntactic function of subject while the others function as complements (direct, indirect, prepositional or verbal), or adverbials (of time, place, manner, etc.). The sentence can be introduced by a 'frame' (for example 'as far as X is concerned', or an adverbial of time or place). The main features of the sentence are the agreement in person and number between the subject and the verb - which marks the relation between the speaker, on the one hand, and his or her interlocutors and any other people, on the other - and time, which situates the action in relation to the present of the speaker or in relation to the time of the other sentences of the text or discourse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, recipes for the production of hydrochloric acid only appear in the late sixteenth century, the earliest being found in Giovanni Battista Della Porta's (1535\u20131615) Magiae naturalis (\"Natural Magic\") and in the works of other contemporary chemists like Andreas Libavius (c. 1550\u20131616), Jean Beguin (1550\u20131620), and Oswald Croll (c. 1563\u2013 1609). The knowledge of mineral acids such as hydrochloric acid would be of key importance to seventeenth-century chemists like Daniel Sennert (1572\u20131637) and Robert Boyle (1627\u20131691), who used their capability to rapidly dissolve metals in their demonstrations of the composite nature of bodies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "- four years study (4 B.Eng. or B.ASc. )Names are traditionally prefixed with the ir.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in particular linear algebra, the Bunch\u2013Nielsen\u2013Sorensen formula, named after James R. Bunch, Christopher P. Nielsen and Danny C. Sorensen, expresses the eigenvectors of the sum of a symmetric matrix A {\\displaystyle A} and the outer product, v v T {\\displaystyle vv^{T}} , of vector v {\\displaystyle v} with itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In functional programming, property-based testing has allowed the mathematical specification and testing (if not exhaustive testing) of the expected behaviour of individual functions. The Object Constraint Language (and specializations such as Java Modeling Language) has allowed object-oriented systems to be formally specified, if not necessarily formally verified.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the Health Insurance Portability and Accountability Act and Health Information Technology for Economic and Clinical Health Act require companies to report data breaches to affected individuals and the federal government. Health Information Privacy Health Insurance Portability and Accountability Act of 1996 (HIPAA). - 45 CFR Parts 160 and 164, Standards for Privacy of Individually Identifiable Health Information and Security Standards for the Protection of Electronic Protected Health Information. HIPAA includes provisions designed to save health care businesses money by encouraging electronic transactions, as well as regulations to protect the security and confidentiality of patient information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, many early email systems were not 8-bit clean; they seemed to transfer typical short text messages properly, but converted \"unusual\" characters (the control characters, the \"high ASCII\" characters) in an irreversible way into some other \"usual\" character. Many of these systems also changed user data in other irreversible ways \u2013 such as inserting linefeeds to make sure each line is less than some maximum length, and inserting a \">\" at the beginning of every line that begins with \"From \". Until 8BITMIME, a variety of binary-to-text encoding techniques have been overlaid on top of such systems to restore transparency \u2013 to make sure that any possible file can be transferred so that the final output \"user data\" is actually identical to the original user data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For positive odd primes p , q {\\displaystyle p,q} the solubility of n 2 \u2212 p \u2261 0 mod q {\\displaystyle n^{2}-p\\equiv 0{\\bmod {q}}} for n {\\displaystyle n} determines the solubility of m 2 \u2212 q \u2261 0 mod p {\\displaystyle m^{2}-q\\equiv 0{\\bmod {p}}} for m {\\displaystyle m} and vice versa by the comparatively simple criterion whether ( \u2212 1 ) p \u2212 1 2 q \u2212 1 2 {\\displaystyle (-1)^{{\\frac {p-1}{2}}{\\frac {q-1}{2}}}} is 1 {\\displaystyle 1} or \u2212 1 {\\displaystyle -1} . By the factor theorem and the behavior of degrees in factorizations the solubility of such quadratic congruence equations is equivalent to the splitting of associated quadratic polynomials over a residue ring into linear factors. In this terminology the law of quadratic reciprocity is stated as follows. For positive odd primes p , q {\\displaystyle p,q} the splitting of the polynomial x 2 \u2212 p {\\displaystyle x^{2}-p} in mod q {\\displaystyle {\\bmod {q}}} -residues determines the splitting of the polynomial x 2 \u2212 q {\\displaystyle x^{2}-q} in mod p {\\displaystyle {\\bmod {p}}} -residues and vice versa through the quantity ( \u2212 1 ) p \u2212 1 2 q \u2212 1 2 \u2208 { \u00b1 1 } {\\displaystyle (-1)^{{\\frac {p-1}{2}}{\\frac {q-1}{2}}}\\in \\{\\pm 1\\}} . This establishes the bridge from the name giving reciprocating behavior of primes introduced by Legendre to the splitting behavior of polynomials used in the generalizations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing and information retrieval, explicit semantic analysis (ESA) is a vectoral representation of text (individual words or entire documents) that uses a document corpus as a knowledge base. Specifically, in ESA, a word is represented as a column vector in the tf\u2013idf matrix of the text corpus and a document (string of words) is represented as the centroid of the vectors representing its words. Typically, the text corpus is English Wikipedia, though other corpora including the Open Directory Project have been used.ESA was designed by Evgeniy Gabrilovich and Shaul Markovitch as a means of improving text categorization and has been used by this pair of researchers to compute what they refer to as \"semantic relatedness\" by means of cosine similarity between the aforementioned vectors, collectively interpreted as a space of \"concepts explicitly defined and described by humans\", where Wikipedia articles (or ODP entries, or otherwise titles of documents in the knowledge base corpus) are equated with concepts. The name \"explicit semantic analysis\" contrasts with latent semantic analysis (LSA), because the use of a knowledge base makes it possible to assign human-readable labels to the concepts that make up the vector space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook\u2013Reckhow propositional proof system, is a system for proving classical propositional tautologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory the hypoexponential distribution or the generalized Erlang distribution is a continuous distribution, that has found use in the same fields as the Erlang distribution, such as queueing theory, teletraffic engineering and more generally in stochastic processes. It is called the hypoexponetial distribution as it has a coefficient of variation less than one, compared to the hyper-exponential distribution which has coefficient of variation greater than one and the exponential distribution which has coefficient of variation of one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For functions of a single real variable whose graphs have a bounded number of intersection points, the complexity of the lower or upper envelope can be bounded using Davenport\u2013Schinzel sequences, and these envelopes can be computed efficiently by a divide-and-conquer algorithm that computes and then merges the envelopes of subsets of the functions.For convex functions or quasiconvex functions, the upper envelope is again convex or quasiconvex. The lower envelope is not, but can be replaced by the lower convex envelope to obtain an operation analogous to the lower envelope that maintains convexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number a/b is a \"good\" approximation of a real number \u03b1 if the absolute value of the difference between a/b and \u03b1 may not decrease if a/b is replaced by another rational number with a smaller denominator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From the 1980s onwards, critics increasingly refused to ask questions about diegetic elements of the text, instead acknowledging that many elements simply cannot be known definitively.Focus shifted away from whether the ghosts were real and onto how James generated and then sustained the text's ambiguity. A study into revisions James made to two paragraphs in the novella concluded that James was not striving for clarity, but to create a text which could not be interpreted definitively in either direction.This is still a position held by many critics, such as Giovanni Bottiroli, who argues that evidence for the intended ambiguity of the text can be found at the beginning of the novella, where Douglas tells his fictional audience that the governess had never told anyone but himself about the events that happened at Bly, and that they \"would easily judge\" why. Bottiroli believes that this address to Douglas' fictional audience is also meant as an address to the reader, telling them that they will \"easily judge\" whether or not the ghosts are real.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A major result of complexity theory is that NP can be characterized as the problems solvable by probabilistically checkable proofs where the verifier uses O(log n) random bits and examines only a constant number of bits of the proof string (the class PCP(log n, 1)). More informally, this means that the NP verifier described above can be replaced with one that just \"spot-checks\" a few places in the proof string, and using a limited number of coin flips can determine the correct answer with high probability. This allows several results about the hardness of approximation algorithms to be proven.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In radio networks, the n nodes may in every round choose to either transmit or receive a message. If no collision detection is available, then a node cannot distinguish between silence or receiving more than one message at a time. Should collision detection be available, then a node may detect more than one incoming message at the same time, even though the messages itself cannot be decoded in that case. In the beeping model, nodes can only distinguish between silence or at least one message via carrier sensing. Known runtimes for single-hop networks range from a constant (expected with collision detection) to O(n log n) rounds (deterministic and no collision detection). In multi-hop networks, known runtimes differ from roughly O((D+ log n)(log2 log n)) rounds (with high probability in the beeping model), O(D log n) (deterministic in the beeping model), O(n) (deterministic with collision detection) to O(n log3/2 n (log log n)0.5) rounds (deterministic and no collision detection).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Search engines rank web pages by their expected relevance to a user's query using a combination of query-dependent and query-independent methods. Query-independent methods attempt to measure the estimated importance of a page, independent of any consideration of how well it matches the specific query. Query-independent ranking is usually based on link analysis; examples include the HITS algorithm, PageRank and TrustRank.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting. It involves determining the best approach to use when looking for a specific item or person in a sizable, uncharted environment. The goal of the theory is to determine the best search strategy, one that maximises the chance of finding the target while minimising search-related expenses. Search theory clarifies how buyers and sellers choose when to acknowledge a coordinating offer for a transaction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical linear algebra, the Rayleigh\u2013Ritz method is commonly applied to approximate an eigenvalue problem for the matrix A \u2208 C N \u00d7 N {\\displaystyle A\\in \\mathbb {C} ^{N\\times N}} of size N {\\displaystyle N} using a projected matrix of a smaller size m < N {\\displaystyle m", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It may be used in both wired or wireless communications, so that adjacent frequency bands on the same media can avoid interference. The spectrum can also be licensed for low-power devices such as a private mobile phone network. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. The framework can be seen as a generalisation of Barendregt's lambda cube, in the sense that all corners of the cube can be represented as instances of a PTS with just two sorts. In fact, Barendregt (1991) framed his cube in this setting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If we consider the thesis and its converse as definition, then the hypothesis is an hypothesis about the application of the mathematical theory developed from the definition. For the acceptance of the hypothesis, there are, as we have suggested, quite compelling grounds. The Church\u2013Turing Thesis: Stephen Kleene, in Introduction To Metamathematics, finally goes on to formally name \"Church's Thesis\" and \"Turing's Thesis\", using his theory of recursive realizability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For each qubit sent, Alice chooses one computational basis state and one Hadamard basis state such that the state of the qubit is one of these two states. Alice then announces those two states. Alice will note whether the state is the computational basis state or the Hadamard basis state; that piece of information makes up the secret bit that Alice wishes to communicate to Bob.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, the tilde is a diacritic mark placed over a letter to indicate a change in its pronunciation:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of L p {\\displaystyle L^{p}} metrics, and measures of central tendency can be characterized as solutions to variational problems. In penalized regression, \"L1 penalty\" and \"L2 penalty\" refer to penalizing either the L 1 {\\displaystyle L^{1}} norm of a solution's vector of parameter values (i.e. the sum of its absolute values), or its L 2 {\\displaystyle L^{2}} norm (its Euclidean length). Techniques which use an L1 penalty, like LASSO, encourage solutions where many parameters are zero. Techniques which use an L2 penalty, like ridge regression, encourage solutions where most parameter values are small. Elastic net regularization uses a penalty term that is a combination of the L 1 {\\displaystyle L^{1}} norm and the L 2 {\\displaystyle L^{2}} norm of the parameter vector.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of database design, a multi-model database is a database management system designed to support multiple data models against a single, integrated backend. In contrast, most database management systems are organized around a single data model that determines how data can be organized, stored, and manipulated. Document, graph, relational, and key\u2013value models are examples of data models that may be supported by a multi-model database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some models, all operations to different locations are relaxed. A read or write may be reordered with respect to a different read or write in a different location. The weak ordering may be classified under this category and two types of release consistency models (RCsc and RCpc) also come under this model. Three commercial architectures are also proposed under this category of relaxation: the Digital Alpha, SPARC V9 relaxed memory order (RMO), and IBM PowerPC models.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the Environmental Protection Agency (EPA) sets performance standards for marine sanitation devices, and the U.S. Coast Guard (USCG) issues regulations governing the design, construction, certification, installation and operation of MSDs.USCG has certified three kinds of marine sanitation devices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions. A weaker condition is also important, respecting only products of coprime numbers, and such functions are called multiplicative functions. Outside of number theory, the term \"multiplicative function\" is often taken to be synonymous with \"completely multiplicative function\" as defined in this article.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "PGP uses key IDs to refer to public keys for a variety of purposes. These are not, properly speaking, fingerprints, since their short length prevents them from being able to securely authenticate a public key. 32bit key ids should not be used as current hardware can generate a colliding 32bit key id in just 4 seconds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Just as in the 2-component cat code, one needs to stabilize the code in order to prevent bit-flips. The same strategies can be used but are challenging to implement experimentally because higher order non-linearities are required. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to generate the next sequence, first take the previous pattern, add the next letter from the alphabet, and then repeat the previous pattern. The first few steps are listed here. A generator can be found here ABACABA is a \"quickly growing word\", often described as chiastic or \"symmetrically organized around a central axis\" (see: Chiastic structure and \u03a7). The number of members in each iteration is a(n) = 2n \u2212 1, the Mersenne numbers (OEIS: A000225).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let A d {\\displaystyle A_{d}} denote the set of elements of A {\\displaystyle A} divisible by d {\\displaystyle d} when d {\\displaystyle d} is a product of distinct primes from P {\\displaystyle P} . Further let A 1 {\\displaystyle A_{1}} denote A {\\displaystyle A} itself. Let z {\\displaystyle z} be a positive real number and P ( z ) {\\displaystyle P(z)} denote the product of the primes in P {\\displaystyle P} which are \u2264 z {\\displaystyle \\leq z} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The initial object in the category of bounded lattices is a Boolean domain. In computer science, a Boolean variable is a variable that takes values in some Boolean domain. Some programming languages feature reserved words or symbols for the elements of the Boolean domain, for example false and true. However, many programming languages do not have a Boolean datatype in the strict sense. In C or BASIC, for example, falsity is represented by the number 0 and truth is represented by the number 1 or \u22121, and all variables that can take these values can also take any other numerical values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here, a conceptual problem arises. The basic reason is that the income of one institutional unit is the expenditure of another, and the input of one institutional unit is the output of another. If therefore we want to measure the total value-added by all institutional units, we need to devise a consistent procedure for grossing and netting the incomes and outlays of all units, within a system of transactors. Lacking such a system, we would end up double counting incomes and expenditures of interacting units, exaggerating the quantity of value-added or investments.To estimate the annual net output of a country, for example, the cost of goods and services used up is deducted from gross revenue, all flows are valued uniformly, and flows which fall outside the production boundary are excluded.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern mathematical language, the problem posed on the tablet is the following: a rectangle has area A = 0.75 and diagonal c = 1.25. What are the lengths a and b of the sides of the rectangle? The solution can be understood as proceeding in two stages: in stage 1, the quantity c 2 \u2212 2 A {\\displaystyle {\\sqrt {c^{2}-2A}}} is computed to be 0.25. In stage 2, the well-attested Old Babylonian method of completing the square is used to solve what is effectively the system of equations b \u2212 a = 0.25, ab = 0.75.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Internet Protocol Suite (TCP/IP), OSI's data link layer functionality is contained within its lowest layer, the link layer. The TCP/IP link layer has the operating scope of the link a host is connected to, and only concerns itself with hardware issues to the point of obtaining hardware (MAC) addresses for locating hosts on the link and transmitting data frames onto the link. The link-layer functionality was described in RFC 1122 and is defined differently than the data link layer of OSI, and encompasses all methods that affect the local link. The TCP/IP model is not a top-down comprehensive design reference for networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, this is true of the order polytope of any partially ordered set, a polytope defined by pairwise inequalities between coordinates corresponding to comparable elements in the set. Another well-known polytope in combinatorial optimization is the matching polytope. Clearly, one seeks for finding matchings algorithmically and one technique is linear programming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, in the word \u5bff\u53f8 (sushi), the two characters are respectively read as su and shi, but the character \u5bff means \"one's natural life span\" and \u53f8 means \"to administer\", neither of which has anything to do with the food \u2013 this is ateji. Conversely, in the word \u7159\u8349 (tabako) for \"tobacco\", the individual kanji respectively mean \"smoke\" and \"herb\", which corresponds to the meaning, while none of their possible readings have a phonetic relationship to the word tabako \u2013 this is jukujikun. In some cases, however, the kanji were chosen for both their semantic and phonetic values, a form of phono-semantic matching.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing probabilities on a logarithmic scale ( \u2212 inf , 0 ] {\\displaystyle (-\\inf ,0]} , instead of the standard  {\\displaystyle } unit interval. Since the probabilities of independent events multiply, and logarithms convert multiplication to addition, log probabilities of independent events add. Log probabilities are thus practical for computations, and have an intuitive interpretation in terms of information theory: the negative of the average log probability is the information entropy of an event. Similarly, likelihoods are often transformed to the log scale, and the corresponding log-likelihood can be interpreted as the degree to which an event supports a statistical model. The log probability is widely used in implementations of computations with probability, and is studied as a concept in its own right in some applications of information theory, such as natural language processing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Born rule associates a probability with each unit vector in the Hilbert space, in such a way that these probabilities sum to 1 for any set of unit vectors comprising an orthonormal basis. Moreover, the probability associated with a unit vector is a function of the density operator and the unit vector, and not of additional information like a choice of basis for that vector to be embedded in. Gleason's theorem establishes the converse: all assignments of probabilities to unit vectors (or, equivalently, to the operators that project onto them) that satisfy these conditions take the form of applying the Born rule to some density operator. Gleason's theorem holds if the dimension of the Hilbert space is 3 or greater; counterexamples exist for dimension 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Because of this, it is less affected by the curse of dimensionality than e.g. a p-dimensional smoother. Furthermore, the AM is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with AM, like many other machine learning methods, include model selection, overfitting, and multicollinearity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-programming or in a multi-user environment, many users may execute the same program, written so that its code and data are in separate pages. To minimize RAM use, all users share a single copy of the program. Each process's page table is set up so that the pages that address code point to the single shared copy, while the pages that address data point to different physical pages for each process. Different programs might also use the same libraries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, the Kahan summation algorithm, also known as compensated summation, significantly reduces the numerical error in the total obtained by adding a sequence of finite-precision floating-point numbers, compared to the obvious approach. This is done by keeping a separate running compensation (a variable to accumulate small errors), in effect extending the precision of the sum by the precision of the compensation variable. In particular, simply summing n {\\displaystyle n} numbers in sequence has a worst-case error that grows proportional to n {\\displaystyle n} , and a root mean square error that grows as n {\\displaystyle {\\sqrt {n}}} for random inputs (the roundoff errors form a random walk). With compensated summation, using a compensation variable with sufficiently high precision the worst-case error bound is effectively independent of n {\\displaystyle n} , so a large number of values can be summed with an error that only depends on the floating-point precision of the result.The algorithm is attributed to William Kahan; Ivo Babu\u0161ka seems to have come up with a similar algorithm independently (hence Kahan\u2013Babu\u0161ka summation). Similar, earlier techniques are, for example, Bresenham's line algorithm, keeping track of the accumulated error in integer operations (although first documented around the same time) and the delta-sigma modulation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of network theory, a complex network is a graph (network) with non-trivial topological features\u2014features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particle physics, a hyperon is any baryon containing one or more strange quarks, but no charm, bottom, or top quark. This form of matter may exist in a stable form within the core of some neutron stars. Hyperons are sometimes generically represented by the symbol Y.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases the two methods may yield essentially the same results. The basis functions are typically found by computing the eigenvectors of the covariance matrix of the data set. A more advanced technique is to form a kernel out of the data, using a fixed kernel. The basis functions from the eigenvectors of the kernel matrix are thus non-linear in the location of the data (see Mercer's theorem and the kernel trick for more information).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In molecular biology and genetics, DNA annotation or genome annotation is the process of describing the structure and function of the components of a genome, by analyzing and interpreting them in order to extract their biological significance and understand the biological processes in which they participate. Among other things, it identifies the locations of genes and all the coding regions in a genome and determines what those genes do.Annotation is performed after a genome is sequenced and assembled, and is a necessary step in genome analysis before the sequence is deposited in a database and described in a published article. Although describing individual genes and their products or functions is sufficient to consider this description as an annotation, the depth of analysis reported in literature for different genomes vary widely, with some reports including additional information that goes beyond a simple annotation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Java Collections Framework, the class List represents an ordered collection of objects of type MyClass. Upper bounds are specified using extends: A List extends MyClass> is a list of objects of some subclass of MyClass, i.e. any object in the list is guaranteed to be of type MyClass, so one can iterate over it using a variable of type MyClass However, it is not guaranteed that one can add any object of type MyClass to that list: The converse is true for lower bounds, which are specified using super: A List super MyClass> is a list of objects of some superclass of MyClass, i.e. the list is guaranteed to be able to contain any object of type MyClass, so one can add any object of type MyClass: However, it is not guaranteed that one can iterate over that list using a variable of type MyClass: In order to be able to do both add objects of type MyClass to the list and iterate over it using a variable of type MyClass, a List is needed, which is the only type of List that is both List extends MyClass> and List super MyClass>.The mnemonics PECS (Producer Extends, Consumer Super) from the book Effective Java by Joshua Bloch gives an easy way to remember when to use wildcards (corresponding to Covariance and Contravariance) in Java.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of nonparametric optimization, Voronoi manifolds serve as valuable tools for reducing the sample size and selecting promising points. They help identify regions of interest where experiments or evaluations should be focused, leading to efficient optimization algorithms and improved convergence rates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The reason is that, in any minimum-length partition, every maximal line-segment can be \"pushed\" until it hits one of the vertices of the boundary, without changing the total length. Therefore, there are only O ( n 2 ) {\\displaystyle O(n^{2})} candidates for a line segment in an optimal partition, and they can be checked efficiently using dynamic programming. : 166\u2013167 If the raw polygon might have holes, even if they are degenerate holes (i.e., single points), the problem is NP-hard.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Binary logarithms are included in the standard C mathematical functions and other mathematical software packages. The integer part of a binary logarithm can be found using the find first set operation on an integer value, or by looking up the exponent of a floating point value. The fractional part of the logarithm can be calculated efficiently.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This objective is a quadratic form in b {\\displaystyle \\mathbf {b} } . Taking the gradient of this quadratic form with respect to b {\\displaystyle \\mathbf {b} } and equating it to zero (when b = \u03b2 ^ {\\displaystyle \\mathbf {b} ={\\hat {\\beta }}} ) gives 2 X T \u03a9 \u2212 1 X \u03b2 ^ \u2212 2 X T \u03a9 \u2212 1 y = 0 {\\displaystyle 2\\mathbf {X} ^{\\mathsf {T}}\\mathbf {\\Omega } ^{-1}\\mathbf {X} {\\hat {\\beta }}-2\\mathbf {X} ^{\\mathsf {T}}\\mathbf {\\Omega } ^{-1}\\mathbf {y} =0} Therefore, the minimum of the objective function can be computed yielding the explicit formula: \u03b2 ^ = ( X T \u03a9 \u2212 1 X ) \u2212 1 X T \u03a9 \u2212 1 y . {\\displaystyle \\mathbf {\\hat {\\beta }} =\\left(\\mathbf {X} ^{\\mathsf {T}}\\mathbf {\\Omega } ^{-1}\\mathbf {X} \\right)^{-1}\\mathbf {X} ^{\\mathsf {T}}\\mathbf {\\Omega } ^{-1}\\mathbf {y} .} The quantity \u03a9 \u2212 1 {\\displaystyle \\mathbf {\\Omega } ^{-1}} is known as the precision matrix (or dispersion matrix), a generalization of the diagonal weight matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship between one or more independent variables and a dependent variable. Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise (i.e. are not robust to assumption violations). Robust regression methods are designed to limit the effect that violations of assumptions by the underlying data-generating process have on regression estimates. For example, least squares estimates for regression models are highly sensitive to outliers: an outlier with twice the error magnitude of a typical observation contributes four (two squared) times as much to the squared error loss, and therefore has more leverage over the regression estimates. The Huber loss function is a robust alternative to standard square error loss that reduces outliers' contributions to the squared error loss, thereby limiting their impact on regression estimates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The number of iterations is then decoupled to the number of points (each point can be considered more than once). The incremental gradient method can be shown to provide a minimizer to the empirical risk. Incremental techniques can be advantageous when considering objective functions made up of a sum of many terms e.g. an empirical error corresponding to a very large dataset.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is an additive definition of the psi function as well. Quoting from Dickson, R. Dedekind proved that, if n {\\displaystyle n} is decomposed in every way into a product a b {\\displaystyle ab} and if e {\\displaystyle e} is the g.c.d. of a , b {\\displaystyle a,b} then \u2211 a ( a / e ) \u03c6 ( e ) = n \u220f p | n ( 1 + 1 p ) {\\displaystyle \\sum _{a}(a/e)\\varphi (e)=n\\prod _{p|n}\\left(1+{\\frac {1}{p}}\\right)} where a {\\displaystyle a} ranges over all divisors of n {\\displaystyle n} and p {\\displaystyle p} over the prime divisors of n {\\displaystyle n} and \u03c6 {\\displaystyle \\varphi } is the totient function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of networking, the Government Secure Intranet (GSi) puts in place a secure link between central government departments. It is an IP-based virtual private network based on broadband technology introduced in April 1998 and further upgraded in February 2004. Among other things, it offers a variety of advanced services including file transfer and search facilities, directory services, email exchange facilities (both between network members and over the Internet) as well as voice and video services. An additional network is currently also under development: the Public Sector Network (PSN) will be the network to interconnect public authorities (including departments and agencies in England; devolved administrations and local governments) and facilitate in particular sharing of information and services among each other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Which one(s) are appropriate depend on a variety of factors, such as: Which assumptions (if any) may be made a priori about the distributions from which the data have been sampled? For example, in many situations it may be assumed that the underlying distributions are normal distributions. In other cases the data are categorical, coming from a discrete distribution over a nominal scale, such as which entry was selected from a menu. Does the hypothesis being tested apply to the distributions as a whole, or just some population parameter, for example the mean or the variance? Is the hypothesis being tested merely that there is a difference in the relevant population characteristics (in which case a two-sided test may be indicated), or does it involve a specific bias (\"A is better than B\"), so that a one-sided test can be used?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many scientists such as Maxwell, Heaviside and Hertz unsuccessfully attempted to solve these problems by incorporating either Fresnel or Stokes' theories into Maxwell's new electromagnetic laws. Hendrik Lorentz spent considerable effort along these lines. After working on this problem for a decade, the issues with Stokes' theory caused him to abandon it and to follow Fresnel's suggestion of a (mostly) stationary aether (1892, 1895).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to encrypt or decrypt data, use the standard block cipher mode of operation on all but the last two blocks of data. The following steps describe how to handle the last two blocks of the plaintext, called Pn\u22121 and Pn, where the length of Pn\u22121 equals the block size of the cipher in bits, B; the length of the last block, Pn, is M bits; and K is the key that is in use. M can range from 1 to B, inclusive, so Pn could possibly be a complete block. The CBC mode description also makes use of the ciphertext block just previous to the blocks concerned, Cn\u22122, which may in fact be the IV if the plaintext fits within two blocks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Well before any significant investments are made, the uncertainty is reduced to a level where the risk can be carried comfortably. In this kind of environment the uncertainty level decreases rapidly in the beginning and the cone shape is less obvious. The software business however is very volatile and there is an external pressure to decrease the uncertainty level over time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2p + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingrun, who proved in 1966 that there are infinitely many such primes. This result would also follow from the truth of the twin prime conjecture as the lower member of a pair of twin primes is by definition a Chen prime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In such a scenario, the second smallest eigenvalue ( \u03bb 2 {\\displaystyle \\lambda _{2}} ) of L {\\displaystyle L} , yields a lower bound on the optimal cost ( c {\\displaystyle c} ) of ratio-cut partition with c \u2265 \u03bb 2 n {\\displaystyle c\\geq {\\frac {\\lambda _{2}}{n}}} . The eigenvector ( V 2 {\\displaystyle V_{2}} ) corresponding to \u03bb 2 {\\displaystyle \\lambda _{2}} , called the Fiedler vector, bisects the graph into only two communities based on the sign of the corresponding vector entry. Division into a larger number of communities can be achieved by repeated bisection or by using multiple eigenvectors corresponding to the smallest eigenvalues. The examples in Figures 1,2 illustrate the spectral bisection approach.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Bayesian (or epistemological) interpretation, probability measures a \"degree of belief\". Bayes' theorem links the degree of belief in a proposition before and after accounting for evidence. For example, suppose it is believed with 50% certainty that a coin is twice as likely to land heads than tails. If the coin is flipped a number of times and the outcomes observed, that degree of belief will probably rise or fall, but might even remain the same, depending on the results. For proposition A and evidence B, P (A), the prior, is the initial degree of belief in A. P (A | B), the posterior, is the degree of belief after incorporating news that B is true. the quotient P(B | A)/P(B) represents the support B provides for A.For more on the application of Bayes' theorem under the Bayesian interpretation of probability, see Bayesian inference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In policy iteration (Howard 1960), step one is performed once, and then step two is performed once, then both are repeated until policy converges. Then step one is again performed once and so on. (Policy iteration was invented by Howard to optimize Sears catalogue mailing, which he had been optimizing using value iteration.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The type of co-ownership does not affect the right of co-owners to sell their fractional interest in the property to others during their lifetimes, but it does affect their power to will the property upon death to their devisees in the case of joint tenants. However, any joint tenant can change this by severing the joint tenancy. This occurs whenever a joint tenant transfers his or her fractional interest in the property. Laws can vary from place to place, and the following general discussion will not be applicable in its entirety to all jurisdictions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom the Data Protection Act 1998 (c 29) (Information Commissioner) implemented the EU Directive on the protection of personal data . It replaced the Data Protection Act 1984 (c 35). The 2016 General Data Protection Regulation supersedes previous Protection Acts. The Data Protection Act 2018 (c 12) updates data protection laws in the UK. It is a national law which complements the European Union's General Data Protection Regulation (GDPR).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the definition given, \u27e8 \u03c1 \u2217 ( g ) \u03c6 , \u03c1 ( g ) v \u27e9 = \u27e8 \u03c1 ( g \u2212 1 ) T \u03c6 , \u03c1 ( g ) v \u27e9 = ( \u03c1 ( g \u2212 1 ) T \u03c6 ) T \u03c1 ( g ) v = \u03c6 T \u03c1 ( g \u2212 1 ) \u03c1 ( g ) v = \u03c6 T v = \u27e8 \u03c6 , v \u27e9 . {\\displaystyle \\langle {\\rho }^{*}(g)\\varphi ,\\rho (g)v\\rangle =\\langle \\rho (g^{-1})^{T}\\varphi ,\\rho (g)v\\rangle =(\\rho (g^{-1})^{T}\\varphi )^{T}\\rho (g)v=\\varphi ^{T}\\rho (g^{-1})\\rho (g)v=\\varphi ^{T}v=\\langle \\varphi ,v\\rangle .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s through the early 1980s, paper tape was commonly used to transfer binary data for incorporation in either mask-programmable read-only memory (ROM) chips or their erasable counterparts EPROMs. A significant variety of encoding formats were developed for use in computer and ROM/EPROM data transfer. Encoding formats commonly used were primarily driven by those formats that EPROM programming devices supported and included various ASCII hex variants as well as a number of proprietary formats. A much more primitive as well as a much longer high-level encoding scheme was also used, BNPF (Begin-Negative-Positive-Finish), also written as BPNF.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, random necklaces can be split equally using fewer cuts. Mathematicians Noga Alon, Dor Elboim, G\u00e1bor Tardos and J\u00e1nos Pach studied the typical number of cuts required to split a random necklace between two thieves. In the model they considered, a necklace is chosen uniformly at random from the set of necklaces with t colors and m beads of each color. As m tends to infinity, the probability that the necklace can be split using \u230a(t + 1)/2\u230b cuts or less tends to zero while the probability that it's possible to split with \u230a(t + 1)/2\u230b + 1 cuts is bounded away from zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle ~{\\frac {a-{\\sqrt {a^{2}-c}}}{2}}~.} Thus x and y are rational if and only if d = a 2 \u2212 c {\\displaystyle d={\\sqrt {a^{2}-c}}~} is a rational number. For explicitly choosing the various signs, one must consider only positive real square roots, and thus assuming c > 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some domains, a few dozen different source and target schema (proprietary data formats) may exist. An \"exchange\" or \"interchange format\" is often developed for a single domain, and then necessary routines (mappings) are written to (indirectly) transform/translate each and every source schema to each and every target schema by using the interchange format as an intermediate step. That requires a lot less work than writing and debugging the hundreds of different routines that would be required to directly translate each and every source schema directly to each and every target schema. Examples of these transformative interchange formats include: Standard Interchange Format for geospatial data; Data Interchange Format for spreadsheet data; Open Document Format for spreadsheets, charts, presentations and word processing documents; GPS eXchange Format or Keyhole Markup Language for describing GPS data; and GDSII for integrated circuit layout.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An important example of normal variance-mean mixtures is the generalised hyperbolic distribution in which the mixing distribution is the generalized inverse Gaussian distribution. The probability density function of a normal variance-mean mixture with mixing probability density g {\\displaystyle g} is f ( x ) = \u222b 0 \u221e 1 2 \u03c0 \u03c3 2 v exp \u2061 ( \u2212 ( x \u2212 \u03b1 \u2212 \u03b2 v ) 2 2 \u03c3 2 v ) g ( v ) d v {\\displaystyle f(x)=\\int _{0}^{\\infty }{\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}v}}}\\exp \\left({\\frac {-(x-\\alpha -\\beta v)^{2}}{2\\sigma ^{2}v}}\\right)g(v)\\,dv} and its moment generating function is M ( s ) = exp \u2061 ( \u03b1 s ) M g ( \u03b2 s + 1 2 \u03c3 2 s 2 ) , {\\displaystyle M(s)=\\exp(\\alpha s)\\,M_{g}\\left(\\beta s+{\\frac {1}{2}}\\sigma ^{2}s^{2}\\right),} where M g {\\displaystyle M_{g}} is the moment generating function of the probability distribution with density function g {\\displaystyle g} , i.e. M g ( s ) = E ( exp \u2061 ( s V ) ) = \u222b 0 \u221e exp \u2061 ( s v ) g ( v ) d v . {\\displaystyle M_{g}(s)=E\\left(\\exp(sV)\\right)=\\int _{0}^{\\infty }\\exp(sv)g(v)\\,dv.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, two objects, especially systems of axioms or semantics for them, are called cryptomorphic if they are equivalent but not obviously equivalent. In particular, two definitions or axiomatizations of the same object are \"cryptomorphic\" if it is not obvious that they define the same object. Examples of cryptomorphic definitions abound in matroid theory and others can be found elsewhere, e.g., in group theory the definition of a group by a single operation of division, which is not obviously equivalent to the usual three \"operations\" of identity element, inverse, and multiplication. This word is a play on the many morphisms in mathematics, but \"cryptomorphism\" is only very distantly related to \"isomorphism\", \"homomorphism\", or \"morphisms\". The equivalence may in a cryptomorphism, if it is not actual identity, be informal, or may be formalized in terms of a bijection or equivalence of categories between the mathematical objects defined by the two cryptomorphic axiom systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One disk is allowed to spin freely, and the other is driven by a motor. Mode locking occurs when the freely-spinning disk turns at a frequency that is a rational multiple of that of the driven rotator. The simplest mathematical model that exhibits mode-locking is the circle map, which attempts to capture the motion of the spinning disks at discrete time intervals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Historically, there have been several formalizations of rewriting in an abstract setting, each with its idiosyncrasies. This is due in part to the fact that some notions are equivalent, see below in this article. The formalization that is most commonly encountered in monographs and textbooks, and which is generally followed here, is due to G\u00e9rard Huet (1980).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The nimber addition and multiplication operations are associative and commutative. Each nimber is its own negative. In particular for some pairs of ordinals, their nimber sum is smaller than either addend. The minimum excludant operation is applied to sets of nimbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if X, Y, and Z are random variables on the same probability space, and the covariance of X and Y is finite, then cov \u2061 ( X , Y ) = E \u2061 ( cov \u2061 ( X , Y \u2223 Z ) ) + cov \u2061 ( E \u2061 ( X \u2223 Z ) , E \u2061 ( Y \u2223 Z ) ) . {\\displaystyle \\operatorname {cov} (X,Y)=\\operatorname {E} (\\operatorname {cov} (X,Y\\mid Z))+\\operatorname {cov} (\\operatorname {E} (X\\mid Z),\\operatorname {E} (Y\\mid Z)).} The nomenclature in this article's title parallels the phrase law of total variance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications (e.g., building data models from only partially observed data) one wants to find the \"nearest\" correlation matrix to an \"approximate\" correlation matrix (e.g., a matrix which typically lacks semi-definite positiveness due to the way it has been computed). In 2002, Higham formalized the notion of nearness using the Frobenius norm and provided a method for computing the nearest correlation matrix using the Dykstra's projection algorithm, of which an implementation is available as an online Web API.This sparked interest in the subject, with new theoretical (e.g., computing the nearest correlation matrix with factor structure) and numerical (e.g. usage the Newton's method for computing the nearest correlation matrix) results obtained in the subsequent years.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the analogous process is usually dividing a difference (a distance) by a scale factor (a measure of statistical dispersion), which yields a dimensionless number, which is called normalization. Most often, this is dividing errors or residuals by the standard deviation or sample standard deviation, respectively, yielding standard scores and studentized residuals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, it remains unproven as of 2022. The number of primes between prime squares is 2, 5, 6, 15, 9, 22, 11, 27, ... OEIS: A050216. Legendre's conjecture that there is a prime between consecutive integer squares directly implies that there are at least two primes between prime squares for pn \u2265 3 since pn+1 \u2212 pn \u2265 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions. When specialized to solving feasible linear optimization problems with rational data, the ellipsoid method is an algorithm which finds an optimal solution in a number of steps that is polynomial in the input size. The ellipsoid method generates a sequence of ellipsoids whose volume uniformly decreases at every step, thus enclosing a minimizer of a convex function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The sequence of output subcommands required to accomplish the input command is generated by situations (i.e., branching conditions) that cause the FSA to transition from one output subcommand to the next. In step 4, each of the situations that are defined in step 3 are analyzed to reveal their dependencies on world and task states. This step identifies the detailed relationships between entities, events, and states of the world that cause a particular situation to be true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the balanced number partitioning problem, there are constraints on the number of items that can be allocated to each subset (these are called cardinality constraints). Another variant is the multidimensional number partitioning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term is also used for other devices which can both transmit and receive through a communications channel, such as optical transceivers which transmit and receive light in optical fiber systems, and bus transceivers which transmit and receive digital data in computer data buses. Radio transceivers are widely used in wireless devices. One large use is in two-way radios, which are audio transceivers used for bidirectional person-to-person voice communication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some texts, a trivial proof refers to a statement involving a material implication P\u2192Q, where the consequent Q, is always true. Here, the proof follows immediately by virtue of the definition of material implication in which as the implication is true regardless of the truth value of the antecedent P if the consequent is fixed as true.A related concept is a vacuous truth, where the antecedent P in a material implication P\u2192Q is false. In this case, the implication is always true regardless of the truth value of the consequent Q \u2013 again by virtue of the definition of material implication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public transportation, schedule adherence or on-time performance refers to the level of success of the service (such as a bus or train) remaining on the published schedule. On time performance, sometimes referred to as on time running, is normally expressed as a percentage, with a higher percentage meaning more vehicles are on time. The level of on time performance for many transport systems is a very important measure of the effectiveness of the system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For this reason, security and access control became a major focus of the Multics project in 1965. Another ongoing issue was properly handling computing resources: users spent most of their time staring at the terminal and thinking about what to input instead of actually using the resources of the computer, and a time-sharing system should give the CPU time to an active user during these periods. Finally, the systems typically offered a memory hierarchy several layers deep, and partitioning this expensive resource led to major developments in virtual memory systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In networking jargon, a computer, phone, or internet of things device connected to a computer network is sometimes referred to as an end system or end station, because it sits at the edge of the network. The end user directly interacts with an end system that provides information or services.End systems that are connected to the Internet are also referred to as internet hosts; this is because they host (run) internet applications such as a web browser or an email retrieval program. The Internet's end systems include some computers with which the end user does not directly interact. These include mail servers, web servers, or database servers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In print, summation and product are represented by special symbols; but other iterated operators often are denoted by larger variants of the symbol for the ordinary binary operator. Thus, the iterations of the four operations mentioned above are denoted \u2211 , \u220f , \u22c3 , {\\displaystyle \\sum ,\\ \\prod ,\\ \\bigcup ,} and \u22c2 {\\displaystyle \\bigcap } , respectively.More generally, iteration of a binary function is generally denoted by a slash: iteration of f {\\displaystyle f} over the sequence ( a 1 , a 2 \u2026 , a n ) {\\displaystyle (a_{1},a_{2}\\ldots ,a_{n})} is denoted by f / ( a 1 , a 2 \u2026 , a n ) {\\displaystyle f/(a_{1},a_{2}\\ldots ,a_{n})} , following the notation for reduce in Bird\u2013Meertens formalism. In general, there is more than one way to extend a binary operation to operate on finite sequences, depending on whether the operator is associative, and whether the operator has identity elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence the degree of \u03c8 \u2113 {\\displaystyle \\psi _{\\ell }} is equal to either 1 2 ( l 2 \u2212 1 ) {\\displaystyle {\\frac {1}{2}}(l^{2}-1)} , 1 2 ( l \u2212 1 ) {\\displaystyle {\\frac {1}{2}}(l-1)} , or 0. Ren\u00e9 Schoof observed that working modulo the \u2113 {\\displaystyle \\ell } th division polynomial allows one to work with all \u2113 {\\displaystyle \\ell } -torsion points simultaneously. This is heavily used in Schoof's algorithm for counting points on elliptic curves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "= \u03bb e \u2212 \u03bb t \u2212 e \u2212 \u03bb t \u2211 u = 1 x \u2212 1 ( \u03bb u t u \u2212 1 ( u \u2212 1 ) ! \u2212 \u03bb u + 1 t u u ! ) {\\displaystyle {\\begin{aligned}f(t)&{}={\\frac {d}{dt}}\\Pr(T_{x}\\leq t)={\\frac {d}{dt}}\\Pr(X_{t}\\geq x)={\\frac {d}{dt}}(1-\\Pr(X_{t}\\leq x-1))\\\\\\\\&{}={\\frac {d}{dt}}\\left(1-\\sum _{u=0}^{x-1}\\Pr(X_{t}=u)\\right)={\\frac {d}{dt}}\\left(1-\\sum _{u=0}^{x-1}{\\frac {(\\lambda t)^{u}e^{-\\lambda t}}{u!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example that follows, there are exactly two complete lead-reductions that produce two very different results. The fact that the results are irreducible (not only lead-irreducible) is specific to the example, although this is rather common with such small examples. In this two variable example, the monomial ordering that is used is the lexicographic order with x > y , {\\displaystyle x>y,} and we consider the reduction of by G = { g 1 , g 2 } , {\\displaystyle G=\\{g_{1},g_{2}\\},} with For the first reduction step, either the first or the second term of f may be reduced. However, the reduction of a term amounts to removing this term at the cost of adding new lower terms; if it is not the first reducible term that is reduced, it may occur that a further reduction adds a similar term, which must be reduced again.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the U.S. Food and Drug Administration (FDA) controls antimicrobial handsoaps and sanitizers as over-the-counter drugs (OTC) because they are intended for topical anti-microbial use to prevent disease in humans.The FDA requires strict labeling which informs consumers on proper use of this OTC drug and dangers to avoid, including warning adults not to ingest, not to use in the eyes, to keep out of the reach of children, and to allow use by children only under adult supervision. According to the American Association of Poison Control Centers, there were nearly 12,000 cases of hand sanitizer ingestion in 2006. If ingested, alcohol-based hand sanitizers can cause alcohol poisoning in small children.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They may be running traditionally in-house software or general purpose software such as DOS. Many of the newer ones have touch screens. They may be connected to computerized point of sale networks using any type of protocol. Such systems may be accessed remotely for the purpose of obtaining records or troubleshooting. Many businesses also use tablet computers as cash registers, utilizing the sale system as downloadable app-software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In designing an artificial intelligence agent, it was soon realized that representing common-sense knowledge, knowledge that humans simply take for granted, was essential to make an AI that could interact with humans using natural language. Cyc was meant to address this problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will include the true value (parameter) of interest. It can be defined as the proportion of instances where the interval surrounds the true value as assessed by long-run frequency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample to another) and its bias (how far off the average estimated value is from the true value). For an unbiased estimator, the MSE is the variance of the estimator. Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form.In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see Toroidal cores below). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs. The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1,400 to 2,000 V) than the voltage of utilization loads (100 V initially preferred).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nonstandard analysis, a monad or also a halo is the set of points infinitesimally close to a given point.Given a hyperreal number x in R\u2217, the monad of x is the set monad ( x ) = { y \u2208 R \u2217 \u2223 x \u2212 y is infinitesimal } . {\\displaystyle {\\text{monad}}(x)=\\{y\\in \\mathbb {R} ^{*}\\mid x-y{\\text{ is infinitesimal}}\\}.} If x is finite (limited), the unique real number in the monad of x is called the standard part of x. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first recall device in the United States was adopted in Los Angeles in 1903. Typically, the process involves the collection of citizen petitions for the recall of an elected official; if a sufficient number of valid signatures are collected and verified, a recall election is triggered. There have been four gubernatorial recall elections in U.S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The linkage criterion determines the distance between sets of observations as a function of the pairwise distances between observations. Some commonly used linkage criteria between two sets of observations A and B and a distance d are: Some of these can only be recomputed recursively (WPGMA, WPGMC), for many a recursive computation with Lance-Williams-equations is more efficient, while for other (Mini-Max, Hausdorff, Medoid) the distances have to be computed with the slower full formula. Other linkage criteria include: The probability that candidate clusters spawn from the same distribution function (V-linkage). The product of in-degree and out-degree on a k-nearest-neighbour graph (graph degree linkage). The increment of some cluster descriptor (i.e., a quantity defined for measuring the quality of a cluster) after merging two clusters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The following Algorithm B doesn't have this disadvantage, but it also doesn't have the fast arithmetic modulo p {\\displaystyle p} Algorithm A has in that case. Algorithm B Select a Q {\\displaystyle Q} -bit prime q {\\displaystyle q} so that q \u2261 7 mod 12 {\\displaystyle q\\equiv 7\\ {\\text{mod}}\\ 12} . Find the roots r 1 {\\displaystyle r_{1}} and r 2 {\\displaystyle r_{2}} of X 2 \u2212 X + 1 mod q {\\displaystyle X^{2}-X+1\\ {\\text{mod}}\\ q} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle. Let S {\\displaystyle S} be a set, and let ( x i ) {\\displaystyle (x_{i})} and ( y i ) {\\displaystyle (y_{i})} , i = 0 , 1 , 2 , \u2026 , {\\displaystyle i=0,1,2,\\ldots ,} be two sequences in S . {\\displaystyle S.} The interleave sequence is defined to be the sequence x 0 , y 0 , x 1 , y 1 , \u2026 {\\displaystyle x_{0},y_{0},x_{1},y_{1},\\dots } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Clustered lasso is a generalization of fused lasso that identifies and groups relevant covariates based on their effects (coefficients). The basic idea is to penalize the differences between the coefficients so that nonzero ones cluster. This can be modeled using the following regularization: \u2211 i < j p | \u03b2 i \u2212 \u03b2 j | \u2264 t 2 . {\\displaystyle \\sum _{i", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Query-dependent methods attempt to measure the degree to which a page matches a specific query, independent of the importance of the page. Query-dependent ranking is usually based on heuristics that consider the number and locations of matches of the various query words on the page itself, in the URL or in any anchor text referring to the page. In webometrics, it is possible to rank institutions according to their presence in the web (number of webpages) and the impact of these contents, such as the Webometrics Ranking of World Universities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first loop, the original (parent) process forks 10 copies of itself. Each of these child processes (detected by the fact that fork() returned zero) prints a message, sleeps, and exits. All of the children are created at essentially the same time (since the parent is doing very little in the loop), so it is somewhat random when each of them gets scheduled for the first time - thus the scrambled order of their messages. During the loop, an array of child process IDs is built.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In medicine, sampling is gathering of matter from the body to aid in the process of a medical diagnosis and/or evaluation of an indication for treatment, further medical tests or other procedures. In this sense, the sample is the gathered matter, and the sampling tool or sampler is the person or material to collect the sample. Sampling is a prerequisite for many medical tests, but generally not for medical history, physical examination and radiologic tests.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bentley also proposed using range trees, which improved query time to O ( log d \u2061 n + k ) {\\displaystyle O(\\log ^{d}n+k)} but increased space to O ( n log d \u2212 1 \u2061 n ) {\\displaystyle O(n\\log ^{d-1}n)} . Dan Willard used downpointers, a special case of fractional cascading to reduce the query time further to O ( log d \u2212 1 \u2061 n + k ) {\\displaystyle O(\\log ^{d-1}n+k)} . While the above results were achieved in the pointer machine model, further improvements have been made in the word RAM model of computation in low dimensions (2D, 3D, 4D).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the ring of adeles. The metaplectic group has a particularly significant infinite-dimensional linear representation, the Weil representation. It was used by Andr\u00e9 Weil to give a representation-theoretic interpretation of theta functions, and is important in the theory of modular forms of half-integral weight and the theta correspondence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. The class of completely regular semigroups forms an important subclass of the class of regular semigroups, the class of inverse semigroups being another such subclass. Alfred H. Clifford was the first to publish a major paper on completely regular semigroups though he used the terminology \"semigroups admitting relative inverses\" to refer to such semigroups. The name \"completely regular semigroup\" stems from Lyapin's book on semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of Regulation (EU) No 910/2014 (eIDAS), a qualified digital certificate is a public key certificate issued by a trust service provider which has government-issued qualifications. The certificate is designed to ensure the authenticity and data integrity of an electronic signature and its accompanying message and/or attached data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since relabels and saturating pushes increase \u03a6, the total number of nonsaturating pushes must make up the difference of (2| V | \u2212 1)(| V | \u2212 2) + (2| V | \u2212 1)(2| V || E |) \u2264 4| V |2| E |. This results in a time bound of O(V 2E) for the nonsaturating push operations. In sum, the algorithm executes O(V 2) relabels, O(VE) saturating pushes and O(V 2E) nonsaturating pushes. Data structures can be designed to pick and execute an applicable operation in O(1) time. Therefore, the time complexity of the algorithm is O(V 2E).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical inference based on regression coefficients, yes; in predictive modelling applications, correction is neither necessary nor appropriate. To understand this, consider the measurement error as follows. Let y be the outcome variable, x be the true predictor variable, and w be an approximate observation of x. Frost and Thompson suggest, for example, that x may be the true, long-term blood pressure of a patient, and w may be the blood pressure observed on one particular clinic visit. Regression dilution arises if we are interested in the relationship between y and x, but estimate the relationship between y and w. Because w is measured with variability, the slope of a regression line of y on w is less than the regression line of y on x. Does this matter?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 2012, the court ruled that under the All Writs Act, the defendant was required to produce an unencrypted hard drive for the court.In many jurisdictions, the legal status of forced disclosure remains unclear. The 2016 FBI\u2013Apple encryption dispute concerns the ability of courts in the United States to compel manufacturers' assistance in unlocking cell phones whose contents are cryptographically protected. As a potential counter-measure to forced disclosure some cryptographic software supports plausible deniability, where the encrypted data is indistinguishable from unused random data (for example such as that of a drive which has been securely wiped).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Zeroth Part, Chapter 0, Conway introduces a specialized form of set notation, having the form {L|R}, where L and R are again of this form, built recursively, terminating in {|}, which is to be read as an analog of the empty set. Given this object, axiomatic definitions for addition, subtraction, multiplication, division and inequality may be given. As long as one insists that L", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Codes such as MARLOWE operate with this approach. The binary collision approximation can also be extended to simulate dynamic composition changes of a material due to prolonged ion irradiation, i.e. due to ion implantation and sputtering.At low ion energies, the approximation of independent collisions between atoms starts to break down.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical group theory, a C-group is a group such that the centralizer of any involution has a normal Sylow 2-subgroup. They include as special cases CIT-groups where the centralizer of any involution is a 2-group, and TI-groups where any Sylow 2-subgroups have trivial intersection. The simple C-groups were determined by Suzuki (1965), and his classification is summarized by Gorenstein (1980, 16.4). The classification of C-groups was used in Thompson's classification of N-groups. The simple C-groups are the projective special linear groups PSL2(p) for p a Fermat or Mersenne prime the projective special linear groups PSL2(9) the projective special linear groups PSL2(2n) for n\u22652 the projective special linear groups PSL3(q) for q a prime power the Suzuki groups Sz(22n+1) for n\u22651 the projective unitary groups PU3(q) for q a prime power", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Uncertainties can also be defined by the relative error (\u0394x)/x, which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, \u03c3, which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval x \u00b1 u. However, the most general way of characterizing uncertainty is by specifying its probability distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 235, 1235, 2345, and 12345 are the patterns related to Braille pattern dots-124, since the two additional dots of kantenji patterns 0124, 1247, and 01247 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So the parser should also use the rule A \u2192 w if \u03b5 is in Fi(w) and it sees on the input stream a symbol that could follow A. Therefore, we also need the Follow-set of A, written as Fo(A) here, which is defined as the set of terminals a such that there is a string of symbols \u03b1Aa\u03b2 that can be derived from the start symbol. We use $ as a special terminal indicating end of input stream, and S as start symbol. Computing the Follow-sets for the nonterminals in a grammar can be done as follows: initialize Fo(S) with { $ } and every other Fo(Ai) with the empty set if there is a rule of the form Aj \u2192 wAiw' , then if the terminal a is in Fi(w' ), then add a to Fo(Ai) if \u03b5 is in Fi(w' ), then add Fo(Aj) to Fo(Ai) if w' has length 0, then add Fo(Aj) to Fo(Ai) repeat step 2 until all Fo sets stay the same.This provides the least fixed point solution to the following system: Fo(S) \u2287 {$} Fo(A) \u2287 Fi(w)\u00b7Fo(B) for each rule of the form B \u2192 ... A wNow we can define exactly which rules will appear where in the parsing table.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus measuring leakage, or Iddq testing, is a quick, inexpensive method for finding defective chips. Increased leakage is a common failure mode resulting from non-catastrophic overstress of a semiconductor device, when the junction or the gate oxide suffers permanent damage not sufficient to cause a catastrophic failure. Overstressing the gate oxide can lead to stress-induced leakage current.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Altmetrics did not originally cover citation counts, but calculate scholar impact based on diverse online research output, such as social media, online news media, online reference managers and so on. It demonstrates both the impact and the detailed composition of the impact. Altmetrics could be applied to research filter, promotion and tenure dossiers, grant applications and for ranking newly-published articles in academic search engines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Infiltrating organizations is an important tool because these institutions are already seen as legitimate in the eyes of the people and provide a platform to express their ideas. When infiltrating, the dissident identifies needs of the organization and then links those needs to solutions that his ideology can provide. This was a technique that the Communist Party USA employed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle X_{0},X_{1},X_{2},...} then X 0 {\\displaystyle X_{0}} is the state which the machine starts in and X 10 {\\displaystyle X_{10}} is the random variable describing its state after 10 transitions. The process continues forever, indexed by the natural numbers. An example of a stochastic process which is not a Markov chain is the model of a machine which has states A and E and moves to A from either state with 50% chance if it has ever visited A before, and 20% chance if it has never visited A before (leaving a 50% or 80% chance that the machine moves to E).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States House of Representatives, a motion to recommit can be made with or without instructions. If the motion is made without instructions, the bill or resolution is simply sent back to the committee. If the motion is made with instructions and the motion is agreed to, the chairman of the committee in question will immediately report the bill or resolution back to the whole House with the new language. In this sense, a motion to recommit with instructions is effectively an amendment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a mobile VPN is a solution that provides data user mobility and ensures secure network access with predictable performance. Data user mobility is defined as uninterrupted connectivity or the ability to stay connected and communicate to a possibly remote data network while changing the network access medium or points of attachment.In 2001, Huawei launched a product named \"MVPN\". In this case \"MVPN\" had a different meaning from the way that later industry sources would use the term. The Huawei product was focused on delivering a seamless corporate phone system to users whether they were on desktop phones or mobile devices. Although the web page is no longer available, the company advertised that their MVPN had the following advantages over a standard phone system: Direct connectivity \u2013 the corporate network becomes part of mobile operator's network through direct connection Private numbering plan \u2013 the communication is tailored to company organization Corporate Business Group \u2013 all offices and employees are part of one common group, that includes all mobile and desk phones Short dialing \u2013 a short number to access each employee, no meter on his mobile or desk phone Smart Divert \u2013 easy divert within company group Groups and subgroups \u2013 Several sub-groups could be defined within the group with different changing as well as with separate numbering plan Calls control \u2013 certain destinations could be allowed or barred both on mobile and desk phones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The internal language of closed symmetric monoidal categories is linear logic and the type system is the linear type system. Many examples of closed monoidal categories are symmetric. However, this need not always be the case, as non-symmetric monoidal categories can be encountered in category-theoretic formulations of linguistics; roughly speaking, this is because word-order in natural language matters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In such games, however, it is often found that creativity is lowered and the words stray towards having obvious associations again. This game is sometimes known as \"Word for Word\". Sometimes, repeated words are forbidden or otherwise noted on a separate list for interest. A variant with an arbitrary name (sometimes called Ultra Word Association) involves associating words in a grid, where the first word is placed in the top-left, and where each word must be placed adjacent to another one and must associate with all those words adjacent to it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s, Noam Elkies, followed by A. O. L. Atkin devised improvements to Schoof's basic algorithm by making a distinction among the primes \u2113 1 , \u2026 , \u2113 s {\\displaystyle \\ell _{1},\\ldots ,\\ell _{s}} that are used. A prime \u2113 {\\displaystyle \\ell } is called an Elkies prime if the characteristic equation of the Frobenius endomorphism, \u03d5 2 \u2212 t \u03d5 + q = 0 {\\displaystyle \\phi ^{2}-t\\phi +q=0} , splits over F \u2113 {\\displaystyle \\mathbb {F} _{\\ell }} . Otherwise \u2113 {\\displaystyle \\ell } is called an Atkin prime. Elkies primes are the key to improving the asymptotic complexity of Schoof's algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An example would be to trade the electric charge, Q, (related to the abelian group U(1) of electromagnetism), for the new quantum number exp(2i\u03c0 Q). Then this becomes a multiplicative quantum number by virtue of the charge being an additive quantum number. However, this route is usually followed only for discrete subgroups of U(1), of which Z2 finds the widest possible use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Digitally modulated signals (e.g. QAM or PSK) are basically made of two CW carriers (the I and Q components, which are out-of-phase carriers). In fact, the information (bits or symbols) is carried by given combinations of phase and/or amplitude of the I and Q components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Available in several varieties; analog, analog spread spectrum (100 kHz bandwidth), digital, and digital spread spectrum, most being sold today are low-cost analog models, which are still susceptible to eavesdropping. Digital variants can still be scanned, but are received as a digital hiss and therefore are difficult to eavesdrop upon. Digital transmission is immune to static interference but can experience signal fade (brief silence) as the phone goes out of range of the base.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the NMOS 6502 and derivatives (e.g., 6510), the simultaneous assertion of a hardware interrupt line and execution of BRK was not accounted for in the design\u2014the BRK instruction will be ignored in such a case. Also, the status of the decimal mode flag in the processor status register is unchanged following an interrupt of any kind. This behavior can potentially result in a difficult to locate bug in the interrupt handler if decimal mode happens to be enabled at the time of an interrupt. These anomalies were corrected in all CMOS versions of the processor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is no standard method for applying the task. The most commonly used one is a letter rating task, which involves having participants judge all the letters of the alphabet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It has also been observed that misinformation and disinformation reappear on social media sites. A research study watched the process of thirteen rumors appearing on Twitter and noticed that eleven of those same stories resurfaced multiple times, after time had passed.A social media app called Parler has caused much chaos as well. Right winged Twitter users who were banned on the app moved to Parler after the Capitol Hill riots, and the app was being used to plan and facilitate more illegal and dangerous activities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the contemporary literature, there are two primary (and non-equivalent) formulations of supervenience (for both definitions let A and B be sets of properties). (1) A-properties supervene on B-properties if and only if all things that are B-indiscernible are A-indiscernible. Formally: \u2200 x \u2200 y ( \u2200 X \u2208 B ( X x \u2194 X y ) \u2192 \u2200 Y \u2208 A ( Y x \u2194 Y y ) ) {\\displaystyle \\forall x\\forall y(\\forall X_{\\in B}(Xx\\leftrightarrow Xy)\\rightarrow \\forall Y_{\\in A}(Yx\\leftrightarrow Yy))} (2) A-properties supervene on B-properties if and only if anything that has an A-property has some B-property such that anything that has that B-property also has that A-property. Formally: \u2200 x \u2200 X \u2208 A ( X x \u2192 \u2203 Y \u2208 B ( Y x \u2227 \u2200 y ( Y y \u2192 X y ) ) ) {\\displaystyle \\forall x\\forall X_{\\in A}(Xx\\rightarrow \\exists Y_{\\in B}(Yx\\land \\forall y(Yy\\rightarrow Xy)))} For example, if one lets A be a set of mental properties, lets B be a set of physical properties, and chooses a domain of discourse consisting of persons, then (1) says that any two persons who are physically indiscernible are mentally indiscernible, and (2) says that any person who has a mental property has some physical property such that any person with that physical property has that mental property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two distinct sub-populations, or may indicate 'correct trial' versus 'measurement error'; this is modeled by a mixture model. In most larger samplings of data, some data points will be further away from the sample mean than what is deemed reasonable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders.There are several common ways of formalizing weak orderings, that are different from each other but cryptomorphic (interconvertable with no loss of information): they may be axiomatized as strict weak orderings (strictly partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible relations exists between every pair of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another representation called a preferential arrangement based on a utility function is also possible. Weak orderings are counted by the ordered Bell numbers. They are used in computer science as part of partition refinement algorithms, and in the C++ Standard Library.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information is a text document transmitted over the Internet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is equal to A.Some authors use the name square root or the notation A1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = BTB = A (for real-valued matrices, where BT is the transpose of B). Less frequently, the name square root may be used for any factorization of a positive semidefinite matrix A as BTB = A, as in the Cholesky factorization, even if BB \u2260 A. This distinct meaning is discussed in Positive definite matrix \u00a7 Decomposition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages and programming environments, the use of a case or switch statement is considered superior to an equivalent series of if else if statements because it is: Easier to debug (e.g. setting breakpoints on code vs. a call table, if the debugger has no conditional breakpoint capability) Easier for a person to read Easier to understand, and consequently easier to maintain Fixed depth: a sequence of \"if else if\" statements may yield deep nesting, making compilation more difficult (especially in automatically generated code) Easier to verify that all values are handled. Compilers can issue a warning if some enum values are not handled.Additionally, an optimized implementation may execute much faster than the alternative, because it is often implemented by using an indexed branch table. For example, deciding program flow based on a single character's value, if correctly implemented, is vastly more efficient than the alternative, reducing instruction path lengths considerably.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Chinese monoid is a monoid generated by a totally ordered alphabet with the relations cba = cab = bca for every a \u2264 b \u2264 c. An algorithm similar to Schensted's algorithm yields characterisation of the equivalence classes and a cross-section theorem. It was discovered by Duchamp & Krob (1994) during their classification of monoids with growth similar to that of the plactic monoid, and studied in detail by Julien Cassaigne, Marc Espie, Daniel Krob, Jean-Christophe Novelli, and Florent Hivert in 2001.The Chinese monoid has a regular language cross-section a \u2217 ( b a ) \u2217 b \u2217 ( c a ) \u2217 ( c b ) \u2217 c \u2217 \u22ef {\\displaystyle a^{*}\\ (ba)^{*}b^{*}\\ (ca)^{*}(cb)^{*}c^{*}\\cdots } and hence polynomial growth of dimension n ( n + 1 ) 2 {\\displaystyle {\\frac {n(n+1)}{2}}} .The Chinese monoid equivalence class of a permutation is the preimage of an involution under the map w \u21a6 w \u2218 w \u2212 1 {\\displaystyle w\\mapsto w\\circ w^{-1}} where \u2218 {\\displaystyle \\circ } denotes the product in the Iwahori-Hecke algebra with q s = 0 {\\displaystyle q_{s}=0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some countries' online banking, the bank sends to the user a numbered list of OTPs that is printed on paper. Other banks send plastic cards with actual OTPs obscured by a layer that the user has to scratch off to reveal a numbered OTP. For every online transaction, the user is required to enter a specific OTP from that list. Some systems ask for the numbered OTPs sequentially, others pseudorandomly choose an OTP to be entered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to discuss the continuous-time Markov decision process, we introduce two sets of notations: If the state space and action space are finite, S {\\displaystyle {\\mathcal {S}}}: State space; A {\\displaystyle {\\mathcal {A}}}: Action space; q ( i \u2223 j , a ) {\\displaystyle q(i\\mid j,a)}: S \u00d7 A \u2192 \u25b3 S {\\displaystyle {\\mathcal {S}}\\times {\\mathcal {A}}\\rightarrow \\triangle {\\mathcal {S}}} , transition rate function; R ( i , a ) {\\displaystyle R(i,a)}: S \u00d7 A \u2192 R {\\displaystyle {\\mathcal {S}}\\times {\\mathcal {A}}\\rightarrow \\mathbb {R} } , a reward function.If the state space and action space are continuous, X {\\displaystyle {\\mathcal {X}}}: state space; U {\\displaystyle {\\mathcal {U}}}: space of possible control; f ( x , u ) {\\displaystyle f(x,u)}: X \u00d7 U \u2192 \u25b3 X {\\displaystyle {\\mathcal {X}}\\times {\\mathcal {U}}\\rightarrow \\triangle {\\mathcal {X}}} , a transition rate function; r ( x , u ) {\\displaystyle r(x,u)}: X \u00d7 U \u2192 R {\\displaystyle {\\mathcal {X}}\\times {\\mathcal {U}}\\rightarrow \\mathbb {R} } , a reward rate function such that r ( x ( t ) , u ( t ) ) d t = d R ( x ( t ) , u ( t ) ) {\\displaystyle r(x(t),u(t))\\,dt=dR(x(t),u(t))} , where R ( x , u ) {\\displaystyle R(x,u)} is the reward function we discussed in previous case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples are cell phones, which transmit and receive the two sides of a phone conversation using radio waves to a cell tower, cordless phones in which both the phone handset and the base station have transceivers to communicate both sides of the conversation, and land mobile radio systems like walkie-talkies and CB radios. Another large use is in wireless modems in mobile networked computer devices such laptops, pads, and cellphones, which both transmit digital data to and receive data from a wireless router. Aircraft carry automated microwave transceivers called transponders which, when they are triggered by microwaves from an air traffic control radar, transmit a coded signal back to the radar to identify the aircraft. Satellite transponders in communication satellites receive digital telecommunication data from a satellite ground station, and retransmit it to another ground station.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To form the product of two 8-bit integers, for example, the digital device forms the sum and difference, looks both quantities up in a table of squares, takes the difference of the results, and divides by four by shifting two bits to the right. For 8-bit integers the table of quarter squares will have 29\u22121=511 entries (one entry for the full range 0..510 of possible sums, the differences using only the first 256 entries in range 0..255) or 29\u22121=511 entries (using for negative differences the technique of 2-complements and 9-bit masking, which avoids testing the sign of differences), each entry being 16-bit wide (the entry values are from (0\u00b2/4)=0 to (510\u00b2/4)=65025). The quarter square multiplier technique has benefited 8-bit systems that do not have any support for a hardware multiplier. Charles Putney implemented this for the 6502.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fourth year of his degree course Richard's research project led him to using Oxford's Ferranti Mercury computer to solve integrals. During a fellowship year in France at Centre de M\u00e9canique Ondulatoire Appliqu\u00e9e, he was able to use more powerful computers. Returning to Oxford, he worked on ab initio computations and applied computational techniques to solving quantum mechanical problems in theoretical chemistry, in particular studying spin-orbit coupling. His influential paper Third age of quantum chemistry (1979) marked the development of computational techniques for theoretical analysis whose precision equaled or surpassed experimental results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By offering a quantity discount for a larger quantity purchased the seller is able to capture some of the consumer surplus but not all. This is because diminishing marginal utility may mean the consumer would not be willing to purchase an additional unit without a discount since the marginal utility received from the good or service is no longer greater than price. However, by offering a discount the seller can capture some of consumers surplus by encouraging them to purchase an additional unit at a discounted price.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Optimization will generally focus on improving just one or two aspects of performance: execution time, memory usage, disk space, bandwidth, power consumption or some other resource. This will usually require a trade-off \u2013 where one factor is optimized at the expense of others. For example, increasing the size of cache improves run time performance, but also increases the memory consumption.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, effective transmission rate (average rate of transmission, effective speed of transmission) is the rate at which information is processed by a transmission facility. The effective transmission rate is calculated as (a) the measured number of units of data, such as bits, characters, blocks, or frames, transmitted during a significant measurement time interval divided by (b) the measurement time interval. The effective transmission rate is usually expressed as a number of units of data per unit time, such as bits per second or characters per second.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always \"better\" than it (or at least sometimes better and never worse), in the precise sense of \"better\" defined below. This concept is analogous to Pareto efficiency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The presumed difficulty of this problem is important for the algorithms used in cryptography such as RSA public-key encryption and the RSA digital signature. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. In 2019, Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thom\u00e9 and Paul Zimmermann factored a 240-digit (795-bit) number (RSA-240) utilizing approximately 900 core-years of computing power.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an iterated function is a function X \u2192 X (that is, a function from some set X to itself) which is obtained by composing another function f: X \u2192 X with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying a given function is fed again in the function as input, and this process is repeated. For example on the image on the right: L = F {\\displaystyle {\\mathit {F}}\\,} ( K ), M = F \u2218 F {\\displaystyle {\\mathit {F}}\\,\\circ {\\mathit {F}}\\,} ( K ) = F 2 {\\displaystyle {\\mathit {F}}\\;^{2}\\,} ( K ),with the circle\u2011shaped symbol of function composition.Iterated functions are objects of study in computer science, fractals, dynamical systems, mathematics and renormalization group physics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, Craig's theorem (also known as Craig's trick) states that any recursively enumerable set of well-formed formulas of a first-order language is (primitively) recursively axiomatizable. This result is not related to the well-known Craig interpolation theorem, although both results are named after the same logician, William Craig.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regional testing, 20 to 50 \u00b5L of liquid stimulus is presented to the anterior and posterior tongue using a pipette, soaked filter-paper disks, or cotton swabs. In whole mouth testing, small quantities (2-10 mL) of solution are administered, and the patient is asked to swish the solution around in the mouth.Threshold tests for sucrose (sweet), citric acid (sour), sodium chloride (salty), and quinine or caffeine (bitter) are frequently performed with natural stimuli. One of the most frequently used techniques is the \"three-drop test.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s a metrication program was initiated in most English-speaking countries, resulting in either the partial or total displacement of the imperial system or the US customary system of measure in those countries. The current status of imperial and US customary units, as summarised by NIST, is that \"the SI metric system is now the official system of units in the United Kingdom, while the customary units are still predominantly used in the United States\".The situation is however not as clear-cut as this. In the United States, for example, the metric system is the predominant system of measure in certain fields such as automobile manufacture even though customary units are used in aircraft manufacture. In the United Kingdom, metric units are required for almost all regulated use of units of measure except for a few specifically exempt areas such as road signs, speedometers and draught beer. Metrication is also all but complete in the Commonwealth countries of Australia, India, New Zealand and South Africa; metrication in Canada has displaced the imperial system in many areas.The imperial and US customary systems of measurement use the SI for their formal definitions, the yard being defined as 0.9144 metres exactly, the pound avoirdupois as 0.45359237 kilograms exactly while both systems of measure share the definition of the second.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a field and its absolute Galois group. It is an interdisciplinary subject as it uses tools from algebraic number theory, arithmetic geometry, algebraic geometry, model theory, the theory of finite groups and of profinite groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 256, 1256, 2456, and 12456 are the patterns related to Braille pattern dots-145, since the two additional dots of kantenji patterns 0145, 1457, and 01457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An element of order 6 in the group S5 can be written in cycle notation as (1 2) (3 4 5). Note that the same argument applies to the number 6, that is, g(6) = 6. There are arbitrarily long sequences of consecutive numbers n, n + 1, \u2026, n + m on which the function g is constant.The integer sequence g(0) = 1, g(1) = 1, g(2) = 2, g(3) = 3, g(4) = 4, g(5) = 6, g(6) = 6, g(7) = 12, g(8) = 15, ... (sequence A000793 in the OEIS) is named after Edmund Landau, who proved in 1902 that lim n \u2192 \u221e ln \u2061 ( g ( n ) ) n ln \u2061 ( n ) = 1 {\\displaystyle \\lim _{n\\to \\infty }{\\frac {\\ln(g(n))}{\\sqrt {n\\ln(n)}}}=1} (where ln denotes the natural logarithm).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UNL approach, information conveyed by natural language is represented sentence by sentence as a hypergraph composed of a set of directed binary labeled links (referred to as relations) between nodes or hypernodes (the Universal Words, or simply UWs), which stand for concepts. UWs can also be annotated with attributes representing context information. As an example, the English sentence \u2018The sky was blue? !\u2019 can be represented in UNL as follows: In the example above, sky(icl>natural world) and blue(icl>color), which represent individual concepts, are UWs; \"aoj\" (= attribute of an object) is a directed binary semantic relation linking the two UWs; and \"@def\", \"@interrogative\", \"@past\", \"@exclamation\" and \"@entry\" are attributes modifying UWs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For a dijoin in the given graph, the corresponding set of edges forms a directed cut in the dual graph, and vice versa. This relationship between these two problems allows the feedback arc set problem to be solved efficiently for planar graphs, even though it is NP-hard for other types of graphs. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In professional usage, digital cameras offer many advantages in speed, precision, flexibility, ease, and cost. Immediacy: image review and deletion are possible immediately; lighting and composition can be assessed immediately, which ultimately conserves storage space. Faster workflow: management (color and file), manipulation, and printing tools are more versatile than conventional film processes. However, batch processing of RAW files can be time-consuming, even on a fast computer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Reiner\u2013Stanton\u2013White paper, the following example is given: Let \u03b1 be a composition of n, and let W(\u03b1) be the set of all words of length n with \u03b1i letters equal to i. A descent of a word w is any index j such that w j > w j + 1 {\\displaystyle w_{j}>w_{j+1}} . Define the major index maj \u2061 ( w ) {\\displaystyle \\operatorname {maj} (w)} on words as the sum of all descents. The triple ( X n , C n \u2212 1 , 1  q  q ) {\\displaystyle (X_{n},C_{n-1},{\\frac {1}{_{q}}}\\left_{q})} exhibit a cyclic sieving phenomenon, where X n {\\displaystyle X_{n}} is the set of non-crossing (1,2)-configurations of .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the central limit theorem states conditions under which the average of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed.Directional statistics is the subdiscipline of statistics that deals with directions (unit vectors in Rn), axes (lines through the origin in Rn) or rotations in Rn. The means and variances of directional quantities are all finite, so that the central limit theorem may be applied to the particular case of directional statistics.This article will deal only with unit vectors in 2-dimensional space (R2) but the method described can be extended to the general case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This makes the reliable modification of static memory values more complex. The load address has to be determined and subtracted from a found memory address to obtain a static memory offset. This offset is often exactly the address of the static variable within the PIE binary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, both of these services allow browsing of their classifications, via Westlaw's West Key Numbers or Lexis' Headnotes. Though these two search algorithms are proprietary and secret, it is known that they employ manual classification of text (though this may be computer-assisted).These systems can help overcome the majority of problems inherent in legal information retrieval systems, in that manual classification has the greatest chances of identifying landmark cases and understanding the issues that arise in the text. In one study, ontological searching resulted in a precision rate of 82% and a recall rate of 97% among legal professionals. The legal texts included, however, were carefully controlled to just a few areas of law in a specific jurisdiction.The major drawback to this approach is the requirement of using highly skilled legal professionals and large amounts of time to classify texts. As the amount of text available continues to increase, some have stated their belief that manual classification is unsustainable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "I am her. Subject + Verb (transitive) + Indirect Object + Direct ObjectExample: She made me a pie.This clause pattern is a derivative of S+V+O, transforming the object of a preposition into an indirect object of the verb, as the example sentence in transformational grammar is actually \"She made a pie for me\". Subject + Verb (transitive) + Object + Object ComplementExample: They made him happy.They did not make \"him\", and they did not make \"happy\"; they made \"him happy\"\u2014the object and its complement form a syntactical unit.Sentences \u2013 which are composed of these clauses, in either \"dependent\" or \"independent\" form \u2013 also have patterns, as explained below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In logics with double negation elimination (where \u00ac \u00ac x \u2261 x {\\displaystyle \\lnot \\lnot x\\equiv x} ) the complementary literal or complement of a literal l {\\displaystyle l} can be defined as the literal corresponding to the negation of l {\\displaystyle l} . We can write l \u00af {\\displaystyle {\\bar {l}}} to denote the complementary literal of l {\\displaystyle l} . More precisely, if l \u2261 x {\\displaystyle l\\equiv x} then l \u00af {\\displaystyle {\\bar {l}}} is \u00ac x {\\displaystyle \\lnot x} and if l \u2261 \u00ac x {\\displaystyle l\\equiv \\lnot x} then l \u00af {\\displaystyle {\\bar {l}}} is x {\\displaystyle x} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In performance testing, it is often crucial for the test conditions to be similar to the expected actual use. However, in practice this is hard to arrange and not wholly possible, since production systems are subjected to unpredictable workloads. Test workloads may mimic occurrences in the production environment as far as possible, but only in the simplest systems can one exactly replicate this workload variability. Loosely-coupled architectural implementations (e.g.: SOA) have created additional complexities with performance testing. To truly replicate production-like states, enterprise services or assets that share a common infrastructure or platform require coordinated performance testing, with all consumers creating production-like transaction volumes and load on shared infrastructures or platforms. Because this activity is so complex and costly in money and time, some organizations now use tools to monitor and simulate production-like conditions (also referred as \"noise\") in their performance testing environments (PTE) to understand capacity and resource requirements and verify / validate quality attributes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 23568, 123568, 234568, and 1234568 are the patterns related to Braille pattern dots-12456, since the two additional dots of kantenji patterns 012456, 124567, and 0124567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As in the case of groups or magmas, the semigroup operation need not be commutative, so x\u00b7y is not necessarily equal to y\u00b7x; a well-known example of an operation that is associative but non-commutative is matrix multiplication. If the semigroup operation is commutative, then the semigroup is called a commutative semigroup or (less often than in the analogous case of groups) it may be called an abelian semigroup. A monoid is an algebraic structure intermediate between semigroups and groups, and is a semigroup having an identity element, thus obeying all but one of the axioms of a group: existence of inverses is not required of a monoid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 19th century, research into the subject started to intensify. Notable developments in this century include the work of Hans Christian \u00d8rsted who discovered in 1820 that an electric current produces a magnetic field that will deflect a compass needle, of William Sturgeon who, in 1825 invented the electromagnet, of Joseph Henry and Edward Davy who invented the electrical relay in 1835, of Georg Ohm, who in 1827 quantified the relationship between the electric current and potential difference in a conductor, of Michael Faraday (the discoverer of electromagnetic induction in 1831), and of James Clerk Maxwell, who in 1873 published a unified theory of electricity and magnetism in his treatise Electricity and Magnetism.In 1782, Georges-Louis Le Sage developed and presented in Berlin probably the world's first form of electric telegraphy, using 24 different wires, one for each letter of the alphabet. This telegraph connected two rooms. It was an electrostatic telegraph that moved gold leaf through electrical conduction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to reduce encryption or signature verification time, it is useful to use a small public exponent ( e {\\displaystyle e} ). In practice, common choices for e {\\displaystyle e} are 3, 17 and 65537 ( 2 16 + 1 ) {\\displaystyle (2^{16}+1)} . These values for e are Fermat primes, sometimes referred to as F 0 , F 2 {\\displaystyle F_{0},F_{2}} and F 4 {\\displaystyle F_{4}} respectively ( F x = 2 2 x + 1 ) {\\displaystyle (F_{x}=2^{2^{x}}+1)} . They are chosen because they make the modular exponentiation operation faster.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The blinking of the text cursor is usually temporarily suspended when it is being moved; otherwise, the cursor may change position when it is not visible, making its location difficult to follow. The concept of a blinking cursor can be attributed to Charles Kiesling Sr. via US Patent 3531796, filed in August 1967.Some interfaces use an underscore or thin vertical bar to indicate that the user is in insert mode, a mode where text will be inserted in the middle of the existing text, and a larger block to indicate that the user is in overtype mode, where inserted text will overwrite existing text. In this way, a block cursor may be seen as a piece of selected text one character wide, since typing will replace the text \"in\" the cursor with the new text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When any two indices are interchanged, equal or not, the symbol is negated: If any two indices are equal, the symbol is zero. When all indices are unequal, we have: where p (called the parity of the permutation) is the number of pairwise interchanges of indices necessary to unscramble i1, i2, ..., in into the order 1, 2, ..., n, and the factor (\u22121)p is called the sign, or signature of the permutation. The value \u03b51 2 ... n must be defined, else the particular values of the symbol for all permutations are indeterminate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multivariate statistics, spectral clustering techniques make use of the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions. The similarity matrix is provided as an input and consists of a quantitative assessment of the relative similarity of each pair of points in the dataset. In application to image segmentation, spectral clustering is known as segmentation-based object categorization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "What stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value?The general solution to this full-information expected rank problem is unknown. The major difficulty is that the problem is fully history-dependent, that is, the optimal rule depends at every stage on all preceding values, and not only on simpler sufficient statistics of these. Only bounds are known for the limiting value v as n goes to infinity, namely 1.908 < v < 2.329. It is known that there is some room to improve the lower bound by further computations for a truncated version of the problem. It is still not known how to improve on the upper bound which stems from the subclass of memoryless threshold rules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions. Linear MMSE estimators are a popular choice since they are easy to use, easy to calculate, and very versatile. It has given rise to many popular estimators such as the Wiener\u2013Kolmogorov filter and Kalman filter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2010s, software has become a key business differentiator. As a result, organizations now expect software development teams to deliver more, and more innovative, software within shorter delivery cycles. To meet these demands, teams have turned to lean approaches, such as Agile, DevOps, and Continuous Delivery, to try to speed up the systems development life cycle (SDLC). After accelerating other aspects of the delivery pipeline, teams typically find that their testing process is preventing them from achieving the expected benefits of their SDLC acceleration initiative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Interaction between 32-bit addresses and two loop control instructions, BXH and BXLE that treated their arguments as signed numbers when doing comparisons (and which was said to be the reason TSS used 31-bit addressing on the Model 67). : 26, note 85 Input from key initial Model 67 sites, which had debated the alternatives during the initial system design period, and had recommended 31 bits (instead of the 32-bit design that was ultimately chosen at the time). : 8\u20139, note 21 Certain machine instructions in this 31-bit addressing mode alter the addressing mode bit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the dynamic topic model, only W t , d , n {\\displaystyle W_{t,d,n}} is observable. Learning the other parameters constitutes an inference problem. Blei and Lafferty argue that applying Gibbs sampling to do inference in this model is more difficult than in static models, due to the nonconjugacy of the Gaussian and multinomial distributions. They propose the use of variational methods, in particular, the Variational Kalman Filtering and the Variational Wavelet Regression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "). Roughly speaking, \u03b4 {\\displaystyle \\delta \\,\\!} minimizes this expectation of expected loss (i.e., is a Bayes rule) if and only if it minimizes the expected loss for each x \u2208 X {\\displaystyle x\\in {\\mathcal {X}}} separately (i.e., is a generalized Bayes rule).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the L\u00e9vy metric is a metric on the space of cumulative distribution functions of one-dimensional random variables. It is a special case of the L\u00e9vy\u2013Prokhorov metric, and is named after the French mathematician Paul L\u00e9vy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For each ordinal \u03b1 {\\displaystyle \\alpha } , \u2135 \u03b1 + 1 {\\displaystyle \\aleph _{\\alpha +1}} is the least cardinal number greater than \u2135 \u03b1 {\\displaystyle \\aleph _{\\alpha }} . The cardinality of the natural numbers is denoted aleph-null ( \u2135 0 {\\displaystyle \\aleph _{0}} ), while the cardinality of the real numbers is denoted by \" c {\\displaystyle {\\mathfrak {c}}} \" (a lowercase fraktur script \"c\"), and is also referred to as the cardinality of the continuum. Cantor showed, using the diagonal argument, that c > \u2135 0 {\\displaystyle {\\mathfrak {c}}>\\aleph _{0}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "fppf stands for fid\u00e8lement plate de pr\u00e9sentation finie, and in this topology, a morphism of affine schemes is a covering morphism if it is faithfully flat and of finite presentation. fpqc stands for fid\u00e8lement plate et quasi-compacte, and in this topology, a morphism of affine schemes is a covering morphism if it is faithfully flat. In both categories, a covering family is defined be a family which is a cover on Zariski open subsets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "passport, are by law one of the few primary documents for proving U.S. citizenship. These certificates are normally not carried on a day-to-day basis; instead, they are used to procure other documents, such as a passport or driver's license, which are then carried and used as a primary means of identification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a local language is a formal language for which membership of a word in the language can be determined by looking at the first and last symbol and each two-symbol substring of the word. Equivalently, it is a language recognised by a local automaton, a particular kind of deterministic finite automaton.Formally, a language L over an alphabet A is defined to be local if there are subsets R and S of A and a subset F of A\u00d7A such that a word w is in L if and only if the first letter of w is in R, the last letter of w is in S and no factor of length 2 in w is in F. This corresponds to the regular expression ( R A \u2217 \u2229 A \u2217 S ) \u2216 A \u2217 F A \u2217 . {\\displaystyle (RA^{*}\\cap A^{*}S)\\setminus A^{*}FA^{*}\\ .} More generally, a k-testable language L is one for which membership of a word w in L depends only on the prefix, suffix and the set of factors of w of length k; a language is locally testable if it is k-testable for some k. A local language is 2-testable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We merely abstain from both assumptions. . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to decouple the real-time operating system platform from the application software, ARINC 653 defines an API called APplication EXecutive (APEX). Each application software is called a partition and has its own memory space. It also has a dedicated time slot allocated by the APEX API. Within each partition, multitasking is allowed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, economics, and computer science, the lattice of stable matchings is a distributive lattice whose elements are stable matchings. For a given instance of the stable matching problem, this lattice provides an algebraic description of the family of all solutions to the problem. It was originally described in the 1970s by John Horton Conway and Donald Knuth.By Birkhoff's representation theorem, this lattice can be represented as the lower sets of an underlying partially ordered set. The elements of this set can be given a concrete structure as rotations, with cycle graphs describing the changes between adjacent stable matchings in the lattice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1847 Gabriel Lam\u00e9 announced a solution of Fermat's Last Theorem for all n > 2 {\\displaystyle n>2} ; that is, that the Fermat equation has no solutions in nonzero integers, but it turned out that his solution hinged on the assumption that the cyclotomic ring Z  {\\displaystyle \\mathbb {Z} } is a UFD. Ernst Kummer had shown three years before that this was not the case already for n = 23 {\\displaystyle n=23} (the full, finite list of values for which Z  {\\displaystyle \\mathbb {Z} } is a UFD is now known). At the same time, Kummer developed powerful new methods to prove Fermat's Last Theorem at least for a large class of prime exponents n {\\displaystyle n} using what we now recognize as the fact that the ring Z  {\\displaystyle \\mathbb {Z} } is a Dedekind domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In realtime scheduling algorithms for periodic jobs, an acceptance test is needed before accepting a sporadic job with a hard deadline. One of the simplest acceptance tests for a sporadic job is calculating the amount of slack time between the release time and deadline of the job.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, this naming scheme was quite temporary, lasting for a few years during the early 1980s.Although the 8086 was primarily developed for embedded systems and small multi-user or single-user computers, largely as a response to the successful 8080-compatible Zilog Z80, the x86 line soon grew in features and processing power. Today, x86 is ubiquitous in both stationary and portable personal computers, and is also used in midrange computers, workstations, servers, and most new supercomputer clusters of the TOP500 list. A large amount of software, including a large list of x86 operating systems are using x86-based hardware.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the STAR, new instructions essentially wrote the loops for the user. The user told the machine where in memory the list of numbers was stored, then fed in a single instruction a(1..1000000) = addv b(1..1000000), c(1..1000000). At first glance it appears the savings are limited; in this case the machine fetches and decodes only a single instruction instead of 1,000,000, thereby saving 1,000,000 fetches and decodes, perhaps one-fourth of the overall time. The real savings are not so obvious.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Property is in a person's presence when it is within the area of their immediate control. The property has to be close enough to the victim's person that the victim could have prevented its taking if he/she had not been placed in fear or intimidation.by force or threat of force \u2013 the use of force or threat of force is the defining element of robbery. For there to be robbery there must be \"force or fear\" in perpetrating the theft.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some of these databases may be shared among several companies, each paying every time a name is \"extracted\". It is for this reason that mobile telephone callers may appear as \"WIRELESS CALLER\", or the central office location of the number. If the call originates on a POTS line (a standard loop-start line), then caller ID is provided by the service provider's local switch.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The application of biotechnology to basic science (for example through the Human Genome Project) has also dramatically improved our understanding of biology and as our scientific knowledge of normal and disease biology has increased, our ability to develop new medicines to treat previously untreatable diseases has increased as well.Genetic testing allows the genetic diagnosis of vulnerabilities to inherited diseases, and can also be used to determine a child's parentage (genetic mother and father) or in general a person's ancestry. In addition to studying chromosomes to the level of individual genes, genetic testing in a broader sense includes biochemical tests for the possible presence of genetic diseases, or mutant forms of genes associated with increased risk of developing genetic disorders. Genetic testing identifies changes in chromosomes, genes, or proteins.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 19th century it became a common technique to gain insight into integer solutions of polynomial equations using rings of algebraic numbers of higher degree. For instance, fix a positive integer m {\\displaystyle m} . In the attempt to determine which integers are represented by the quadratic form x 2 + m y 2 {\\displaystyle x^{2}+my^{2}} , it is natural to factor the quadratic form into ( x + \u2212 m y ) ( x \u2212 \u2212 m y ) {\\displaystyle (x+{\\sqrt {-m}}y)(x-{\\sqrt {-m}}y)} , the factorization taking place in the ring of integers of the quadratic field Q ( \u2212 m ) {\\displaystyle \\mathbb {Q} ({\\sqrt {-m}})} . Similarly, for a positive integer n {\\displaystyle n} the polynomial z n \u2212 y n {\\displaystyle z^{n}-y^{n}} (which is relevant for solving the Fermat equation x n + y n = z n {\\displaystyle x^{n}+y^{n}=z^{n}} ) can be factored over the ring Z  {\\displaystyle \\mathbb {Z} } , where \u03b6 n {\\displaystyle \\zeta _{n}} is a primitive n-th root of unity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series \u2211 n = 1 \u221e a n {\\displaystyle \\sum _{n=1}^{\\infty }a_{n}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "in the interpretation above, the only partition of { 1 , 2 , 3 } {\\textstyle \\{1,2,3\\}} into 1 set can have its set ordered in 6 ways: L ( 3 , 2 ) {\\textstyle L(3,2)} is equal to 6, because there are six partitions of { 1 , 2 , 3 } {\\textstyle \\{1,2,3\\}} into two ordered parts: L ( n , n ) {\\textstyle L(n,n)} is always 1 because the only way to partition { 1 , 2 , \u2026 , n } {\\textstyle \\{1,2,\\ldots ,n\\}} into n {\\displaystyle n} non-empty subsets results in subsets of size 1, that can only be permuted in one way. In the more recent literature, Karamata\u2013Knuth style notation has taken over. Lah numbers are now often written as", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The intuitive meaning of a stack is that it is a fibred category such that \"all possible gluings work\". The specification of gluings requires a definition of coverings with regard to which the gluings can be considered. It turns out that the general language for describing these coverings is that of a Grothendieck topology. Thus a stack is formally given as a fibred category over another base category, where the base has a Grothendieck topology and where the fibred category satisfies a few axioms that ensure existence and uniqueness of certain gluings with respect to the Grothendieck topology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is a sharper bound than the first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, when applied to sums the Chernoff bound requires the random variables to be independent, a condition that is not required by either Markov's inequality or Chebyshev's inequality (although Chebyshev's inequality does require the random variables to be pairwise independent). The Chernoff bound is related to the Bernstein inequalities. It is also used to prove Hoeffding's inequality, Bennett's inequality, and McDiarmid's inequality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This language became quite popular in the early 1980s, and thus may also have been instrumental in spreading the style outside PARC. Upper camel case (or \"Pascal case\") is used in Wolfram Language in computer algebraic system Mathematica for predefined identifiers. User defined identifiers should start with a lower case letter. This avoids the conflict between predefined and user defined identifiers both today and in all future versions. C# variable names are recommended to follow the lower camel case convention.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Properties of time-aggregated network snapshots are able to be studied in terms of F ( x ) {\\displaystyle F(x)} . For example, since each node j {\\displaystyle j} after T {\\displaystyle T} timesteps will have on average m \u03b7 x i T {\\displaystyle m\\eta x_{i}T} outgoing links, the degree distribution after T {\\displaystyle T} timesteps in the time-aggregated network will be related to the activity-potential distribution by P T ( k ) \u221d F ( k m \u03b7 T ) . {\\displaystyle P_{T}(k)\\propto F\\left({\\frac {k}{m\\eta T}}\\right).} Spreading behavior according to the SIS epidemic model was investigated on activity-driven networks, and the following condition was derived for large-scale outbreaks to be possible: \u03b2 \u03bb > 2 \u27e8 a \u27e9 \u27e8 a \u27e9 + \u27e8 a 2 \u27e9 , {\\displaystyle {\\frac {\\beta }{\\lambda }}>{\\frac {2\\langle a\\rangle }{\\langle a\\rangle +{\\sqrt {\\langle a^{2}\\rangle }}}},} where \u03b2 {\\displaystyle \\beta } is the per-contact transmission probability, \u03bb {\\displaystyle \\lambda } is the per-timestep recovery probability, and ( \u27e8 a \u27e9 {\\displaystyle \\langle a\\rangle } , \u27e8 a 2 \u27e9 {\\displaystyle \\langle a^{2}\\rangle } ) are the first and second moments of the random activity-rate a j {\\displaystyle a_{j}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 17th century Conrad Henfling writing to Leibniz about music theory and the tuning of musical instruments makes use of the Euclidean algorithm in his reasoning.Viggo Brun investigated the use of Euclidean Algorithm in terms of constructing scales up to 4 different size intervals. Erv Wilson explored both using ratios andscale steps of which Kraig Grady applied torhythms within long meters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, it would be possible to inflate the number of bytes in an encoding by padding the code point with leading 0s. To encode the euro sign \u20ac from the above example in four bytes instead of three, it could be padded with leading 0s until it was 21 bits long \u2013 000 000010 000010 101100, and encoded as 11110000 10000010 10000010 10101100 (or F0 82 82 AC in hexadecimal). This is called an overlong encoding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "His device was the foundation for further developments in analog computing.The differential analyser, a mechanical analog computer designed to solve differential equations by integration using wheel-and-disc mechanisms, was conceptualized in 1876 by James Thomson, the brother of the more famous Lord Kelvin. He explored the possible construction of such calculators, but was stymied by the limited output torque of the ball-and-disk integrators. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In anti addition, two substituents are added to opposite sides (or faces) of a double bond or triple bond, once again resulting in a decrease in bond order and increase in number of substituents. The classical example of this is bromination (any halogenation) of alkenes. An anti addition reaction results in a trans-isomer of the products, as the substituents are on opposite faces of the bond.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to achieve the required amount of 'testing volume' needed to validate real-world testing, three points must be considered: System accuracy Federal and/or state health and safety guidelines and/or standards Economic viability based on the first two points.Once a particular portable emissions system has been identified and pronounced as accurate, the next step is to ensure that the worker(s) are properly protected from work hazards associated with the task(s) being performed in the use of the testing equipment. For example, typical functions for a worker may be to transport the equipment to the jobsite (i.e. car, truck, train, or plane), carry the equipment to the jobsite, and lift the equipment into position.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some literature articles, the terms \"mechanism of action\" and \"mode of action\" are used interchangeably, typically referring to the way in which the drug interacts and produces a medical effect. However, in actuality, a mode of action describes functional or anatomical changes, at the cellular level, resulting from the exposure of a living organism to a substance. This differs from a mechanism of action since it is a more specific term that focuses on the interaction between the drug itself and an enzyme or receptor and its particular form of interaction, whether through inhibition, activation, agonism, or antagonism. Furthermore, the term \"mechanism of action\" is the main term that is primarily used in pharmacology, whereas \"mode of action\" will more often appear in the field of microbiology or certain aspects of biology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most computer programming languages, a while loop is a control flow statement that allows code to be executed repeatedly based on a given Boolean condition. The while loop can be thought of as a repeating if statement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, combinatorial data analysis (CDA) is the study of data sets where the order in which objects are arranged is important. CDA can be used either to determine how well a given combinatorial construct reflects the observed data, or to search for a suitable combinatorial construct that does fit the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some situations, the set of edges that are required is different from the edges in the graph. This is modeled by the Rural Postman Problem (RPP), where the required edges are a subset of the system of edges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a bipartite matroid is a matroid all of whose circuits have even size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1950, Waldo Tobler published a paper titled \"Automation and Cartography\" that established the first use case for computers as aids in cartography. In this paper, Tobler established what he referred to as a \"map in\u2013map out\" (MIMO) system, which facilitated digitization of traditional maps, changing them, and reproducing them. The MIMO system, while simple, established the use of computers for map making in the literature and set the stage for more advanced Geographic information systems in later years by geographers such as Roger Tomlinson.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is typically done with polynomial or rational (ratio of polynomials) approximations. The objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's floating point arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function. Narrowing the domain can often be done through the use of various addition or scaling formulas for the function being approximated. Modern mathematical libraries often reduce the domain into many tiny segments and use a low-degree polynomial for each segment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A learning process that involves a method of reward and punishment must be in place that will select desirable patterns in the mind. This whole process, Turing mentions, to a large extent is similar to that of evolution by natural selection where the similarities are: Structure of the child machine = hereditary material Changes of the child machine = mutations Natural selection = judgment of the experimenterFollowing this discussion Turing addresses certain specific aspects of the learning machine: Nature of inherent complexity: The child machine could either be one that is as simple as possible, merely maintaining consistency with general principles, or the machine could be one with a complete system of logical inference programmed into it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence the result by Cole and Vishkin raised the question of whether there is a constant-time distributed algorithm for 3-coloring an n-cycle. Linial (1992) showed that this is not possible: any deterministic distributed algorithm requires \u03a9(log* n) communication steps to reduce an n-coloring to a 3-coloring in an n-cycle. The technique by Cole and Vishkin can be applied in arbitrary bounded-degree graphs as well; the running time is poly(\u0394) + O(log* n).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable.It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the data), in which case it may be known as mean square deviation. When the reference value is the assumed true value, the result is known as mean squared error. A typical estimate for the sample variance from a set of sample values x i {\\displaystyle x_{i}} uses a divisor of the number of values minus one, n-1, rather than n as in a simple quadratic mean, and this is still called the \"mean square\" (e.g. in analysis of variance): s 2 = 1 n \u2212 1 \u2211 ( x i \u2212 x \u00af ) 2 {\\displaystyle s^{2}=\\textstyle {\\frac {1}{n-1}}\\sum (x_{i}-{\\bar {x}})^{2}} The second moment of a random variable, E ( X 2 ) {\\displaystyle E(X^{2})} is also called the mean square. The square root of a mean square is known as the root mean square (RMS or rms), and can be used as an estimate of the standard deviation of a random variable. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Besicovitch inequality asserts that The inequality can be generalized in the following way. Given an n-dimensional Riemannian manifold M with connected boundary and a smooth map f: M \u2192  n {\\displaystyle f:M\\rightarrow ^{n}} , such that the restriction of f to the boundary of M is a degree 1 map onto \u2202  n {\\displaystyle \\partial ^{n}} , define Then \u220f i d i \u2265 V o l ( M ) {\\displaystyle \\prod _{i}d_{i}\\geq Vol(M)} . The Besicovitch inequality was used to prove systolic inequalities on surfaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order theory a better-quasi-ordering or bqo is a quasi-ordering that does not admit a certain type of bad array. Every better-quasi-ordering is a well-quasi-ordering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The chromatic polynomial, a polynomial whose values at integer arguments give the number of colorings of the graph with that many colors. The dichromatic polynomial, a 2-variable generalization of the chromatic polynomial The flow polynomial, a polynomial whose values at integer arguments give the number of nowhere-zero flows with integer flow amounts modulo the argument. The (inverse of the) Ihara zeta function, defined as a product of binomial terms corresponding to certain closed walks in a graph. The Martin polynomial, used by Pierre Martin to study Euler tours The matching polynomials, several different polynomials defined as the generating function of the matchings of a graph. The reliability polynomial, a polynomial that describes the probability of remaining connected after independent edge failures The Tutte polynomial, a polynomial in two variables that can be defined (after a small change of variables) as the generating function of the numbers of connected components of induced subgraphs of the given graph, parameterized by the number of vertices in the subgraph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. Polynomial factorization is one of the fundamental components of computer algebra systems. The first polynomial factorization algorithm was published by Theodor von Schubert in 1793. Leopold Kronecker rediscovered Schubert's algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Individual U.S. states set their own policies for state and local government employees (i.e. public sector employees).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In molecular biology, a batch effect occurs when non-biological factors in an experiment cause changes in the data produced by the experiment. Such effects can lead to inaccurate conclusions when their causes are correlated with one or more outcomes of interest in an experiment. They are common in many types of high-throughput sequencing experiments, including those using microarrays, mass spectrometers, and single-cell RNA-sequencing data. They are most commonly discussed in the context of genomics and high-throughput sequencing research, but they exist in other fields of science as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Bertrand's postulate is a theorem stating that for any integer n > 3 {\\displaystyle n>3} , there always exists at least one prime number p {\\displaystyle p} with n < p < 2 n \u2212 2. {\\displaystyle n 1 {\\displaystyle n>1} , there is always at least one prime p {\\displaystyle p} such that n < p < 2 n . {\\displaystyle n", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Laws issue out a command to their constituents which can be realized as an action. When forming a legal contract, speech acts can be made when people are making or accepting an offer. Considering the theory of freedom of speech, some speech acts may not be legally protected. For example, a death threat is a type of speech act and is considered to exist outside of the protection of freedom of speech as it is treated as a criminal act.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially linear algebra, an M-matrix is a Z-matrix with eigenvalues whose real parts are nonnegative. The set of non-singular M-matrices are a subset of the class of P-matrices, and also of the class of inverse-positive matrices (i.e. matrices with inverses belonging to the class of positive matrices). The name M-matrix was seemingly originally chosen by Alexander Ostrowski in reference to Hermann Minkowski, who proved that if a Z-matrix has all of its row sums positive, then the determinant of that matrix is positive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since functional programming languages, by definition, support function literals, which can also be stored in records, records types with subtyping provide some of the features of object-oriented programming. Typically, functional programming languages also provide some, usually restricted, form of parametric polymorphism. In a theoretical setting, it is desirable to study the interaction of the two features; a common theoretical setting is system F<:.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As well as log2, an alternative notation for the binary logarithm is lb (the notation preferred by ISO 31-11 and ISO 80000-2). Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in information theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years commercial ADNs have begun to include application firewall functionality to further secure applications during the delivery process. This is a hotly debated subject with many security professionals arguing that the functionality included in an application firewall are unnecessary and should be handled by the application while others consider employing as much security as possible, regardless of position in the delivery network, to be the best practice. Many commercial ADN companies have acquired and integrated these functions and present such features as part of a defense in depth strategy often cited by security professionals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Ranked set sampling uses a two-phase sampling design that identifies sets of field locations, utilizes inexpensive measurements to rank locations within each set, and then selects one location from each set for sampling. In ranked set sampling, m sets (each of size r) of field locations are identified using simple random sampling. The locations are ranked independently within each set using professional judgment or inexpensive, fast, or surrogate measurements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables). For example, assume there are three random variables x 1 , x 2 , x 3 {\\displaystyle x_{1},x_{2},x_{3}} where each has K {\\displaystyle K} states. Then, the conditional probability table of x 1 {\\displaystyle x_{1}} provides the conditional probability values P ( x 1 = a k \u2223 x 2 , x 3 ) {\\displaystyle P(x_{1}=a_{k}\\mid x_{2},x_{3})} \u2013 where the vertical bar | {\\displaystyle |} means \u201cgiven the values of\u201d \u2013 for each of the K possible values a k {\\displaystyle a_{k}} of the variable x 1 {\\displaystyle x_{1}} and for each possible combination of values of x 2 , x 3 . {\\displaystyle x_{2},\\,x_{3}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to get a grasp on the motivations which inspired the development of the idea of coordinative definitions, it is important to understand the doctrine of formalism as it is conceived in the philosophy of mathematics. For the formalists, mathematics, and particularly geometry, is divided into two parts: the pure and the applied. The first part consists in an uninterpreted axiomatic system, or syntactic calculus, in which terms such as point, straight line and between (the so-called primitive terms) have their meanings assigned to them implicitly by the axioms in which they appear. On the basis of deductive rules eternally specified in advance, pure geometry provides a set of theorems derived in a purely logical manner from the axioms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to design a form or document, the writer should understand and evaluate the different constraints in the rhetorical situation; this is called functional analysis. One of the biggest components in analyzing a form or document is to determine the communicative purpose of the form or document. Leo Lentz and Henk Pander Maat, at the University of Utrecht, break down communicative purpose into four elements: intended communicative effect: the intended effect should fall into one of three categories; \"a cognitive change in the mental state of the reader, who learns something or forms a particular attitude, a change in the reader's behavior, such as handling a machine or buying a product, or a change in the social reality as a result of the collective behavior of readers, such as the sale of a product\". topic: this is based on the reader's needs, since the reader is the one expected to act on the information. target group: this should be a specific group described either by demographic variables or communicative predispositions. organizational goal: this is the change that should occur in every individual reader.After analyzing the communicative purpose, the technical communicator can design a form or document that will match the requirements and meet expectations for it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When programming in machine code, assembly language, and certain other programming languages, programmers work with the low-level digital structure of the data registers. These registers operate on voltages, where zero volts represents Boolean 0, and a reference voltage (often +5 V, +3.3 V, +1.8 V) represents Boolean 1. Such languages support both numeric operations and logical operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural resources management and environmental policy more generally, demand management refers to policies to control consumer demand for environmentally sensitive or harmful goods such as water and energy. Within manufacturing firms the term is used to describe the activities of demand forecasting, planning, and order fulfillment. In the environmental context demand management is increasingly taken seriously to reduce the economy's throughput of scarce resources for which market pricing does not reflect true costs. Examples include metering of municipal water, and carbon taxes on gasoline.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group). The study of modular invariants was originated in about 1914 by Dickson (2004).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Testing and the overall quality process remain problematic for several key reasons. Traditional testing processes are too slow.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, there are other number systems that are not accurately described by these axioms; in particular, the theory defined in the same way for integers instead of real numbers is undecidable, even for existential sentences (Diophantine equations) by Matiyasevich's theorem.The existential theory of the reals is the fragment of the first-order theory consisting of sentences in which all the quantifiers are existential and they appear before any of the other symbols. That is, it is the set of all true sentences of the form where F ( X 1 , \u2026 X n ) {\\displaystyle F(X_{1},\\dots X_{n})} is a quantifier-free formula involving equalities and inequalities of real polynomials. The decision problem for the existential theory of the reals is the algorithmic problem of testing whether a given sentence belongs to this theory; equivalently, for strings that pass the basic syntactical checks (they use the correct symbols with the correct syntax, and have no unquantified variables) it is the problem of testing whether the sentence is a true statement about the real numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Standard Model of particle physics, the Cabibbo\u2013Kobayashi\u2013Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix which contains information on the strength of the flavour-changing weak interaction. Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. It is important in the understanding of CP violation. This matrix was introduced for three generations of quarks by Makoto Kobayashi and Toshihide Maskawa, adding one generation to the matrix previously introduced by Nicola Cabibbo. This matrix is also an extension of the GIM mechanism, which only includes two of the three current families of quarks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the coclass of a finite p-group of order pn is n \u2212 c, where c is the class.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of sensor net, public-key based access control (PKC) may be a good solution in the future to cover some issues in wireless access control. For sensor net, the danger from attackers includes; impersonation which grants access to malicious users, replay attack where the adversary captures sensitive information by replaying it, interleaving which selectively combines messages from previous sessions, reflection where an adversary sends an identical message to the originator similar to impersonation, forced delay which blocks communication message to be sent at a later time, and chosen-text attack where the attacker tries to extract the keys to access the sensor. The solution to this may be public key-based cryptography as a study done by Haodong Wang shows that PKC-based protocol presented is better than the traditional symmetric key in regards to memory usage, message complexity, and security resilience.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of centralized linear-quadratic control, with additive uncertainty in the equation of evolution but no uncertainty about coefficient values in that equation, the optimal solution for the control variables taking into account the uncertainty is the same as the solution ignoring uncertainty. This property, which gives a zero expected value of including uncertainty, is called certainty equivalence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "]_{f}} or  ] o \u2208  ] f {\\displaystyle \\! ]_{o}\\in \\! ]_{f}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Category has the value noun phrase whereas the value of agreement is indicated by another feature structure with the features number and person being singular and third. This particular notation is called attribute value matrix (AVM). The matrix has two columns, one for the feature names and the other for the values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The CARP can be solved with combinatorial optimization including convex hulls. The large-scale capacitated arc routing problem (LSCARP) is a variant of the capacitated arc routing problem that applies to hundreds of edges and nodes to realistically simulate and model large complex environments. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to reduce the reliance on legal professionals and the amount of time needed, efforts have been made to create a system to automatically classify legal text and queries. Adequate translation of both would allow accurate information retrieval without the high cost of human classification. These automatic systems generally employ Natural Language Processing (NLP) techniques that are adapted to the legal domain, and also require the creation of a legal ontology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in abstract algebra, power associativity is a property of a binary operation that is a weak form of associativity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The user can direct dial from their handset if the network they are roaming in supports CAMEL (Customized Applications for Mobile networks Enhanced Logic). This allows real time billing by the home operator without having to dial the customer back. The advantage is that it is more natural and works seamlessly. The disadvantage is that not all networks support CAMEL so the list of countries where a prepaid customer can use their phone abroad is smaller than for postpaid mobile phones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems architecture a reference monitor concept defines a set of design requirements on a reference validation mechanism, which enforces an access control policy over subjects' (e.g., processes and users) ability to perform operations (e.g., read and write) on objects (e.g., files and sockets) on a system. The properties of a reference monitor are captured by the acronym NEAT, which means: The reference validation mechanism must be Non-bypassable, so that an attacker cannot bypass the mechanism and violate the security policy. The reference validation mechanism must be Evaluable, i.e., amenable to analysis and tests, the completeness of which can be assured (verifiable). Without this property, the mechanism might be flawed in such a way that the security policy is not enforced.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a test case is a specification of the inputs, execution conditions, testing procedure, and expected results that define a single test to be executed to achieve a particular software testing objective, such as to exercise a particular program path or to verify compliance with a specific requirement. Test cases underlie testing that is methodical rather than haphazard. A battery of test cases can be built to produce the desired coverage of the software being tested. Formally defined test cases allow the same tests to be run repeatedly against successive versions of the software, allowing for effective and consistent regression testing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, r = 1 2 {\\displaystyle r={\\frac {1}{2}}} , so b = b 1 / 2 {\\displaystyle {\\sqrt {b}}=b^{1/2}} . The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices. Exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public-key cryptography.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first pass, the forward\u2013backward algorithm computes a set of forward probabilities which provide, for all t \u2208 { 1 , \u2026 , T } {\\displaystyle t\\in \\{1,\\dots ,T\\}} , the probability of ending up in any particular state given the first t {\\displaystyle t} observations in the sequence, i.e. P ( X t | o 1: t ) {\\displaystyle P(X_{t}\\ |\\ o_{1:t})} . In the second pass, the algorithm computes a set of backward probabilities which provide the probability of observing the remaining observations given any starting point t {\\displaystyle t} , i.e. P ( o t + 1: T | X t ) {\\displaystyle P(o_{t+1:T}\\ |\\ X_{t})} . These two sets of probability distributions can then be combined to obtain the distribution over states at any specific point in time given the entire observation sequence: P ( X t | o 1: T ) = P ( X t | o 1: t , o t + 1: T ) \u221d P ( o t + 1: T | X t ) P ( X t | o 1: t ) {\\displaystyle P(X_{t}\\ |\\ o_{1:T})=P(X_{t}\\ |\\ o_{1:t},o_{t+1:T})\\propto P(o_{t+1:T}\\ |\\ X_{t})P(X_{t}|o_{1:t})} The last step follows from an application of the Bayes' rule and the conditional independence of o t + 1: T {\\displaystyle o_{t+1:T}} and o 1: t {\\displaystyle o_{1:t}} given X t {\\displaystyle X_{t}} . As outlined above, the algorithm involves three steps: computing forward probabilities computing backward probabilities computing smoothed values.The forward and backward steps may also be called \"forward message pass\" and \"backward message pass\" - these terms are due to the message-passing used in general belief propagation approaches.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\Omega .} Define u ( h , k ) = f ( a + h , b + k ) \u2212 f ( a + h , b ) , v ( h , k ) = f ( a + h , b + k ) \u2212 f ( a , b + k ) , w ( h , k ) = f ( a + h , b + k ) \u2212 f ( a + h , b ) \u2212 f ( a , b + k ) + f ( a , b ) . {\\displaystyle {\\begin{aligned}u\\left(h,\\,k\\right)&=f\\left(a+h,\\,b+k\\right)-f\\left(a+h,\\,b\\right),\\\\v\\left(h,\\,k\\right)&=f\\left(a+h,\\,b+k\\right)-f\\left(a,\\,b+k\\right),\\\\w\\left(h,\\,k\\right)&=f\\left(a+h,\\,b+k\\right)-f\\left(a+h,\\,b\\right)-f\\left(a,\\,b+k\\right)+f\\left(a,\\,b\\right).\\end{aligned}}} These functions are defined for | h | , | k | < \u03b5 {\\displaystyle \\left|h\\right|,\\,\\left|k\\right|<\\varepsilon } , where \u03b5 > 0 {\\displaystyle \\varepsilon >0} and  \u00d7  {\\displaystyle \\left\\times \\left} is contained in \u03a9 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems engineering, the system usability scale (SUS) is a simple, ten-item attitude Likert scale giving a global view of subjective assessments of usability. It was developed by John Brooke at Digital Equipment Corporation in the UK in 1986 as a tool to be used in usability engineering of electronic office systems. The usability of a system, as defined by the ISO standard ISO 9241 Part 11, can be measured only by taking into account the context of use of the system\u2014i.e., who is using the system, what they are using it for, and the environment in which they are using it. Furthermore, measurements of usability have several different aspects: effectiveness (can users successfully achieve their objectives) efficiency (how much effort and resource is expended in achieving those objectives) satisfaction (was the experience satisfactory)Measures of effectiveness and efficiency are also context specific.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Different websites and systems have different algorithms, but one approach, used by Amazon (company) for its online store, is to indicate to a user: \"customers who bought x also bought y\" (affinity analysis, collaborative filtering). This example is oriented around online purchasing behaviour, but an algorithm could also be programmed to provide suggestions based on other factors (e.g., searching, viewing, etc.).Discoverability is typically referred to in connection with search engines. A highly \"discoverable\" piece of content would appear at the top, or near the top of a user's search results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The latter are referred to as vector magnetographs. These measurements are made by exploiting the Zeeman effect or, less frequently, the Hanle effect.The first magnetograph was constructed by George Ellery Hale in 1908. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is called the Harvard architecture after the Harvard Mark I computer. Modern von Neumann computers display some traits of the Harvard architecture in their designs, such as in CPU caches.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, for positive integers k and s, a vectorial addition chain is a sequence V of k-dimensional vectors of nonnegative integers vi for \u2212k + 1 \u2264 i \u2264 s together with a sequence w, such that v\u2212k+1 =  v\u2212k+2 =  \u22ee \u22ee v0 = vi =vj+vr for all 1\u2264i\u2264s with -k+1\u2264j, r\u2264i-1 vs =  w = (w1,...ws), wi=(j,r).For example, a vectorial addition chain for  is V=(,,,,,,,,,,,) w=((-2,-1),(1,1),(2,2),(-2,3),(4,4),(1,5),(0,6),(7,7),(0,8))Vectorial addition chains are well suited to perform multi-exponentiation: Input: Elements x0,...,xk-1 of an abelian group G and a vectorial addition chain of dimension k computing  Output:The element x0n0...xk-1nr-1for i =-k+1 to 0 do yi \u2192 xi+k-1 for i = 1 to s do yi \u2192yj\u00d7yr return ys", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. \"a measured value was 0.01023 \u00b0C with an uncertainty of 70 \u03bcK\". This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin. Notwithstanding the official endorsement provided by decision no. 3 of Resolution 3 of the 13th CGPM, which stated \"a temperature interval may also be expressed in degrees Celsius\", the practice of simultaneously using both \u00b0C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as \"\u03bc\u00b0C\" or \"microdegrees Celsius\") to express a temperature interval has not been well adopted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. An example is the sequence of primes (3, 7, 11), which is given by a n = 3 + 4 n {\\displaystyle a_{n}=3+4n} for 0 \u2264 n \u2264 2 {\\displaystyle 0\\leq n\\leq 2} . According to the Green\u2013Tao theorem, there exist arbitrarily long sequences of primes in arithmetic progression. Sometimes the phrase may also be used about primes which belong to an arithmetic progression which also contains composite numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A CCS (centacall-second) is often used to describe 100 call-seconds, so 3600 call-seconds = 36 CCS = 1 call-hour. In a communication network, a trunk (link) can carry numerous concurrent calls by means of multiplexing. Hence a particular number of call-seconds can be carried in infinitely many ways as calls are established and cleared over time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a formal theory is a set of sentences within a formal language. A sentence is a well-formed formula with no free variables. A sentence that is a member of a theory is one of its theorems, and the theory is the set of its theorems. Usually a theory is understood to be closed under the relation of logical consequence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing via Student's t-test. The t-statistic is used in a t-test to determine whether to support or reject the null hypothesis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt G\u00f6del to provide a consistency proof of arithmetic. The name of the interpretation comes from the journal Dialectica, where G\u00f6del's paper was published in a 1958 special issue dedicated to Paul Bernays on his 70th birthday.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The two measures are complementary in sense that if one knows the mid-range and the range, one can find the sample maximum and minimum values. The mid-range is rarely used in practical statistical analysis, as it lacks efficiency as an estimator for most distributions of interest, because it ignores all intermediate points, and lacks robustness, as outliers change it significantly. Indeed, for many distributions it is one of the least efficient and least robust statistics. However, it finds some use in special cases: it is the maximally efficient estimator for the center of a uniform distribution, trimmed mid-ranges address robustness, and as an L-estimator, it is simple to understand and compute.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociology, a social system is the patterned network of relationships constituting a coherent whole that exist between individuals, groups, and institutions. It is the formal structure of role and status that can form in a small, stable group. An individual may belong to multiple social systems at once; examples of social systems include nuclear family units, communities, cities, nations, college campuses, religions, corporations, and industries. The organization and definition of groups within a social system depend on various shared properties such as location, socioeconomic status, race, religion, societal function, or other distinguishable features.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in the category of rings. Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings. For example, the Chinese remainder theorem may be stated as: if m and n are coprime integers, the quotient ring Z / m n Z {\\displaystyle \\mathbb {Z} /mn\\mathbb {Z} } is the product of Z / m Z {\\displaystyle \\mathbb {Z} /m\\mathbb {Z} } and Z / n Z . {\\displaystyle \\mathbb {Z} /n\\mathbb {Z} .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points. Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently which, along with their relative ease of implementation, has led to the widespread use of FDM in modern numerical analysis. Today, FDM are one of the most common approaches to the numerical solution of PDE, along with finite element methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In that work: \"A viewpoint can be thought of as a combination of the idea of an \u201cactor\u201d, \u201cknowledge source\u201d, \u201crole\u201d or \u201cagent\u201d in the development process and the idea of a \u201cview\u201d or \u201cperspective\u201d which an actor maintains.\" An important idea in this paper was to distinguish \"a representation style, the scheme and notation by which the viewpoint expresses what it can see\" and \"a specification, the statements expressed in the viewpoint's style describing particular domains\". Subsequent work, such as IEEE 1471, preserved this distinction by utilizing two separate terms: viewpoint and view, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "337). We have R+ = R if, and only if, R itself is transitive. Conversely, transitive reduction adduces a minimal relation S from a given relation R such that they have the same closure, that is, S+ = R+; however, many different S with this property may exist. Both transitive closure and transitive reduction are also used in the closely related area of graph theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, particularly with noun and adjective phrases, it is not always clear which dependents are to be classed as complements, and which as adjuncts. Although in principle the head-directionality parameter concerns the order of heads and complements only, considerations of head-initiality and head-finality sometimes take account of the position of the head in the phrase as a whole, including adjuncts. The structure of the various types of phrase is analyzed below in relation to specific languages, with a focus on the ordering of head and complement. In some cases (such as English and Japanese) this ordering is found to be the same in practically all types of phrase, whereas in others (such as German and Gbe) the pattern is less consistent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again continuous, and the identity function is continuous. The study of Top and of properties of topological spaces using the techniques of category theory is known as categorical topology. N.B. Some authors use the name Top for the categories with topological manifolds, with compactly generated spaces as objects and continuous maps as morphisms or with the category of compactly generated weak Hausdorff spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples of this are the iAPX 432 (a project originally named the Intel 8800), the Intel 960, Intel 860 and the Intel/Hewlett-Packard Itanium architecture. However, the continuous refinement of x86 microarchitectures, circuitry and semiconductor manufacturing would make it hard to replace x86 in many segments. AMD's 64-bit extension of x86 (which Intel eventually responded to with a compatible design) and the scalability of x86 chips in the form of modern multi-core CPUs, is underlining x86 as an example of how continuous refinement of established industry standards can resist the competition from completely new architectures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The information integration of heterogeneous data sources in traditional database is intricate, which requires the redesign of the database table such as changing the structure and/or addition of new data. In the case of semantic query, SPARQL query reflects the relationships between entities in a way that aligned with human's understanding of the domain, so the semantic intention of the query can be seen on the query itself. Unlike SPARQL, SQL query, which reflects the specific structure of the database and derived from matching the relevant primary and foreign keys of tables, loses the semantics of the query by missing the relationships between entities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In speech, common combinations of conjugation and auxiliary verbs are contracted in a fairly regular manner. There are occasional others, such as -aranai \u2192 -annai as in wakaranai (\u5206\u304b\u3089\u306a\u3044, don't understand) \u2192 wakannai (\u5206\u304b\u3093\u306a\u3044) and tsumaranai (\u3064\u307e\u3089\u306a\u3044, boring) \u2192 tsumannai (\u3064\u307e\u3093\u306a\u3044) \u2013 these are considered quite casual and are more common among the younger generation.Contractions differ by dialect, but behave similarly to the standard ones given above. For example, in the Kansai dialect, -te shimau (\u301c\u3066\u3057\u307e\u3046) \u2192 -temau (\u301c\u3066\u307e\u3046).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All direct neighbors of s are visited in the first step, which form the next frontier. After each layer-traversal, the \"next frontier\" is switched to the frontier and new vertices will be stored in the new next frontier. The following pseudo-code outlines the idea of it, in which the data structures for the frontier and next frontier are called FS and NS respectively. 1 define bfs_sequential(graph(V,E), source s): 2 for all v in V do 3 d = -1; 4 d = 0; level = 1; FS = {}; NS = {}; 5 push(s, FS); 6 while FS !empty do 7 for u in FS do 8 for each neighbour v of u do 9 if d = -1 then 10 push(v, NS); 11 d = level; 12 FS = NS, NS = {}, level = level + 1;", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. The term is also interchangeable with the geographically weighted Principal components analysis in geophysics.The i th basis function is chosen to be orthogonal to the basis functions from the first through i \u2212 1, and to minimize the residual variance. That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible. The method of EOF analysis is similar in spirit to harmonic analysis, but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A strategic minority could overpower an honest majority. This problem can be minimized through education or ballot design to encourage uninformed voters to give more-extreme rankings. A different path to minimize this problem is to use median scores instead of total scores, as median scores are less amenable to exaggeration, as in majority judgment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle V^{-}.} We denote with \u03b4 ( V + ) {\\displaystyle \\delta (V^{+})} the set of edges that connect the two sets. We can then rewrite the Hamiltonian as H  = \u2212 \u2211 i j \u2208 E ( V + ) J i j \u2212 \u2211 i j \u2208 E ( V \u2212 ) J i j + \u2211 i j \u2208 \u03b4 ( V + ) J i j = \u2212 \u2211 i j \u2208 E ( G ) J i j + 2 \u2211 i j \u2208 \u03b4 ( V + ) J i j = C + 2 \u2211 i j \u2208 \u03b4 ( V + ) J i j {\\displaystyle {\\begin{aligned}H&=-\\sum _{ij\\in E(V^{+})}J_{ij}-\\sum _{ij\\in E(V^{-})}J_{ij}+\\sum _{ij\\in \\delta (V^{+})}J_{ij}\\\\&=-\\sum _{ij\\in E(G)}J_{ij}+2\\sum _{ij\\in \\delta (V^{+})}J_{ij}\\\\&=C+2\\sum _{ij\\in \\delta (V^{+})}J_{ij}\\end{aligned}}} Minimizing this energy is equivalent to the min-cut problem or by setting the graph weights as w i j = \u2212 J i j , {\\displaystyle w_{ij}=-J_{ij},} the max-cut problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "CHANGE-LABEL: It works exactly the same as CHANGE-EDGE.As a summary, we conclude that having n 1 {\\displaystyle n_{1}} calls to CREATE_NODE and n 2 {\\displaystyle n_{2}} calls to CHANGE_EDGE will result in the creation of 2 \u22c5 n 1 + n 2 {\\displaystyle 2\\cdot n_{1}+n_{2}} tables. Since each table has size O ( d ) {\\displaystyle O(d)} without taking into account the recursive calls, then filling in a table requires O ( d 2 ) {\\displaystyle O(d^{2})} where the additional d factor comes from updating the inedges at other nodes. Therefore the amount of work required to complete a sequence of operations is bounded by the number of tables created multiplied by O ( d 2 ) {\\displaystyle O(d^{2})} . Each access operation can be done in O ( L o g ( d ) ) {\\displaystyle O(Log(d))} and there are m {\\displaystyle m} edge and label operations, thus it requires m \u22c5 O ( L o g ( d ) ) {\\displaystyle m\\cdot O(Log(d))} . We conclude that There exists a data structure that can complete any n {\\displaystyle n} sequence of CREATE-NODE, CHANGE-EDGE and CHANGE-LABEL in O ( n \u22c5 d 2 ) + m \u22c5 O ( L o g ( d ) ) {\\displaystyle O(n\\cdot d^{2})+m\\cdot O(Log(d))} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an algebraic matroid is a matroid, a combinatorial structure, that expresses an abstraction of the relation of algebraic independence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order of net exports in 2011, 2009 and 2006 in thousand bbl/d and thousand m3/d: Source: US Energy Information Administration 1 peak production already passed in this state 2 Canadian statistics are complicated by the fact it is both an importer and exporter of crude oil, and refines large amounts of oil for the U.S. market. It is the leading source of U.S. imports of oil and products, averaging 2,500,000 bbl/d (400,000 m3/d) in August 2007. Total world production/consumption (as of 2005) is approximately 84 million barrels per day (13,400,000 m3/d).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The probability that at least one of the events will occur is equal to one. For example, there are theoretically only two possibilities for flipping a coin. Flipping a head and flipping a tail are collectively exhaustive events, and there is a probability of one of flipping either a head or a tail.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern poetry, Formalist poets may be considered as the opposite of writers of free verse. These are only labels, and rarely sum up matters satisfactorily. 'Formalism' in poetry represents an attachment to poetry that recognises and uses schemes of rhyme and rhythm to create poetic effects and to innovate. To distinguish it from archaic poetry the term 'neo-formalist' is sometimes used. See for example: The Formalist, a literary magazine (now defunct) for formalist poetry New Formalism, a movement within the poetry of the United States.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Muller\u2013Schupp theorem states that a finitely generated group G has context-free word problem if and only if G is virtually free. The theorem was proved by David Muller and Paul Schupp in 1983.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most dynamically-typed languages, the list of methods on an object can be altered at runtime. This requires late binding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formally, a relation R over a set X can be seen as a set of ordered pairs (x, y) of members of X. The relation R holds between x and y if (x, y) is a member of R. For example, the relation \"is less than\" on the natural numbers is an infinite set Rless of pairs of natural numbers that contains both (1,3) and (3,4), but neither (3,1) nor (4,4). The relation \"is a nontrivial divisor of\" on the set of one-digit natural numbers is sufficiently small to be shown here: Rdiv = { (2,4), (2,6), (2,8), (3,6), (3,9), (4,8) }; for example 2 is a nontrivial divisor of 8, but not vice versa, hence (2,8) \u2208 Rdiv, but (8,2) \u2209 Rdiv. If R is a relation that holds for x and y one often writes xRy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the abstract setting of oriented matroids, Bland's rule cycles on some examples. A restricted class of oriented matroids on which Bland's rule avoids cycling has been termed \"Bland oriented matroids\" by Jack Edmonds. Another pivoting rule, the criss-cross algorithm, avoids cycles on all oriented-matroid linear-programs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, G\u00f6del's \u03b2 function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The \u03b2 function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions. The \u03b2 function was introduced without the name in the proof of the first of G\u00f6del's incompleteness theorems (G\u00f6del 1931). The \u03b2 function lemma given below is an essential step of that proof. G\u00f6del gave the \u03b2 function its name in (G\u00f6del 1934).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such implausible equilibria might arise also in games with complete information, but they may be eliminated by applying subgame perfect Nash equilibrium. However, Bayesian games often contain non-singleton information sets and since subgames must contain complete information sets, sometimes there is only one subgame\u2014the entire game\u2014and so every Nash equilibrium is trivially subgame perfect. Even if a game does have more than one subgame, the inability of subgame perfection to cut through information sets can result in implausible equilibria not being eliminated. To summarize: in this variant of the gift game, there are two SPEs: either the sender always gives and the receiver always accepts, or the sender always does not give and the receiver always rejects. From these, only the first one is a PBE; the other is not a PBE since it cannot be supported by any belief-system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In effect, work stealing distributes the scheduling work over idle processors, and as long as all processors have work to do, no scheduling overhead occurs.Work stealing contrasts with work sharing, another popular scheduling approach for dynamic multithreading, where each work item is scheduled onto a processor when it is spawned. Compared to this approach, work stealing reduces the amount of process migration between processors, because no such migration occurs when all processors have work to do.The idea of work stealing goes back to the implementation of the Multilisp programming language and work on parallel functional programming languages in the 1980s. It is employed in the scheduler for the Cilk programming language, the Java fork/join framework, the .NET Task Parallel Library, and the Rust Tokio runtime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In morphometrics, landmark point or shortly landmark is a point in a shape object in which correspondences between and within the populations of the object are preserved. In other disciplines, landmarks may be known as vertices, anchor points, control points, sites, profile points, 'sampling' points, nodes, markers, fiducial markers, etc. Landmarks can be defined either manually by experts or automatically by a computer program. There are three basic types of landmarks: anatomical landmarks, mathematical landmarks or pseudo-landmarks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an analytic proof is a proof of a theorem in analysis that only makes use of methods from analysis, and which does not predominantly make use of algebraic or geometrical methods. The term was first used by Bernard Bolzano, who first provided a non-analytic proof of his intermediate value theorem and then, several years later provided a proof of the theorem that was free from intuitions concerning lines crossing each other at a point, and so he felt happy calling it analytic (Bolzano 1817). Bolzano's philosophical work encouraged a more abstract reading of when a demonstration could be regarded as analytic, where a proof is analytic if it does not go beyond its subject matter (Sebastik 2007). In proof theory, an analytic proof has come to mean a proof whose structure is simple in a special way, due to conditions on the kind of inferences that ensure none of them go beyond what is contained in the assumptions and what is demonstrated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of relational database design, normalization is a systematic way of ensuring that a database structure is suitable for general-purpose querying and free of certain undesirable characteristics\u2014insertion, update, and deletion anomalies that could lead to loss of data integrity. A standard piece of database design guidance is that the designer should create a fully normalized design; selective denormalization can subsequently be performed, but only for performance reasons. The trade-off is storage space vs performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Borrow 1 from the thousands place for a ten in the hundreds place, minus 7 from the row below, the difference 3 is added to the 2 on top to form 5. The 7 on the bottom is subtracted, shown by the space. Borrow 1 from the hundreds place, which leaves 4.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0\u20131 integer program, all constraints are of the form x i \u2208 { 0 , 1 } {\\displaystyle x_{i}\\in \\{0,1\\}} .The relaxation of the original integer program instead uses a collection of linear constraints 0 \u2264 x i \u2264 1. {\\displaystyle 0\\leq x_{i}\\leq 1.} The resulting relaxation is a linear program, hence the name. This relaxation technique transforms an NP-hard optimization problem (integer programming) into a related problem that is solvable in polynomial time (linear programming); the solution to the relaxed linear program can be used to gain information about the solution to the original integer program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming, behavioral subtyping is the principle that subclasses should satisfy the expectations of clients accessing subclass objects through references of superclass type, not just as regards syntactic safety (such as the absence of \"method-not-found\" errors) but also as regards behavioral correctness. Specifically, properties that clients can prove using the specification of an object's presumed type should hold even though the object is actually a member of a subtype of that type. For example, consider a type Stack and a type Queue, which both have a put method to add an element and a get method to remove one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In project management, resource leveling is defined by A Guide to the Project Management Body of Knowledge (PMBOK Guide) as \"A technique in which start and finish dates are adjusted based on resource limitation with the goal of balancing demand for resources with the available supply.\" Resource leveling problem could be formulated as an optimization problem. The problem could be solved by different optimization algorithms such as exact algorithms or meta-heuristic methods.When performing project planning activities, the manager will attempt to schedule certain tasks simultaneously. When more resources such as machines or people are needed than are available, or perhaps a specific person is needed in both tasks, the tasks will have to be rescheduled concurrently or even sequentially to manage the constraint.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to determine how judges weigh the different factors, 103 written judgements of commonplace cases were used to establish a database comprising 94 relevant factors for percentage split determination. : 273 The factors relevant for a percentage split determination are: Past contributions of a husband relative to those of a wife The husband's future needs relative to those of the wife The wealth of the marriageThe factors relevant for a determination of past contributions are The relative direct and indirect contributions of both parties The length of the marriage The relative contributions of both parties to the homemaking roleThe hierarchy provides a structure that is used to decompose the task of predicting an outcome into 35 subtasks. Outputs of tasks further down the hierarchy are used as inputs into sub-tasks higher up the hierarchy. Each sub-task is treated as a separate and smaller data mining exercise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a \"two by three matrix\", a \" 2 \u00d7 3 {\\displaystyle 2\\times 3} matrix\", or a matrix of dimension 2 \u00d7 3 {\\displaystyle 2\\times 3} . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In rank selection, the selection probability does not depend directly on the fitness, but on the fitness rank of an individual within the population. This puts large fitness differences into perspective; moreover, the exact fitness values themselves do not have to be available, but only a sorting of the individuals according to quality. Linear ranking, which goes back to Baker, is often used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2357, 12357, 23457, and 123457 are the patterns related to Braille pattern dots-1234, since the two additional dots of kantenji patterns 01234, 12347, and 012347 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, a separation oracle can be implemented using n-1 applications of the minimum cut procedure. The maximum independent set problem. It can be approximated by an LP with a constraint for every odd-length cycle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a congruum (plural congrua) is the difference between successive square numbers in an arithmetic progression of three squares. That is, if x 2 {\\displaystyle x^{2}} , y 2 {\\displaystyle y^{2}} , and z 2 {\\displaystyle z^{2}} (for integers x {\\displaystyle x} , y {\\displaystyle y} , and z {\\displaystyle z} ) are three square numbers that are equally spaced apart from each other, then the spacing between them, z 2 \u2212 y 2 = y 2 \u2212 x 2 {\\displaystyle z^{2}-y^{2}=y^{2}-x^{2}} , is called a congruum. The congruum problem is the problem of finding squares in arithmetic progression and their associated congrua. It can be formalized as a Diophantine equation: find integers x {\\displaystyle x} , y {\\displaystyle y} , and z {\\displaystyle z} such that When this equation is satisfied, both sides of the equation equal the congruum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization algorithms. It is also known as Rosenbrock's valley or Rosenbrock's banana function. The global minimum is inside a long, narrow, parabolic shaped flat valley. To find the valley is trivial.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the Ackley function is a non-convex function used as a performance test problem for optimization algorithms. It was proposed by David Ackley in his 1987 PhD dissertation.On a 2-dimensional domain it is defined by: f ( x , y ) = \u2212 20 exp \u2061  \u2212 exp \u2061  + e + 20 {\\displaystyle {\\begin{aligned}f(x,y)=-20&{}\\exp \\left\\\\&{}-\\exp \\left+e+20\\end{aligned}}} Its global optimum point is f ( 0 , 0 ) = 0. {\\displaystyle f(0,0)=0.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Ankeny\u2013Artin\u2013Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number h of a real quadratic field of discriminant d > 0. If the fundamental unit of the field is \u03b5 = t + u d 2 {\\displaystyle \\varepsilon ={\\frac {t+u{\\sqrt {d}}}{2}}} with integers t and u, it expresses in another form h t u ( mod p ) {\\displaystyle {\\frac {ht}{u}}{\\pmod {p}}\\;} for any prime number p > 2 that divides d. In case p > 3 it states that \u2212 2 m h t u \u2261 \u2211 0 < k < d \u03c7 ( k ) k \u230a k / p \u230b ( mod p ) {\\displaystyle -2{mht \\over u}\\equiv \\sum _{0", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example, we use the keys JANEAUSTEN and AEROPLANES to encrypt the following plaintext: \"Transposition ciphers scramble letters like puzzle pieces to create an indecipherable arrangement.\" The colors show how the letters are scrambled in each transposition step. While a single step only causes a minor rearrangement, the second step leads to a significant scrambling effect if the last row of the grid is incomplete.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The overlapping sequences are then aligned into contigs and merged. Usually, several samples are pooled in one run, and each sample is characterized by a short DNA fragment, the tag. In a demultiplexing step, sequences are sorted using these tags to reassemble the separate samples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The problem of packet size distribution is fairly well-understood today. Existing models of packet sizes have proven to be valid and simple. Most packet size models do not consider the problem of order in packet sizes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The denominator is the number of total such friendships, which is twice the total edges in the network (one from the u's perspective and the other from the v's). After this analysis, Feld goes on to make some more qualitative assumptions about the statistical correlation between the number of friends that two friends have, based on theories of social networks such as assortative mixing, and he analyzes what these assumptions imply about the number of people whose friends have more friends than they do. Based on this analysis, he concludes that in real social networks, most people are likely to have fewer friends than the average of their friends' numbers of friends.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A task as simple as counting backwards can change memory recall; however an empty delay interval has no effect. This is because the person can continue to rehearse the items in their working memory to be remembered without interference. Cohen (1989) found that there is better recall for an action in the presence of interference if that action is physically performed during the encoding phase. It has also been found that recalling some items can interfere and inhibit the recall of other items. Another stream of thought and evidence suggests that the effects of interference on recency and primacy are relative, determined by the ratio rule (retention interval to inter item presentation distractor rate) and they exhibit time-scale invariance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or deception in the presentation of the proof. For example, the reason why validity fails may be attributed to a division by zero that is hidden by algebraic notation. There is a certain quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the conditional distribution of Y {\\displaystyle Y} given X {\\displaystyle X} is a continuous distribution, then its probability density function is known as the conditional density function. The properties of a conditional distribution, such as the moments, are often referred to by corresponding names such as the conditional mean and conditional variance. More generally, one can refer to the conditional distribution of a subset of a set of more than two variables; this conditional distribution is contingent on the values of all the remaining variables, and if more than one variable is included in the subset then this conditional distribution is the conditional joint distribution of the included variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C programming language, Duff's device is a way of manually implementing loop unrolling by interleaving two syntactic constructs of C: the do-while loop and a switch statement. Its discovery is credited to Tom Duff in November 1983, when Duff was working for Lucasfilm and used it to speed up a real-time animation program. Loop unrolling attempts to reduce the overhead of conditional branching needed to check whether a loop is done, by executing a batch of loop bodies per iteration. To handle cases where the number of iterations is not divisible by the unrolled-loop increments, a common technique among assembly language programmers is to jump directly into the middle of the unrolled loop body to handle the remainder. Duff implemented this technique in C by using C's case label fall-through feature to jump into the unrolled body.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A notable series of analog calculating machines were developed by Leonardo Torres Quevedo since 1895, including one that was able to compute the roots of arbitrary polynomials of order eight, including the complex ones, with a precision down to thousandths. An important advance in analog computing was the development of the first fire-control systems for long range ship gunlaying. When gunnery ranges increased dramatically in the late 19th century it was no longer a simple matter of calculating the proper aim point, given the flight times of the shells.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The hierarchical softmax (introduced by Morin and Bengio in 2005) uses a binary tree structure where the outcomes (vocabulary words) are the leaves and the intermediate nodes are suitably selected \"classes\" of outcomes, forming latent variables. The desired probability (softmax value) of a leaf (outcome) can then be calculated as the product of the probabilities of all nodes on the path from the root to that leaf. Ideally, when the tree is balanced, this would reduce the computational complexity from O ( K ) {\\displaystyle O(K)} to O ( log 2 \u2061 K ) {\\displaystyle O(\\log _{2}K)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It gets stuck at a basic feasible solution (a corner of the feasible polytope) and changes bases in a cyclic way without decreasing the minimization target. Such cycles are avoided by Bland's rule for choosing a column to enter and a column to leave the basis. Bland's rule was developed by Robert G. Bland, now an Emeritus Professor of operations research at Cornell University, while he was a research fellow at the Center for Operations Research and Econometrics in Belgium.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this way they also form two boxes, this time in consecutive corners, with areas a 2 {\\displaystyle a^{2}} and b 2 {\\displaystyle b^{2}} which will again lead to a second square of with the area 2 a b + a 2 + b 2 {\\displaystyle 2ab+a^{2}+b^{2}} . English mathematician Sir Thomas Heath gives this proof in his commentary on Proposition I.47 in Euclid's Elements, and mentions the proposals of German mathematicians Carl Anton Bretschneider and Hermann Hankel that Pythagoras may have known this proof. Heath himself favors a different proposal for a Pythagorean proof, but acknowledges from the outset of his discussion \"that the Greek literature which we possess belonging to the first five centuries after Pythagoras contains no statement specifying this or any other particular great geometric discovery to him.\" Recent scholarship has cast increasing doubt on any sort of role for Pythagoras as a creator of mathematics, although debate about this continues.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, a metric should score highly translations that humans score highly, and give low scores to those humans give low scores. Human judgment is the benchmark for assessing automatic metrics, as humans are the end-users of any translation output. The measure of evaluation for metrics is correlation with human judgment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (i.e., no solution for it is known). In the history of science, some of these supposed open problems were \"solved\" by means of showing that they were not well-defined. In mathematics, many open problems are concerned with the question of whether a certain definition is or is not consistent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of machine learning, D KL ( P \u2225 Q ) {\\displaystyle D_{\\text{KL}}(P\\parallel Q)} is often called the information gain achieved if P {\\displaystyle P} would be used instead of Q {\\displaystyle Q} which is currently used. By analogy with information theory, it is called the relative entropy of P {\\displaystyle P} with respect to Q {\\displaystyle Q} . Expressed in the language of Bayesian inference, D KL ( P \u2225 Q ) {\\displaystyle D_{\\text{KL}}(P\\parallel Q)} is a measure of the information gained by revising one's beliefs from the prior probability distribution Q {\\displaystyle Q} to the posterior probability distribution P {\\displaystyle P} . In other words, it is the amount of information lost when Q {\\displaystyle Q} is used to approximate P {\\displaystyle P} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Discovery with Model method, a model is developed via prediction, clustering or by human reasoning knowledge engineering and then used as a component in another analysis, namely in prediction and relationship mining. In the prediction method use, the created model's predictions are used to predict a new variable. For the use of relationship mining, the created model enables the analysis between new predictions and additional variables in the study.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle S^{1}.} The proof is based on normal surface techniques originated by Hellmuth Kneser. Existence was proven by Kneser, but the exact formulation and proof of the uniqueness was done more than 30 years later by John Milnor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This project, known as Hilbert's program, was seriously affected by G\u00f6del's incompleteness theorems, which show that the consistency of formal theories of arithmetic cannot be established using methods formalizable in those theories. Gentzen showed that it is possible to produce a proof of the consistency of arithmetic in a finitary system augmented with axioms of transfinite induction, and the techniques he developed to do so were seminal in proof theory. A second thread in the history of foundations of mathematics involves nonclassical logics and constructive mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a pseudomanifold is a special type of topological space. It looks like a manifold at most of its points, but it may contain singularities. For example, the cone of solutions of z 2 = x 2 + y 2 {\\displaystyle z^{2}=x^{2}+y^{2}} forms a pseudomanifold. A pseudomanifold can be regarded as a combinatorial realisation of the general idea of a manifold with singularities. The concepts of orientability, orientation and degree of a mapping make sense for pseudomanifolds and moreover, within the combinatorial approach, pseudomanifolds form the natural domain of definition for these concepts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Perform Cholesky decomposition (a variant of Gaussian elimination for symmetric matrices), ordering the elimination of the variables by the recursive structure of the partition: each of the two subgraphs formed by removing the separator is eliminated first, and then the separator vertices are eliminated.As a consequence of this algorithm, the fill-in (the set of nonzero matrix entries created in the Cholesky decomposition that are not part of the input matrix structure) is limited to at most the square of the separator size at each level of the recursive partition. In particular, for planar graphs (frequently arising in the solution of sparse linear systems derived from two-dimensional finite element method meshes) the resulting matrix has O(n log n) nonzeros, due to the planar separator theorem guaranteeing separators of size O(\u221an). For arbitrary graphs there is a nested dissection that guarantees fill-in within a O ( min { d log 4 \u2061 n , m 1 / 4 log 3.5 \u2061 n } ) {\\displaystyle O(\\min\\{{\\sqrt {d}}\\log ^{4}n,m^{1/4}\\log ^{3.5}n\\})} factor of optimal, where d is the maximum degree and m is the number of non-zeros.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These conditions are very loose, and allow enormous flexibility in the choice of open sets. For example, every subset can be open (the discrete topology), or no subset can be open except the space itself and the empty set (the indiscrete topology).In practice, however, open sets are usually chosen to provide a notion of nearness that is similar to that of metric spaces, without having a notion of distance defined. In particular, a topology allows defining properties such as continuity, connectedness, and compactness, which were originally defined by means of a distance. The most common case of a topology without any distance is given by manifolds, which are topological spaces that, near each point, resemble an open set of a Euclidean space, but on which no distance is defined in general. Less intuitive topologies are used in other branches of mathematics; for example, the Zariski topology, which is fundamental in algebraic geometry and scheme theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In separate chaining, the process involves building a linked list with key\u2013value pair for each search array index. The collided items are chained together through a single linked list, which can be traversed to access the item with a unique search key. : 464 Collision resolution through chaining with linked list is a common method of implementation of hash tables. Let T {\\displaystyle T} and x {\\displaystyle x} be the hash table and the node respectively, the operation involves as follows:: 258 Chained-Hash-Insert(T, k) insert x at the head of linked list T Chained-Hash-Search(T, k) search for an element with key k in linked list T Chained-Hash-Delete(T, k) delete x from the linked list T If the element is comparable either numerically or lexically, and inserted into the list by maintaining the total order, it results in faster termination of the unsuccessful searches. : 520\u2013521", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The notion directly extends to the product of an arbitrary finite number of types (a n-ary product type), and in this case, it characterizes the expressions which behave as tuples of expressions of the corresponding types. A degenerated form of product type is the unit type: it is the product of no types. In call-by-value programming languages, a product type can be interpreted as a set of pairs whose first component is a value in the first type and whose second component is a value in the second type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the data warehouse process, data can be aggregated in data marts at different levels of abstraction. The user may start looking at the total sale units of a product in an entire region. Then the user looks at the states in that region. Finally, they may examine the individual stores in a certain state. Therefore, typically, the analysis starts at a higher level and drills down to lower levels of details.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "12n(\u03c0(n+1)+1)where \u03c0(n) is the prime-counting function. This was subsequently improved by Hans Frederick Blichfeldt who replaced the 12 with a 6. Unpublished work on the finite case was also done by Boris Weisfeiler. Subsequently, Michael Collins, using the classification of finite simple groups, showed that in the finite case, one can take \u0192(n) = (n + 1)! when n is at least 71, and gave near complete descriptions of the behavior for smaller n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some studies suggest that these errors can be anywhere between 5 and 10 degrees.These goniometers come in different forms that some argue increase reliability. The universal standard goniometer is a plastic or metal tool with 1 degree increments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scalar languages such as C and Pascal, operations apply only to single values, so a+b expresses the addition of two numbers. In such languages, adding one array to another requires indexing and looping, the coding of which is tedious. In array-based languages, for example in Fortran, the nested for-loop above can be written in array-format in one line, or alternatively, to emphasize the array nature of the objects, While scalar languages like C do not have native array programming elements as part of the language proper, this does not mean programs written in these languages never take advantage of the underlying techniques of vectorization (i.e., utilizing a CPU's vector-based instructions if it has them or by using multiple CPU cores). Some C compilers like GCC at some optimization levels detect and vectorize sections of code that its heuristics determine would benefit from it. Another approach is given by the OpenMP API, which allows one to parallelize applicable sections of code by taking advantage of multiple CPU cores.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of government documents, redaction (also called sanitization) generally refers more specifically to the process of removing sensitive or classified information from a document prior to its publication, during declassification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other authors call a set directed if and only if it is directed both upward and downward.Directed sets are a generalization of nonempty totally ordered sets. That is, all totally ordered sets are directed sets (contrast partially ordered sets, which need not be directed). Join-semilattices (which are partially ordered sets) are directed sets as well, but not conversely.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a matrix coefficient (or matrix element) is a function on a group of a special form, which depends on a linear representation of the group and additional data. Precisely, it is a function on a compact topological group G obtained by composing a representation of G on a vector space V with a linear map from the endomorphisms of V into V's underlying field. It is also called a representative function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is called the policy cycle as the final stage (evaluation) often leads back to the first stage (problem definition), thus restarting the cycle. Harold Lasswell's popular model of the policy cycle divided the process into seven distinct stages, asking questions of both how and why public policies should be made. With the stages ranging from (1) intelligence, (2) promotion, (3) prescription, (4) invocation, (5) application, (6) termination and (7) appraisal, this process inherently attempts to combine policy implementation to formulated policy goals.One version by James E. Anderson, in his Public Policy-Making (1974) has the following stages: Agenda setting (Problem identification) \u2013 The recognition of certain subject as a problem demanding further government attention.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to compete with Intel's Advanced Programmable Interrupt Controller (APIC), which had enabled the first Intel 486-based multiprocessor systems, in early 1995 AMD and Cyrix proposed as somewhat similar-in-purpose OpenPIC architecture supporting up to 32 processors. The OpenPIC architecture had at least declarative support from IBM and Compaq around 1995. No x86 motherboard was released with OpenPIC however. After the OpenPIC's failure in the x86 market, AMD licensed the Intel APIC Architecture for its AMD Athlon and later processors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If we assume that a function f: R n \u2192 R {\\displaystyle f:\\mathbb {R} ^{n}\\to \\mathbb {R} } is globally continuous and separately differentiable on each variable (all partial derivatives exist everywhere), it is not true that f {\\displaystyle f} will necessarily be differentiable. A counterexample in two dimensions is given by f ( x , y ) = 2 x 2 y + y 3 x 2 + y 2 . {\\displaystyle f(x,y)={\\dfrac {2x^{2}y+y^{3}}{x^{2}+y^{2}}}.} If in addition we define f ( 0 , 0 ) = 0 {\\displaystyle f(0,0)=0} , this function is everywhere continuous and has well-defined partial derivatives in x {\\displaystyle x} and y {\\displaystyle y} everywhere (also at the origin), but is not differentiable at the origin.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of bioinformatics, a sequence database is a type of biological database that is composed of a large collection of computerized (\"digital\") nucleic acid sequences, protein sequences, or other polymer sequences stored on a computer. The UniProt database is an example of a protein sequence database. As of 2013 it contained over 40 million sequences and is growing at an exponential rate. Historically, sequences were published in paper form, but as the number of sequences grew, this storage method became unsustainable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alternatively the two distributions can both be empirically estimated ones; this is called the two-sample case. The criterion is named after Harald Cram\u00e9r and Richard Edler von Mises who first proposed it in 1928\u20131930. The generalization to two samples is due to Anderson.The Cram\u00e9r\u2013von Mises test is an alternative to the Kolmogorov\u2013Smirnov test (1933).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In typical applications, e.g., when discretizing integral equations, preconditioning the resulting systems of linear equations, or solving elliptic partial differential equations, a rank proportional to log \u2061 ( 1 / \u03f5 ) \u03b3 {\\displaystyle \\log(1/\\epsilon )^{\\gamma }} with a small constant \u03b3 {\\displaystyle \\gamma } is sufficient to ensure an accuracy of \u03f5 {\\displaystyle \\epsilon } . Compared to many other data-sparse representations of non-sparse matrices, hierarchical matrices offer a major advantage: the results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximated in O ( n k \u03b1 log \u2061 ( n ) \u03b2 ) {\\displaystyle O(nk^{\\alpha }\\,\\log(n)^{\\beta })} operations, where \u03b1 , \u03b2 \u2208 { 1 , 2 , 3 } . {\\displaystyle \\alpha ,\\beta \\in \\{1,2,3\\}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the signal magnitude area (abbreviated SMA or sma) is a statistical measure of the magnitude of a varying quantity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If all coefficients in r {\\displaystyle r} are negative, then z 0 {\\displaystyle z_{0}} is an optimal solution, since all variables (including all non-basic variables) must be at least 0, so the second line implies z \u2264 z 0 {\\displaystyle z\\leq z_{0}} . If some coefficients in r {\\displaystyle r} are positive, then it may be possible to increase the maximization target.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, the speed of the CPU has grown many times in comparison to the access speed of the main memory. Care needs to be taken to reduce the number of times main memory is accessed in order to maintain performance. If, for instance, every instruction run in the CPU requires an access to memory, the computer gains nothing for increased CPU speed\u2014a problem referred to as being memory bound. It is possible to make extremely fast memory, but this is only practical for small amounts of memory for cost, power and signal routing reasons.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, neighborhood search is a technique that tries to find good or near-optimal solutions to a combinatorial optimisation problem by repeatedly transforming a current solution into a different solution in the neighborhood of the current solution. The neighborhood of a solution is a set of similar solutions obtained by relatively simple modifications to the original solution. For a very large-scale neighborhood search, the neighborhood is large and possibly exponentially sized. The resulting algorithms can outperform algorithms using small neighborhoods because the local improvements are larger.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages such as REXX, the precision of all calculations must be set before doing a calculation. Other languages, such as Python and Ruby, extend the precision automatically to prevent overflow.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fortran did not have an equality operator (it was only possible to compare an expression to zero, using the arithmetic IF statement) until FORTRAN IV was released in 1962, since when it has used the four characters .EQ. to test for equality. The language B introduced the use of == with this meaning, which has been copied by its descendant C and most later languages where = means assignment. The equal sign is also used in defining attribute\u2013value pairs, in which an attribute is assigned a value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical physics and gauge theory, the ADHM construction or monad construction is the construction of all instantons using methods of linear algebra by Michael Atiyah, Vladimir Drinfeld, Nigel Hitchin, Yuri I. Manin in their paper \"Construction of Instantons.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Krener's theorem is a result attributed to Arthur J. Krener in geometric control theory about the topological properties of attainable sets of finite-dimensional control systems. It states that any attainable set of a bracket-generating system has nonempty interior or, equivalently, that any attainable set has nonempty interior in the topology of the corresponding orbit. Heuristically, Krener's theorem prohibits attainable sets from being hairy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Whitney's planarity criterion is a matroid-theoretic characterization of planar graphs, named after Hassler Whitney. It states that a graph G is planar if and only if its graphic matroid is also cographic (that is, it is the dual matroid of another graphic matroid). In purely graph-theoretic terms, this criterion can be stated as follows: There must be another (dual) graph G'=(V',E') and a bijective correspondence between the edges E' and the edges E of the original graph G, such that a subset T of E forms a spanning tree of G if and only if the edges corresponding to the complementary subset E-T form a spanning tree of G'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Z is sometimes called the Boltzmann sum over states (or \"Zustandssumme\" in the original German). If we index the summation via the energy eigenvalues instead of all possible states, degeneracy must be taken into account. The probability of our system having energy \u03b5 i {\\displaystyle \\varepsilon _{i}} is simply the sum of the probabilities of all corresponding microstates: P ( \u03b5 i ) = 1 Z g i e \u2212 \u03b5 i / k T {\\displaystyle P(\\varepsilon _{i})={\\frac {1}{Z}}g_{i}e^{-\\varepsilon _{i}/kT}} where, with obvious modification, Z = \u2211 j g j e \u2212 \u03b5 j / k T , {\\displaystyle Z=\\sum _{j}g_{j}e^{-\\varepsilon _{j}/kT},} this is the same result as before.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of time-dependent vector fields F: R n \u00d7 R \u2192 R n {\\displaystyle {\\boldsymbol {F}}:\\mathbb {R} ^{n}\\times \\mathbb {R} \\to \\mathbb {R} ^{n}} , one denotes \u03c6 t , t 0 ( x 0 ) = x ( t + t 0 ) , {\\displaystyle \\varphi ^{t,t_{0}}({\\boldsymbol {x}}_{0})={\\boldsymbol {x}}(t+t_{0}),} where x: R \u2192 R n {\\displaystyle {\\boldsymbol {x}}:\\mathbb {R} \\to \\mathbb {R} ^{n}} is the solution of x \u02d9 ( t ) = F ( x ( t ) , t ) , x ( t 0 ) = x 0 . {\\displaystyle {\\dot {\\boldsymbol {x}}}(t)={\\boldsymbol {F}}({\\boldsymbol {x}}(t),t),\\qquad {\\boldsymbol {x}}(t_{0})={\\boldsymbol {x}}_{0}.} Then \u03c6 t , t 0 ( x 0 ) {\\displaystyle \\varphi ^{t,t_{0}}({\\boldsymbol {x}}_{0})} is the time-dependent flow of F. It is not a \"flow\" by the definition above, but it can easily be seen as one by rearranging its arguments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More generally, addition-chain exponentiation may also refer to exponentiation by non-minimal addition chains constructed by a variety of algorithms (since a shortest addition chain is very difficult to find). The shortest addition-chain algorithm requires no more multiplications than binary exponentiation and usually less. The first example of where it does better is for a15, where the binary method needs six multiplications but the shortest addition chain requires only five: a 15 = a \u00d7 ( a \u00d7  2 ) 2 {\\displaystyle a^{15}=a\\times (a\\times ^{2})^{2}\\!}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Unidirectional mode of operation, packets are only sent in one direction: from compressor to decompressor. This mode therefore makes ROHC usable over links where a return path from decompressor to compressor is unavailable or undesirable. In order to handle potential decompression errors, the compressor sends periodic refreshes of the stream context to the decompressor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the pointwise product of two functions is another function, obtained by multiplying the images of the two functions at each value in the domain. If f and g are both functions with domain X and codomain Y, and elements of Y can be multiplied (for instance, Y could be some set of numbers), then the pointwise product of f and g is another function from X to Y which maps x in X to f (x)g(x) in Y.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "count t max {\\displaystyle t_{\\max }}: max. countSince the number of indexed items per descriptor is usually distributed according to a power law, for larger ranges of values, a logarithmic representation makes sense.Implementations of tag clouds also include text parsing and filtering out unhelpful tags such as common words, numbers, and punctuation. There are also websites creating artificially or randomly weighted tag clouds, for advertising, or for humorous results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "n ) ( \u2207 p 0 . n ) \u2212 \u03c0 ( \u2207 u 0 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This approach allows the system to gather information about the frequency with which various constructions occur in specific contexts. (See machine learning.) Approaches which have been used include straightforward PCFGs (probabilistic context-free grammars), maximum entropy, and neural nets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This concept can be extended to the multivariate context by an extension of the simple sum to a number of F {\\displaystyle F} sums that cover all dimensions in the feature space: p w ( \u03b8 \u2192 ) = \u2211 k 1 , . . . , k F = \u2212 \u221e \u221e p ( \u03b8 \u2192 + 2 \u03c0 k 1 e 1 + \u22ef + 2 \u03c0 k F e F ) {\\displaystyle p_{w}({\\vec {\\theta }})=\\sum _{k_{1},...,k_{F}=-\\infty }^{\\infty }{p({\\vec {\\theta }}+2\\pi k_{1}\\mathbf {e} _{1}+\\dots +2\\pi k_{F}\\mathbf {e} _{F})}} where e k = ( 0 , \u2026 , 0 , 1 , 0 , \u2026 , 0 ) T {\\displaystyle \\mathbf {e} _{k}=(0,\\dots ,0,1,0,\\dots ,0)^{\\mathsf {T}}} is the k {\\displaystyle k} th Euclidean basis vector.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Usually, the price also includes a mark-up for profit over the cost of production. More generalized in the field of economics, cost is a metric that is totaling up as a result of a process or as a differential for the result of a decision.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some developing countries, many people do not have access to banking facilities, especially in tier II and tier III cities. Taking the example of India, there are more mobile phone users than there are people with active bank accounts. Telecom operators, in such locations, have started offering mobile money wallets which allow adding funds easily through their existing mobile subscription number, by visiting physical recharge points close to their homes and offices and converting their cash into mobile wallet currency. This can be used for online transaction and eCommerce purchases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In processing electronic audio signals, pre-emphasis refers to a system process designed to increase (within a frequency band) the magnitude of some (usually higher) frequencies with respect to the magnitude of other (usually lower) frequencies in order to improve the overall signal-to-noise ratio by minimizing the adverse effects of such phenomena as attenuation distortion or saturation of recording media in subsequent parts of the system. The mirror operation is called de-emphasis, and the system as a whole is called emphasis. Pre-emphasis is achieved with a pre-emphasis network which is essentially a calibrated filter. The frequency response is decided by special time constants.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An important aspect of this stage is verification. This effort verifies that the requirement has been implemented correctly. There are 4 methods of verification: analysis, inspection, testing, and demonstration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The version without negations is sometimes called weakly injective. The existence of value collisions is a strong notion of non-injectivity. And regarding surjectivity, similar considerations exist for outlier-production in the codomain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Middle East, Hasan Ibn al-Haytham, Latinized as Alhazen (c. 965 \u2013 c. 1040 CE) derived a formula for the sum of fourth powers. He used the results to carry out what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid. Roshdi Rashed has argued that the 12th century mathematician Sharaf al-D\u012bn al-T\u016bs\u012b must have used the derivative of cubic polynomials in his Treatise on Equations. Rashed's conclusion has been contested by other scholars, who argue that he could have obtained his results by other methods which do not require the derivative of the function to be known.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"If the cause, assigned for any effect, be not sufficient to produce it, we must either reject that cause, or add to it such qualities as will give it a just proportion to the effect.\" Occam's razor: Explanations which require fewer unjustified assumptions are more likely to be correct; avoid unnecessary or improbable assumptions. Popper's falsifiability principle: For a theory to be considered scientific, it must be falsifiable. Sagan standard: Extraordinary claims require extraordinary evidence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the book written by Frank Rosenblatt, published in 1961, a three-layer Multilayer Perceptron (MLP) model with skip connections was presented (Chapter 15, p313 in ). The model was referred to as a \"cross-coupled system\", and the skip connections were forms of cross-coupled connections. In two books published in 1994 and 1996, \"skip-layer\" connections were presented in feed-forward MLP models: \"The general definition  allows more than one hidden layer, and it also allows 'skip-layer' connections from input to output\" (p261 in, p144 in ), \"... which allows the non-linear units to perturb a linear functional form\" (p262 in ). This description suggests that the non-linear MLP performs like a residual function (perturbation) added to a linear function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonology, voicing (or sonorization) is a sound change where a voiceless consonant becomes voiced due to the influence of its phonological environment; shift in the opposite direction is referred to as devoicing or desonorization. Most commonly, the change is a result of sound assimilation with an adjacent sound of opposite voicing, but it can also occur word-finally or in contact with a specific vowel. For example, the English suffix -s is pronounced  when it follows a voiceless phoneme (cats), and  when it follows a voiced phoneme (dogs). This type of assimilation is called progressive, where the second consonant assimilates to the first; regressive assimilation goes in the opposite direction, as can be seen in have to .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is impossible for an unprivileged application to access a page that has not been explicitly allocated to it, because every memory address either points to a page allocated to that application, or generates an interrupt called a page fault. Unallocated pages, and pages allocated to any other application, do not have any addresses from the application point of view. A page fault may not necessarily indicate an error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical computer science, a set constraint is an equation or an inequation between sets of terms. Similar to systems of (in)equations between numbers, methods are studied for solving systems of set constraints. Different approaches admit different operators (like \"\u222a\", \"\u2229\", \"\\\", and function application) on sets and different (in)equation relations (like \"=\", \"\u2286\", and \"\u2288\") between set expressions. Systems of set constraints are useful to describe (in particular infinite) sets of ground terms. They arise in program analysis, abstract interpretation, and type inference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a long-distance call (U.S.) or trunk call (also known as a toll call in the U.K.) is a telephone call made to a location outside a defined local calling area.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, remote call forwarding is a service feature that allows incoming calls to be forwarded to a remote call forwarding number, such as a cell phone or another office location and is designated by the call receiver.Customers may have a remote-forwarding telephone number in a central switching office without having any other local telephone service in that office. One common purpose for this service is to enable customers to retain their telephone number when they move to a location serviced by a different telephone exchange. The service is useful for business customers with widely advertised numbers which appear on headed paper, vehicles and various marketing literature. When customers ring, their calls are forwarded to the new location.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to maintain good programming practice, a number of compiler options and flags designed for safety have been enabled by default to help in spotting potential issues so they can be fixed earlier (-Wall, -Werror, -Wextra, -Wuninitialized). There have also been code readability updates which help future contributors in verifying program correctness (KNF, white-space, line-wrapping, etc.). Modification or removal of unneeded method wrappers and macros also help with code readability and auditing (Error and I/O abstraction library references). Changes were made to ensure that LibreSSL will be year 2038 compatible along with maintaining portability for other similar platforms. In addition, explicit_bzero and bn_clear calls were added to prevent the compiler from optimizing them out and prevent attackers from reading previously allocated memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Females only lay one test clutch and return shortly after laying it. Capable males prove their parental quality by defending the brood and not cannibalizing the eggs. Test eggs are energetically expensive to create, so this strategy is typically only used by large females at the beginning of the mating phase.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One special type of operand is the parenthesis group. An expression enclosed in parentheses is typically recursively evaluated to be treated as a single operand on the next evaluation level. Each operator is given a position, precedence, and an associativity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of information theory, entropy is considered to be a measure of the uncertainty in a message. To put it intuitively, suppose p = 0 {\\displaystyle p=0} . At this probability, the event is certain never to occur, and so there is no uncertainty at all, leading to an entropy of 0. If p = 1 {\\displaystyle p=1} , the result is again certain, so the entropy is 0 here as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather than natural numbers. They were introduced by Jensen & Karp (1971).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Iteration length has changed from months to weeks or days with the rising popularity of Agile, DevOps, and Continuous Delivery. Traditional methods of testing, which rely heavily on manual testing and automated GUI tests that require frequent updating, cannot keep pace.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, there are O(V) saturating pushes on (u, v), and the total number of saturating pushes is at most 2| V || E |. This results in a time bound of O(VE) for the saturating push operations. Bounding the number of nonsaturating pushes can be achieved via a potential argument.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, since 2010 the Insurance Institute for Highway Safety uses a scheme it has developed that takes into account a combination of both vehicle footprint (length times width) and weight. The United States National Highway Traffic Safety Administration (NHTSA) separates vehicles into classes by the curb weight of the vehicle with standard equipment including the maximum capacity of fuel, oil, coolant, and air conditioning, if so equipped. The United States Federal Highway Administration has developed a classification scheme used for automatically calculating road use tolls. There are two broad categories depending on whether the vehicle carries passengers or commodities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Suppose further that the researcher wants to estimate a bivariate linear model via least squares: Y i = \u03b2 0 + \u03b2 1 X 1 i + \u03b2 2 X 2 i + e i {\\displaystyle Y_{i}=\\beta _{0}+\\beta _{1}X_{1i}+\\beta _{2}X_{2i}+e_{i}} . If the researcher only has access to N = 2 {\\displaystyle N=2} data points, then they could find infinitely many combinations ( \u03b2 ^ 0 , \u03b2 ^ 1 , \u03b2 ^ 2 ) {\\displaystyle ({\\hat {\\beta }}_{0},{\\hat {\\beta }}_{1},{\\hat {\\beta }}_{2})} that explain the data equally well: any combination can be chosen that satisfies Y ^ i = \u03b2 ^ 0 + \u03b2 ^ 1 X 1 i + \u03b2 ^ 2 X 2 i {\\displaystyle {\\hat {Y}}_{i}={\\hat {\\beta }}_{0}+{\\hat {\\beta }}_{1}X_{1i}+{\\hat {\\beta }}_{2}X_{2i}} , all of which lead to \u2211 i e ^ i 2 = \u2211 i ( Y ^ i \u2212 ( \u03b2 ^ 0 + \u03b2 ^ 1 X 1 i + \u03b2 ^ 2 X 2 i ) ) 2 = 0 {\\displaystyle \\sum _{i}{\\hat {e}}_{i}^{2}=\\sum _{i}({\\hat {Y}}_{i}-({\\hat {\\beta }}_{0}+{\\hat {\\beta }}_{1}X_{1i}+{\\hat {\\beta }}_{2}X_{2i}))^{2}=0} and are therefore valid solutions that minimize the sum of squared residuals. To understand why there are infinitely many options, note that the system of N = 2 {\\displaystyle N=2} equations is to be solved for 3 unknowns, which makes the system underdetermined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E2. It is a geometric space in which two real numbers are required to determine the position of each point. It is an affine space, which includes in particular the concept of parallel lines. It has also metrical properties induced by a distance, which allows to define circles, and angle measurement. A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane. The set R 2 {\\displaystyle \\mathbb {R} ^{2}} of the pairs of real numbers (the real coordinate plane), equipped with the dot product, is often called the Euclidean plane, since every Euclidean plane is isomorphic to it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some Boolean operations, in particular do not have inverses that may be defined as functions. In particular the disjunction \"or\" has inverses that allow two values. In natural language \"or\" represents alternate possibilities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If all elements in each sampled cluster are sampled, then this is referred to as a \"one-stage\" cluster sampling plan. If a simple random subsample of elements is selected within each of these groups, this is referred to as a \"two-stage\" cluster sampling plan. A common motivation for cluster sampling is to reduce the total number of interviews and costs given the desired accuracy. For a fixed sample size, the expected random error is smaller when most of the variation in the population is present internally within the groups, and not between the groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In stochastic gradient descent, feature scaling can sometimes improve the convergence speed of the algorithm. In support vector machines, it can reduce the time to find support vectors. Note that feature scaling changes the SVM result.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software testing, test automation is the use of software separate from the software being tested to control the execution of tests and the comparison of actual outcomes with predicted outcomes. Test automation can automate some repetitive but necessary tasks in a formalized testing process already in place, or perform additional testing that would be difficult to do manually. Test automation is critical for continuous delivery and continuous testing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It also debuted atop the US Billboard Top Rock Albums chart and was later ranked at number 62 on the chart's year-end version. Elsewhere in North America, the album peaked at number 19 on the Billboard Canadian Albums Chart. In the Asia-Pacific region, Notes on a Conditional Form reached the top of the Australian Albums chart, number four on the New Zealand Albums chart, number 14 on the Billboard Japan Hot Albums chart and number 17 on the Japanese Albums chart.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a private VoIP system, the primary telephony system itself is located within the private infrastructure of the end-user organization. Usually, the system will be deployed on-premises at a site within the direct control of the organization. This can provide numerous benefits in terms of QoS control (see below), cost scalability, and ensuring privacy and security of communications traffic. However, the responsibility for ensuring that the VoIP system remains performant and resilient is predominantly vested in the end-user organization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, it should be possible to optimize x86 code to favor Code Morphing Software, or even for compilers to target the native VLIW architecture directly. However, writing in 2003, Linus Torvalds apparently dismissed these approaches as unrealistic: The native crusoe code \u2013 even if it was documented and available \u2013 is not very conducive to general-purpose OS stuff. It has no notion of memory protection, and there's no MMU for code accesses, so things like kernel modules simply wouldn't work. The translations are usually better than statically compiled native code (because the whole CPU is designed for speculation, and the static compilers don't know how to do that), and thus going to native mode is not necessarily a performance improvement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, BOOK, CHOICE, or DECIDE. The lowercase letters l, o, s, x and z are rotationally symmetrical, while pairs such as b/q, d/p, m/w, n/u, and in some typefaces h/y and a/e, are rotations of each other. Thus, the words \"sos\", \"pod\", \"suns\", \"yeah\", \"swims\", \"dollop\", or \"passed\" form natural rotational ambigrams.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For high-dimensional problems, the exact computation of the Hessian is usually prohibitively expensive, and even its storage can be problematic, requiring O ( N 2 ) {\\displaystyle O(N^{2})} memory (but see the limited-memory L-BFGS quasi-Newton method). The conjugate gradient method can also be derived using optimal control theory. In this accelerated optimization theory, the conjugate gradient method falls out as a nonlinear optimal feedback controller, u = k ( x , x \u02d9 ) := \u2212 \u03b3 a \u2207 x f ( x ) \u2212 \u03b3 b x \u02d9 {\\displaystyle u=k(x,{\\dot {x}}):=-\\gamma _{a}\\nabla _{x}f(x)-\\gamma _{b}{\\dot {x}}} for the double integrator system, x \u00a8 = u {\\displaystyle {\\ddot {x}}=u} The quantities \u03b3 a > 0 {\\displaystyle \\gamma _{a}>0} and \u03b3 b > 0 {\\displaystyle \\gamma _{b}>0} are variable feedback gains.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, the trace of the matrix equals the sum of its eigenvalues. From this point of view, we can define the pseudo-determinant for a singular matrix to be the product of its nonzero eigenvalues (the density of multivariate normal distribution will need this quantity). In many applications, such as PageRank, one is interested in the dominant eigenvalue, i.e. that which is largest in absolute value. In other applications, the smallest eigenvalue is important, but in general, the whole spectrum provides valuable information about a matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "B1 generates a random bit b in a secure laboratory and gives it to A1 at a time t1. B0 and B1 communicate a {\\displaystyle a} and b through a secure and authenticated channel. Similarly, A0 and A1 communicate a {\\displaystyle a} and b through a secure and authenticated channel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a random recursive tree is a rooted tree chosen uniformly at random from the recursive trees with a given number of vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "See  for more details on complex applications. Metaheuristics fall in two categories: trajectory-based metaheuristics and population-based metaheuristics. The main difference of these two kind of methods relies in the number of tentative solutions used in each step of the (iterative) algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In orbital mechanics, a frozen orbit is an orbit for an artificial satellite in which natural drifting due to the central body's shape has been minimized by careful selection of the orbital parameters. Typically, this is an orbit in which, over a long period of time, the satellite's altitude remains constant at the same point in each orbit. Changes in the inclination, position of the apsis of the orbit, and eccentricity have been minimized by choosing initial values so that their perturbations cancel out., which results in a long-term stable orbit that minimizes the use of station-keeping propellant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle |S|.} Obviously | S | = \u0394 ( C o u t ( m 1 ) , C o u t ( m 2 ) ) \u2a7e ( 1 \u2212 R ) N {\\displaystyle |S|=\\Delta (C_{out}(m_{1}),C_{out}(m_{2}))\\geqslant (1-R)N} . Due to the Wozencraft Ensemble Theorem, there are at most \u03b5 N {\\displaystyle \\varepsilon N} linear codes having distance less than H q \u2212 1 ( 1 2 \u2212 \u03b5 ) \u22c5 2 k , {\\displaystyle H_{q}^{-1}({\\tfrac {1}{2}}-\\varepsilon )\\cdot 2k,} so T \u2a7e | S | \u2212 \u03b5 N \u2a7e ( 1 \u2212 R ) N \u2212 \u03b5 N = ( 1 \u2212 R \u2212 \u03b5 ) N .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regular grammars, the left hand side is again only a single nonterminal symbol, but now the right-hand side is also restricted. The right side may be the empty string, or a single terminal symbol, or a single terminal symbol followed by a nonterminal symbol, but nothing else. (Sometimes a broader definition is used: one can allow longer strings of terminals or single nonterminals without anything else, making languages easier to denote while still defining the same class of languages.) The language { a n b n \u2223 n \u2265 1 } {\\displaystyle \\left\\{a^{n}b^{n}\\mid n\\geq 1\\right\\}} defined above is not regular, but the language { a n b m \u2223 m , n \u2265 1 } {\\displaystyle \\left\\{a^{n}b^{m}\\mid m,n\\geq 1\\right\\}} (at least 1 a {\\displaystyle a} followed by at least 1 b {\\displaystyle b} , where the numbers may be different) is, as it can be defined by the grammar G 3 {\\displaystyle G_{3}} with N = { S , A , B } {\\displaystyle N=\\left\\{S,A,B\\right\\}} , \u03a3 = { a , b } {\\displaystyle \\Sigma =\\left\\{a,b\\right\\}} , S {\\displaystyle S} the start symbol, and the following production rules: S \u2192 a A {\\displaystyle S\\rightarrow aA} A \u2192 a A {\\displaystyle A\\rightarrow aA} A \u2192 b B {\\displaystyle A\\rightarrow bB} B \u2192 b B {\\displaystyle B\\rightarrow bB} B \u2192 \u03f5 {\\displaystyle B\\rightarrow \\epsilon } All languages generated by a regular grammar can be recognized in O ( n ) {\\displaystyle O(n)} time by a finite-state machine. Although in practice, regular grammars are commonly expressed using regular expressions, some forms of regular expression used in practice do not strictly generate the regular languages and do not show linear recognitional performance due to those deviations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Dickson's lemma states that every set of n {\\displaystyle n} -tuples of natural numbers has finitely many minimal elements. This simple fact from combinatorics has become attributed to the American algebraist L. E. Dickson, who used it to prove a result in number theory about perfect numbers. However, the lemma was certainly known earlier, for example to Paul Gordan in his research on invariant theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Furthermore, rectangles can exist (a statement equivalent to the parallel postulate) only in Euclidean geometry. A Saccheri quadrilateral is a quadrilateral which has two sides of equal length, both perpendicular to a side called the base. The other two angles of a Saccheri quadrilateral are called the summit angles and they have equal measure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers. Stated another way, the set of solutions in integers x, y, n, m of the exponential diophantine equation y m = x n + 1 , {\\displaystyle y^{m}=x^{n}+1,} for exponents n and m greater than one, is finite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a Pitman\u2013Yor process denoted PY(d, \u03b8, G0), is a stochastic process whose sample path is a probability distribution. A random sample from this process is an infinite discrete probability distribution, consisting of an infinite set of atoms drawn from G0, with weights drawn from a two-parameter Poisson-Dirichlet distribution. The process is named after Jim Pitman and Marc Yor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sequential search models are used in the field of finance to examine how investors look for information on stocks and other financial assets. The assumption that consumers know what they are looking for and what the standard of the product or service should be is one of the limitations of sequential search models. This presumption might not always be accurate in practical circumstances. Another drawback is that sequential search models don't account for the possibility that customers could find out more about the calibre of a good or service as they search further.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Forwarding (described below) helps correct such errors by depending on the fact that the output of i1 (which is 3) can be used by subsequent instructions before the value 3 is committed to/stored in Register 1. Forwarding applied to the example means that there is no wait to commit/store the output of i1 in Register 1 (in this example, the output is 3) before making that output available to the subsequent instruction (in this case, i2).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "He believed that scientific analysis would lead to the discovery of the \"one best way\" to do things or carrying out an operation. This, according to him could help save cost and time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, Veblen's theorem applies also to disconnected graphs, and can be generalized to infinite graphs in which every vertex has finite degree (Sabidussi 1964). If a countably infinite graph G has no odd-degree vertices, then it may be written as a union of disjoint (finite) simple cycles if and only if every finite subgraph of G can be extended (by including more edges and vertices from G) to a finite Eulerian graph. In particular, every countably infinite graph with only one end and with no odd vertices can be written as a union of disjoint cycles (Sabidussi 1964).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "n j = \u2211 i = 1 N ( q i = j ) {\\displaystyle n_{j}=\\sum _{i=1}^{N}(q_{i}=j)} The total number of permutation of q \u2192 {\\displaystyle {\\vec {q}}} can be represented by a multinomial as N ! \u220f j = 0 k n j ! {\\displaystyle {\\frac {N!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "IBM however developed their Multiprocessor Interrupt Controller (MPIC) based on the OpenPIC register specification. In the reference IBM design, the processors share the MPIC over a DCR bus, with their access to the bus controlled by a DCR Arbiter. MPIC supports up to four processors and up to 128 interrupt sources.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pharmacology and biochemistry, mode of action (MoA) describes a functional or anatomical change, resulting from the exposure of a living organism to a substance. In comparison, a mechanism of action (MOA) describes such changes at the molecular level.A mode of action is important in classifying chemicals, as it represents an intermediate level of complexity in between molecular mechanisms and physiological outcomes, especially when the exact molecular target has not yet been elucidated or is subject to debate. A mechanism of action of a chemical could be \"binding to DNA\" while its broader mode of action would be \"transcriptional regulation\". However, there is no clear consensus and the term mode of action is also often used, especially in the study of pesticides, to describe molecular mechanisms such as action on specific nuclear receptors or enzymes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the academic field of films and cinema, several studies involving research have discovered a positive connection between film critics evaluating films and how well the films perform with audience members. Also, studies involving research in the fields of films and cinema have discovered a connection between film critics evaluating films and audience members having interests or no interests in viewing those films. Based in the perspective of an audience member, a review serves as more than an object that is useful for making decisions. Listening to a review from a critic, watching a critic's review, and reading a critic's review are all ways in which the review is useful to an audience member. The critic's review is able to be referenced in conversations where audience members communicate with other individuals, and audience members can communicate messages about the artistic film that was critically examined or connect the criticism to problems that occur in society.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real mode, the interrupt table is called IVT (interrupt vector table). Up to the 80286, the IVT always resided at the same location in memory, ranging from 0x0000 to 0x03ff, and consisted of 256 far pointers. Hardware interrupts may be mapped to any of the vectors by way of a programmable interrupt controller. On the 80286 and later, the size and locations of the IVT can be changed in the same way as it is done with the IDT (Interrupt descriptor table) in protected mode (i.e., via the LIDT (Load Interrupt Descriptor Table Register) instruction) though it does not change the format of it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Deterministic context-free grammars were particularly useful because they could be parsed sequentially by a deterministic pushdown automaton, which was a requirement due to computer memory constraints. In 1965, Donald Knuth invented the LR(k) parser and proved that there exists an LR(k) grammar for every deterministic context-free language. This parser still required a lot of memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 3568, 13568, 34568, and 134568 are the patterns related to Braille pattern dots-2456, since the two additional dots of kantenji patterns 02456, 24567, and 024567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the branch of linguistics known as pragmatics, a presupposition (or PSP) is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. Examples of presuppositions include: Jane no longer writes fiction. Presupposition: Jane once wrote fiction. Have you stopped eating meat?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the capacitated arc routing problem (CARP) is that of finding the shortest tour with a minimum graph/travel distance of a mixed graph with undirected edges and directed arcs given capacity constraints for objects that move along the graph that represent snow-plowers, street sweeping machines, or winter gritters, or other real-world objects with capacity constraints. The constraint can be imposed for the length of time the vehicle is away from the central depot, or a total distance traveled, or a combination of the two with different weighting factors. There are many different variations of the CARP described in the book Arc Routing:Problems, Methods, and Applications by \u00c1ngel Corber\u00e1n and Gilbert Laporte.Solving the CARP involves the study of graph theory, arc routing, operations research, and geographical routing algorithms to find the shortest path efficiently. The CARP is NP-hard arc routing problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1990s, when desktop mapping and presentation graphics became accessible to the average office user, data2map hired software engineers and GIS-specialists to develop several vector-map series for easy customization by the end user. The prime objective was to enable office users and professional graphics artists to visualize geo-referenced information on pre-designed country- and world-maps within their favorite standard off-the-shelf software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These also may include full copies of the system images from which machines have their operating systems initially installed, or available for repair of any system files that may get corrupted during a machine's lifecycle. Some software may require quite substantial storage space or might be undergoing rapid (perhaps internal) development. In those cases the software may be installed on, and configured to be run directly from, the file servers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. According to the Pythagorean theorem, for a triangle with sides a {\\displaystyle a} and b {\\displaystyle b} , this length can be calculated as where \u2295 {\\displaystyle \\oplus } denotes the Pythagorean addition operation.This operation can be used in the conversion of Cartesian coordinates to polar coordinates. It also provides a simple notation and terminology for some formulas when its summands are complicated; for example, the energy-momentum relation in physics becomes It is implemented in many programming libraries as the hypot function, in a way designed to avoid errors arising due to limited-precision calculations performed on computers. In its applications to signal processing and propagation of measurement uncertainty, the same operation is also called addition in quadrature.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Over time, less key travel was accepted in the market, finally landing on 0.110 inches (2.79 mm). Coincident with this, Key Tronic was the first company to introduce a keyboard that was only about one inch thick.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples of their use are: In quantum teleportation, a classical channel together with a previously prepared entangled quantum state are used to transmit quantum information between two parties. Neither the classical channel nor the previously prepared quantum state alone can do this task. In quantum cryptography, a classical channel is used along with a quantum channel in protocols for quantum key exchange. In quantum communication, the information rate of a noisy quantum channel can be increased when used together with a noise-free classical channel. In particular, some very noisy quantum channels cannot transmit quantum information if used alone but can transmit it if used together with a classical channel (which is not capable of transmitting quantum information by itself).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, an arithmetic number is an integer for which the average of its positive divisors is also an integer. For instance, 6 is an arithmetic number because the average of its divisors is 1 + 2 + 3 + 6 4 = 3 , {\\displaystyle {\\frac {1+2+3+6}{4}}=3,} which is also an integer. However, 2 is not an arithmetic number because its only divisors are 1 and 2, and their average 3/2 is not an integer. The first numbers in the sequence of arithmetic numbers are 1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, ... (sequence A003601 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In older distributors, adjusting the ignition timing is usually achieved through both mechanical advance and vacuum advance. Mechanical advance adjusts the timing based on the engine speed (rpm), using a set of hinged weights attached to the distributor shaft. These weights cause the breaker points mounting plate to slightly rotate, thereby advancing the ignition timing. Vacuum advance typically uses manifold vacuum to adjust the ignition timing, for example to improve fuel economy and driveability when minimal power is required from the engine. Most distributors used on electronic fuel injection engines use electronics to adjust the ignition timing, instead of vacuum and centrifugal systems. This allows the ignition timing to be optimised based on factors other than engine speed and manifold vacuum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Current views vary on whether all languages have a verb phrase; some schools of generative grammar (such as principles and parameters) hold that all languages have a verb phrase, while others (such as lexical functional grammar) take the view that at least some languages lack a verb phrase constituent, including those languages with a very free word order (the so-called non-configurational languages, such as Japanese, Hungarian, or Australian aboriginal languages), and some languages with a default VSO order (several Celtic and Oceanic languages). Phrase structure grammars view both finite and nonfinite verb phrases as constituent phrases and, consequently, do not draw any key distinction between them. Dependency grammars (described below) are much different in this regard.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metropolitan areas, FOMA uses the UMTS band I around 2100 MHz, which has been originally assigned to IMT-2000 services worldwide, except in the Americas. In order to improve coverage in rural and mountainous areas, NTT DoCoMo also offers FOMA services in the 800 MHz band originally assigned to the 2G PDC mova service, which corresponds to UMTS band VI and is similar to band V used in the United States. These extended service areas are branded FOMA Plus-Area (FOMA\u30d7\u30e9\u30b9\u30a8\u30ea\u30a2) and require multiband terminals. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To emphasize that there are an infinite number of terms, a series may be called an infinite series. Such a series is represented (or denoted) by an expression like or, using the summation sign, The infinite sequence of additions implied by a series cannot be effectively carried on (at least in a finite amount of time). However, if the set to which the terms and their finite sums belong has a notion of limit, it is sometimes possible to assign a value to a series, called the sum of the series.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Kent's coin tossing protocol, Alice has two agents A0 and A1, and Bob has two agents B0 and B1. Ai and Bi are at location Li, for i \u2208 { 0 , 1 } {\\displaystyle i\\in \\{0,1\\}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience. Applications of network theory include logistical networks, the World Wide Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc.; see List of network theory topics for more examples. Euler's solution of the Seven Bridges of K\u00f6nigsberg problem is considered to be the first true proof in the theory of networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Starting from the basic fact stated above that, for any positive integer n {\\displaystyle n} , b n {\\displaystyle b^{n}} is n {\\displaystyle n} occurrences of b {\\displaystyle b} all multiplied by each other, several other properties of exponentiation directly follow. In particular: In other words, when multiplying a base raised to one exponent by the same base raised to another exponent, the exponents add. From this basic rule that exponents add, we can derive that b 0 {\\displaystyle b^{0}} must be equal to 1 for any b \u2260 0 {\\displaystyle b\\neq 0} , as follows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In star topology, every peripheral node (computer workstation or any other peripheral) is connected to a central node called a hub or switch. The hub is the server and the peripherals are the clients. The network does not necessarily have to resemble a star to be classified as a star network, but all of the peripheral nodes on the network must be connected to one central hub. All traffic that traverses the network passes through the central hub, which acts as a signal repeater.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Under one definition, an undirected hypergraph ( X , E ) {\\displaystyle (X,E)} is a directed hypergraph which has a symmetric edge set: If ( D , C ) \u2208 E {\\displaystyle (D,C)\\in E} then ( C , D ) \u2208 E {\\displaystyle (C,D)\\in E} . For notational simplicity one can remove the \"duplicate\" hyperedges since the modifier \"undirected\" is precisely informing us that they exist: If ( D , C ) \u2208 E {\\displaystyle (D,C)\\in E} then ( C , D ) \u2208 \u2192 E {\\displaystyle (C,D){\\vec {\\in }}E} where \u2208 \u2192 {\\displaystyle {\\vec {\\in }}} means implicitly in. While graph edges connect only 2 nodes, hyperedges connect an arbitrary number of nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real-time computing, the priority ceiling protocol is a synchronization protocol for shared resources to avoid unbounded priority inversion and mutual deadlock due to wrong nesting of critical sections. In this protocol each resource is assigned a priority ceiling, which is a priority equal to the highest priority of any task which may lock the resource. The protocol works by temporarily raising the priorities of tasks in certain situations, thus it requires a scheduler that supports dynamic priority scheduling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-agent system research, distributed knowledge is all the knowledge that a community of agents possesses and might apply in solving a problem. Distributed knowledge is approximately what \"a wise man knows\", or what someone who has complete knowledge of what each member of the community knows knows. Distributed knowledge might also be called the aggregate knowledge of a community, as it represents all the knowledge that a community might bring to bear to solve a problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, various sublanguages of set theory are decidable. These include: Sets with Monotone, Additive, and Multiplicative Functions. Sets with restricted quantifiers. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to define a specific proof of knowledge, one need not only define the language, but also the witnesses the verifier should know. In some cases proving membership in a language may be easy, while computing a specific witness may be hard. This is best explained using an example: Let \u27e8 g \u27e9 {\\displaystyle \\langle g\\rangle } be a cyclic group with generator g {\\displaystyle g} in which solving the discrete logarithm problem is believed to be hard. Deciding membership of the language L = { x \u2223 g w = x } {\\displaystyle L=\\{x\\mid g^{w}=x\\}} is trivial, as every x {\\displaystyle x} is in \u27e8 g \u27e9 {\\displaystyle \\langle g\\rangle } . However, finding the witness w {\\displaystyle w} such that g w = x {\\displaystyle g^{w}=x} holds corresponds to solving the discrete logarithm problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in order theory and functional analysis, the order dual of an ordered vector space X {\\displaystyle X} is the set Pos \u2061 ( X \u2217 ) \u2212 Pos \u2061 ( X \u2217 ) {\\displaystyle \\operatorname {Pos} \\left(X^{*}\\right)-\\operatorname {Pos} \\left(X^{*}\\right)} where Pos \u2061 ( X \u2217 ) {\\displaystyle \\operatorname {Pos} \\left(X^{*}\\right)} denotes the set of all positive linear functionals on X {\\displaystyle X} , where a linear function f {\\displaystyle f} on X {\\displaystyle X} is called positive if for all x \u2208 X , {\\displaystyle x\\in X,} x \u2265 0 {\\displaystyle x\\geq 0} implies f ( x ) \u2265 0. {\\displaystyle f(x)\\geq 0.} The order dual of X {\\displaystyle X} is denoted by X + {\\displaystyle X^{+}} . Along with the related concept of the order bound dual, this space plays an important role in the theory of ordered topological vector spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Typically both transactions will be cancelled and rolled back, and then they will be started again in a different order, automatically, so that the deadlock doesn't occur again. Or sometimes, just one of the deadlocked transactions will be cancelled, rolled back, and automatically restarted after a short delay. Deadlocks can also occur among three or more transactions. The more transactions involved, the more difficult they are to detect, to the point that transaction processing systems find there is a practical limit to the deadlocks they can detect.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Nemenyi test is a post-hoc test intended to find the groups of data that differ after a global statistical test (such as the Friedman test) has rejected the null hypothesis that the performance of the comparisons on the groups of data is similar. The test makes pair-wise tests of performance. The test is named after Peter Nemenyi.The test is sometimes referred to as the \"Nemenyi\u2013Damico\u2013Wolfe test\", when regarding one-sided multiple comparisons of \"treatments\" versus \"control\", but it can also be referred to as the \"Wilcoxon\u2013Nemenyi\u2013McDonald\u2013Thompson test\", when regarding two-sided multiple comparisons of \"treatments\" versus \"treatments\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To make the perfect and pluperfect tenses, the first consonant of the verb's root is usually repeated with the vowel \u03b5 (e), for example: \u03b3\u03c1\u03ac\u03c6\u03c9, \u03b3\u03ad\u03b3\u03c1\u03b1\u03c6\u03b1 (g\u00e9grapha) \"I write, I have written\", \u03bb\u1fe1\u0301\u03c9, \u03bb\u03ad\u03bb\u03c5\u03ba\u03b1 (l\u016b\u0301\u014d, l\u00e9luka) \"I free, I have freed\", \u03b4\u03b9\u03b4\u03ac\u03c3\u03ba\u03c9, \u03b4\u03b5\u03b4\u03af\u03b4\u03b1\u03c7\u03b1 (did\u00e1sk\u014d, ded\u00eddakha) \"I teach, I have taught\" (all present, perfect). This is called \"reduplication\". Some verbs, however, where reduplication is not convenient, use an augment instead, e.g. \u1f14\u03c3\u03c7\u03bf\u03bd, \u1f14\u03c3\u03c7\u03b7\u03ba\u03b1 (\u00e9skhon, \u00e9skh\u0113ka) \"I had, I have had\" (aorist, perfect), \u03b5\u1f51\u03c1\u03af\u03c3\u03ba\u03c9, \u03b7\u1f55\u03c1\u03b7\u03ba\u03b1 (heur\u00edsk\u014d, h\u0113\u00far\u0113ka) \"I find, I have found\" (present, perfect). This reduplication or perfect-tense augment appears in every part of the verb, not in the indicative only.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Knuth himself attributes the first study of multisets to the Indian mathematician Bh\u0101skar\u0101ch\u0101rya, who described permutations of multisets around 1150. Other names have been proposed or used for this concept, including list, bunch, bag, heap, sample, weighted set, collection, and suite. : 694", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Picture Concepts task, children have presented with a series of pictures on two or three rows and asked which pictures (one from each row) belong together based on some common characteristic. This task assesses the child's ability to discover the underlying characteristic (e.g., rule, concept, trend, class membership) that governs a set of materials.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Kolmogorov\u2013Smirnov statistic quantifies a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two samples. The null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the reference distribution (in the one-sample case) or that the samples are drawn from the same distribution (in the two-sample case). In the one-sample case, the distribution considered under the null hypothesis may be continuous (see Section 2), purely discrete or mixed (see Section 2.2).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational database management systems, a unique key is a candidate key. All the candidate keys of a relation can uniquely identify the records of the relation, but only one of them is used as the primary key of the relation. The remaining candidate keys are called unique keys because they can uniquely identify a record in a relation. Unique keys can consist of multiple columns.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "}}\\end{cases}}} Euler's criterion can be concisely reformulated using the Legendre symbol: ( a p ) \u2261 a p \u2212 1 2 ( mod p ) . {\\displaystyle \\left({\\frac {a}{p}}\\right)\\equiv a^{\\tfrac {p-1}{2}}{\\pmod {p}}.} The criterion first appeared in a 1748 paper by Leonhard Euler.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In straight line fitting, the model is y i = \u03b1 + \u03b2 x i + \u03b5 i {\\displaystyle y_{i}=\\alpha +\\beta x_{i}+\\varepsilon _{i}\\,} where y i {\\displaystyle y_{i}} is the response variable, x i {\\displaystyle x_{i}} is the explanatory variable, \u03b5i is the random error, and \u03b1 {\\displaystyle \\alpha } and \u03b2 {\\displaystyle \\beta } are parameters. The mean, and predicted, response value for a given explanatory value, xd, is given by y ^ d = \u03b1 ^ + \u03b2 ^ x d , {\\displaystyle {\\hat {y}}_{d}={\\hat {\\alpha }}+{\\hat {\\beta }}x_{d},} while the actual response would be y d = \u03b1 + \u03b2 x d + \u03b5 d {\\displaystyle y_{d}=\\alpha +\\beta x_{d}+\\varepsilon _{d}\\,} Expressions for the values and variances of \u03b1 ^ {\\displaystyle {\\hat {\\alpha }}} and \u03b2 ^ {\\displaystyle {\\hat {\\beta }}} are given in linear regression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Within distributed morphology (DM), this is where morphological structure is constructed, where the hierarchical syntactic structure is transformed into a linearized structure, and syntactic features are replaced with vocabulary items, among other things.According to some theories of prosody, the prosodic representation is derived with direct reference to the hierarchical syntactic structure. For example, Selkirk (2011, and others) proposes that prosodic structure is constructed by a process of matching, although imperfectly, prosodic constituents to syntactic constituents. Kahnemuyipour (2009) demonstrates, using evidence from several languages, how information structure can be represented in the transfer from syntax to phonology, arguing that transfer can only be uni-directional, from syntax to phonology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle p_{w}(s)={\\frac {\\pi s}{2}}e^{-\\pi s^{2}/4}.} Here, s = S D {\\displaystyle s={\\frac {S}{D}}} where S is a particular spacing and D is the mean distance between neighboring intervals.In a mixed sequence (spin and parity are different), the probability density function can be obtained by randomly superimposing simple sequences.The above result is exact for 2 \u00d7 2 {\\displaystyle 2\\times 2} real symmetric matrices M {\\displaystyle M} , with elements that are independent standard gaussian random variables, with joint distribution proportional to e \u2212 1 2 T r ( M 2 ) = e \u2212 1 2 T r ( a b b c ) 2 = e \u2212 1 2 a 2 \u2212 1 2 c 2 \u2212 b 2 . {\\displaystyle e^{-{\\frac {1}{2}}{\\rm {Tr}}(M^{2})}=e^{-{\\frac {1}{2}}{\\rm {Tr}}\\left({\\begin{array}{cc}a&b\\\\b&c\\\\\\end{array}}\\right)^{2}}=e^{-{\\frac {1}{2}}a^{2}-{\\frac {1}{2}}c^{2}-b^{2}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modified policy iteration (van Nunen 1976; Puterman & Shin 1978), step one is performed once, and then step two is repeated several times. Then step one is again performed once and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the years 1994 to 2004 the elder 5-ton van 'VaMoRs' was used to develop the capabilities needed for driving on networks of minor (also unsealed) roads and for cross-country driving including avoidance of negative obstacles like ditches. Turning off onto crossroads of unknown width and intersection angles required a big effort, but has been achieved with \"Expectation-based, Multi-focal, Saccadic vision\" (EMS-vision). This vertebrate-type vision uses animation capabilities based on knowledge about subject classes (including the autonomous vehicle itself) and their potential behaviour in certain situations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantitative linguistics, linguistic laws are statistical regularities emerging across different linguistic scales (i.e. phonemes, syllables, words or sentences) that can be formulated mathematically and that have been deduced from certain theoretical assumptions. They are also required to have been successfully tested through the use of data, that is, not to have been refuted by empirical evidence. Among the main linguistic laws proposed by various authors, the following can be highlighted: Zipf's law: The frequency of words is inversely proportional to their rank in frequency lists. Similar distribution between rank and frequency of sounds, phonemes, and letters can be observed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The numbers 3 {\\displaystyle {\\sqrt {3}}} and 2 3 {\\displaystyle 2{\\sqrt {3}}} are also commensurable because their ratio, 3 2 3 = 1 2 {\\textstyle {\\frac {\\sqrt {3}}{2{\\sqrt {3}}}}={\\frac {1}{2}}} , is a rational number. However, the numbers 3 {\\textstyle {\\sqrt {3}}} and 2 are incommensurable because their ratio, 3 2 {\\textstyle {\\frac {\\sqrt {3}}{2}}} , is an irrational number. More generally, it is immediate from the definition that if a and b are any two non-zero rational numbers, then a and b are commensurable; it is also immediate that if a is any irrational number and b is any non-zero rational number, then a and b are incommensurable. On the other hand, if both a and b are irrational numbers, then a and b may or may not be commensurable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Information can be transmitted either during the given time interval, or encoded as the presence or absence of a change in the received signal.Significant conditions are recognized by an appropriate device called a receiver, demodulator, or decoder. The decoder translates the actual signal received into its intended logical value such as a binary digit (0 or 1), an alphabetic character, a mark, or a space. Each significant instant is determined when the appropriate device assumes a condition or state usable for performing a specific function, such as recording, processing, or gating.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the branch of combinatorics, a graded poset is a partially-ordered set (poset) P equipped with a rank function \u03c1 from P to the set N of all natural numbers. \u03c1 must satisfy the following two properties: The rank function is compatible with the ordering, meaning that for all x and y in the order, if x < y then \u03c1(x) < \u03c1(y), and The rank is consistent with the covering relation of the ordering, meaning that for all x and y, if y covers x then \u03c1(y) = \u03c1(x) + 1.The value of the rank function for an element of the poset is called its rank. Sometimes a graded poset is called a ranked poset but that phrase has other meanings; see Ranked poset. A rank or rank level of a graded poset is the subset of all the elements of the poset that have a given rank value.Graded posets play an important role in combinatorics and can be visualized by means of a Hasse diagram.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most variants of realizability begin with a theorem that any statement that is provable in the formal system being studied is realizable. The realizer, however, usually gives more information about the formula than a formal proof would directly provide. Beyond giving insight into intuitionistic provability, realizability can be applied to prove the disjunction and existence properties for intuitionistic theories and to extract programs from proofs, as in proof mining. It is also related to topos theory via realizability topoi.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (or mechanism) for addition throughout the whole range. For a given number of places half of the possible representations of numbers encode the positive numbers, the other half represents their respective additive inverses. The pairs of mutually additive inverse numbers are called complements. Thus subtraction of any number is implemented by adding its complement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This means that the justification ensures that the belief is true. For example, Richard Kirkham argues that the justification required for knowledge must be based on self-evident premises that deductively entail the held belief.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, trellis modulation (also known as trellis coded modulation, or simply TCM) is a modulation scheme that transmits information with high efficiency over band-limited channels such as telephone lines. Gottfried Ungerboeck invented trellis modulation while working for IBM in the 1970s, and first described it in a conference paper in 1976. It went largely unnoticed, however, until he published a new, detailed exposition in 1982 that achieved sudden and widespread recognition. In the late 1980s, modems operating over plain old telephone service (POTS) typically achieved 9.6 kbit/s by employing four bits per symbol QAM modulation at 2,400 baud (symbols/second). This bit rate ceiling existed despite the best efforts of many researchers, and some engineers predicted that without a major upgrade of the public phone infrastructure, the maximum achievable rate for a POTS modem might be 14 kbit/s for two-way communication (3,429 baud \u00d7 4 bits/symbol, using QAM).14 kbit/s is only 40% of the theoretical maximum bit rate predicted by Shannon's theorem for POTS lines (approximately 35 kbit/s). Ungerboeck's theories demonstrated that there was considerable untapped potential in the system, and by applying the concept to new modem standards, speed rapidly increased to 14.4, 28.8 and ultimately 33.6 kbit/s.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Indeed, a greedy algorithm finds the k-combination corresponding to N: take ck maximal with ( c k k ) \u2264 N {\\displaystyle {\\tbinom {c_{k}}{k}}\\leq N} , then take ck\u22121 maximal with ( c k \u2212 1 k \u2212 1 ) \u2264 N \u2212 ( c k k ) {\\displaystyle {\\tbinom {c_{k-1}}{k-1}}\\leq N-{\\tbinom {c_{k}}{k}}} , and so forth. Finding the number N, using the formula above, from the k-combination (ck, ..., c2, c1) is also known as \"ranking\", and the opposite operation (given by the greedy algorithm) as \"unranking\"; the operations are known by these names in most computer algebra systems, and in computational mathematics.The originally used term \"combinatorial representation of integers\" was shortened to \"combinatorial number system\" by Knuth, who also gives a much older reference; the term \"combinadic\" is introduced by James McCaffrey (without reference to previous terminology or work). Unlike the factorial number system, the combinatorial number system of degree k is not a mixed radix system: the part ( c i i ) {\\displaystyle {\\tbinom {c_{i}}{i}}} of the number N represented by a \"digit\" ci is not obtained from it by simply multiplying by a place value. The main application of the combinatorial number system is that it allows rapid computation of the k-combination that is at a given position in the lexicographic ordering, without having to explicitly list the k-combinations preceding it; this allows for instance random generation of k-combinations of a given set. Enumeration of k-combinations has many applications, among which are software testing, sampling, quality control, and the analysis of lottery games.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It waits for the child that slept 10 seconds first; all the others have long since exited, so all of the messages (except the first) appear in quick succession. There is no possibility of random ordering here, since it is driven by a loop in a single process. The first parent message actually appeared before any of the children messages - the parent was able to continue into the second loop before any of the child processes were able to start.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to route calls to a phone, cell towers listen for a signal sent from the phone and negotiate which tower is best able to communicate with the phone. As the phone changes location, the antenna towers monitor the signal, and the phone is \"roamed\" to an adjacent tower as appropriate. By comparing the relative signal strength from multiple antenna towers, a general location of a phone can be roughly determined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here \u03b1 can be large. The following form of this inequality is often seen in more analytic contexts: with the same assumptions on f, for every p \u2208 U there is a possibly smaller open neighborhood W of p and constants \u03b8 \u2208 (0,1) and c > 0 such that | f ( x ) \u2212 f ( p ) | \u03b8 \u2264 c | \u2207 f ( x ) | . {\\displaystyle |f(x)-f(p)|^{\\theta }\\leq c|\\nabla f(x)|.} A special case of the \u0141ojasiewicz inequality, due to Polyak, is commonly used to prove linear convergence of gradient descent algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These ran UTX-32, Gould's version of Unix based on a BSD 4.2 kernel developed by Purdue University to support multiprocessor systems. The Powernode 9080 was a symmetrical dual processor system, with both processors having full access to memory and the I/O bus, and capable of being booted up from either processor. It was the first such commercially available system to run any version of Unix.The CPU for these system ballooned to about a dozen boards because of the low-density ECL chip footprint.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the category of sets, injections, surjections, and bijections correspond precisely to monomorphisms, epimorphisms, and isomorphisms, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Failure modes analysis is used to identify and order the impediments to reuse in a given organization. Reusability metrics indicate the likelihood that an artifact is reusable. Reuse library metrics are used to manage and track usage of a reuse repository.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the theory can be traced to Laplace, the formalization started with insurance mathematics, namely ruin theory with Cram\u00e9r and Lundberg. A unified formalization of large deviation theory was developed in 1966, in a paper by Varadhan. Large deviations theory formalizes the heuristic ideas of concentration of measures and widely generalizes the notion of convergence of probability measures. Roughly speaking, large deviations theory concerns itself with the exponential decline of the probability measures of certain kinds of extreme or tail events.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the term \"standard of review\" has several different meanings in different contexts and thus there are several standards of review on appeal used in federal courts depending on the nature of the question being appealed and the body that made the decision.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of mathematics called combinatorial group theory, the Schreier coset graph is a graph associated with a group G, a generating set {xi: i in I } of G, and a subgroup H \u2264 G. The Schreier graph encodes the abstract structure of a group modulo an equivalence relation formed by the coset. The graph is named after Otto Schreier, who used the term \u201cNebengruppenbild\u201d. An equivalent definition was made in an early paper of Todd and Coxeter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The maximum number of edges for an undirected graph is ( | V | 2 ) = | V | ( | V | \u2212 1 ) 2 {\\displaystyle {\\binom {|V|}{2}}={\\frac {|V|(|V|-1)}{2}}} , so the maximal density is 1 (for complete graphs) and the minimal density is 0 (Coleman & Mor\u00e9 1983). For families of graphs of increasing size, one often calls them sparse if D \u2192 0 {\\displaystyle D\\rightarrow 0} as | V | \u2192 \u221e {\\displaystyle |V|\\rightarrow \\infty } . Sometimes, in computer science, a more restrictive definition of sparse is used like | E | = O ( | V | log \u2061 | V | ) {\\displaystyle |E|=O(|V|\\log |V|)} or even | E | = O ( | V | ) {\\displaystyle |E|=O(|V|)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "( k \u2212 1 ) ! ( k + \u03c1 ) ! .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One may also regard the unit type as the type of 0-tuples, i.e. the product of no types. The unit type is the terminal object in the category of types and typed functions. It should not be confused with the zero or bottom type, which allows no values and is the initial object in this category.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The UNIVAC 1004 was a plug-board programmed punched card data processing system, introduced in 1962 by UNIVAC. Total memory was 961 characters (6 bits) of core memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Common notions such as injectivity and surjectivity can be expressed in a bounded fashion as well, and thus so is bijectivity. Both of these tie in to notions of size. Importantly, injection existence between any two sets provides a preorder.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is a generalization and improvement of the MINRES method due to Paige and Saunders in 1975. The MINRES method requires that the matrix is symmetric, but has the advantage that it only requires handling of three vectors. GMRES is a special case of the DIIS method developed by Peter Pulay in 1980. DIIS is applicable to non-linear systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\forall y\\in Y,\\exists x\\in X{\\text{ such that }}y=f(x).} The function is bijective (one-to-one and onto, one-to-one correspondence, or invertible) if each element of the codomain is mapped to by exactly one element of the domain. That is, the function is both injective and surjective.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This resulted in the move to use microkernels which used a minimal set of the operating system functions. Systems such as Mach at Carnegie Mellon University and ChorusOS at INRIA were examples of early microkernels.The separation of the operating system into separate components became necessary as supercomputers developed different types of nodes, e.g., compute nodes versus I/O nodes. Thus modern supercomputers usually run different operating systems on different nodes, e.g., using a small and efficient lightweight kernel such as CNK or CNL on compute nodes, but a larger system such as a Linux-derivative on server and I/O nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The value of \u03c8 ( n ) {\\displaystyle \\psi (n)} for the first few integers n {\\displaystyle n} is: 1, 3, 4, 6, 6, 12, 8, 12, 12, 18, 12, 24, ... (sequence A001615 in the OEIS).The function \u03c8 ( n ) {\\displaystyle \\psi (n)} is greater than n {\\displaystyle n} for all n {\\displaystyle n} greater than 1, and is even for all n {\\displaystyle n} greater than 2. If n {\\displaystyle n} is a square-free number then \u03c8 ( n ) = \u03c3 ( n ) {\\displaystyle \\psi (n)=\\sigma (n)} , where \u03c3 ( n ) {\\displaystyle \\sigma (n)} is the divisor function. The \u03c8 {\\displaystyle \\psi } function can also be defined by setting \u03c8 ( p n ) = ( p + 1 ) p n \u2212 1 {\\displaystyle \\psi (p^{n})=(p+1)p^{n-1}} for powers of any prime p {\\displaystyle p} , and then extending the definition to all integers by multiplicativity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following two examples, we always assume it is difficult to factorize a large composite number (see Integer factorization).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Researchers have begun to use deep learning techniques for language modeling as well. In the long history of speech recognition, both shallow form and deep form (e.g. recurrent nets) of artificial neural networks had been explored for many years during 1980s, 1990s and a few years into the 2000s. But these methods never won over the non-uniform internal-handcrafting Gaussian mixture model/Hidden Markov model (GMM-HMM) technology based on generative models of speech trained discriminatively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Eve first captures the photon sent by Alice and then generates another photon to send to Bob. Eve manipulates the phase and timing of the \"faked\" photon in a way that prevents Bob from detecting the presence of an eavesdropper. The only way to eliminate this vulnerability is to eliminate differences in photodetector efficiency, which is difficult to do given finite manufacturing tolerances that cause optical path length differences, wire length differences, and other defects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States there is a rule that wrong-side failures are to be reported to the Federal Railroad Administration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Double negation elimination occurs in classical logics but not in intuitionistic logic. In the context of a formula in the conjunctive normal form, a literal is pure if the literal's complement does not appear in the formula. In Boolean functions, each separate occurrence of a variable, either in inverse or uncomplemented form, is a literal. For example, if A {\\displaystyle A} , B {\\displaystyle B} and C {\\displaystyle C} are variables then the expression A \u00af B C {\\displaystyle {\\bar {A}}BC} contains three literals and the expression A \u00af C + B \u00af C \u00af {\\displaystyle {\\bar {A}}C+{\\bar {B}}{\\bar {C}}} contains four literals. However, the expression A \u00af C + B \u00af C {\\displaystyle {\\bar {A}}C+{\\bar {B}}C} would also be said to contain four literals, because although two of the literals are identical ( C {\\displaystyle C} appears twice) these qualify as two separate occurrences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This value indicates the mapping of the two items. Zero values indicate that no relationship exists. It must be determined if a relationship must be made.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more general sense, each column is treated as a polynomial over GF \u2061 ( 2 8 ) {\\displaystyle \\operatorname {GF} (2^{8})} and is then multiplied modulo 01 16 \u22c5 z 4 + 01 16 {\\displaystyle {01}_{16}\\cdot z^{4}+{01}_{16}} with a fixed polynomial c ( z ) = 03 16 \u22c5 z 3 + 01 16 \u22c5 z 2 + 01 16 \u22c5 z + 02 16 {\\displaystyle c(z)={03}_{16}\\cdot z^{3}+{01}_{16}\\cdot z^{2}+{01}_{16}\\cdot z+{02}_{16}} . The coefficients are displayed in their hexadecimal equivalent of the binary representation of bit polynomials from GF \u2061 ( 2 )  {\\displaystyle \\operatorname {GF} (2)} . The MixColumns step can also be viewed as a multiplication by the shown particular MDS matrix in the finite field GF \u2061 ( 2 8 ) {\\displaystyle \\operatorname {GF} (2^{8})} . This process is described further in the article Rijndael MixColumns.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two mappings are homotopic if one can be continuously deformed into the other. These homotopy classes form a group, called the n-th homotopy group, \u03c0 n ( X ) , {\\displaystyle \\pi _{n}(X),} of the given space X with base point. Topological spaces with differing homotopy groups are never equivalent (homeomorphic), but topological spaces that are not homeomorphic can have the same homotopy groups. The notion of homotopy of paths was introduced by Camille Jordan.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is typically subject to constraints such as: A variable must be initialized before its value is used. In strongly typed languages, each variable is assigned a type, and all uses of the variable must respect its type. Often, its type must be declared explicitly, before use.W-grammars are based on the idea of providing the nonterminal symbols of context-free grammars with attributes (or affixes) that pass information between the nodes of the parse tree, used to constrain the syntax and to specify the semantics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter. For practical statistics problems, it is important to determine the MVUE if one exists, since less-than-optimal procedures would naturally be avoided, other things being equal. This has led to substantial development of statistical theory related to the problem of optimal estimation. While combining the constraint of unbiasedness with the desirability metric of least variance leads to good results in most practical settings\u2014making MVUE a natural starting point for a broad range of analyses\u2014a targeted specification may perform better for a given problem; thus, MVUE is not always the best stopping point.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible set is a convex polytope: a region in multidimensional space whose boundaries are formed by hyperplanes and whose corners are vertices. Constraint satisfaction is the process of finding a point in the feasible region.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As of February 2020, the smallest 23 of the 54 listed numbers have been factored. While the RSA challenge officially ended in 2007, people are still attempting to find the factorizations. According to RSA Laboratories, \"Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, type inference is undecidable. A logic is represented in the LF logical framework by the judgements-as-types representation mechanism. This is inspired by Per Martin-L\u00f6f's development of Kant's notion of judgement, in the 1983 Siena Lectures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A simple algorithm with logarithmic regret is proposed in: UCB-ALP algorithm: The framework of UCB-ALP is shown in the right figure. UCB-ALP is a simple algorithm that combines the UCB method with an Adaptive Linear Programming (ALP) algorithm, and can be easily deployed in practical systems. It is the first work that show how to achieve logarithmic regret in constrained contextual bandits. Although is devoted to a special case with single budget constraint and fixed cost, the results shed light on the design and analysis of algorithms for more general CCB problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, Naming and Design Rules are the formal rules associated with how data elements are structured within a process of creating exchange documents between organizations. Naming and Design Rules are a set of guidelines and naming conventions that go beyond what a single data exchange standard specification will permit. The most common standard that Naming and Design Rules are created on is XML Schema.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ".Both these two groups and the dihedral group are semidirect products of a cyclic group of order 2n\u22121 with a cyclic group of order 2. Such a non-abelian semidirect product is uniquely determined by an element of order 2 in the group of units of the ring Z / 2 n \u2212 1 Z {\\displaystyle \\mathbb {Z} /2^{n-1}\\mathbb {Z} } and there are precisely three such elements, 2 n \u2212 1 \u2212 1 {\\displaystyle 2^{n-1}-1} , 2 n \u2212 2 \u2212 1 {\\displaystyle 2^{n-2}-1} , and 2 n \u2212 2 + 1 {\\displaystyle 2^{n-2}+1} , corresponding to the dihedral group, the quasidihedral, and the modular maximal-cyclic group. The generalized quaternion group, the dihedral group, and the quasidihedral group of order 2n all have nilpotency class n \u2212 1, and are the only isomorphism classes of groups of order 2n with nilpotency class n \u2212 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Because of this need for the traditional channel, the speed of teleportation can be no faster than the speed of light (hence the no-communication theorem is not violated). The main advantage with this is that Bell states can be shared using photons from lasers making teleportation achievable through open space having no need to send information through physical cables or optical fibers. Quantum states can be encoded in various degrees of freedom of atoms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the trace field of a linear group is the field generated by the traces of its elements. It is mostly studied for Kleinian and Fuchsian groups, though related objects are used in the theory of lattices in Lie groups, often under the name field of definition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, voice and video services that are provided using Internet protocol technology may be classified as \u201cinformation services\u201d and therefore not subject to traditional voice or video regulation. The distinction in the 1996 Act between telecommunications services and information services was an outgrowth of a series of FCC Orders and decisions dating back to the 1970s that distinguished between \u201cbasic\u201d services that were subject to regulation and \u201cenhanced\u201d services that the Commission chose not to regulate in order to foster their development and deployment. The Act places on all telecommunications services providers the duty to interconnect \u201c...directly or indirectly with the facilities and equipment of other telecommunications carriers...\u201d Keeping with this regulatory history, the Commission has chosen to forbear from regulating information services, again seeking to foster their development and deployment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The resulting instance will inherit all the methods and properties that were defined in the class, which acts as a kind of template from which similarly typed objects can be constructed. Systems that support ex nihilo object creation allow new objects to be created from scratch without cloning from an existing prototype. Such systems provide a special syntax for specifying the properties and behaviors of new objects without referencing existing objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and social science, a collaboration graph is a graph modeling some social network where the vertices represent participants of that network (usually individual people) and where two distinct participants are joined by an edge whenever there is a collaborative relationship between them of a particular kind. Collaboration graphs are used to measure the closeness of collaborative relationships between the participants of the network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the Brownian tree, or Aldous tree, or Continuum Random Tree (CRT) is a random real tree that can be defined from a Brownian excursion. The Brownian tree was defined and studied by David Aldous in three articles published in 1991 and 1993. This tree has since then been generalized.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the computer industry, the inverted text usually displays a selected block of text, the current menu item. Many older people have a slight, comfortable astigmatism. At the high resolution of modern computer screens, they better see black letters on white background rather than vice versa. Therefore, long reversed texts are rare. The reversing is widely used in the various equipment design (from television remotes to dump trucks): a half-erased button or plate remains readable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this regard, some theorists have argued that the additional component would have to ensure that the belief is true. This approach is reflected in the idea that knowledge implies a form of certainty. But it sets the standards of knowledge very high and may require that a belief has to be infallible to amount to knowledge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other. It is possible to derive an evaluation order or the absence of an evaluation order that respects the given dependencies from the dependency graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Job j {\\displaystyle j} takes time p j {\\displaystyle p_{j}} on any machine it is scheduled to. Q: Uniform-machines scheduling. There are m {\\displaystyle m} parallel machines, and they have different given speeds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Much of our day-to-day lives are significantly influenced by digital data and this would not be possible without Shannon-Fano coding and the ongoing evolution of its methods.In Shannon coding, the symbols are arranged in order from most probable to least probable, and assigned codewords by taking the first l i = \u2308 \u2212 log 2 \u2061 p i \u2309 {\\displaystyle l_{i}=\\left\\lceil -\\log _{2}p_{i}\\right\\rceil } bits from the binary expansions of the cumulative probabilities \u2211 k = 1 i \u2212 1 p k . {\\displaystyle \\sum \\limits _{k=1}^{i-1}p_{k}.} Here \u2308 x \u2309 {\\displaystyle \\lceil x\\rceil } denotes the ceiling function (which rounds x {\\displaystyle x} up to the next integer value).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of fluorescence microscopy, the probability of measuring a set of number of photons (or digitalization counts proportional to detected light) m =  {\\displaystyle \\mathbf {m} =} for expected values E =  {\\displaystyle \\mathbf {E} =} for a detector with K + 1 {\\displaystyle K+1} pixels is given by P ( m | E ) = \u220f i K P o i s s o n ( E i ) = \u220f i K E i m i e \u2212 E i m i ! {\\displaystyle P(\\mathbf {m} \\vert \\mathbf {E} )=\\prod _{i}^{K}\\mathrm {Poisson} (E_{i})=\\prod _{i}^{K}{\\frac {{E_{i}}^{m_{i}}e^{-E_{i}}}{m_{i}!}}} it is convenient to work with ln \u2061 ( P ) {\\displaystyle \\ln(P)} since in the context of maximum likelihood estimation we want to find the position of the maximum of the likelihood function and we are not interested in its absolute value. ln \u2061 ( P ( m | E ) ) = \u2211 i K  {\\displaystyle \\ln(P(m\\vert E))=\\sum _{i}^{K}\\left} Again since ln \u2061 ( m i ! )", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. The history monoid provides a set of synchronization primitives (such as locks, mutexes or thread joins) for providing rendezvous points between a set of independently executing processes or threads. History monoids occur in the theory of concurrent computation, and provide a low-level mathematical foundation for process calculi, such as CSP the language of communicating sequential processes, or CCS, the calculus of communicating systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It may give detailed instructions to each participant about how to test, and how to record bugs found. In some organizations, a bug-bashing session is followed by a party and a prize to the person who finds the worst bug, and/or the person who finds the greatest total of bugs. Bug Bash is a collaboration event, the step-by-step procedure has been given in the article 'Bug Bash\u2014A Collaboration Episode'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Superscalar CPUs use hardware to decide which operations can run in parallel at runtime, while VLIW CPUs use software (the compiler) to decide which operations can run in parallel in advance. Because the complexity of instruction scheduling is moved into the compiler, complexity of hardware can be reduced substantially.A similar problem occurs when the result of a parallelizable instruction is used as input for a branch. Most modern CPUs guess which branch will be taken even before the calculation is complete, so that they can load the instructions for the branch, or (in some architectures) even start to compute them speculatively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This final form is unique; in other words, it is independent of the sequence of row operations used. For example, in the following sequence of row operations (where two elementary operations on different rows are done at the first and third steps), the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form. \u2192  \u2192  \u2192  {\\displaystyle {\\begin{bmatrix}1&3&1&9\\\\1&1&-1&1\\\\3&11&5&35\\end{bmatrix}}\\to {\\begin{bmatrix}1&3&1&9\\\\0&-2&-2&-8\\\\0&2&2&8\\end{bmatrix}}\\to {\\begin{bmatrix}1&3&1&9\\\\0&-2&-2&-8\\\\0&0&0&0\\end{bmatrix}}\\to {\\begin{bmatrix}1&0&-2&-3\\\\0&1&1&4\\\\0&0&0&0\\end{bmatrix}}} Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss\u2013Jordan elimination. In this case, the term Gaussian elimination refers to the process until it has reached its upper triangular, or (unreduced) row echelon form. For computational reasons, when solving systems of linear equations, it is sometimes preferable to stop row operations before the matrix is completely reduced.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Main memory was also moved to an ECL implementation and the machine was equipped with a whopping-for-the-times 256k-words (2 megabytes) standard. The design spread the memory across 64 banks for fast access at about 8 ns/word, even though the cycle time of any one bank was about 250 ns. A high-speed core memory with a 20 ns access (overall) was also designed as a backup to the semiconductor memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By reversing the steps or using the extended Euclidean algorithm, the GCD can be expressed as a linear combination of the two original numbers, that is the sum of the two numbers, each multiplied by an integer (for example, 21 = 5 \u00d7 105 + (\u22122) \u00d7 252). The fact that the GCD can always be expressed in this way is known as B\u00e9zout's identity. The version of the Euclidean algorithm described above (and by Euclid) can take many subtraction steps to find the GCD when one of the given numbers is much bigger than the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They needed to know a network of people so that when the time comes for marriage, they were able to seek the services of the match-makers. Finally, when someone came to the match-maker, she must be able to pick out a matching suitors according to her knowledge of the local residents. Normally a perfect couple must have similar social status, economic status, and age.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s, Michael D. Plummer and L\u00e1szl\u00f3 Lov\u00e1sz conjectured that every bridgeless cubic graph has an exponential number of perfect matchings, strengthening Petersen's theorem that at least one perfect matching exists. In a pair of papers with different sets of co-authors, Kr\u00e1\u013e was able to show that this conjecture is true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alice determines which operation to perform accordingly to the pair of bits she wants to transmit. She then sends Bob the qubit state evolved through the chosen gate. Said qubit thus encodes information about the two bits Alice used to select the operation, and this information can be retrieved by Bob thanks to pre-shared entanglement between them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multilinear algebra, a tensor decomposition is any scheme for expressing a \"data tensor\" (M-way array) as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some matrix decompositions.Tensors are generalizations of matrices to higher dimensions (or rather to higher orders, i.e. the higher number of dimensions) and can consequently be treated as multidimensional fields. The main tensor decompositions are: Tensor rank decomposition; Higher-order singular value decomposition; Tucker decomposition; matrix product states, and operators or tensor trains; Online Tensor Decompositions hierarchical Tucker decomposition; block term decomposition", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain. It has been generalized to any ring, with a formulation involving two-sided ideals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 \u2264 j \u2264 n, where n is the dimension of the polytope) \u2014 cells, faces and so on \u2014 are also transitive on the symmetries of the polytope, and are regular polytopes of dimension \u2264 n. Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube). The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians. Classically, a regular polytope in n dimensions may be defined as having regular facets (-faces) and regular vertex figures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the application of the section 3 of the 1952 Act to Scotland it means any of the following offences: theft, housebreaking with intent to steal, opening lockfast places with intent to steal, reset, plagium, breach of trust and embezzlement, falsehood, fraud and wilful imposition, threats to extort money or with intent to extort money, and malicious mischief any offence under section 28 of the Road Traffic Act 1930 any of the following offences in connection with such an attack as is mentioned in section 1(1)(b) of the Internationally Protected Persons Act 1978: an offence of wilful fireraising an offence under section 2 of the Explosive Substances Act 1883 of causing an explosion likely to cause serious injury to property an offence under section 2 of the Nuclear Material (Offences) Act 1983, where the circumstances are that either, in the case of a contravention of subsection (2), the act falling within paragraph (a) or (b) of that subsection would, had it been done, have constituted an offence falling within sub-paragraph (a) or (b) of this paragraph, or, in the case of a contravention of subsection (3) or (4), the act threatened would, had it been done, have constituted such an offence any of the following offences in connection with such an attack as is mentioned in section 2(1) of the United Nations Personnel Act 1997 an offence of wilful fireraising an offence under section 2 of the Explosive Substances Act 1883 of causing an explosion likely to cause serious injury to property", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The unintended consequences of sharing can be complex to analyze and should not necessarily be left to the discretion of users who may have a narrow focus on their own critical need. These documents provide standards guidance on risk management: \"Recommended Security Controls for Federal Information Systems & Organizations\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another notation for the sign of a permutation is given by the more general Levi-Civita symbol (\u03b5\u03c3), which is defined for all maps from X to X, and has value zero for non-bijective maps. The sign of a permutation can be explicitly expressed as sgn(\u03c3) = (\u22121)N(\u03c3)where N(\u03c3) is the number of inversions in \u03c3. Alternatively, the sign of a permutation \u03c3 can be defined from its decomposition into the product of transpositions as sgn(\u03c3) = (\u22121)mwhere m is the number of transpositions in the decomposition. Although such a decomposition is not unique, the parity of the number of transpositions in all decompositions is the same, implying that the sign of a permutation is well-defined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the \"Twitter revolution\", the relationship between the new media and social movement has three distinct characteristics: 1) The Twitter streams represent the interaction mechanism of ecological network 2) The Twitter streams embedding or be embedded into different types of control process; 3) The Twitter streams reflect the change of social movement ecology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle A-(B\\cap C)=(A-B)\\cup (A-C).} Applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. De Morgan's laws are an example of a more general concept of mathematical duality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Fekete problem is, given a natural number N and a real s \u2265 0, to find the points x1,...,xN on the 2-sphere for which the s-energy, defined by \u2211 1 \u2264 i < j \u2264 N \u2016 x i \u2212 x j \u2016 \u2212 s {\\displaystyle \\sum _{1\\leq i 0 and by \u2211 1 \u2264 i < j \u2264 N log \u2061 \u2016 x i \u2212 x j \u2016 \u2212 1 {\\displaystyle \\sum _{1\\leq i 0, such points are called s-Fekete points, and for s = 0, logarithmic Fekete points (see Saff & Kuijlaars (1997)). More generally, one can consider the same problem on the d-dimensional sphere, or on a Riemannian manifold (in which case ||xi \u2212xj|| is replaced with the Riemannian distance between xi and xj). The problem originated in the paper by Michael Fekete (1923) who considered the one-dimensional, s = 0 case, answering a question of Issai Schur. An algorithmic version of the Fekete problem is number 7 on the list of problems discussed by Smale (1998).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exist nearly optimal solutions to some optimization problems. Ekeland's principle can be used when the lower level set of a minimization problems is not compact, so that the Bolzano\u2013Weierstrass theorem cannot be applied. The principle relies on the completeness of the metric space.The principle has been shown to be equivalent to completeness of metric spaces. In proof theory, it is equivalent to \u03a011CA0 over RCA0, i.e. relatively strong. It also leads to a quick proof of the Caristi fixed point theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 237, 1237, 2347, and 12347 are the patterns related to Braille pattern dots-123, since the two additional dots of kantenji patterns 0123, 1237, and 01237 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general, type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed \u03bb-calculus and Per Martin-L\u00f6f's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation, a common one is Thierry Coquand's Calculus of Inductive Constructions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Once an agreement is reached, the partnership is typically enforceable by civil law, especially if well documented. Partners who wish to make their agreement affirmatively explicit and enforceable typically draw up Articles of Partnership. Trust and pragmatism are also essential as it cannot be expected that everything can be written in the initial partnership agreement, therefore quality governance and clear communication are critical success factors in the long run. It is common for information about formally partnered entities to be made public, such as through a press release, a newspaper ad, or public records laws.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of mathematics known as Ramsey theory, a Ramsey class is one which satisfies a generalization of Ramsey's theorem. Suppose A {\\displaystyle A} , B {\\displaystyle B} and C {\\displaystyle C} are structures and k {\\displaystyle k} is a positive integer. We denote by ( B A ) {\\displaystyle {\\binom {B}{A}}} the set of all subobjects A \u2032 {\\displaystyle A'} of B {\\displaystyle B} which are isomorphic to A {\\displaystyle A} . We further denote by C \u2192 ( B ) k A {\\displaystyle C\\rightarrow (B)_{k}^{A}} the property that for all partitions X 1 \u222a X 2 \u222a \u22ef \u222a X k {\\displaystyle X_{1}\\cup X_{2}\\cup \\dots \\cup X_{k}} of ( C A ) {\\displaystyle {\\binom {C}{A}}} there exists a B \u2032 \u2208 ( C B ) {\\displaystyle B'\\in {\\binom {C}{B}}} and an 1 \u2264 i \u2264 k {\\displaystyle 1\\leq i\\leq k} such that ( B \u2032 A ) \u2286 X i {\\displaystyle {\\binom {B'}{A}}\\subseteq X_{i}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The principle of the number field sieve (both special and general) can be understood as an improvement to the simpler rational sieve or quadratic sieve. When using such algorithms to factor a large number n, it is necessary to search for smooth numbers (i.e. numbers with small prime factors) of order n1/2. The size of these values is exponential in the size of n (see below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network theory, multidimensional networks, a special type of multilayer network, are networks with multiple kinds of relations. Increasingly sophisticated attempts to model real-world systems as multidimensional networks have yielded valuable insight in the fields of social network analysis, economics, urban and international transport, ecology, psychology, medicine, biology, commerce, climatology, physics, computational neuroscience, operations management, and finance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A simple application of functional dependencies is Heath's theorem; it says that a relation R over an attribute set U and satisfying a functional dependency X \u2192 Y can be safely split in two relations having the lossless-join decomposition property, namely into \u03a0 X Y ( R ) \u22c8 \u03a0 X Z ( R ) = R {\\displaystyle \\Pi _{XY}(R)\\bowtie \\Pi _{XZ}(R)=R} where Z = U \u2212 XY are the rest of the attributes. (Unions of attribute sets are customarily denoted by there juxtapositions in database theory.) An important notion in this context is a candidate key, defined as a minimal set of attributes that functionally determine all of the attributes in a relation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the set has n elements, the number of k-combinations, denoted by C ( n , k ) {\\displaystyle C(n,k)} or C k n {\\displaystyle C_{k}^{n}} , is equal to the binomial coefficient which can be written using factorials as n ! k ! ( n \u2212 k ) !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a matrix is a rectangular array of numbers or other data. In physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way. A matrix model describes the behavior of a set of matrices within the framework of quantum mechanics.One important example of a matrix model is the BFSS matrix model proposed by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind in 1997. This theory describes the behavior of a set of nine large matrices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, in a few limited instances, a healthcare worker can share personal information without consent if it is in the public interest. These instances are set out in guidance from the General Medical Council, which is the regulatory body for doctors. Sometimes the healthcare worker has to provide the information \u2013 if required by law or in response to a court order. The National AIDS Trust has written a guide for people living with HIV to confidentiality in the NHS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In processing the recall, a Health Hazard Assessment will be conducted by the FDA to determine the recall class (defined above). Level, notification, instructions, mechanics, impacts on economy, and individual consumer must all be considered in determining recall strategy. Level of recall refers to which part of the distribution chain to which the recall is extended (wholesale, retail, pharmacy, medical user, etc.). Notification is the way consumers are alerted to the recall.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and \u22121s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. These matrices generalize permutation matrices and arise naturally when using Dodgson condensation to compute a determinant. They are also closely related to the six-vertex model with domain wall boundary conditions from statistical mechanics. They were first defined by William Mills, David Robbins, and Howard Rumsey in the former context.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Control surfaces with motorized faders can read and write mix automation. The control surface connects to the host computer via many different interfaces. MIDI was the first major interface created for this purpose, although many devices now use USB, FireWire, or Ethernet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, naive Bayes classifiers are a family of simple \"probabilistic classifiers\" based on applying Bayes' theorem with strong (naive) independence assumptions between the features (see Bayes classifier). They are among the simplest Bayesian network models, but coupled with kernel density estimation, they can achieve high accuracy levels.Naive Bayes classifiers are highly scalable, requiring a number of parameters linear in the number of variables (features/predictors) in a learning problem. Maximum-likelihood training can be done by evaluating a closed-form expression,: 718 which takes linear time, rather than by expensive iterative approximation as used for many other types of classifiers. In the statistics literature, naive Bayes models are known under a variety of names, including simple Bayes and independence Bayes. All these names reference the use of Bayes' theorem in the classifier's decision rule, but naive Bayes is not (necessarily) a Bayesian method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 20th century, many generalizations of sets were invented, e.g., fuzzy sets (Zadeh, 1965), or rediscovered, e.g., multisets (Knuth, 1997). As a result, these generalizations created a unification problem in the foundation of mathematics. The concept of a named set was created as a solution to this problem. Its generalization of mathematical structures allowed for the unification of all known generalizations of sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to deal with high data-rates, several architectural paradigms are commonly used: Pipeline of processors - each stage of the pipeline consisting of a processor performing one of the functions listed above. Parallel processing with multiple processors, often including multithreading. Specialized microcoded engines to more efficiently accomplish the tasks at hand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, if two random variables X {\\displaystyle X} and Y {\\displaystyle Y} (in L 2 ( \u03a9 , P ) {\\displaystyle L^{2}(\\Omega ,P)} ) are independent, then the centered random variables X \u2212 E ( X ) {\\displaystyle X-E(X)} and Y \u2212 E ( Y ) {\\displaystyle Y-E(Y)} are orthogonal. (This means that the two variables have zero covariance: they are uncorrelated.) In that case, the Pythagorean theorem in the kernel of the expectation operator implies that the variances of X {\\displaystyle X} and Y {\\displaystyle Y} satisfy the identity: sometimes called the Pythagorean theorem of statistics, and is of importance in linear regression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With dataflow path widths of 8 bits to 64 bits and beyond, they nevertheless present a common architecture at the machine language level across the entire line. Using microcode to implement an emulator enables the computer to present the architecture of an entirely different computer. The System/360 line used this to allow porting programs from earlier IBM machines to the new family of computers, e.g. an IBM 1401/1440/1460 emulator on the IBM S/360 model 40.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, coded mark inversion (CMI) is a non-return-to-zero (NRZ) line code. It encodes zero bits as a half bit time of zero followed by a half bit time of one, and while one bits are encoded as a full bit time of a constant level. The level used for one bits alternates each time one is coded. This is vaguely reminiscent of, but quite different from, Miller encoding, which also uses half-bit and full-bit pulses, but additionally uses the half-one/half-zero combination and arranges them so that the signal always spends at least a full bit time at a particular level before transitioning again. CMI doubles the bitstream frequency, when compared to its simple NRZ equivalent, but allows easy and reliable clock recovery.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the direct scheme, the destination decodes the data using the signal received from the source node on the first phase where the second phase transmission is omitted so that the relay node is not involved in transmission. The decoding signal received from the source node is written as: r d , s = h d , s x s + n d , s {\\displaystyle r_{d,s}=h_{d,s}x_{s}+n_{d,s}\\quad } While the advantage of the direct scheme is its simplicity in terms of the decoding processing, the received signal power can be severely low if the distance between the source node and the destination node is large. Thus, in the following we consider non-cooperative scheme which exploits signal relaying to improve the signal quality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the X.509 trust model, a certificate authority (CA) is responsible for signing certificates. These certificates act as an introduction between two parties, which means that a CA acts as a trusted third party. A CA processes requests from people or organizations requesting certificates (called subscribers), verifies the information, and potentially signs an end-entity certificate based on that information. To perform this role effectively, a CA needs to have one or more broadly trusted root certificates or intermediate certificates and the corresponding private keys.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics, one sometimes uses negative temperatures to describe systems with population inversion, which can be considered to have a temperature greater than positive infinity, because the coefficient of energy in the population distribution function is \u22121/Temperature. In this context, a temperature of \u22120 is a (theoretical) temperature larger than any other negative temperature, corresponding to the (theoretical) maximum conceivable extent of population inversion, the opposite extreme to +0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the (currently used) Gregorian calendar, alongside Tuesday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Thursday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400. 400 year cycle century 1: 9, 15, 26, 37, 43, 54, 65, 71, 82, 93, 99 century 2: 105, 111, 122, 133, 139, 150, 161, 167, 178, 189, 195 century 3: 201, 207, 218, 229, 235, 246, 257, 263, 274, 285, 291 century 4: 303, 314, 325, 331, 342, 353, 359, 370, 381, 387, 398", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, often where the changes are the most striking, Unicode has encoded variant characters, making it unnecessary to switch between fonts or lang attributes. However, some variants with arguably minimal differences get distinct codepoints, and not every variant with arguably substantial changes gets a unique codepoint. As an example, take a character such as \u5165 (U+5165), for which the only way to display the variants is to change font (or lang attribute) as described in the previous table. On the other hand, for \u5167 (U+5167), the variant of \u5185 (U+5185) gets a unique codepoint.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Algorithm Delete(r): D1. Find the host leaf: Perform an exact match search to find the leaf node L that contains r.D2. Delete r: Remove r from node L.D3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1975 IBM started a project to develop a telephone switch that required performance about three times that of their fastest contemporary computers. To reach this goal, the development team began to study the massive amount of performance data IBM had collected over the last decade. This study demonstrated that the complex ISA was in fact a significant problem; because only the most basic instructions were guaranteed to be implemented in hardware, compilers ignored the more complex ones that only ran in hardware on certain machines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "MAIN - This is the normal setting when the engine is running. Sometimes this position is labeled \"ON\" or \"RUN\". RESERVE - In this position, a known but small volume of fuel is available to allow the rider to be able to reach a petrol station.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most used simple caching to provide extremely fast RISC machines, with very compact code. Another benefit was that the interrupt latencies were very small, smaller than most CISC machines (a rare trait in RISC machines). The Burroughs large systems architecture used this approach.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Mersenne conjectures concern the characterization of a kind of prime numbers called Mersenne primes, meaning prime numbers that are a power of two minus one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Because its location in parent\u2019s node is the only thing of importance, it is symbolised by (meaning: the current node N is a NIL node and left child) in the left column of the delete diagrams. As the operation proceeds also proper nodes (of black height \u2265 1) may become current (see e. g. case D2). By counting the black bullets ( and ) in a delete diagram it can be observed that the paths through N have one bullet less than the other paths.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The closer the approximation is to zero or one, the more helpful the approximation is in linear cryptanalysis. However, in practice, the binary variables are not independent, as is assumed in the derivation of the piling-up lemma. This consideration has to be kept in mind when applying the lemma; it is not an automatic cryptanalysis formula.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The specification includes signal names and functions, timing, and electrical constraints. The last MIPI board-adopted version of Specification for Parallel Trace Interface is version 2.0 (October 2011).The MIPI High-Speed Trace Interface (MIPI HTI) specifies how to stream trace data over the physical layer of standard interfaces, such as PCI Express, DisplayPort, HDMI, or USB. The current version of the specification allows for one to six lanes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically in computational algebra, a straight-line program (SLP) for a finite group G = \u27e8S\u27e9 is a finite sequence L of elements of G such that every element of L either belongs to S, is the inverse of a preceding element, or the product of two preceding elements. An SLP L is said to compute a group element g \u2208 G if g \u2208 L, where g is encoded by a word in S and its inverses. Intuitively, an SLP computing some g \u2208 G is an efficient way of storing g as a group word over S; observe that if g is constructed in i steps, the word length of g may be exponential in i, but the length of the corresponding SLP is linear in i. This has important applications in computational group theory, by using SLPs to efficiently encode group elements as words over a given generating set. Straight-line programs were introduced by Babai and Szemer\u00e9di in 1984 as a tool for studying the computational complexity of certain matrix group properties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to explore more complex relationships, axes must be reordered. By arranging the axes in 3-dimensional space (however, still in parallel, like nails in a nail bed), an axis can have more than two neighbors in a circle around the central attribute, and the arrangement problem gets easier (for example by using a minimum spanning tree). A prototype of this visualization is available as extension to the data mining software ELKI. However, the visualization is harder to interpret and interact with than a linear order.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and in particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function x \u21a6 f(x) to its translation x \u21a6 f(x + a). In time series analysis, the shift operator is called the lag operator. Shift operators are examples of linear operators, important for their simplicity and natural occurrence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Kleene\u2013Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Haskell Curry's combinatory logic introduced in 1930, and Alonzo Church's original lambda calculus, introduced in 1932\u20131933, both originally intended as systems of formal logic. The paradox was exhibited by Stephen Kleene and J. B. Rosser in 1935.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As such, the child object can continue to be modified and amended over time without rearranging the structure of its associated prototype as in class-based systems. It is also important to note that not only data, but also methods can be added or changed. For this reason, some prototype-based languages refer to both data and methods as \"slots\" or \"members\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To prove this, consider the function g which maps x to f(x) \u2212 x. It is \u2265 0 on a and \u2264 0 on b. By the intermediate value theorem, g has a zero in ; this zero is a fixed point. Brouwer is said to have expressed this as follows: \"Instead of examining a surface, we will prove the theorem about a piece of string. Let us begin with the string in an unfolded state, then refold it. Let us flatten the refolded string. Again a point of the string has not changed its position with respect to its original position on the unfolded string.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, the inspiration of colleagues was accounted for to have expanded. Along these lines, adopting agile practices in a distributed environment has demonstrated to be valuable for the quality of the project and its execution. Thus, these can be seen as some of the advantages achieved by combining agile in distributed development, however, the list is exhaustive. The main benefits can be listed as follows:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Turian et al. (2003) point out that, \"Any MT evaluation measure is less reliable on shorter translations\", and show that increasing the amount of data improves the reliability of a metric. However, they add that \"... reliability on shorter texts, as short as one sentence or even one phrase, is highly desirable because a reliable MT evaluation measure can greatly accelerate exploratory data analysis\".Banerjee et al. (2005) highlight five attributes that a good automatic metric must possess; correlation, sensitivity, consistency, reliability and generality. Any good metric must correlate highly with human judgment, it must be consistent, giving similar results to the same MT system on similar text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the field of group theory, a modular subgroup is a subgroup that is a modular element in the lattice of subgroups, where the meet operation is defined by the intersection and the join operation is defined by the subgroup generated by the union of subgroups. By the modular property of groups, every quasinormal subgroup (that is, a subgroup that permutes with all subgroups) is modular. In particular, every normal subgroup is modular.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Stanford DASH multiprocessor system implements a variation of processor consistency which is incomparable (neither weaker nor stronger) to Goodman's definitions. All processors need to be consistent in the order in which they see writes by one processor and in the way they see writes by different processors to the same location. However, they do not need to be consistent when the writes are by different processors to different locations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These theorems provide necessary conditions for planarity that are not sufficient conditions, and therefore can only be used to prove a graph is not planar, not that it is planar. If both theorem 1 and 2 fail, other methods may be used. Whitney's planarity criterion gives a characterization based on the existence of an algebraic dual; Mac Lane's planarity criterion gives an algebraic characterization of finite planar graphs, via their cycle spaces; The Fraysseix\u2013Rosenstiehl planarity criterion gives a characterization based on the existence of a bipartition of the cotree edges of a depth-first search tree. It is central to the left-right planarity testing algorithm; Schnyder's theorem gives a characterization of planarity in terms of partial order dimension; Colin de Verdi\u00e8re's planarity criterion gives a characterization based on the maximum multiplicity of the second eigenvalue of certain Schr\u00f6dinger operators defined by the graph. The Hanani\u2013Tutte theorem states that a graph is planar if and only if it has a drawing in which each independent pair of edges crosses an even number of times; it can be used to characterize the planar graphs via a system of equations modulo 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The former is supported through some form of object literal, declarations where objects can be defined at runtime through special syntax such as {...} and passed directly to a variable. While most systems support a variety of cloning, ex nihilo object creation is not as prominent.In class-based languages, a new instance is constructed through a class's constructor function, a special function that reserves a block of memory for the object's members (properties and methods) and returns a reference to that block. An optional set of constructor arguments can be passed to the function and are usually held in properties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in particular the study of abstract algebra, a Dedekind\u2013Hasse norm is a function on an integral domain that generalises the notion of a Euclidean function on Euclidean domains.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "First minimize the maximal value of the load on all of the network routing node links Do that by minimizing a load upper bound value that is applied to all links. The full mass of the flow will be split equally across the possible parallel routes. Find the bottleneck links of the first layer (see below), then set their loading amount at the found minimum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although the enhancement of the output code was considerable, the resulting increase in complexity of the compiler caused problems with the limited address space. At the time, better optimized code was seen to be an enabler to bootstrapping the code in Pascal. In retrospect, the remaining assembly written sections WERE the problem, and needed to be eliminated, the sooner the better. Another way to say this is that the space problems could be transient, but having significant program sections written in assembly are a serious and lasting problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Expert systems tend to capture the expertise, of individuals in different organizations, on the same topic. By contrast a KBS, produced by logico-linguistic modeling, seeks to capture the expertise of individuals in the same organization on different topics. The emphasis is on the elicitation of organizational or group knowledge rather than individual experts. In logico-linguistic modeling the stakeholders become the experts. The end point of this stage is an SSM style conceptual models such as figure 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An alternative and equivalent definition is that a family of sets forms a delta-matroid when the convex hull of its indicator vectors (the analogue of a matroid polytope) has the property that every edge length is either one or the square root of two. Delta-matroids were defined by Andr\u00e9 Bouchet in 1987. Algorithms for matroid intersection and the matroid parity problem can be extended to some cases of delta-matroids.Delta-matroids have also been used to study constraint satisfaction problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Multiple edges, not allowed under the definition above, are two or more edges that join the same two vertices. In one more general sense of the term allowing multiple edges, a graph is an ordered triple G = ( V , E , \u03d5 ) {\\displaystyle G=(V,E,\\phi )} comprising: V {\\displaystyle V} , a set of vertices (also called nodes or points); E {\\displaystyle E} , a set of edges (also called links or lines); \u03d5: E \u2192 { { x , y } \u2223 x , y \u2208 V and x \u2260 y } {\\displaystyle \\phi :E\\to \\{\\{x,y\\}\\mid x,y\\in V\\;{\\textrm {and}}\\;x\\neq y\\}} , an incidence function mapping every edge to an unordered pair of vertices (that is, an edge is associated with two distinct vertices).To avoid ambiguity, this type of object may be called precisely an undirected multigraph. A loop is an edge that joins a vertex to itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming, an edge case typically involves input values that require special handling in an algorithm behind a computer program. As a measure for validating the behavior of computer programs in such cases, unit tests are usually created; they are testing boundary conditions of an algorithm, function or method. A series of edge cases around each \"boundary\" can be used to give reasonable coverage and confidence using the assumption that if it behaves correctly at the edges, it should behave everywhere else.For example, a function that divides two numbers might be tested using both very large and very small numbers. This assumes that if it works for both ends of the magnitude spectrum, it should work correctly in between.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "3).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Interest in these primes first arose due to their connection with Fermat's Last Theorem. Wolstenholme primes are also related to other special classes of numbers, studied in the hope to be able to generalize a proof for the truth of the theorem to all positive integers greater than two. The only two known Wolstenholme primes are 16843 and 2124679 (sequence A088164 in the OEIS). There are no other Wolstenholme primes less than 109.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities. For example, for a set { f i } {\\displaystyle \\{f_{i}\\}} of polynomials over a ring R {\\displaystyle R} , the solution set is the subset of R {\\displaystyle R} on which the polynomials all vanish (evaluate to 0), formally { x \u2208 R: \u2200 i \u2208 I , f i ( x ) = 0 } {\\displaystyle \\{x\\in R:\\forall i\\in I,f_{i}(x)=0\\}} The feasible region of a constrained optimization problem is the solution set of the constraints.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In painting, \u201cbrownness\u201d defines earth tone. At the beginning of a painting, primitive painters used soil, animal fat, minerals, charcoal, and chalk combined to be a color around 40,000 years ago. Therefore, the first group of colors was a natural palette by themselves. And earth tone palette was very handy to mix from scratch.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The principle of integrity furthers this concept into honesty and accuracy throughout all professional psychological endeavors.Another area where APA guidelines move beyond the Belmont report is in the setting of standards. The APA establishes standards for all reputable members of the psychology community (particularly those members of the American Psychological Association). The association sets a code of conduct for all APA individuals, which, when violated, can result in termination of professional licensure or membership.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Every song or recording has a unique identity by which they are licensed and tracked. Details of songs or recordings are notified to the PROs directly, or through Catco, an electronic tracking system. It needs to be clarified that while blanket licenses are commonly issued to music-users, the latter are responsible for \"usage returns\" \u2013 the actual frequency of performances under the license \u2013 which then becomes the basis for the PRO to apportion royalties to writers, publishers, and record labels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In concurrency control, path expressions are a mechanism for expressing permitted sequences of execution. For example, a path expression like \" {read}, write\" might specify that either multiple simultaneous executions of read or a single execution of write but not both are allowed at any point in time. It is important to know that the path expressions are a mechanism for the synchronization of processes at the monitor level in the software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a bundle map (or bundle morphism) is a morphism in the category of fiber bundles. There are two distinct, but closely related, notions of bundle map, depending on whether the fiber bundles in question have a common base space. There are also several variations on the basic theme, depending on precisely which category of fiber bundles is under consideration. In the first three sections, we will consider general fiber bundles in the category of topological spaces. Then in the fourth section, some other examples will be given.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle F(x,0)=f(x).} The dual problem with respect to the chosen perturbation function is given by sup y \u2217 \u2208 Y \u2217 \u2212 F \u2217 ( 0 , y \u2217 ) {\\displaystyle \\sup _{y^{*}\\in Y^{*}}-F^{*}\\left(0,y^{*}\\right)} where F \u2217 {\\displaystyle F^{*}} is the convex conjugate in both variables of F . {\\displaystyle F.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A similar situation exists regarding the Korean KS X 1001 character set, in which Microsoft maps the EUC-KR or UHC code for the wave dash (0xA1AD) to U+223C \u223c TILDE OPERATOR, while IBM and Apple map it to U+301C. Microsoft also uses U+FF5E to map the KS X 1001 raised tilde (0xA2A6), while Apple uses U+02DC \u02dc SMALL TILDE.The current Unicode reference glyph for U+301C has been corrected to match the JIS standard in response to a 2014 proposal, which noted that while the existing Unicode reference glyph had been matched by fonts from the discontinued Windows XP, all other major platforms including later versions of Microsoft Windows shipped with fonts matching the JIS reference glyph for U+301C.The JIS / Shift JIS wave dash is still formally mapped to U+301C as of JIS X 0213, whereas the WHATWG Encoding Standard used by HTML5 follows Microsoft in mapping 0x8160 to U+FF5E. These two code points have a similar or identical glyph in several fonts, reducing the confusion and incompatibility.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., \"MECE\"). The events 1 and 6 are mutually exclusive but not collectively exhaustive. The events \"even\" (2,4 or 6) and \"not-6\" (1,2,3,4, or 5) are also collectively exhaustive but not mutually exclusive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Extreme storm flood protection levels have been revised based on new Federal Emergency Management Agency guidelines for 100-year and 500-year design flood elevations.In the New Orleans Metropolitan Area, 35 percent of which sits below sea level, is protected by hundreds of miles of levees and flood gates. This system failed catastrophically, with numerous breaks, during Hurricane Katrina (2005) in the city proper and in eastern sections of the Metro Area, resulting in the inundation of approximately 50 percent of the metropolitan area, ranging from a few inches to twenty feet in coastal communities. The Morganza Spillway provides a method of diverting water from the Mississippi River when a river flood threatens New Orleans, Baton Rouge and other major cities on the lower Mississippi.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, such as substring search, one can compute a hash function h for every k-character substring of a given n-character string by advancing a window of width k characters along the string; where k is a fixed integer, and n is greater than k. The straightforward solution, which is to extract such a substring at every character position in the text and compute h separately, requires a number of operations proportional to k\u00b7n. However, with the proper choice of h, one can use the technique of rolling hash to compute all those hashes with an effort proportional to mk + n where m is the number of occurrences of the substring.The most familiar algorithm of this type is Rabin-Karp with best and average case performance O(n+mk) and worst case O(n\u00b7k) (in all fairness, the worst case here is gravely pathological: both the text string and substring are composed of a repeated single character, such as t=\"AAAAAAAAAAA\", and s=\"AAA\"). The hash function used for the algorithm is usually the Rabin fingerprint, designed to avoid collisions in 8-bit character strings, but other suitable hash functions are also used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of theoretical computer science the computability and complexity of computational problems are often sought-after. Computability theory describes the degree to which problems are computable, whereas complexity theory describes the asymptotic degree of resource consumption. Computational problems are therefore confined into complexity classes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After completing the customer migration, Sprint PCS sold the GSM radio interface network equipment to Omnipoint Communications in January 2000. Omnipoint was later purchased by VoiceStream Wireless which subsequently became T-Mobile US. In August 2022, T-Mobile US announced dead-zone cell phone coverage across the US using \"midband\" (1900 MHz) PCS spectrum and Starlink Gen2 satellite cell coverage, to begin testing in 2023. Using this satellite and midband spectrum, T-Mobile plans to be able to connect by satellite to common mobile devices, unlike previous generations of satellite phones which used specialized Earth-bound radios to connect to geosynchronous satellites with characteristic long lag time in communications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical genetics, Felsenstein's tree-pruning algorithm (or Felsenstein's tree-peeling algorithm), attributed to Joseph Felsenstein, is an algorithm for computing the likelihood of an evolutionary tree from nucleic acid sequence data. The algorithm is often used as a subroutine in a search for a maximum likelihood estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using likelihood ratio tests). It can also be used to provide error estimates for the parameters describing an evolutionary tree. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The following problem is the main open problem in this area of research: find an explicit polynomial of polynomial degree that requires circuits of superpolynomial size. The state of the art is a \u03a9 ( n log \u2061 d ) {\\displaystyle \\Omega (n\\log d)} lower bound for the size of a circuit computing, e.g., the polynomial x 1 d + \u22ef + x n d {\\displaystyle x_{1}^{d}+\\cdots +x_{n}^{d}} given by Strassen and by Baur and Strassen. More precisely, Strassen used B\u00e9zout's lemma to show that any circuit that simultaneously computes the n {\\displaystyle n} polynomials x 1 d , \u2026 , x n d {\\displaystyle x_{1}^{d},\\ldots ,x_{n}^{d}} is of size \u03a9 ( n log \u2061 d ) , {\\displaystyle \\Omega (n\\log d),} and later Baur and Strassen showed the following: given an arithmetic circuit of size s {\\displaystyle s} computing a polynomial f , {\\displaystyle f,} one can construct a new circuit of size at most O ( s ) {\\displaystyle O(s)} that computes f {\\displaystyle f} and all the n {\\displaystyle n} partial derivatives of f .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The relative simplicity of the algorithm makes it a popular first choice amongst optimizing algorithms. It is used widely in artificial intelligence, for reaching a goal state from a starting node. Different choices for next nodes and starting nodes are used in related algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the Legendre symbol, the law of quadratic reciprocity states for positive odd primes p , q {\\displaystyle p,q} we have ( p q ) ( q p ) = ( \u2212 1 ) p \u2212 1 2 q \u2212 1 2 . {\\displaystyle \\left({\\frac {p}{q}}\\right)\\left({\\frac {q}{p}}\\right)=(-1)^{{\\frac {p-1}{2}}{\\frac {q-1}{2}}}.} Using the definition of the Legendre symbol this is equivalent to a more elementary statement about equations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Because of the high value of these 'A' items, frequent value analysis is required. In addition to that, an organization needs to choose an appropriate order pattern (e.g. 'just-in-time') to avoid excess capacity. 'B' items are important, but of course less important than 'A' items and more important than 'C' items. Therefore, 'B' items are intergroup items. 'C' items are marginally important.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such a point, if it exists, is called a global minimum point of the function and its value at this point is called the global minimum (value) of the function. If the function takes \u2212 \u221e {\\displaystyle -\\infty } as a value then \u2212 \u221e {\\displaystyle -\\infty } is necessarily the global minimum value and the minimization problem can be answered; this is ultimately the reason why the definition of \"proper\" requires that the function never take \u2212 \u221e {\\displaystyle -\\infty } as a value. Assuming this, if the function's domain is empty or if the function is identically equal to + \u221e {\\displaystyle +\\infty } then the minimization problem once again has an immediate answer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The order dimension of a partial order is the minimum number of linear orders whose intersection is the given partial order. If a partial order has bounded order dimension, then an adjacency labeling scheme for the vertices in its comparability graph may be defined by labeling each vertex with its position in each of the defining linear orders, and determining that two vertices are adjacent if each corresponding pair of numbers in their labels has the same order relation as each other pair. In particular, this allows for an adjacency labeling scheme for the chordal comparability graphs, which come from partial orders of dimension at most four.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a proprietary protocol is a communications protocol owned by a single organization or individual.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In cryptography, modular arithmetic directly underpins public key systems such as RSA and Diffie\u2013Hellman, and provides finite fields which underlie elliptic curves, and is used in a variety of symmetric key algorithms including Advanced Encryption Standard (AES), International Data Encryption Algorithm (IDEA), and RC4. RSA and Diffie\u2013Hellman use modular exponentiation. In computer algebra, modular arithmetic is commonly used to limit the size of integer coefficients in intermediate calculations and data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, constraint counting is counting the number of constraints in order to compare it with the number of variables, parameters, etc. that are free to be determined, the idea being that in most cases the number of independent choices that can be made is the excess of the latter over the former. For example, in linear algebra if the number of constraints (independent equations) in a system of linear equations equals the number of unknowns then precisely one solution exists; if there are fewer independent equations than unknowns, an infinite number of solutions exist; and if the number of independent equations exceeds the number of unknowns, then no solutions exist. In the context of partial differential equations, constraint counting is a crude but often useful way of counting the number of free functions needed to specify a solution to a partial differential equation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Robinson\u2013Schensted\u2013Knuth correspondence, also referred to as the RSK correspondence or RSK algorithm, is a combinatorial bijection between matrices A with non-negative integer entries and pairs (P,Q) of semistandard Young tableaux of equal shape, whose size equals the sum of the entries of A. More precisely the weight of P is given by the column sums of A, and the weight of Q by its row sums. It is a generalization of the Robinson\u2013Schensted correspondence, in the sense that taking A to be a permutation matrix, the pair (P,Q) will be the pair of standard tableaux associated to the permutation under the Robinson\u2013Schensted correspondence. The Robinson\u2013Schensted\u2013Knuth correspondence extends many of the remarkable properties of the Robinson\u2013Schensted correspondence, notably its symmetry: transposition of the matrix A results in interchange of the tableaux P,Q.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to Q, the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem. It was in the process of his deep investigations of the arithmetic of these fields (for prime n) \u2013 and more precisely, because of the failure of unique factorization in their rings of integers \u2013 that Ernst Kummer first introduced the concept of an ideal number and proved his celebrated congruences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, the term access control is defined in U.S. Federal Standard 1037C with the following meanings: A service feature or technique used to permit or deny use of the components of a communication system. A technique used to define or restrict the rights of individuals or application programs to obtain data from, or place data onto, a storage device. The definition or restriction of the rights of individuals or application programs to obtain data from, or place data into, a storage device. The process of limiting access to the resources of an AIS (Automated Information System) to authorized users, programs, processes, or other systems. That function performed by the resource controller that allocates system resources to satisfy user requests.This definition depends on several other technical terms from Federal Standard 1037C.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1980s, when Simple Mail Transfer Protocol (SMTP) was designed, it provided for no real verification of sending user or system. This was not a problem while email systems were run by trusted corporations and universities, but since the commercialization of the Internet in the early 1990s, spam, phishing, and other crimes have been found to increasingly involve email. Email authentication is a necessary first step towards identifying the origin of messages, and thereby making policies and laws more enforceable. Hinging on domain ownership is a stance that emerged in the early 2000.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following discussion, the following conventions are adopted. K {\\displaystyle \\mathbb {K} } will denote one of the fields of real or complex numbers, denoted R {\\displaystyle \\mathbb {R} } , C {\\displaystyle \\mathbb {C} } , respectively. The vector space of m \u00d7 n {\\displaystyle m\\times n} matrices over K {\\displaystyle \\mathbb {K} } is denoted by K m \u00d7 n {\\displaystyle \\mathbb {K} ^{m\\times n}} . For A \u2208 K m \u00d7 n {\\displaystyle A\\in \\mathbb {K} ^{m\\times n}} , A T {\\displaystyle A^{\\textsf {T}}} and A \u2217 {\\displaystyle A^{*}} denote the transpose and Hermitian transpose (also called conjugate transpose) respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In organisms with a changeable shape, such as amoeboid organisms, most directional terms are meaningless, since the shape of the organism is not constant and no distinct axes are fixed. Similarly, in spherically symmetrical organisms, there is nothing to distinguish one line through the centre of the organism from any other. An indefinite number of triads of mutually perpendicular axes could be defined, but any such choice of axes would be useless, as nothing would distinguish a chosen triad from any others. In such organisms, only terms such as superficial and deep, or sometimes proximal and distal, are usefully descriptive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Processes are complex events constituted by a sequence of events. But even simple events can be conceived as complex entities involving an object, a time and the property exemplified by the object at this time. Traditionally, metaphysicians tended to emphasize static being over dynamic events. This tendency has been opposed by so-called process philosophy or process ontology, which ascribes ontological primacy to events and processes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In source code, the null character is often represented as the escape sequence \\0 in string literals (for example, \"abc\\0def\") or in character constants ('\\0'); the latter may also be written instead simply as 0 (without quotes nor slash). In many languages (such as C, which introduced this notation), this is not a separate escape sequence, but an octal escape sequence with a single octal digit 0; as a consequence, \\0 must not be followed by any of the digits 0 through 7; otherwise it is interpreted as the start of a longer octal escape sequence. Other escape sequences that are found in use in various languages are \\000, \\x00, \\z, or \\u0000. A null character can be placed in a URL with the percent code %00.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 5th century BC, Hippocrates of Chios showed that the Lune of Hippocrates and two other lunes could be exactly squared (converted into a square having the same area) by straightedge and compass. In 1766 the Finnish mathematician Daniel Wijnquist, quoting Daniel Bernoulli, listed all five geometrical squareable lunes, adding to those known by Hippocrates. In 1771 Leonard Euler gave a general approach and obtained certain equation to the problem. In 1933 and 1947 it was proven by Nikolai Chebotaryov and his student Anatoly Dorodnov that these five are the only squarable lunes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this case, to ensure that an application of a rewriting rule is not going to interfere with other resolution steps, a safe solution is to create a copy of the node represented by clause \u03b4 {\\displaystyle \\delta } . This solution increases proof size and some caution is needed when doing this. The heuristic for rule selection is important to achieve a good compression performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each of the standards has been placed in one of four fundamental categories to promote educational evaluations that are proper, useful, feasible, and accurate. In these sets of standards, validity and reliability considerations are covered under the accuracy topic. The tests are aimed at ensuring that student evaluations will provide sound, accurate, and credible information about student learning and performance, however; standardized tests offer narrow information on many forms of intelligence and relying on them harms students because they inaccurately measure a student's potential for success.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The problem was not so acute on minicomputers and mainframes where the vendor often specified standards for their libraries, but on microcomputers the programming systems were generally delivered by a variety of 3rd party companies with no interest in standardization. Nevertheless, this problem was being addressed in the early 1990s through the introduction of various shared library systems. These were actually intended to ease resource use on smaller platforms, by allowing a number of programs using a common resource, like the GUI, to share a single copy of code instead of each loading a separate copy into memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Scores using this metric have historically been known as \"raw\" scores. Tests taken in October 2004 or later have a score range from 200 to 600. The median score is 400, with a standard deviation of 25 points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally described by Valerii Denisovich Goppa, but the binary structure gives it several mathematical advantages over non-binary variants, also providing a better fit for common usage in computers and telecommunication. Binary Goppa codes have interesting properties suitable for cryptography in McEliece-like cryptosystems and similar setups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some systems and in the context of message processing systems (often real-time systems), this term also refers to the goal of establishing a single agreed sequence of messages within a database formed by a particular but arbitrary sequencing of records. The key concept is that data combined in a certain sequence is a \"truth\" which may be analyzed and processed giving particular results, and that although the sequence is arbitrary (and thus another correct but equally arbitrary sequencing would ultimately provide different results in any analysis), it is desirable to agree that the sequence enshrined in the \"single version of the truth\" is the version that will be considered \"the truth\", and that any conclusions drawn from analysis of the database are valid and unarguable, and (in a technical context) the database may be duplicated to a backup environment to ensure a persistent record is kept of the \"single version of the truth\". The key point is when the database is created using an external data source (such as a sequence of trading messages from a stock exchange) an arbitrary selection is made of one possibility from two or more equally valid representations of the input data, but henceforth the decision sets \"in stone\" one and only one version of the truth.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of performance, virtualization imposes a cost in the additional work the CPU has to perform to virtualize the underlying hardware. Instructions that perform this extra work, and other activities that require virtualization, tend to lie in operating system calls. In an unmodified operating system, OS calls introduce the greatest portion of virtualization \"overhead\".Paravirtualization or other virtualization techniques may help with these issues. VMware developed the Virtual Machine Interface for this purpose, and selected operating systems currently support this. A comparison between full virtualization and paravirtualization for the ESX Server shows that in some cases paravirtualization is much faster.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, call setup is the process of establishing a virtual circuit across a telecommunications network. Call setup is typically accomplished using a signaling protocol. The term call set-up time has the following meanings: The overall length of time required to establish a circuit-switched call between users. For data communication, the overall length of time required to establish a circuit-switched call between terminals; i.e., the time from the initiation of a call request to the beginning of the call message.Note: Call set-up time is the summation of: (a) call request time\u2014the time from initiation of a calling signal to the delivery to the caller of a proceed-to-select signal; (b) selection time\u2014the time from the delivery of the proceed-to-select signal until all the selection signals have been transmitted; and (c) post selection time\u2014the time from the end of the transmission of the selection signals until the delivery of the call-connected signal to the originating terminal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The modulo operation, as implemented in many programming languages and calculators, is an application of modular arithmetic that is often used in this context. The logical operator XOR sums 2 bits, modulo 2. In music, arithmetic modulo 12 is used in the consideration of the system of twelve-tone equal temperament, where octave and enharmonic equivalency occurs (that is, pitches in a 1:2 or 2:1 ratio are equivalent, and C-sharp is considered the same as D-flat).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the IBM System/360 and its successors, including the current z/Architecture machines, the boot process is known as Initial Program Load (IPL). IBM coined this term for the 7030 (Stretch), revived it for the design of the System/360, and continues to use it in those environments today. In the System/360 processors, an IPL is initiated by the computer operator by selecting the three hexadecimal digit device address (CUU; C=I/O Channel address, UU=Control unit and Device address) followed by pressing the LOAD button. On the high end System/360 models, most System/370 and some later systems, the functions of the switches and the LOAD button are simulated using selectable areas on the screen of a graphics console, often an IBM 2250-like device or an IBM 3270-like device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, it is required to compute an envy-minimizing allocation in a distributed manner, i.e., each agent should compute his/her own allocation, in a way that guarantees that the resulting allocation is consistent. This problem can be solved by presenting it as an Asymmetric distributed constraint optimization problem (ADCOP) as follows. Add a binary variable vij for each agent i and item j. The variable value is \"1\" if the agent gets the item, and \"0\" otherwise. The variable is owned by agent i. To express the constraint that each item is given to at most one agent, add binary constraints for each two different variables related to the same item, with an infinite cost if the two variables are simultaneously \"1\", and a zero cost otherwise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some have a bell inlet for a faster more effective flush. A problem with the valve type flush mechanism is that it invariably starts to leak after a couple of years use due to wear and tear of the valve, particles, etc. trapped in the valve.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The use of a high level language (C) to implement the operating system, and the reliance on standardized interfaces was in contrast to the assembly language oriented approaches of the past. As hardware vendors adapted Unix to their systems, new and useful features were added to Unix, e.g., fast file systems and tunable process schedulers. However, all the companies that adapted Unix made unique changes to it, rather than collaborating on an industry standard to create \"Unix for supercomputers\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If all of the residuals are equal, or do not fan out, they exhibit homoscedasticity. However, a terminological difference arises in the expression mean squared error (MSE). The mean squared error of a regression is a number computed from the sum of squares of the computed residuals, and not of the unobservable errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After its cancellation when the work has been finished, the switching schedule then facilitates restoration of the normal running arrangements. Switching components can also be tagged to reflect any Operational Restrictions that are in force. The network component/connectivity model, and associated diagrams, must always be kept absolutely up to date. The switching schedule facility therefore also allows 'patches' to the network model to be applied to the live version at the appropriate stage(s) of the jobs. The term 'patch' is derived from the method previously used to maintain the wallboard diagrams.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "AM, a computer mathematician that generates new mathematical concepts. It managed to produce by itself the notion of prime number and the Goldbach conjecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, people are called on to abide by a secret law. At least two things need to be examined: First is that the operation of a more general \"chilling effect\" that imposing a non disclosed law may have and; Secondly the social effects of discrimination, which take an entirely new light in the context of no longer discriminating against race creed color age or religion, but on the basis of a number, a number which has been assigned to all members of society reflecting information about that person which is unknown. Accordingly, there can be no definition at present of what information credit repositories collect or even what the use of that information is or what it reflects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "His tests were shorter, but used similar techniques. Wundt also measured mental processes and acknowledged the fact that there are individual differences between people.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, bit pairing is the practice of establishing, within a code set, a number of subsets that have an identical bit representation except for the state of a specified bit. Note: An example of bit pairing occurs in the International Alphabet No. 5 and the American Standard Code for Information Interchange (ASCII), where the upper case letters are related to their respective lower case letters by the state of bit six.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Good metric performance, across text types or domains, is important for the reusability of the metric. A metric that only works for text in a specific domain is useful, but less useful than one that works across many domains\u2014because creating a new metric for every new evaluation or domain is undesirable. Another important factor in the usefulness of an evaluation metric is to have a good correlation, even when working with small amounts of data, that is candidate sentences and reference translations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years a number of neural and deep-learning techniques have been proposed. Some generalize traditional Matrix factorization algorithms via a non-linear neural architecture, or leverage new model types like Variational Autoencoders. While deep learning has been applied to many different scenarios: context-aware, sequence-aware, social tagging etc. its real effectiveness when used in a simple collaborative recommendation scenario has been put into question.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The adjective which corresponds to squaring is quadratic. The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables. Marginal variables are those variables in the subset of variables being retained.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the form stated here, the splitting lemma does not hold in the full category of groups, which is not an abelian category.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f \u22121(Y ) = {x \u2208 Rn | f(x) \u2208 Y }. It can also be viewed as the problem of describing the solution set of the quantified constraint \"Y(f (x))\", where Y( y) is a constraint, e.g. an inequality, describing the set Y. In most applications, f is a function from Rn to Rp and the set Y is a box of Rp (i.e. a Cartesian product of p intervals of R). When f is nonlinear the set inversion problem can be solved using interval analysis combined with a branch-and-bound algorithm.The main idea consists in building a paving of Rp made with non-overlapping boxes. For each box , we perform the following tests: if f () \u2282 Y we conclude that  \u2282 X; if f () \u2229 Y = \u2205 we conclude that  \u2229 X = \u2205; Otherwise, the box  the box is bisected except if its width is smaller than a given precision.To check the two first tests, we need an interval extension (or an inclusion function)  for f. Classified boxes are stored into subpavings, i.e., union of non-overlapping boxes. The algorithm can be made more efficient by replacing the inclusion tests by contractors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the permutation (1 3 2 4) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 is a 4-cycle, and the permutation (1 3 2)(4) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 is considered a 3-cycle by some authors. On the other hand, the permutation (1 3)(2 4) that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs {1, 3} and {2, 4}. The set of elements that are not fixed by a cyclic permutation is called the orbit of the cyclic permutation. Every permutation on finitely many elements can be decomposed into cyclic permutations on disjoint orbits. The individual cyclic parts of a permutation are also called cycles, thus the second example is composed of a 3-cycle and a 1-cycle (or fixed point) and the third is composed of two 2-cycles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical field of combinatorial geometry, the Littlewood\u2013Offord problem is the problem of determining the number of subsums of a set of vectors that fall in a given convex set. More formally, if V is a vector space of dimension d, the problem is to determine, given a finite subset of vectors S and a convex subset A, the number of subsets of S whose summation is in A. The first upper bound for this problem was proven (for d = 1 and d = 2) in 1938 by John Edensor Littlewood and A. Cyril Offord. This Littlewood\u2013Offord lemma states that if S is a set of n real or complex numbers of absolute value at least one and A is any disc of radius one, then not more than ( c log \u2061 n / n ) 2 n {\\displaystyle {\\Big (}c\\,\\log n/{\\sqrt {n}}{\\Big )}\\,2^{n}} of the 2n possible subsums of S fall into the disc. In 1945 Paul Erd\u0151s improved the upper bound for d = 1 to ( n \u230a n / 2 \u230b ) \u2248 2 n 1 n {\\displaystyle {n \\choose \\lfloor {n/2}\\rfloor }\\approx 2^{n}\\,{\\frac {1}{\\sqrt {n}}}} using Sperner's theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is because painting is a subtractive color process, for which red and blue are secondary, not primary, colors. Although flawed in principle, the split-primary system can be successful in practice, because the recommended blue-biased red and green-biased blue positions are often filled by near approximations of magenta and cyan, respectively, while orange-biased red and violet-biased blue serve as secondary colors, which tend to further widen the mixable gamut. This system is in effect a simplified version of Newton's geometrical rule that colors closer together on the hue circle will produce more vibrant mixtures. A mixture, however, produced from two primary colors will be much more highly saturated than one produced from two secondary colors, even though both pairs are the same distance apart on the hue circle, revealing the limitations of the circular model in the prediction of color mixing results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Scandinavian languages, adjectives (both attributive and predicative) are declined according to the gender, number, and definiteness of the noun they modify. In Icelandic and Faroese, adjectives are also declined according to grammatical case, unlike the other Scandinavian languages. In some cases in Swedish, Norwegian and Danish, adjectives and participles as predicates appear to disagree with their subjects. This phenomenon is referred to as pancake sentences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum x \u2217 {\\displaystyle \\mathbf {x} ^{*}} of an objective function f: R n \u2192 R {\\displaystyle f:\\mathbb {R} ^{n}\\to \\mathbb {R} } . The other approach is trust region. The line search approach first finds a descent direction along which the objective function f {\\displaystyle f} will be reduced and then computes a step size that determines how far x {\\displaystyle \\mathbf {x} } should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either exactly or inexactly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the quasi-dihedral groups, also called semi-dihedral groups, are certain non-abelian groups of order a power of 2. For every positive integer n greater than or equal to 4, there are exactly four isomorphism classes of non-abelian groups of order 2n which have a cyclic subgroup of index 2. Two are well known, the generalized quaternion group and the dihedral group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to de-risk the programme Atlas and the MOD took an incremental approach to the development and implementation of DII, with a separate contract for each increment. The extended timeline allowed the MOD flexibility in defining its requirements. Increment 1: Contract awarded March 2005. This covered 70,000 user access devices (UADs) and 200,000 user accounts in the Restricted and Secret domains in 680 fixed locations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, let X {\\displaystyle X} be our n {\\displaystyle n} -dimensional input space. Let H {\\displaystyle {\\mathcal {H}}} be a class of functions that we wish to use in order to learn a { 0 , 1 } {\\displaystyle \\{0,1\\}} -valued target function f {\\displaystyle f} defined over X {\\displaystyle X} . Let D {\\displaystyle {\\mathcal {D}}} be the distribution of the inputs over X {\\displaystyle X} . The goal of a learning algorithm A {\\displaystyle {\\mathcal {A}}} is to choose the best function h \u2208 H {\\displaystyle h\\in {\\mathcal {H}}} such that it minimizes e r r o r ( h ) = P x \u223c D ( h ( x ) \u2260 f ( x ) ) {\\displaystyle error(h)=P_{x\\sim {\\mathcal {D}}}(h(x)\\neq f(x))} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States and Canada, almost all public libraries have computers available for the use of patrons, though some libraries will impose a time limit on users to ensure others will get a turn and keep the library less busy. Users are often allowed to print documents that they have created using these computers, though sometimes for a small fee.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Information policy is playing a greater role in the economy leading to the production of goods and services, as well as selling them directly to consumers (UCLA, 2009). The cost of information varies from a tangible good in that initial costs of the first unit are large and fixed; however, after that, marginal costs are relatively low (MacInnes, 2011). As an increase from the information services, information can be paralleled to that of manufacturing several years ago (UCLA, 2009). The digitalization of information allows businesses to make better justified business decisions (MacInnes, 2011).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Often identical files are installed on multiple computers, for example operating system files. With single-instance storage, only one copy of a file is written to the backup media therefore reducing space. This becomes more important when the storage is offsite and on cloud storage such as Amazon S3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, although simple examples illustrate that linear uncorrelatedness of two random variables does not in general imply their independence, it is sometimes mistakenly thought that it does imply that when the two random variables are normally distributed. This article demonstrates that assumption of normal distributions does not have that consequence, although the multivariate normal distribution, including the bivariate normal distribution, does. To say that the pair ( X , Y ) {\\displaystyle (X,Y)} of random variables has a bivariate normal distribution means that every linear combination a X + b Y {\\displaystyle aX+bY} of X {\\displaystyle X} and Y {\\displaystyle Y} for constant (i.e. not random) coefficients a {\\displaystyle a} and b {\\displaystyle b} (not both equal to zero) has a univariate normal distribution. In that case, if X {\\displaystyle X} and Y {\\displaystyle Y} are uncorrelated then they are independent. However, it is possible for two random variables X {\\displaystyle X} and Y {\\displaystyle Y} to be so distributed jointly that each one alone is marginally normally distributed, and they are uncorrelated, but they are not independent; examples are given below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In later work by Vila Casado et al., alternative update techniques were studied, in which variable nodes are updated with the newest available check-node information.The intuition behind these algorithms is that variable nodes whose values vary the most are the ones that need to be updated first. Highly reliable nodes, whose log-likelihood ratio (LLR) magnitude is large and does not change significantly from one update to the next, do not require updates with the same frequency as other nodes, whose sign and magnitude fluctuate more widely. These scheduling algorithms show greater speed of convergence and lower error floors than those that use flooding. These lower error floors are achieved by the ability of the Informed Dynamic Scheduling (IDS) algorithm to overcome trapping sets of near codewords.When nonflooding scheduling algorithms are used, an alternative definition of iteration is used. For an (n, k) LDPC code of rate k/n, a full iteration occurs when n variable and n \u2212 k constraint nodes have been updated, no matter the order in which they were updated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The native thread remains attached to the VM until it calls DetachCurrentThread() to detach itself.The JNI framework does not provide any automatic garbage collection for non-JVM memory resources allocated by code executing on the native side. Consequently, native side code (such as assembly language) assumes the responsibility for explicitly releasing any such memory resources that the native code acquires. On Linux and Solaris platforms, if the native code registers itself as a signal handler, it could intercept signals intended for the JVM.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music, a monad is a single note or pitch. The Western chromatic scale, for example, is composed of twelve monads. Monads are contrasted to dyads, groups of two notes, triads, groups of three, and so on. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The mutant should be the specification that the engineer guesses the programmer has implemented. Then, the engineer has to calculate the subset of the VIS that yields different results in both specifications. The predicate of this set is used to derive a new test class.Some other testing tactics that may also be used are the following: In Set Extension (ISE).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An occasional darkly discolored or corroded nickel, dime, quarter, or half dollar can fool the collector by its edge, giving off the appearance of a silver coin. Often coin roll hunters also collect special proof coins, tokens and other exonumia, and foreign coins. Others attempt to find and complete a set of coins, like the America the Beautiful Quarters, 50 State Quarters, Presidential Dollars, or even every year and mint of regular designs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. Euclid poses the problem thus: \"Given two numbers not prime to one another, to find their greatest common measure\". He defines \"A number  a multitude composed of units\": a counting number, a positive integer not including zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of modern algebra known as group theory, the Thompson group Th is a sporadic simple group of order 215 \u00b7 310 \u00b7 53 \u00b7 72 \u00b7 13 \u00b7 19 \u00b7 31 = 90745943887872000 \u2248 9\u00d71016.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\Delta \\left(C^{*}(m_{1}),C^{*}(m_{2})\\right)\\geqslant H_{q}^{-1}\\left({\\tfrac {1}{2}}-\\varepsilon \\right)\\cdot 2k\\cdot T.} So now the final task is to find a lower bound for T {\\displaystyle T} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following theorems A , P , Q \u2208 R n \u00d7 n {\\displaystyle A,P,Q\\in \\mathbb {R} ^{n\\times n}} , and P {\\displaystyle P} and Q {\\displaystyle Q} are symmetric. The notation P > 0 {\\displaystyle P>0} means that the matrix P {\\displaystyle P} is positive definite. Theorem (continuous time version). Given any Q > 0 {\\displaystyle Q>0} , there exists a unique P > 0 {\\displaystyle P>0} satisfying A T P + P A + Q = 0 {\\displaystyle A^{T}P+PA+Q=0} if and only if the linear system x \u02d9 = A x {\\displaystyle {\\dot {x}}=Ax} is globally asymptotically stable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. The principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the principle has never been explicitly stated by Frege, and arguably it was already assumed by George Boole decades before Frege's work. The principle of compositionality is highly debated in linguistics. Among its most challenging problems there are the issues of contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a polling system or polling model is a system where a single server visits a set of queues in some order. The model has applications in computer networks and telecommunications, manufacturing and road traffic management. The term polling system was coined at least as early as 1968 and the earliest study of such a system in 1957 where a single repairman servicing machines in the British cotton industry was modelled.Typically it is assumed that the server visits the different queues in a cyclic manner. Exact results exist for waiting times, marginal queue lengths and joint queue lengths at polling epochs in certain models. Mean value analysis techniques can be applied to compute average quantities.In a fluid limit, where a very large number of small jobs arrive the individual nodes can be viewed to behave similarly to fluid queues (with a two state process).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first factor corresponds to how likely it is that the chosen edge contains the vertex, which increases when the vertex has more friends. The halving factor simply comes from the fact that each edge has two vertices. So the expected value of the number of friends of a (randomly chosen) friend is \u2211 v ( d ( v ) | E | 1 2 ) d ( v ) = \u2211 v d ( v ) 2 2 | E | .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Enabling PAE (by setting bit 5, PAE, of the system register CR4) causes major changes to this scheme. By default, the size of each page remains as 4 KB. Each entry in the page table and page directory becomes 64 bits long (8 bytes), instead of 32 bits, to allow for additional address bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that in these cases the handle must be something other than a systemwide-unique small integer, otherwise it is forgeable. Such an integer may nevertheless be used to identify a capability inside a process; e.g., file descriptor in Linux is unforgeable because its numerical value alone is meaningless, and only in the process context may refer to anything. Transferring such a handle requires special care though, as its value often has to be different in the sending and receiving processes. In non-capability-based systems, on the other hand, each process must acquire its own separate handle, by specifying the identity of the resource and the desired access rights (e.g., each process must open a file itself, by giving the filename and access mode). Such usage is more common even in modern systems that do support passing handles, but it is subject to vulnerabilities like the confused deputy problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each user will be associated to a row of the first matrix and each item with a column of the second matrix. The row or column associated to a specific user or item is called latent factors. When a new item is added it has no associated latent factors and the lack of interactions does not allow to learn them, as it was done with other items.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements. For example, the sequence \u27e8 A , B , D \u27e9 {\\displaystyle \\langle A,B,D\\rangle } is a subsequence of \u27e8 A , B , C , D , E , F \u27e9 {\\displaystyle \\langle A,B,C,D,E,F\\rangle } obtained after removal of elements C , {\\displaystyle C,} E , {\\displaystyle E,} and F . {\\displaystyle F.} The relation of one sequence being the subsequence of another is a preorder.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming languages, and other related fields, encapsulation refers to one of two related but distinct notions, and sometimes to the combination thereof: A language mechanism for restricting direct access to some of the object's components. A language construct that facilitates the bundling of data with the methods (or other functions) operating on those data.Some programming language researchers and academics use the first meaning alone or in combination with the second as a distinguishing feature of object-oriented programming, while some programming languages that provide lexical closures view encapsulation as a feature of the language orthogonal to object orientation. The second definition is motivated by the fact that in many object-oriented languages, and other related fields, the components are not hidden automatically and this can be overridden; thus, information hiding is defined as a separate notion by those who prefer the second definition. The features of encapsulation are supported using classes in most object-oriented languages, although other alternatives also exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of clients and services. Each service comprises one or more servers and exports operations that clients invoke by making requests. Although using a single, centralized server is the simplest way to implement a service, the resulting service can only be as fault tolerant as the processor executing that server. If this level of fault tolerance is unacceptable, then multiple servers that fail independently can be used. Usually, replicas of a single server are executed on separate processors of a distributed system, and protocols are used to coordinate client interactions with these replicas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the Legendre symbol, the law of quadratic reciprocity for positive odd primes states ( p q ) ( q p ) = ( \u2212 1 ) p \u2212 1 2 q \u2212 1 2 . {\\displaystyle \\left({\\frac {p}{q}}\\right)\\left({\\frac {q}{p}}\\right)=(-1)^{{\\frac {p-1}{2}}{\\frac {q-1}{2}}}.} A reciprocity law is a generalization of the law of quadratic reciprocity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The EI condition implies that the total cake-price should be 2, so q + 2 p = 1 {\\displaystyle q+2p=1} . The EI condition again implies that, in any connected CEEI division, the cake is cut in the middle. Both Alice and George receive two peripheral slices and one central slice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, econometrics and related fields, multidimensional analysis (MDA) is a data analysis process that groups data into two categories: data dimensions and measurements. For example, a data set consisting of the number of wins for a single football team at each of several years is a single-dimensional (in this case, longitudinal) data set. A data set consisting of the number of wins for several football teams in a single year is also a single-dimensional (in this case, cross-sectional) data set. A data set consisting of the number of wins for several football teams over several years is a two-dimensional data set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, the observations within each pair can only take the values 0 or 1. For example, 0 may indicate failure and 1 may indicate success. There are 4 possible pairs: {0,0}, {0,1}, {1,0}, and {1,1}. In these cases, the same procedure as the sign test is used, but is known as McNemar's test.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Put in simple technical terms, Cochran's Q test requires that there only be a binary response (e.g. success/failure or 1/0) and that there be more than 2 groups of the same size. The test assesses whether the proportion of successes is the same between groups. Often it is used to assess if different observers of the same phenomenon have consistent results (interobserver variability).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are three major kinds of qualities or characteristics: types or kinds (e.g. mammal), properties (e.g. short, strong), and relations (e.g. father of, next to). These are all different types of universals.Paradigmatically, universals are abstract (e.g. humanity), whereas particulars are concrete (e.g. the personhood of Socrates).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of S is variously denoted as P(S), \ud835\udcab(S), P(S), P ( S ) {\\displaystyle \\mathbb {P} (S)} , \u2118 ( S ) {\\displaystyle \\wp (S)} , or 2S. The notation 2S, meaning the set of all functions from S to a given set of two elements (e.g., {0, 1}), is used because the powerset of S can be identified with, equivalent to, or bijective to the set of all the functions from S to the given two elements set.Any subset of P(S) is called a family of sets over S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements (c. 300 BC).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the computer science fields of knowledge engineering and ontology, the Sigma knowledge engineering environment is an open source computer program for the development of formal ontologies. It is designed for use with the Suggested Upper Merged Ontology. It originally included only the Vampire theorem prover as its core deductive inference engine, but now allows use of many other provers that have participated in the CASC/CADE competitions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by making an incremental change to the solution. If the change produces a better solution, another incremental change is made to the new solution, and so on until no further improvements can be found. For example, hill climbing can be applied to the travelling salesman problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, the solution x 0 = A \u2212 1 b {\\displaystyle x_{0}=A^{-1}\\mathbf {b} } only exists where an actual corner exists in the window N {\\displaystyle N} . A methodology for performing automatic scale selection for this corner localization method has been presented by Lindeberg by minimizing the normalized residual d ~ min = c \u2212 b T A \u2212 1 b trace \u2061 A {\\displaystyle {\\tilde {d}}_{\\min }={\\frac {c-b^{T}A^{-1}b}{\\operatorname {trace} A}}} over scales.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "p ) \u22c5 \u03b2 q ( \u03c3 \u2218 \u03b9 p , p + 1 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is guaranteed to be a vertex of the convex hull of the polygon. Alternatively, the vertex with the smallest Y-coordinate among the ones with the largest X-coordinates or the vertex with the smallest X-coordinate among the ones with the largest Y-coordinates (or any other of 8 \"smallest, largest\" X/Y combinations) will do as well. Once a vertex of the convex hull is chosen, one can then apply the formula using the previous and next vertices, even if those are not on the convex hull, as there can be no local concavity on this vertex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of broadcast packets over a switching loop, the situation may develop into a broadcast storm. In a very simple example, a switch with three ports A, B, and C has a normal node connected to port A while ports B and C are connected to each other in a loop. All ports have the same link speed and run in full duplex mode. Now, when a broadcast frame enters the switch through port A, this frame is forwarded to all ports but the source port, i.e. ports B and C. Both frames exiting ports B and C traverse the loop in opposite directions and reenter the switch through their counterpart port.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most current use cases, the letters A\u2013F or a\u2013f represent the values 10\u201315, while the numerals 0\u20139 are used to represent their decimal values. There is no universal convention to use lowercase or uppercase, so each is prevalent or preferred in particular environments by community standards or convention; even mixed case is used. Seven-segment displays use mixed-case AbCdEF to make digits that can be distinguished from each other. There is some standardization of using spaces (rather than commas or another punctuation mark) to separate hex values in a long list. For instance, in the following hex dump, each 8-bit byte is a 2-digit hex number, with spaces between them, while the 32-bit offset at the start is an 8-digit hex number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These algorithms are called auction algorithms, push-relabel algorithms, or preflow-push algorithms. Some of these algorithms were shown to be equivalent.Some of the local methods assume that the graph admits a perfect matching; if this is not the case, then some of these methods might run forever. : 3 A simple technical way to solve this problem is to extend the input graph to a complete bipartite graph, by adding artificial edges with very large weights.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The algebra is named for logicians Adolf Lindenbaum and Alfred Tarski. Starting in the academic year 1926-1927, Lindenbaum pioneered his method in Jan \u0141ukasiewicz's mathematical logic seminar, and the method was popularized and generalized in subsequent decades through work by Tarski. The Lindenbaum\u2013Tarski algebra is considered the origin of the modern algebraic logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This statistic is named after Major Percy Alexander MacMahon who showed in 1913 that the distribution of the major index on all permutations of a fixed length is the same as the distribution of inversions. That is, the number of permutations of length n with k inversions is the same as the number of permutations of length n with major index equal to k. (These numbers are known as Mahonian numbers, also in honor of MacMahon.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the van den Berg\u2013Kesten (BK) inequality or van den Berg\u2013Kesten\u2013Reimer (BKR) inequality states that the probability for two random events to both happen, and at the same time one can find \"disjoint certificates\" to show that they both happen, is at most the product of their individual probabilities. The special case for two monotone events (the notion as used in the FKG inequality) was first proved by van den Berg and Kesten in 1985, who also conjectured that the inequality holds in general, not requiring monotonicity. Reimer later proved this conjecture. : 159: 44 The inequality is applied to probability spaces with a product structure, such as in percolation problems. : 829", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of constituency tree, a subtree is defined as a node and all its children (e.g., ] ]] is a subtree of the two trees). Terminals are not considered subtree (e.g.  is not a subtree). The subtree kernel count the number of common subtrees between two given trees. In this example, there are seven common subtrees: ] ]], ] ]], ], ], ], ] (counted twice as it appears twice).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix A {\\displaystyle A} , the algorithm will produce a number \u03bb {\\displaystyle \\lambda } , which is the greatest (in absolute value) eigenvalue of A {\\displaystyle A} , and a nonzero vector v {\\displaystyle v} , which is a corresponding eigenvector of \u03bb {\\displaystyle \\lambda } , that is, A v = \u03bb v {\\displaystyle Av=\\lambda v} . The algorithm is also known as the Von Mises iteration.Power iteration is a very simple algorithm, but it may converge slowly. The most time-consuming operation of the algorithm is the multiplication of matrix A {\\displaystyle A} by a vector, so it is effective for a very large sparse matrix with appropriate implementation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 267, 1267, 2467, and 12467 are the patterns related to Braille pattern dots-135, since the two additional dots of kantenji patterns 0135, 1357, and 01357 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From the definition of the square root, we have that b \u00d7 b = b {\\displaystyle {\\sqrt {b}}\\times {\\sqrt {b}}=b} . Therefore, the exponent r {\\displaystyle r} must be such that b r \u00d7 b r = b {\\displaystyle b^{r}\\times b^{r}=b} . Using the fact that multiplying makes exponents add gives b r + r = b {\\displaystyle b^{r+r}=b} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, anticommutativity is a specific property of some non-commutative mathematical operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is the inverse of the result with unswapped arguments. The notion inverse refers to a group structure on the operation's codomain, possibly with another operation. Subtraction is an anticommutative operation because commuting the operands of a \u2212 b gives b \u2212 a = \u2212(a \u2212 b); for example, 2 \u2212 10 = \u2212(10 \u2212 2) = \u22128. Another prominent example of an anticommutative operation is the Lie bracket. In mathematical physics, where symmetry is of central importance, these operations are mostly called antisymmetric operations, and are extended in an associative setting to cover more than two arguments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We conclude that supp \u2061 ( \u03b4 p ) {\\displaystyle \\operatorname {supp} (\\delta _{p})} is the closure of the singleton set { p } , {\\displaystyle \\{p\\},} which is { p } {\\displaystyle \\{p\\}} itself. In fact, a measure \u03bc {\\displaystyle \\mu } on the real line is a Dirac measure \u03b4 p {\\displaystyle \\delta _{p}} for some point p {\\displaystyle p} if and only if the support of \u03bc {\\displaystyle \\mu } is the singleton set { p } . {\\displaystyle \\{p\\}.} Consequently, Dirac measure on the real line is the unique measure with zero variance (provided that the measure has variance at all).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, a polygon has to be covered not with arbitrary rectangles but with rectangles from a finite family.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively (just notation, not necessarily the elementary arithmetic multiplication): x\u00b7y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y). Associativity is formally expressed as that (x\u00b7y)\u00b7z = x\u00b7(y\u00b7z) for all x, y and z in the semigroup. Semigroups may be considered a special case of magmas, where the operation is associative, or as a generalization of groups, without requiring the existence of an identity element or inverses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, a special information tone (SIT) is an in-band international standard call progress tone consisting of three rising tones indicating a call has failed. It usually precedes a recorded announcement describing the problem.Because the SIT is well known in many countries, callers can understand that their call has failed, even though they do not understand the language of the recorded announcement (e.g., when calling internationally) instead of assuming the recording is voicemail or some other intended function. Like a dial tone or busy signal, the SIT is an in-band signal intended both to be heard by the caller, and to be detected by automated dialing equipment to determine a call has failed. In North America, the AT&T/Bellcore SIT standard allows the frequency and duration of the tones to vary slightly - making eight distinct messages specifically for automated equipment; indicating not only a failed call, but also the specific reason for the failure (e.g., disconnected number, busy circuits, dialing error, etc.).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There exists a dedicated group of enthusiasts who use TVRO (TV receive-only) gear such as satellite dishes to peek in on backhaul signals that are available on any of the dozens of broadcast satellites that are visible from almost any point on Earth. In its early days, their hobby was strengthened by the fact that most backhaul was analog and in the clear (unscrambled or unencrypted) which made for a vast smorgasbord of free television available for the technically inclined amateur. In recent years, full-time content and cable channels have added encryption and conditional access, and occasional signals are steadily becoming digital, which has had a deleterious effect on the hobby.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In summer, the so-called \u201cfast\u201d search robot was launched, working in parallel with the actual pages intended for indexing. The base of the \"fast robot\" is updated every 1.5\u20132 hours.The ranking algorithm has been improved to increase search accuracy.Search capabilities have been expanded with the help of Yandex. Dictionaries \u201dand\u201c Yandex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Kellerer and Woeginger study a variant in which there are at most 3*m jobs, and each machine must contain at most 3 jobs (this can be seen as a generalization of 3-partition problem). They show that MLPT attains at most ( 4 m \u2212 1 ) / ( 3 m ) {\\displaystyle (4m-1)/(3m)} of the minimum largest sum, which the same approximation ratio that LPT attains for the unconstrained problem. The bound is tight for MLPT.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A field with a single derivation operator is called an ordinary differential field; if there is a finite set containing several commuting derivation operators the field is called a partial differential field. Here differential operators with derivatives \u2202 x = \u2202 \u2202 x {\\textstyle \\partial _{x}={\\frac {\\partial }{\\partial x}}} and \u2202 y = \u2202 \u2202 y {\\textstyle \\partial _{y}={\\frac {\\partial }{\\partial y}}} with coefficients from some differential field are considered. Its elements have the form \u2211 i , j r i , j ( x , y ) \u2202 x i \u2202 y j {\\textstyle \\sum _{i,j}r_{i,j}(x,y)\\partial _{x}^{i}\\partial _{y}^{j}} ; almost all coefficients r i , j {\\displaystyle r_{i,j}} are zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, Rosser's trick is a method for proving G\u00f6del's incompleteness theorems without the assumption that the theory being considered is \u03c9-consistent (Smorynski 1977, p. 840; Mendelson 1977, p. 160). This method was introduced by J. Barkley Rosser in 1936, as an improvement of G\u00f6del's original proof of the incompleteness theorems that was published in 1931. While G\u00f6del's original proof uses a sentence that says (informally) \"This sentence is not provable\", Rosser's trick uses a formula that says \"If this sentence is provable, there is a shorter proof of its negation\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonetics, a continuant is a speech sound produced without a complete closure in the oral cavity. By one defintion, continuant is a distinctive feature that refers to any sound produced with an incomplete closure of the vocal tract, thus encompassing all sounds (including vowels) except stops, affricates and nasals. By another definition, it refers exclusively to consonantal sounds produced with an incomplete closure of the oral cavity, prototypically approximants and fricatives, but sometimes also trills.Compare sonorants (resonants), a class of speech sounds which includes vowels, approximants and nasals (but not fricatives), and contrasts with obstruents.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Joan Clarke was also one such woman who made immense contributions to computing during World War II. She was a British mathematician and codebreaker who worked at Bletchley Park on breaking codes generated by Enigma machines, eventually developing Alan Turing's bombe technology to aid in deciphering complex Nazi messages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and information theory, adjusted mutual information, a variation of mutual information may be used for comparing clusterings. It corrects the effect of agreement solely due to chance between clusterings, similar to the way the adjusted rand index corrects the Rand index. It is closely related to variation of information: when a similar adjustment is made to the VI index, it becomes equivalent to the AMI. The adjusted measure however is no longer metrical.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the external memory model, the number of memory transfers it needs to perform a sort of N {\\displaystyle N} items on a machine with cache of size Z {\\displaystyle Z} and cache lines of length L {\\displaystyle L} is O ( N L log Z \u2061 N ) {\\displaystyle O\\left({\\tfrac {N}{L}}\\log _{Z}N\\right)} , under the tall cache assumption that Z = \u03a9 ( L 2 ) {\\displaystyle Z=\\Omega (L^{2})} . This number of memory transfers has been shown to be asymptotically optimal for comparison sorts. Funnelsort also achieves the asymptotically optimal runtime complexity of \u0398 ( N log \u2061 N ) {\\displaystyle \\Theta (N\\log N)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Later authors such as Diana L. Paxson and Freya Aswynn follow Blum (1989) in drawing a direct correlation between runic divination and tarot divination. They may discuss runes in the context of \"spreads\" and advocate the usage of \"rune cards\". Modern authors like Ralph Blum sometimes include a \"blank rune\" in their sets. Some were to replace a lost rune, but according to Ralph Blum this was the god Odin's rune, the rune of the beginning and the end, representing \"the divine in all human transactions\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts. The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to mount a brute-force or dictionary based WPA password cracking attack on a WiFi user with WPA or WPA2 enabled, a hacker must first sniff the WPA 4-way handshake. The user can be elicited to provide this sequence by first forcing them offline with the deauthentication attack.In a similar phishing style attack without password cracking, Wifiphisher starts with a deauthentication attack to disconnect the user from their legitimate base station, then mounts a man-in-the-middle attack to collect passwords supplied by an unwitting user.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fuzzy logic is increasingly employed in diagnostic and medical equipment capable of measuring gradations of a condition. In information services, fuzzy concepts are frequently encountered because a customer or client asks a question about something which could be interpreted in different ways, or, a document is transmitted of a type or meaning which cannot be easily allocated to a known type or category, or to a known procedure. It might take considerable inquiry to \"place\" the information, or establish in what framework it should be understood.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These weights should exceed the weights of all existing matchings, to prevent appearance of artificial edges in the possible solution. As shown by Mulmuley, Vazirani and Vazirani, the problem of minimum weight perfect matching is converted to finding minors in the adjacency matrix of a graph. Using the isolation lemma, a minimum weight perfect matching in a graph can be found with probability at least 1\u20442. For a graph with n vertices, it requires O ( log 2 \u2061 ( n ) ) {\\displaystyle O(\\log ^{2}(n))} time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of structure, a triglyph may be carved from a single block with a metope, or the triglyph block may have slots cut into it to allow a separately cut metope (in stone or wood) to be slid into place, as at the Temple of Aphaea. Of the two groups of 6th-century metopes from Foce del Sele, now in the museum at Paestum, the earlier uses the first method, the later the second. There may be some variation in design within a single structure to allow for corner contraction, an adjustment of the column spacing and arrangement of the Doric frieze in a temple to make the design appear more harmonious. In the evolution of the Doric order, the placing of the triglyphs evolved somewhat, especially at corners.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an alternating group is the group of even permutations of a finite set. The alternating group on a set of n elements is called the alternating group of degree n, or the alternating group on n letters and denoted by An or Alt(n).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, signaling is the use of signals for controlling communications. This may constitute an information exchange concerning the establishment and control of a telecommunication circuit and the management of the network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The technique is known as a \"trivial hash function\" or, when used specifically for branch tables, \"double dispatch\". For this to be feasible, the range of all possible values of the data needs to be small (e.g. an ASCII or EBCDIC character value which have a range of hexadecimal '00' \u2013 'FF'. If the actual range is guaranteed to be smaller than this, the array can be truncated to less than 256 bytes).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are several algorithms for subband tree structuring that find a set of optimal bases that provide the most desirable representation of the data relative to a particular cost function (entropy, energy compaction, etc.). There were relevant studies in signal processing and communications fields to address the selection of subband trees (orthogonal basis) of various kinds, e.g. regular, dyadic, irregular, with respect to performance metrics of interest including energy compaction (entropy), subband correlations and others. Discrete wavelet transform theory (continuous in the time variable) offers an approximation to transform discrete (sampled) signals. In contrast, the discrete-time subband transform theory enables a perfect representation of already sampled signals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers n = x 2 + y 2 + z 2 {\\displaystyle n=x^{2}+y^{2}+z^{2}} if and only if n is not of the form n = 4 a ( 8 b + 7 ) {\\displaystyle n=4^{a}(8b+7)} for nonnegative integers a and b. The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as n = 4 a ( 8 b + 7 ) {\\displaystyle n=4^{a}(8b+7)} ) are 7, 15, 23, 28, 31, 39, 47, 55, 60, 63, 71 ... (sequence A004215 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Unified Modeling Language (UML), an object diagram focuses on some particular set of objects and attributes, and the links between these instances. A correlated set of object diagrams provides insight into how an arbitrary view of a system is expected to evolve over time. Early UML specifications described object diagrams as such: \"An object diagram is a graph of instances, including objects and data values. A static object diagram is an instance of a class diagram; it shows a snapshot of the detailed state of a system at a point in time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a uniform matroid is a matroid in which the independent sets are exactly the sets containing at most r elements, for some fixed integer r. An alternative definition is that every permutation of the elements is a symmetry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, every process\u2014including the X Server\u2014should be able to command the kernel to perform mode-setting operations, and the kernel would ensure that concurrent operations don't result in an inconsistent state. The new kernel API and code added to the DRM module to perform these mode-setting operations was called Kernel Mode-Setting (KMS).Kernel Mode-Setting provides several benefits. The most immediate is of course the removal of duplicate mode-setting code, from both the kernel (Linux console, fbdev) and user space (X Server DDX drivers).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More generally, recall is simply the complement of the type II error rate (i.e., one minus the type II error rate). Precision is related to the type I error rate, but in a slightly more complicated way, as it also depends upon the prior distribution of seeing a relevant vs. an irrelevant item. The above cat and dog example contained 8 \u2212 5 = 3 type I errors (false positives) out of 10 total cats (true negatives), for a type I error rate of 3/10, and 12 \u2212 5 = 7 type II errors, for a type II error rate of 7/12. Precision can be seen as a measure of quality, and recall as a measure of quantity. Higher precision means that an algorithm returns more relevant results than irrelevant ones, and high recall means that an algorithm returns most of the relevant results (whether or not irrelevant ones are also returned).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The presence of an increasing amount of on-line data will necessitate greater use of automatic data processing in decision-making. Saving data on multiple memory locations will guarantee the safekeeping of the acts. Statistical data will be available in real time and under multiple profiles, with great benefits for top level decision-making.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to increase traffic capacity and safety, a route may have two or more separate roads for each direction of traffic. Alternatively, a given road might be declared one-way.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, the class of exponential dispersion models (EDM) is a set of probability distributions that represents a generalisation of the natural exponential family. Exponential dispersion models play an important role in statistical theory, in particular in generalized linear models because they have a special structure which enables deductions to be made about appropriate statistical inference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Implicit regularization is essentially ubiquitous in modern machine learning approaches, including stochastic gradient descent for training deep neural networks, and ensemble methods (such as random forests and gradient boosted trees).In explicit regularization, independent of the problem or model, there is always a data term, that corresponds to a likelihood of the measurement and a regularization term that corresponds to a prior. By combining both using Bayesian statistics, one can compute a posterior, that includes both information sources and therefore stabilizes the estimation process. By trading off both objectives, one chooses to be more addictive to the data or to enforce generalization (to prevent overfitting).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The manuscripts available are of variable quality, and invariably incomplete. By careful analysis of the translations and originals, hypotheses have been made about the contents of the original text (copies of which are no longer available). Ancient texts which refer to the Elements itself, and to other mathematical theories that were current at the time it was written, are also important in this process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such procedures are often implemented in various convenience routines such as daemon(3) in Unix. Systems often start daemons at boot time that will respond to network requests, hardware activity, or other programs by performing some task. Daemons such as cron may also perform defined tasks at scheduled times.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural languages, the meaning of a complex spoken sentence can be understood by decomposing it into smaller lexical segments (roughly, the words of the language), associating a meaning to each segment, and combining those meanings according to the grammar rules of the language. Though lexical recognition is not thought to be used by infants in their first year, due to their highly limited vocabularies, it is one of the major processes involved in speech segmentation for adults. Three main models of lexical recognition exist in current research: first, whole-word access, which argues that words have a whole-word representation in the lexicon; second, decomposition, which argues that morphologically complex words are broken down into their morphemes (roots, stems, inflections, etc.) and then interpreted and; third, the view that whole-word and decomposition models are both used, but that the whole-word model provides some computational advantages and is therefore dominant in lexical recognition.To give an example, in a whole-word model, the word \"cats\" might be stored and searched for by letter, first \"c\", then \"ca\", \"cat\", and finally \"cats\". The same word, in a decompositional model, would likely be stored under the root word \"cat\" and could be searched for after removing the \"s\" suffix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, continuous integration (CI) is the practice of merging all developers' working copies to a shared mainline several times a day. Nowadays it is typically implemented in such a way that it triggers an automated build with testing. Grady Booch first proposed the term CI in his 1991 method, although he did not advocate integrating several times a day. Extreme programming (XP) adopted the concept of CI and did advocate integrating more than once per day \u2013 perhaps as many as tens of times per day.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, fractional programming is a generalization of linear-fractional programming. The objective function in a fractional program is a ratio of two functions that are in general nonlinear. The ratio to be optimized often describes some kind of efficiency of a system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to find and communicate with clients in proximity of a device, the protocol makes use of both the server and client modes of Bluetooth LE, switching between the two frequently. In server mode the device advertises its EphID to be read by clients, with clients scanning for servers. When a client and server meet, the client reads the EphID and subsequently writes its own EphID to the server. The two devices then store the encounter in their respective contact logs in addition to a coarse timestamp and signal strength. The signal strength is later used as part of the infection reporting process to estimate the distance between an infected patient and the user.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that the polynomial is a q-analogue of the hook length formula. Furthermore, let \u03bb be a rectangular partition of size n, and let X be the set of semi-standard Young tableaux of shape \u03bb. Let C = Z/kZ act on X via k-promotion. Then ( X , C , q \u2212 \u03ba ( \u03bb ) s \u03bb ( 1 , q , q 2 , \u2026 , q k \u2212 1 ) ) {\\displaystyle (X,C,q^{-\\kappa (\\lambda )}s_{\\lambda }(1,q,q^{2},\\dotsc ,q^{k-1}))} exhibit the cyclic sieving phenomenon.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern protocol design, protocols are layered to form a protocol stack. Layering is a design principle that divides the protocol design task into smaller steps, each of which accomplishes a specific part, interacting with the other parts of the protocol only in a small number of well-defined ways. Layering allows the parts of a protocol to be designed and tested without a combinatorial explosion of cases, keeping each design relatively simple. The communication protocols in use on the Internet are designed to function in diverse and complex settings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in the area of abstract algebra dealing with ordered structures on abelian groups, the Hahn embedding theorem gives a simple description of all linearly ordered abelian groups. It is named after Hans Hahn.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, B\u00fcchi's problem, also known as the n squares' problem, is an open problem named after the Swiss mathematician Julius Richard B\u00fcchi. It asks whether there is a positive integer M such that every sequence of M or more integer squares, whose second difference is constant and equal to 2, is necessarily a sequence of squares of the form (x + i)2, i = 1, 2, ..., M,... for some integer x. In 1983, Douglas Hensley observed that B\u00fcchi's problem is equivalent to the following: Does there exist a positive integer M such that, for all integers x and a, the quantity (x + n)2 + a cannot be a square for more than M consecutive values of n, unless a = 0?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practical applications, one would have several BDKs on record, possibly for different customers, or to contain the scope of key compromise. When processing transactions, it is important for the receiver to know which BDK was used to initialize the originating device. To achieve this, the 80-bit KSN is structured into three parts: as Key Set ID, a TRSM ID, and the transaction counter. The algorithm specifies that the transaction counter is 21-bits, but treats the remaining 59 bits opaquely (the algorithm only specifies that unused bits be 0-padded to a nibble boundary, and then 'f' padded to the 80-bit boundary).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above experiment, participants were presented with a list of 100 familiar words and were asked to read them aloud while simultaneously trying to remember each one. Subsequent to this, participants were asked to make a recognition decision based on the number of \"yes\" responses that were accompanied by some recollective experience. The results demonstrate the differing relationships between the \"yes\" and \"no\" conditions and \"remember\" and \"know\" memory performance. The outcome confirms that although familiarity and recollection may involve different processes, the remember/know exemplar does not probe them directly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(This step is the same as in Factor analysis). Estimate the Discriminant Function Coefficients and determine the statistical significance and validity\u2014Choose the appropriate discriminant analysis method. The direct method involves estimating the discriminant function so that all the predictors are assessed simultaneously.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "First, they define a set of items that are called small. Let T be the total size of all small items. Then, they construct a matrix A representing all configurations with sum < 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a regular matroid is a matroid that can be represented over all fields.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In studies of the networks of citations between scientific papers, Derek de Solla Price showed in 1965 that the number of links to papers\u2014i.e., the number of citations they receive\u2014had a heavy-tailed distribution following a Pareto distribution or power law, and thus that the citation network is scale-free. He did not however use the term \"scale-free network\", which was not coined until some decades later. In a later paper in 1976, Price also proposed a mechanism to explain the occurrence of power laws in citation networks, which he called \"cumulative advantage\" but which is today more commonly known under the name preferential attachment. Recent interest in scale-free networks started in 1999 with work by Albert-L\u00e1szl\u00f3 Barab\u00e1si and R\u00e9ka Albert at the University of Notre Dame who mapped the topology of a portion of the World Wide Web, finding that some nodes, which they called \"hubs\", had many more connections than others and that the network as a whole had a power-law distribution of the number of links connecting to a node.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1980s, NLP was advertised as an important advance in psychotherapy and counseling, and attracted some interest in counseling research and clinical psychology. However, as controlled trials failed to show any benefit from NLP and its advocates made increasingly dubious claims, scientific interest in NLP faded.Numerous literature reviews and meta-analyses have failed to show evidence for NLP's assumptions or effectiveness as a therapeutic method. While some NLP practitioners have argued that the lack of empirical support is due to insufficient research which tests NLP, the consensus scientific opinion is that NLP is pseudoscience and that attempts to dismiss the research findings based on these arguments \"s an admission that NLP does not have an evidence base and that NLP practitioners are seeking a post-hoc credibility.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The equation a 2 = c + d 2 {\\displaystyle a^{2}=c+d^{2}} shows that |a| > \u221ac. Thus, if the nested radical is real, and if denesting is possible, then a > 0. Then the solution is", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Chevalley\u2013Shephard\u2013Todd theorem in invariant theory of finite groups states that the ring of invariants of a finite group acting on a complex vector space is a polynomial ring if and only if the group is generated by pseudoreflections. In the case of subgroups of the complex general linear group the theorem was first proved by G. C. Shephard and J. A. Todd (1954) who gave a case-by-case proof. Claude Chevalley (1955) soon afterwards gave a uniform proof. It has been extended to finite linear groups over an arbitrary field in the non-modular case by Jean-Pierre Serre.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Different kinds of Kolmogorov complexity are studied: the uniform complexity, prefix complexity, monotone complexity, time-bounded Kolmogorov complexity, and space-bounded Kolmogorov complexity. An axiomatic approach to Kolmogorov complexity based on Blum axioms (Blum 1967) was introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov. The axiomatic approach encompasses other approaches to Kolmogorov complexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "String metrics and edit distances. There are many ways of measuring distances between strings of characters, which may represent sentences in computational linguistics or code words in coding theory. Edit distances attempt to measure the number of changes necessary to get from one string to another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This little program prints three \u201c1\u201ds to the right, reverses direction and moves left printing 0\u2019s until it hits a blank. We will print all the symbols that our machine uses: Here at the end we find that a blank on the left has \u201ccome into play\u201d so we leave it as part of the total configuration. Given that we have done our job correctly, we add the starting conditions and see \u201cwhere the theorem goes\u201d.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In naive set theory, a set is described as a well-defined collection of objects. These objects are called the elements or members of the set. Objects can be anything: numbers, people, other sets, etc. For instance, 4 is a member of the set of all even integers. Clearly, the set of even numbers is infinitely large; there is no requirement that a set be finite. The definition of sets goes back to Georg Cantor. He wrote in his 1915 article Beitr\u00e4ge zur Begr\u00fcndung der transfiniten Mengenlehre: \u201cUnter einer 'Menge' verstehen wir jede Zusammenfassung M von bestimmten wohlunterschiedenen Objekten unserer Anschauung oder unseres Denkens (welche die 'Elemente' von M genannt werden) zu einem Ganzen.\u201d \u2013 Georg Cantor \u201cA set is a gathering together into a whole of definite, distinct objects of our perception or of our thought\u2014which are called elements of the set.\u201d \u2013 Georg Cantor", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical researchers can then avoid going down blind alleys and learn to modify conjectures to produce provable theorems. It is sometimes said that mathematical development consists primarily in finding (and proving) theorems and counterexamples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years many other matrix factorization models have been developed to exploit the ever increasing amount and variety of available interaction data and use cases. Hybrid matrix factorization algorithms are capable of merging explicit and implicit interactions or both content and collaborative data", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Excessive use of whitespace, especially trailing whitespace at the end of lines, is considered a nuisance. However correct use of whitespace can make the code easier to read and help group related logic. Most languages only recognize ASCII characters as whitespace, or in some cases Unicode newlines as well, but not most of the characters listed above. The C language defines whitespace characters to be \"space, horizontal tab, new-line, vertical tab, and form-feed\". The HTTP network protocol requires different types of whitespace to be used in different parts of the protocol, such as: only the space character in the status line, CRLF at the end of a line, and \"linear whitespace\" in header values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "0&0&1&0&0\\\\0&0&0&0&1\\\\0&0&0&1&0\\end{pmatrix}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "RANAP handles signaling for the Iu-PS - RNC and 3G SGSN and Iu-CS - RNC and 3G MSC . It also provides the signaling channel to transparently pass messages between the User Equipment (UE) and the CN. In LTE, RANAP has been replaced by S1AP. In SA (standalone) installations of 5G, S1AP will be replaced by NGAP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, a single recursive call locates the desired element in the correct partition, and we build upon this for quickselect: // Returns the k-th smallest element of list within left..right inclusive // (i.e. left <= k <= right). function select(list, left, right, k) is if left = right then // If the list contains only one element, return list // return that element pivotIndex := ... // select a pivotIndex between left and right, // e.g., left + floor(rand() % (right \u2212 left + 1)) pivotIndex := partition(list, left, right, pivotIndex) // The pivot is in its final sorted position if k = pivotIndex then return list else if k < pivotIndex then return select(list, left, pivotIndex \u2212 1, k) else return select(list, pivotIndex + 1, right, k) Note the resemblance to quicksort: just as the minimum-based selection algorithm is a partial selection sort, this is a partial quicksort, generating and partitioning only O ( log \u2061 n ) {\\displaystyle O(\\log n)} of its O ( n ) {\\displaystyle O(n)} partitions. This simple procedure has expected linear performance, and, like quicksort, has quite good performance in practice. It is also an in-place algorithm, requiring only constant memory overhead if tail call optimization is available, or if eliminating the tail recursion with a loop: function select(list, left, right, k) is loop if left = right then return list pivotIndex := ... // select pivotIndex between left and right pivotIndex := partition(list, left, right, pivotIndex) if k = pivotIndex then return list else if k < pivotIndex then right := pivotIndex \u2212 1 else left := pivotIndex + 1", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", AN) with A0 = 0. Then the largest stopping time to exercise the American option in an optimal way is \u03c4 max := { N if A N = 0 , min { n \u2208 { 0 , \u2026 , N \u2212 1 } \u2223 A n + 1 < 0 } if A N < 0. {\\displaystyle \\tau _{\\text{max}}:={\\begin{cases}N&{\\text{if }}A_{N}=0,\\\\\\min\\{n\\in \\{0,\\dots ,N-1\\}\\mid A_{n+1}<0\\}&{\\text{if }}A_{N}<0.\\end{cases}}} Since A is predictable, the event {\u03c4max = n} = {An = 0, An+1 < 0} is in Fn for every n \u2208 {0, 1, .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the number of comparisons, the performance of binary search can be analyzed by viewing the run of the procedure on a binary tree. The root node of the tree is the middle element of the array. The middle element of the lower half is the left child node of the root, and the middle element of the upper half is the right child node of the root. The rest of the tree is built in a similar fashion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\mathbb {N} .} N {\\displaystyle \\mathbb {N} } is the intersection of all sets satisfying (1) and (2).There are many sets that satisfy (1) and (2) \u2013 for example, the set {1, 1.649, 2, 2.649, 3, 3.649, \u2026} satisfies the definition. However, condition (3) specifies the set of natural numbers by removing the sets with extraneous members.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 2000s, some Web developers began to question why Web authors ever made the leap into authoring in XHTML. Others countered that the problems ascribed to the use of XHTML could mostly be attributed to two main sources: the production of invalid XHTML documents by some Web authors and the lack of support for XHTML built into Internet Explorer 6. They went on to describe the benefits of XML-based Web documents (i.e. XHTML) regarding searching, indexing, and parsing as well as future-proofing the Web itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is basically testing how well a system recovers from crashes, hardware failures, or other catastrophic problems Examples of recovery testing: While an application is running, suddenly restart the computer, and afterwards check the validness of the application's data integrity. While an application is receiving data from a network, unplug the connecting cable. After some time, plug the cable back in and analyze the application's ability to continue receiving data from the point at which the network connection disappeared.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is the part of the observed score that would recur across different measurement occasions in the absence of error. Errors of measurement are composed of both random error and systematic error. It represents the discrepancies between scores obtained on tests and the corresponding true scores. This conceptual breakdown is typically represented by the simple equation: Observed test score = true score + errors of measurement", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a stochastic process is said to have stationary increments if its change only depends on the time span of observation, but not on the time when the observation was started. Many large families of stochastic processes have stationary increments either by definition (e.g. L\u00e9vy processes) or by construction (e.g. random walks)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, a short introduction to input-output analysis and its environmental extension for the calculation of material footprints or RME indicators is provided. The inter-industry flows within an economy form an n\u00d7n matrix Z and the total output of each industry forms an n\u00d71 vector x. By dividing each flow into an industry (i.e., each element of Z) by the total output of that same industry, we obtain an n\u00d7n matrix of so-called technical coefficients A. In matrix algebra, this reads as follows: A = Z \u00d7 x ^ \u2212 1 {\\displaystyle A=Z\\times {\\hat {x}}^{-1}} where: x ^ {\\displaystyle {\\hat {x}}} represents the vector x diagonlized into a matrix ( x ^ = I x \u2192 {\\displaystyle {\\hat {x}}=I{\\vec {x}}} )Matrix A contains the multipliers for the inter-industry inputs required to supply one unit of industry output. A certain total economic output x is required to satisfy a given level of final demand y. This final demand may be domestic (for private households as well as the public sector) or foreign (exports) and can be written as an n\u00d71 vector. When this vector of final demand y is multiplied by the Leontief inverse (I\u2212A)\u22121, we obtain total output x. I is the identity matrix so that the following matrix equation is the result of equivalence operations in our previous equation: x \u2192 = ( I \u2212 A ) \u2212 1 \u00d7 y \u2192 {\\displaystyle {\\vec {x}}=\\left(I-A\\right)^{-1}\\times {\\vec {y}}} The Leontief inverse contains the multipliers for the direct and indirect inter-industry inputs required to provide 1 unit of output to final demand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although these examples offer alternate strategies for achieving the same abstraction, they do not fundamentally alter the need to support abstract nouns in code \u2013 all programming relies on an ability to abstract verbs as functions, nouns as data structures, and either as processes. Consider for example a sample Java fragment to represent some common farm \"animals\" to a level of abstraction suitable to model simple aspects of their hunger and feeding. It defines an Animal class to represent both the state of the animal and its functions: With the above definition, one could create objects of type Animal and call their methods like this: In the above example, the class Animal is an abstraction used in place of an actual animal, LivingThing is a further abstraction (in this case a generalisation) of Animal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development or backward compatibility is a general notion of interoperation between software pieces that will not produce any errors when its functionality is invoked via API. The software is considered stable when its API that is used to invoke functions is stable across different versions. In operating systems upgraded to a newer versions are said to be backward compatible if executable and other files from previous versions will work as usual.In compilers backward compatibility may refer to the ability of a compiler of a newer version of the language to accept source code of programs or data that worked under the previous version.A data format is said to be backward compatible when a newer version of program that can open it opens it without errors just like its predecessor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Jordan\u2013H\u00f6lder theorem is a more precise way of stating this fact about finite groups. However, a significant difference from integer factorization is that such \"building blocks\" do not necessarily determine a unique group, since there might be many non-isomorphic groups with the same composition series or, put in another way, the extension problem does not have a unique solution. Gorenstein (d.1992), Lyons, and Solomon are gradually publishing a simplified and revised version of the proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phylogenetics, informative site is a term used when maximum parsimony is the optimality criterion for construction of a phylogenetic tree. It refers to a characteristic for which the number of character-state evolutionary changes of at this site depends on the topology of the tree. The charactetistics can take on multiple types of data, including morphological (such as the presence of wings, tentacles, etc.) or molecular information such as sequences of DNA or proteins. The informative site is a position in the relevant set of aligned sequences at which there are at least two different character states and each of those states occurs in at least two of the sequences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the encoded format a \"1\" bit indicates a flux transition, while a \"0\" indicates that the magnetic field on the disk does not change for that time interval.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In science and engineering, a system is the part of the universe that is being studied, while the environment is the remainder of the universe that lies outside the boundaries of the system. It is also known as the surroundings or neighborhood, and in thermodynamics, as the reservoir. Depending on the type of system, it may interact with the environment by exchanging mass, energy (including heat and work), linear momentum, angular momentum, electric charge, or other conserved properties. In some disciplines, such as information theory, information may also be exchanged. The environment is ignored in analysis of the system, except in regard to these interactions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Advantages of this approach include the general increased quality of the data returned in searches and with proper tagging, ontologies finding entries that may not explicitly state the search term but are still relevant. One disadvantage of this approach is that the results that are returned come in the format of the database of their origin and as such, direct comparisons may be difficult. Another problem is that the terms used in tagging and searching can sometimes be ambiguous and may cause confusion among the results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, multiple access schemes are orthogonal when an ideal receiver can completely reject arbitrarily strong unwanted signals from the desired signal using different basis functions. One such scheme is time-division multiple access (TDMA), where the orthogonal basis functions are nonoverlapping rectangular pulses (\"time slots\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was later argued that it has strong biological motivations and mathematical justifications. In 2011 it was found to enable better training of deeper networks, compared to the widely used activation functions prior to 2011, e.g., the logistic sigmoid (which is inspired by probability theory; see logistic regression) and its more practical counterpart, the hyperbolic tangent. The rectifier is, as of 2017, the most popular activation function for deep neural networks.Rectified linear units find applications in computer vision and speech recognition using deep neural nets and computational neuroscience.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to understand morphogenetic events, i.e. the growth and shaping of tissues and organs, it is necessary to analyze the packing of cells into tissues. In that context, an analysis of patterning processes can help to identify the underlying mechanisms that drive morphogenesis. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s, there was a general confusion about the proper character encoding to use to write text in Latin Croatian on computers. An attempt was made to apply the 7-bit \"YUSCII\", later \"CROSCII\", which included the five letters with diacritics at the expense of five non-letter characters (, {, }, @), but it was ultimately unsuccessful. Because the ASCII character @ sorts before A, this led to jokes calling it \u017eabeceda (\u017eaba=frog, abeceda=alphabet). Other short-lived vendor-specific efforts were also undertaken.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Previous work includes the work of D. Coppersmith about the DLP in fields of characteristic two. The discrete logarithm problem in a finite field consists of solving the equation a x = b {\\displaystyle a^{x}=b} for a , b \u2208 F p n {\\displaystyle a,b\\in \\mathbb {F} _{p^{n}}} , p {\\displaystyle p} a prime number and n {\\displaystyle n} an integer. The function f: F p n \u2192 F p n , x \u21a6 a x {\\displaystyle f:\\mathbb {F} _{p^{n}}\\to \\mathbb {F} _{p^{n}},x\\mapsto a^{x}} for a fixed a \u2208 F p n {\\displaystyle a\\in \\mathbb {F} _{p^{n}}} is a one-way function used in cryptography. Several cryptographic methods are based on the DLP such as the Diffie-Hellman key exchange, the El Gamal cryptosystem and the Digital Signature Algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing this process is known as discrete convolution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, the value of the coefficient of determination will shrink relative to the original data. To lessen the chance or amount of overfitting, several techniques are available (e.g., model comparison, cross-validation, regularization, early stopping, pruning, Bayesian priors, or dropout). The basis of some techniques is either (1) to explicitly penalize overly complex models or (2) to test the model's ability to generalize by evaluating its performance on a set of data not used for training, which is assumed to approximate the typical unseen data that a model will encounter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Q-matrix is a square matrix whose associated linear complementarity problem LCP(M,q) has a solution for every vector q.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some consider it to be an anti-pattern. There are valid forms of the pattern, including the use of the volatile keyword in Java and explicit memory barriers in C++.The pattern is typically used to reduce locking overhead when implementing \"lazy initialization\" in a multi-threaded environment, especially as part of the Singleton pattern. Lazy initialization avoids initializing a value until the first time it is accessed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of a jump process that takes states in a state space S {\\displaystyle \\mathrm {S} } , consider the set of random variables ( X n , T n ) {\\displaystyle (X_{n},T_{n})} , where T n {\\displaystyle T_{n}} represents the jump times and X n {\\displaystyle X_{n}} represents the associated states in the sequence of states (see Figure). Let the sequence of inter-arrival times \u03c4 n = T n \u2212 T n \u2212 1 {\\displaystyle \\tau _{n}=T_{n}-T_{n-1}} . In order for the sequence ( X n , T n ) {\\displaystyle (X_{n},T_{n})} to be considered a Markov renewal process the following condition should hold: Pr ( \u03c4 n + 1 \u2264 t , X n + 1 = j \u2223 ( X 0 , T 0 ) , ( X 1 , T 1 ) , \u2026 , ( X n = i , T n ) ) = Pr ( \u03c4 n + 1 \u2264 t , X n + 1 = j \u2223 X n = i ) \u2200 n \u2265 1 , t \u2265 0 , i , j \u2208 S {\\displaystyle {\\begin{aligned}&\\Pr(\\tau _{n+1}\\leq t,X_{n+1}=j\\mid (X_{0},T_{0}),(X_{1},T_{1}),\\ldots ,(X_{n}=i,T_{n}))\\\\={}&\\Pr(\\tau _{n+1}\\leq t,X_{n+1}=j\\mid X_{n}=i)\\,\\forall n\\geq 1,t\\geq 0,i,j\\in \\mathrm {S} \\end{aligned}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fields of machine learning, the theory of computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position if its covariance matrix is equal to the identity matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are two running instances of each role. In this example, the cache is distributed across all instances of the dedicated Cache1 role. A dedicated topology has the advantage of scaling the caching tier independently of any other role in the cloud service. For the best Caching performance, a dedicated topology is recommended because the role instances do not share their resources with other application code and services.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the values are frequently represented as 1 or 0, which corresponds to counting the number of successes in a single trial: 1 (success) or 0 (failure); see \u00a7 Counting. Often, binary data is used to represent one of two conceptually opposed values, e.g.: the outcome of an experiment (\"success\" or \"failure\") the response to a yes\u2013no question (\"yes\" or \"no\") presence or absence of some feature (\"is present\" or \"is not present\") the truth or falsehood of a proposition (\"true\" or \"false\", \"correct\" or \"incorrect\")However, it can also be used for data that is assumed to have only two possible values, even if they are not conceptually opposed or conceptually represent all possible values in the space. For example, binary data is often used to represent the party choices of voters in elections in the United States, i.e. Republican or Democratic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to explain column-level encryption it is important to outline basic database structure. A typical relational database is divided into tables that are divided into columns that each have rows of data. Whilst TDE usually encrypts an entire database, column-level encryption allows for individual columns within a database to be encrypted. It is important to establish that the granularity of column-level encryption causes specific strengths and weaknesses to arise when compared to encrypting an entire database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formally, a sequence of numbers s 0 , s 1 , s 2 , s 3 , \u2026 {\\displaystyle s_{0},s_{1},s_{2},s_{3},\\ldots } is constant-recursive if it satisfies a recurrence relation where c i {\\displaystyle c_{i}} are constants. For example, the Fibonacci sequence satisfies the recurrence relation F n = F n \u2212 1 + F n \u2212 2 , {\\displaystyle F_{n}=F_{n-1}+F_{n-2},} where F n {\\displaystyle F_{n}} is the n {\\displaystyle n} th Fibonacci number. Constant-recursive sequences are studied in combinatorics and the theory of finite differences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In his formal published treatises, Archimedes solved the same problem using the method of exhaustion. The 15th century saw the work of Nicholas of Cusa, further developed in the 17th century by Johannes Kepler, in particular, the calculation of the area of a circle by representing the latter as an infinite-sided polygon. Simon Stevin's work on the decimal representation of all numbers in the 16th century prepared the ground for the real continuum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to evaluate the outcomes of a program, the evaluator first needs to monitor the process in order to assess the implementation of the intervention. The reason for this is that many program failures are due to failures in the implementation of the program. Therefore, in order to determine whether or not the planned outcomes have been reached, the evaluator needs to assess how the intervention was implemented.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Computer manufacturers who had a significant business in the defense, aerospace, or related industries, also offered Ada compilers and tools on their platforms; these included Concurrent Computer Corporation, Cray Research, Inc., Digital Equipment Corporation, Harris Computer Systems, and Siemens Nixdorf Informationssysteme AG.In 1991, the US Department of Defense began to require the use of Ada (the Ada mandate) for all software, though exceptions to this rule were often granted. The Department of Defense Ada mandate was effectively removed in 1997, as the DoD began to embrace commercial off-the-shelf (COTS) technology. Similar requirements existed in other NATO countries: Ada was required for NATO systems involving command and control and other functions, and Ada was the mandated or preferred language for defense-related applications in countries such as Sweden, Germany, and Canada.By the late 1980s and early 1990s, Ada compilers had improved in performance, but there were still barriers to fully exploiting Ada's abilities, including a tasking model that was different from what most real-time programmers were used to.Because of Ada's safety-critical support features, it is now used not only for military applications, but also in commercial projects where a software bug can have severe consequences, e.g., avionics and air traffic control, commercial rockets such as the Ariane 4 and 5, satellites and other space systems, railway transport and banking.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following examples, computed values are in bold, while Register numbers are not.For example, to write the value 3 to register 1, (which already contains a 6), and then add 7 to register 1 and store the result in register 2, i.e.: i0: R1 = 6 i1: R1 = 3 i2: R2 = R1 + 7 = 10 Following execution, register 2 should contain the value 10. However, if i1 (write 3 to register 1) does not fully exit the pipeline before i2 starts executing, it means that R1 does not contain the value 3 when i2 performs its addition. In such an event, i2 adds 7 to the old value of register 1 (6), and so register 2 contains 13 instead, i.e.: i0: R1 = 6 i2: R2 = R1 + 7 = 13 i1: R1 = 3 This error occurs because i2 reads Register 1 before i1 has committed/stored the result of its write operation to Register 1. So when i2 is reading the contents of Register 1, register 1 still contains 6, not 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By taking the determiner, a function word, to be head over the noun, a structure is established that is analogous to the structure of the finite clause, with a complementizer. Apart from the minimalist program, however, the DP hypothesis is rejected by most other modern theories of syntax and grammar, in part because these theories lack the relevant functional categories. Dependency grammars, for instance, almost all assume the traditional NP analysis of noun phrases. For illustrations of different analyses of noun phrases depending on whether the DP hypothesis is rejected or accepted, see the next section.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid taken to be conjunction, the set of all formal languages over a given alphabet \u03a3 under concatenation, the set of all binary relations on a given set X under relational composition, and more generally the power set of any equivalence relation, again under relational composition. The original application was to relation algebras as a finitely axiomatized generalization of the binary relation example, but there exist interesting examples of residuated Boolean algebras that are not relation algebras, such as the language example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a signature matrix is a diagonal matrix whose diagonal elements are plus or minus 1, that is, any matrix of the form: A = ( \u00b1 1 0 \u22ef 0 0 0 \u00b1 1 \u22ef 0 0 \u22ee \u22ee \u22f1 \u22ee \u22ee 0 0 \u22ef \u00b1 1 0 0 0 \u22ef 0 \u00b1 1 ) {\\displaystyle A={\\begin{pmatrix}\\pm 1&0&\\cdots &0&0\\\\0&\\pm 1&\\cdots &0&0\\\\\\vdots &\\vdots &\\ddots &\\vdots &\\vdots \\\\0&0&\\cdots &\\pm 1&0\\\\0&0&\\cdots &0&\\pm 1\\end{pmatrix}}} Any such matrix is its own inverse, hence is an involutory matrix. It is consequently a square root of the identity matrix. Note however that not all square roots of the identity are signature matrices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The distinction between data and derived value is illustrated by the information ladder. However, data has staged a comeback with the popularisation of the term big data, which refers to the collection and analyses of massive sets of data. Several organisations have established data management centers (DMC) for their operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One start code, one house code, and one function code is known as an X10 frame and represent the minimum components of a valid X10 data packet. Each frame is sent twice in succession to make sure the receivers understand it over any power line noise for purposes of redundancy, reliability, and to accommodate line repeaters. After allowing for retransmission, line control, etc., data rates are around 20 bit/s, making X10 data transmission so slow that the technology is confined to turning devices on and off or other very simple operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We also add a team node for each team and connect each game node {i, j} with i < j to V, and connects each of them from s by an edge with capacity rij \u2013 which represents the number of plays between these two teams. We also add a team node for each team and connect each game node {i, j} with two team nodes i and j to ensure one of them wins. One does not need to restrict the flow value on these edges. Finally, edges are made from team node i to the sink node t and the capacity of wk + rk \u2013 wi is set to prevent team i from winning more than wk + rk. Let S be the set of all teams participating in the league and let r ( S \u2212 { k } ) = \u2211 i , j \u2208 { S \u2212 { k } } i < j r i j {\\displaystyle r(S-\\{k\\})=\\sum _{i,j\\in \\{S-\\{k\\}\\} \\atop i", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a branch of mathematics Poisson-Dirichlet distributions are probability distributions on the set of nonnegative, non-decreasing sequences with sum 1, depending on two parameters \u03b1 \u2208 [ 0 , 1 ) {\\displaystyle \\alpha \\in [0,1)} and \u03b8 \u2208 ( \u2212 \u03b1 , \u221e ) {\\displaystyle \\theta \\in (-\\alpha ,\\infty )} . It can be defined as follows. One considers independent random variables ( Y n ) n \u2265 1 {\\displaystyle (Y_{n})_{n\\geq 1}} such that Y n {\\displaystyle Y_{n}} follows the beta distribution of parameters 1 \u2212 \u03b1 {\\displaystyle 1-\\alpha } and \u03b8 + n \u03b1 {\\displaystyle \\theta +n\\alpha } . Then, the Poisson-Dirichlet distribution P D ( \u03b1 , \u03b8 ) {\\displaystyle PD(\\alpha ,\\theta )} of parameters \u03b1 {\\displaystyle \\alpha } and \u03b8 {\\displaystyle \\theta } is the law of the random decreasing sequence containing Y 1 {\\displaystyle Y_{1}} and the products Y n \u220f k = 1 n \u2212 1 ( 1 \u2212 Y k ) {\\displaystyle Y_{n}\\prod _{k=1}^{n-1}(1-Y_{k})} . This definition is due to Jim Pitman and Marc Yor. It generalizes Kingman's law, which corresponds to the particular case \u03b1 = 0 {\\displaystyle \\alpha =0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(Why do we have all these abbreviations anyway? Saving bandwidth?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Kleene algebra ( KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operations known from regular expressions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(1) This is a bank. This bank accepted my identification. (2) She is a bank teller.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Created in 1978, it is still used today for applications involving digital signatures. Using number theory, the RSA algorithm selects two prime numbers, which help generate both the encryption and decryption keys.A publicly available public-key encryption application called Pretty Good Privacy (PGP) was written in 1991 by Phil Zimmermann, and distributed free of charge with source code. PGP was purchased by Symantec in 2010 and is regularly updated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Lucas's theorem expresses the remainder of division of the binomial coefficient ( m n ) {\\displaystyle {\\tbinom {m}{n}}} by a prime number p in terms of the base p expansions of the integers m and n. Lucas's theorem first appeared in 1878 in papers by \u00c9douard Lucas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the classical setting, RG can be viewed as the following problem. Alice, Bob, and the referee is given some statement. Alice is trying to convince the referee that the statement is true while Bob is trying to convince the referee that the statement is false. The referee, who has limited computing power, will look at the proofs provided by Alice and Bob, ask them questions, and at the end of the day decide which player is correct (wins).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory and order theory, the Cantor\u2013Bernstein theorem states that the cardinality of the second type class, the class of countable order types, equals the cardinality of the continuum. It was used by Felix Hausdorff and named by him after Georg Cantor and Felix Bernstein. Cantor constructed a family of countable order types with the cardinality of the continuum, and in his 1901 inaugural dissertation Bernstein proved that such a family can have no higher cardinality. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In partition calculus, part of combinatorial set theory, a branch of mathematics, the Erd\u0151s\u2013Rado theorem is a basic result extending Ramsey's theorem to uncountable sets. It is named after Paul Erd\u0151s and Richard Rado. It is sometimes also attributed to \u0110uro Kurepa who proved it under the additional assumption of the generalised continuum hypothesis, and hence the result is sometimes also referred to as the Erd\u0151s\u2013Rado\u2013Kurepa theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One picks a set \u03b9 to be the type of individuals. For example, \u03b9 might be the set of natural numbers, or the set of atoms (in a set theory with atoms) or any other set one is interested in. Then if \u03c41,...,\u03c4m are types, the type (\u03c41,...,\u03c4m) is the power set of the product \u03c41\u00d7...\u00d7\u03c4m, which can also be thought of informally as the set of (propositional predicative) functions from this product to a 2-element set {true,false}. The ramified type (\u03c41,...,\u03c4m|\u03c31,...,\u03c3n) can be modeled as the product of the type (\u03c41,...,\u03c4m,\u03c31,...,\u03c3n) with the set of sequences of n quantifiers (\u2200 or \u2203) indicating which quantifier should be applied to each variable \u03c3i. (One can vary this slightly by allowing the \u03c3s to be quantified in any order, or allowing them to occur before some of the \u03c4s, but this makes little difference except to the bookkeeping.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In summary, each perspective focuses attention on the same fundamental questions, then answers those questions from that viewpoint, creating different descriptive representations (i.e., models), which translate from higher to lower perspectives. The basic model for the focus (or product abstraction) remains constant. The basic model of each column is uniquely defined, yet related across and down the matrix. In addition, the six categories of enterprise architecture components, and the underlying interrogatives that they answer, form the columns of the Zachman Framework and these are: Inventory Sets \u2014 What Process Flows \u2014 How Distribution Networks \u2014 Where Responsibility Assignments \u2014 Who Timing Cycles \u2014 When Motivation Intentions \u2014 WhyIn Zachman's opinion, the single factor that makes his framework unique is that each element on either axis of the matrix is explicitly distinguishable from all the other elements on that axis. The representations in each cell of the matrix are not merely successive levels of increasing detail, but actually are different representations \u2014 different in context, meaning, motivation, and use. Because each of the elements on either axis is explicitly different from the others, it is possible to define precisely what belongs in each cell.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Stack overflow may be difficult to avoid when using recursive procedures since many compilers assume that the recursion stack is a contiguous area of memory, and some allocate a fixed amount of space for it. Compilers may also save more information in the recursion stack than is strictly necessary, such as return address, unchanging parameters, and the internal variables of the procedure. Thus, the risk of stack overflow can be reduced by minimizing the parameters and internal variables of the recursive procedure or by using an explicit stack structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a block check character (BCC) is a character added to a transmission block to facilitate error detection. In longitudinal redundancy checking and cyclic redundancy checking, block check characters are computed for, and added to, each message block transmitted. This block check character is compared with a second block check character computed by the receiver to determine whether the transmission is error free.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above UML class diagram, the Client class refers to the common AbstractExpression interface for interpreting an expression interpret(context). The TerminalExpression class has no children and interprets an expression directly. The NonTerminalExpression class maintains a container of child expressions (expressions) and forwards interpret requests to these expressions. The object collaboration diagram shows the run-time interactions: The Client object sends an interpret request to the abstract syntax tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, if all voter factions have the same proportion of strategic and honest voters, simulations show that any significant proportion of honest voters will lead to results which tend to be more satisfying to voters than approval voting, and indeed, more satisfying than any other method with the same unbiased proportion of strategic voters.Strategic voters are faced with the initial tactic as to how highly to score their second-choice candidate. The voter may want to retain expression of a high preference of their favorite candidate over their second choice. But that does not allow the same voter to express a high preference of their second choice over any others. In a simulation study using polling data collected under a majority judgment method, that method's designers found that score voting was more vulnerable to strategy than any other method they studied, including plurality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reverse accumulation AD, the dependent variable to be differentiated is fixed and the derivative is computed with respect to each sub-expression recursively. In a pen-and-paper calculation, the derivative of the outer functions is repeatedly substituted in the chain rule: In reverse accumulation, the quantity of interest is the adjoint, denoted with a bar w \u00af i {\\displaystyle {\\bar {w}}_{i}} ; it is a derivative of a chosen dependent variable with respect to a subexpression w i {\\displaystyle w_{i}}: Using the chain rule, if w i {\\displaystyle w_{i}} has successors in the computational graph: w \u00af i = \u2211 j \u2208 { successors of i } w \u00af j \u2202 w j \u2202 w i {\\displaystyle {\\bar {w}}_{i}=\\sum _{j\\in \\{{\\text{successors of i}}\\}}{\\bar {w}}_{j}{\\frac {\\partial w_{j}}{\\partial w_{i}}}} Reverse accumulation traverses the chain rule from outside to inside, or in the case of the computational graph in Figure 3, from top to bottom. The example function is scalar-valued, and thus there is only one seed for the derivative computation, and only one sweep of the computational graph is needed to calculate the (two-component) gradient. This is only half the work when compared to forward accumulation, but reverse accumulation requires the storage of the intermediate variables wi as well as the instructions that produced them in a data structure known as a \"tape\" or a Wengert list (however, Wengert published forward accumulation, not reverse accumulation), which may consume significant memory if the computational graph is large.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "See Linearization\u00a7Transformation, below, for more details. In general, there is no closed-form expression for the best-fitting parameters, as there is in linear regression. Usually numerical optimization algorithms are applied to determine the best-fitting parameters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Eliminating the systematic error improves accuracy but does not change precision. A measurement system is considered valid if it is both accurate and precise. Related terms include bias (non-random or directed effects caused by a factor or factors unrelated to the independent variable) and error (random variability).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, two-dimensional convex hulls can be computed using predicates that test the sign of quadratic polynomials, and therefore may require twice as many bits of precision within these calculations as the input numbers. When integer arithmetic cannot be used (for instance, when the result of a calculation is an algebraic number rather than an integer or rational number), a second method is to use symbolic algebra to perform all computations with exactly represented algebraic numbers rather than numerical approximations to them. A third method, sometimes called a \"floating point filter\", is to compute numerical predicates first using an inexact method based on floating-point arithmetic, but to maintain bounds on how accurate the result is, and repeat the calculation using slower symbolic algebra methods or numerically with additional precision when these bounds do not separate the calculated value from zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode, the pairwise summation algorithm for an array x of length n \u2265 0 can be written: s = pairwise(x) if n \u2264 N base case: naive summation for a sufficiently small array s = 0 for i = 1 to n s = s + x else divide and conquer: recursively sum two halves of the array m = floor(n / 2) s = pairwise(x) + pairwise(x) end if For some sufficiently small N, this algorithm switches to a naive loop-based summation as a base case, whose error bound is O(N\u03b5). The entire sum has a worst-case error that grows asymptotically as O(\u03b5 log n) for large n, for a given condition number (see below). In an algorithm of this sort (as for divide and conquer algorithms in general), it is desirable to use a larger base case in order to amortize the overhead of the recursion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If all weights are integers, then the run-time can be improved to O ( m n + n 2 log \u2061 log \u2061 n ) {\\displaystyle O(mn+n^{2}\\log \\log n)} , but the resulting algorithm is only weakly-polynomial. If the weights are integers, and all weights are at most C (where C>1 is some integer), then the problem can be solved in O ( m n log \u2061 ( n \u22c5 C ) ) {\\displaystyle O(m{\\sqrt {n}}\\log(n\\cdot C))} weakly-polynomial time in a method called weight scaling.In addition to the global methods, there are local methods which are based on finding local updates (rather than full augmenting paths). These methods have worse asymptotic runtime guarantees, but they often work better in practice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If we compute the cross products, we have M = | e x e y e z x A \u2212 x 0 0 0 \u2212 F 0 | + | e x e y e z \u2212 x 0 0 0 R 0 0 | = F ( x \u2212 x A ) e z \u2212 R 0 x e z = \u2212 F x A L ( L \u2212 x ) e z . {\\displaystyle \\mathbf {M} =\\left|{\\begin{matrix}\\mathbf {e} _{x}&\\mathbf {e} _{y}&\\mathbf {e} _{z}\\\\x_{A}-x&0&0\\\\0&-F&0\\end{matrix}}\\right|+\\left|{\\begin{matrix}\\mathbf {e} _{x}&\\mathbf {e} _{y}&\\mathbf {e} _{z}\\\\-x&0&0\\\\0&R_{0}&0\\end{matrix}}\\right|=F(x-x_{A})\\,\\mathbf {e} _{z}-R_{0}x\\,\\mathbf {e} _{z}=-{\\frac {Fx_{A}}{L}}(L-x)\\,\\mathbf {e} _{z}\\,.} Thanks to the equilibrium, the internal bending moment due to external forces to the left of X must be exactly balanced by the internal turning force obtained by considering the part of the beam to the right of X M + M x z = 0 . {\\displaystyle \\mathbf {M} +\\mathbf {M} _{xz}=\\mathbf {0} \\,.} which is clearly the case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This combinator may be used in implementing Curry's paradox. The heart of Curry's paradox is that untyped lambda calculus is unsound as a deductive system, and the Y combinator demonstrates this by allowing an anonymous expression to represent zero, or even many values. This is inconsistent in mathematical logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Lemoine's conjecture, named after \u00c9mile Lemoine, also known as Levy's conjecture, after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the IMS it is possible for a user to have multiple terminals (e.g. a mobile phone, a computer) or application instances (e.g. video telephony, instant messaging, voice mail) that are identified with the same public identity (i.e. SIP URI). Therefore, a mechanism is needed in order to route requests to the desired device or application. That is what a Globally Routable User Agent URI (GRU) is: a URI that identifies a specific user agent instance (i.e. terminal or application instance) and it does it globally (i.e. it is valid to route messages to that user agent from any other user agent on the Internet). These URIs are constructed by adding the gr parameter to a SIP URI, either to the public SIP URI with a value that identifies the user agent instance, or to a specially created URI that does not reveal the relationship between the GRUU and the user's identity, for privacy purposes. They are commonly obtained during the registration process: the registering user agent sends a Uniform Resource Name (URN) that uniquely identifies that SIP instance, and the registrar (i.e. S-CSCF) builds the GRUU, associates it to the registered identity and SIP instance and sends it back to the user agent in the response. When the S-CSCF receives a request for that GRUU, it will be able to route the request to the registered SIP instance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If this presupposition is satisfied, \u223c {\\displaystyle \\sim } passes along its overt argument's ordinary denotation while \"resetting\" its focus denotation. In other words, when the presupposition is satisfied,  ] o =  ] o {\\displaystyle \\!]_{o}=\\! ]_{o}} and  ] f = {  ] o } {\\displaystyle \\!]_{f}=\\{\\! ]_{o}\\}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a topological group G is called a discrete group if there is no limit point in it (i.e., for each element in G, there is a neighborhood which only contains that element). Equivalently, the group G is discrete if and only if its identity is isolated.A subgroup H of a topological group G is a discrete subgroup if H is discrete when endowed with the subspace topology from G. In other words there is a neighbourhood of the identity in G containing no other element of H. For example, the integers, Z, form a discrete subgroup of the reals, R (with the standard metric topology), but the rational numbers, Q, do not. Any group can be endowed with the discrete topology, making it a discrete topological group. Since every map from a discrete space is continuous, the topological homomorphisms between discrete groups are exactly the group homomorphisms between the underlying groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, an extender is a system of ultrafilters which represents an elementary embedding witnessing large cardinal properties. A nonprincipal ultrafilter is the most basic case of an extender. A (\u03ba, \u03bb)-extender can be defined as an elementary embedding of some model M {\\displaystyle M} of ZFC\u2212 (ZFC minus the power set axiom) having critical point \u03ba \u03b5 M, and which maps \u03ba to an ordinal at least equal to \u03bb. It can also be defined as a collection of ultrafilters, one for each n {\\displaystyle n} -tuple drawn from \u03bb.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The alternative hypothesis corresponds to the position against the defendant. Specifically, the null hypothesis also involves the absence of a difference or the absence of an association. Thus, the null hypothesis can never be that there is a difference or an association.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a paper published in 1982, Benioff further developed his original model of quantum mechanical Turing machines. This work put quantum computers on a solid theoretical foundation. Richard Feynman then produced a universal quantum simulator. Building on the work of Benioff and Feynman, Deutsch proposed that quantum mechanics can be used to solve computational problems faster than classical computers, and in 1994, Shor described a factoring algorithm that is considered to have an exponential speedup over classical computers.After Benioff and his peers in the field published several more papers on quantum computers, the idea began to gain traction with industry, banking, and government agencies. The field is now a fast-growing area of research that could have applications in cybersecurity, cryptography, quantum system modeling and more.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The algorithm was first published in 1944 by Kenneth Levenberg, while working at the Frankford Army Arsenal. It was rediscovered in 1963 by Donald Marquardt, who worked as a statistician at DuPont, and independently by Girard, Wynne and Morrison.The LMA is used in many software applications for solving generic curve-fitting problems. By using the Gauss\u2013Newton algorithm it often converges faster than first-order methods. However, like other iterative optimization algorithms, the LMA finds only a local minimum, which is not necessarily the global minimum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Proving that such a system is thermodynamically stable is called the stability of matter problem and it is very difficult due to the long range of the Coulomb potential. Stability should be a consequence of screening effects, but those are hard to quantify. Let us denote by H N , K = \u2212 \u2211 i = 1 N \u0394 x i 2 \u2212 \u2211 k = 1 K \u0394 R k 2 M k \u2212 \u2211 i = 1 N \u2211 k = 1 K z k | x i \u2212 R k | + \u2211 1 \u2264 i < j \u2264 N 1 | x i \u2212 x j | + \u2211 1 \u2264 k < m \u2264 K z k z m | R k \u2212 R m | {\\displaystyle H_{N,K}=-\\sum _{i=1}^{N}{\\frac {\\Delta _{x_{i}}}{2}}-\\sum _{k=1}^{K}{\\frac {\\Delta _{R_{k}}}{2M_{k}}}-\\sum _{i=1}^{N}\\sum _{k=1}^{K}{\\frac {z_{k}}{|x_{i}-R_{k}|}}+\\sum _{1\\leq i", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Rp is defined for sets S1 and S2 of cardinal number n and S3 of cardinal number n-1 as: Rp(S1,S2) iff (S3 \u2282 S1, S3 \u2282 S2)Meaning that S1 and S2 each have all the pitch-classes of S3 (transposed or inverted), plus one. he pc similarity relation Rp is not especially significant when taken alone, since by that measure a given set may be similar to many others. When Rp is combined with the  similarity measures, however, a considerable reduction is effected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mobile telephony a bearer service is a link between two points, which is defined by a certain set of characteristics. Whenever user equipment (UE) is being provided with any service (CS/PS service), the service has to be associated with a Radio Bearer specifying the configuration for layer 2 and physical layer in order to have its QoS clearly defined. Radio bearers are channels offered by Layer 2 to higher layers for the transfer of either user or control data. In other words, Layer 2 offers to the upper layers the service of information transmission between the UE and the UTRAN by means of the Radio Bearers (RBs) and Signaling Radio Bearers (SRBs). Therefore, the service access points between Layer 2 and upper layers are RBs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, test effort refers to the expenses for (still to come) tests. There is a relation with test costs and failure costs (direct, indirect, costs for fault correction). Some factors which influence test effort are: maturity of the software development process, quality and testability of the testobject, test infrastructure, skills of staff members, quality goals and test strategy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some functional elements, described using a software language, may actually be implemented as hardware (FPGA, ASIC) Hardware views \u2013 Describes the hardware engineering aspects of the system, hardware design, selection and implementation of all of the physical components to be assembled into the system. There may be many of these views, each specific to a different engineering discipline. Communications Protocol view \u2013 Describes the end to end design of the communications protocols and related data transport and data management services, shows the protocol stacks as they are implemented on each of the physical components of the system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In present-day vocabulary, the term cast steel is almost always used in its sense referring to steel castings. Between the late 19th and mid 20th centuries, this was not always true, which is worth understanding if one is reading historical documents; see cast steel for details.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, label is an optional identifier terminated by a colon, and block is a sequence of one of more Perl statements surrounded by braces. All looping constructs except for the C-style for-loop can have a continue block that is executed after each iteration of the loop body, before the loop condition is evaluated again. label for ( expr1 ; expr2 ; expr3 ) block This is the so-called C-style for loop. The first expression is evaluated prior to the first loop iteration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multilinear algebra, the tensor rank decomposition or the r a n k \u2212 R {\\displaystyle rank-R} decomposition of a tensor is the decomposition of a tensor in terms of a sum of minimum R {\\displaystyle R} r a n k \u2212 1 {\\displaystyle rank-1} tensors. This is an open problem. Canonical polyadic decomposition (CPD) is a variant of the rank decomposition which computes the best fitting K {\\displaystyle K} r a n k \u2212 1 {\\displaystyle rank-1} terms for a user specified K {\\displaystyle K} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In papers published since 2008, ASJP has employed a similarity judgment program based on Levenshtein distance (LD). This approach was found to produce better classificatory results measured against expert opinion than the method used initially. LD is defined as the minimum number of successive changes necessary to convert one word into another, where each change is the insertion, deletion, or substitution of a symbol. Within the Levenshtein approach, differences in word length can be corrected for by dividing LD by the number of symbols of the longer of the two compared words.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, a node is given a high hub score by linking to nodes that are considered to be authorities on the subject.The Hub score and Authority score for a node is calculated with the following algorithm: Start with each node having a hub score and authority score of 1. Run the authority update rule Run the hub update rule Normalize the values by dividing each Hub score by square root of the sum of the squares of all Hub scores, and dividing each Authority score by square root of the sum of the squares of all Authority scores. Repeat from the second step as necessary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two octads intersect (have 1's in common) in 0, 2, or 4 coordinates in the binary vector representation (these are the possible intersection sizes in the subset representation). An octad and a dodecad intersect at 2, 4, or 6 coordinates. Up to relabeling coordinates, W is unique.The binary Golay code, G23 is a perfect code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical morphology, a structuring element is a shape, used to probe or interact with a given image, with the purpose of drawing conclusions on how this shape fits or misses the shapes in the image. It is typically used in morphological operations, such as dilation, erosion, opening, and closing, as well as the hit-or-miss transform. According to Georges Matheron, knowledge about an object (e.g., an image) depends on the manner in which we probe (observe) it. In particular, the choice of a certain structuring element for a particular morphological operation influences the information one can obtain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since we continue to use a g - 1 coding scheme, it is in fact the \u22121 coded group that will not produce data, hence the fact that we are least interested in that group. A code of 0 is assigned to all other groups. The b values should be interpreted such that the experimental group is being compared against the mean of all groups combined (or weighted grand mean in the case of weighted effects coding).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. In particular, the sets must have the form (p, p + 2, p + 6) or (p, p + 4, p + 6). With the exceptions of (2, 3, 5) and (3, 5, 7), this is the closest possible grouping of three prime numbers, since one of every three sequential odd numbers is a multiple of three, and hence not prime (except for 3 itself).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a (B, N) pair is a structure on groups of Lie type that allows one to give uniform proofs of many results, instead of giving a large number of case-by-case proofs. Roughly speaking, it shows that all such groups are similar to the general linear group over a field. They were introduced by the mathematician Jacques Tits, and are also sometimes known as Tits systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In networks with unit capacities, a much stronger time bound holds. Each blocking flow can be found in O ( E ) {\\displaystyle O(E)} time, and it can be shown that the number of phases does not exceed O ( E ) {\\displaystyle O({\\sqrt {E}})} and O ( V 2 / 3 ) {\\displaystyle O(V^{2/3})} . Thus the algorithm runs in O ( min { V 2 / 3 , E 1 / 2 } E ) {\\displaystyle O(\\min\\{V^{2/3},E^{1/2}\\}E)} time.In networks that arise from the bipartite matching problem, the number of phases is bounded by O ( V ) {\\displaystyle O({\\sqrt {V}})} , therefore leading to the O ( V E ) {\\displaystyle O({\\sqrt {V}}E)} time bound. The resulting algorithm is also known as Hopcroft\u2013Karp algorithm. More generally, this bound holds for any unit network \u2014 a network in which each vertex, except for source and sink, either has a single entering edge of capacity one, or a single outgoing edge of capacity one, and all other capacities are arbitrary integers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spite of the negative theoretical results on the joint spectral radius computability, methods have been proposed that perform well in practice. Algorithms are even known, which can reach an arbitrary accuracy in an a priori computable amount of time. These algorithms can be seen as trying to approximate the unit ball of a particular vector norm, called the extremal norm. One generally distinguishes between two families of such algorithms: the first family, called polytope norm methods, construct the extremal norm by computing long trajectories of points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, any vector space V {\\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V , {\\displaystyle V,} together with the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called the continuous dual space. Dual vector spaces find application in many branches of mathematics that use vector spaces, such as in tensor analysis with finite-dimensional vector spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If two dice are thrown and their values added, the resulting distribution is no longer uniform because not all sums have equal probability. Although it is convenient to describe discrete uniform distributions over integers, such as this, one can also consider discrete uniform distributions over any finite set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another example is lay, which may be the past tense of lie, but is also an independent verb (regular in pronunciation, but with irregular spelling: lay\u2013laid\u2013laid). In fact the past tense verb lay derives from a causative of the verb from which lie derives. The two verbs are sometimes confused, with lay used in the intransitive senses prescriptively reserved for lie.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Only O ( N l o g ( N ) ) {\\displaystyle O(Nlog(N))} operations are needed to detect edges, where N {\\displaystyle N} is the number of pixels. During the following years, other problems have been considered: classification, segmentation, inpainting and super-resolution. This approach can be applied to gray-level or color images.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, context-free rules cannot express agreement or reference (anaphora), where two different parts of the sentence must agree with each other in some way. These can be readily expressed in W-grammars.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A system or application will hit a bottleneck if the work arrives at a comparatively faster pace relative to other processing components. According to the theory of constraints, improving on the occurrences of hot-spot point of the bottleneck constraint improves the overall processing speed of the software. A thought-provoking stipulation of the theory reveals that improving the efficiency of a particular process stage rather than the constraint can generate even more delay and decrease overall processing capabilities of a software. The process of tracking down bottlenecks (also referred as \"hot spots\" - sections of the code that execute most frequently - i.e. have the highest execution count) is called performance analysis. Reduction is achieved with the utilization of specialized tools such as performance analyzers or profilers, the objective being to make particular sections of code perform as effectively as possible to improve overall algorithmic efficiency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic or powering of matrices. For semigroups for which additive notation is commonly used, like elliptic curves used in cryptography, this method is also referred to as double-and-add.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Reidl \"in 1998 extends and proposes a new way to taxonomize information visualization techniques by using the Data State Model. Many of the techniques share similar operating steps that can easily be reused. The Data State Model not only helps researchers understand the space of design, but also helps implementers understand how information visualization techniques can be applied more broadly\".In 1999 Stuart Card, Jock D. Mackinlay, and Ben Shneiderman present their own interpretation of this pattern, dubbing it the information visualization reference model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of neighborhood interchangeable algorithm, if we assign the worst case bound to each loop. Then for n variables, which have at most d values for a variable, then we have a bound of: O ( n d ( n \u2212 l ) \u2217 d ) = O ( n 2 d 2 ) {\\displaystyle O(nd(n-l)*d)=O(n^{2}d^{2})} . Similarly, the complexity analysis of the k-interchangeability algorithm for a worst case O ( n k \u2212 1 ) {\\displaystyle O(n^{k-1})} , with ( k \u2212 1 ) {\\displaystyle (k-1)} -tuples of variables and d k \u2212 1 {\\displaystyle d^{k-1}} , for ( k \u2212 1 ) {\\displaystyle (k-1)} -tuples of values, then the bound is: O ( n d n k \u2212 l d k \u2212 1 ) = O ( n k d k ) {\\displaystyle O(ndn^{k-l}d^{k-1})=O(n^{k}d^{k})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental representation of a finite field with its group extension to the automorphic forms under which it is invariant. This is accomplished through abstraction to higher dimensional integration, by an equivalence to a certain analytical group as an absolute extension of its algebra. Consequently, this allows an analytical functional construction of powerful invariance transformations for a number field to its own algebraic structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the bin packing problem, there are n items with different sizes. The goal is to pack the items into a minimum number of bins, where each bin can contain at most B. A feasible configuration is a set of sizes with a sum of at most B. Example: suppose the item sizes are 3,3,3,3,3,4,4,4,4,4, and B=12. Then the possible configurations are: 3333; 333; 33, 334; 3, 34, 344; 4, 44, 444. If we had only three items of size 3, then we could not use the 3333 configuration.Denote by S the set of different sizes (and their number).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series. Formally, a ring is an abelian group whose operation is called addition, with a second binary operation called multiplication that is associative, is distributive over the addition operation, and has a multiplicative identity element.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sorting n objects, merge sort has an average and worst-case performance of O(n log n). If the running time of merge sort for a list of length n is T(n), then the recurrence relation T(n) = 2T(n/2) + n follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists). The closed form follows from the master theorem for divide-and-conquer recurrences. The number of comparisons made by merge sort in the worst case is given by the sorting numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Minkowski's theorem is the statement that every convex set in R n {\\displaystyle \\mathbb {R} ^{n}} which is symmetric with respect to the origin and which has volume greater than 2 n {\\displaystyle 2^{n}} contains a non-zero integer point (meaning a point in Z n {\\displaystyle \\mathbb {Z} ^{n}} that is not the origin). The theorem was proved by Hermann Minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers. It can be extended from the integers to any lattice L {\\displaystyle L} and to any symmetric convex set with volume greater than 2 n d ( L ) {\\displaystyle 2^{n}\\,d(L)} , where d ( L ) {\\displaystyle d(L)} denotes the covolume of the lattice (the absolute value of the determinant of any of its bases).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Operators had to maintain a steady rhythm, and the usual speed of operation was 30 words per minute.The table \"shows the allocation of the Baudot code which was employed in the British Post Office for continental and inland services. A number of characters in the continental code are replaced by fractionals in the inland code. Code elements 1, 2 and 3 are transmitted by keys 1, 2 and 3, and these are operated by the first three fingers of the right hand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The intent is to create standardized rules to maintain data integrity and enforce business rules throughout one or more related applications. Some industries use generalized data dictionaries as technical standards to ensure interoperability between systems. The real estate industry, for example, abides by a RESO's Data Dictionary to which the National Association of REALTORS mandates its MLSs comply with through its policy handbook. This intermediate mapping layer for MLSs' native databases is supported by software companies which provide API services to MLS organizations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A different fairness notion, that can be guaranteed to more than 1/2 of the agents in each group, is the ordinal maximin-share approximation. For every integer c, there exists a ( 1 \u2212 1 / 2 c \u2212 1 ) {\\displaystyle (1-1/2^{c-1})} -democratic 1-out-of-c MMS-fair allocation. These allocations can be found efficiently using a variant of round-robin item allocation, with weighted approval voting inside each group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more concrete terms, the uniform word problem can be expressed as a rewriting question, for literal strings. For a presentation P of a group G, P will specify a certain number of generators x, y, z, ...for G. We need to introduce one letter for x and another (for convenience) for the group element represented by x\u22121. Call these letters (twice as many as the generators) the alphabet \u03a3 {\\displaystyle \\Sigma } for our problem. Then each element in G is represented in some way by a product abc ... pqrof symbols from \u03a3 {\\displaystyle \\Sigma } , of some length, multiplied in G. The string of length 0 (null string) stands for the identity element e of G. The crux of the whole problem is to be able to recognise all the ways e can be represented, given some relations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a demand-side policy component may include placing public transit stops near development, in order to maximize walkability.Additionally, California state law requires minimum energy conservation levels for all new and/or existing development projects. The seller of a home is required to include information regarding energy conservation retrofitting and thermal insulation in the sales contract. : 133", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum computing, classical shadow is a protocol for predicting functions of a quantum state using only a logarithmic number of measurements. Given an unknown state \u03c1 {\\displaystyle \\rho } , a tomographically complete set of gates U {\\displaystyle U} (e.g Clifford gates), a set of M {\\displaystyle M} observables { O i } {\\displaystyle \\{O_{i}\\}} and a quantum channel M {\\displaystyle M} (defined by randomly sampling from U {\\displaystyle U} , applying it to \u03c1 {\\displaystyle \\rho } and measuring the resulting state); predict the expectation values tr \u2061 ( O i \u03c1 ) {\\displaystyle \\operatorname {tr} (O_{i}\\rho )} . A list of classical shadows S {\\displaystyle S} is created using \u03c1 {\\displaystyle \\rho } , U {\\displaystyle U} and M {\\displaystyle M} by running a Shadow generation algorithm. When predicting the properties of \u03c1 {\\displaystyle \\rho } , a Median-of-means estimation algorithm is used to deal with the outliers in S {\\displaystyle S} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first version of the AKS primality test paper, a conjecture about Sophie Germain primes is used to lower the worst-case complexity from O(log12n) to O(log6n). A later version of the paper is shown to have time complexity O(log7.5n) which can also be lowered to O(log6n) using the conjecture. Later variants of AKS have been proven to have complexity of O(log6n) without any conjectures or use of Sophie Germain primes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance T is a metric on the space of density matrices and gives a measure of the distinguishability between two states. It is the quantum generalization of the Kolmogorov distance for classical probability distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Finnish Pig Latin is called Kontinkieli (\"container language\"). After each word you add the word kontti \"container\", then switch the first syllables, So every sentence is converted to twice as many pseudo-words. For example,\"wikipedia\" \u27f6 \"wikipedia kontti\" \u27f6 \"kokipedia wintti\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root. The notion of multiplicity is important to be able to count correctly without specifying exceptions (for example, double roots counted twice).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Percentile scores and percentile ranks are often used in the reporting of test scores from norm-referenced tests, but, as just noted, they are not the same. For percentile ranks, a score is given and a percentage is computed. Percentile ranks are exclusive: if the percentile rank for a specified score is 90%, then 90% of the scores were lower. In contrast, for percentiles a percentage is given and a corresponding score is determined, which can be either exclusive or inclusive. The score for a specified percentage (e.g., 90th) indicates a score below which (exclusive definition) or at or below which (inclusive definition) other scores in the distribution fall.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s, many of the notable early successes on statistical methods in natural-language programming (NLP) occurred in the field of machine translation, due especially to work at IBM Research. These systems were able to take advantage of existing multilingual textual corpora that had been produced by the Parliament of Canada and the European Union as a result of laws calling for the translation of all governmental proceedings into all official languages of the corresponding systems of government. There are corpora in non-European languages as well. For example, the National Institute for Japanese Language and Linguistics in Japan has built a number of corpora of spoken and written Japanese.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables. Distance correlation can be used to perform a statistical test of dependence with a permutation test. One first computes the distance correlation (involving the re-centering of Euclidean distance matrices) between two random vectors, and then compares this value to the distance correlations of many shuffles of the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A best-effort network or service does not support quality of service. An alternative to complex QoS control mechanisms is to provide high quality communication over a best-effort network by over-provisioning the capacity so that it is sufficient for the expected peak traffic load. The resulting absence of network congestion reduces or eliminates the need for QoS mechanisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the algorithm, each sequence of concatenated strong characters is called a \"run\". A \"weak\" character that is located between two \"strong\" characters with the same orientation will inherit their orientation. A \"weak\" character that is located between two \"strong\" characters with a different writing direction will inherit the main context's writing direction (in an LTR document the character will become LTR, in an RTL document, it will become RTL).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order theory, a discipline within mathematics, a critical pair is a pair of elements in a partially ordered set that are incomparable but that could be made comparable without requiring any other changes to the partial order. Formally, let P = (S, \u2264) be a partially ordered set. Then a critical pair is an ordered pair (x, y) of elements of S with the following three properties: x and y are incomparable in P, for every z in S, if z < x then z < y, and for every z in S, if y < z then x < z.If (x, y) is a critical pair, then the binary relation obtained from P by adding the single relationship x \u2264 y is also a partial order. The properties required of critical pairs ensure that, when the relationship x \u2264 y is added, the addition does not cause any violations of the transitive property. A set R of linear extensions of P is said to reverse a critical pair (x, y) in P if there exists a linear extension in R for which y occurs earlier than x. This property may be used to characterize realizers of finite partial orders: A nonempty set R of linear extensions is a realizer if and only if it reverses every critical pair.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Smith\u2013Volterra\u2013Cantor set (SVC), fat Cantor set, or \u03b5-Cantor set is an example of a set of points on the real line that is nowhere dense (in particular it contains no intervals), yet has positive measure. The Smith\u2013Volterra\u2013Cantor set is named after the mathematicians Henry Smith, Vito Volterra and Georg Cantor. In an 1875 paper, Smith discussed a nowhere-dense set of positive measure on the real line, and Volterra introduced a similar example in 1881. The Cantor set as we know it today followed in 1883. The Smith\u2013Volterra\u2013Cantor set is topologically equivalent to the middle-thirds Cantor set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, an 1871 census in the UK (the first of its kind, but personal data from other censuses dates back to 1841 and numerical data back to 1801) found the average male life expectancy as being 44, but if infant mortality is subtracted, males who lived to adulthood averaged 75 years. The present life expectancy in the UK is 77 years for males and 81 for females, while the United States averages 74 for males and 80 for females. Studies have shown that black American males have the shortest lifespans of any group of people in the US, averaging only 69 years (Asian-American females average the longest).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the notion of polyconvexity is a generalization of the notion of convexity for functions defined on spaces of matrices. Let Mm\u00d7n(K) denote the space of all m \u00d7 n matrices over the field K, which may be either the real numbers R, or the complex numbers C. A function f: Mm\u00d7n(K) \u2192 R \u222a {\u00b1\u221e} is said to be polyconvex if A \u21a6 f ( A ) {\\displaystyle A\\mapsto f(A)} can be written as a convex function of the p \u00d7 p subdeterminants of A, for 1 \u2264 p \u2264 min{m, n}. Polyconvexity is a weaker property than convexity. For example, the function f given by f ( A ) = { 1 det ( A ) , det ( A ) > 0 ; + \u221e , det ( A ) \u2264 0 ; {\\displaystyle f(A)={\\begin{cases}{\\frac {1}{\\det(A)}},&\\det(A)>0;\\\\+\\infty ,&\\det(A)\\leq 0;\\end{cases}}} is polyconvex but not convex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a ring class field is the abelian extension of an algebraic number field K associated by class field theory to the ring class group of some order O of the ring of integers of K.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The problem of determining whether a formula in propositional logic is satisfiable is decidable, and is known as the Boolean satisfiability problem, or SAT. In general, the problem of determining whether a sentence of first-order logic is satisfiable is not decidable. In universal algebra, equational theory, and automated theorem proving, the methods of term rewriting, congruence closure and unification are used to attempt to decide satisfiability. Whether a particular theory is decidable or not depends whether the theory is variable-free and on other conditions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2356, 12356, 23456, and 123456 are the patterns related to Braille pattern dots-1245, since the two additional dots of kantenji patterns 01245, 12457, and 012457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2367, 12367, 23467, and 123467 are the patterns related to Braille pattern dots-1235, since the two additional dots of kantenji patterns 01235, 12357, and 012357 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Unlike Javadoc tags, Java annotations can also be embedded in and read from Java class files generated by the Java compiler. This allows annotations to be retained by the Java virtual machine at run-time and read via reflection. It is possible to create meta-annotations out of the existing ones in Java.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical psychology and education theory, a knowledge space is a combinatorial structure used to formulate mathematical models describing the progression of a human learner. Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne, and remain in extensive use in the education theory. Modern applications include two computerized tutoring systems, ALEKS and the defunct RATH.Formally, a knowledge space assumes that a domain of knowledge is a collection of concepts or skills, each of which must be eventually mastered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociology of science, the graphism thesis is a proposition of Bruno Latour that graphs are important in science. Research has shown that one can distinguish between hard science and soft science disciplines based on the level of graph use, so it can be argued that there is a correlation between scientificity and visuality. Furthermore, natural sciences publications appear to make heavier use of graphs than mathematical and social sciences.It has been claimed that an example of a discipline that uses graphs heavily but is not at all scientific is technical analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the notion of an (exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are a generalisation of the simple \"diameter to the dimension\" power law used in the construction of s-dimensional Hausdorff measure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Given a linear system A x = b {\\displaystyle \\mathbf {A} \\mathbf {x} =\\mathbf {b} } where A is an n \u00d7 n {\\displaystyle n\\times n} real symmetric sparse square matrix. The Cholesky factor L will typically suffer 'fill in', that is have more non-zeros than the upper triangle of A. We seek a permutation matrix P, so that the matrix P T A P {\\displaystyle \\mathbf {P} ^{T}\\mathbf {A} \\mathbf {P} } , which is also symmetric, has the least possible fill in its Cholesky factor. We solve the reordered system ( P T A P ) ( P T x ) = P T b .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Testing for failures such as ABA can be exceedingly difficult, because the problematic sequence of events is very rare. Model checking is an excellent way to uncover such problems. See for instance exercise 7.3.3 in \"Modeling and analysis of communicating Systems\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the agricultural industry, sodium polyacrylate is used to help plants retain moisture in the soil. It can act as a water reservoir for plants and is commonly used by florists to keep flowers fresh. Furthermore, the use of sodium polyacrylate for growing domestic fruit and vegetables has been approved by the U.S. Department of Agriculture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, many reuse metrics and models are metrics used to measure code reuse and reusability. A metric is a quantitative indicator of an attribute of a thing. A model specifies relationships among metrics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum computing, modular exponentiation appears as the bottleneck of Shor's algorithm, where it must be computed by a circuit consisting of reversible gates, which can be further broken down into quantum gates appropriate for a specific physical device. Furthermore, in Shor's algorithm it is possible to know the base and the modulus of exponentiation at every call, which enables various circuit optimizations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Particularly in large software systems, any change to the source code may have unintended consequences, potentially introducing new bugs; thus, a code freeze helps ensure that a portion of the program that is known to work correctly will continue to do so. Code freezes are often employed in the final stages of development, when a particular release or iteration is being tested, but may also be used to prevent changes to one portion of a program while another is undergoing development. For example: \"physics freeze\" means no changes whatsoever will be permitted to the physics portion of the code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a message exchange pattern (MEP) describes the pattern of messages required by a communications protocol to establish or use a communication channel. The communications protocol is the format used to represent the message which all communicating parties agree on (or are capable to process). The communication channel is the infrastructure that enables messages to \"travel\" between the communicating parties. The message exchange patterns describe the message flow between parties in the communication process, there are two major message exchange patterns \u2014 a request\u2013response pattern, and a one-way pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In radio network protocols, leader election is often used as a first step to approach more advanced communication primitives, such as message gathering or broadcasts. The very nature of wireless networks induces collisions when adjacent nodes transmit at the same time; electing a leader allows to better coordinate this process. While the diameter D of a network is a natural lower bound for the time needed to elect a leader, upper and lower bounds for the leader election problem depend on the specific radio model studied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions.The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability, a singular distribution is a probability distribution concentrated on a set of Lebesgue measure zero, where the probability of each point in that set is zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let G {\\displaystyle G} be a group. Then the following is equivalent: G {\\displaystyle G} is abelian. Every function on G {\\displaystyle G} is a class function. All irreducible representations of G {\\displaystyle G} have degree 1. {\\displaystyle 1.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In silico PCR refers to computational tools used to calculate theoretical polymerase chain reaction (PCR) results using a given set of primers (probes) to amplify DNA sequences from a sequenced genome or transcriptome.These tools are used to optimize the design of primers for target DNA or cDNA sequences. Primer optimization has two goals: efficiency and selectivity. Efficiency involves taking into account such factors as GC-content, efficiency of binding, complementarity, secondary structure, and annealing and melting point (Tm). Primer selectivity requires that the primer pairs not fortuitously bind to random sites other than the target of interest, nor should the primer pairs bind to conserved regions of a gene family.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A definition of distance between any two monads is defined and from this and probabilistic mathematical tools emerges a three-dimensional space.Axiomatic pregeometry by Perez, Bergliaffa, Romero and Vucetich An assortment of ontological presuppositions describes spacetime a result of relations between objectively existing entities. From presuppositions emerges the topology and metric of Minkowski spacetime.Cellular networks by Requardt Space is described by a graph with densely entangled sub-clusters of nodes (with differential states) and bonds (either vanishing at 0 or directed at 1). Rules describe the evolution of the graph from a chaotic patternless pre-Big Bang condition to a stable spacetime in the present.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Efforts to minimize leakage include the use of strained silicon, high-\u03ba dielectrics, and/or stronger dopant levels in the semiconductor. Leakage reduction to continue Moore's law will not only require new material solutions but also proper system design. Certain types of semiconductor manufacturing defects exhibit themselves as increased leakage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the explanations below, any indication of a bit's position is counted from the right (least significant) side, advancing left. For example, the binary value 0001 (decimal 1) has zeroes at every position but the first (i.e., the rightmost) one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Written test cases should include a description of the functionality to be tested, and the preparation required to ensure that the test can be conducted. A formal written test case is characterized by a known input and by an expected output, which is worked out before the test is executed. The known input should test a precondition and the expected output should test a postcondition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to evaluate the methods a well understood family of languages is chosen, with a reliable dataset. This family is often the IE one but others have been used. After applying the methods to be compared to the database, the resulting trees are compared with the reference tree determined by traditional linguistic methods. The aim is to have no conflicts in topology, for example no missing sub-groups, and compatible dates. The families suggested for this analysis by Nichols and Warnow are Germanic, Romance, Slavic, Common Turkic, Chinese, and Mixe Zoque as well as older groups such as Oceanic and IE.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Any non-zero output indicates the offset error in the converter. That is, if the measurement of ground resulted in an output of 0.001 volts, one can assume that all measurements will be offset by the same amount and can subtract 0.001 from all subsequent results. Gain error can similarly be measured and corrected internally (again assuming that there is a constant gain error over the entire output range).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative (or, loosely speaking, higher-order terms) of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one restricted but very common sense of the term, a graph is an ordered pair G = ( V , E ) {\\displaystyle G=(V,E)} comprising: V {\\displaystyle V} , a set of vertices (also called nodes or points); E \u2286 { { x , y } \u2223 x , y \u2208 V and x \u2260 y } {\\displaystyle E\\subseteq \\{\\{x,y\\}\\mid x,y\\in V\\;{\\textrm {and}}\\;x\\neq y\\}} , a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with two distinct vertices).To avoid ambiguity, this type of object may be called precisely an undirected simple graph. In the edge { x , y } {\\displaystyle \\{x,y\\}} , the vertices x {\\displaystyle x} and y {\\displaystyle y} are called the endpoints of the edge. The edge is said to join x {\\displaystyle x} and y {\\displaystyle y} and to be incident on x {\\displaystyle x} and on y {\\displaystyle y} . A vertex may exist in a graph and not belong to an edge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sanity testing and smoke testing avoid wasting time and effort by quickly determining whether an application is too flawed to merit more rigorous QA testing, but needs more developer debugging. Groups of sanity tests are often bundled together for automated unit testing of functions, libraries, or applications prior to merging development code into a testing or trunk version control branch, for automated building, or for continuous integration and continuous deployment.Another common usage of sanity test is to denote checks which are performed within programme code, usually on arguments to functions or returns therefrom, to see if the answers can be assumed to be correct. The more complicated the routine, the more important that its response be checked.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, the term security kernel has the following meanings: In computer and communications security, the central part of a computer or communications system hardware, firmware, and software that implements the basic security procedures for controlling access to system resources. A self-contained usually small collection of key security-related statements that (a) works as a part of an operating system to prevent unauthorized access to, or use of, the system and (b) contains criteria that must be met before specified programs can be accessed. Hardware, firmware, and software elements of a trusted computing base that implement the reference monitor concept.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages, name resolution can be performed either at compile time or at runtime. The former is called static name resolution, the latter is called dynamic name resolution. A somewhat common misconception is that dynamic typing implies dynamic name resolution. For example, Erlang is dynamically typed but has static name resolution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, the gender of nouns can mostly be determined by physical (semantic) attributes, although there remain some nouns whose gender is not assigned in this way (Corbett calls this \"semantic residue\"). The world view (e.g. mythology) of the speakers may influence the division of categories. Zande has four genders: male human, female human, animal, and inanimate. However, there are about 80 nouns representing inanimate entities which are nonetheless animate in gender: heavenly objects (moon, rainbow), metal objects (hammer, ring), edible plants (sweet potato, pea), and non-metallic objects (whistle, ball).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model checking, a subfield of computer science, a signal or timed state sequence is an extension of the notion of words in a formal language, in which letters are continuously emitted. While a word is traditionally defined as a function from a set of non-negative integers to letters, a signal is a function from a set of real numbers to letters. This allow the use of formalisms similar to the ones of automata theory to deal with continuous signals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof complexity, a Frege system is a propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally complete inference rules. Frege systems (more often known as Hilbert systems in general proof theory) are named after Gottlob Frege.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the minimum rank is a graph parameter mr \u2061 ( G ) {\\displaystyle \\operatorname {mr} (G)} for a graph G. It was motivated by the Colin de Verdi\u00e8re graph invariant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the National Weather Service gives out the advice \"Turn Around, Don't Drown\" for floods; that is, it recommends that people get out of the area of a flood, rather than trying to cross it. At the most basic level, the best defense against floods is to seek higher ground for high-value uses while balancing the foreseeable risks with the benefits of occupying flood hazard zones. : 22\u201323 Critical community-safety facilities, such as hospitals, emergency-operations centers, and police, fire, and rescue services, should be built in areas least at risk of flooding. Structures, such as bridges, that must unavoidably be in flood hazard areas should be designed to withstand flooding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The receiving application may ask for this information to be retransmitted, possibly resulting in congestive collapse or unacceptable delays in the overall transmission. Errors Sometimes packets are corrupted due to bit errors caused by noise and interference, especially in wireless communications and long copper wires.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., f P: O Y , f ( P ) \u2192 O X , P {\\displaystyle f_{P}\\colon {\\mathcal {O}}_{Y,f(P)}\\to {\\mathcal {O}}_{X,P}} is a flat map for all P in X. A map of rings A \u2192 B {\\displaystyle A\\to B} is called flat if it is a homomorphism that makes B a flat A-module. A morphism of schemes is called faithfully flat if it is both surjective and flat.Two basic intuitions regarding flat morphisms are: flatness is a generic property; and the failure of flatness occurs on the jumping set of the morphism.The first of these comes from commutative algebra: subject to some finiteness conditions on f, it can be shown that there is a non-empty open subscheme Y \u2032 {\\displaystyle Y'} of Y, such that f restricted to Y\u2032 is a flat morphism (generic flatness). Here 'restriction' is interpreted by means of the fiber product of schemes, applied to f and the inclusion map of Y \u2032 {\\displaystyle Y'} into Y. For the second, the idea is that morphisms in algebraic geometry can exhibit discontinuities of a kind that are detected by flatness. For instance, the operation of blowing down in the birational geometry of an algebraic surface, can give a single fiber that is of dimension 1 when all the others have dimension 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the binary number system, each numerical digit has two possible states (0 or 1) and each successive digit represents an increasing power of two. Note: What follows is but one of several possible schemes for assigning the values 1, 2, 4, 8, 16, etc. to fingers, not necessarily the best. (see below the illustrations. ): The rightmost digit represents two to the zeroth power (i.e., it is the \"ones digit\"); the digit to its left represents two to the first power (the \"twos digit\"); the next digit to the left represents two to the second power (the \"fours digit\"); and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the graph query does the data inference through the connected relations, instead of repeated full search of the tables in relational database. KG facilitates the integration of new heterogeneous data by just adding new relationships between existing information and new entities. This facilitation is emphasized for the integration with existing popular linked open data source such as Wikidata.org.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We will also assume that all rings are unital, and all ring homomorphisms are unital. Many authors consider the more general concept of an associative algebra over a commutative ring R, instead of a field: An R-algebra is an R-module with an associative R-bilinear binary operation, which also contains a multiplicative identity. For examples of this concept, if S is any ring with center C, then S is an associative C-algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Barbara Blackburn, who failed her QWERTY typing class in high school, first encountered the Dvorak layout in 1938 and then she quickly learned to achieve very high speeds of typing, also she occasionally toured giving speed-typing demonstrations during her secretarial career. She appeared on Late Night with David Letterman on January 24, 1985, but felt that Letterman made a spectacle of her.The recent emergence of several competitive typing websites has allowed fast typists on computer keyboards to emerge along with new records, though many of these are unverifiable. Some notable, verified records include 255 wpm on a one-minute, random-word test by a user under the username slekap and occasionally bailey, 213 wpm on a 1-hour, random-word test by Joshua Hu, 221 wpm average on 10 random quotes by Joshua Hu, and first place in the 2020 Ultimate Typing Championship by Anthony Ermollin based on an average of 180.88 wpm on texts of various lengths.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Region extraction: left and right hand detection based on a comparison between them. Characteristic extraction: location of the fingertips and to detect if it is a peak or a valley. To classify the point, peaks or valleys, these are transformed to 3D vectors, usually named pseudo vectors in the xy-plane, and then to compute the cross product.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A graph G is k-edge-choosable if every instance of list edge-coloring that has G as its underlying graph and that provides at least k allowed colors for each edge of G has a proper coloring. The edge choosability, or list edge colorability, list edge chromatic number, or list chromatic index, ch\u2032(G) of graph G is the least number k such that G is k-edge-choosable. It is conjectured that it always equals the chromatic index.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. The most common construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In monolithic kernels, device drivers reside in the kernel. Thus, when a new peripheral is installed, unknown, untrusted code is inserted in the kernel. One bad line of code in a driver can bring down the system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2020s, concerns over ACs vulnerability to cyberattacks and data theft emerged.In 2018 and 2019 former Apple engineers were charged with stealing information related to Apple's self-driving car project. In 2021 the United States Department of Justice (DOJ) accused Chinese security officials of coordinating a hacking campaign to steal information from government entities, including research related to autonomous vehicles. China has prepared \"the Provisions on Management of Automotive Data Security (Trial) to protect its own data\".Cellular Vehicle-to-Everything technologies are based on 5G wireless networks. As of November 2022, the US Congress was considering the possibility that imported Chinese AC technology could facilitate espionage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In older architectures, NMIs were used for interrupts which were typically never disabled because of the required response time. They were hidden signals. Examples include the floppy disk controller on the Amstrad PCW, the 8087 coprocessor on the x86 when used in the IBM PC or its compatibles (even though Intel recommended connecting it to a normal interrupt), and the Low Battery signal on the HP 95LX. In the original IBM PC, an NMI was triggered if a parity error was detected in system memory, or reported by an external device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and control, and can be formulated to construct solutions in a memory-efficient, factored form. It is also used to numerically solve parabolic and elliptic partial differential equations, and is a classic method used for modeling heat conduction and solving the diffusion equation in two or more dimensions. It is an example of an operator splitting method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Internet protocols are designed for simplicity and modularity and fit into a coarse hierarchy of functional layers defined in the Internet Protocol Suite. The first two cooperating protocols, the Transmission Control Protocol (TCP) and the Internet Protocol (IP) resulted from the decomposition of the original Transmission Control Program, a monolithic communication protocol, into this layered communication suite. The OSI model was developed internationally based on experience with networks that predated the internet as a reference model for general communication with much stricter rules of protocol interaction and rigorous layering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random variable. It is closely related to the chi-squared distribution. It arises in Bayesian inference, where it can be used as the prior and posterior distribution for an unknown variance of the normal distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics and mathematics, the Bethe lattice (also called a regular tree) is an infinite connected cycle-free graph where all vertices have the same number of neighbors. The Bethe lattice was introduced into the physics literature by Hans Bethe in 1935. In such a graph, each node is connected to z neighbors; the number z is called either the coordination number or the degree, depending on the field. Due to its distinctive topological structure, the statistical mechanics of lattice models on this graph are often easier to solve than on other lattices. The solutions are related to the often used Bethe ansatz for these systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Netherlands the then state-owned phone company PTT (now KPN) operated two platforms: Viditel (launched in 1980) and Videotex Nederland. From the user perspective the main difference between these systems was that Viditel used standard dial-in phone numbers where Videotex used premium-rate telephone numbers. For Viditel you needed a (paid) subscription and on top of that you paid for each page you visited. For Videotex services you normally didn't need a subscription nor was there the need to authenticate: you paid for the services via the premium rate of the modem-connection based on connection time, regardless of the pages or services you retrieved.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multivariate statistics, if \u03b5 {\\displaystyle \\varepsilon } is a vector of n {\\displaystyle n} random variables, and \u039b {\\displaystyle \\Lambda } is an n {\\displaystyle n} -dimensional symmetric matrix, then the scalar quantity \u03b5 T \u039b \u03b5 {\\displaystyle \\varepsilon ^{T}\\Lambda \\varepsilon } is known as a quadratic form in \u03b5 {\\displaystyle \\varepsilon } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Semantically textual data can be represented in binary format (e.g. when compressed or in certain formats that intermix various sorts of formatting codes, as in the doc format used by Microsoft Word); contrarily, image data is sometimes represented in textual format (e.g. the X PixMap image format used in the X Window System). 1 and 0 are nothing but just two different voltage levels. You can make the computer understand 1 for higher voltage and 0 for lower voltage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Article 14 bis of the DADVSI law explicitly exempts from this regime the act of downloading a copyrighted work on a peer-to-peer network. This exemption is further extended to the act of making some copyrighted work available to the public without any commercial purpose, when this is an automatic result of the use of a peer-to-peer network for obtaining it; this clause was added because many peer-to-peer networks automatically make downloaded content available to other users, thus merely exempting downloads from the counterfeiting felony would not have been sufficient.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the European Union, the treatment of VoIP service providers is a decision for each national telecommunications regulator, which must use competition law to define relevant national markets and then determine whether any service provider on those national markets has \"significant market power\" (and so should be subject to certain obligations). A general distinction is usually made between VoIP services that function over managed networks (via broadband connections) and VoIP services that function over unmanaged networks (essentially, the Internet).The relevant EU Directive is not clearly drafted concerning obligations that can exist independently of market power (e.g., the obligation to offer access to emergency calls), and it is impossible to say definitively whether VoIP service providers of either type are bound by them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the neighboring site is S, then let it become I. Repeat as long as there are S sites available.Making a list of I sites makes this run quickly. The net rate of infecting one neighbor over the rate of removal is \u03bb = (1-c)/c. For the synchronous model, all sites are updated simultaneously (using two copies of the lattice) as in a cellular automaton.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example, the text \"Paul Schuster was born in Dresden\" on a website will be annotated, connecting a person with their place of birth. The following HTML fragment shows how a small graph is being described, in RDFa-syntax using a schema.org vocabulary and a Wikidata ID: The example defines the following five triples (shown in Turtle syntax). Each triple represents one edge in the resulting graph: the first element of the triple (the subject) is the name of the node where the edge starts, the second element (the predicate) the type of the edge, and the last and third element (the object) either the name of the node where the edge ends or a literal value (e.g. a text, a number, etc.).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "the first instance of \"crypto\" lines up with \"abcdef\" and the second instance lines up with \"cdefab\". The two instances will encrypt to different ciphertexts and the Kasiski examination will reveal nothing. However, with a 5-character keyword \"abcde\" (5 divides into 20): abcdeabcdeabcdeabcdeabcdeabcdeabc crypto is short for cryptography. both occurrences of \"crypto\" line up with \"abcdea\". The two instances will encrypt to the same ciphertext and the Kasiski examination will be effective.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the classic M\u00f6bius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand M\u00f6bius.A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with M\u00f6bius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Class 2 comprises mechanically propelled vehicles such as motorized wheelchairs and mobility scooters, limited to 4 mph. Class 3 consists mostly of mobility scooters. They are limited to 8 mph, with a further limiter set to 4 mph which must be enabled when used on a pavement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These problems already trivially lie in co-NP. This was the first strong evidence that these problems are not NP-complete, since if they were, it would imply that NP is subset of co-NP, a result widely believed to be false; in fact, this was the first demonstration of a problem in NP intersect co-NP not known, at the time, to be in P. Producing certificates for the complement problem, to establish that a number is composite, is straightforward: it suffices to give a nontrivial divisor. Standard probabilistic primality tests such as the Baillie\u2013PSW primality test, the Fermat primality test, and the Miller\u2013Rabin primality test also produce compositeness certificates in the event where the input is composite, but do not produce certificates for prime inputs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Depending on the author, such mappings may or may not be assumed to be linear, or to be defined on the whole space X . {\\displaystyle X.} In computer science, it is synonymous with higher-order functions, that is, functions that take functions as arguments or return them.This article is mainly concerned with the second concept, which arose in the early 18th century as part of the calculus of variations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(Conversation, in formal or informal settings is an example.) Written language, on the other hand, is the common mode used to convey objective information.Both vocal and sign languages are composed of words. In vocal languages, words are made up from a limited set of vowels and consonants, and often tone. In sign languages, words are made up from a limited set of shapes, orientations, locations movements of the hands, and often facial expressions; in both cases, the building blocks are called phonemes. In both vocal and sign languages, words are grammatically and prosodically linked into phrases, clauses, and larger units of discourse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Interfaces are described in Microsoft Interface Definition Language. Type libraries can be viewed using various tools, such as the Microsoft OLE/COM Object Viewer (oleview.exe, part of the Microsoft Platform SDK) or the Object Browser in Visual Basic (up to version 6) and Visual Studio .NET. Type libraries are used to generate Proxy pattern/stub code for interoperating between COM and other platforms, such as Microsoft .NET and Java.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A system of equations is a subset E of the Cartesian product X\u2217 \u00d7 X\u2217 of the free monoid (finite strings) over X with itself. The system E is satisfiable in S if there is a map f from X to S, which extends to a semigroup morphism f from X+ to S, such that for all (u,v) in E we have f(u) = f(v) in S. Such an f is a solution, or satisfying assignment, for the system E.Two systems of equations are equivalent if they have the same set of satisfying assignments. A system of equations if independent if it is not equivalent to a proper subset of itself. A semigroup is compact if every independent system of equations is finite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To find an answer to this problem, a bipartite graph G' = (A \u222a B, E) is created where each flight has a copy in set A and set B. If the same plane can perform flight j after flight i, i\u2208A is connected to j\u2208B. A matching in G' induces a schedule for F and obviously maximum bipartite matching in this graph produces an airline schedule with minimum number of crews. As it is mentioned in the Application part of this article, the maximum cardinality bipartite matching is an application of maximum flow problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Silver proved the consistency of Chang's conjecture from the consistency of an \u03c91-Erd\u0151s cardinal. Hans-Dieter Donder showed a weak version of the reverse implication: if CC is not only consistent but actually holds, then \u03c92 is \u03c91-Erd\u0151s in K. More generally, Chang's conjecture for two pairs (\u03b1,\u03b2), (\u03b3,\u03b4) of cardinals is the claim that every model of type (\u03b1,\u03b2) for a countable language has an elementary submodel of type (\u03b3,\u03b4). The consistency of ( \u03c9 3 , \u03c9 2 ) \u21a0 ( \u03c9 2 , \u03c9 1 ) {\\displaystyle (\\omega _{3},\\omega _{2})\\twoheadrightarrow (\\omega _{2},\\omega _{1})} was shown by Laver from the consistency of a huge cardinal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", then adding the transformed vectors. A v \u2192 + B v \u2192 = ( A + B ) v \u2192 {\\displaystyle \\mathbf {A} {\\vec {v}}+\\mathbf {B} {\\vec {v}}=(\\mathbf {A} +\\mathbf {B} ){\\vec {v}}\\!} However, there are other operations that could also be considered addition for matrices, such as the direct sum and the Kronecker sum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory.A Boolean function takes the form f: { 0 , 1 } k \u2192 { 0 , 1 } {\\displaystyle f:\\{0,1\\}^{k}\\to \\{0,1\\}} , where { 0 , 1 } {\\displaystyle \\{0,1\\}} is known as the Boolean domain and k {\\displaystyle k} is a non-negative integer called the arity of the function. In the case where k = 0 {\\displaystyle k=0} , the function is a constant element of { 0 , 1 } {\\displaystyle \\{0,1\\}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can be solved with a variant of Mahler and De Weger's lattice based analysis of N-adic numbers when N = 2 {\\displaystyle N=2} ; by a variant of the Euclidean algorithm when N is prime; and in general by Xu's adaptation of the Berlekamp-Massey algorithm. If L is the size of the smallest FCSR that outputs the sequence (called the N-adic complexity of the sequence), then all these algorithms require a prefix of length about 2 L {\\displaystyle 2L} to be successful and have quadratic time complexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most reactor designs, as a safety measure, control rods are attached to the lifting machinery by electromagnets, rather than direct mechanical linkage. This means that in the event of power failure, or if manually invoked due to failure of the lifting machinery, the control rods fall automatically, under gravity, all the way into the pile to stop the reaction. A notable exception to this fail-safe mode of operation is the BWR, which requires hydraulic insertion in the event of an emergency shut-down, using water from a special tank under high pressure. Quickly shutting down a reactor in this way is called scramming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It does not explicitly require the compiler to understand instruction names, as the compiler is only needed to substitute its register assignments, plus a few mov operations, to handle the input requirements. However, the user is prone to specifying clobbered registers incorrectly. The MSVC form of an embedded domain-specific language provides ease of writing, but it requires the compiler itself to know about opcode names and their clobbering properties, demanding extra attention in maintenance and porting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many sets that arise in mathematics do not allow a bijection to be established with {1, 2, ..., n} for any natural number n; these are called infinite sets, while those sets for which such a bijection does exist (for some n) are called finite sets. Infinite sets cannot be counted in the usual sense; for one thing, the mathematical theorems which underlie this usual sense for finite sets are false for infinite sets. Furthermore, different definitions of the concepts in terms of which these theorems are stated, while equivalent for finite sets, are inequivalent in the context of infinite sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Hoeffding's lemma is an inequality that bounds the moment-generating function of any bounded random variable. It is named after the Finnish\u2013American mathematical statistician Wassily Hoeffding. The proof of Hoeffding's lemma uses Taylor's theorem and Jensen's inequality. Hoeffding's lemma is itself used in the proof of McDiarmid's inequality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Dirichlet process (DP) is one of the most popular Bayesian nonparametric models. It was introduced by Thomas Ferguson as a prior over probability distributions. A Dirichlet process D P ( s , G 0 ) {\\displaystyle \\mathrm {DP} \\left(s,G_{0}\\right)} is completely defined by its parameters: G 0 {\\displaystyle G_{0}} (the base distribution or base measure) is an arbitrary distribution and s {\\displaystyle s} (the concentration parameter) is a positive real number (it is often denoted as \u03b1 {\\displaystyle \\alpha } ). According to the Bayesian paradigm these parameters should be chosen based on the available prior information on the domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first glance but is, in fact, true. While it may seem surprising that only 23 individuals are required to reach a 50% probability of a shared birthday, this result is made more intuitive by considering that the birthday comparisons will be made between every possible pair of individuals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then: x  = \u2211 k x k  , {\\displaystyle x=\\sum _{k}x_{k},\\,} and y can be written as a sum of short convolutions: y  = ( \u2211 k x k  ) \u2217 h  = \u2211 k ( x k  \u2217 h  ) = \u2211 k y k  , {\\displaystyle {\\begin{aligned}y=\\left(\\sum _{k}x_{k}\\right)*h&=\\sum _{k}\\left(x_{k}*h\\right)\\\\&=\\sum _{k}y_{k},\\end{aligned}}} where the linear convolution y k  \u225c x k  \u2217 h  {\\displaystyle y_{k}\\ \\triangleq \\ x_{k}*h\\,} is zero outside the region . And for any parameter N \u2265 L + M \u2212 1 , {\\displaystyle N\\geq L+M-1,\\,} it is equivalent to the N-point circular convolution of x k  {\\displaystyle x_{k}\\,} with h  {\\displaystyle h\\,} in the region . The advantage is that the circular convolution can be computed more efficiently than linear convolution, according to the circular convolution theorem: where: DFTN and IDFTN refer to the Discrete Fourier transform and its inverse, evaluated over N discrete points, and L is customarily chosen such that N = L+M-1 is an integer power-of-2, and the transforms are implemented with the FFT algorithm, for efficiency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. The RVM has an identical functional form to the support vector machine, but provides probabilistic classification. It is actually equivalent to a Gaussian process model with covariance function: k ( x , x \u2032 ) = \u2211 j = 1 N 1 \u03b1 j \u03c6 ( x , x j ) \u03c6 ( x \u2032 , x j ) {\\displaystyle k(\\mathbf {x} ,\\mathbf {x'} )=\\sum _{j=1}^{N}{\\frac {1}{\\alpha _{j}}}\\varphi (\\mathbf {x} ,\\mathbf {x} _{j})\\varphi (\\mathbf {x} ',\\mathbf {x} _{j})} where \u03c6 {\\displaystyle \\varphi } is the kernel function (usually Gaussian), \u03b1 j {\\displaystyle \\alpha _{j}} are the variances of the prior on the weight vector w \u223c N ( 0 , \u03b1 \u2212 1 I ) {\\displaystyle w\\sim N(0,\\alpha ^{-1}I)} , and x 1 , \u2026 , x N {\\displaystyle \\mathbf {x} _{1},\\ldots ,\\mathbf {x} _{N}} are the input vectors of the training set.Compared to that of support vector machines (SVM), the Bayesian formulation of the RVM avoids the set of free parameters of the SVM (that usually require cross-validation-based post-optimizations). However RVMs use an expectation maximization (EM)-like learning method and are therefore at risk of local minima. This is unlike the standard sequential minimal optimization (SMO)-based algorithms employed by SVMs, which are guaranteed to find a global optimum (of the convex problem). The relevance vector machine was patented in the United States by Microsoft (patent expired September 4, 2019).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"B\" routes are less significant routes, either as an alternative to an \"A\" or \"M\" route, or linking smaller population centres to larger regional centres, but without being a major through-route in the region. These are the major road links in areas without \"A\" routes. \"C\" routes link smaller settlements and towns to the rest of the major road network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-state models, the recurrent event processes of individuals are described by different states. The different states may describe the recurrence number, or whether the subject is at risk of recurrence. A change of state is called a transition (or an event) and is central in this framework, which is fully characterized through estimation of transition probabilities between states and transition intensities that are defined as instantaneous hazards of progression to one state, conditional on occupying another state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(c) Overproduction of information. (d) Restricted capacity of the individual's brain which can lead to excessive specialization, with consequent dangers of degeneration. (e) A crisis precipitated by the creation of artificial intelligent beings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A blocking device (a duplexer), shut the receiver input when the transmitter pulsed. A Braun tube (a CRT) was used for displaying the range. The equipment was first tested at a NVA site at the L\u00fcbecker Bay near Pelzerhaken.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While not widely reported, it has been noted that the genre, or domain, of a text has an effect on the correlation obtained when using metrics. Coughlin (2003) reports that comparing the candidate text against a single reference translation does not adversely affect the correlation of metrics when working in a restricted domain text. Even if a metric correlates well with human judgment in one study on one corpus, this successful correlation may not carry over to another corpus.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, the base 10 definition of the unit (one million bits) is standard. In the semiconductor industry, it is still common practice to designate random-access memory (RAM), read-only memory (ROM) in a binary interpretation of the metric prefixes, such as the megabit, so that one megabit represents 220bits=1048576bits. For example, a single discrete DDR3 chip specified at \"512 Mb\" contains 229 bits = 536870912bits = 512 Mibit (approximately 536.87 Mbit) of storage, or 671088648-bit bytes, variously referred to as either 64 mebibytes or 64 (binary) megabytes. During the 16-bit game console era, the megabit (Mb) was a commonly used measure of the size (computer data storage capacity) of game cartridges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a natural number a is a unitary divisor (or Hall divisor) of a number b if a is a divisor of b and if a and b a {\\displaystyle {\\frac {b}{a}}} are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and 60 5 = 12 {\\displaystyle {\\frac {60}{5}}=12} have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and 60 6 = 10 {\\displaystyle {\\frac {60}{6}}=10} have a common factor other than 1, namely 2. 1 is a unitary divisor of every natural number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, the active record pattern is an architectural pattern. It is found in software that stores in-memory object data in relational databases. It was named by Martin Fowler in his 2003 book Patterns of Enterprise Application Architecture. The interface of an object conforming to this pattern would include functions such as Insert, Update, and Delete, plus properties that correspond more or less directly to the columns in the underlying database table.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the algorithm as written above, there are two expensive operations during each iteration: the multiplication s \u00d7 s, and the mod M operation. The mod M operation can be made particularly efficient on standard binary computers by observing that k \u2261 ( k mod 2 n ) + \u230a k / 2 n \u230b ( mod 2 n \u2212 1 ) . {\\displaystyle k\\equiv (k\\,{\\bmod {\\,}}2^{n})+\\lfloor k/2^{n}\\rfloor {\\pmod {2^{n}-1}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, the Official Charts Company has included streaming into the UK Albums Chart since March 2015. The change was decided after the massive growth of streaming; the number of tracks streamed in the UK in a year doubled from 7.5 billion in 2013 to just under 15 billion in 2014. Under the new methodology, Official Charts Company takes the 12 most-streamed tracks from an album, with the top two songs being given lesser weight so that the figure will reflect the popularity of the album as a whole rather than of one or two successful singles. The adjusted total is divided by 1000 and added to the album sales figure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the category of medial magmas, also known as the medial category, and denoted Med, is the category whose objects are medial magmas (that is, sets with a medial binary operation), and whose morphisms are magma homomorphisms (which are equivalent to homomorphisms in the sense of universal algebra). The category Med has direct products, so the concept of a medial magma object (internal binary operation) makes sense. As a result, Med has all its objects as medial objects, and this characterizes it. There is an inclusion functor from Set to Med as trivial magmas, with operations being the right projections (x, y) \u2192 y.An injective endomorphism can be extended to an automorphism of a magma extension\u2014the colimit of the constant sequence of the endomorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This allows the typesetter to distinguish sentence endings from abbreviations and to typeset them differently. Early versions of Troff, which only typeset in fixed-width fonts, would automatically add a second space between sentences, which were detected based on the combination of terminal punctuation and a line feed. In the April 2020 update, Microsoft Word started highlighting two spaces after a period as an error and offers a correction of one space.Multiple spaces are eliminated by default in most World Wide Web content, whether or not they are associated with sentences. There are options for preserving spacing, such as the CSS white-space property, and the tag.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the broader sense of the term, game engines themselves can be described as middleware. In the context of video games, however, the term \"middleware\" is often used to refer to subsystems of functionality within a game engine. Some game middleware does only one thing but does it more convincingly or more efficiently than general purpose middleware. The four most widely used middleware packages that provide subsystems of functionality include RAD Game Tools' Bink, Firelight FMOD, Havok, and Scaleform GFx.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 367, 1367, 3467, and 13467 are the patterns related to Braille pattern dots-235, since the two additional dots of kantenji patterns 0235, 2357, and 02357 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Jaccard is not cited in the paper, and it seems likely that the authors were not aware of it.Tanimoto goes on to define a \"distance coefficient\" based on this ratio, defined for bitmaps with non-zero similarity: T d ( X , Y ) = \u2212 log 2 \u2061 ( T s ( X , Y ) ) {\\displaystyle T_{d}(X,Y)=-\\log _{2}(T_{s}(X,Y))} This coefficient is, deliberately, not a distance metric. It is chosen to allow the possibility of two specimens, which are quite different from each other, to both be similar to a third. It is easy to construct an example which disproves the property of triangle inequality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of reliability weights, the weights are normalized: V 1 = \u2211 i = 1 N w i = 1. {\\displaystyle V_{1}=\\sum _{i=1}^{N}w_{i}=1.} (If they are not, divide the weights by their sum to normalize prior to calculating V 1 {\\displaystyle V_{1}}: w i \u2032 = w i \u2211 i = 1 N w i {\\displaystyle w_{i}'={\\frac {w_{i}}{\\sum _{i=1}^{N}w_{i}}}} Then the weighted mean vector \u03bc \u2217 {\\displaystyle \\mathbf {\\mu ^{*}} } can be simplified to \u03bc \u2217 = \u2211 i = 1 N w i x i . {\\displaystyle \\mathbf {\\mu ^{*}} =\\sum _{i=1}^{N}w_{i}\\mathbf {x} _{i}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In television, a similar idea is used to signal to a control room that a transition of some sort is about to occur on the broadcast (such as a commercial break). The most common type of television cue dot is the IBA style, used only in the United Kingdom, which consists of a small square in the top right corner of the screen, with black and white moving stripes. The other is a proprietary system used principally by the BBC (who do not air commercials). This version is a static square in the top left corner with a white-black-white pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on the number of ones (or zeros) in the input. For this reason they are also known as Boolean counting functions.There are 2n+1 symmetric n-ary Boolean functions. Instead of the truth table, traditionally used to represent Boolean functions, one may use a more compact representation for an n-variable symmetric Boolean function: the (n + 1)-vector, whose i-th entry (i = 0, ..., n) is the value of the function on an input vector with i ones. Mathematically, the symmetric Boolean functions correspond one-to-one with the functions that map n+1 elements to two elements, f: { 0 , 1 , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set\u2014something that cannot happen with proper subsets of finite sets. There is a transfinite sequence of cardinal numbers: 0 , 1 , 2 , 3 , \u2026 , n , \u2026 ; \u2135 0 , \u2135 1 , \u2135 2 , \u2026 , \u2135 \u03b1 , \u2026 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of two explanatory variables, this indicator function was defined as yk when n = 1 and 1-yk when n = 0. This was convenient, but not necessary. Again, the optimum beta coefficients may be found by maximizing the log-likelihood function generally using numerical methods. A possible method of solution is to set the derivatives of the log-likelihood with respect to each beta coefficient equal to zero and solve for the beta coefficients: \u2202 \u2113 \u2202 \u03b2 n m = 0 = \u2211 k = 1 K \u0394 ( n , y k ) x m k \u2212 \u2211 k = 1 K p n ( x k ) x m k {\\displaystyle {\\frac {\\partial \\ell }{\\partial \\beta _{nm}}}=0=\\sum _{k=1}^{K}\\Delta (n,y_{k})x_{mk}-\\sum _{k=1}^{K}p_{n}({\\boldsymbol {x}}_{k})x_{mk}} where \u03b2 n m {\\displaystyle \\beta _{nm}} is the m-th coefficient of the \u03b2 n {\\displaystyle {\\boldsymbol {\\beta }}_{n}} vector and x m k {\\displaystyle x_{mk}} is the m-th explanatory variable of the k-th measurement. Once the beta coefficients have been estimated from the data, we will be able to estimate the probability that any subsequent set of explanatory variables will result in any of the possible outcome categories.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optical mesh networks, nodes are junctions of fiber spans. Some nodes might contain highly sophisticated routing equipment\u2014 while others may be just a patch panel. Whatever the case, a node is a shared risk node group\u2014because if the node fails, the failure affects all signals through that particular node.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Trace data generated and merged to a trace stream within the SoC can be streamed, via a dedicated unidirectional trace interface, off-chip to a trace analysis tool. The MIPI Debug Architecture provides specifications for both parallel and serial trace ports. The MIPI Parallel Trace Interface (MIPI PTI) specifies how to pass the trace data to multiple data pins and a clock pin (single-ended).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In polyalphabetic substitution ciphers where the substitution alphabets are chosen by the use of a keyword, the Kasiski examination allows a cryptanalyst to deduce the length of the keyword. Once the length of the keyword is discovered, the cryptanalyst lines up the ciphertext in n columns, where n is the length of the keyword. Then each column can be treated as the ciphertext of a monoalphabetic substitution cipher. As such, each column can be attacked with frequency analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-fuzzy clustering (also known as hard clustering), data are divided into distinct clusters, where each data point can only belong to exactly one cluster. In fuzzy clustering, data points can potentially belong to multiple clusters. For example, an apple can be red or green (hard clustering), but an apple can also be red AND green (fuzzy clustering).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since 2010, a new open source instruction set architecture (ISA), RISC-V, has been under development at the University of California, Berkeley, for research purposes and as a free alternative to proprietary ISAs. As of 2014, version 2 of the user space ISA is fixed. The ISA is designed to be extensible from a barebones core sufficient for a small embedded processor to supercomputer and cloud computing use with standard and chip designer\u2013defined extensions and coprocessors. It has been tested in silicon design with the ROCKET SoC, which is also available as an open-source processor generator in the CHISEL language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!. It is named after Adrien-Marie Legendre. It is also sometimes known as de Polignac's formula, after Alphonse de Polignac.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel to the development of the 1972 edition of ISO 646, which revised the standard to introduce the concept of national versions of the code in addition to the US-originated ASCII, work was also underway with the purpose of defining extension mechanisms for ASCII, applicable to both 7-bit and 8-bit environments, which would be published as ECMA-35 and ISO 2022.These mechanisms were designed so that any conformant 8-bit code could be converted to a corresponding 7-bit code, and vice versa. In a 7-bit environment, the Shift Out (SO) control would change the meaning of the 94 bytes 0x21 through 0x7E (i.e. the graphical codes, excluding the space) to invoke characters from an alternative set, and the Shift In (SI) control would change them back. In an 8-bit environment, instead of using shift codes, the eighth bit was set on a byte referencing the additional graphic character set. This meant that bytes 0xA1 through 0xFE were used for the additional graphic characters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the field of group theory, especially in the study of p-groups and pro-p-groups, the concept of powerful p-groups plays an important role. They were introduced in (Lubotzky & Mann 1987), where a number of applications are given, including results on Schur multipliers. Powerful p-groups are used in the study of automorphisms of p-groups (Khukhro 1998), the solution of the restricted Burnside problem (Vaughan-Lee 1993), the classification of finite p-groups via the coclass conjectures (Leedham-Green & McKay 2002), and provided an excellent method of understanding analytic pro-p-groups (Dixon et al. 1991).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a \"planned state\" these work orders have estimates such as 2 electricians for 8 hours. These work orders have other attributes such as report date, priority, asset operational requirements, and safety concerns. These same organizations have a need to create weekly schedules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example S L 2 ( Z ) . {\\displaystyle \\mathrm {SL} _{2}(\\mathbb {Z} ).} They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theory. They also give rise to very interesting examples of Riemannian manifolds and hence are objects of interest in differential geometry and topology. Finally, these two topics join in the theory of automorphic forms which is fundamental in modern number theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern computers many processes run at once. Active processes are placed in an array called a run queue, or runqueue. The run queue may contain priority values for each process, which will be used by the scheduler to determine which process to run next. To ensure each program has a fair share of resources, each one is run for some time period (quantum) before it is paused and placed back into the run queue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead, the following heuristics are used. 1D partitioning: Every processor gets n / p {\\displaystyle n/p} vertices and the corresponding outgoing edges. This can be understood as a row-wise or column-wise decomposition of the adjacency matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "4. Creating a model, likeness, analogy, metaphor, prototype or narrative which shows what the concept is about or how it is applied (isomorphism, simulation or successive approximation ). 5.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As another issue, for some programs, the method of taking the greatest lower bound at converging execution paths and adding corresponding down-coercion operations appears to be inadequate. For example, before the return 1 in the following program, all components x, y, and z of coord are initialized, but Strom's and Yemini's approach fails to recognize this, since each initialization of a struct component in the loop body has to be down-coerced at loop re-entry to meet the typestate of the very first loop entry, viz. \u22a5. A related problem is that this example would require overloading of typestate transitions; for example, parse_int_attr(\"x\",&coord->x) changes a typestate \"no component initialized\" to \"x component initialized\", but also \"y component initialized\" to \"x and y component initialized\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead of simply \u201ctaking in\u201d new information, one goes back to look at their understandings and pulls together information that was \u201ctriggered\u201d and forms a new connection. This connection becomes tighter and one's understanding of a certain concept is solidified or \u201cstable\u201d (Pangaro, 2003).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If R is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The resulting contradiction is Russell's paradox.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of quantum information theory, the operators {Vi} are called the Kraus operators (after Karl Kraus) of \u03a6. Notice, given a completely positive \u03a6, its Kraus operators need not be unique. For example, any \"square root\" factorization of the Choi matrix C\u03a6 = B\u2217B gives a set of Kraus operators. Let B \u2217 =  , {\\displaystyle B^{*}=,} where bi*'s are the row vectors of B, then C \u03a6 = \u2211 i = 1 n m b i b i \u2217 . {\\displaystyle C_{\\Phi }=\\sum _{i=1}^{nm}b_{i}b_{i}^{*}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All hardware architectures in common use are optimized for strict languages, so the best compilers for non-strict languages produce slower code than the best compilers for strict languages. Space complexity of non-strict programs is difficult to understand and predict.Strict programming languages are often associated with eager evaluation, and non-strict languages with lazy evaluation, but other evaluation strategies are possible in each case. The terms \"eager programming language\" and \"lazy programming language\" are often used as synonyms for \"strict programming language\" and \"non-strict programming language\" respectively. In many strict languages, some advantages of non-strict functions can be obtained through the use of macros or thunks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 2000s, many of the existing copyright laws were designed around printed books, magazines and newspapers. For example, copyright laws often set limits on how much of a book can be mechanically reproduced or copied. Electronic publishing raises new questions in relation to copyright, because if an e-book or e-journal is available online, millions of Internet users may be able to view a single electronic copy of the document, without any \"copies\" being made. Emerging evidence suggests that e-publishing may be more collaborative than traditional paper-based publishing; e-publishing often involves more than one author, and the resulting works are more accessible, since they are published online.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The probability of doing so in two draws depends on whether the first card drawn was replaced before the second drawing since without replacement there is one fewer card after the first card was drawn. The probabilities of the individual events (red, and club) are multiplied rather than added. The probability of drawing a red and a club in two drawings without replacement is then 26/52 \u00d7 13/51 \u00d7 2 = 676/2652, or 13/51.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Data elements are defined by the metamodel view and they are referred to by functional objects in other views.Functional viewpointFunctional Dataflow view \u2013 An abstract view that describes the functional elements in the system, their interactions, behavior, provided services, constraints and data flows among them. Defines which functions the system is capable of performing, regardless of how these functions are actually implemented. Functional Control view \u2013 Describes the control flows and interactions among functional elements within the system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a bulk queue (sometimes batch queue) is a general queueing model where jobs arrive in and/or are served in groups of random size. : vii Batch arrivals have been used to describe large deliveries and batch services to model a hospital out-patient department holding a clinic once a week, a transport link with fixed capacity and an elevator.Networks of such queues are known to have a product form stationary distribution under certain conditions. Under heavy traffic conditions a bulk queue is known to behave like a reflected Brownian motion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Vadim Schechtman and Alexander Varchenko introduced a matrix indexed by the regions. The matrix element for the region R i {\\displaystyle R_{i}} and R j {\\displaystyle R_{j}} is given by the product of indeterminate variables a H {\\displaystyle a_{H}} for every hyperplane H that separates these two regions. If these variables are specialized to be all value q, then this is called the q-matrix (over the Euclidean domain Q  {\\displaystyle \\mathbb {Q} } ) for the arrangement and much information is contained in its Smith normal form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Franklin proved that the chromatic number of a graph embedded in the Klein bottle can be as large as 6 {\\displaystyle 6} , but never exceeds 6 {\\displaystyle 6} . Later it was proved in the works of Gerhard Ringel, J. W. T. Youngs, and other contributors that the complete graph with H ( S ) {\\displaystyle H(S)} vertices can be embedded in the surface S {\\displaystyle S} unless S {\\displaystyle S} is the Klein bottle. This established that Heawood's bound could not be improved. For example, the complete graph on 7 {\\displaystyle 7} vertices can be embedded in the torus as follows: The case of the sphere is the four-color conjecture, which was settled by Kenneth Appel and Wolfgang Haken in 1976.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Evaluation \u2013 Assesses the effectiveness of a public policy in terms of its perceived intentions and results. Policy actors attempt to determine whether the course of action is a success or failure by examining its impact and outcomes.Anderson's version of the stages model is the most common and widely recognised out of the models. However, it could also be seen as flawed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is a whole research branch dealing with all possible regularizations. In practice, one usually tries a specific regularization and then figures out the probability density that corresponds to that regularization to justify the choice. It can also be physically motivated by common sense or intuition. In machine learning, the data term corresponds to the training data and the regularization is either the choice of the model or modifications to the algorithm. It is always intended to reduce the generalization error, i.e. the error score with the trained model on the evaluation set and not the training data.One of the earliest uses of regularization is Tikhonov regularization, related to the method of least squares.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two binary variables are considered positively associated if most of the data falls along the diagonal cells. In contrast, two binary variables are considered negatively associated if most of the data falls off the diagonal. If we have a 2\u00d72 table for two random variables x and y where n11, n10, n01, n00, are non-negative counts of numbers of observations that sum to n, the total number of observations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a system that supports simultaneous voice and data (SVD) is one that can transceive both voice and primary data concurrently over one PSTN modem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Fibonacci numbers form a sequence defined recursively by: F n = { 0 n = 0 1 n = 1 F n \u2212 1 + F n \u2212 2 n > 1 {\\displaystyle F_{n}={\\begin{cases}0&n=0\\\\1&n=1\\\\F_{n-1}+F_{n-2}&n>1\\end{cases}}} That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1, by adding more than two numbers to generate the next number, or by adding objects other than numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing the convergence or divergence of an infinite series or an improper integral. In both cases, the test works by comparing the given series or integral to one whose convergence properties are known.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 5678, 15678, 45678, and 145678 are the patterns related to Braille pattern dots-3456, since the two additional dots of kantenji patterns 03456, 34567, and 034567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A network or protocol that supports QoS may agree on a traffic contract with the application software and reserve capacity in the network nodes, for example during a session establishment phase. During the session it may monitor the achieved level of performance, for example the data rate and delay, and dynamically control scheduling priorities in the network nodes. It may release the reserved capacity during a tear down phase.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The reference validation mechanism must be Always invoked. Without this property, it is possible for the mechanism to not perform when intended, allowing an attacker to violate the security policy. The reference validation mechanism must be Tamper-proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statically typed languages such as Go or ML, a variable also has a type, meaning that only certain kinds of values can be stored in it. For example, a variable of type \"integer\" is prohibited from storing text values. In dynamically typed languages such as Python, a variable's type is inferred by its value, and can change according to its value. In Common Lisp, both situations exist simultaneously: A variable is given a type (if undeclared, it is assumed to be T, the universal supertype) which exists at compile time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software architecture, a messaging pattern is an architectural pattern which describes how two different parts of an application, or different systems connect and communicate with each other. There are many aspects to the concept of messaging which can be divided in the following categories: hardware device messaging (telecommunications, computer networking, IoT, etc.) and software data exchange (the different data exchange formats and software capabilities of such data exchange). Despite the difference in the context, both categories exhibit common traits for data exchange.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics.Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code. The verification of these systems is done by providing a formal proof on an abstract mathematical model of the system, the correspondence between the mathematical model and the nature of the system being otherwise known by construction. Examples of mathematical objects often used to model systems are: finite-state machines, labelled transition systems, Petri nets, vector addition systems, timed automata, hybrid automata, process algebra, formal semantics of programming languages such as operational semantics, denotational semantics, axiomatic semantics and Hoare logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first eight units were delivered to the office of the then Prime Minister, Pierre Elliot Trudeau, in February 1974. Despite these predecessors, Wang's product was a standout, and by 1978 it had sold more of these systems than any other vendor.The phrase \"word processor\" rapidly came to refer to CRT-based machines similar to the AES 90.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When analyzing a population, one of the main sources used to gather the required information is insurance by obtaining individual records that belong to a specific population. These are called mortality tables if they show death rates, and morbidity tables if they show various types of sickness or disability rates. The availability of computers and the proliferation of data gathering about individuals has made possible calculations that are more voluminous and intensive than those used in the past (i.e. they crunch more numbers) and it is more common to attempt to provide different tables for different uses, and to factor in a range of non-traditional behaviors (e.g. gambling, debt load) into specialized calculations utilized by some institutions for evaluating risk. This is particularly the case in non-life insurance (e.g. the pricing of motor insurance can allow for a large number of risk factors, which requires a correspondingly complex table of expected claim rates). However the expression \"life table\" normally refers to human survival rates and is not relevant to non-life insurance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the simple addition of the particle ni \"at\", for example, /hasi\ua71cni/ h\u00e0sh\u00ed-n\u00ec \"at the bridge\" acquires a marked drop in pitch, while /hasini/ h\u00e0shi-ni \"at the edge\" does not. However, because the downstep occurs after the first mora of the accented syllable, a word with a final long accented syllable would contrast all three patterns even in isolation: an accentless word nihon, for example, would be pronounced , differently from either of the words above. In 2014, a study recording the electrical activity of the brain showed that native Japanese speakers mainly use context, rather than pitch accent information, to contrast between words that differ only in pitch.This property of the Japanese language allows for a certain type of pun, called dajare (\u99c4\u6d12\u843d, \u3060\u3058\u3083\u308c), combining two words with the same or very similar sounds but different pitch accents and thus meanings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another strategy to deal with small sample size is to use a shrinkage estimator of the covariance matrix, which can be expressed mathematically as \u03a3 = ( 1 \u2212 \u03bb ) \u03a3 + \u03bb I {\\displaystyle \\Sigma =(1-\\lambda )\\Sigma +\\lambda I\\,} where I {\\displaystyle I} is the identity matrix, and \u03bb {\\displaystyle \\lambda } is the shrinkage intensity or regularisation parameter. This leads to the framework of regularized discriminant analysis or shrinkage discriminant analysis.Also, in many practical cases linear discriminants are not suitable. LDA and Fisher's discriminant can be extended for use in non-linear classification via the kernel trick.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the SAME system, messages are constructed in four parts, the first and last of which are digital and the middle two are audio. The digital sections of a SAME message are AFSK data bursts, with individual bits lasting 1920 \u03bcs (1.92 ms) each, giving a bit rate of 5205\u20446 bits per second. A mark bit is four complete cycles of a sine wave, translating to a mark frequency of 20831\u20443 Hz, and a space bit is three complete sine wave cycles, making the space frequency 1562.5 Hz. The data is sent isochronously and encoded in 8-bit bytes with the most-significant bit of each ASCII byte set to zero. The least-significant bit of each byte is transmitted first, including the preamble. The data stream is bit and byte synchronized on the preamble.Since there is no error correction, the digital part of a SAME message is transmitted three times, so that decoders can pick \"best two out of three\" for each byte, thereby eliminating most errors which can cause an activation to fail.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, the cluster decomposition property states that experiments carried out far from each other cannot influence each other. Usually applied to quantum field theory, it requires that vacuum expectation values of operators localized in bounded regions factorize whenever these regions becomes sufficiently distant from each other. First formulated by Eyvind H. Wichmann and James H. Crichton in 1963 in the context of the S-matrix, it was conjectured by Steven Weinberg that in the low energy limit the cluster decomposition property, together with Lorentz invariance and quantum mechanics, inevitably lead to quantum field theory. String theory satisfies all three of the conditions and so provides a counter-example against this being true at all energy scales.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the OSI model, the definition of the application layer is narrower in scope. The OSI model defines the application layer as only the interface responsible for communicating with host-based and user-facing applications. OSI then explicitly distinguishes the functionality of two additional layers, the session layer and presentation layer, as separate levels below the application layer and above the transport layer. OSI specifies a strict modular separation of functionality at these layers and provides protocol implementations for each. In contrast, the Internet Protocol Suite compiles these functions into a single layer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This algorithm was popular, but significantly more efficient algorithms exist. Algorithms based on the Newton\u2013Raphson method are able to compute quadrature rules for significantly larger problem sizes. In 2014, Ignace Bogaert presented explicit asymptotic formulas for the Gauss\u2013Legendre quadrature weights and nodes, which are accurate to within double-precision machine epsilon for any choice of n \u2265 21. This allows for computation of nodes and weights for values of n exceeding one billion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some used sign-magnitude arithmetic (-1 = 10001), or ones' complement (-1 = 11110), rather than modern two's complement arithmetic (-1 = 11111). Most computers used six-bit character sets because they adequately encoded Hollerith punched cards. It was a major revelation to designers of this period to realize that the data word should be a multiple of the character size. They began to design computers with 12-, 24- and 36-bit data words (e.g., see the TX-2). In this era, Grosch's law dominated computer design: computer cost increased as the square of its speed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical classification, two main approaches are called the generative approach and the discriminative approach. These compute classifiers by different approaches, differing in the degree of statistical modelling. Terminology is inconsistent, but three major types can be distinguished, following Jebara (2004): A generative model is a statistical model of the joint probability distribution P ( X , Y ) {\\displaystyle P(X,Y)} on given observable variable X and target variable Y; A discriminative model is a model of the conditional probability P ( Y \u2223 X = x ) {\\displaystyle P(Y\\mid X=x)} of the target Y, given an observation x; and Classifiers computed without using a probability model are also referred to loosely as \"discriminative\".The distinction between these last two classes is not consistently made; Jebara (2004) refers to these three classes as generative learning, conditional learning, and discriminative learning, but Ng & Jordan (2002) only distinguish two classes, calling them generative classifiers (joint distribution) and discriminative classifiers (conditional distribution or no distribution), not distinguishing between the latter two classes. Analogously, a classifier based on a generative model is a generative classifier, while a classifier based on a discriminative model is a discriminative classifier, though this term also refers to classifiers that are not based on a model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The summation of an explicit sequence is denoted as a succession of additions. For example, summation of  is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need of parentheses, and the result is the same irrespective of the order of the summands.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to improve the optimisation of the valve timing for differing engine speeds and loads, the system is able to vary the timing and duration of the inlet valve opening. It achieves this by using a complex and finely machined mechanism to drive the inlet camshafts. This mechanism can accelerate and decelerate the rotational speed of the camshaft during different parts of its cycle. e.g. to produce longer opening duration, it slows the rotation during the valve open part of the cycle and speeds it up during the valve closed period.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Lingvo \". The search engine has learned to understand queries like \u201cWhat is  in Spanish\u201d and automatically translate them. It became possible to limit search results by region.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Even tiny measurement errors, when integrated, add up to an appreciable error known as \"drift\". For instance, the N-1 navigation system developed for the SM-64 Navaho cruise missile drifted at a rate of 1 nautical mile per hour, meaning that after a two-hour flight the INS would be indicating a position 2 nautical miles (3.7 km; 2.3 mi) away from its actual location. This was outside the desired accuracy of about half a mile.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above example of coin-tossing we explicitly assumed that each toss is an independent trial, and the probability of getting head or tail is always the same. Let X , X 1 , X 2 , \u2026 {\\displaystyle X,X_{1},X_{2},\\ldots } be independent and identically distributed (i.i.d.) random variables whose common distribution satisfies a certain growth condition. Then the following limit exists: lim N \u2192 \u221e 1 N ln \u2061 P ( M N > x ) = \u2212 I ( x ) {\\displaystyle \\lim _{N\\to \\infty }{\\frac {1}{N}}\\ln P(M_{N}>x)=-I(x)} .Here M N = 1 N \u2211 i = 1 N X i {\\displaystyle M_{N}={\\frac {1}{N}}\\sum _{i=1}^{N}X_{i}} ,as before.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In materials management, ABC analysis is an inventory categorisation technique. ABC analysis divides an inventory into three categories\u2014\"A items\" with very tight control and accurate records, \"B items\" with less tightly controlled and good records, and \"C items\" with the simplest controls possible and minimal records. The ABC analysis provides a mechanism for identifying items that will have a significant impact on overall inventory cost, while also providing a mechanism for identifying different categories of stock that will require different management and controls. The ABC analysis suggests that inventories of an organization are not of equal value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Reification data is often said to be made a first class object. Reification, at least partially, has been experienced in many languages to date: in early Lisp dialects and in current Prolog dialects, programs have been treated as data, although the causal connection has often been left to the responsibility of the programmer. In Smalltalk-80, the compiler from the source text to bytecode has been part of the run-time system since the very first implementations of the language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Adding the constraint forces does not change the total energy, as the net work done by the constraint forces (taken over the set of particles that the constraints act on) is zero. Note that the sign on \u03bb k {\\displaystyle \\lambda _{k}} is arbitrary and some references have an opposite sign. From integrating both sides of the equation with respect to the time, the constrained coordinates of particles at the time, t + \u0394 t {\\displaystyle t+\\Delta t} , are given, x i ( t + \u0394 t ) = x ^ i ( t + \u0394 t ) + \u2211 k = 1 n \u03bb k \u2202 \u03c3 k ( t ) \u2202 x i ( \u0394 t ) 2 m i \u2212 1 , i = 1 \u2026 N {\\displaystyle \\mathbf {x} _{i}(t+\\Delta t)={\\hat {\\mathbf {x} }}_{i}(t+\\Delta t)+\\sum _{k=1}^{n}\\lambda _{k}{\\frac {\\partial \\sigma _{k}(t)}{\\partial \\mathbf {x} _{i}}}\\left(\\Delta t\\right)^{2}m_{i}^{-1},\\quad i=1\\ldots N} where x ^ i ( t + \u0394 t ) {\\displaystyle {\\hat {\\mathbf {x} }}_{i}(t+\\Delta t)} is the unconstrained (or uncorrected) position of the ith particle after integrating the unconstrained equations of motion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UK, the Data Protection Act is used to ensure that personal data is accessible to those whom it concerns, and provides redress to individuals if there are inaccuracies. This is particularly important to ensure individuals are treated fairly, for example for credit checking purposes. The Data Protection Act states that only individuals and companies with legitimate and lawful reasons can process personal information and cannot be shared.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, an automated attendant (also auto attendant, auto-attendant, autoattendant, automatic phone menus, AA, or virtual receptionist) allows callers to be automatically transferred to an extension without the intervention of an operator/receptionist. Many AAs will also offer a simple menu system (\"for sales, press 1, for service, press 2,\" etc.). An auto attendant may also allow a caller to reach a live operator by dialing a number, usually \"0\". Typically the auto attendant is included in a business's phone system such as a PBX, but some services allow businesses to use an AA without such a system. Modern AA services (which now overlap with more complicated interactive voice response or IVR systems) can route calls to mobile phones, VoIP virtual phones, other AAs/IVRs, or other locations using traditional land-line phones or voice message machines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With 23 individuals, there are 23 \u00d7 22/2 = 253 pairs to consider, far more than half the number of days in a year. Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any object in n-dimensional Euclidean space.In geometry, one often assumes uniform mass density, in which case the barycenter or center of mass coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin.In physics, if variations in gravity are considered, then a center of gravity can be defined as the weighted mean of all points weighted by their specific weight. In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "During the 1980s, approaches to achieve inferential programming mostly involved techniques for logical inference. Today the term is sometimes used in connection with evolutionary computation techniques that enable a computer to evolve a solution in response to a problem posed as a fitness or reward function. In July 2022, GitHub Copilot was released, which is an example of inferential programming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They have proved that when perfect noiseless recovery occurs, then matrix completion is stable vis a vis perturbations. The error is proportional to the noise level \u03b4 {\\displaystyle \\delta } . Therefore, when the noise level is small, the error is small.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If in addition p and q are congruent to 1 modulo 8, let p = c2 + 2d2 and q = C2 + 2D2. Then ( p | q ) 8 = ( q | p ) 8 = ( a B \u2212 b A | q ) 4 ( c D \u2212 d C | q ) 2 . {\\displaystyle (p|q)_{8}=(q|p)_{8}=(aB-bA|q)_{4}(cD-dC|q)_{2}\\ .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 \u00f7 2n equals 1 \u00f7 (2n), not (1 \u00f7 2)n. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division, and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.This ambiguity is often exploited in internet memes such as \"8\u00f72(2+2)\", for which there are two conflicting interpretations: 8\u00f7 = 1 and (2+2) = 16. The expression \"6\u00f72(1+2)\" also gained notoriety in the exact same manner, with the two interpretations resulting in the answers 1 and 9.Ambiguity can also be caused by the use of the slash symbol, '/', for division. The Physical Review submission instructions suggest to avoid expressions of the form a/b/c; ambiguity can be avoided by instead writing (a/b)/c or a/(b/c).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The PRISM design was notable for several aspects of its instruction set. Notably, PRISM included Epicode (extended processor instruction code), which defined a number of \"special\" instructions intended to offer the operating system a stable ABI across multiple implementations. Epicode was given its own set of 22 32-bit registers to use. A set of vector processing instructions were later added as well, supported by an additional sixteen 64-bit vector registers that could be used in a variety of ways.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At the same time the student is generating a list of the multiples of the small number (i.e., partial quotients) that have so far been taken away, which when added up together would then become the whole number quotient itself. For example, to calculate 132 \u00f7 8, one might successively subtract 80, 40 and 8 to leave 4: 132 80 (10 \u00d7 8) -- 52 40 ( 5 \u00d7 8) -- 12 8 ( 1 \u00d7 8) -- 4 -------- 132 = 16 \u00d7 8 + 4 Because 10 + 5 + 1 = 16, 132 \u00f7 8 is 16 with 4 remaining. In the UK, this approach for elementary division sums has come into widespread classroom use in primary schools since the late 1990s, when the National Numeracy Strategy in its \"numeracy hour\" brought in a new emphasis on more free-form oral and mental strategies for calculations, rather than the rote learning of standard methods.Compared to the short division and long division methods that are traditionally taught, chunking may seem strange, unsystematic, and arbitrary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the English language, a hate crime (also known as a \"bias-motivated crime\") generally refers to criminal acts which are seen to have been motivated by hate. Those who commit hate crimes target victims because of their perceived membership in a certain social group, usually defined by race, gender, religion, sexual orientation, mental disorder, disability, class, ethnicity, nationality, age, gender identity, or political affiliation. Incidents may involve physical assault, destruction of property, bullying, harassment, verbal abuse or insults, or offensive graffiti or letters (hate mail).Hate speech is speech perceived to disparage a person or group of people based on their social or ethnic group, such as race, sex, age, ethnicity, nationality, religion, sexual orientation, gender identity, mental disorder, disability, language ability, ideology, social class, occupation, appearance (height, weight, skin color, etc.), mental capacity, and any other distinction that might be considered a liability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the action executes, and what its actual inputs are, is determined by the concrete action and the behaviors in which it is used. An action is the specification of an executable statement and is the fundamental unit of processing or behavior in an activity node that represents some transformation in the modeled system. An action forms an abstraction of a computational procedure which is an atomic execution and therefore completes without interruption.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A song sold on iTunes gives the artist 9 cents in profit. They also reported that customers were purchasing 2.5 million songs a week which translates to a projected annual run rate of 130 million songs a year. The 50 millionth song was \"The Path of Thorns\" by Sarah McLachlan.On April 28, 2004, iTunes Music Store marked its first anniversary with 70 million songs sold, clear dominance in the paid online music market and a slight profit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It can be proved by a back-and-forth method that is also sometimes attributed to Cantor but was actually published later, by Felix Hausdorff. The same back-and-forth method also proves that countable dense unbounded orders are highly symmetric, and can be applied to other kinds of structures. However, Cantor's original proof only used the \"going forth\" half of this method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semantic hashing documents are mapped to memory addresses by means of a neural network in such a way that semantically similar documents are located at nearby addresses. Deep neural network essentially builds a graphical model of the word-count vectors obtained from a large set of documents. Documents similar to a query document can then be found by simply accessing all the addresses that differ by only a few bits from the address of the query document. This way of extending the efficiency of hash-coding to approximate matching is much faster than locality sensitive hashing, which is the fastest current method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more sophisticated systems such as large cities, this concept is further extended: some streets are marked as being one-way, and on those streets all traffic must flow in only one direction. Pedestrians on the sidewalks are generally not limited to one-way movement. Drivers wishing to reach a destination they have already passed must return via other streets. One-way streets, despite the inconveniences to some individual drivers, can greatly improve traffic flow since they usually allow traffic to move faster and tend to simplify intersections.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As per the standard: \"An equal month is presumed to have 30.41666 days (i.e. 365/12) regardless of whether or not it is a leap year.\" The result is to be expressed to at least one decimal place.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of textual scholarship and the editing of historic texts, the term \"normalization\" implies a degree of modernization and standardization \u2013 for example in the extension of scribal abbreviations and the transliteration of the archaic glyphs typically found in manuscript and early printed sources. A normalized edition is therefore distinguished from a diplomatic edition (or semi-diplomatic edition), in which some attempt is made to preserve these features. The aim is to strike an appropriate balance between, on the one hand, rigorous fidelity to the source text (including, for example, the preservation of enigmatic and ambiguous elements); and, on the other, producing a new text that will be comprehensible and accessible to the modern reader. The extent of normalization is therefore at the discretion of the editor, and will vary. Some editors, for example, choose to modernize archaic spellings and punctuation, but others do not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Genus types with sufficient vertical extent to occupy more than one level do not carry any altitude-related prefixes. They are classified formally as low- or mid-level depending on the altitude at which each initially forms, and are also more informally characterized as multi-level or vertical. Most of the ten genera derived by this method of classification can be subdivided into species and further subdivided into varieties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The even dimensional space of dimension d {\\displaystyle d} can be described using complex coordinates w i \u2208 C d / 2 {\\displaystyle w_{i}\\in \\mathbb {C} ^{d/2}} with a metric g i j \u00af = ( 1 + \u03c1 d r d ) 2 / d  , {\\displaystyle g_{i{\\bar {j}}}={\\bigg (}1+{\\frac {\\rho ^{d}}{r^{d}}}{\\bigg )}^{2/d}{\\bigg },} where \u03c1 {\\displaystyle \\rho } is a scale setting constant and r 2 = | w | C d / 2 2 {\\displaystyle r^{2}=|w|_{\\mathbb {C} ^{d/2}}^{2}} . Aside from its inherent importance in pure geometry, the space is important in string theory. Certain types of K3 surfaces can be approximated as a combination of several Eguchi\u2013Hanson metrics since both have the same holonomy group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music, a rewrite rule is a recursive generative grammar, which creates a chord progression from another. Steedman (1984) has proposed a set of recursive \"rewrite rules\" which generate all well-formed transformations of jazz, basic I\u2013IV\u2013I\u2013V\u2013I twelve-bar blues chord sequences, and, slightly modified, non-twelve-bar blues I\u2013IV\u2013V sequences (\"rhythm changes\"). The typical 12-bar blues progression can be notated 1 2 3 4 5 6 7 8 9 10 11 12 I / I / I / I // IV /IV / I / I // V / IV / I / I where the top line numbers each bar, one slash indicates a bar line, two indicate both a bar line and a phrase ending and a Roman numeral indicates the chord function. Important transformations include replacement or substitution of a chord by its dominant or subdominant: 1 2 3 4 5 6 7 8 9 10 11 12 I / IV / I / I7 // IV / VII7 / III7 / VI7 // II7 / V7 / I / I // use of chromatic passing chords: ...7 8 9 ... ...III7 / \u266dIII7 / II7... and chord alterations such as minor chords, diminished sevenths, etc.Sequences by fourth, rather than fifth, include Jimi Hendrix's version of \"Hey Joe\" and Deep Purple's \"Hush\": 1 2 3 4 5 6 7 8 9 10 11 12 \u266dVI, \u266dIII / \u266dVII, IV / I / I // \u266dVI, \u266dIII / \u266dVII, IV / I / I // \u266dVI, \u266dIII / \u266dVII, IV / I / I // These often result in Aeolian harmony and lack perfect cadences (V\u2013I).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "OSes have grown immensely in their size and complexity resulting in attempts to reduce OS overhead and improve performance including Microkernel, Exokernel, Tiny-OS, OS-Kit, Palacios and Kitten, IO_Lite, bare-metal Linux, IBM-Libra and other lean kernels. In addition to the above approaches, in embedded systems such as smart phones, a small and dedicated portion of an OS and a given set of applications are closely integrated with the hardware. There are also a myriad of industrial control and gaming applications that run directly on the hardware.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by Kolyvagin (1990) in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper Kolyvagin (1988) and the work of Thaine (1988). Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product. Euler systems can be used to construct annihilators of ideal class groups or Selmer groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some Tate-Shafarevich groups. This led to Karl Rubin's new proof of the main conjecture of Iwasawa theory, considered simpler than the original proof due to Barry Mazur and Andrew Wiles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other regression methods that can be used in place of ordinary least squares include least absolute deviations (minimizing the sum of absolute values of residuals) and the Theil\u2013Sen estimator (which chooses a line whose slope is the median of the slopes determined by pairs of sample points). Deming regression (total least squares) also finds a line that fits a set of two-dimensional sample points, but (unlike ordinary least squares, least absolute deviations, and median slope regression) it is not really an instance of simple linear regression, because it does not separate the coordinates into one dependent and one independent variable and could potentially return a vertical line as its fit. The remainder of the article assumes an ordinary least squares regression. In this case, the slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. The intercept of the fitted line is such that the line passes through the center of mass (x, y) of the data points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The case (x, y, z) = (2, 6, n) and all its permutations were proven for n \u2265 3 by Michael Bennett and Imin Chen in 2011 and by Bennett, Chen, Dahmen and Yazdani in 2014. The case (x, y, z) = (2, 2n, 3) and all its permutations were proven for 3 \u2264 n \u2264 107 except n = 7 and various modulo congruences when n is prime to have no non-Catalan solution by Bennett, Chen, Dahmen and Yazdani. The cases (x, y, z) = (2, 2n, 9), (2, 2n, 10), (2, 2n, 15) and all their permutations were proven for n \u2265 2 by Bennett, Chen, Dahmen and Yazdani in 2014.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Z i {\\displaystyle Z_{i}} is the idiosyncratic component, the \u2018strength\u2019 of entity i, possibly measured by entity i's stock price return. From equation (10) we see, that the correlation between entities i is modeled indirectly by conditioning the latent variable x i {\\displaystyle x_{i}} on the common factor M {\\displaystyle M} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Java programming language, heap pollution is a situation that arises when a variable of a parameterized type refers to an object that is not of that parameterized type. This situation is normally detected during compilation and indicated with an unchecked warning. Later, during runtime heap pollution will often cause a ClassCastException.Heap pollution in Java can occur when type arguments and variables are not reified at run-time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 \u00d7 3. The usual notation for the square of a number n is not the product n \u00d7 n, but the equivalent exponentiation n2, usually pronounced as \"n squared\". The name square number comes from the name of the shape.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Almost all even positive numbers can be expressed as the sum of two primes. : 489 Almost all primes are isolated. Moreover, for every positive integer g, almost all primes have prime gaps of more than g both to their left and to their right; that is, there is no other prime between p \u2212 g and p + g.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of indivisible item assignment, when the utility functions of all agents are GS (and thus an equilibrium exists), it is possible to find a competitive equilibrium using an ascending auction. In an ascending auction, the auctioneer publishes a price vector, initially zero, and the buyers declare their favorite bundle under these prices. In case each item is desired by at most a single bidder, the items are divided and the auction is over.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Unix-world, there is commonly a special filesystem mounted at /proc. This filesystem is implemented within the kernel and publishes information about processes. For each process, there is a directory (named by the process ID), containing detailed information about the process: status, open files, memory maps, mounts, etc. /proc first appeared in Unix 8th Edition, and its functionality was greatly expanded in Plan 9 from Bell Labs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To this end the 56800 series added a complete MCU which created a single-chip \"DSPcontroller\" solution, while the opposite occurred in the 68456, a 68000 with a 56000 on it. A still quite prevalent model of the 56000 is the third generation 56300 family, starting with the 56301, which features several models with special applications hard- and firmware built-in, like PCI interface logic, CRC processors, or audio companders. Core clock frequencies ranged up to 250 MHz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The receiver un-does these transformations in reverse order: demodulation, trellis decoding, error detection and correction, decompression. Some communication systems omit one or more of these steps, or use techniques that combine several of these steps together. For example, a Morse code transmitter combines source coding, channel coding, and line coding into one step, typically followed by an amplitude modulation step. Barcodes, on the other hand, add a checksum digit during channel coding, then translate each digit into a barcode symbol during line coding, omitting modulation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The F1 score is the harmonic mean of the precision and recall. It thus symmetrically represents both precision and recall in one metric. The more generic F \u03b2 {\\displaystyle F_{\\beta }} score applies additional weights, valuing one of precision or recall more than the other. The highest possible value of an F-score is 1.0, indicating perfect precision and recall, and the lowest possible value is 0, if either precision or recall are zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an algebra such as ( R , + , \u22c5 ) {\\displaystyle (\\mathbb {R} ,+,\\cdot )} has multiplication \u22c5 {\\displaystyle \\cdot } whose associativity is well-defined on the nose. This means for any real numbers a , b , c \u2208 R {\\displaystyle a,b,c\\in \\mathbb {R} } we have a \u22c5 ( b \u22c5 c ) \u2212 ( a \u22c5 b ) \u22c5 c = 0 {\\displaystyle a\\cdot (b\\cdot c)-(a\\cdot b)\\cdot c=0} .But, there are algebras R {\\displaystyle R} which are not necessarily associative, meaning if a , b , c \u2208 R {\\displaystyle a,b,c\\in R} then a \u22c5 ( b \u22c5 c ) \u2212 ( a \u22c5 b ) \u22c5 c \u2260 0 {\\displaystyle a\\cdot (b\\cdot c)-(a\\cdot b)\\cdot c\\neq 0} in general. There is a notion of algebras, called A \u221e {\\displaystyle A_{\\infty }} -algebras, which still have a property on the multiplication which still acts like the first relation, meaning associativity holds, but only holds up to a homotopy, which is a way to say after an operation \"compressing\" the information in the algebra, the multiplication is associative. This means although we get something which looks like the second equation, the one of inequality, we actually get equality after \"compressing\" the information in the algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Proth's theorem is a primality test for Proth numbers. It states that if p is a Proth number, of the form k2n + 1 with k odd and k < 2n, and if there exists an integer a for which a p \u2212 1 2 \u2261 \u2212 1 ( mod p ) , {\\displaystyle a^{\\frac {p-1}{2}}\\equiv -1{\\pmod {p}},} then p is prime. In this case p is called a Proth prime. This is a practical test because if p is prime, any chosen a has about a 50 percent chance of working, furthermore, since the calculation is mod p, only values of a smaller than p have to be taken into consideration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel to the development of L4Ka::Hazelnut, in 1998 the Operating Systems Group TUD:OS of the TU Dresden started to develop their own C++ implementation of the L4 kernel interface, named L4/Fiasco. In contrast to L4Ka::Hazelnut, which allows no concurrency in the kernel, and its successor L4Ka::Pistachio, which allows interrupts in the kernel only at specific preemption points, L4/Fiasco was fully preemptible (with the exception of extremely short atomic operations) to achieve a low interrupt latency. This was considered necessary because L4/Fiasco is used as the basis of DROPS, a hard real-time computing capable operating system, also developed at the TU Dresden. However, the complexities of a fully preemptible design prompted later versions of Fiasco to return to the traditional L4 approach of running the kernel with interrupts disabled, except for a limited number of preemption points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In text-based electronic communication, the sign of the horns is represented with the \\../, \\m/ or |m| emoticon and sometimes with /../. The Unicode character U+1F918 \ud83e\udd18 SIGN OF THE HORNS was introduced in Unicode 8.0 as an emoji, on June 17, 2015.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of sieve theory the Selberg sieve is of combinatorial type: that is, derives from a careful use of the inclusion\u2013exclusion principle. Selberg replaced the values of the M\u00f6bius function which arise in this by a system of weights which are then optimised to fit the given problem. The result gives an upper bound for the size of the sifted set. Let A {\\displaystyle A} be a set of positive integers \u2264 x {\\displaystyle \\leq x} and let P {\\displaystyle P} be a set of primes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Modern power systems are designed to be resistant to this sort of cascading failure, but it may be unavoidable (see below). Moreover, since there is no short-term economic benefit to preventing rare large-scale failures, researchers have expressed concern that there is a tendency to erode the resilience of the network over time, which is only corrected after a major failure occurs. In a 2003 publication, Carreras and co-authors claimed that reducing the likelihood of small outages only increases the likelihood of larger ones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra and worked on \"the beginnings of the link between algebra and geometry\".He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Suppose the documentation associated with these types specifies that type Stack's methods shall behave as expected for stacks (i.e. they shall exhibit LIFO behavior), and that type Queue's methods shall behave as expected for queues (i.e. they shall exhibit FIFO behavior). Suppose, now, that type Stack was declared as a subclass of type Queue. Most programming language compilers ignore documentation and perform only the checks that are necessary to preserve type safety.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, a test suite, less commonly known as a validation suite, is a collection of test cases that are intended to be used to test a software program to show that it has some specified set of behaviors. A test suite often contains detailed instructions or goals for each collection of test cases and information on the system configuration to be used during testing. A group of test cases may also contain prerequisite states or steps, and descriptions of the following tests. Collections of test cases are sometimes termed a test plan, a test script, or even a test scenario.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They can also be described as subsets of a set of 24 elements, where addition is defined as taking the symmetric difference of the subsets. In the extended binary Golay code, all code words have Hamming weights of 0, 8, 12, 16, or 24. Code words of weight 8 are called octads and code words of weight 12 are called dodecads.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predictive analytics, a table of confusion (sometimes also called a confusion matrix) is a table with two rows and two columns that reports the number of true positives, false negatives, false positives, and true negatives. This allows more detailed analysis than simply observing the proportion of correct classifications (accuracy). Accuracy will yield misleading results if the data set is unbalanced; that is, when the numbers of observations in different classes vary greatly. For example, if there were 95 cancer samples and only 5 non-cancer samples in the data, a particular classifier might classify all the observations as having cancer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In structural typing, an element is considered to be compatible with another if, for each feature within the second element's type, a corresponding and identical feature exists in the first element's type. Some languages may differ on the details, such as whether the features must match in name. This definition is not symmetric, and includes subtype compatibility. Two types are considered to be identical if each is compatible with the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Again in contrast to linear regression, there may be many local minima of the function to be optimized and even the global minimum may produce a biased estimate. In practice, estimated values of the parameters are used, in conjunction with the optimization algorithm, to attempt to find the global minimum of a sum of squares. For details concerning nonlinear data modeling see least squares and non-linear least squares.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In measure theory, given a measurable space ( X , \u03a3 ) {\\displaystyle (X,\\Sigma )} and a signed measure \u03bc {\\displaystyle \\mu } on it, a set A \u2208 \u03a3 {\\displaystyle A\\in \\Sigma } is called a positive set for \u03bc {\\displaystyle \\mu } if every \u03a3 {\\displaystyle \\Sigma } -measurable subset of A {\\displaystyle A} has nonnegative measure; that is, for every E \u2286 A {\\displaystyle E\\subseteq A} that satisfies E \u2208 \u03a3 , {\\displaystyle E\\in \\Sigma ,} \u03bc ( E ) \u2265 0 {\\displaystyle \\mu (E)\\geq 0} holds. Similarly, a set A \u2208 \u03a3 {\\displaystyle A\\in \\Sigma } is called a negative set for \u03bc {\\displaystyle \\mu } if for every subset E \u2286 A {\\displaystyle E\\subseteq A} satisfying E \u2208 \u03a3 , {\\displaystyle E\\in \\Sigma ,} \u03bc ( E ) \u2264 0 {\\displaystyle \\mu (E)\\leq 0} holds. Intuitively, a measurable set A {\\displaystyle A} is positive (resp. negative) for \u03bc {\\displaystyle \\mu } if \u03bc {\\displaystyle \\mu } is nonnegative (resp.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software testing, error guessing is a test method in which test cases used to find bugs in programs are established based on experience in prior testing. The scope of test cases usually rely on the software tester involved, who uses experience and intuition to determine what situations commonly cause software failure, or may cause errors to appear. Typical errors include divide by zero, null pointers, or invalid parameters.Error guessing has no explicit rules for testing; test cases can be designed depending on the situation, either drawing from functional documents or when an unexpected/undocumented error is found while testing operations. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization, a gradient method is an algorithm to solve problems of the form min x \u2208 R n f ( x ) {\\displaystyle \\min _{x\\in \\mathbb {R} ^{n}}\\;f(x)} with the search directions defined by the gradient of the function at the current point. Examples of gradient methods are the gradient descent and the conjugate gradient.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. The estimator has a breakdown point of 50%. Although it is equivariant under scaling, or under linear transformations of either its explanatory variable or its response variable, it is not under affine transformations that combine both variables. It can be calculated in O ( n 2 ) {\\displaystyle O(n^{2})} time by brute force, in O ( n log 2 \u2061 n ) {\\displaystyle O(n\\log ^{2}n)} time using more sophisticated techniques, or in O ( n log \u2061 n ) {\\displaystyle O(n\\log n)} randomized expected time. It may also be calculated using an on-line algorithm with O ( n ) {\\displaystyle O(n)} update time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852. The four color theorem was ultimately proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In focused calculi, it is possible to define positive connectives by giving only their introduction rules, with the shape of the elimination rules being forced by this choice. (Symmetrically, negative connectives can be defined in focused calculi by giving only the elimination rules, with the introduction rules forced by this choice.) The second view, which might be termed the computational or Brouwer\u2013Heyting\u2013Kolmogorov interpretation of propositions, takes the view that we fix a computational system up front, and then give a realizability interpretation of propositions to give them constructive content.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Next, Kleene proceeds to present \"Turing's thesis\", where results are shown to be uncomputable, using his simplified derivation of a Turing machine based on the work of Emil Post. Both theses are proven equivalent by use of \"Theorem XXX\". Thesis I. Every effectively calculable function (effectively decidable predicate) is general recursive. Theorem XXX: The following classes of partial functions are coextensive, i.e. have the same members: (a) the partial recursive functions, (b) the computable functions ... Turing's thesis: Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i.e. by one of his machines, is equivalent to Church's thesis by Theorem XXX. Kleene, finally, uses for the first time the term the \"Church-Turing thesis\" in a section in which he helps to give clarifications to concepts in Alan Turing's paper \"The Word Problem in Semi-Groups with Cancellation\", as demanded in a critique from William Boone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2-ary case, there can be zero or one identity elements: the empty set is a 2-ary group, since the empty set is both a semigroup and a quasigroup, and every inhabited 2-ary group is a group. In n-ary groups for n \u2265 3 there can be zero, one, or many identity elements. An n-ary groupoid (G, f) with f = (x1 \u25e6 x2 \u25e6 \u22ef \u25e6 xn), where (G, \u25e6) is a group is called reducible or derived from the group (G, \u25e6). In 1928 D\u00f6rnte published the first main results: An n-ary groupoid which is reducible is an n-ary group, however for all n > 2 there exist inhabited n-ary groups which are not reducible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A {\\displaystyle A} , the set of all subsets of A , {\\displaystyle A,} the power set of A , {\\displaystyle A,} has a strictly greater cardinality than A {\\displaystyle A} itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n {\\displaystyle n} elements has a total of 2 n {\\displaystyle 2^{n}} subsets, and the theorem holds because 2 n > n {\\displaystyle 2^{n}>n} for all non-negative integers. Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It follows that, as with LFSRs and linear complexity, any stream cipher whose N-adic complexity is low should not be used for cryptography. FCSRs and LFSRs are special cases of a very general algebraic construction of sequence generators called Algebraic Feedback Shift Registers (AFSRs) in which the integers are replaced by an arbitrary ring R and N is replaced by an arbitrary non-unit in R. A general reference on the subject of LFSRs, FCSRs, and AFSRs is the book. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the books were most popular as A5-sized paperback volumes, and were usually between 150 and 200 pages long, divided into just under thirty chapters. The front covers featured images of the narrating Animorph undergoing the various stages of one of the morphs from the story, with a few exceptions (noted in each book's article). Behind the morphing character were images of clouds and skies, which became more colorful and elaborate as the series progressed. All the covers of the regular series books had a small cutout over part of the full morph's anatomy, revealing a computer-generated illustration on the first page, which was printed on glossy paper.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be Euclidean spaces or more general parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In message queueing a dead letter queue (DLQ) is a service implementation to store messages that the messaging system cannot or should not deliver. Although implementation-specific, messages can be routed to the DLQ for the following reasons: The message is sent to a queue that does not exist. The maximum queue length is exceeded. The message exceeds the size limit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "CDMA, by comparison, supports \"soft hand-off\" which allows a mobile phone to be in communication with up to 6 base stations simultaneously, a type of \"same-frequency handover\". The incoming packets are compared for quality, and the best one is selected. CDMA's \"cell breathing\" characteristic, where a terminal on the boundary of two congested cells will be unable to receive a clear signal, can often negate this advantage during peak periods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other applications are in statistics, and another is in elliptic geometry.For n > 1, there are two kinds of conference matrix. Let us normalize C by, first (if the more general definition is used), rearranging the rows so that all the zeros are on the diagonal, and then negating any row or column whose first entry is negative. (These operations do not change whether a matrix is a conference matrix.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "has been applied as the formal type parameter of a method, no actual parameters can be passed to it. However, objects of the unknown type can be read from the generic object and assigned to a variable of a supertype of the upperbound. Sample code for the Generic class: Sample code that uses the Generic class:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The groups of each of these 8 types were classified by various authors. They consist mainly of groups of Lie type with all roots of the same length over the field with 2 elements, but also include many exceptional cases, including the majority of the sporadic simple groups. Smith (1980) gave a survey of this work. Smith (1979, p.279) gives a table of simple groups containing a large extraspecial 2-group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a basis of a matroid is a maximal independent set of the matroid\u2014that is, an independent set that is not contained in any other independent set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines, although it may be proved without these theorems. The inequality can be viewed intuitively in either R2 or R3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, the term cyclic prefix refers to the prefixing of a symbol with a repetition of the end. The receiver is typically configured to discard the cyclic prefix samples, but the cyclic prefix serves two purposes: It provides a guard interval to eliminate intersymbol interference from the previous symbol. It repeats the end of the symbol so the linear convolution of a frequency-selective multipath channel can be modeled as circular convolution, which in turn may transform to the frequency domain via a discrete Fourier transform. This approach accommodates simple frequency domain processing, such as channel estimation and equalization.For the cyclic prefix to serve its objectives, it must have a length at least equal to the length of the multipath channel. The concept of a cyclic prefix is traditionally associated with OFDM systems, however the cyclic prefix is now also used in single carrier systems to improve the robustness to multipath propagation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is used in polynomial factorization, a problem for which all known efficient algorithms use modular arithmetic. It is used by the most efficient implementations of polynomial greatest common divisor, exact linear algebra and Gr\u00f6bner basis algorithms over the integers and the rational numbers. As posted on Fidonet in the 1980s and archived at Rosetta Code, modular arithmetic was used to disprove Euler's sum of powers conjecture on a Sinclair QL microcomputer using just one-fourth of the integer precision used by a CDC 6600 supercomputer to disprove it two decades earlier via a brute force search.In computer science, modular arithmetic is often applied in bitwise operations and other operations involving fixed-width, cyclic data structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Data collection with proton precession instruments was slow, making high sample density surveys impracticable. Data were manually recorded and plotted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many linguistic anthropologists have come to understand that language and culture are not separate entities, but are in fact processes that work hand in hand. These contextualization cues are culturally specific and usually unconscious. Linguistic anthropology helps make explicit the implicit features of culture that can often be unknown to the speaker.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In standard linear regression models one observes data { y i , x i j } i = 1 , \u2026 , n , j = 2 , \u2026 , k {\\displaystyle \\{y_{i},x_{ij}\\}_{i=1,\\dots ,n,j=2,\\dots ,k}} on n statistical units. The response values are placed in a vector y = ( y 1 , \u2026 , y n ) T {\\displaystyle \\mathbf {y} =\\left(y_{1},\\dots ,y_{n}\\right)^{\\mathsf {T}}} , and the predictor values are placed in the design matrix X = ( x 1 T , \u2026 , x n T ) T {\\displaystyle \\mathbf {X} =\\left(\\mathbf {x} _{1}^{\\mathsf {T}},\\dots ,\\mathbf {x} _{n}^{\\mathsf {T}}\\right)^{\\mathsf {T}}} , where x i = ( 1 , x i 2 , \u2026 , x i k ) {\\displaystyle \\mathbf {x} _{i}=\\left(1,x_{i2},\\dots ,x_{ik}\\right)} is a vector of the k predictor variables (including a constant) for the ith unit. The model forces the conditional mean of y {\\displaystyle \\mathbf {y} } given X {\\displaystyle \\mathbf {X} } to be a linear function of X {\\displaystyle \\mathbf {X} } and assumes the conditional variance of the error term given X {\\displaystyle \\mathbf {X} } is a known nonsingular covariance matrix \u03a9 {\\displaystyle \\mathbf {\\Omega } } . This is usually written as y = X \u03b2 + \u03b5 , E \u2061  = 0 , Cov \u2061  = \u03a9 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The trainer gets active when the object has been allocated and deactivates itself again when the object is freed. Modern operating systems also come with position-independent executables (PIE) for security. Together with ASLR, the binaries are loaded to a different virtual memory address each code execution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 2009, Gu et al. presented a class of infinite physical systems that exhibits non-computable macroscopic properties. More precisely, if one could compute certain macroscopic properties of these systems from the microscopic description of these systems, then one would be able to solve computational problems known to be undecidable in computer science. These results concern infinite systems, finite systems being considered computable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which the elements are partitioned into different categories. For each category, there is a capacity constraint - a maximum number of allowed elements from this category. The independent sets of a partition matroid are exactly the sets in which, for each category, the number of elements from this category is at most the category capacity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a multi-band device (including (2) dual-band, (3) tri-band, (4) quad-band and (5) penta-band devices) is a communication device (especially a mobile phone) that supports multiple radio frequency bands. All devices which have more than one channel use multiple frequencies; a band however is a group of frequencies containing many channels. Multiple bands in mobile devices support roaming between different regions where different standards are used for mobile telephone services. Where the bands are widely separated in frequency, parallel transmit and receive signal path circuits must be provided, which increases the cost, complexity and power demand of multi-band devices.The term quad-band describes a device that supports four frequency bands: the 850 and 1900 MHz bands, which are used in the Americas, and 900 / 1800, which are used in most other parts of the world.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hartogs\u2013Rosenthal theorem is a classical result in complex analysis on the uniform approximation of continuous functions on compact subsets of the complex plane by rational functions. The theorem was proved in 1931 by the German mathematicians Friedrich Hartogs and Arthur Rosenthal and has been widely applied, particularly in operator theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and combinatorial mathematics, group testing is any procedure that breaks up the task of identifying certain objects into tests on groups of items, rather than on individual ones. First studied by Robert Dorfman in 1943, group testing is a relatively new field of applied mathematics that can be applied to a wide range of practical applications and is an active area of research today. A familiar example of group testing involves a string of light bulbs connected in series, where exactly one of the bulbs is known to be broken. The objective is to find the broken bulb using the smallest number of tests (where a test is when some of the bulbs are connected to a power supply).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", 1123456789, 10123456789, ... (sequence A134596 in the OEIS)Primeval numbers can be composite. The first is 1037 = 17\u00d761. A Primeval prime is a primeval number which is also a prime number: 2, 13, 37, 107, 113, 137, 1013, 1237, 1367, 10079, 10139, 12379, 13679, 100279, 100379, 123479, 1001237, 1002347, 1003679, 1012379, ... (sequence A119535 in the OEIS)The following table shows the first seven primeval numbers with the obtainable primes and the number of them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion, retrogradation, circular permutation (also called rotation), or multiplicative operations (such as the cycle of fourths and cycle of fifths transforms). These may produce reorderings of the members of the set, or may simply map the set onto itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Eventually, one ends up with a day-count to which one applies modulo 7 to determine the day of the week of the date.Some methods do all the additions first and then cast out sevens, whereas others cast them out at each step, as in Lewis Carroll's method. Either way is quite viable: the former is easier for calculators and computer programs, the latter for mental calculation (it is quite possible to do all the calculations in one's head with a little practice). None of the methods given here perform range checks, so unreasonable dates will produce erroneous results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If we make a change of variables, w k = v k + 1 \u2212 v k , k = 0 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Requires constraint states that if cause 1 is true, then cause 2 must be true, and it is impossible for 1 to be true and 2 to be false. For effects, valid constraint symbol is M (Mask). The mask constraint states that if effect 1 is true then effect 2 is false.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an elliptic divisibility sequence (EDS) is a sequence of integers satisfying a nonlinear recursion relation arising from division polynomials on elliptic curves. EDS were first defined, and their arithmetic properties studied, by Morgan Ward in the 1940s. They attracted only sporadic attention until around 2000, when EDS were taken up as a class of nonlinear recurrences that are more amenable to analysis than most such sequences. This tractability is due primarily to the close connection between EDS and elliptic curves. In addition to the intrinsic interest that EDS have within number theory, EDS have applications to other areas of mathematics including logic and cryptography.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages with a built-in Boolean data type, such as Pascal and Java, the comparison operators such as > and \u2260 are usually defined to return a Boolean value. Conditional and iterative commands may be defined to test Boolean-valued expressions. Languages with no explicit Boolean data type, like C90 and Lisp, may still represent truth values by some other data type. Common Lisp uses an empty list for false, and any other value for true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus \u00ac is a dual automorphism of (A, \u2228, \u2227, 0, 1). If the lattice is defined in terms of the order instead, i.e. (A, \u2264) is a bounded partial order with a least upper bound and greatest lower bound for every pair of elements, and the meet and join operations so defined satisfy the distributive law, then the complementation can also be defined as an involutive anti-automorphism, that is, a structure A = (A, \u2264, \u00ac) such that: (A, \u2264) is a bounded distributive lattice, and \u00ac\u00acx = x, and x \u2264 y \u2192 \u00acy \u2264 \u00acx.De Morgan algebras were introduced by Grigore Moisil around 1935, although without the restriction of having a 0 and a 1. They were then variously called quasi-boolean algebras in the Polish school, e.g. by Rasiowa and also distributive i-lattices by J. A. Kalman.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A formal proof or derivation is a finite sequence of well-formed formulas (which may be interpreted as sentences, or propositions) each of which is an axiom or follows from the preceding formulas in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system. Formal proofs are useful because their theorems can be interpreted as true propositions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They have introduced finite and infinite mixture models of inverted Dirichlet distributions using the Newton\u2013Raphson technique to estimate the parameters and the Dirichlet process to model infinite mixtures. T. Bdiri et al. have also used the inverted Dirichlet distribution to propose an approach to generate Support Vector Machine kernels basing on Bayesian inference and another approach to establish hierarchical clustering. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most experiments, measurements are repeatedly made at the same two locations. A local hidden variable theory could exploit the memory of past measurement settings and outcomes in order to increase the violation of a Bell inequality. Moreover, physical parameters might be varying in time. It has been shown that, provided each new pair of measurements is done with a new random pair of measurement settings, that neither memory nor time inhomogeneity have a serious effect on the experiment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization problems in applied mathematics, the duality gap is the difference between the primal and dual solutions. If d \u2217 {\\displaystyle d^{*}} is the optimal dual value and p \u2217 {\\displaystyle p^{*}} is the optimal primal value then the duality gap is equal to p \u2217 \u2212 d \u2217 {\\displaystyle p^{*}-d^{*}} . This value is always greater than or equal to 0 (for minimization problems). The duality gap is zero if and only if strong duality holds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "7. Examining how likely it is that the concept applies, statistically or intuitively (probability theory).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The software can be more usable and has a better chance to focus on business problems that are critical to end users rather than technical problems of interest to developers. However, this excludes other categories of what are usually known as Non-functional requirements (AKA constraints or quality attributes) including security and portability. Risk control.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical classification, the rule which assigns a class to a new data-item can be considered to be a special type of estimator. A number of invariance-type considerations can be brought to bear in formulating prior knowledge for pattern recognition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of nonmonotonic logics, a group of logics related to artificial intelligence, he focused on investigations of Reiter's default logic, and autoepistemic logic of R. Moore. These investigations led to a form of logic programming called answer set programming a computational knowledge representation formalism, studied both in Europe and in the United States. Together with Miros\u0142aw Truszczynski, he proved that the problem of existence of stable models of logic programs is NP-complete. In a stronger formalism admitting function symbols, along with Nerode and Remmel he showed that the analogous problem is \u03a311-complete.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the conventional sequential BFS algorithm, two data structures are created to store the frontier and the next frontier. The frontier contains all vertices that have the same distance (also called \"level\") from the source vertex, these vertices need to be explored in BFS. Every neighbor of these vertices will be checked, some of these neighbors which are not explored yet will be discovered and put into the next frontier. At the beginning of the BFS algorithm, a given source vertex s is the only vertex in the frontier.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example test case graph, all test cases and their isolated conditions are marked by colors, and the remaining paths are implicitly passed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Personal information must be handled properly. Information must be kept accurate and relevant, used only for the stated purposes, and retained only for as long as reasonably needed. The law required entities to be active in ensuring that unauthorized parties do not have access to their customers' information. Personal information must be disposed in way that unauthorized third parties could not access the discarded data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An eight step policy cycle is developed in detail in The Australian Policy Handbook by Peter Bridgman and Glyn Davis: (now with Catherine Althaus in its 4th and 5th editions) Issue identification Policy analysis Consultation (which permeates the entire process) Policy instrument development Building coordination and coalitions Program Design: Decision making Policy Implementation Policy EvaluationThe Althaus, Bridgman & Davis model is heuristic and iterative. It is intentionally normative and not meant to be diagnostic or predictive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: \"All dogs are mammals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The signature of the form determines the group up to isomorphism; interchanging p with q amounts to replacing the metric by its negative, and so gives the same group. If either p or q equals zero, then the group is isomorphic to the ordinary orthogonal group O(n). We assume in what follows that both p and q are positive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Homomorphic encryption is a form of encryption that allows computation on ciphertext, such as arithmetic on numeric values stored in an encrypted database. RLWE is more properly called learning with errors over rings and is simply the larger learning with errors (LWE) problem specialized to polynomial rings over finite fields. Because of the presumed difficulty of solving the RLWE problem even on a quantum computer, RLWE based cryptography may form the fundamental base for public-key cryptography in the future just as the integer factorization and discrete logarithm problem have served as the base for public key cryptography since the early 1980s. An important feature of basing cryptography on the ring learning with errors problem is the fact that the solution to the RLWE problem can be used to solve a version of the shortest vector problem (SVP) in a lattice (a polynomial-time reduction from this SVP problem to the RLWE problem has been presented).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is usually least stiff in the radial direction (between the growth rings), and is intermediate in the circumferential direction. This anisotropy was provided by evolution, as it best enables the tree to remain upright.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In protected mode with paging enabled (bit 31, PG, of control register CR0 is set), but without PAE, x86 processors use a two-level page translation scheme. Control register CR3 holds the page-aligned physical address of a single 4 KB long page directory. This is divided into 1024 four-byte page directory entries that in turn, if valid, hold the page-aligned physical addresses of page tables, each 4 KB in size. These similarly consist of 1024 four-byte page table entries which, if valid, hold the page-aligned physical addresses of 4 KB long pages of physical memory (RAM).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These human computers worked with electrical engineers to help figure out how to boost signals with vacuum tube amplifiers. One of the computers, Clara Froelich, was eventually moved along with the other computers to their own division where they worked with a mathematician, Thornton Fry, to create new computational methods. Froelich studied IBM tabulating equipment and desk calculating machines to see if she could adapt the machine method to calculations.Edith Clarke was the first woman to earn a degree in electrical engineering and who worked as the first professionally employed electrical engineer in the United States.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory and related branches of mathematics, a family (or collection) can mean any of set indexed set multiset classdepending upon the context. A collection F {\\displaystyle F} of subsets of a given set S {\\displaystyle S} is called a family of subsets of S {\\displaystyle S} , or a family of sets over S . {\\displaystyle S.} More generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "And these will always start as there blanks with the scanned square on the left: i.e. bbb. With two symbols 1, 0 and blank we can have 27 distinct configurations: bbb, bb0, bb1, b0b, b00, b01, b1b, b10, b11, 0bb, 0b0, 0b1, 00b, 000, 001, 01b, 010, 011, 1bb, 1b0, 1b1, 10b, 100, 101, 11b, 110, 111 We must be careful here, because it is quite possible that an algorithm will (temporarily) leave blanks in between figures, then come back and fill something in. More likely, an algorithm may do this intentionally.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the smallest item size is eB (for some fraction e in (0,1)), then there can be up to 1/e items in each bin, so the number of configurations C ~ S1/e, which can be very large if e is small (if e is considered a constant, then the integer LP can be solved by exhaustive search: there are at most S1/e configurations, and for each configuration there are at most n possible values, so there are at most n S 1 / e {\\displaystyle n^{S^{1/e}}} combinations to check. For each combination, we have to check S constraints, so the run-time is S \u22c5 n S 1 / e {\\displaystyle S\\cdot n^{S^{1/e}}} , which is polynomial in n when S, e are constant).However, this ILP serves as a basis for several approximation algorithms. The main idea of these algorithms is to reduce the original instance into a new instance in which S is small and e is large, so C is relatively small. Then, the ILP can be solved either by complete search (if S, C are sufficiently small), or by relaxing it into a fractional LP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These three operations are repeated until no new states can be added to the set. The set is generally implemented as a queue of states to process, with the operation to be performed depending on what kind of state it is. The algorithm accepts if (X \u2192 \u03b3 \u2022, 0) ends up in S(n), where (X \u2192 \u03b3) is the top level-rule and n the input length, otherwise it rejects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, unlike Conway's Life, cells that have become dead never become alive again. It can also be viewed as an epidemic model in which inactive cells are considered as infected and active cells with too many infected neighbors become infected themselves. The smallest threshold that allows some cells of an initial cluster to survive is called the degeneracy of its adjacency graph, and the remnant of a cluster that survives with threshold k is called the k-core of this graph.One application of bootstrap percolation arises in the study of fault tolerance for distributed computing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social psychology, ambiguity is a factor used in determining peoples' responses to various situations. High levels of ambiguity in an emergency (e.g. an unconscious man lying on a park bench) make witnesses less likely to offer any sort of assistance, due to the fear that they may have misinterpreted the situation and acted unnecessarily. Alternately, non-ambiguous emergencies (e.g. an injured person verbally asking for help) elicit more consistent intervention and assistance. With regard to the bystander effect, studies have shown that emergencies deemed ambiguous trigger the appearance of the classic bystander effect (wherein more witnesses decrease the likelihood of any of them helping) far more than non-ambiguous emergencies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity for factoring an integer n (consisting of \u230alog2 n\u230b + 1 bits) is of the form exp \u2061 ( ( ( 64 / 9 ) 1 / 3 + o ( 1 ) ) ( log \u2061 n ) 1 / 3 ( log \u2061 log \u2061 n ) 2 / 3 ) = L n  {\\displaystyle \\exp \\left(\\left((64/9)^{1/3}+o(1)\\right)\\left(\\log n\\right)^{1/3}\\left(\\log \\log n\\right)^{2/3}\\right)=L_{n}\\left} in O and L-notations. It is a generalization of the special number field sieve: while the latter can only factor numbers of a certain special form, the general number field sieve can factor any number apart from prime powers (which are trivial to factor by taking roots).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Power ISA v3.0 allows 64 bits for an effective address, mapped to a segmented address with between 65 and 78 bits allowed, for virtual memory, and, for any given processor, up to 60 bits for physical memory.The Oracle SPARC Architecture 2015 allows 64 bits for virtual memory and, for any given processor, between 40 and 56 bits for physical memory.The ARM AArch64 Virtual Memory System Architecture allows 48 bits for virtual memory and, for any given processor, from 32 to 48 bits for physical memory.The DEC Alpha specification requires minimum of 43 bits of virtual memory address space (8 TiB) to be supported, and hardware need to check and trap if the remaining unsupported bits are zero (to support compatibility on future processors). Alpha 21064 supported 43 bits of virtual memory address space (8 TiB) and 34 bits of physical memory address space (16 GiB). Alpha 21164 supported 43 bits of virtual memory address space (8 TiB) and 40 bits of physical memory address space (1 TiB). Alpha 21264 supported user-configurable 43 or 48 bits of virtual memory address space (8 TiB or 256 TiB) and 44 bits of physical memory address space (16 TiB).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, the intersection of two sets A {\\displaystyle A} and B , {\\displaystyle B,} denoted by A \u2229 B , {\\displaystyle A\\cap B,} is the set containing all elements of A {\\displaystyle A} that also belong to B {\\displaystyle B} or equivalently, all elements of B {\\displaystyle B} that also belong to A . {\\displaystyle A.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, semantic role labeling (also called shallow semantic parsing or slot-filling) is the process that assigns labels to words or phrases in a sentence that indicates their semantic role in the sentence, such as that of an agent, goal, or result. It serves to find the meaning of the sentence. To do this, it detects the arguments associated with the predicate or verb of a sentence and how they are classified into their specific roles. A common example is the sentence \"Mary sold the book to John.\" The agent is \"Mary,\" the predicate is \"sold\" (or rather, \"to sell,\") the theme is \"the book,\" and the recipient is \"John.\" Another example is how \"the book belongs to me\" would need two labels such as \"possessed\" and \"possessor\" and \"the book was sold to John\" would need two other labels such as theme and recipient, despite these two clauses being similar to \"subject\" and \"object\" functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Linguistic signs may also derive nonreferential meaning from indexicality, for example when features of a speaker's register indexically signal their social class. Nonlinguistic signs may also display indexicality: for example, a pointing index finger may index (without referring to) some object in the direction of the line implied by the orientation of the finger, and smoke may index the presence of a fire. In linguistics and philosophy of language, the study of indexicality tends to focus specifically on deixis, while in semiotics and anthropology equal attention is generally given to nonreferential indexicality, including altogether nonlinguistic indexicality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the PIC instruction set, the REPEAT and DO instructions implement zero-overhead loops. REPEAT only repeats a single instruction, while DO repeats a specified number of following instructions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical computer science, a pattern is an unavoidable pattern if it is unavoidable on any finite alphabet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Beginning in 1969 the U.S. Army Mobility Equipment Research and Development Command (MERADCOM) reverse-engineered the Russian PMP design to develop the improved float bridge (IFB), later known as the standard ribbon bridge (SRB). The IFB/SRB was type classified in 1972 and first deployed in service in 1976.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2358, 12358, 23458, and 123458 are the patterns related to Braille pattern dots-1246, since the two additional dots of kantenji patterns 01246, 12467, and 012467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, it does compile in C/C++ and some other languages, yielding surprising result (as true would be represented by the number 1 here). It is possible to give the expression x < y < z its familiar mathematical meaning, and some programming languages such as Python and Raku do that. Others, such as C# and Java, do not, partly because it would differ from the way most other infix operators work in C-like languages. The D programming language does not do that since it maintains some compatibility with C, and \"Allowing C expressions but with subtly different semantics (albeit arguably in the right direction) would add more confusion than convenience\".Some languages, like Common Lisp, use multiple argument predicates for this. In Lisp (<= 1 x 10) is true when x is between 1 and 10.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, a pointer can reference another pointer, requiring multiple dereference operations to get to the original value. While each level of indirection may add a performance cost, it is sometimes necessary in order to provide correct behavior for complex data structures. For example, in C it is typical to define a linked list in terms of an element that contains a pointer to the next element of the list: This implementation uses a pointer to the first element in the list as a surrogate for the entire list. If a new value is added to the beginning of the list, head has to be changed to point to the new element. Since C arguments are always passed by value, using double indirection allows the insertion to be implemented correctly, and has the desirable side-effect of eliminating special case code to deal with insertions at the front of the list: In this case, if the value of item is less than that of head, the caller's head is properly updated to the address of the new item. A basic example is in the argv argument to the main function in C (and C++), which is given in the prototype as char **argv\u2014this is because the variable argv itself is a pointer to an array of strings (an array of arrays), so *argv is a pointer to the 0th string (by convention the name of the program), and **argv is the 0th character of the 0th string.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Russian \u043d\u043e\u0441 \"nose\" (unpalatalized /n/)\u043d\u0451\u0441 \"(he) carried\" (palatalized /n\u02b2/)Irish b\u00f3 \"cow\" (velarized b)beo \"alive\" (palatalized b)Some palatalized phonemes undergo change beyond phonetic palatalization. For instance, the unpalatalized sibilant (Irish /s\u02e0/, Scottish /s\u032a/) has a palatalized counterpart that is actually postalveolar , not phonetically palatalized , and the velar fricative /x/ in both languages has a palatalized counterpart that is actually palatal  rather than palatalized velar . These shifts in primary place of articulation are examples of the sound change of palatalization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signalling models, one party chooses how and whether or not to present information about itself to another party to reduce the information asymmetry between them. In signaling models, the signaling party agent and the receiving party principal have access to different information. The challenge for the receiving party is to decipher the credibility of the signaling party so as to assess their capabilities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Post-Soviet states DD.MM.YYYY format is used with dot as a separator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Classic Mac OS, Multiprocessing Services is not the only threading mechanism; cooperatively scheduled threads can be created with the Thread Manager. While applications using Multiprocessing Services have their threads preemptively scheduled, the application as a whole is still cooperatively scheduled with other running applications. Non-Multiprocessing Services tasks remain scheduled on a single processor, and tasks using the Macintosh Toolbox cannot be preemptively scheduled.When a process uses Multiprocessing Services, in addition to the preemptive tasks it creates, an additional task exists, deth, which waits for other tasks created by the process to terminate and cleans up their resources when they do.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the matching distance is a metric on the space of size functions. The core of the definition of matching distance is the observation that the information contained in a size function can be combinatorially stored in a formal series of lines and points of the plane, called respectively cornerlines and cornerpoints. Given two size functions \u2113 1 {\\displaystyle \\ell _{1}} and \u2113 2 {\\displaystyle \\ell _{2}} , let C 1 {\\displaystyle C_{1}} (resp. C 2 {\\displaystyle C_{2}} ) be the multiset of all cornerpoints and cornerlines for \u2113 1 {\\displaystyle \\ell _{1}} (resp.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Suppose that when the screening test is applied to a person not having the disease, there is a 1% chance of getting a false positive result (and hence 99% chance of getting a true negative result, a number known as the specificity of the test), i.e. P ( positive | well ) = 1 % , and P ( negative | well ) = 99 % . {\\displaystyle P({\\text{positive}}|{\\text{well}})=1\\%,{\\text{ and }}P({\\text{negative}}|{\\text{well}})=99\\%.} Finally, suppose that when the test is applied to a person having the disease, there is a 1% chance of a false negative result (and 99% chance of getting a true positive result, known as the sensitivity of the test), i.e. P ( negative | ill ) = 1 % and P ( positive | ill ) = 99 % . {\\displaystyle P({\\text{negative}}|{\\text{ill}})=1\\%{\\text{ and }}P({\\text{positive}}|{\\text{ill}})=99\\%.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an E n {\\displaystyle {\\mathcal {E}}_{n}} -algebra in a symmetric monoidal infinity category C consists of the following data: An object A ( U ) {\\displaystyle A(U)} for any open subset U of Rn homeomorphic to an n-disk. A multiplication map: \u03bc: A ( U 1 ) \u2297 \u22ef \u2297 A ( U m ) \u2192 A ( V ) {\\displaystyle \\mu :A(U_{1})\\otimes \\cdots \\otimes A(U_{m})\\to A(V)} for any disjoint open disks U j {\\displaystyle U_{j}} contained in some open disk Vsubject to the requirements that the multiplication maps are compatible with composition, and that \u03bc {\\displaystyle \\mu } is an equivalence if m = 1 {\\displaystyle m=1} . An equivalent definition is that A is an algebra in C over the little n-disks operad.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing fast modular multiplication. It was introduced in 1985 by the American mathematician Peter L. Montgomery.Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab using division by N and keeping only the remainder.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Prior to coding, the algorithm had been identified and understood. The flowchart represented a high level definition of the solution to be implemented on a machine. Although they were working only with numerical algorithms, they proposed a programming methodology which has since become standard practice in the computer programming field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to limit production cost, Busicom wanted to design a calculator engine that would be based on a few integrated circuits (ICs), containing some ROMs and shift registers and that could be adapted to a broad range of calculators by just changing the ROM IC chips. Busicom's engineers came up with a design that required 12 ICs: 263\u2013265 and asked Intel, a company founded one year earlier in 1968 for the purpose of making solid state random-access memory (RAM), to finalize and manufacture their calculator engine. People who were influential in convincing Busicom to switch to using microprocessors were Tadashi Sasaki and Robert Noyce.Intel's Ted Hoff was assigned to studying Busicom's design, and came up with a much more elegant, 4 ICs architecture centered on what was to become the 4004 microprocessor surrounded by a mixture of 3 different ICs containing ROM, shift registers, input/output ports and RAM\u2014Intel's first product (1969) was the 3101 Schottky TTL bipolar 64-bit SRAM.Busicom's management agreed to Hoff's new approach and the chips' implementation was led by Federico Faggin who had previously developed the Silicon Gate Technology at Fairchild Semiconductor. It was this technology that made possible the design of the microprocessor and the dynamic RAMs. The 4 ICs were delivered to Busicom in January 1971.In mid-1971 Busicom, which had exclusive right to the design and its components, asked Intel to lower their prices. Intel renegotiated their contract and Busicom gave up its exclusive rights to the chips.A few months later, on November 15, 1971, Intel announced the immediate availability of the first microprocessor chipset family, the MCS-4 micro computer set (all from the Busicom design) with an advertisement in Electronic News.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , n \u2212 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 357, 1357, 3457, and 13457 are the patterns related to Braille pattern dots-234, since the two additional dots of kantenji patterns 0234, 2347, and 02347 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The accuracy of flowmeters could be used in two different metering systems that ultimately have different calculated uncertainties due to other factors in the system that affect flow calculations. Uncertainty even includes such factors as the flow computer's A/D converter accuracy. The quest for accuracy in a custody transfer system requires meticulous attention to detail.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So if for some 1 \u2a7d i \u2a7d N , c i 1 \u2260 c i 2 {\\displaystyle 1\\leqslant i\\leqslant N,c_{i}^{1}\\neq c_{i}^{2}} and the code C i n i {\\displaystyle C_{in}^{i}} has distance \u2a7e H q \u2212 1 ( 1 2 \u2212 \u03b5 ) \u22c5 2 k , {\\displaystyle \\geqslant H_{q}^{-1}\\left({\\tfrac {1}{2}}-\\varepsilon \\right)\\cdot 2k,} then \u0394 ( C i n i ( c i 1 ) , C i n i ( c i 2 ) ) \u2a7e H q \u2212 1 ( 1 2 \u2212 \u03b5 ) \u22c5 2 k . {\\displaystyle \\Delta \\left(C_{in}^{i}\\left(c_{i}^{1}\\right),C_{in}^{i}\\left(c_{i}^{2}\\right)\\right)\\geqslant H_{q}^{-1}\\left({\\tfrac {1}{2}}-\\varepsilon \\right)\\cdot 2k.} Further, if we have T {\\displaystyle T} numbers 1 \u2a7d i \u2a7d N {\\displaystyle 1\\leqslant i\\leqslant N} such that c i 1 \u2260 c i 2 {\\displaystyle c_{i}^{1}\\neq c_{i}^{2}} and the code C i n i {\\displaystyle C_{in}^{i}} has distance \u2a7e H q \u2212 1 ( 1 2 \u2212 \u03b5 ) \u22c5 2 k , {\\displaystyle \\geqslant H_{q}^{-1}({\\tfrac {1}{2}}-\\varepsilon )\\cdot 2k,} then \u0394 ( C \u2217 ( m 1 ) , C \u2217 ( m 2 ) ) \u2a7e H q \u2212 1 ( 1 2 \u2212 \u03b5 ) \u22c5 2 k \u22c5 T .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Symbolically, if the cardinality of N {\\displaystyle \\mathbb {N} } is denoted as \u2135 0 {\\displaystyle \\aleph _{0}} , the cardinality of the continuum is This was proven by Georg Cantor in his uncountability proof of 1874, part of his groundbreaking study of different infinities. The inequality was later stated more simply in his diagonal argument in 1891. Cantor defined cardinality in terms of bijective functions: two sets have the same cardinality if, and only if, there exists a bijective function between them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern digital communications, Gray codes play an important role in error correction. For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point. This makes the transmission system less susceptible to noise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to understand ODS, it is necessary to understand the normal anatomy and defecation process.The pelvic floor (pelvic diaphragm) can be divided into 4 compartments: Anterior or urinary (bladder, bladder neck, and urethra), Middle or genital (vagina and uterus in women, prostate in men), Posterior (anus, anal canal, sigmoid, and rectum), and Peritoneal (endopelvic fascia and perineal membrane).Defecation is a complex physiologic process, involving interaction between neural processes, reflexes, colorectal contractility and the biomechanics of straining.When feces reach the rectum, the rectal walls become naturally distended, stimulating nerve receptors. Brain centres for defecation respond to this sensation and stimulate mass colonic movement in the colon and the rectum. These mass contractions move feces along the colon and into the rectum. Occasionally some straining helps, which normally transmits forces to the upper part of the rectum, and aids defecation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Stemming and lemmatization Different tokens might carry out similar information (e.g. tokenization and tokenizing). And we can avoid calculating similar information repeatedly by reducing all tokens to its base form using various stemming and lemmatization dictionaries. 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Historically, however, that was not always the case. Mobile UIs, or front-ends, rely on mobile back-ends to support access to enterprise systems. The mobile back-end facilitates data routing, security, authentication, authorization, working off-line, and service orchestration. This functionality is supported by a mix of middleware components including mobile app server, mobile backend as a service (MBaaS), and service-oriented architecture (SOA) infrastructure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where the order s {\\displaystyle s} is an integer, it will be represented by s = n {\\displaystyle s=n} (or s = \u2212 n {\\displaystyle s=-n} when negative). It is often convenient to define \u03bc = ln \u2061 ( z ) {\\displaystyle \\mu =\\ln(z)} where ln \u2061 ( z ) {\\displaystyle \\ln(z)} is the principal branch of the complex logarithm Ln \u2061 ( z ) {\\displaystyle \\operatorname {Ln} (z)} so that \u2212 \u03c0 < Im \u2061 ( \u03bc ) \u2264 \u03c0 . {\\displaystyle -\\pi <\\operatorname {Im} (\\mu )\\leq \\pi .} Also, all exponentiation will be assumed to be single-valued: z s = exp \u2061 ( s ln \u2061 ( z ) ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The language of thought theory allows the mind to process more complex representations with the help of semantics. (See below in semantics of mental states). Recent work has suggested that we make a distinction between the mind and cognition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent research, storage strength (how well an item is learned) and retrieval strength (how well an item can be retrieved) have become separate measures for retrieval practice. Retrieval strength (also known as recall accuracy) is typically higher for restudied words when tested immediately after practice, whereas tested words were higher as time moves on. This suggests using tests is more beneficial for long term memory and retrieval which some authors believe is due to limited retrieval success during practice supporting the idea that tests are learning opportunities.Functional magnetic resonance imaging suggests that retrieval practice strengthens subsequent retention of learning through a \"dual action\" affecting the anterior and posterior hippocampus regions of the brain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, more specifically the study of random matrices, the circular law concerns the distribution of eigenvalues of an n \u00d7 n random matrix with independent and identically distributed entries in the limit n \u2192 \u221e. It asserts that for any sequence of random n \u00d7 n matrices whose entries are independent and identically distributed random variables, all with mean zero and variance equal to 1/n, the limiting spectral distribution is the uniform distribution over the unit disc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, Himmelblau's function is a multi-modal function, used to test the performance of optimization algorithms. The function is defined by: f ( x , y ) = ( x 2 + y \u2212 11 ) 2 + ( x + y 2 \u2212 7 ) 2 . {\\displaystyle f(x,y)=(x^{2}+y-11)^{2}+(x+y^{2}-7)^{2}.\\quad } It has one local maximum at x = \u2212 0.270845 {\\displaystyle x=-0.270845} and y = \u2212 0.923039 {\\displaystyle y=-0.923039} where f ( x , y ) = 181.617 {\\displaystyle f(x,y)=181.617} , and four identical local minima: f ( 3.0 , 2.0 ) = 0.0 , {\\displaystyle f(3.0,2.0)=0.0,\\quad } f ( \u2212 2.805118 , 3.131312 ) = 0.0 , {\\displaystyle f(-2.805118,3.131312)=0.0,\\quad } f ( \u2212 3.779310 , \u2212 3.283186 ) = 0.0 , {\\displaystyle f(-3.779310,-3.283186)=0.0,\\quad } f ( 3.584428 , \u2212 1.848126 ) = 0.0. {\\displaystyle f(3.584428,-1.848126)=0.0.\\quad } The locations of all the minima can be found analytically. However, because they are roots of cubic polynomials, when written in terms of radicals, the expressions are somewhat complicated.The function is named after David Mautner Himmelblau (1924\u20132011), who introduced it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Policy cycles are typically characterized as adopting a classical approach, and tend to describe processes from the perspective of policy decision makers. Accordingly, some postpositivist academics challenge cyclical models as unresponsive and unrealistic, preferring systemic and more complex models. They consider a broader range of actors involved in the policy space that includes civil society organisations, the media, intellectuals, think tanks or policy research institutes, corporations, lobbyists, etc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(X is a developable space. )Moore spaces are generally interesting in mathematics because they may be applied to prove interesting metrization theorems. The concept of a Moore space was formulated by R. L. Moore in the earlier part of the 20th century.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of abstract algebra known as group theory, the diameter of a finite group is a measure of its complexity. Consider a finite group ( G , \u2218 ) {\\displaystyle \\left(G,\\circ \\right)} , and any set of generators S. Define D S {\\displaystyle D_{S}} to be the graph diameter of the Cayley graph \u039b = ( G , S ) {\\displaystyle \\Lambda =\\left(G,S\\right)} . Then the diameter of ( G , \u2218 ) {\\displaystyle \\left(G,\\circ \\right)} is the largest value of D S {\\displaystyle D_{S}} taken over all generating sets S. For instance, every finite cyclic group of order s, the Cayley graph for a generating set with one generator is an s-vertex cycle graph. The diameter of this graph, and of the group, is \u230a s / 2 \u230b {\\displaystyle \\lfloor s/2\\rfloor } .It is conjectured, for all non-abelian finite simple groups G, that diam \u2061 ( G ) \u2a7d ( log \u2061 | G | ) O ( 1 ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a point-to-point connection refers to a communications connection between two communication endpoints or nodes. An example is a telephone call, in which one telephone is connected with one other, and what is said by one caller can only be heard by the other. This is contrasted with a point-to-multipoint or broadcast connection, in which many nodes can receive information transmitted by one node. Other examples of point-to-point communications links are leased lines and microwave radio relay.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first 16 terms of the binary Van der Corput sequence 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15one of the longest increasing subsequences is 0, 2, 6, 9, 11, 15.This subsequence has length six; the input sequence has no seven-member increasing subsequences. The longest increasing subsequence in this example is not the only solution: for instance, 0, 4, 6, 9, 11, 15 0, 2, 6, 9, 13, 15 0, 4, 6, 9, 13, 15are other increasing subsequences of equal length in the same input sequence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "2. In telecommunications management, a resource within the telecommunications environment that may be managed through the use of operation, administration, maintenance, and provisioning (OAMP) application protocols.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the probabilistic method is used to prove the existence of mathematical objects with desired combinatorial properties. The proofs are probabilistic \u2014 they work by showing that a random object, chosen from some probability distribution, has the desired properties with positive probability. Consequently, they are nonconstructive \u2014 they don't explicitly describe an efficient method for computing the desired objects. The method of conditional probabilities (Spencer 1987), (Raghavan 1988) converts such a proof, in a \"very precise sense\", into an efficient deterministic algorithm, one that is guaranteed to compute an object with the desired properties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix multiplication is an example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural science, impossibility assertions (like other assertions) come to be widely accepted as overwhelmingly probable rather than considered proved to the point of being unchallengeable. The basis for this strong acceptance is a combination of extensive evidence of something not occurring, combined with an underlying theory, very successful in making predictions, whose assumptions lead logically to the conclusion that something is impossible. Two examples of widely accepted impossibilities in physics are perpetual motion machines, which violate the law of conservation of energy, and exceeding the speed of light, which violates the implications of special relativity. Another is the uncertainty principle of quantum mechanics, which asserts the impossibility of simultaneously knowing both the position and the momentum of a particle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An infix operator is positioned in between a left and a right operand, as in x+y. Some languages, most notably the C-syntax family, stretches this conventional terminology and speaks also of ternary infix operators (a?b:c). Theoretically it would even be possible (but not necessarily practical) to define parenthesization as a unary bifix operation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory the n conjecture is a conjecture stated by Browkin & Brzezi\u0144ski (1994) as a generalization of the abc conjecture to more than three integers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, the term transmission block has the following meanings: A group of characters or bits transmitted as a block, unit, message, or packet. It usually includes additional encoded characters for error detection and correction. In data transmission, a group of records sent, processed, or recorded as a unit.Some protocols require each transmission block to end with an end-of-message marker. This is often a control character such as End-of-Text (ETX), End-of-Transmission-Block (ETB), or End-of-Transmission (EOT). Some protocols (especially those requiring ETX) require each transmission block to begin with a Start-of-Text character (STX).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Post strongly disagreed with Church's \"identification\" of effective computability with the \u03bb-calculus and recursion, stating: Actually the work already done by Church and others carries this identification considerably beyond the working hypothesis stage. But to mask this identification under a definition\u2026 blinds us to the need of its continual verification. Rather, he regarded the notion of \"effective calculability\" as merely a \"working hypothesis\" that might lead by inductive reasoning to a \"natural law\" rather than by \"a definition or an axiom\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The combination of possible states can generate a wide variety of events, thus defining a more complex production cycle. As a consequence, cycles are usually far to be simple linear sequences. There are commonly parallel branches running together and alternatives selected according to different events, schematically represented below: s:stage c:condition s1 | |-c2 | s2 | ---------- | | |-c31 |-c32 | | s31 s32 | | |-c41 |-c42 | | ---------- | s4", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociology, dirty data refer to secretive data the discovery of which is discrediting to those who kept the data secret. Following the definition of Gary T. Marx, Professor Emeritus of MIT, dirty data are one among four types of data: Nonsecretive and nondiscrediting data: Routinely available information. Secretive and nondiscrediting data: Strategic and fraternal secrets, privacy. Nonsecretive and discrediting data: sanction immunity, normative dissensus, selective dissensus, making good on a threat for credibility, discovered dirty data. Secretive and discrediting data: Hidden and dirty data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Against Method (3rd ed.). p.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Williams showed that the first moment can be matched as far as N \u2212 2 {\\displaystyle ~N^{-2}~} if the test statistic is divided by a factor given by q 1 = 1 + \u2211 i = 1 k \u03c0 i \u2212 1 \u2212 1 6 N ( k \u2212 1 ) . {\\displaystyle ~q_{1}=1+{\\frac {\\;\\sum _{i=1}^{k}\\pi _{i}^{-1}\\,-\\,1\\;}{6N(k-1)}}~.} In the special case where the null hypothesis is that all the values \u03c0 i {\\displaystyle \\pi _{i}} are equal to 1 / k {\\displaystyle ~1/k~} (i.e. it stipulates a uniform distribution), this simplifies to q 1 = 1 + k + 1 6 N .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the demographic transition model, the size and shape of population pyramids vary. In stage one of the demographic transition model, the pyramids have the most defined shape. They have the ideal big base and a skinny top. In stage two, the pyramid looks similar but starts to widen in the middle age groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most basic metaheuristics are sequential. Although their utilization allows to significantly reduce the temporal complexity of the search process, this latter remains high for real-world problems arising in both academic and industrial domains. Therefore, parallelism comes as a natural way not to only reduce the search time, but also to improve the quality of the provided solutions. For a comprehensive discussion on how parallelism can be mixed with metaheuristics see .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spite of various uncertainties or possible criticisms of cost\u2013benefit analysis, it does have several strengths: It offers an internally consistent and global comprehensive analysis of impacts. : 955 Sensitivity analysis allows critical assumptions in the analysis to be changed. This can identify areas where the value of information is highest and where additional research might have the highest payoffs. : 119 As uncertainty is reduced, the integrated models used in producing cost\u2013benefit analysis might become more realistic and useful.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In shared memory model the processors are all connected to a \"globally available\" memory, via either software or hardware means. The operating system usually maintains its memory coherence.From a programmer's point of view, this memory model is better understood than the distributed memory model. Another advantage is that memory coherence is managed by the operating system and not the written program. Two known disadvantages are: scalability beyond thirty-two processors is difficult, and the shared memory model is less flexible than the distributed memory model.There are many examples of shared memory (multiprocessors): UMA (uniform memory access), COMA (cache-only memory access).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1970s, ICL signed an OEM agreement with the Canadian company, Consolidated Computers Ltd (later Consolidated Computer Inc.) to distribute CCL's key-to-disk data entry product, Key-Edit, in the British Commonwealth of countries as well as in western and eastern Europe. Models included Key Edit 100, 50, 59, 1000, and 2000. In the mid-1980s a version of the Key Edit 59 operating system was ported (in emulation mode) to the DRS 20 series and marketed as Data Entry 20.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The legitimacy of this method relies on the assumption that the observed coincidences constitute a fair sample of the emitted pairs. Following local realist assumptions as in Bell's paper, the estimated quantum correlation converges after a sufficient number of trials to Q C ( a , b ) = \u222b d \u03bb \u03c1 ( \u03bb ) A ( a , \u03bb ) B ( b , \u03bb ) {\\displaystyle QC(a,b)=\\int d\\lambda \\rho (\\lambda )A(a,\\lambda )B(b,\\lambda )} where a and b are detector settings and \u03bb is the hidden variable, drawn from a distribution \u03c1(\u03bb). The quantum correlation is the key statistic in the CHSH inequality and some of the other Bell inequalities, tests that open the way for experimental discrimination between quantum mechanics and local realism or local hidden-variable theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Virtual memory was introduced to the x86 architecture with the protected mode of the Intel 80286 processor, but its segment swapping technique scaled poorly to larger segment sizes. The Intel 80386 introduced paging support underneath the existing segmentation layer, enabling the page fault exception to chain with other exceptions without double fault. However, loading segment descriptors was an expensive operation, causing operating system designers to rely strictly on paging rather than a combination of paging and segmentation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The concept of square can be extended to some other number systems. If rational numbers are included, then a square is the ratio of two square integers, and, conversely, the ratio of two square integers is a square, for example, 4 9 = ( 2 3 ) 2 {\\displaystyle \\textstyle {\\frac {4}{9}}=\\left({\\frac {2}{3}}\\right)^{2}} . Starting with 1, there are \u230a m \u230b {\\displaystyle \\lfloor {\\sqrt {m}}\\rfloor } square numbers up to and including m, where the expression \u230a x \u230b {\\displaystyle \\lfloor x\\rfloor } represents the floor of the number x.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A Lagrangian relaxation of a complicated problem in combinatorial optimization penalizes violations of some constraints, allowing an easier relaxed problem to be solved. Relaxation techniques complement or supplement branch and bound algorithms of combinatorial optimization; linear programming and Lagrangian relaxations are used to obtain bounds in branch-and-bound algorithms for integer programming.The modeling strategy of relaxation should not be confused with iterative methods of relaxation, such as successive over-relaxation (SOR); iterative methods of relaxation are used in solving problems in differential equations, linear least-squares, and linear programming. However, iterative methods of relaxation have been used to solve Lagrangian relaxations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Each partial order as well as each equivalence relation needs to be transitive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is why there arises the following natural question. Suppose that the conditions of the characterization theorem are fulfilled not exactly but only approximately. May we assert that the conclusion of the theorem is also fulfilled approximately? The theorems in which the problems of this kind are considered are called stability characterizations of probability distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Comparisons can be made between the clusters and how they show up more or less in certain features in contrast to each other. To calculate a cluster's presence within a certain feature, it is determined if a nuclear profile is present within a window that is detected within a feature. The percentage of how often nuclear profiles within a cluster occur within the same windows that are detected within a feature are then displayed by the radar chart.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is called the cyclic or adjacency property of the code.In modern digital communications, Gray codes play an important role in error correction. For example, in a digital modulation scheme such as QAM where data is typically transmitted in symbols of 4 bits or more, the signal's constellation diagram is arranged so that the bit patterns conveyed by adjacent constellation points differ by only one bit. By combining this with forward error correction capable of correcting single-bit errors, it is possible for a receiver to correct any transmission errors that cause a constellation point to deviate into the area of an adjacent point.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system A x = b {\\displaystyle {\\boldsymbol {Ax}}={\\boldsymbol {b}}} where A {\\displaystyle {\\boldsymbol {A}}} is symmetric positive-definite. The conjugate gradient method can be derived from several different perspectives, including specialization of the conjugate direction method for optimization, and variation of the Arnoldi/Lanczos iteration for eigenvalue problems. The intent of this article is to document the important steps in these derivations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In propositional logic a resolution proof of a clause \u03ba {\\displaystyle \\kappa } from a set of clauses C is a directed acyclic graph (DAG): the input nodes are axiom inferences (without premises) whose conclusions are elements of C, the resolvent nodes are resolution inferences, and the proof has a node with conclusion \u03ba {\\displaystyle \\kappa } .The DAG contains an edge from a node \u03b7 1 {\\displaystyle \\eta _{1}} to a node \u03b7 2 {\\displaystyle \\eta _{2}} if and only if a premise of \u03b7 1 {\\displaystyle \\eta _{1}} is the conclusion of \u03b7 2 {\\displaystyle \\eta _{2}} . In this case, \u03b7 1 {\\displaystyle \\eta _{1}} is a child of \u03b7 2 {\\displaystyle \\eta _{2}} , and \u03b7 2 {\\displaystyle \\eta _{2}} is a parent of \u03b7 1 {\\displaystyle \\eta _{1}} . A node with no children is a root. A proof compression algorithm will try to create a new DAG with fewer nodes that represents a valid proof of \u03ba {\\displaystyle \\kappa } or, in some cases, a valid proof of a subset of \u03ba {\\displaystyle \\kappa } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Satisfiability and validity are defined for a single formula, but can be generalized to an arbitrary theory or set of formulas: a theory is satisfiable if at least one interpretation makes every formula in the theory true, and valid if every formula is true in every interpretation. For example, theories of arithmetic such as Peano arithmetic are satisfiable because they are true in the natural numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The sequences which are solutions of these equations are called holonomic, P-recursive or D-finite. From the late 1980s, the first algorithms were developed to find solutions for these equations. Sergei A. Abramov, Marko Petkov\u0161ek and Mark van Hoeij described algorithms to find polynomial, rational, hypergeometric and d'Alembertian solutions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of modern algebra known as group theory, the Held group He is a sporadic simple group of order 210 \u00b7 33 \u00b7 52 \u00b7 73 \u00b7 17 = 4030387200 \u2248 4\u00d7109.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to apply the theory of NP-completeness to the minimum feedback arc set, it is necessary to modify the problem from being an optimization problem (how few edges can be removed to break all cycles) to an equivalent decision version, with a yes or no answer (is it possible to remove k {\\displaystyle k} edges). Thus, the decision version of the feedback arc set problem takes as input both a directed graph and a number k {\\displaystyle k} . It asks whether all cycles can be broken by removing at most k {\\displaystyle k} edges, or equivalently whether there is an acyclic subgraph with at least | E ( G ) | \u2212 k {\\displaystyle |E(G)|-k} edges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice the use of MAST includes three steps: Preceding assessment Multidisciplinary assessment Transferability assessmentFirstly, the assessment must start with preceding considerations in order to determine whether it is relevant for an institution at a given point in time to carry out the assessment. This step involves mainly assessment of the maturity of the technology and the organization planning to use it. If the technology is not matured and have not been tested in practice, then pilot studies must be carried out to mature the technology before a multidisciplinary study is initiated. Secondly, after the preceding considerations, the multidisciplinary assessment is carried out in order to describe and assess the different outcomes of the telemedicine application. This involves assessment of outcomes within the following seven domains: Domain 1: Health problem and characteristics of the application Domain 2: Safety Domain 3: Clinical effectiveness Domain 4: Patient perspectives Domain 5: Economic aspects Domain 6: Organizational aspects Domain 7: Socio-cultural, ethical and legal aspectsThirdly, in relation to the description of the outcomes, an assessment should also be made of the transferability of the results to other settings or countries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s, Chomsky introduced two central ideas relevant to the construction and evaluation of grammatical theories.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent times, the use of blessed salt is found within some Catholic and Anglican liturgies of Holy Baptism, and in the blessing of holy water, sometimes called lustral water. The Anglican Missal, used by some Anglo-Catholics, in The Order of Blessing Water, includes an English translation of traditional prayers for the exorcism and blessing of salt. The Collect reads: Almighty and everlasting God, we humbly beseech thy infinite goodness, that thou wouldest vouchsafe of thy mercy to ble+ss and sanct+ify this thy creature of salt, which thou hast bestowed for the necessities of mankind: let it be profitable for all them that receive it for their healing both in body and soul: and grant that all such things as are touched or sprinkled with the same may be delivered from all uncleanliness, and defended against the assaults of all spiritual wickedness. Through Jesus Christ our Lord.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In measure theory, the following implications hold between measures: So every probability measure is a sub-probability measure, but the converse is not true. Also every sub-probability measure is a finite measure and a \u03c3-finite measure, but the converse is again not true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, given a partial order \u2aaf {\\displaystyle \\preceq } and \u2291 {\\displaystyle \\sqsubseteq } on a set A {\\displaystyle A} and B {\\displaystyle B} , respectively, the product order (also called the coordinatewise order or componentwise order) is a partial ordering \u2264 {\\displaystyle \\leq } on the Cartesian product A \u00d7 B . {\\displaystyle A\\times B.} Given two pairs ( a 1 , b 1 ) {\\displaystyle \\left(a_{1},b_{1}\\right)} and ( a 2 , b 2 ) {\\displaystyle \\left(a_{2},b_{2}\\right)} in A \u00d7 B , {\\displaystyle A\\times B,} declare that ( a 1 , b 1 ) \u2264 ( a 2 , b 2 ) {\\displaystyle \\left(a_{1},b_{1}\\right)\\leq \\left(a_{2},b_{2}\\right)} if a 1 \u2aaf a 2 {\\displaystyle a_{1}\\preceq a_{2}} and b 1 \u2291 b 2 . {\\displaystyle b_{1}\\sqsubseteq b_{2}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each finite continued fraction of the sequence is obtained by using a finite prefix of the infinite continued fraction's defining sequence of integers. Moreover, every irrational number \u03b1 {\\displaystyle \\alpha } is the value of a unique infinite regular continued fraction, whose coefficients can be found using the non-terminating version of the Euclidean algorithm applied to the incommensurable values \u03b1 {\\displaystyle \\alpha } and 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, the specification of the arithmetic circuit is not given to the PIT solver, and the PIT solver can only input values into a \"black box\" that implements the circuit, and then analyze the output. Note that the solutions below assume that any operation (such as multiplication) in the given field takes constant time; further, all black-box algorithms below assume the size of the field is larger than the degree of the polynomial. The Schwartz\u2013Zippel algorithm provides a practical probabilistic solution, by simply randomly testing inputs and checking whether the output is zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then whatever A does (or fails to do) today will make no difference; similarly, whatever B does (or fails to do) today will make no difference: the outcome is already settled. Or again, suppose 'A wins' is today false. Then no matter what A does today (or fails to do), it will make no difference; similarly, no matter what B does (or fails to do), it will make no difference: the outcome is already settled.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The external cooling system was considerably larger than the machine itself. The electronic components were likewise improved over previous designs. The main CPU circuits moved to ECL-based logic, enabling a clock speed increase to 125 MHz (8 ns cycle time) from the 7600's 36.4 MHz (27.5 ns cycle time) an increase of about four times.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are several approaches to platform virtualization. Examples of virtualization use cases: Running one or more applications that are not supported by the host OS: A virtual machine running the required guest OS could permit the desired applications to run, without altering the host OS. Evaluating an alternate operating system: The new OS could be run within a VM, without altering the host OS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, G\u00f6del's speed-up theorem, proved by G\u00f6del (1936), shows that there are theorems whose proofs can be drastically shortened by working in more powerful axiomatic systems. Kurt G\u00f6del showed how to find explicit examples of statements in formal systems that are provable in that system but whose shortest proof is unimaginably long. For example, the statement: \"This statement cannot be proved in Peano arithmetic in fewer than a googolplex symbols\"is provable in Peano arithmetic (PA) but the shortest proof has at least a googolplex symbols, by an argument similar to the proof of G\u00f6del's first incompleteness theorem: If PA is consistent, then it cannot prove the statement in fewer than a googolplex symbols, because the existence of such a proof would itself be a theorem of PA, a contradiction. But simply enumerating all strings of length up to a googolplex and checking that each such string is not a proof (in PA) of the statement, yields a proof of the statement (which is necessarily longer than a googolplex symbols).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the branch of mathematics called graph theory, the strength of an undirected graph corresponds to the minimum ratio edges removed/components created in a decomposition of the graph in question. It is a method to compute partitions of the set of vertices and detect zones of high concentration of edges, and is analogous to graph toughness which is defined similarly for vertex removal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the form of energy keeps changing. One may wonder if there is any such law for the conservation of information. In the classical world, information can be copied and deleted perfectly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of linear programming, one can think of any linear program as a covering problem if the coefficients in the constraint matrix, the objective function, and right-hand side are nonnegative. More precisely, consider the following general integer linear program: Such an integer linear program is called a covering problem if a j i , b j , c i \u2265 0 {\\displaystyle a_{ji},b_{j},c_{i}\\geq 0} for all i = 1 , \u2026 , n {\\displaystyle i=1,\\dots ,n} and j = 1 , \u2026 , m {\\displaystyle j=1,\\dots ,m} . Intuition: Assume having n {\\displaystyle n} types of object and each object of type i {\\displaystyle i} has an associated cost of c i {\\displaystyle c_{i}} . The number x i {\\displaystyle x_{i}} indicates how many objects of type i {\\displaystyle i} we buy. If the constraints A x \u2265 b {\\displaystyle A\\mathbf {x} \\geq \\mathbf {b} } are satisfied, it is said that x {\\displaystyle \\mathbf {x} } is a covering (the structures that are covered depend on the combinatorial context). Finally, an optimal solution to the above integer linear program is a covering of minimal cost.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many developers feel that CW's are not efficient because of the amount of time they take and the time pressures that they are facing. A design team spends their time trying to resolve the problem, during the CW instead of after the results have been formulated. Evaluation time is spent re-designing, this inhibits the effectiveness of the walkthrough and leads to lengthy design discussions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "9. The utility and advantages of the patent property over the old modes or devices, if any, that had been used for working out similar results. 10.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formal theories cannot dispense with primitive notions, under pain of infinite regress (per the regress problem). For example, in contemporary geometry, point, line, and contains are some primitive notions. Instead of attempting to define them, their interplay is ruled (in Hilbert's axiom system) by axioms like \"For every two points there exists a line that contains them both\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In photography, reversal film or slide film is a type of photographic film that produces a positive image on a transparent base. Instead of negatives and prints, reversal film is processed to produce transparencies or diapositives (abbreviated as \"diafilm\" or \"dia\" in some languages like German or Hungarian). Reversal film is produced in various sizes, from 35 mm to roll film to 8\u00d710 inch sheet film.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although the recurrence is easily observed, it eventually became apparent that over much, much longer time periods, the system does eventually thermalize. Multiple competing theories have been proposed to explain the behavior of the system, and it remains a topic of active research. The original intent was to find a physics problem worthy of numerical simulation on the then-new MANIAC computer. Fermi felt that thermalization would pose such a challenge. As such, it represents one of the earliest uses of digital computers in mathematical research; simultaneously, the unexpected results launched the study of nonlinear systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This algorithm is implemented by RivEX, an ESRI ArcGIS 10.7 tool. The input to their algorithm is a network of the centre lines of the bodies of water, represented as arcs (or edges) joined at nodes. Lake boundaries and river banks should not be used as arcs, as these will generally form a non-tree network with an incorrect topology. Alternative stream ordering systems have been developed by Shreve and Hodgkinson et al. A statistical comparison of Strahler and Shreve systems, together with an analysis of stream/link lengths, is given by Smart.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the MaxClique algorithm the approximate coloring algorithm is used to obtain set of color classes C. The ColorSort algorithm is an improved algorithm of the approximate coloring algorithm. In the approximate coloring algorithm vertices are colored one by one in the same order as they appear in a set of candidate vertices R so that if the next vertex p is non-adjacent to all vertices in the some color class it is added to this class and if p is adjacent to at least one vertex in every one of existing color classes it is put into a new color class. The MaxClique algorithm returns vertices R ordered by their colors. By looking at the MaxClique algorithm it is clear that vertices v \u2208 R with colors C(v) < |Qmax| \u2212 |Q| + 1 will never be added to the current clique Q. Therefore, sorting those vertices by color is of no use to MaxClique algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Notice that if C o u t ( m ) = ( c 1 , \u22ef , c N ) {\\displaystyle C_{out}(m)=(c_{1},\\cdots ,c_{N})} , then C \u2217 ( m ) = ( C i n 1 ( c 1 ) , \u22ef , C i n N ( c N ) ) {\\displaystyle C^{*}(m)=(C_{in}^{1}(c_{1}),\\cdots ,C_{in}^{N}(c_{N}))} . So for the lower bound \u0394 ( C \u2217 ( m 1 ) , C \u2217 ( m 2 ) ) {\\displaystyle \\Delta (C^{*}(m_{1}),C^{*}(m_{2}))} , we need to take into account the distance of C i n 1 , \u22ef , C i n N . {\\displaystyle C_{in}^{1},\\cdots ,C_{in}^{N}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programs, the required amount of memory depends on what the user may enter. In such cases the programmer needs to allocate memory dynamically. This is done by allocating memory at the heap rather than on the stack, where variables usually are stored (although variables can also be stored in the CPU registers). Dynamic memory allocation can only be made through pointers, and names \u2013 like with common variables \u2013 cannot be given.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming, the rule of least power is a design principle that \"suggests choosing the least powerful  language suitable for a given purpose\". Stated alternatively, given a choice among computer languages, classes of which range from descriptive (or declarative) to procedural, the less procedural, more descriptive the language one chooses, the more one can do with the data stored in that language. This rule is an application of the principle of least privilege to protocol design. The Rule of Least Power is an example in context of the centuries older principle known as Occam's razor in philosophy. In particular, arguments for and against the Rule of Least Power are subject to the same analysis as for Occam's razor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "R6RS specifies a more sophisticated transformation system, syntax-case, which has been available as a language extension to R5RS Scheme for some time. Invocations of macros and procedures bear a close resemblance\u2014both are s-expressions\u2014but they are treated differently. When the compiler encounters an s-expression in the program, it first checks to see if the symbol is defined as a syntactic keyword within the current lexical scope.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, a branch of mathematics, a set A {\\displaystyle A} is called transitive if either of the following equivalent conditions hold: whenever x \u2208 A {\\displaystyle x\\in A} , and y \u2208 x {\\displaystyle y\\in x} , then y \u2208 A {\\displaystyle y\\in A} . whenever x \u2208 A {\\displaystyle x\\in A} , and x {\\displaystyle x} is not an urelement, then x {\\displaystyle x} is a subset of A {\\displaystyle A} .Similarly, a class M {\\displaystyle M} is transitive if every element of M {\\displaystyle M} is a subset of M {\\displaystyle M} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle {\\boldsymbol {\\hat {\\beta }}}=(X^{\\mathrm {T} }X)^{-1}X^{\\mathrm {T} }\\mathbf {y} .} The matrix ( X T X ) \u2212 1 X T {\\displaystyle (X^{\\mathrm {T} }X)^{-1}X^{\\mathrm {T} }} is known as the Moore\u2013Penrose pseudoinverse of X. The use of the matrix inverse in this formula requires that X is of full rank, i.e. there is not perfect multicollinearity among different explanatory variables (i.e. no explanatory variable can be perfectly predicted from the others). In such cases, the singular value decomposition can be used to compute the pseudoinverse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the theory of minimum norm quadratic unbiased estimation (MINQUE) was developed by C. R. Rao. Its application was originally to the problem of heteroscedasticity and the estimation of variance components in random effects models. The theory involves three stages: defining a general class of potential estimators as quadratic functions of the observed data, where the estimators relate to a vector of model parameters; specifying certain constraints on the desired properties of the estimators, such as unbiasedness; choosing the optimal estimator by minimising a \"norm\" which measures the size of the covariance matrix of the estimators. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other cases, a word may be usable in multiple genders indifferently. For example, in Bulgarian the word \u043f\u0443\u0300\u0441\u0442\u043e\u0448, (pustosh, \"wilderness\") may be either masculine (definite form \u043f\u0443\u0300\u0441\u0442\u043e\u0448\u0430, pustosh\u0259) or feminine (definite form \u043f\u0443\u0441\u0442\u043e\u0448\u0442\u0430\u0300, pustoshta) without any change in meaning and no preference in usage. In Norwegian, many nouns can be either feminine or masculine according to the dialect, level of formality or whim of the speaker/writer. Even the two written forms of the language have many nouns whose gender is optional.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\forall x\\,A.} And as a rule of inference it is from \u22a2 \u2200 x A {\\displaystyle \\vdash \\forall xA} infer \u22a2 A { x \u21a6 a } . {\\displaystyle \\vdash A\\{x\\mapsto a\\}.} Irving Copi noted that universal instantiation \"...follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanis\u0142aw Ja\u015bkowski in 1934.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A source code repository is a place where large amounts of source code are kept, either publicly or privately. Source code repositories are used most basically for backups and versioning, and on multi-developer projects to handle various source code versions and to provide aid in resolving conflicts that arise from developers submitting overlapping modifications. Subversion, Git and Mercurial are examples of popular tools used to handle this workflow, which are common in open source projects. For smaller projects, its code may be kept as a non-managed set of files (even the Linux kernel was maintained as a set of files for many years).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population. The shape of a distribution may be considered either descriptively, using terms such as \"J-shaped\", or numerically, using quantitative measures such as skewness and kurtosis. Considerations of the shape of a distribution arise in statistical data analysis, where simple quantitative descriptive statistics and plotting techniques such as histograms can lead on to the selection of a particular family of distributions for modelling purposes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was especially noted that it received a score of 45% from the online review aggregator Rotten Tomatoes\u2014the worst score received by any Best Picture nominee in the site's history.Some critics think the term is overused. \"If I were Oscar-blogging this year,< a long rant about the empty foolishness of the phrase 'Oscar bait' would be on the way,\" tweeted film historian Mark Harris in early December 2012, before some of that year's likely Oscar nominees had even been released. Four years later, he explained his objections in a conversation with fellow Vulture editor Kyle Buchanan.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first figure of the syllogism (see term logic for an outline of syllogistic theory) is best adapted to demonstration, because it affords conclusions universally affirmative. This figure is commonly used by mathematicians. The demonstration of an affirmative proposition is preferable to that of a negative; the demonstration of a universal to that of a particular; and direct demonstration to a reductio ad absurdum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the rapid foundational changes of the 1950s Weil's approach became obsolete. In scheme theory, though, from 1957, generic points returned: this time \u00e0 la Zariski. For example for R a discrete valuation ring, Spec(R) consists of two points, a generic point (coming from the prime ideal {0}) and a closed point or special point coming from the unique maximal ideal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the balanced ternary system the value of a digit n places left of the radix point is the product of the digit and 3n. This is useful when converting between decimal and balanced ternary. In the following the strings denoting balanced ternary carry the suffix, bal3. For instance, 10bal3 = 1 \u00d7 31 + 0 \u00d7 30 = 3dec 10\ud835\uddb3bal3 = 1 \u00d7 32 + 0 \u00d7 31 + (\u22121) \u00d7 30 = 8dec \u22129dec = \u22121 \u00d7 32 + 0 \u00d7 31 + 0 \u00d7 30 = \ud835\uddb300bal3 8dec = 1 \u00d7 32 + 0 \u00d7 31 + (\u22121) \u00d7 30 = 10\ud835\uddb3bal3Similarly, the first place to the right of the radix point holds 3\u22121 = 1/3, the second place holds 3\u22122 = 1/9, and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In science and information science, an ontology formally represents knowledge as a set of concepts within a domain, and the relationships between those concepts. It can be used to reason about the entities within that domain and may be used to describe the domain. More specifically, an ontology is a model for describing the world that consists of a set of types, properties, and relationship types. Exactly what is provided around these varies, but they are the essentials of an ontology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical mathematics, hierarchical matrices (H-matrices) are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension n {\\displaystyle n} can be represented efficiently in O ( n ) {\\displaystyle O(n)} units of storage by storing only its non-zero entries, a non-sparse matrix would require O ( n 2 ) {\\displaystyle O(n^{2})} units of storage, and using this type of matrices for large problems would therefore be prohibitively expensive in terms of storage and computing time. Hierarchical matrices provide an approximation requiring only O ( n k log \u2061 ( n ) ) {\\displaystyle O(nk\\,\\log(n))} units of storage, where k {\\displaystyle k} is a parameter controlling the accuracy of the approximation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the domain of central processing unit (CPU) design, hazards are problems with the instruction pipeline in CPU microarchitectures when the next instruction cannot execute in the following clock cycle, and can potentially lead to incorrect computation results. Three common types of hazards are data hazards, structural hazards, and control hazards (branching hazards).There are several methods used to deal with hazards, including pipeline stalls/pipeline bubbling, operand forwarding, and in the case of out-of-order execution, the scoreboarding method and the Tomasulo algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most jurisdictions the subdivision of the band into different operating modes is according to informal convention rather than legal requirement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically group theory, a descendant tree is a hierarchical structure that visualizes parent-descendant relations between isomorphism classes of finite groups of prime power order p n {\\displaystyle p^{n}} , for a fixed prime number p {\\displaystyle p} and varying integer exponents n \u2265 0 {\\displaystyle n\\geq 0} . Such groups are briefly called finite p-groups. The vertices of a descendant tree are isomorphism classes of finite p-groups. Additionally to their order p n {\\displaystyle p^{n}} , finite p-groups have two further related invariants, the nilpotency class c {\\displaystyle c} and the coclass r = n \u2212 c {\\displaystyle r=n-c} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reconstructions of the Proto-Indo-European language (PIE), the verb form that has traditionally been called \"perfect\" in fact signified stative aspect (a current state of being). The name was assigned based on similarity to the Greek or Latin perfect tense, before the stative nature of the form was fully recognized. For details of its formation, see Proto-Indo-European verbs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to use Bluetooth, a device must be compatible with the subset of Bluetooth profiles (often called services or functions) necessary to use the desired services. A Bluetooth profile is a specification regarding an aspect of Bluetooth-based wireless communication between devices. It resides on top of the Bluetooth Core Specification and (optionally) additional protocols. While the profile may use certain features of the core specification, specific versions of profiles are rarely tied to specific versions of the core specification, making them independent of each other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(It would also be possible to add clauses to the formula to ensure that the three color classes are disjoint, but this makes no difference to the result.) Thus, by Courcelle's theorem, 3-colorability of graphs of bounded treewidth may be tested in linear time. For this variation of graph logic, Courcelle's theorem can be extended from treewidth to clique-width: for every fixed MSO1 property \u03a0 {\\displaystyle \\Pi } , and every fixed bound b {\\displaystyle b} on the clique-width of a graph, there is a linear-time algorithm for testing whether a graph of clique-width at most b {\\displaystyle b} has property \u03a0 {\\displaystyle \\Pi } . The original formulation of this result required the input graph to be given together with a construction proving that it has bounded clique-width, but later approximation algorithms for clique-width removed this requirement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These concepts are \"marginal\" because they can be found by summing values in a table along rows or columns, and writing the sum in the margins of the table. The distribution of the marginal variables (the marginal distribution) is obtained by marginalizing (that is, focusing on the sums in the margin) over the distribution of the variables being discarded, and the discarded variables are said to have been marginalized out.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The phone then identifies itself to the network through the control channel. Once this is successfully completed, the phone is said to be attached to the network. The key feature of a mobile phone is the ability to receive and make calls in any area where coverage is available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer\u2013Griess monster, or the friendly giant) is the largest sporadic simple group, having order 246 \u00b7 320 \u00b7 59 \u00b7 76 \u00b7 112 \u00b7 133 \u00b7 17 \u00b7 19 \u00b7 23 \u00b7 29 \u00b7 31 \u00b7 41 \u00b7 47 \u00b7 59 \u00b7 71 = 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 \u2248 8\u00d71053. The finite simple groups have been completely classified. Every such group belongs to one of 18 countably infinite families, or is one of 26 sporadic groups that do not follow such a systematic pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, an 8-bit byte can have values ranging from 00000000 to 11111111 (0 to 255 decimal) in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value 24,779 would be expressed in hexadecimal as 60CB16.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to their number of cycles (counting fixed points as cycles of length one). The Stirling numbers of the first and second kind can be understood as inverses of one another when viewed as triangular matrices. This article is devoted to specifics of Stirling numbers of the first kind. Identities linking the two kinds appear in the article on Stirling numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen\u2013Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other languages \u2013 including most Indo-European and Afro-Asiatic languages \u2013 third-person personal pronouns (at least those used to refer to people) intrinsically distinguish male from female. This feature commonly co-exists with a full system of grammatical gender, where all nouns are assigned to classes such as masculine, feminine and neuter. In languages with grammatical gender, even pronouns which are semantically gender-neutral may be required to take a gender for such purposes as grammatical agreement. Thus in French, for example, the first- and second-person personal pronouns may behave as either masculine or feminine depending on the sex of the referent; and indefinite pronouns such as quelqu'un ('someone') and personne ('no one') are treated conventionally as masculine, even though personne as a noun ('person') is only feminine regardless of the sex of the referent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some demonstrations prove only that the things are a certain way, rather than why they are so. The latter are the most perfect.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In replicated-write protocols, unlike the primary-based protocol, all updates are carried out to all replicas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "1,000 bits a second. Well, we'll surely be able to figure out something to do with that.'\" \u2014 Saverah Warenstein, former programmer at Lincoln Laboratory, IBM", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C programming language, data types constitute the semantics and characteristics of storage of data elements. They are expressed in the language syntax in form of declarations for memory locations or variables. Data types also determine the types of operations or methods of processing of data elements. The C language provides basic arithmetic types, such as integer and real number types, and syntax to build array and compound types. Headers for the C standard library, to be used via include directives, contain definitions of support types, that have additional properties, such as providing storage with an exact size, independent of the language implementation on specific hardware platforms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In places, licensure may still be a lifelong privilege, but increasingly nowadays, it requires periodic review by peers and renewal. It is very common for license renewal to depend, at least in part, on academia. In the United Kingdom such regular upgrading of skills is often termed continuous professional development, or CPD. In many professions this is fast becoming a standard, mandatory and annual requirement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Goidelic languages, dependent and independent verb forms are distinct verb forms; each tense of each verb exists in both forms. Verbs are often preceded by a particle which marks negation, or a question, or has some other force. The dependent verb forms are used after a particle, while independent forms are used when the verb is not subject to a particle. For example, in Irish, the past tense of the verb feic (\"to see\") has two forms: the independent form chonaic and the dependent form faca. The independent form is used when no particle precedes the verb, as in Chonaic m\u00e9 Se\u00e1n (\"I saw John\"). The dependent form is used when a particle such as n\u00ed (\"not\") precedes the verb, as in N\u00ed fhaca m\u00e9 Se\u00e1n (\"I did not see John\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some mathematical operators have inherent associativity. For example, subtraction and division, as used in conventional math notation, are inherently left-associative. Addition and multiplication, by contrast, are both left and right associative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems, a giant lock, also known as a big-lock or kernel-lock, is a lock that may be used in the kernel to provide concurrency control required by symmetric multiprocessing (SMP) systems. A giant lock is a solitary global lock that is held whenever a thread enters kernel space and released when the thread returns to user space; a system call is the archetypal example. In this model, threads in user space can run concurrently on any available processors or processor cores, but no more than one thread can run in kernel space; any other threads that try to enter kernel space are forced to wait. In other words, the giant lock eliminates all concurrency in kernel space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Romance languages, prepositions combine with stressed pronominal forms that are distinct from the unstressed clitic pronouns used with verbs. In French, prepositions combine with disjunctive pronouns, which are also found in other syntactic contexts (see French disjunctive pronouns). In Portuguese, Spanish, Italian, and Romanian, prepositions generally combine with pronouns that are identical in form to nominative (subject) pronouns, but there are unique prepositional forms for the 1st and 2nd person singular (and 3rd person reflexive). This is also true in Catalan, but the 2nd person singular prepositional form is identical to the nominative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Importantly, the law applies (as the name indicates) only when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be \"balanced\" by the others (see the gambler's fallacy). The LLN only applies to the average. Therefore, while other formulas that look similar are not verified, such as the raw deviation from \"theoretical results\": not only does it not converge toward zero as n increases, but it tends to increase in absolute value as n increases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Squaring both sides yields 2b2 = a2. Since the expression on the left is an integer multiple of 2, the right expression is by definition divisible by 2. That is, a2 is even, which implies that a must also be even, as seen in the proposition above (in #Proof by contraposition).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The theory of Linear Programming dictates that under mild assumptions (if the linear program has an optimal solution, and if the feasible region does not contain a line), one can always find an extreme point or a corner point that is optimal. The obtained optimum is tested for being an integer solution. If it is not, there is guaranteed to exist a linear inequality that separates the optimum from the convex hull of the true feasible set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic and computer science, the lambda-mu calculus is an extension of the lambda calculus introduced by M. Parigot. It introduces two new operators: the \u03bc operator (which is completely different both from the \u03bc operator found in computability theory and from the \u03bc operator of modal \u03bc-calculus) and the bracket operator. Proof-theoretically, it provides a well-behaved formulation of classical natural deduction. One of the main goals of this extended calculus is to be able to describe expressions corresponding to theorems in classical logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most non-strict languages the non-strictness extends to data constructors. This allows conceptually infinite data structures (such as the list of all prime numbers) to be manipulated in the same way as ordinary finite data structures. It also allows for the use of very large but finite data structures such as the complete game tree of chess. Non-strictness has several disadvantages which have prevented widespread adoption: Because of the uncertainty regarding if and when expressions will be evaluated, non-strict languages generally must be purely functional to be useful.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another constraint is adjacency. This constraint applies to the case when the \"cake\" is a disputed territory that has to be divided among neighboring countries. In this case, it may required that the piece allocated to each country is adjacent to its current territory; this constraint is handled by Hill's land division problem. In land division there are often two-dimensional geometric constraints, e.g., each piece should be a square or (more generally) a fat object.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Define the constant \u03a6 {\\displaystyle \\Phi } as \u03a6 = min S \u2282 X , \u03c0 ( S ) \u2264 1 2 Q ( S \u00d7 S c ) \u03c0 ( S ) . {\\displaystyle \\Phi =\\min _{S\\subset X,\\pi (S)\\leq {\\frac {1}{2}}}{\\frac {Q(S\\times S^{c})}{\\pi (S)}}.} The operator K , {\\displaystyle K,} acting on the space of functions from | X | {\\displaystyle |X|} to | X | {\\displaystyle |X|} , defined by ( K \u03d5 ) ( x ) = \u2211 y K ( x , y ) \u03d5 ( y ) {\\displaystyle (K\\phi )(x)=\\sum _{y}K(x,y)\\phi (y)} has eigenvalues \u03bb 1 \u2265 \u03bb 2 \u2265 \u22ef \u2265 \u03bb n {\\displaystyle \\lambda _{1}\\geq \\lambda _{2}\\geq \\cdots \\geq \\lambda _{n}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some sense the 0-1 indicator function is the most natural loss function for classification. It takes the value 0 if the predicted output is the same as the actual output, and it takes the value 1 if the predicted output is different from the actual output. For binary classification with Y = { \u2212 1 , 1 } {\\displaystyle Y=\\{-1,1\\}} , this is: V ( f ( x \u2192 ) , y ) = \u03b8 ( \u2212 y f ( x \u2192 ) ) {\\displaystyle V(f({\\vec {x}}),y)=\\theta (-yf({\\vec {x}}))} where \u03b8 {\\displaystyle \\theta } is the Heaviside step function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, an identification scheme is used to identify unique records in a set. If a data element is used to identify a record within a data set, the data element uses the Identifier representation term. An identification scheme should be contrasted with a classification scheme. Classification schemes are used to classify individual records into categories. Many records in a data set may be in a single category.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a remote digital terminal (RDT) typically accepts E1, T1 or OC-3 digital lines to communicate with a telephone Access network (AN) or telephone exchange (Local Digital Switch, LDS) on one side, and forms a local exchange (LE) on the other, which is connected to \"plain old telephone service\" (POTS) lines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and machine learning, lasso (least absolute shrinkage and selection operator; also Lasso or LASSO) is a regression analysis method that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the resulting statistical model. It was originally introduced in geophysics, and later by Robert Tibshirani, who coined the term. Lasso was originally formulated for linear regression models. This simple case reveals a substantial amount about the estimator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following table are the decimal values of the Kaktovik digits up to three places to the left and to the right of the units' place.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational algebra, a rename is a unary operation written as \u03c1 a / b ( R ) {\\displaystyle \\rho _{a/b}(R)} where: R is a relation a and b are attribute names b is an attribute of RThe result is identical to R except that the b attribute in all tuples is renamed to a. For an example, consider the following invocation of \u03c1 on an Employee relation and the result of that invocation: Formally, the semantics of the rename operator is defined as follows: \u03c1 a / b ( R ) = { t : t \u2208 R } , {\\displaystyle \\rho _{a/b}(R)=\\{\\ t:t\\in R\\ \\},} where t  {\\displaystyle t} is defined as the tuple t, with the b attribute renamed to a, so that: t  = { ( c , v ) | ( c , v ) \u2208 t , c \u2260 b } \u222a { ( a , t ( b ) ) } . {\\displaystyle t=\\{\\ (c,v)\\ |\\ (c,v)\\in t,\\ c\\neq b\\ \\}\\cup \\{\\ (a,\\ t(b))\\ \\}.} == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Operation itself is triggered by writing data to a triggering operand of an operation. Thus, an operation is executed as a side effect of the triggering data transport. Therefore, executing an addition operation in TTA requires three data transport definitions, also called moves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a joint distribution can be factorized into a product between conditional and marginal distributions Q ( X , Y ) = P ( X \u2223 Y ) \u03c0 ( Y ) {\\displaystyle Q(X,Y)=P(X\\mid Y)\\pi (Y)} The analog of this rule in the kernel embedding framework states that C X Y \u03c0 , {\\displaystyle {\\mathcal {C}}_{XY}^{\\pi },} the joint embedding of Q ( X , Y ) , {\\displaystyle Q(X,Y),} can be factorized as a composition of conditional embedding operator with the auto-covariance operator associated with \u03c0 ( Y ) {\\displaystyle \\pi (Y)} C X Y \u03c0 = C X \u2223 Y C Y Y \u03c0 {\\displaystyle {\\mathcal {C}}_{XY}^{\\pi }={\\mathcal {C}}_{X\\mid Y}{\\mathcal {C}}_{YY}^{\\pi }} where C X Y \u03c0 = E  , {\\displaystyle {\\mathcal {C}}_{XY}^{\\pi }=\\mathbb {E} ,} C Y Y \u03c0 = E  . {\\displaystyle {\\mathcal {C}}_{YY}^{\\pi }=\\mathbb {E} .} In practical implementations, the kernel chain rule takes the following form C ^ X Y \u03c0 = C ^ X \u2223 Y C ^ Y Y \u03c0 = \u03a5 ( G + \u03bb I ) \u2212 1 G ~ diag \u2061 ( \u03b1 ) \u03a6 ~ T {\\displaystyle {\\widehat {\\mathcal {C}}}_{XY}^{\\pi }={\\widehat {\\mathcal {C}}}_{X\\mid Y}{\\widehat {\\mathcal {C}}}_{YY}^{\\pi }={\\boldsymbol {\\Upsilon }}(\\mathbf {G} +\\lambda \\mathbf {I} )^{-1}{\\widetilde {\\mathbf {G} }}\\operatorname {diag} ({\\boldsymbol {\\alpha }}){\\boldsymbol {\\widetilde {\\Phi }}}^{T}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "to 4:00 p.m. Eastern time. Index ETFs are also sometimes weighted by revenue rather than market capitalization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory and constructive mathematics, the principle of independence of premise states that if \u03c6 and \u2203x \u03b8 are sentences in a formal theory and \u03c6 \u2192 \u2203x \u03b8 is provable, then \u2203x (\u03c6 \u2192 \u03b8) is provable. Here x cannot be a free variable of \u03c6, while \u03b8 can be a predicate depending on it. The main application of the principle is in the study of intuitionistic logic, where the principle is not generally valid. The principle is valid in classical logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In project management, communication management must address the following questions: What information needs to flow in and out of the project? Who needs what information? When is the information needed?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints. However, it may happen that an algebra admits no involution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. A twice-differentiable function of a single variable is convex if and only if its second derivative is nonnegative on its entire domain. Well-known examples of convex functions of a single variable include a linear function f ( x ) = c x {\\displaystyle f(x)=cx} (where c {\\displaystyle c} is a real number), a quadratic function c x 2 {\\displaystyle cx^{2}} ( c {\\displaystyle c} as a nonnegative real number) and a exponential function c e x {\\displaystyle ce^{x}} ( c {\\displaystyle c} as a nonnegative real number).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In taxonomy, an undescribed taxon is a taxon (for example, a species) that has been discovered, but not yet formally described and named. The various Nomenclature Codes specify the requirements for a new taxon to be validly described and named. Until such a description has been published, the taxon has no formal or official name, although a temporary, informal name is often used. A published scientific name may not fulfil the requirements of the Codes for various reasons.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, especially as that field is used in statistics, a group family of probability distributions is a family obtained by subjecting a random variable with a fixed distribution to a suitable family of transformations such as a location-scale family, or otherwise a family of probability distributions acted upon by a group.Consideration of a particular family of distributions as a group family can, in statistical theory, lead to the identification of an ancillary statistic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for programs and interrupt handlers to work without interference and share the same hardware memory and access to the I/O system, in a multitasking operating systems running on a digital system with a single CPU/MCU it is required to have some sort of software and hardware facilities to keep track of an executing processes data (memory page addresses, registers etc.) and to save and recover them back to the state they were in before they were suspended. This is achieved by a context switching. : 3.3 The running programs are often assigned a Process Context IDentifiers (PCID). In Linux-based operating systems, a set of data stored in registers is usually saved into a process descriptor in memory to implement switching of context. PCIDs are also used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, if this would result in the same output level as the previous bit time, a 0 level is output instead. Initially, the encoder output present state is assumed at 0 level when the first bit arrives at the encoder input.The new line-coding scheme violates the encoding rule of NRZ-L when a sequence of 1s or 0s arrives and hence, it overcomes some of their deficiencies. During the violation period for a run of 1s or 0s, it operates on the same encoding rule of the polar RZ but with pulse occupancy of full period.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model theory, a mathematical discipline, a \u03b2-model (from the French \"bon ordre\", well-ordering) is a model which is correct about statements of the form \"X is well-ordered\". The term was introduced by Mostowski (1959) as a strengthening of the notion of \u03c9-model. In contrast to the notation for set-theoretic properties named by ordinals, such as \u03be {\\displaystyle \\xi } -indescribability, the letter \u03b2 here is only denotational.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-channel systems, channels are used for separate purposes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of modern algebra known as group theory, a Tarski monster group, named for Alfred Tarski, is an infinite group G, such that every proper subgroup H of G, other than the identity subgroup, is a cyclic group of order a fixed prime number p. A Tarski monster group is necessarily simple. It was shown by Alexander Yu. Olshanskii in 1979 that Tarski groups exist, and that there is a Tarski p-group for every prime p > 1075. They are a source of counterexamples to conjectures in group theory, most importantly to Burnside's problem and the von Neumann conjecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n as the sum of k squares, where representations that differ only in the order of the summands or in the signs of the numbers being squared are counted as different, and is denoted by rk(n).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Tsallis distributions have been applied to problems in the fields of statistical mechanics, geology, anatomy, astronomy, economics, finance, and machine learning. The distributions are often used for their heavy tails. Note that Tsallis distributions are obtained as Box\u2013Cox transformation over usual distributions, with deformation parameter \u03bb = 1 \u2212 q {\\displaystyle \\lambda =1-q} . This deformation transforms exponentials into q-exponentials.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In October 2006, HTML inventor and W3C chair Tim Berners-Lee, introducing a major W3C effort to develop a new HTML specification, posted in his blog that, \"The attempt to get the world to switch to XML ... all at once didn't work. The large HTML-generating public did not move ... Some large communities did shift and are enjoying the fruits of well-formed systems ... The plan is to charter a completely new HTML group.\" The current HTML5 working draft says \"special attention has been given to defining clear conformance criteria for user agents in an effort to improve interoperability ... while at the same time updating the HTML specifications to address issues raised in the past few years.\" Ian Hickson, editor of the HTML5 specification criticizing the improper use of XHTML in 2002, is a member of the group developing this specification and is listed as one of the co-editors of the current working draft.Simon Pieters researched the XML-compliance of mobile browsers and concluded \"the claim that XHTML would be needed for mobile devices is simply a myth\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nor can there be an infinite number of middle terms between the first principle and the conclusion. In all demonstration, the first principles, the conclusion, and all the intermediate propositions, must be necessary, general and eternal truths. Of things that happen by chance, or contingently, or which can change, or of individual things, there is no demonstration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We call it \u03b2 2 , {\\displaystyle \\beta _{2},} and define a new sequence \u27e8 \u03b2 2 , i \u27e9 {\\displaystyle \\langle \\beta _{2,i}\\rangle } similar to the previous sequence. We can repeat this process, getting a sequence of sequences \u27e8 \u03b2 j , i \u27e9 {\\displaystyle \\langle \\beta _{j,i}\\rangle } where each element of a sequence is greater than every member of the previous sequences. Then for each i < \u03b1 , {\\displaystyle i<\\alpha ,} \u27e8 \u03b2 j , i \u27e9 {\\displaystyle \\langle \\beta _{j,i}\\rangle } is an increasing sequence contained in C i , {\\displaystyle C_{i},} and all these sequences have the same limit (the limit of \u27e8 \u03b2 j , i \u27e9 {\\displaystyle \\langle \\beta _{j,i}\\rangle } ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 356, 1356, 3456, and 13456 are the patterns related to Braille pattern dots-245, since the two additional dots of kantenji patterns 0245, 2457, and 02457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the European Union, the proposed Artificial Intelligence Act includes requirements to disclose copyrighted material used to train generative AI systems, and to label any AI-generated output as such.In the United States, a group of companies including OpenAI, Alphabet, and Meta signed a voluntary agreement with the White House in July 2023 to watermark AI-generated content.In China, the Interim Measures for the Management of Generative AI Services introduced by the Cyberspace Administration of China regulates any public-facing generative AI. It includes requirements to watermark generated images or videos, regulations on training data and label quality, restrictions on personal data collection, and a guideline that generative AI must \"adhere to socialist core values\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For detecting performance regressions, software performance tests are run on a regular basis, to monitor the response time and resource usage metrics of the software after subsequent changes. Unlike functional regression tests, the results of performance tests are subject to variance - that is, results can differ between tests due to variance in performance measurements; as a result, a decision must be made on whether a change in performance numbers constitutes a regression, based on experience and end-user demands. Approaches such as statistical significance testing and change point detection are sometimes used to aid in this decision.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Finnish language, there are three classes of vowels \u2013 front, back, and neutral, where each front vowel has a back vowel pairing. Grammatical endings such as case and derivational endings \u2013 but not enclitics \u2013 have only archiphonemic vowels U, O, A, which are realized as either back  or front  inside a single word. From vowel harmony it follows that the initial syllable of each single (non-compound) word controls the frontness or backness of the entire word. Non-initially, the neutral vowels are transparent to and unaffected by vowel harmony.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a noncototient is a positive integer n that cannot be expressed as the difference between a positive integer m and the number of coprime integers below it. That is, m \u2212 \u03c6(m) = n, where \u03c6 stands for Euler's totient function, has no solution for m. The cototient of n is defined as n \u2212 \u03c6(n), so a noncototient is a number that is never a cototient. It is conjectured that all noncototients are even. This follows from a modified form of the slightly stronger version of the Goldbach conjecture: if the even number n can be represented as a sum of two distinct primes p and q, then p q \u2212 \u03c6 ( p q ) = p q \u2212 ( p \u2212 1 ) ( q \u2212 1 ) = p + q \u2212 1 = n \u2212 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Selberg's identity is an approximate identity involving logarithms of primes named after Atle Selberg. The identity, discovered jointly by Selberg and Paul Erd\u0151s, was used in the first elementary proof for the prime number theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, coupling is a proof technique that allows one to compare two unrelated random variables (distributions) X and Y by creating a random vector W whose marginal distributions correspond to X and Y respectively. The choice of W is generally not unique, and the whole idea of \"coupling\" is about making such a choice so that X and Y can be related in a particularly desirable way.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the dynamics of the sandpile automaton defined above, some stable configurations ( 0 \u2264 z ( v ) < 4 {\\displaystyle 0\\leq z(v)<4} for all v \u2208 G \u2216 { s } {\\displaystyle v\\in G\\setminus \\{s\\}} ) appear infinitely often, while others can only appear a finite number of times (if at all). The former are referred to as recurrent configurations, while the latter are referred to as transient configurations. The recurrent configurations thereby consist of all stable non-negative configurations which can be reached from any other stable configuration by repeatedly adding grains of sand to vertices and toppling. It is easy to see that the minimally stable configuration z m {\\displaystyle z_{m}} , where every vertex carries z m ( v ) = d e g ( v ) \u2212 1 {\\displaystyle z_{m}(v)=deg(v)-1} grains of sand, is reachable from any other stable configuration (add d e g ( v ) \u2212 z ( v ) \u2212 1 \u2265 0 {\\displaystyle deg(v)-z(v)-1\\geq 0} grains to every vertex).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Kenkichi Iwasawa (1941) proved that a p-group G is an Iwasawa group if and only if one of the following cases happens: G is a Dedekind group, or G contains an abelian normal subgroup N such that the quotient group G/N is a cyclic group and if q denotes a generator of G/N, then for all n \u2208 N, q\u22121nq = n1+ps where s \u2265 1 in general, but s \u2265 2 for p=2.In Berkovich & Janko (2008, p. 257), Iwasawa's proof was deemed to have essential gaps, which were filled by Franco Napolitani and Zvonimir Janko. Roland Schmidt (1994) has provided an alternative proof along different lines in his textbook.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, there are a wide rarity of methods that are utilized, most of which are reconstruct 3-D information (volume) from 2-D signals (image). Typically used methods are CT, MRI, PET and SPECT. And the filtered back projection based on the principles introduced above are commonly applied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational database management systems, a user-defined function provides a mechanism for extending the functionality of the database server by adding a function, that can be evaluated in standard query language (usually SQL) statements. The SQL standard distinguishes between scalar and table functions. A scalar function returns only a single value (or NULL), whereas a table function returns a (relational) table comprising zero or more rows, each row with one or more columns. User-defined functions in SQL are declared using the CREATE FUNCTION statement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, for AES with a 256-bit key, K {\\displaystyle K} is a 256-bit number and F {\\displaystyle F} is a 128-bit number. Encrypting block P {\\displaystyle P} with logical index (tweak) I {\\displaystyle I} uses the following formula: X = F \u2297 I , C = E K ( P \u2295 X ) \u2295 X . {\\displaystyle {\\begin{aligned}X&=F\\otimes I,\\\\C&=E_{K}(P\\oplus X)\\oplus X.\\end{aligned}}} Here multiplication \u2297 {\\displaystyle \\otimes } and addition \u2295 {\\displaystyle \\oplus } are performed in the finite field ( GF ( 2 128 ) {\\displaystyle {\\text{GF}}\\left(2^{128}\\right)} for AES).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The solution corresponding to the original constrained optimization is always a saddle point of the Lagrangian function, which can be identified among the stationary points from the definiteness of the bordered Hessian matrix.The great advantage of this method is that it allows the optimization to be solved without explicit parameterization in terms of the constraints. As a result, the method of Lagrange multipliers is widely used to solve challenging constrained optimization problems. Further, the method of Lagrange multipliers is generalized by the Karush\u2013Kuhn\u2013Tucker conditions, which can also take into account inequality constraints of the form h ( x ) \u2264 c {\\displaystyle h(\\mathbf {x} )\\leq c} for a given constant c {\\displaystyle c~} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In synchronous duplex mode of operation hardware coupling is provided between two processors which execute same set of instructions and compare the results continuously. If mismatch occurs then the faulty processor is identified and taken out of service within a few milliseconds. When system is operating normally, the two processors have same data in memories at all times and simultaneously receive information from exchange environment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedness, which allows distinguishing a circle from two non-intersecting circles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is especially useful when dealing with the semantics of different side effects, such as nontermination, mutable state or nondeterminism. Instead of giving two variants of the semantics, one for the call-by-name evaluation order and one for the call-by-value one, one can simply give a semantics for the CBPV term language; one gets two semantics for lambda-calculus by composing this CBPV semantics with the same CBV and CBN translations from lambda-calculus. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One way to construct a family of sets with these parameters, each two sharing an element, is to choose a single element to belong to all the subsets, and then form all of the subsets that contain the chosen element. The Erd\u0151s\u2013Ko\u2013Rado theorem states that when n {\\displaystyle n} is large enough for the problem to be nontrivial ( n \u2265 2 r {\\displaystyle n\\geq 2r} ) this construction produces the largest possible intersecting families.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, many arithmetic functions are integer-valued.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Lucas\u2013Carmichael number is a positive composite integer n such that if p is a prime factor of n, then p + 1 is a factor of n + 1; n is odd and square-free.The first condition resembles the Korselt's criterion for Carmichael numbers, where -1 is replaced with +1. The second condition eliminates from consideration some trivial cases like cubes of prime numbers, such as 8 or 27, which otherwise would be Lucas\u2013Carmichael numbers (since n3 + 1 = (n + 1)(n2 \u2212 n + 1) is always divisible by n + 1). They are named after \u00c9douard Lucas and Robert Carmichael.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psychology, data collection often relies on samples drawn from Western, Educated, Industrialized, Rich and Democratic (WEIRD) populations, which impedes the overall generalizability of findings. Crowdsourcing the data collection process by relying on multi-lab data collection and online crowdsourcing platforms (e.g., Amazon Mechanical Turk, Prolific) makes it easier to reach a wider audience of participants from different cultural backgrounds and non-WEIRD populations. When the research question makes it possible to rely on internet samples, it is also an easy way to recruit larger samples of participants with minimal financial input and within short amounts of time.Most of the time, members of the general public are recruited to undergo studies as research participants but they can also be recruited to collect data and observations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the character sets developed for computing, each upper- and lower-case letter is encoded as a separate character. In order to enable case folding and case conversion, the software needs to link together the two characters representing the case variants of a letter. (Some old character-encoding systems, such as the Baudot code, are restricted to one set of letters, usually represented by the upper-case variants.) Case-insensitive operations can be said to fold case, from the idea of folding the character code table so that upper- and lower-case letters coincide.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example, there is a common Swedish surname \u00c5str\u00f6m written in the two alternative methods, the first one with a precomposed \u00c5 (U+00C5) and \u00f6 (U+00F6), and the second one using a decomposed base letter A (U+0041) with a combining ring above (U+030A) and an o (U+006F) with a combining diaeresis (U+0308). \u00c5str\u00f6m (U+00C5 U+0073 U+0074 U+0072 U+00F6 U+006D) \u00c5str\u00f6m (U+0041 U+030A U+0073 U+0074 U+0072 U+006F U+0308 U+006D)Except for the different colors, the two solutions are equivalent and should render identically. In practice, however, some Unicode implementations still have difficulties with decomposed characters. In the worst case, combining diacritics may be disregarded or rendered as unrecognized characters after their base letters, as they are not included in all fonts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Jackson and Mr C.B. Thompson. Proper time studies are based on repeated observation, so that motions performed on the same part differently by one or many workers can be recorded, to determine those values that are truly repetitive and measurable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This discrete problem may be ill-conditioned, depending on the original problem and the chosen quadrature rule. Since the linear equations require O ( n 3 ) {\\displaystyle O(n^{3})} operations to solve, high-order quadrature rules perform better because low-order quadrature rules require large n {\\displaystyle n} for a given accuracy. Gaussian quadrature is normally a good choice for smooth, non-singular problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "6. Evaluation and visualization Finally, the clustering models can be assessed by various metrics. And it is sometimes helpful to visualize the results by plotting the clusters into low (two) dimensional space. See multidimensional scaling as a possible approach.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems, assuming intelligence is computational, is equivalent to that of solving the central artificial intelligence problem\u2014making computers as intelligent as people, or strong AI. To call a problem AI-complete reflects an attitude that it would not be solved by a simple specific algorithm. AI-complete problems are hypothesised to include computer vision, natural language understanding, and dealing with unexpected circumstances while solving any real-world problem.Currently, AI-complete problems cannot be solved with modern computer technology alone, but would also require human computation. This property could be useful, for example, to test for the presence of humans as CAPTCHAs aim to do, and for computer security to circumvent brute-force attacks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is to say, when one or more values are missing for a case, most statistical packages default to discarding any case that has a missing value, which may introduce bias or affect the representativeness of the results. Imputation preserves all cases by replacing missing data with an estimated value based on other available information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where R X = 3 {\\displaystyle R_{X}=3} and R Y = 7 {\\displaystyle R_{Y}=7} , the length of an input variable y {\\displaystyle \\mathbf {y} } from source Y {\\displaystyle Y} is 7 bits, therefore it can be sent lossless with 7 bits independent of any other bits. Based on the knowledge that x {\\displaystyle \\mathbf {x} } and y {\\displaystyle \\mathbf {y} } have Hamming distance at most one, for input x {\\displaystyle \\mathbf {x} } from source X {\\displaystyle X} , since the receiver already has y {\\displaystyle \\mathbf {y} } , the only possible x {\\displaystyle \\mathbf {x} } are those with at most 1 distance from y {\\displaystyle \\mathbf {y} } . If we model the correlation between two sources as a virtual channel, which has input x {\\displaystyle \\mathbf {x} } and output y {\\displaystyle \\mathbf {y} } , as long as we get y {\\displaystyle \\mathbf {y} } , all we need to successfully \"decode\" x {\\displaystyle \\mathbf {x} } is \"parity bits\" with particular error correction ability, taking the difference between x {\\displaystyle \\mathbf {x} } and y {\\displaystyle \\mathbf {y} } as channel error. We can also model the problem with cosets partition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In symmetric pairing-based cryptography the group G {\\displaystyle G} is equipped with a pairing e: G \u00d7 G \u2192 T {\\displaystyle e:G\\times G\\to T} which is bilinear. This map gives an efficient algorithm to solve the decisional Diffie-Hellman problem. Given input ( g , g a , g b , h ) {\\displaystyle (g,\\,g^{a},\\,g^{b},\\,h)} , it is easy to check if h {\\displaystyle h} is equal to g a b {\\displaystyle g^{ab}} . This follows by using the pairing: note that e ( g a , g b ) = e ( g , g ) a b = e ( g , g a b ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The goal may be to visualize such data by points in Euclidean space whose distance matrix approximates a given dissimilarity matrix as well as possible \u2014 this is known as multidimensional scaling. Alternatively, given two sets of data already represented by points in Euclidean space, one may ask how similar they are in shape, that is, how closely can they be related by a distance-preserving transformation \u2014 this is Procrustes analysis. Some of the distances may also be missing or come unlabelled (as an unordered set or multiset instead of a matrix), leading to more complex algorithmic tasks, such as the graph realization problem or the turnpike problem (for points on a line).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of linguistics, the term passive is applied to a wide range of grammatical structures. Linguists therefore find it difficult to define the term in a way that makes sense across all human languages. The canonical passive in European languages has the following properties: The subject is not an agent. There is a change in: word order; or in nominal morphology\u2014the form of the nouns in the sentence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. The adjacency matrix of a simple undirected graph is a real symmetric matrix and is therefore orthogonally diagonalizable; its eigenvalues are real algebraic integers. While the adjacency matrix depends on the vertex labeling, its spectrum is a graph invariant, although not a complete one. Spectral graph theory is also concerned with graph parameters that are defined via multiplicities of eigenvalues of matrices associated to the graph, such as the Colin de Verdi\u00e8re number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Dirac representation, the four contravariant gamma matrices are \u03b3 0 = ( 1 0 0 0 0 1 0 0 0 0 \u2212 1 0 0 0 0 \u2212 1 ) , \u03b3 1 = ( 0 0 0 1 0 0 1 0 0 \u2212 1 0 0 \u2212 1 0 0 0 ) , \u03b3 2 = ( 0 0 0 \u2212 i 0 0 i 0 0 i 0 0 \u2212 i 0 0 0 ) , \u03b3 3 = ( 0 0 1 0 0 0 0 \u2212 1 \u2212 1 0 0 0 0 1 0 0 ) . {\\displaystyle {\\begin{aligned}\\gamma ^{0}&={\\begin{pmatrix}1&0&0&0\\\\0&1&0&0\\\\0&0&-1&0\\\\0&0&0&-1\\end{pmatrix}},&\\gamma ^{1}&={\\begin{pmatrix}0&0&0&1\\\\0&0&1&0\\\\0&-1&0&0\\\\-1&0&0&0\\end{pmatrix}},\\\\\\\\\\gamma ^{2}&={\\begin{pmatrix}0&0&0&-i\\\\0&0&i&0\\\\0&i&0&0\\\\-i&0&0&0\\end{pmatrix}},&\\gamma ^{3}&={\\begin{pmatrix}0&0&1&0\\\\0&0&0&-1\\\\-1&0&0&0\\\\0&1&0&0\\end{pmatrix}}~.\\end{aligned}}} \u03b3 0 {\\displaystyle \\gamma ^{0}} is the time-like, Hermitian matrix. The other three are space-like, anti-Hermitian matrices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering and mathematics, numerical error is the error in the numerical computations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a consequence, the cardinality of the real numbers, which is the same as that of the power set of the integers, is strictly larger than the cardinality of the integers; see Cardinality of the continuum for details. The theorem is named for German mathematician Georg Cantor, who first stated and proved it at the end of the 19th century.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the reflexive closure of a binary relation R {\\displaystyle R} on a set X {\\displaystyle X} is the smallest reflexive relation on X {\\displaystyle X} that contains R . {\\displaystyle R.} A relation is called reflexive if it relates every element of X {\\displaystyle X} to itself. For example, if X {\\displaystyle X} is a set of distinct numbers and x R y {\\displaystyle xRy} means \" x {\\displaystyle x} is less than y {\\displaystyle y} \", then the reflexive closure of R {\\displaystyle R} is the relation \" x {\\displaystyle x} is less than or equal to y {\\displaystyle y} \".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that the bit b i {\\displaystyle b_{i}} is what decides which basis a i {\\displaystyle a_{i}} is encoded in (either in the computational basis or the Hadamard basis). The qubits are now in states which are not mutually orthogonal, and thus it is impossible to distinguish all of them with certainty without knowing b {\\displaystyle b} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As the names of these two tests implies, destructive testing will destroy the part that is being tested while nondestructive testing enables the test piece to be used afterwards. There are several methods available in each of these types. This section outlines some requirements of testing plastic welds as well as the different types of destructive and non-destructive methods that are applicable to plastic welding and go over some of the advantages and disadvantages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In addition: Rule A2 does not perform any reduction on its own. However, it is still useful, because of its \"shuffling\" effect that can create new opportunities for applying the other rules; Rule A1 is not used in practice, because it may increase proof size; Rules B1, B2, B2' and B3 are directly responsible for the reduction, as they produce a transformed root clause stronger than the original one; The application of a B rule may lead to an illegal proof (see the example below), as some literals missing in the transformed root clause may be involved in another resolution step along the path to the proof root. Therefore, the algorithm also has to \"reconstruct\" a legal proof when this happen.The following example shows a situation where the proof becomes illegal after the application of B2' rule: Applying rule B2' to the highlighted context: The proof is now illegal because the literal o {\\displaystyle o} is missing from the transformed root clause.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some early DSP and RISC processors, the documentation advises programmers to avoid such dependencies in adjacent and nearly adjacent instructions (called delay slots), or declares that the second instruction uses an old value rather than the desired value (in the example above, the processor might counter-intuitively copy the unincremented value), or declares that the value it uses is undefined. The programmer may have unrelated work that the processor can do in the meantime; or, to ensure correct results, the programmer may insert NOPs into the code, partly negating the advantages of pipelining.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Further, the single pass aspect slowed or prevented getting the compiler bootstrapped out of Z80 assembly language and onto Pascal itself. Since the compiler was monolithic, the conversion to Pascal could not be done one section at a time, but had to proceed as a wholesale replacement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If one also assumes the Axiom of Choice, then all sets can be enumerated so that it coincides up to relabeling with the most general form of enumerations. Since set theorists work with infinite sets of arbitrarily large cardinalities, the default definition among this group of mathematicians of an enumeration of a set tends to be any arbitrary \u03b1-sequence exactly listing all of its elements. Indeed, in Jech's book, which is a common reference for set theorists, an enumeration is defined to be exactly this. Therefore, in order to avoid ambiguity, one may use the term finitely enumerable or denumerable to denote one of the corresponding types of distinguished countable enumerations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spring 2008 Nokia introduced a built in SIP VoIP client for the very first time to the mass market device (Nokia 6300i) running Series 40 operating system. Later that year (Nokia 6260 Slide was introduced introducing slightly updated SIP VoIP client. Nokia maintains a list of all phones that have an integrated VoIP client in Forum Nokia.Aircell's battle with some companies allowing VoIP calls on flights is another example of the growing conflict of interest between incumbent operators and new VoIP operators.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing models, a discipline within the mathematical theory of probability, the quasi-birth\u2013death process describes a generalisation of the birth\u2013death process. : 118 As with the birth-death process it moves up and down between levels one at a time, but the time between these transitions can have a more complicated distribution encoded in the blocks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real-life data, particularly for large datasets, the notions of rough approximations were found to be excessively restrictive. Therefore, an extension of DRSA, based on stochastic model (Stochastic DRSA), which allows inconsistencies to some degree, has been introduced. Having stated the probabilistic model for ordinal classification problems with monotonicity constraints, the concepts of lower approximations are extended to the stochastic case. The method is based on estimating the conditional probabilities using the nonparametric maximum likelihood method which leads to the problem of isotonic regression. Stochastic dominance-based rough sets can also be regarded as a sort of variable-consistency model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a scan statistic or window statistic is a problem relating to the clustering of randomly positioned points. An example of a typical problem is the maximum size of a cluster of points on a line or the longest series of successes recorded by a moving window of fixed length.Joseph Naus first published on the problem in the 1960s, and has been called the \"father of the scan statistic\" in honour of his early contributions. The results can be applied in epidemiology, public health and astronomy to find unusual clusters of events.It was extended by Martin Kulldorff to multidimensional settings and varying window sizes in a 1997 paper, which is (as of 11 October 2015) the most cited article in its journal, Communications in Statistics \u2013 Theory and Methods. This work lead to the creation of the software SaTScan, a program trademarked by Martin Kulldorff that applies his methods to data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, formal methods are mathematical approaches to solving software (and hardware) problems at the requirements, specification, and design levels. Formal methods are most likely to be applied to safety-critical or security-critical software and systems, such as avionics software. Software safety assurance standards, such as DO-178C allows the usage of formal methods through supplementation, and Common Criteria mandates formal methods at the highest levels of categorization. For sequential software, examples of formal methods include the B-Method, the specification languages used in automated theorem proving, RAISE, and the Z notation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of coronals, the symbols \u27e8t, d\u27e9 are normally used for the stop portion of the affricate regardless of place. For example,  is commonly seen for . The exemplar languages are ones that have been reported to have these sounds, but in several cases, they may need confirmation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, L\u00f6b's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that \"if P is provable in PA then P is true\", then P is provable in PA. If Prov(P) means that the formula P is provable, we may express this more formally as If P A \u22a2 P r o v ( P ) \u2192 P {\\displaystyle {\\mathit {PA}}\\vdash {\\mathrm {Prov} (P)\\rightarrow P}} then P A \u22a2 P {\\displaystyle {\\mathit {PA}}\\vdash P} .An immediate corollary (the contrapositive) of L\u00f6b's theorem is that, if P is not provable in PA, then \"if P is provable in PA, then P is true\" is not provable in PA. For example, \"If 1 + 1 = 3 {\\displaystyle 1+1=3} is provable in PA, then 1 + 1 = 3 {\\displaystyle 1+1=3} \" is not provable in PA.L\u00f6b's theorem is named for Martin Hugo L\u00f6b, who formulated it in 1955. It is related to Curry's paradox.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such groups are elementarily equivalent to the integers ( Z , + , < ) {\\displaystyle (\\mathbb {Z} ,+,<)} . Z-groups are an alternative presentation of Presburger arithmetic. occasionally, (Z)-group is used to mean a Zassenhaus group, a special type of permutation group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The pixel X is predicted by the LOCO-I predictor according to the following guesses: X = { min ( A , B ) if C \u2265 max ( A , B ) max ( A , B ) if C \u2264 min ( A , B ) A + B \u2212 C otherwise . {\\displaystyle X=\\left\\{{\\begin{aligned}&\\min(A,B)\\quad \\,{\\mbox{if}}\\,C\\geq \\max(A,B)\\\\&\\max(A,B)\\quad {\\mbox{if}}\\,C\\leq \\min(A,B)\\\\&A+B-C\\quad \\,{\\mbox{otherwise}}.\\\\\\end{aligned}}\\right.} The three simple predictors are selected according to the following conditions: (1) it tends to pick B in cases where a vertical edge exists left of the X, (2) A in cases of an horizontal edge above X, or (3) A + B \u2013 C if no edge is detected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the era of rapid technology evolution, it is not the biggest that survives, but the fastest. The sooner the end product is delivered without major defects, the sooner feedback can be received, and incorporated into the next iteration. The shorter the iterations, the better the learning and communication within the team. With speed, decisions can be delayed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This problem was solved, with an algorithm, in the same original paper by Gale and Shapley, in which the stable marriage problem was solved.The hospitals/residents problem with couples allows the set of residents to include couples who must be assigned together, either to the same hospital or to a specific pair of hospitals chosen by the couple (e.g., a married couple want to ensure that they will stay together and not be stuck in programs that are far away from each other). The addition of couples to the hospitals/residents problem renders the problem NP-complete.The assignment problem seeks to find a matching in a weighted bipartite graph that has maximum weight.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational databases, a table can be a (mathematical) set or a multiset, depending on the presence of unicity constraints on some columns (which turns it into a candidate key). SQL allows the selection of rows from a relational table: this operation will in general yield a multiset, unless the keyword DISTINCT is used to force the rows to be all different, or the selection includes the primary (or a candidate) key. In ANSI SQL the MULTISET keyword can be used to transform a subquery into a collection expression: is a general select that can be used as subquery expression of another more general query, while transforms the subquery into a collection expression that can be used in another query, or in assignment to a column of appropriate collection type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, cluster sampling is a sampling plan used when mutually homogeneous yet internally heterogeneous groupings are evident in a statistical population. It is often used in marketing research. In this sampling plan, the total population is divided into these groups (known as clusters) and a simple random sample of the groups is selected. The elements in each cluster are then sampled.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The symbol \"\u2248\" is also used for this purpose. In physics and astronomy, a tilde can be used between two expressions (e.g. h ~ 10\u221234 J s) to state that the two are of the same order of magnitude.In statistics and probability theory, the tilde means \"is distributed as\"; see random variable(e.g. X ~ B(n,p) for a binomial distribution). A tilde can also be used to represent geometric similarity (e.g. \u2206ABC ~ \u2206DEF, meaning triangle ABC is similar to DEF).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the surgery structure set S ( X ) {\\displaystyle {\\mathcal {S}}(X)} is the basic object in the study of manifolds which are homotopy equivalent to a closed manifold X. It is a concept which helps to answer the question whether two homotopy equivalent manifolds are diffeomorphic (or PL-homeomorphic or homeomorphic). There are different versions of the structure set depending on the category (DIFF, PL or TOP) and whether Whitehead torsion is taken into account or not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If two of these symbols are used, one on the left and the mirror image of it on the right, it almost always indicates a set, as in { a , b , c } {\\displaystyle \\{a,b,c\\}} , the set containing three members, a {\\displaystyle a} , b {\\displaystyle b} , and c {\\displaystyle c} . But if it is used only on the left, it groups two or more simultaneous equations. There are other symbols of grouping.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 80386 microprocessor and later, virtual 8086 mode (also called virtual real mode, V86-mode, or VM86) allows the execution of real mode applications that are incapable of running directly in protected mode while the processor is running a protected mode operating system. It is a hardware virtualization technique that allowed multiple 8086 processors to be emulated by the 386 chip. It emerged from the painful experiences with the 80286 protected mode, which by itself was not suitable to run concurrent real-mode applications well. John Crawford developed the Virtual Mode bit at the register set, paving the way to this environment.VM86 mode uses a segmentation scheme identical to that of real mode (for compatibility reasons), which creates 20-bit linear addresses in the same manner as 20-bit physical addresses are created in real mode, but are subject to protected mode's memory paging mechanism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to prevent Intel x86-specific code from slipping into the operating system, due to developers being used to developing on x86 chips, Windows NT 3.1 was initially developed using non-x86 development systems and then ported to the x86 architecture. This work was initially based on the Intel i860-based Dazzle system and, later, the MIPS R4000-based Jazz platform. Both systems were designed internally at Microsoft.Windows NT 3.1 was released for Intel x86 PC compatible, PC-98, DEC Alpha, and ARC-compliant MIPS platforms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In n-dimensional Euclidean space over the real numbers, R n {\\displaystyle \\mathbb {R} ^{n}} , the standard basis is denoted e1, e2, e3, ... en. Each basis vector ei points along the positive xi axis, with the basis being orthonormal. Component j of ei is given by the Kronecker delta: A vector in R n {\\displaystyle \\mathbb {R} ^{n}} takes the form: Similarly for the order-2 tensor above, for each vector a and b in R n {\\displaystyle \\mathbb {R} ^{n}}: or more generally:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Mathematical theorems are known about combinations of relation properties, such as \"A transitive relation is irreflexive if, and only if, it is asymmetric\". Of particular importance are relations that satisfy certain combinations of properties. A partial order is a relation that is reflexive, antisymmetric, and transitive, an equivalence relation is a relation that is reflexive, symmetric, and transitive, a function is a relation that is right-unique and left-total (see below).Since relations are sets, they can be manipulated using set operations, including union, intersection, and complementation, and satisfying the laws of an algebra of sets. Beyond that, operations like the converse of a relation and the composition of relations are available, satisfying the laws of a calculus of relations.The above concept of relation has been generalized to admit relations between members of two different sets (heterogeneous relation, like \"lies on\" between the set of all points and that of all lines in geometry), relations between three or more sets (Finitary relation, like \"person x lives in town y at time z\"), and relations between classes (like \"is an element of\" on the class of all sets, see Binary relation \u00a7 Sets versus classes).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1960s Peter Swinnerton-Dyer used the EDSAC-2 computer at the University of Cambridge Computer Laboratory to calculate the number of points modulo p (denoted by Np) for a large number of primes p on elliptic curves whose rank was known. From these numerical results Birch & Swinnerton-Dyer (1965) conjectured that Np for a curve E with rank r obeys an asymptotic law \u220f p \u2264 x N p p \u2248 C log \u2061 ( x ) r as x \u2192 \u221e {\\displaystyle \\prod _{p\\leq x}{\\frac {N_{p}}{p}}\\approx C\\log(x)^{r}{\\mbox{ as }}x\\rightarrow \\infty } where C is a constant. Initially this was based on somewhat tenuous trends in graphical plots; this induced a measure of skepticism in J. W. S. Cassels (Birch's Ph.D.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is easy to find an initial solution that visits all the cities but will likely be very poor compared to the optimal solution. The algorithm starts with such a solution and makes small improvements to it, such as switching the order in which two cities are visited. Eventually, a much shorter route is likely to be obtained.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mid-1822 Hamilton began a systematic study of Laplace's M\u00e9canique C\u00e9leste. In November and December 1822 he completed his first three original mathematical papers. On his first visit to Dunsink Observatory, he showed two of them to Brinkley, who asked for a more developed form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relation to the 2016 United States presidential election, individuals associated with online message boards, such as 4chan, noted a similarity between Kek and the character Pepe the Frog. This was later paired with images of Pepe, resulting in a resurgence of interest in the ancient deity.Believers in Kek say that repeating integers, often called \u201cdubs\u201d, are the prima materia of reality, and that their occurrence invoke the deity. Elon Musk has made numerous references to Pepe and even to kek, among others within the perceived Illuminati such as Donald Trump, who tweeted himself as a version of the frog. Believers have cited this as evidence of memetic synchronicity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Darmon\u2013Granville theorem uses Faltings's theorem to show that for every specific choice of exponents (x, y, z), there are at most finitely many coprime solutions for (A, B, C). : p.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Together with K.-M. Chung, D. Schuch, W. Ulmer and B. Zeiger a unified understanding of molecular interactions was developed based on a nonlinear Schr\u00f6dinger equation. Hartmann thereby pioneered the discovery of one self-interacting field as the foundation of chemistry. H. Hartman emerited in 1982 and died two years later. H. Hartmann was honoured as member of the Deutsche Akademie der Naturforscher Leopoldina, the Gesellschaft \u00d6sterreichischer Chemiker, the Accademia Nazionale die Lincei, the Royal Danish Academy of Sciences and Letters, the Comitato Premio of Fondazione Balzan, the International Academy of Quantum Molecular Science, and the Akademie der Wissenschaften und der Literatur zu Mainz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by Ren\u00e9 Descartes (1637), Robert Hooke (1665), and Christiaan Huygens (1678); however, particle models remained dominant, chiefly due to the influence of Isaac Newton. In the early 19th century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light, and by 1850 wave models were generally accepted. James Clerk Maxwell's 1865 prediction that light was an electromagnetic wave \u2013 which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves \u2013 seemed to be the final blow to particle models of light.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a linear normalization, the weight t i {\\displaystyle t_{i}} of a descriptor is mapped to a size scale of 1 through f, where t min {\\displaystyle t_{\\min }} and t max {\\displaystyle t_{\\max }} are specifying the range of available weights. s i = \u2308 f max \u22c5 ( t i \u2212 t min ) t max \u2212 t min \u2309 {\\displaystyle s_{i}=\\left\\lceil {\\frac {f_{\\max }\\cdot (t_{i}-t_{\\min })}{t_{\\max }-t_{\\min }}}\\right\\rceil } for t i > t min {\\displaystyle t_{i}>t_{\\min }} ; else s i = 1 {\\displaystyle s_{i}=1} s i {\\displaystyle s_{i}}: display fontsize f max {\\displaystyle f_{\\max }}: max. fontsize t i {\\displaystyle t_{i}}: count t min {\\displaystyle t_{\\min }}: min.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a factorion in a given number base b {\\displaystyle b} is a natural number that equals the sum of the factorials of its digits. The name factorion was coined by the author Clifford A. Pickover.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consider a class that contains the following procedure to print a string on standard output after a new line: The following snippet, assumed to be in the same class, uses print_on_new_line to demonstrate the mixing of open arguments and open targets in agents used as arguments to the same routine. This example uses the procedure do_all for linear structures, which executes the routine modeled by an agent for each item in the structure. The sequence of three instructions prints the strings in my_list, converts the strings to lowercase, and then prints them again. Procedure do_all iterates across the structure executing the routine substituting the current item for either the open argument (in the case of the agents based on print_on_new_line), or the open target (in the case of the agent based on to_lower). Open and closed arguments and targets also allow the use of routines that call for more arguments than are required by closing all but the necessary number of arguments: The Eiffel agent mechanism is detailed in the Eiffel ISO/ECMA standard document.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was introduced by Gottlob Frege, developed by Moses Sch\u00f6nfinkel, and further developed by Haskell Curry.Uncurrying is the dual transformation to currying, and can be seen as a form of defunctionalization. It takes a function f {\\displaystyle f} whose return value is another function g {\\displaystyle g} , and yields a new function f \u2032 {\\displaystyle f'} that takes as parameters the arguments for both f {\\displaystyle f} and g {\\displaystyle g} , and returns, as a result, the application of f {\\displaystyle f} and subsequently, g {\\displaystyle g} , to those arguments. The process can be iterated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, an adversarial queueing network is a model where the traffic to the network is supplied by an opponent rather than as the result of a stochastic process. The model has seen use in describing the impact of packet injections on the performance of communication networks. The model was first introduced in 1996.The stability of an adversarial queueing network can be determined by considering a fluid limit. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each base station is adapted to communicate over a radio link with at least one user's mobile station located within the radio range of said base station. The advantage is that the equipment for WiFi, 5G and other protocols can be centralized in one place, with remote antennas attached via fiber optic serving all protocols. It greatly reduces the equipment and maintenance cost of the network.RoF technology enables convergence of fixed and mobile networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Plan 9 operating system from Bell Labs (mid-1980s onward), union mounting is a central concept, replacing several older Unix conventions with union directories; for example, several directories containing executables, unioned together at a single /bin directory, replace the PATH variable for command lookup in the shell.Plan 9 union semantics are greatly simplified compared to the implementations for POSIX-style operating systems: the union of two directories is simply the concatenation of their contents, so a directory listing of the union may display duplicate names. Also, no effort is made to recursively merge subdirectories, leading to an extremely simple implementation. Directories are unioned in a controllable order; u/name, where u is a union directory, denotes the file called name in the first constituent directory that contains such a file.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a monogenic semigroup is a semigroup generated by a single element. Monogenic semigroups are also called cyclic semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, sentence embedding has seen a growing level of interest due to its applications in natural language queryable knowledge bases through the usage of vector indexing for semantic search. LangChain for instance utilizes sentence transformers for purposes of indexing documents. In particular, an indexing is generated by generating embeddings for chunks of documents and storing (document chunk, embedding) tuples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a fact is a statement (called a theorem) that can be proven by logical argument from certain axioms and definitions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Unlike stochastic independence and uncorrelatedness, mean independence is not symmetric: it is possible for Y {\\displaystyle Y} to be mean-independent of X {\\displaystyle X} even though X {\\displaystyle X} is mean-dependent on Y {\\displaystyle Y} . The concept of mean independence is often used in econometrics to have a middle ground between the strong assumption of independent random variables ( X 1 \u22a5 X 2 {\\displaystyle X_{1}\\perp X_{2}} ) and the weak assumption of uncorrelated random variables ( Cov \u2061 ( X 1 , X 2 ) = 0 ) . {\\displaystyle (\\operatorname {Cov} (X_{1},X_{2})=0).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, many sequences of numbers or of polynomials are indexed by nonnegative integers, for example, the Bernoulli numbers and the Bell numbers. In both mechanics and statistics, the zeroth moment is defined, representing total mass in the case of physical density, or total probability, i.e. one, for a probability distribution. The zeroth law of thermodynamics was formulated after the first, second, and third laws, but considered more fundamental, thus its name. In biology, an organism is said to have zero-order intentionality if it shows \"no intention of anything at all\". This would include a situation where the organism's genetically predetermined phenotype results in a fitness benefit to itself, because it did not \"intend\" to express its genes. In the similar sense, a computer may be considered from this perspective a zero-order intentional entity, as it does not \"intend\" to express the code of the programs it runs.In biological or medical experiments, initial measurements made before any experimental time has passed are said to be on the 0 day of the experiment.In genomics, both 0-based and 1-based systems are used for genome coordinates.Patient zero (or index case) is the initial patient in the population sample of an epidemiological investigation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics, the softargmax function is known as the Boltzmann distribution (or Gibbs distribution):: 7 the index set 1 , \u2026 , k {\\displaystyle {1,\\,\\dots ,\\,k}} are the microstates of the system; the inputs z i {\\displaystyle z_{i}} are the energies of that state; the denominator is known as the partition function, often denoted by Z; and the factor \u03b2 is called the coldness (or thermodynamic beta, or inverse temperature).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in abstract algebra, a semigroup with involution or a *-semigroup is a semigroup equipped with an involutive anti-automorphism, which\u2014roughly speaking\u2014brings it closer to a group because this involution, considered as unary operator, exhibits certain fundamental properties of the operation of taking the inverse in a group: uniqueness, double application \"cancelling itself out\", and the same interaction law with the binary operation as in the case of the group inverse. It is thus not a surprise that any group is a semigroup with involution. However, there are significant natural examples of semigroups with involution that are not groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Newton's identities, also known as the Girard\u2013Newton formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials. Evaluated at the roots of a monic polynomial P in one variable, they allow expressing the sums of the k-th powers of all roots of P (counted with their multiplicity) in terms of the coefficients of P, without actually finding those roots. These identities were found by Isaac Newton around 1666, apparently in ignorance of earlier work (1629) by Albert Girard. They have applications in many areas of mathematics, including Galois theory, invariant theory, group theory, combinatorics, as well as further applications outside mathematics, including general relativity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to speak to larger groups of people, a need arose to increase the volume of the human voice. The earliest devices used to achieve this were acoustic megaphones. Some of the first examples, from fifth-century-BC Greece, were theater masks with horn-shaped mouth openings that acoustically amplified the voice of actors in amphitheaters. In 1665, the English physicist Robert Hooke was the first to experiment with a medium other than air with the invention of the \"lovers' telephone\" made of stretched wire with a cup attached at each end.In 1856, Italian inventor Antonio Meucci developed a dynamic microphone based on the generation of electric current by moving a coil of wire to various depths in a magnetic field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On x86-64 processors in native long mode, the address translation scheme uses PAE but adds a fourth table, the 512-entry page-map level 4 table, and extends the page directory pointer table to 512 entries instead of the original 4 entries it has in protected mode. This means that 48 bits of virtual page number are translated, giving a virtual address space of up to 256 TB. For some processors, a mode can be enabled with a fifth table, the 512-entry page-map level 5 table; this means that 57 bits of virtual page number are translated, giving a virtual address space of up to 128 PB. : 141\u2013153 In the page table entries, in the original specification, 40 bits of physical page number are implemented. Page table structures", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they form a natural generalization of Stone's representation theorem for Boolean algebras. These concepts are named in honor of Marshall Stone. Stone-type dualities also provide the foundation for pointless topology and are exploited in theoretical computer science for the study of formal semantics. This article gives pointers to special cases of Stone duality and explains a very general instance thereof in detail.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Except for certain logical issues, in this case CbD specializes to traditional treatments of contextuality in quantum physics. In particular, for consistently connected cyclic systems the noncontextuality criterion above reduces to D ( C n ) \u2264 n \u2212 2 , {\\displaystyle D\\left({\\mathcal {C}}_{n}\\right)\\leq n-2,} which includes the Bell/CHSH inequality ( n = 4 {\\displaystyle n=4} ), KCBS inequality ( n = 5 {\\displaystyle n=5} ), and other famous inequalities. That nonlocality is a special case of contextuality follows in CbD from the fact that being jointly distributed for random variables is equivalent to being measurable functions of one and the same random variable (this generalizes Arthur Fine's analysis of Bell's theorem).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, all powers of three are perfect totient numbers. The sums of distinct powers of three form a Stanley sequence, the lexicographically smallest sequence that does not contain an arithmetic progression of three elements. A conjecture of Paul Erd\u0151s states that this sequence contains no powers of two other than 1, 4, and 256.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Multicast Dissemination Protocol (MDP) was an initial attempt to ensure reliability and to address the problem of ACK implosions through the use of NACKs. MDP used selective negative acknowledgement (NACK) to support reliability. Additionally, MDP implemented probabilistic techniques to suppress redundant NACKs in the multicast group (and thereby avoid NACK implosions).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The SCP responds with a geographic number, e.g. 0121 XXX XXXX, and the call is actually routed to a phone. By this architecture: 08XXX (non-geographic numbers) can be set up in a few SCP nodes rather than having to be set up in every telephone exchange in the country. geographic numbers can be hidden revenue can be generated by non-telecoms companies from people making telephone calls to services \u2013 e.g. telephone voting", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One of the first system calls made by the C standard I/O library is in an isatty() call used to determine if the program is being run interactively by a human (in which case isatty() will succeed and the library will write its output a line at a time so the user sees a regular flow of text) or as part of a pipeline (in which case it writes a block at a time for efficiency). If a library routine fails for some reason unrelated to a system call (for example, because a user name wasn't found in the password file) and a na\u00efve programmer blindly calls the normal error reporting routine perror() on every failure, the leftover ENOTTY will result in an utterly inappropriate \"Not a typewriter\" (or \"Not a teletype\", or \"Inappropriate ioctl for device\") being delivered to the user. For many years the UNIX mail program sendmail contained this bug: when mail was delivered from another system, the mail program was being run non-interactively. If the destination address was local, but referred to a user name not found in the local password file, the message sent back to the originator of the email was the announcement that the person they were attempting to communicate with was not a typewriter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, finite field arithmetic is arithmetic in a finite field (a field containing a finite number of elements) contrary to arithmetic in a field with an infinite number of elements, like the field of rational numbers. There are infinitely many different finite fields. Their number of elements is necessarily of the form pn where p is a prime number and n is a positive integer, and two finite fields of the same size are isomorphic. The prime p is called the characteristic of the field, and the positive integer n is called the dimension of the field over its prime field. Finite fields are used in a variety of applications, including in classical coding theory in linear block codes such as BCH codes and Reed\u2013Solomon error correction, in cryptography algorithms such as the Rijndael (AES) encryption algorithm, in tournament scheduling, and in the design of experiments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function.The method can be summarized as follows: In order to find the maximum or minimum of a function f ( x ) {\\displaystyle f(x)} subjected to the equality constraint g ( x ) = 0 {\\displaystyle g(x)=0} , form the Lagrangian function, L ( x , \u03bb ) \u2261 f ( x ) + \u03bb \u22c5 g ( x ) {\\displaystyle {\\mathcal {L}}(x,\\lambda )\\equiv f(x)+\\lambda \\cdot g(x)} and find the stationary points of L {\\displaystyle {\\mathcal {L}}} considered as a function of x {\\displaystyle x} and the Lagrange multiplier \u03bb {\\displaystyle \\lambda ~} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to allow the system to work even with the high inter-unit latencies, each processor used an 8-deep instruction pipeline. Branches used a variable delay slot, the end of which was signaled by a bit in the next instruction. The bit indicated that the results of the branch had to be re-merged at this point, stalling the processor until this took place.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From the beginning, descriptively near sets have proved to be useful in applications of topology, and visual pattern recognition , spanning a broad spectrum of applications that include camouflage detection, micropaleontology, handwriting forgery detection, biomedical image analysis, content-based image retrieval, population dynamics, quotient topology, textile design, visual merchandising, and topological psychology. As an illustration of the degree of descriptive nearness between two sets, consider an example of the Henry colour model for varying degrees of nearness between sets of picture elements in pictures (see, e.g., \u00a74.3). The two pairs of ovals in Fig. 1 and Fig. 2 contain coloured segments. Each segment in the figures corresponds to an equivalence class where all pixels in the class have similar descriptions, i.e., picture elements with similar colours. The ovals in Fig.1 are closer to each other descriptively than the ovals in Fig. 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the Hamming distance measures the minimal number of substitutions needed, while the Levenshtein distance measures the minimal number of deletions, insertions, and substitutions; both of these can be thought of as distances in an appropriate graph. Graph edit distance is a measure of dissimilarity between two graphs, defined as the minimal number of graph edit operations required to transform one graph into another. Wasserstein metrics measure the distance between two measures on the same metric space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In ontologies designed to serve natural language processing (NLP) and natural language understanding (NLU) systems, ontology concepts are usually connected and symbolized by terms. This kind of connection represents a linguistic realization. Terms are words or a combination of words (multi-word units), in different languages, used to describe in natural language an element from reality, and hence connected to that formal ontology concept that frames this element in reality. The lexicon, the collection of terms and their inflections assigned to the concepts and relationships in an ontology, forms the \u2018ontology interface to natural language\u2019, the channel through which the ontology can be accessed from a natural language input.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model theory, a forking extension of a type is an extension of that type that is not free whereas a non-forking extension is an extension that is as free as possible. This can be used to extend the notions of linear or algebraic independence to stable theories. These concepts were introduced by S. Shelah.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Like ordinary categories, they contain objects (the 0-simplices of the simplicial set) and morphisms between these objects (1-simplices). But unlike categories, the composition of two morphisms need not be uniquely defined. All the morphisms that can serve as composition of two given morphisms are related to each other by higher order invertible morphisms (2-simplices thought of as \"homotopies\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In structural proof theory, the nested sequent calculus is a reformulation of the sequent calculus to allow deep inference. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases it may be desirable to add logic redundancy. One of those cases is to avoid race conditions whereby an output can fluctuate because different terms are \"racing\" to turn off and on. To explain this in more concrete terms the Karnaugh map to the right shows the minterms for the following function: f ( A , B , C , D ) = E ( 6 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ) . {\\displaystyle f(A,B,C,D)=E(6,8,9,10,11,12,13,14).\\ } The boxes represent the minimal AND/OR terms needed to implement this function: f = A C \u00af + A B \u00af + B C D \u00af .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases were checked by a computer program, not by hand. The shortest known proof of the four color theorem as of 2011 still has over 600 cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, kernel-independent component analysis (kernel ICA) is an efficient algorithm for independent component analysis which estimates source components by optimizing a generalized variance contrast function, which is based on representations in a reproducing kernel Hilbert space. Those contrast functions use the notion of mutual information as a measure of statistical independence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of actual computer processing, the principal steps are to 1) digitize the performed, analog music, 2) do successive short-term, fast Fourier transform (FFTs) to obtain the time-varying spectra, 3) identify the peaks in each spectrum, 4) analyze the spectral peaks to get pitch candidates, 5) connect the strongest individual pitch candidates to get the most likely time-varying, pitch contour, 6) map this physical data into the closest music-notation terms. These fundamental steps, originated by Piszczalski in the 1970s, became the foundation of automatic music transcription. The most controversial and difficult step in this process is detecting pitch . The most successful pitch methods operate in the frequency domain, not the time domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Fenchel's duality theorem is a result in the theory of convex functions named after Werner Fenchel. Let \u0192 be a proper convex function on Rn and let g be a proper concave function on Rn. Then, if regularity conditions are satisfied, inf x ( f ( x ) \u2212 g ( x ) ) = sup p ( g \u2217 ( p ) \u2212 f \u2217 ( p ) ) . {\\displaystyle \\inf _{x}(f(x)-g(x))=\\sup _{p}(g_{*}(p)-f^{*}(p)).} where \u0192 * is the convex conjugate of \u0192 (also referred to as the Fenchel\u2013Legendre transform) and g * is the concave conjugate of g. That is, f \u2217 ( x \u2217 ) := sup { \u27e8 x \u2217 , x \u27e9 \u2212 f ( x ) | x \u2208 R n } {\\displaystyle f^{*}\\left(x^{*}\\right):=\\sup \\left\\{\\left.\\left\\langle x^{*},x\\right\\rangle -f\\left(x\\right)\\right|x\\in \\mathbb {R} ^{n}\\right\\}} g \u2217 ( x \u2217 ) := inf { \u27e8 x \u2217 , x \u27e9 \u2212 g ( x ) | x \u2208 R n } {\\displaystyle g_{*}\\left(x^{*}\\right):=\\inf \\left\\{\\left.\\left\\langle x^{*},x\\right\\rangle -g\\left(x\\right)\\right|x\\in \\mathbb {R} ^{n}\\right\\}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of digital privacy, individual privacy is the notion that individuals have a right to exist freely on the internet, in that they can choose what type of information they are exposed to, and more importantly, that unwanted information should not interrupt them. An example of a digital breach of individual privacy would be an internet user receiving unwanted ads and emails/spam, or a computer virus that forces the user to take actions, which otherwise they would not. In such cases, the individual does not exist digitally without interruption from unwanted information; thus their individual privacy has been infringed upon.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to define a model structure on the category of simplicial sets, one has to define fibrations, cofibrations and weak equivalences. One can define fibrations to be Kan fibrations. A map of simplicial sets is defined to be a weak equivalence if its geometric realization is a weak homotopy equivalence of spaces. A map of simplicial sets is defined to be a cofibration if it is a monomorphism of simplicial sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a subring of R is a subset of a ring that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and which shares the same multiplicative identity as R. For those who define rings without requiring the existence of a multiplicative identity, a subring of R is just a subset of R that is a ring for the operations of R (this does imply it contains the additive identity of R). The latter gives a strictly weaker condition, even for rings that do have a multiplicative identity, so that for instance all ideals become subrings (and they may have a multiplicative identity that differs from the one of R). With definition requiring a multiplicative identity (which is used in this article), the only ideal of R that is a subring of R is R itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1990s, engineers at Japan's Hitachi found ways to compress the reduced instruction sets so they fit in even smaller memory systems than CISCs. Such compression schemes were used for the instruction set of their SuperH series of microprocessors, introduced in 1992. The SuperH instruction set was later adapted for ARM architecture's Thumb instruction set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These three people are the most commonly cited fastest typists in online typing communities. All of their records were set on the QWERTY keyboard layout.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bf6 f3 40. gxf3 exf3 41. Bxg5 Bxh3 42. Bf4+ 1\u20130", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "He identifies commitment as the distinguishing factor between desire and intention, noting that it leads to (1) temporal persistence in plans and (2) further plans being made on the basis of those to which it is already committed. The BDI software model partially addresses these issues. Temporal persistence, in the sense of explicit reference to time, is not explored.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is to be contrasted with principal component analysis which seeks to minimize the mean square error of all residuals. Before the advent of high-speed computers, considerable effort was devoted to finding approximate solutions to the problem, particularly in estimating the communalities by other means, which then simplifies the problem considerably by yielding a known reduced correlation matrix. This was then used to estimate the factors and the loadings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a real number is said to be simply normal in an integer base b if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b. A number is said to be normal in base b if, for every positive integer n, all possible strings n digits long have density b\u2212n. Intuitively, a number being simply normal means that no digit occurs more frequently than any other. If a number is normal, no finite combination of digits of a given length occurs more frequently than any other combination of the same length.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a semigroup with no elements (the empty semigroup) is a semigroup in which the underlying set is the empty set. Many authors do not admit the existence of such a semigroup. For them a semigroup is by definition a non-empty set together with an associative binary operation. However not all authors insist on the underlying set of a semigroup being non-empty.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s, Rump made an example. He made a complicated function and tried to obtain its value. Single precision, double precision, extended precision results seemed to be correct, but its plus-minus sign was different from the true value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The model is formulated in such a way that given X i {\\displaystyle X_{i}} , Y i {\\displaystyle Y_{i}} are independent (conditional independence of the observable variables given the Markov random field). In the vast majority of the related literature, the number of possible latent states is considered a user-defined constant. However, ideas from nonparametric Bayesian statistics, which allow for data-driven inference of the number of states, have been also recently investigated with success, e.g.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. An operation of arity two that involves several sets is sometimes also called a binary operation. For example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Such binary operations may be called simply binary functions. Binary operations are the keystone of most algebraic structures that are studied in algebra, in particular in semigroups, monoids, groups, rings, fields, and vector spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Mercury system, two series of rotors were used. The first series, dubbed the control maze, had four rotors, and stepped cyclometrically as in Typex. Five outputs from the control maze were used to determine the stepping of five rotors in the second series of rotors, the message maze, the latter used to encrypt and decrypt the plaintext and ciphertext. A sixth rotor in the message maze was controlled independently and stepped in the opposite direction to the others.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to improve the speed of floating-point division calculations on the Pentium chip over the 486DX, Intel opted to replace the shift-and-subtract division algorithm with the Sweeney, Robertson, and Tocher (SRT) algorithm. The SRT algorithm can generate two bits of the division result per clock cycle, whereas the 486's algorithm could only generate one. It is implemented using a programmable logic array with 2,048 cells, of which 1,066 cells should have been populated with one of five values: \u22122, \u22121, 0, +1, +2. When the original array for the Pentium was compiled, five values were not correctly downloaded into the equipment that etches the arrays into the chips \u2013 thus five of the array cells contained zero when they should have contained +2.As a result, calculations that rely on these five cells acquire errors; these errors can accumulate repeatedly owing to the recursive nature of the SRT algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many browser games became free to play in order to attract more visits. At the early age of smartphones, mobile games were paid to download because there was usually no interface for a smartphone to install a physical copy. Standardization and the ubiquity of mobile platforms that allowed for easy purchases by customers, brought on initially by the iPhone App Store and followed closely by the Android Marketplace and other competitors, resulted in a wide spread move towards microtransactions and indirect monetization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to grow their collections, music librarians purchase books and music reference materials, subscribe to serials, order music scores and sound recordings, and buy or license electronic resources. This involves not only contact with publishers and other agencies that provide music materials, but also budgetary management of library funds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To retain compatibility with the 7-bit representation, the behaviour of bytes 0xA0 and 0xFF was originally left undefined.The first C1 control code set to be registered for use with ISO 2022 was DIN 31626, a specialised set for bibliographic use which was registered in 1979. The general-use ISO/IEC 6429 set was registered in 1983, although the ECMA-48 specification upon which it was based had been first published in 1976.Further editions of the standards altered the provisions to an extent. For instance, a further revision to ECMA-35 and ISO 2022 in 1985 introduced the concept of a 96-code graphical character set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Selective retention \u2013 refers to the process of categorizing and interpreting information in a way that favors one category or interpretation over another. Furthermore, they just simply forget the unsympathetic material.Groups and group norms work as mediators.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the database system does not guarantee any ordering of the rows unless an ORDER BY clause is specified in the SELECT statement that queries the table. An equally valid representation of a relation is as an n-dimensional chart, where n is the number of attributes (a table's columns). For example, a relation with two attributes and three values can be represented as a table with two columns and three rows, or as a two-dimensional graph with three points. The table and graph representations are only equivalent if the ordering of rows is not significant, and the table has no duplicate rows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a fluid queue (fluid model, fluid flow model or stochastic fluid model) is a mathematical model used to describe the fluid level in a reservoir subject to randomly determined periods of filling and emptying. The term dam theory was used in earlier literature for these models. The model has been used to approximate discrete models, model the spread of wildfires, in ruin theory and to model high speed data networks. The model applies the leaky bucket algorithm to a stochastic source.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The hardware tracing modules (ETM and ETB) are compatible, but updated, versions of those used in the ARM9. In particular, trace semantics were updated to address parallel instruction execution and data transfers. ARM makes an effort to promote recommended Verilog coding styles and techniques.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most systems a stack frame has a field to contain the previous value of the frame pointer register, the value it had while the caller was executing. For example, the stack frame of DrawLine would have a memory location holding the frame pointer value that DrawSquare uses (not shown in the diagram above). The value is saved upon entry to the subroutine. Having such a field in a known location in the stack frame enables code to access each frame successively underneath the currently executing routine's frame, and also allows the routine to easily restore the frame pointer to the caller's frame, just before it returns.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonetics, a bilabial consonant is a labial consonant articulated with both lips.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to avoid O(n log n) complexity, the LISP 2 algorithm uses three different passes over the heap. In addition, heap objects must have a separate forwarding pointer slot that is not used outside of garbage collection. After standard marking, the algorithm proceeds in the following three passes: Compute the forwarding location for live objects. Keep track of a free and live pointer and initialize both to the start of heap.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small). If k = 1, then the object is simply assigned to the class of that single nearest neighbor. In k-NN regression, the output is the property value for the object.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "What is the format of the information? Who will be responsible for transmitting and providing the information?Moreover, this only serves as guidelines and must take into account other factors like cost and access to information.As defined by the Project Management Institute (1996), project communications management includes processes required to ensure timely and appropriate generation, collection, dissemination, storage, and ultimate disposition of project information. The following communication processes are involved in Project Communications Management, to wit: Communication planning \u2013 In this phase, the problems, needs and future plans are being identified to ensure attainment of goals and objectives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic and computer science, homotopy type theory (HoTT ) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory applies. This includes, among other lines of work, the construction of homotopical and higher-categorical models for such type theories; the use of type theory as a logic (or internal language) for abstract homotopy theory and higher category theory; the development of mathematics within a type-theoretic foundation (including both previously existing mathematics and new mathematics that homotopical types make possible); and the formalization of each of these in computer proof assistants. There is a large overlap between the work referred to as homotopy type theory, and as the univalent foundations project.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in abstract algebra, a ring R is said to be stably finite (or weakly finite) if, for all square matrices A and B of the same size with entries in R, AB = 1 implies BA = 1. This is a stronger property for a ring than having the invariant basis number (IBN) property. Namely, any nontrivial stably finite ring has IBN. Commutative rings, noetherian rings and artinian rings are stably finite. Subrings of stably finite rings and matrix rings over stably finite rings are stably finite. A ring satisfying Klein's nilpotence condition is stably finite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It applies to predicates of the form e x p r \u2208 { e x p r 1 , \u2026 , e x p r n } {\\displaystyle expr\\in \\{expr_{1},\\dots ,expr_{n}\\}} . In this case, it generates n test classes such that a predicate of the form e x p r = e x p r i {\\displaystyle expr=expr_{i}} is added to each of them. Mandatory Test Set (MTS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by S. Bochner (1946). The term formal group sometimes means the same as formal group law, and sometimes means one of several generalizations. Formal groups are intermediate between Lie groups (or algebraic groups) and Lie algebras. They are used in algebraic number theory and algebraic topology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This allows for rapid prototyping.Lazy evaluation is often combined with memoization, as described in Jon Bentley's Writing Efficient Programs. After a function's value is computed for that parameter or set of parameters, the result is stored in a lookup table that is indexed by the values of those parameters; the next time the function is called, the table is consulted to determine whether the result for that combination of parameter values is already available. If so, the stored result is simply returned.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Their correct definition is rather technical. They are specifically defined as sheaves of sets or as sheaves of rings, for example, depending on the type of data assigned to the open sets. There are also maps (or morphisms) from one sheaf to another; sheaves (of a specific type, such as sheaves of abelian groups) with their morphisms on a fixed topological space form a category.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, a zip tone (also known as a whisper tone or call waiting tone) is a call-progress tone which indicates a new incoming call is either connecting or waiting depending on the application. Unlike a ringtone, which alerts those near a telephone to answer it, a zip tone alerts someone already on the line\u2014for example a telephone operator, call center agent, or telephone subscriber with call waiting service\u2014that action is needed for an incoming call such as pressing a button or reciting a phrase (e.g. \"May I help you?\"). This way of offering an incoming call to an available call center agent is also referred to as 'forced calling'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", s n {\\displaystyle s_{1},...,s_{n}} are the n {\\displaystyle n} sentences in the corpus, but N {\\displaystyle N} is the number of words in the corpus. This normalizes the perplexity by the length of the text, allowing for more meaningful comparisons between different texts or models. Suppose the average sentence xi in the corpus has a probability of 2 \u2212 190 {\\displaystyle 2^{-190}} according to the language model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A closely related vector is the angular wave vector (or angular wavevector), with a typical unit being radian per metre. The wave vector and angular wave vector are related by a fixed constant of proportionality, 2\u03c0 radians per cycle.It is common in several fields of physics to refer to the angular wave vector simply as the wave vector, in contrast to, for example, crystallography. It is also common to use the symbol k for whichever is in use. In the context of special relativity, wave vector can refer to a four-vector, in which the (angular) wave vector and (angular) frequency are combined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. It is used for classification and regression. In both cases, the input consists of the k closest training examples in a data set. The output depends on whether k-NN is used for classification or regression: In k-NN classification, the output is a class membership.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) x i / N {\\textstyle \\textstyle {x_{i}/N}} , and the uniform probability 1 / d {\\textstyle \\textstyle {1/d}} . Invoking Laplace's rule of succession, some authors have argued that \u03b1 should be 1 (in which case the term add-one smoothing is also used), though in practice a smaller value is typically chosen. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter \u03b1 as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a beta distribution as the conjugate prior for the parameters of the binomial distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the US and some other countries, the industry standard today for physical properties and raw materials constituents is ASTM C 1364, the Standard Specification for Architectural Cast Stone. Membership in ASTM International (founded in 1898 as the American Chapter of the International Association for Testing and Materials and most recently known as the American Society for Testing and Materials) exceeds 30,000 technical experts from more than 100 countries who comprise a worldwide standards forum. The ASTM method of developing standards has been based on consensus of both users and producers of all kinds of materials.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the clustering coefficient is much higher for the movie actor network. The network characteristics and scaling exponents given by Barab\u00e1si and Albert (1999), indicates the scale-free behavior:Size: 212 250 Average degree: 28.78 Cutoff for power-law scaling: 900 Clustering coefficient: 0.79Therefore, the underlying network has the scale-free degree distribution p(k) ~ k\u2212\u03b3actor, with an exponent \u03b3actor = 2.3 \u00b1 0.1 (Barab\u00e1si and Albert, 1999), (Albert and Barab\u00e1si, 2000). According to (Newman, Strogatz, and Watts, 2001), the movie actor network can be described by a bipartite graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. Implicit regularization is all other forms of regularization. This includes, for example, early stopping, using a robust loss function, and discarding outliers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". , + n , \u2212 n } {\\displaystyle L:V(T)\\to \\{+1,-1,+2,-2,...,+n,-n\\}} be a labeling of the vertices of T which is an odd function on S n \u2212 1 {\\displaystyle S_{n-1}} , i.e, L ( \u2212 v ) = \u2212 L ( v ) {\\displaystyle L(-v)=-L(v)} for every vertex v \u2208 S n \u2212 1 {\\displaystyle v\\in S_{n-1}} . Then Tucker's lemma states that T contains a complementary edge - an edge (a 1-simplex) whose vertices are labelled by the same number but with opposite signs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias) are frequently used. When a biased estimator is used, bounds of the bias are calculated. A biased estimator may be used for various reasons: because an unbiased estimator does not exist without further assumptions about a population; because an estimator is difficult to compute (as in unbiased estimation of standard deviation); because a biased estimator may be unbiased with respect to different measures of central tendency; because a biased estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased estimators (notably in shrinkage estimators); or because in some cases being unbiased is too strong a condition, and the only unbiased estimators are not useful.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Because it is impossible for banks to know every cheque that a customer writes and which may or may not be fraudulent, the onus is on the clients to make the bank aware of what cheques they write. These systems allow customers to upload their cheque files to the bank including the cheque number, the amount of money, and in some cases, the payee name. Now, when a cheque is presented for payment, the bank scrubs it against the information on file.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hurwitz problem (named after Adolf Hurwitz) is the problem of finding multiplicative relations between quadratic forms which generalise those known to exist between sums of squares in certain numbers of variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, \"Gangnam Style\" debuted at number 64 the Billboard Hot 100 in the week of September 22, 2012, with 61,000 downloads sold, more than the total number of previous weeks (57,000), becoming the second K-pop song to enter the chart behind the Wonder Girls' \"Nobody,\" which spent a week at number 76 on the October 31, 2009 chart. The following week, the song rocketed to number 11 on the chart with 188,000 downloads, seeing a sales increase of 210% after Psy appeared on various TV shows such as The Ellen DeGeneres Show and NBC's Today. In its third week, it rose to number two on the chart, topping the Hot Digital Songs chart with a 60% increase to 301,000 downloads sold and climbing to number nine on On-Demand Songs chart. After that, the song peaked at the runner-up spot for seven consecutive weeks behind Maroon 5's \"One More Night,\" failing to gain in enough radio audience to ascend to the summit, although it ruled Hot Digital Songs for a fourth week and On-Demand Songs for a fifth week during that period.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a network created by people analyzing their understanding of the word (such as Wordnet) the links and decomposition structures of the network are few in number and kind, and include part of, kind of, and similar links. In automated ontologies the links are computed vectors without explicit meaning. Various automated technologies are being developed to compute the meaning of words: latent semantic indexing and support vector machines, as well as natural language processing, artificial neural networks and predicate calculus techniques.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical computer science, entropy compression is an information theoretic method for proving that a random process terminates, originally used by Robin Moser to prove an algorithmic version of the Lov\u00e1sz local lemma.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Indeed, he would look favourably on an application for tenure by a young scientist who \"got busy and found himself 43 coauthors.\" In John Quiggin's opinion, the social network analysis was not based on meaningful criteria, did not prove a conflict of interest and did not apply at the time of the 1998 and 1999 publications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a classifying topos for some sort of structure is a topos T such that there is a natural equivalence between geometric morphisms from a cocomplete topos E to T and the category of models for the structure in E.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). It is suboptimal in the sense that it does not achieve the lowest possible expected code word length like Huffman coding does, and never better than but sometimes equal to the Shannon\u2013Fano coding (Fano's method). The method was the first of its type, the technique was used to prove Shannon's noiseless coding theorem in his 1948 article \"A Mathematical Theory of Communication\", and is therefore a centerpiece of the information age. Shannon\u2013Fano coding methods gave rise to the field of information theory and without its contributions, the world would not have any of the many successors; for example Huffman coding, or arithmetic coding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern mathematics, a common proof involves B\u00e9zout's identity, which was unknown at Euclid's time. B\u00e9zout's identity states that if x and y are coprime integers (i.e. they share no common divisors other than 1 and \u22121) there exist integers r and s such that r x + s y = 1. {\\displaystyle rx+sy=1.} Let a and n be coprime, and assume that n|ab.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to guarantee interoperability, DCF specifies the file system for image and sound files to be used on formatted DCF media (like removable or non-removable memory) as FAT12, FAT16, FAT32, or exFAT. Media with a capacity of more than 2 GB must be formatted using FAT32 or exFAT. The filesystem in a digital camera contains a DCIM (Digital Camera IMages) directory, which can contain multiple subdirectories with names such as \"123ABCDE\" that consist of a unique directory number (in the range 100...999) and five alphanumeric characters, which may be freely chosen and often refer to a camera maker.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s the RCA 1802 was used for many missions\u2014like Galileo. This mission and other missions started the trend away from custom built NASA CPUs in spacecraft. The exploration of the inner and outer parts of the solar system would have to be done with existing (civilian and military-aerospace) CPUs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a function f: R n \u2192 R {\\displaystyle f:\\mathbb {R} ^{n}\\rightarrow \\mathbb {R} } is said to be closed if for each \u03b1 \u2208 R {\\displaystyle \\alpha \\in \\mathbb {R} } , the sublevel set { x \u2208 dom f | f ( x ) \u2264 \u03b1 } {\\displaystyle \\{x\\in {\\mbox{dom}}f\\vert f(x)\\leq \\alpha \\}} is a closed set. Equivalently, if the epigraph defined by epi f = { ( x , t ) \u2208 R n + 1 | x \u2208 dom f , f ( x ) \u2264 t } {\\displaystyle {\\mbox{epi}}f=\\{(x,t)\\in \\mathbb {R} ^{n+1}\\vert x\\in {\\mbox{dom}}f,\\;f(x)\\leq t\\}} is closed, then the function f {\\displaystyle f} is closed. This definition is valid for any function, but most used for convex functions. A proper convex function is closed if and only if it is lower semi-continuous. For a convex function which is not proper there is disagreement as to the definition of the closure of the function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, such concepts as primitive recursive functions and \u03bc-recursive functions represent integer-valued functions of several natural variables or, in other words, functions on Nn. G\u00f6del numbering, defined on well-formed formulae of some formal language, is a natural-valued function. Computability theory is essentially based on natural numbers and natural (or integer) functions on them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that the noise can be either stochastic or deterministic. Alternatively the model can be expressed as P \u03a9 ( Y ) = P \u03a9 ( M ) + P \u03a9 ( Z ) , {\\displaystyle P_{\\Omega }(Y)=P_{\\Omega }(M)+P_{\\Omega }(Z),} where Z {\\displaystyle Z} is an n \u00d7 n {\\displaystyle n\\times n} matrix with entries Z i j {\\displaystyle Z_{ij}} for ( i , j ) \u2208 \u03a9 {\\displaystyle (i,j)\\in \\Omega } assuming that \u2016 P \u03a9 ( Z ) \u2016 F \u2264 \u03b4 {\\displaystyle \\|P_{\\Omega }(Z)\\|_{F}\\leq \\delta } for some \u03b4 > 0 {\\displaystyle \\delta >0} .To recover the incomplete matrix, we try to solve the following optimization problem: min X \u2016 X \u2016 \u2217 subject to \u2016 P \u03a9 ( X \u2212 Y ) \u2016 F \u2264 \u03b4 {\\displaystyle {\\begin{aligned}&{\\underset {X}{\\text{min}}}&\\|X\\|_{*}\\\\&{\\text{subject to}}&\\|P_{\\Omega }(X-Y)\\|_{F}\\leq \\delta \\\\\\end{aligned}}} Among all matrices consistent with the data, find the one with minimum nuclear norm. Cand\u00e8s and Plan have shown that this reconstruction is accurate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern English, there are several conventions for abbreviations, and the choice may be confusing. The only rule universally accepted is that one should be consistent, and to make this easier, publishers express their preferences in a style guide. Some questions which arise are shown below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "+ x 5 5 ! \u2212 x 7 7 !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, the coverage of a radio station is the geographic area where the station can communicate. Broadcasters and telecommunications companies frequently produce coverage maps to indicate to users the station's intended service area. Coverage depends on several factors, such as orography (i.e. mountains) and buildings, technology, radio frequency and perhaps most importantly for two-way telecommunications the sensitivity and transmit efficiency of the consumer equipment. Some frequencies provide better regional coverage, while other frequencies penetrate better through obstacles, such as buildings in cities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, an expectation\u2013maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regards to implicit/automatic versus explicit proximity search, as of November 2008, most Internet search engines only implement an implicit proximity search functionality. That is, they automatically rank those search results higher where the user keywords have a good \"overall proximity score\" in such results. If only two keywords are in the search query, this has no difference from an explicit proximity search which puts a NEAR operator between the two keywords. However, if three or more than three keywords are present, it is often important for the user to specify which subsets of these keywords expect a proximity in search results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Assume this chain has stationary distribution \u03c0 {\\displaystyle \\pi } . Define Q ( x , y ) = \u03c0 ( x ) K ( x , y ) {\\displaystyle Q(x,y)=\\pi (x)K(x,y)} and for A , B \u2282 X {\\displaystyle A,B\\subset X} define Q ( A \u00d7 B ) = \u2211 x \u2208 A , y \u2208 B Q ( x , y ) . {\\displaystyle Q(A\\times B)=\\sum _{x\\in A,y\\in B}Q(x,y).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In strictly horological terms, \"rating\" a chronometer means that prior to the instrument entering service, the average rate of gaining or losing per day is observed and recorded on a rating certificate which accompanies the instrument. This daily rate is used in the field to correct the time indicated by the instrument to get an accurate time reading. Even the best-made chronometer with the finest temperature compensation etc. exhibits two types of error, (1) random and (2) consistent. The quality of design and manufacture of the instrument keeps the random errors small. In principle, the consistent errors should be amenable to elimination by adjustment, but in practice it is not possible to make the adjustment so precisely that this error is completely eliminated, so the technique of rating is used. The rate will also change while the instrument is in service due to e.g. thickening of the oil, so on long expeditions the instrument's rate would be periodically checked against accurate time determined by astronomical observations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1) = 1 and whenever a and b are coprime. An arithmetic function f(n) is said to be completely multiplicative (or totally multiplicative) if f(1) = 1 and f(ab) = f(a)f(b) holds for all positive integers a and b, even when they are not coprime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the decentralized federated learning setting, the nodes are able to coordinate themselves to obtain the global model. This setup prevents single point failures as the model updates are exchanged only between interconnected nodes without the orchestration of the central server. Nevertheless, the specific network topology may affect the performances of the learning process. See blockchain-based federated learning and the references therein.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is called the \"Receiving Party Pays\" model. In China, it was reported that both of its two operators will adopt the caller-pays approach as early as January 2007.One disadvantage of the receiving party pays systems is that phone owners keep their phones turned off to avoid receiving unwanted calls, which results in the total voice usage rates (and profits) in Calling Party Pays countries outperform those in Receiving Party Pays countries. To avoid the problem of users keeping their phone turned off, most Receiving Party Pays countries have either switched to Calling Party Pays, or their carriers offer additional incentives such as a large number of monthly minutes at a sufficiently discounted rate to compensate for the inconvenience. Note that when a user roaming in another country, international roaming tariffs apply to all calls received, regardless of the model adopted in the home country.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In early days, the user space programs that wanted to use the graphical framebuffer were also responsible for providing the mode-setting operations, and therefore they needed to run with privileged access to the video hardware. In Unix-type operating systems, the X Server was the most prominent example, and its mode-setting implementation lived in the DDX driver for each specific type of video card. This approach, later referred as User space Mode-Setting or UMS, poses several issues.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel computing, an embarrassingly parallel workload or problem (also called embarrassingly parallelizable, perfectly parallel, delightfully parallel or pleasingly parallel) is one where little or no effort is needed to separate the problem into a number of parallel tasks. This is often the case where there is little or no dependency or need for communication between those parallel tasks, or for results between them.Thus, these are different from distributed computing problems that need communication between tasks, especially communication of intermediate results. They are easy to perform on server farms which lack the special infrastructure used in a true supercomputer cluster. They are thus well suited to large, Internet-based volunteer computing platforms such as BOINC, and do not suffer from parallel slowdown.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The pair type is a special case of the dependent pair type, where the type B may depend on the instance picked from A. In many languages, product types take the form of a record type, for which the components of a tuple can be accessed by label. In languages that have algebraic data types, as in most functional programming languages, algebraic data types with one constructor are isomorphic to a product type. In the Curry\u2013Howard correspondence, product types are associated with logical conjunction (AND) in logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In system high mode of operation, all users must have: Signed NDA for ALL information on the system. Proper clearance for ALL information on the system. Formal access approval for ALL information on the system. A valid need to know for SOME information on the system.All users can access SOME data, based on their need to know.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the double null chart for Minkowski spacetime, d s 2 = \u2212 2 d u d v + d x 2 + d y 2 , \u2212 \u221e < u , v , x , y < \u221e {\\displaystyle ds^{2}=-2\\,du\\,dv+dx^{2}+dy^{2},\\;\\;\\;-\\infty", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Einstein notation, covariant components are denoted with lower indices as in w = w i e i . {\\displaystyle \\mathbf {w} =w_{i}\\mathbf {e} ^{i}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Combining 256 consecutive 20-bit samples can increase the SNR by a factor of 16, effectively adding 4 bits to the resolution and producing a single sample with 24-bit resolution.The number of samples required to get n {\\displaystyle n} bits of additional data precision is number of samples = ( 2 n ) 2 = 2 2 n . {\\displaystyle {\\mbox{number of samples}}=(2^{n})^{2}=2^{2n}.} To get the mean sample scaled up to an integer with n {\\displaystyle n} additional bits, the sum of 2 2 n {\\displaystyle 2^{2n}} samples is divided by 2 n {\\displaystyle 2^{n}}: scaled mean = \u2211 i = 0 2 2 n \u2212 1 2 n data i 2 2 n = \u2211 i = 0 2 2 n \u2212 1 data i 2 n .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of tax policy, Exchange of Information is a critical tool in assuring compliance with tax codes. As the economy becomes increasingly globalized taxpayers gain greater freedom to move between countries and regions. Tax authorities, however, are restrained by national borders. In order for governments to ensure the proper application of their tax laws, the free and accurate exchange of information is critical. The OECD Centre for Tax Policy and Administration works to improve flow of information in this area and establish a legal framework to facilitate it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, restriction of scalars (also known as \"Weil restriction\") is a functor which, for any finite extension of fields L/k and any algebraic variety X over L, produces another variety ResL/kX, defined over k. It is useful for reducing questions about varieties over large fields to questions about more complicated varieties over smaller fields.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the maximum-minimums identity is a relation between the maximum element of a set S of n numbers and the minima of the 2n \u2212 1 non-empty subsets of S. Let S = {x1, x2, ..., xn}. The identity states that max { x 1 , x 2 , \u2026 , x n } = \u2211 i = 1 n x i \u2212 \u2211 i < j min { x i , x j } + \u2211 i < j < k min { x i , x j , x k } \u2212 \u22ef \u22ef + ( \u2212 1 ) n + 1 min { x 1 , x 2 , \u2026 , x n } , {\\displaystyle {\\begin{aligned}\\max\\{x_{1},x_{2},\\ldots ,x_{n}\\}&=\\sum _{i=1}^{n}x_{i}-\\sum _{i", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of computational musicology, LDA has been used to discover tonal structures in different corpora.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions V1, V2, ..., Vn taking y as an argument representing the state of the system at times i from 1 to n. The definition of Vn(y) is the value obtained in state y at the last time n. The values Vi at earlier times i = n \u22121, n \u2212 2, ..., 2, 1 can be found by working backwards, using a recursive relationship called the Bellman equation. For i = 2, ..., n, Vi\u22121 at any state y is calculated from Vi by maximizing a simple function (usually the sum) of the gain from a decision at time i \u2212 1 and the function Vi at the new state of the system if this decision is made. Since Vi has already been calculated for the needed states, the above operation yields Vi\u22121 for those states. Finally, V1 at the initial state of the system is the value of the optimal solution. The optimal values of the decision variables can be recovered, one by one, by tracking back the calculations already performed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying additional properties or conditions. Thus the class of commutative semigroups consists of all those semigroups in which the binary operation satisfies the commutativity property that ab = ba for all elements a and b in the semigroup. The class of finite semigroups consists of those semigroups for which the underlying set has finite cardinality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But there are some efforts to characterize nonlinear systems, such as Volterra and Wiener series using polynomial integrals as the use of those methods naturally extend the signal into multi-dimensions. Another example is the Empirical mode decomposition method using Hilbert transform instead of Fourier Transform for nonlinear multi-dimensional systems. This method is an empirical method and can be directly applied to data sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some statically-typed languages such as Boo and D, class type checking can be specified to occur at runtime rather than at compile time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, for example English, there is often a similarity between clauses expressing an action or event in the passive voice and clauses expressing a state. For example, the string of words \"The dog is fed\" can have the following two different meanings: The dog is fed (twice a day). The dog is fed (so we can leave now).The additions in parentheses \"force\" the same string of words to clearly show only one of their two possible grammatical functions and the related meaning. In the first sentence, the combination of the auxiliary verb \"is\" and the past participle \"fed\" is a regular example of the construction of the passive voice in English.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some auxiliary information is needed in order to break symmetry. A standard assumption is that initially each node has a unique identifier, for example, from the set {1, 2, ..., n}. Put otherwise, we assume that we are given an n-coloring.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It not only connects POTS phone lines with the rest of the PSTN, but also replaces DSL by connecting directly to Ethernet wired into the home. Asynchronous Transfer Mode is often the communications protocol used.Cable TV has long carried multiplexed television channels, and late in the 20th century began offering the same services as telephone companies. IPTV also depends on multiplexing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Delannoy number D {\\displaystyle D} describes the number of paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (m, n), using only single steps north, northeast, or east. The Delannoy numbers are named after French army officer and amateur mathematician Henri Delannoy.The Delannoy number D ( m , n ) {\\displaystyle D(m,n)} also counts the number of global alignments of two sequences of lengths m {\\displaystyle m} and n {\\displaystyle n} , the number of points in an m-dimensional integer lattice or cross polytope which are at most n steps from the origin, and, in cellular automata, the number of cells in an m-dimensional von Neumann neighborhood of radius n while the number of cells on a surface of an m-dimensional von Neumann neighborhood of radius n is given with (sequence A266213 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Based on the philosophical assumption of the strong Church-Turing thesis, a mathematical criterion for evaluation of evidence has been conjectured, with the criterion having a resemblance to the idea of Occam's razor that the simplest comprehensive description of the evidence is most likely correct. It states formally, \"The ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability, and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized.\" However, some philosophers (including Richard Boyd, Mario Bunge, John D. Norton, and Elliott Sober) have adopted a skeptical or deflationary view of the role of simplicity in science, arguing in various ways that its importance has been overemphasized.Emphasis on hypothesis testing as the essence of science is prevalent among both scientists and philosophers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The underlying assumption with descriptively close sets is that such sets contain elements that have location and measurable features such as colour and frequency of occurrence. The description of the element of a set is defined by a feature vector. Comparison of feature vectors provides a basis for measuring the closeness of descriptively near sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In single-stage job scheduling problems, there are four main categories of machine environments: 1: Single-machine scheduling. There is a single machine. P: Identical-machines scheduling. There are m {\\displaystyle m} parallel machines, and they are identical.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In philosophical ethics, the naturalistic fallacy is the claim that it is possible to give a reductive explanation of good, in terms of natural properties such as pleasant or desirable. The term was introduced by British philosopher G. E. Moore in his 1903 book Principia Ethica.Moore's naturalistic fallacy is closely related to the is\u2013ought problem, which comes from David Hume's A Treatise of Human Nature (1738\u201340). However, unlike Hume's view of the is\u2013ought problem, Moore (and other proponents of ethical non-naturalism) did not consider the naturalistic fallacy to be at odds with moral realism. The naturalistic fallacy should not be confused with the appeal to nature, which is exemplified by forms of reasoning such as \"Something is natural; therefore, it is morally acceptable\" or \"This property is unnatural; therefore, this property is undesirable.\" Such inferences are common in discussions of medicine, sexuality, environmentalism, gender roles, race, and carnism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth categorical data. Given a set of observation counts x = \u27e8 x 1 , x 2 , \u2026 , x d \u27e9 {\\textstyle \\textstyle {\\mathbf {x} \\ =\\ \\left\\langle x_{1},\\,x_{2},\\,\\ldots ,\\,x_{d}\\right\\rangle }} from a d {\\textstyle \\textstyle {d}} -dimensional multinomial distribution with N {\\textstyle \\textstyle {N}} trials, a \"smoothed\" version of the counts gives the estimator: \u03b8 ^ i = x i + \u03b1 N + \u03b1 d ( i = 1 , \u2026 , d ) , {\\displaystyle {\\hat {\\theta }}_{i}={\\frac {x_{i}+\\alpha }{N+\\alpha d}}\\qquad (i=1,\\ldots ,d),} where the smoothed count x ^ i = N \u03b8 ^ i {\\textstyle \\textstyle {{\\hat {x}}_{i}=N{\\hat {\\theta }}_{i}}} and the \"pseudocount\" \u03b1 > 0 is a smoothing parameter. \u03b1 = 0 corresponds to no smoothing. (This parameter is explained in \u00a7 Pseudocount below.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In packed BCD, the number 127 is represented by 0001 0010 0111 1100 (127C) and \u2212127 is represented by 0001 0010 0111 1101 (127D). Burroughs systems used 1101 (D) for negative, and any other value is considered a positive sign value (the processors will normalize a positive sign to 1100 (C)). No matter how many bytes wide a word is, there is always an even number of nibbles because each byte has two of them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the syntactic monoid M ( L ) {\\displaystyle M(L)} of a formal language L {\\displaystyle L} is the smallest monoid that recognizes the language L {\\displaystyle L} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 2001, Thinsoft BeTwin offered a multiseat solution for Windows, utilizing multiple graphics cards and peripherals attached to a single host PC.In 2002 a Canadian company, Userful Corporation, released Userful Multiplier, a multiseat Linux software solution that enables up to 10 users to simultaneously share one computer. Earlier they worked on a kernel-based approach to a multi-station platform computer, but abandoned the idea due to a problem with multiple video card support. Other solutions appeared in 2003, such Svetoslav Slavtchev, Aivils Stoss and James Simmons worked, with the evdev and Faketty approach modifying the Linux kernel and letting more than one user independently use the same machine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an integer matrix is a matrix whose entries are all integers. Examples include binary matrices, the zero matrix, the matrix of ones, the identity matrix, and the adjacency matrices used in graph theory, amongst many others. Integer matrices find frequent application in combinatorics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The C0 control characters, being unaffected by the shift state of a 7-bit code, were to always be represented in an 8-bit code with the eighth bit unset. The consequently otherwise-unused bytes in the range 0x80 through 0x9F could be used for additional control codes, which would instead be represented as 0x1B 0x40 through 0x1B 0x5F (ESC @ through ESC _) in a 7-bit code. These additional control codes become known as the C1 control codes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It can be proven that if for a transformation g \u2032 {\\displaystyle g^{\\prime }} , support set will also lie within g \u2032 G 0 {\\displaystyle g^{\\prime }G_{0}} , then signature of I {\\displaystyle I} is invariant with respect to g \u2032 {\\displaystyle g^{\\prime }} . This theorem determines the range of transformations for which invariance is guaranteed to hold. One can see that the smaller is supp \u2061 ( \u27e8 I , g \u2212 1 t k \u27e9 ) {\\displaystyle \\operatorname {supp} (\\langle I,g^{-1}t_{k}\\rangle )} , the larger is the range of transformations for which invariance is guaranteed to hold.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Only one processor can access a block at a time.The following two algorithms solve the CREW and EREW problem if P \u2264 B {\\displaystyle P\\leq B} processors write to the same block simultaneously. A first approach is to serialize the write operations. Only one processor after the other writes to the block.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some countries, crash type classification exists for statistical purpose so that a crash is counted in one type or another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In an attempt to duplicate Mills & Boon's success in North America, Harlequin improved their distribution and marketing system. By choosing to sell their books \"where the women are,\" they allowed many mass-market merchandisers and even supermarkets to sell the books, all of which were exactly 192 pages. Harlequin then began a reader service, selling directly to readers who agreed to purchase a certain number of books each month.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle g_{i}(x_{0})>0.} Equality constraints are always active.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the following is an instruction for the Super Harvard Architecture Single-Chip Computer (SHARC). In one cycle, it does a floating-point multiply, a floating-point add, and two autoincrement loads. All of this fits in one 48-bit instruction: f12 = f0 * f4, f8 = f8 + f12, f0 = dm(i0, m3), f4 = pm(i8, m9); Since the earliest days of computer architecture, some CPUs have added several arithmetic logic units (ALUs) to run in parallel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set of prime numbers is not almost N {\\displaystyle \\mathbb {N} } , because there are infinitely many natural numbers that are not prime numbers. The set of transcendental numbers are almost R {\\displaystyle \\mathbb {R} } , because the algebraic real numbers form a countable subset of the set of real numbers (which is uncountable). The Cantor set is uncountably infinite, but has Lebesgue measure zero. So almost all real numbers in (0, 1) are members of the complement of the Cantor set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonology, an idiosyncratic property contrasts with a systematic regularity. While systematic regularities in the sound system of a language are useful for identifying phonological rules during analysis of the forms morphemes can take, idiosyncratic properties are those whose occurrence is not determined by those rules. For example, the fact that the English word cab starts with a /c/ is an idiosyncratic property; on the other hand that its vowel is longer than in the English word cap is a systematic regularity, as it arises from the fact that the final consonant is voiced rather than voiceless.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in Rp\u00d7p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, software aging is the tendency for software to fail or cause a system failure after running continuously for a certain time, or because of ongoing changes in systems surrounding the software. Software aging has several causes, including the inability of old software to adapt to changing needs or changing technology platforms, and the tendency of software patches to introduce further errors. As the software gets older it becomes less well-suited to its purpose and will eventually stop functioning as it should. Rebooting or reinstalling the software can act as a short-term fix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Primitive ideals are prime. The quotient of a ring by a left primitive ideal is a left primitive ring. For commutative rings the primitive ideals are maximal, and so commutative primitive rings are all fields.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In orthogonal range searching, the set S consists of n {\\displaystyle n} points in d {\\displaystyle d} dimensions, and the query consists of intervals in each of those dimensions. Thus, the query consists of a multi-dimensional axis-aligned rectangle. With an output size of k {\\displaystyle k} , Jon Bentley used a k-d tree to achieve (in Big O notation) O ( n ) {\\displaystyle O(n)} space and O ( n 1 \u2212 1 d + k ) {\\displaystyle O{\\big (}n^{1-{\\frac {1}{d}}}+k{\\big )}} query time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. The stack-sortable permutations are exactly the permutations that do not contain the permutation pattern 231; they are counted by the Catalan numbers, and may be placed in bijection with many other combinatorial objects with the same counting function including Dyck paths and binary trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A set of intervals J is called a covering of P if each point in P is contained in at least one interval of Q. The Rainbow covering problem is the problem of finding a rainbow set Q that is a covering of P.The problem is NP-hard (by reduction from linear SAT). A more general notion is conflict-free covering. In this problem: There is a set O of m objects, and a conflict-graph GO on O. A subset Q of O is called conflict-free if it is an independent set in GO, that is, no two objects in Q are connected by an edge in GO.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the beginning of a scenario, one might calculate the probability of a certain event. However, as soon as one gains more information about the scenario, one may need to re-calculate the probability accordingly. For example, when being told that a woman has two children, one might be interested in knowing if either of them is a girl, and if yes, what is probability that the other child is also a girl. Considering the two events independently, one might expect that the probability that the other child is female is \u00bd (50%), but by building a probability space illustrating all possible outcomes, one would notice that the probability is actually only \u2153 (33%).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If Bob measures in the computational basis, his only possible measurement is | \u03c8 00 \u27e9 {\\displaystyle |\\psi _{00}\\rangle } . This outcome is clearly consistent with the state having been | \u03c8 00 \u27e9 {\\displaystyle |\\psi _{00}\\rangle } , but it would also be a possible outcome if the state had been | \u03c8 01 \u27e9 {\\displaystyle |\\psi _{01}\\rangle } . If Bob measures in the Hadamard basis, either | \u03c8 01 \u27e9 {\\displaystyle |\\psi _{01}\\rangle } or | \u03c8 11 \u27e9 {\\displaystyle |\\psi _{11}\\rangle } could be measured, each with probability \u00bd. If the outcome is | \u03c8 01 \u27e9 {\\displaystyle |\\psi _{01}\\rangle } then again this state is consistent with either starting state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most common example of a host is a PC but some cell phones and PDAs also can be hosts. The HID protocol makes implementation of devices very simple. Devices define their data packets and then present a \"HID descriptor\" to the host.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, like English, palatalization is allophonic. Some phonemes have palatalized allophones in certain contexts, typically before front vowels and unpalatalized allophones elsewhere. Because it is allophonic, palatalization of this type does not distinguish words and often goes unnoticed by native speakers. Phonetic palatalization occurs in American English. Stops are palatalized before the front vowel /i/ and not palatalized in other cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In our initial formulation, introduce a binary variable x i {\\displaystyle x_{i}} for i = 1 , \u2026 , n {\\displaystyle i=1,\\dots ,n} , where x i = 1 {\\displaystyle x_{i}=1} if facility i {\\displaystyle i} is open, and x i = 0 {\\displaystyle x_{i}=0} otherwise. Further introduce the variable y i j {\\displaystyle y_{ij}} for i = 1 , \u2026 , n {\\displaystyle i=1,\\dots ,n} and j = 1 , \u2026 , m {\\displaystyle j=1,\\dots ,m} which represents the fraction of the demand d j {\\displaystyle d_{j}} filled by facility i {\\displaystyle i} . The so-called capacitated facility location problem is then given by Note that the second set of constraints ensures that if x i = 0 {\\displaystyle x_{i}=0} , that is, facility i {\\displaystyle i} isn't open, then y i j = 0 {\\displaystyle y_{ij}=0} for all j {\\displaystyle j} , that is, no demand for any customer can be filled from facility i {\\displaystyle i} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to maintain the structure of the tango tree (auxiliary trees correspond to preferred paths), we must do some updating work whenever preferred children change as a result of searches. When a preferred child changes, the top part of a preferred path becomes detached from the bottom part (which becomes its own preferred path) and reattached to another preferred path (which becomes the new bottom part). In order to do this efficiently, we'll define cut and join operations on our auxiliary trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The very first attempt to devise an algorithmic language was undertaken in 1948 by K. Zuse. His notation was quite general, but the proposal never attained the consideration it deserved. Unable to continue building computers \u2013 which was also forbidden by the Allied Powers \u2013 Zuse devoted his time to the development of a higher-level programming model and language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Reading accuracy is sometimes a problem with goniometers. Issues with the intra-measure (between measures) and inter-tester (between clinicians) reliability may increase as the experience of the examiner decreases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Vehicles that carry commodities are further subdivided by number of axles and number of units, including both power and trailer units.The United States Environmental Protection Agency (US EPA) has developed a classification scheme used to compare fuel economy among similar vehicles. Passenger vehicles are classified based on a vehicle's total interior passenger and cargo volumes. Trucks are classified based upon their gross vehicle weight rating (GVWR). Heavy-duty vehicles are not included within the EPA scheme. Certain cities in the United States in the 1920s chose to exempt electric-powered vehicles because officials believed those vehicles did not cause \"substantial wear upon the pavements\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that the example below uses the C# Null coalescing operator to guarantee error free invocation, where it could also have used a more mundane if...then...else. The following example only works when you do not care the existence of null, or you treat null and empty string the same. The assumption may not hold in other applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of computing, a few experimental Soviet computers were built with balanced ternary instead of binary, the most famous being the Setun, built by Nikolay Brusentsov and Sergei Sobolev. The notation has a number of computational advantages over traditional binary and ternary. Particularly, the plus\u2013minus consistency cuts down the carry rate in multi-digit multiplication, and the rounding\u2013truncation equivalence cuts down the carry rate in rounding on fractions. In balanced ternary, the one-digit multiplication table remains one-digit and has no carry and the addition table has only two carries out of nine entries, compared to unbalanced ternary with one and three respectively. Knuth wrote that \"Perhaps the symmetric properties and simple arithmetic of this number system will prove to be quite important some day,\" noting that, The complexity of arithmetic circuitry for balanced ternary arithmetic is not much greater than it is for the binary system, and a given number requires only log 3 \u2061 2 \u2248 63 % {\\displaystyle \\log _{3}2\\approx 63\\%} as many digit positions for its representation.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Visitor1 class implements the operation (visitElementB(e:ElementB)). The UML sequence diagram shows the run-time interactions: The Client object traverses the elements of an object structure (ElementA,ElementB) and calls accept(visitor) on each element. First, the Client calls accept(visitor) on ElementA, which calls visitElementA(this) on the accepted visitor object. The element itself (this) is passed to the visitor so that it can \"visit\" ElementA (call operationA()). Thereafter, the Client calls accept(visitor) on ElementB, which calls visitElementB(this) on the visitor that \"visits\" ElementB (calls operationB()).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements. The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the join and meet are given by intersection and union, and the subset relation itself is the Boolean inclusion relation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Common mathematical expressions for a characterization of X in terms of P include \"P is necessary and sufficient for X\", and \"X holds if and only if P\". It is also common to find statements such as \"Property Q characterizes Y up to isomorphism\". The first type of statement says in different words that the extension of P is a singleton set, while the second says that the extension of Q is a single equivalence class (for isomorphism, in the given example \u2014 depending on how up to is being used, some other equivalence relation might be involved).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following compilation, m is the length of the pattern, n the length of the searchable text, and k = |\u03a3| is the size of the alphabet. 1.^ Asymptotic times are expressed using O, \u03a9, and \u0398 notation. 2.^ Used to implement the memmem and strstr search functions in the glibc and musl C standard libraries. 3.^ Can be extended to handle approximate string matching and (potentially-infinite) sets of patterns represented as regular languages.The Boyer\u2013Moore string-search algorithm has been the standard benchmark for the practical string-search literature.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical applications, many problems can be formulated in the following way. One is interested in the expectation of a response function g: R d \u2192 R {\\displaystyle g:\\mathbb {R} ^{d}\\rightarrow \\mathbb {R} } applied to some random vector ( X 1 , \u2026 , X d ) {\\displaystyle (X_{1},\\dots ,X_{d})} . If we denote the CDF of this random vector with H {\\displaystyle H} , the quantity of interest can thus be written as E \u2061  = \u222b R d g ( x 1 , \u2026 , x d ) d H ( x 1 , \u2026 , x d ) . {\\displaystyle \\operatorname {E} \\left=\\int _{\\mathbb {R} ^{d}}g(x_{1},\\dots ,x_{d})\\,\\mathrm {d} H(x_{1},\\dots ,x_{d}).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Written multiplication is also based on the distributive law. Second example (with variables) Third example (with two sums) Here the distributive law was applied twice, and it does not matter which bracket is first multiplied out. Fourth exampleHere the distributive law is applied the other way around compared to the previous examples. Consider Since the factor 6 a 2 b {\\displaystyle 6a^{2}b} occurs in all summands, it can be factored out. That is, due to the distributive law one obtains", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, software durability means the solution ability of serviceability of software and to meet user's needs for a relatively long time. Software durability is important for user's satisfaction. For a software security to be durable, it must allow an organization to adjust the software to business needs that are constantly evolving, often in impulsive ways.Durability of software depends on four characteristics mainly; i.e. software trustworthiness, Human Trust for Serviceability, software dependability and software usability. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Liouville's theorem, originally formulated by Joseph Liouville in 1833 to 1841, places an important restriction on antiderivatives that can be expressed as elementary functions. The antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions. These are called nonelementary antiderivatives. A standard example of such a function is e \u2212 x 2 , {\\displaystyle e^{-x^{2}},} whose antiderivative is (with a multiplier of a constant) the error function, familiar from statistics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Hilbert space viewpoint, one considers an H {\\displaystyle H} -valued random element X {\\displaystyle X} , where H {\\displaystyle H} is a separable Hilbert space such as the space of square-integrable functions L 2  {\\displaystyle L^{2}} . Under the integrability condition that E \u2016 X \u2016 L 2 2 = E ( \u222b 0 1 | X ( t ) | 2 d t ) < \u221e {\\displaystyle \\mathbb {E} \\|X\\|_{L^{2}}^{2}=\\mathbb {E} (\\int _{0}^{1}|X(t)|^{2}dt)<\\infty } , one can define the mean of X {\\displaystyle X} as the unique element \u03bc \u2208 H {\\displaystyle \\mu \\in H} satisfying E \u27e8 X , h \u27e9 = \u27e8 \u03bc , h \u27e9 , h \u2208 H . {\\displaystyle \\mathbb {E} \\langle X,h\\rangle =\\langle \\mu ,h\\rangle ,\\qquad h\\in H.} This formulation is the Pettis integral but the mean can also be defined as Bochner integral \u03bc = E X {\\displaystyle \\mu =\\mathbb {E} X} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of independence, a finite matroid M {\\displaystyle M} is a pair ( E , I ) {\\displaystyle (E,{\\mathcal {I}})} , where E {\\displaystyle E} is a finite set (called the ground set) and I {\\displaystyle {\\mathcal {I}}} is a family of subsets of E {\\displaystyle E} (called the independent sets) with the following properties: (I1) The empty set is independent, i.e., \u2205 \u2208 I {\\displaystyle \\emptyset \\in {\\mathcal {I}}} . (I2) Every subset of an independent set is independent, i.e., for each A \u2032 \u2286 A \u2286 E {\\displaystyle A'\\subseteq A\\subseteq E} , if A \u2208 I {\\displaystyle A\\in {\\mathcal {I}}} then A \u2032 \u2208 I {\\displaystyle A'\\in {\\mathcal {I}}} . This is sometimes called the hereditary property, or the downward-closed property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nevil Maskelyne, the newly appointed Astronomer Royal who was on the Board of Longitude, started with Mayer's tables and after his own experiments at sea trying out the lunar distance method, proposed annual publication of pre-calculated lunar distance predictions in an official nautical almanac for the purpose of finding longitude at sea. Being very enthusiastic for the lunar distance method, Maskelyne and his team of computers worked feverishly through the year 1766, preparing tables for the new Nautical Almanac and Astronomical Ephemeris. Published first with data for the year 1767, it included daily tables of the positions of the Sun, Moon, and planets and other astronomical data, as well as tables of lunar distances giving the distance of the Moon from the Sun and nine stars suitable for lunar observations (ten stars for the first few years).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set of all possible feature vectors constitutes a feature space.A common example of feature vectors appears when each image point is to be classified as belonging to a specific class. Assuming that each image point has a corresponding feature vector based on a suitable set of features, meaning that each class is well separated in the corresponding feature space, the classification of each image point can be done using standard classification method. Another and related example occurs when neural network-based processing is applied to images. The input data fed to the neural network is often given in terms of a feature vector from each image point, where the vector is constructed from several different features extracted from the image data. During a learning phase, the network can itself find which combinations of different features are useful for solving the problem at hand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In producing, people must continually maintain their assets, replace assets, and consume things but they also can create more beyond those requirements, assuming sufficient productivity of labour.This social surplus product can be: destroyed, or wasted held in reserve, or hoarded consumed traded or otherwise transferred to or from others reinvestedThus, for a simple example, surplus seeds could be left to rot, stored, eaten, traded for other products, or sown on new fields. But if, for example, 90 people own 5 sacks of grain, and 10 people own 100 sacks of grain, it would be physically impossible for those 10 people to use all that grain themselves\u2014most likely they would either trade that grain, or employ other people to farm it. Since 5 sacks of grain are insufficient for 90 people, it is likely that the 90 people would be willing to work for the 10 people who own more grain than they can consume, in order to get some extra grain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some situations, there is a risk of losing track of block boundaries. This is often seen in large sections of code containing many compound statements nested to many levels of indentations. By the time the programmer scrolls to the bottom of a huge set of nested statements, they may have lost track of which control statements go where. However, overly-long code could have other causes, such as being too complex, and a programmer facing this problem might instead consider whether code refactoring would help in the longer term.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The validity of an argument is not a guarantee of the truth of its conclusion. A valid argument may have false premises that render it inconclusive: the conclusion of a valid argument with one or more false premises may be true or false. Logic seeks to discover the forms that make arguments valid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the envy-free cake-cutting problem, a \"cake\" (a heterogeneous divisible resource) has to be divided among n partners with different preferences over parts of the cake. The cake has to be divided to n pieces such that: (a) each partner receives a single connected piece, and (b) each partner believes that his piece is (weakly) better than all other pieces. A protocol for solving this problem was developed by Forest Simmons in 1980, in a correspondence with Michael Starbird. It was first publicized by Francis Su in 1999.Given a cut-set (i.e. a certain partition of the cake to n pieces), we say that a partner prefers a given piece if he believes that this piece is weakly better than all other pieces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\u2113 2 {\\displaystyle \\ell _{2}} ) counted with their multiplicities, augmented by adding a countable infinity of points of the diagonal { ( x , y ) \u2208 R 2: x = y } {\\displaystyle \\{(x,y)\\in \\mathbb {R} ^{2}:x=y\\}} . The matching distance between \u2113 1 {\\displaystyle \\ell _{1}} and \u2113 2 {\\displaystyle \\ell _{2}} is given by d match ( \u2113 1 , \u2113 2 ) = min \u03c3 max p \u2208 C 1 \u03b4 ( p , \u03c3 ( p ) ) {\\displaystyle d_{\\text{match}}(\\ell _{1},\\ell _{2})=\\min _{\\sigma }\\max _{p\\in C_{1}}\\delta (p,\\sigma (p))} where \u03c3 {\\displaystyle \\sigma } varies among all the bijections between C 1 {\\displaystyle C_{1}} and C 2 {\\displaystyle C_{2}} and \u03b4 ( ( x , y ) , ( x \u2032 , y \u2032 ) ) = min { max { | x \u2212 x \u2032 | , | y \u2212 y \u2032 | } , max { y \u2212 x 2 , y \u2032 \u2212 x \u2032 2 } } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In n {\\displaystyle n} -dimensional space R n {\\displaystyle \\mathbb {R} ^{n}} , uniform scaling by a factor v {\\displaystyle v} is accomplished by scalar multiplication with v {\\displaystyle v} , that is, multiplying each coordinate of each point by v {\\displaystyle v} . As a special case of linear transformation, it can be achieved also by multiplying each point (viewed as a column vector) with a diagonal matrix whose entries on the diagonal are all equal to v {\\displaystyle v} , namely v I {\\displaystyle vI} . Non-uniform scaling is accomplished by multiplication with any symmetric matrix. The eigenvalues of the matrix are the scale factors, and the corresponding eigenvectors are the axes along which each scale factor applies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Moessner's theorem or Moessner's magic is related to an arithmetical algorithm to produce an infinite sequence of the exponents of positive integers 1 n , 2 n , 3 n , 4 n , \u22ef , {\\displaystyle 1^{n},2^{n},3^{n},4^{n},\\cdots ~,} with n \u2265 1 , {\\displaystyle n\\geq 1~,} by recursively manipulating the sequence of integers algebraically. The algorithm was first published by Alfred Moessner in 1951; the first proof of its validity was given by Oskar Perron that same year.For example, for n = 2 {\\displaystyle n=2} , one can remove every even number, resulting in ( 1 , 3 , 5 , 7 \u22ef ) {\\displaystyle (1,3,5,7\\cdots )} , and then add each odd number to the sum of all previous elements, providing ( 1 , 4 , 9 , 16 , \u22ef ) = ( 1 2 , 2 2 , 3 2 , 4 2 \u22ef ) {\\displaystyle (1,4,9,16,\\cdots )=(1^{2},2^{2},3^{2},4^{2}\\cdots )} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the category of sets, an exponential object Z Y {\\displaystyle Z^{Y}} is the set of all functions Y \u2192 Z {\\displaystyle Y\\to Z} . The map e v a l: ( Z Y \u00d7 Y ) \u2192 Z {\\displaystyle \\mathrm {eval} \\colon (Z^{Y}\\times Y)\\to Z} is just the evaluation map, which sends the pair ( f , y ) {\\displaystyle (f,y)} to f ( y ) {\\displaystyle f(y)} . For any map g: X \u00d7 Y \u2192 Z {\\displaystyle g\\colon X\\times Y\\to Z} the map \u03bb g: X \u2192 Z Y {\\displaystyle \\lambda g\\colon X\\to Z^{Y}} is the curried form of g {\\displaystyle g}: \u03bb g ( x ) ( y ) = g ( x , y ) . {\\displaystyle \\lambda g(x)(y)=g(x,y).\\,} A Heyting algebra H {\\displaystyle H} is just a bounded lattice that has all exponential objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In that time, the Linux Console Project also proposed an idea to use multiple independent consoles and then multiple independent keyboards and mice in a project called \"Backstreet Ruby\". Backstreet Ruby is a kernel patch for the Linux kernel. It is a back port to Linux-2.4 of the Ruby kernel tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the NKS framework, these themselves should be simple programs, and subject to the same goals and methodology. An extension of this idea is that the human mind is itself a computational system, and hence providing it with raw data in as effective a way as possible is crucial to research. Wolfram believes that programs and their analysis should be visualized as directly as possible, and exhaustively examined by the thousands or more. Since this new field concerns abstract rules, it can in principle address issues relevant to other fields of science. However, in general Wolfram's idea is that novel ideas and mechanisms can be discovered in the computational universe, where they can be represented in their simplest forms, and then other fields can choose among these discoveries for those they find relevant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Dirichlet processes (after the distribution associated with Peter Gustav Lejeune Dirichlet) are a family of stochastic processes whose realizations are probability distributions. In other words, a Dirichlet process is a probability distribution whose range is itself a set of probability distributions. It is often used in Bayesian inference to describe the prior knowledge about the distribution of random variables\u2014how likely it is that the random variables are distributed according to one or another particular distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, a high-privilege application assumes that it would only be provided with input matching its interface specification, thus doesn't validate this input. Then, an attacker may be able to exploit this assumption, in order to run unauthorized code with the application's privileges: Some Windows services are configured to run under the Local System user account. A vulnerability such as a buffer overflow may be used to execute arbitrary code with privilege elevated to Local System. Alternatively, a system service that is impersonating a lesser user can elevate that user's privileges if errors are not handled correctly while the user is being impersonated (e.g. if the user has introduced a malicious error handler) Under some legacy versions of the Microsoft Windows operating system, the All Users screensaver runs under the Local System account \u2013 any account that can replace the current screensaver binary in the file system or Registry can therefore elevate privileges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the LP phase of SLQP, the following linear program is solved: min d f ( x k ) + \u2207 f ( x k ) T d s . t . b ( x k ) + \u2207 b ( x k ) T d \u2265 0 c ( x k ) + \u2207 c ( x k ) T d = 0. {\\displaystyle {\\begin{array}{rl}\\min \\limits _{d}&f(x_{k})+\\nabla f(x_{k})^{T}d\\\\\\mathrm {s.t.} &b(x_{k})+\\nabla b(x_{k})^{T}d\\geq 0\\\\&c(x_{k})+\\nabla c(x_{k})^{T}d=0.\\end{array}}} Let A k {\\displaystyle {\\cal {A}}_{k}} denote the active set at the optimum d LP \u2217 {\\displaystyle d_{\\text{LP}}^{*}} of this problem, that is to say, the set of constraints that are equal to zero at d LP \u2217 {\\displaystyle d_{\\text{LP}}^{*}} . Denote by b A k {\\displaystyle b_{{\\cal {A}}_{k}}} and c A k {\\displaystyle c_{{\\cal {A}}_{k}}} the sub-vectors of b {\\displaystyle b} and c {\\displaystyle c} corresponding to elements of A k {\\displaystyle {\\cal {A}}_{k}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to increase the decimal division accuracy add as many zeros as required to the right of the dividend but still input it right justified and then proceed as with an integer division. It is important to know where the decimal point is, when you read the quotient (some markers, first ivory and then metal, were usually sold with the machine and used for this purpose).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The preconditioner matrix M has to be symmetric positive-definite and fixed, i.e., cannot change from iteration to iteration. If any of these assumptions on the preconditioner is violated, the behavior of the preconditioned conjugate gradient method may become unpredictable. An example of a commonly used preconditioner is the incomplete Cholesky factorization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the calculus of constructions, denoted as \u03bbC in the cube or as \u03bbP\u03c9,: 130 these four features cohabit, so that both types and terms can depend on types and terms. The clear border that exists in \u03bb\u2192 between terms and types is somewhat abolished, as all types except the universal \u25fb {\\displaystyle \\square } are themselves terms with a type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the cases below where n is an exponent, multiples of n are also proven, since a kn-th power is also an n-th power. Where solutions involving a second power are alluded to below, they can be found specifically at Fermat\u2013Catalan conjecture#Known solutions. All cases of the form (2, 3, n) or (2, n, 3) have the solution 23 + 1n = 32 which is referred below as the Catalan solution. The case x = y = z \u2265 3 (and thus the case gcd(x, y, z) \u2265 3) is Fermat's Last Theorem, proven to have no solutions by Andrew Wiles in 1994.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of Kripke semantics, S5 is characterized by models where the accessibility relation is an equivalence relation: it is reflexive, transitive, and symmetric. Determining the satisfiability of an S5 formula is an NP-complete problem. The hardness proof is trivial, as S5 includes the propositional logic. Membership is proved by showing that any satisfiable formula has a Kripke model where the number of worlds is at most linear in the size of the formula.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By subtracting 1 2 \u2211 i = 1 n v i {\\displaystyle {\\frac {1}{2}}\\sum _{i=1}^{n}v_{i}} from each possible subsum (that is, by changing the origin and then scaling by a factor of 2), the Littlewood\u2013Offord problem is equivalent to the problem of determining the number of sums of the form \u2211 i = 1 n \u03b5 i v i {\\displaystyle \\sum _{i=1}^{n}\\varepsilon _{i}v_{i}} that fall in the target set A, where \u03b5 i {\\displaystyle \\varepsilon _{i}} takes the value 1 or \u22121. This makes the problem into a probabilistic one, in which the question is of the distribution of these random vectors, and what can be said knowing nothing more about the vi. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. This initiality provides a general framework for induction and recursion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The probability measure is then defined by the function: So the full probability space which defines a fair coin is the triplet ( \u03a9 , F , P ) {\\displaystyle (\\Omega ,{\\mathcal {F}},P)} as defined above. Note that this is not a random variable because heads and tails don't have inherent numerical values like you might find on a fair two-valued die. A random variable adds the additional structure of assigning a numerical value to each outcome. Common choices are ( H , T ) \u2192 ( 1 , 0 ) {\\displaystyle (H,T)\\to (1,0)} or ( H , T ) \u2192 ( 1 , \u2212 1 ) {\\displaystyle (H,T)\\to (1,-1)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The generalized Petersen graphs are non-strict unit distance graphs. An unsolved problem of Paul Erd\u0151s asks how many edges a unit distance graph on n {\\displaystyle n} vertices can have. The best known lower bound is slightly above linear in n {\\displaystyle n} \u2014far from the upper bound, proportional to n 4 / 3 {\\displaystyle n^{4/3}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If different resulting states can occur, the selection of the respective resulting state can be modeled explicitly as a decision function using logical connectors. Functions can be refined into another EPC. In this case it is called a hierarchical function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, total dual integrality is a sufficient condition for the integrality of a polyhedron. Thus, the optimization of a linear objective over the integral points of such a polyhedron can be done using techniques from linear programming. A linear system A x \u2264 b {\\displaystyle Ax\\leq b} , where A {\\displaystyle A} and b {\\displaystyle b} are rational, is called totally dual integral (TDI) if for any c \u2208 Z n {\\displaystyle c\\in \\mathbb {Z} ^{n}} such that there is a feasible, bounded solution to the linear program max c T x A x \u2264 b , {\\displaystyle {\\begin{aligned}&&\\max c^{\\mathrm {T} }x\\\\&&Ax\\leq b,\\end{aligned}}} there is an integer optimal dual solution.Edmonds and Giles showed that if a polyhedron P {\\displaystyle P} is the solution set of a TDI system A x \u2264 b {\\displaystyle Ax\\leq b} , where b {\\displaystyle b} has all integer entries, then every vertex of P {\\displaystyle P} is integer-valued. Thus, if a linear program as above is solved by the simplex algorithm, the optimal solution returned will be integer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, the Weierstrass method or Durand\u2013Kerner method, discovered by Karl Weierstrass in 1891 and rediscovered independently by Durand in 1960 and Kerner in 1966, is a root-finding algorithm for solving polynomial equations. In other words, the method can be used to solve numerically the equation f(x) = 0,where f is a given polynomial, which can be taken to be scaled so that the leading coefficient is 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to be executed by the system (such as an operating system, firmware, or boot loader), an executable file must conform to the system's application binary interface (ABI). In simple interfaces, a file is executed by loading it into memory and jumping to the start of the address space and executing from there. In more complicated interfaces, executable files have additional metadata specifying a separate entry point. For example, in ELF, the entry point is defined in the header's e_entry field, which specifies the (virtual) memory address at which to start execution. In the GNU Compiler Collection, this field is set by the linker based on the _start symbol.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Whereas the sieve of Eratosthenes marks off each non-prime for each of its prime factors, the sieve of Pritchard avoids considering almost all non-prime numbers by building progressively larger wheels, which represent the pattern of numbers not divisible by any of the primes processed thus far. It thereby achieves a better asymptotic complexity, and was the first sieve with a running time sublinear in the specified bound. Its asymptotic running-time has not been improved on, and it deletes fewer composites than any other known sieve. It was created in 1979 by Paul Pritchard.Since Pritchard has created a number of other sieve algorithms for finding prime numbers, the sieve of Pritchard is sometimes singled out by being called the wheel sieve (by Pritchard himself) or the dynamic wheel sieve.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, a set of bases in Hilbert space Cd are are said to be mutually unbiased to mean, that, if a system is prepared in an eigen state of one of the bases, then all outcomes of the measurement with respect to the other basis are predicted to occur with an equal probability inexorably equal to 1/d.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, the corestriction onto the image always exists and it is sometimes simply called the corestriction of f {\\displaystyle f} . More generally, one can consider corestriction of a morphism in general categories with images.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The column assignment shows an assignment of N before entering a subsequent step. This possibly induces a reassignment of the other nodes P, G, U also. If something has been changed by the case, this is shown in the column group after.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, in some cases, additional marks fulfil the role of diacritics, to differentiate distinct characters. Such additional marks constitute glyphs. Some characters such as \"\u00e6\" in Icelandic and the \"\u00df\" in German may be regarded as glyphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Dixon's factorization method (also Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method. Unlike for other factor base methods, its run-time bound comes with a rigorous proof that does not rely on conjectures about the smoothness properties of the values taken by a polynomial. The algorithm was designed by John D. Dixon, a mathematician at Carleton University, and was published in 1981.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonology, segments are categorized into natural classes on the basis of their distinctive features. Each feature is a quality or characteristic of the natural class, such as voice or manner. A unique combination of features defines a phoneme.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order theory, arbitrary meets can be expressed in terms of arbitrary joins and vice versa (for details, see completeness (order theory)). In effect, this means that it is sufficient to require the existence of either all meets or all joins to obtain the class of all complete lattices. As a consequence, some authors use the terms complete meet-semilattice or complete join-semilattice as another way to refer to complete lattices. Though similar on objects, the terms entail different notions of homomorphism, as will be explained in the below section on morphisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "M Flag (1 bit) 1 means more fragments follow; 0 means last fragment. Identification (32 bits) Packet identification value, generated by the source node. Needed for reassembly of the original packet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonetics, labiodentals are consonants articulated with the lower lip and the upper teeth.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the IMS framework, it is required that once the callee is alerted, the chances of a session failure are minimum. An important source of failure is the inability to reserve network resources to support the session, so these resources should be allocated before the phone rings. However, in the IMS, to reserve resources the network needs to know the callee's IP address, port and session parameters and therefore it is necessary that the initial offer/answer exchange to establish a session has started (INVITE request). In basic SIP, this exchange eventually causes the callee to be alerted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence R \u2260 S = \u2205 . {\\displaystyle {\\mathcal {R}}\\neq {\\mathcal {S}}=\\emptyset \\;.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics there is the concept of proof of impossibility referring to problems impossible to solve. The difference between this impossibility and that of the no-go theorems is: a proof of impossibility states a category of logical proposition that may never be true; a no-go theorem instead presents a sequence of events that may never occur.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most multiprocessor systems, each processor schedules and controls itself, therefore there's no \"supervisor\" processor, and kernel data structures are globally shared; sections of code that access those shared data structures are critical sections. This design choice is made to improve scaling, reliability and modularity. Examples of such kernel data structure are ready list and communication channels. A \"conflict\" happens when more than one processor is trying to access the same resource (a memory portion) at the same time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle +:=.} \u22c5  :=  . {\\displaystyle \\cdot :=.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the chart below, the Carian letter is given, followed by the transcription. Where the transcription differs from IPA, the phonetic value is given in brackets. Many Carian phonemes were represented by multiple letter forms in various locations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "SR shows that these concepts are all different aspects of the same physical quantity in much the same way that it shows space and time to be interrelated. Consequently, another modification is the concept of the center of mass of a system, which is straightforward to define in classical mechanics but much less obvious in relativity \u2013 see relativistic center of mass for details. The equations become more complicated in the more familiar three-dimensional vector calculus formalism, due to the nonlinearity in the Lorentz factor, which accurately accounts for relativistic velocity dependence and the speed limit of all particles and fields. However, they have a simpler and elegant form in four-dimensional spacetime, which includes flat Minkowski space (SR) and curved spacetime (GR), because three-dimensional vectors derived from space and scalars derived from time can be collected into four vectors, or four-dimensional tensors. However, the six component angular momentum tensor is sometimes called a bivector because in the 3D viewpoint it is two vectors (one of these, the conventional angular momentum, being an axial vector).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom a Migration Authorisation Code (MAC) was a 17 to 19-character unique identifier code used by DSL customers when they wish to switch internet service provider (ISP). A MAC is generated by the actual telecommunication provider (most commonly BT), identifies the local loop (telephone line) to be switched, and authorises the provider to switch the customer to the new ISP. MACs usually begin with \"BBIP\", \"FTIP\", \"BBDS\", or \"BBDP\", and consist of 4 letters, 7 digits (sometimes up to 9), a slash, 2 letters, 2 digits (this indicates the day in the month the MAC was issued), and 1 final letter. (For example: BBIP87654321/AB12C).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Typically an algorithm which solves a problem in polylogarithmic time in the network size is considered efficient in this model. Another commonly used measure is the total number of bits transmitted in the network (cf. communication complexity). The features of this concept are typically captured with the CONGEST(B) model, which is similarly defined as the LOCAL model, but where single messages can only contain B bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For ill-structured problems, on the other hand, it is not clear what steps need to be taken, i.e. there is no clear formula that would lead to success if followed correctly. In this case, the solution may sometimes come in a flash of insight in which the problem is suddenly seen in a new light. Another way to categorize different forms of problem solving is by distinguishing between algorithms and heuristics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In structural complexity theory, the Berman\u2013Hartmanis conjecture is an unsolved conjecture named after Leonard C. Berman and Juris Hartmanis that states that all NP-complete languages look alike, in the sense that they can be related to each other by polynomial time isomorphisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the aerospace industry, equipment on-board aircraft must be tested in situ, or in place, to confirm everything functions properly as a system. Individually, each piece may work but interference from nearby equipment may create unanticipated problems. Special test equipment is available for this in situ testing. It can also refer to repairs made to the aircraft structure or flight controls while still in place.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This enables training very deep recurrent neural networks with a very long time span t. A later LSTM version published in 2000 modulates the identity LSTM connections by so-called forget gates such that their weights are not fixed to 1.0 but can be learned. In experiments, the forget gates were initialized with positive bias weights, thus being opened, addressing the vanishing gradient problem. The Highway Network of May 2015 applies these principles to feedforward neural networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hypergraphs can be viewed as incidence structures. In particular, there is a bipartite \"incidence graph\" or \"Levi graph\" corresponding to every hypergraph, and conversely, every bipartite graph can be regarded as the incidence graph of a hypergraph when it is 2-colored and it is indicated which color class corresponds to hypergraph vertices and which to hypergraph edges. Hypergraphs have many other names.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s, Charles Forgy developed a successor to the Rete algorithm named Rete II. Unlike the original Rete (which is public domain) this algorithm was not disclosed. Rete II claims better performance for more complex problems (even orders of magnitude), and is officially implemented in CLIPS/R2, a C/++ implementation and in OPSJ, a Java implementation in 1998.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Internet Engineering Task Force, two working groups in the Operations & Maintenance Area deal with aspects of performance. The Interprovider Performance Measurement (IPPM) group focuses, as its name would suggest, on operational measurement of services. Performance measurements on single routers, or narrowly defined systems of routers, are the province of the Benchmarking Working Group (BMWG). RFC 2544 is the key BMWG document. A classic RFC 2544 benchmark uses half the router's (i.e., the device under test (DUT)) ports for input of a defined load, and measures the time at which the outputs appear at the output ports.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An alternative direction is to aggregate word embeddings, such as those returned by Word2vec, into sentence embeddings. The most straightforward approach is to simply compute the average of word vectors, known as continuous bag-of-words (CBOW). However, more elaborate solutions based on word vector quantization have also been proposed. One such approach is the vector of locally aggregated word embeddings (VLAWE), which demonstrated performance improvements in downstream text classification tasks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a nonlinear expectation is a nonlinear generalization of the expectation. Nonlinear expectations are useful in utility theory as they more closely match human behavior than traditional expectations. The common use of nonlinear expectations is in assessing risks under uncertainty. Generally, nonlinear expectations are categorized into sub-linear and super-linear expectations dependent on the additive properties of the given sets. Much of the study of nonlinear expectation is attributed to work of mathematicians within the past two decades.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More formally, a relatively well-defined usage refers to a conditional statement (or a universal conditional statement) with a false antecedent. One example of such a statement is \"if Tokyo is in France, then the Eiffel Tower is in Bolivia\". Such statements are considered vacuous truths, because the fact that the antecedent is false prevents using the statement to infer anything about the truth value of the consequent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In morphology, taxonomy and other descriptive disciplines in which a term for such shapes is necessary, terms such as trapezoidal or trapeziform commonly are useful in descriptions of particular organs or forms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of semigroups, since the binary operation is required to satisfy only the associativity property the problem of classification is considered extremely difficult. Descriptions of structures have been obtained for certain special classes of semigroups. For example, the structure of the sets of idempotents of regular semigroups is completely known.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z  {\\displaystyle \\mathbf {Z} } or Z  . {\\displaystyle \\mathbb {Z} .} Gaussian integers share many properties with integers: they form a Euclidean domain, and have thus a Euclidean division and a Euclidean algorithm; this implies unique factorization and many related properties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a Poisson process is a stochastic process of which the simplest case involves \"occurrences\" at random times, the waiting time until the next occurrence having a memoryless exponential distribution, and the number of \"occurrences\" in any time interval having a Poisson distribution whose expected value is proportional to the length of the time interval. Let Xt be the number of \"occurrences\" before time t, and let Tx be the waiting time until the xth \"occurrence\". We seek the probability density function of the random variable Tx. We use the probability mass function for the Poisson distribution, which tells us that Pr ( X t = x ) = ( \u03bb t ) x e \u2212 \u03bb t x !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, Brown clustering or IBM clustering is a form of hierarchical clustering of words based on the contexts in which they occur, proposed by Peter Brown, William A. Brown, Vincent Della Pietra, Peter de Souza, Jennifer Lai, and Robert Mercer of IBM in the context of language modeling. The intuition behind the method is that a class-based language model (also called cluster n-gram model), i.e. one where probabilities of words are based on the classes (clusters) of previous words, is used to address the data sparsity problem inherent in language modeling. The method has been successfully used to improve parsing , domain adaptation, and name d entity recognition.Jurafsky and Martin give the example of a flight reservation system that needs to estimate the likelihood of the bigram \"to Shanghai\", without having seen this in a training set. The system can obtain a good estimate if it can cluster \"Shanghai\" with other city names, then make its estimate based on the likelihood of phrases such as \"to London\", \"to Beijing\" and \"to Denver\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Lehmer mean of a tuple x {\\displaystyle x} of positive real numbers, named after Derrick Henry Lehmer, is defined as: L p ( x ) = \u2211 k = 1 n x k p \u2211 k = 1 n x k p \u2212 1 . {\\displaystyle L_{p}(\\mathbf {x} )={\\frac {\\sum _{k=1}^{n}x_{k}^{p}}{\\sum _{k=1}^{n}x_{k}^{p-1}}}.} The weighted Lehmer mean with respect to a tuple w {\\displaystyle w} of positive weights is defined as: L p , w ( x ) = \u2211 k = 1 n w k \u22c5 x k p \u2211 k = 1 n w k \u22c5 x k p \u2212 1 . {\\displaystyle L_{p,w}(\\mathbf {x} )={\\frac {\\sum _{k=1}^{n}w_{k}\\cdot x_{k}^{p}}{\\sum _{k=1}^{n}w_{k}\\cdot x_{k}^{p-1}}}.} The Lehmer mean is an alternative to power means for interpolating between minimum and maximum via arithmetic mean and harmonic mean.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So while these ad-hoc manufacturer-specific solutions were effective, they were not standardized, and there were no provisions for providing interoperability. This drew the attention of the VESA consortium and resulted in a proposal for a voluntary and royalty-free local bus standard in 1992. An additional benefit from this standardization (beyond the primary goal of greater graphics card performance) was that other devices could also be designed to utilize the performance offered from VLB; notably, mass-storage controllers were offered for VLB, providing increased hard-disk performance. VLB bandwidth depended on the CPU's bus speed: It started at 100 MB/s for CPUs with a 25 MHz bus, increased to 133 MB/s at 33 MHz and 160 MB/s at 40 MHz, and reached 200 MB/s at 50 MHz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution. Many techniques for carrying out regression analysis have been developed. Familiar methods, such as linear regression, are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data (e.g. using ordinary least squares). Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then let F: X \u00d7 Y \u2192 R \u222a { + \u221e } {\\displaystyle F:X\\times Y\\to \\mathbb {R} \\cup \\{+\\infty \\}} be a perturbation function such that F ( x , 0 ) = f ( x ) {\\displaystyle F(x,0)=f(x)} . The duality gap is the difference given by inf x \u2208 X  \u2212 sup y \u2217 \u2208 Y \u2217  {\\displaystyle \\inf _{x\\in X}-\\sup _{y^{*}\\in Y^{*}}} where F \u2217 {\\displaystyle F^{*}} is the convex conjugate in both variables.In computational optimization, another \"duality gap\" is often reported, which is the difference in value between any dual solution and the value of a feasible but suboptimal iterate for the primal problem. This alternative \"duality gap\" quantifies the discrepancy between the value of a current feasible but suboptimal iterate for the primal problem and the value of the dual problem; the value of the dual problem is, under regularity conditions, equal to the value of the convex relaxation of the primal problem: The convex relaxation is the problem arising replacing a non-convex feasible set with its closed convex hull and with replacing a non-convex function with its convex closure, that is the function that has the epigraph that is the closed convex hull of the original primal objective function. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\u03b1 = sup h \u2208 H 0 P ( test rejects H 0 \u2223 h ) . {\\displaystyle \\alpha =\\sup _{h\\in H_{0}}P({\\text{test rejects }}H_{0}\\mid h).} A test is said to have significance level \u03b1 {\\displaystyle \\alpha } if its size is less than or equal to \u03b1 {\\displaystyle \\alpha } . In many cases the size and level of a test are equal. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Code elements 4 and 5 are transmitted by keys 4 and 5, and these are operated by the first two fingers of the left hand. \"Baudot's code became known as the International Telegraph Alphabet No. 1 (ITA1). It is no longer used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical linear algebra, the Cuthill\u2013McKee algorithm (CM), named after Elizabeth Cuthill and James McKee, is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a band matrix form with a small bandwidth. The reverse Cuthill\u2013McKee algorithm (RCM) due to Alan George and Joseph Liu is the same algorithm but with the resulting index numbers reversed. In practice this generally results in less fill-in than the CM ordering when Gaussian elimination is applied.The Cuthill McKee algorithm is a variant of the standard breadth-first search algorithm used in graph algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recursive implementations of D&C algorithms, one must make sure that there is sufficient memory allocated for the recursion stack, otherwise, the execution may fail because of stack overflow. D&C algorithms that are time-efficient often have relatively small recursion depth. For example, the quicksort algorithm can be implemented so that it never requires more than log 2 \u2061 n {\\displaystyle \\log _{2}n} nested recursive calls to sort n {\\displaystyle n} items.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fair cake-cutting problem, the partners often have different entitlements. For example, the resource may belong to two shareholders such that Alice holds 8/13 and George holds 5/13. This leads to the criterion of weighted proportionality (WPR): there are several weights w i {\\displaystyle w_{i}} that sum up to 1, and every partner i {\\displaystyle i} should receive at least a fraction w i {\\displaystyle w_{i}} of the resource by their own valuation. In contrast, in the simpler proportional cake-cutting setting, the weights are equal: w i = 1 / n {\\displaystyle w_{i}=1/n} for all i {\\displaystyle i} Several algorithms can be used to find a WPR division.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using the load balancer, user can create systems that are responsive to user actions. Apps in the cloud are run independently of each other. This allows multiple versions support of the same app and \"soft migration\" set up for moving users to updated versions of products. Apps can be tested in the cloud by in an isolated environment run. This way, program errors will not affect the physical system or other apps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A common case of the ABA problem is encountered when implementing a lock-free data structure. If an item is removed from the list, deleted, and then a new item is allocated and added to the list, it is common for the allocated object to be at the same location as the deleted object due to MRU memory allocation. A pointer to the new item is thus often equal to a pointer to the old item, causing an ABA problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the advent of multicore architectures, network processors can be used for higher layer (L4-L7) processing.Additionally, traffic management, which is a critical element in L2-L3 network processing and used to be executed by a variety of co-processors, has become an integral part of the network processor architecture, and a substantial part of its silicon area (\"real estate\") is devoted to the integrated traffic manager. Modern network processors are also equipped with low-latency high-throughput on-chip interconnection networks optimized for the exchange of small messages among cores (few data words). Such networks can be used as an alternative facility for the efficient inter-core communication aside of the standard use of shared memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Advances in LTE and other technologies are rapidly improving the ability to transfer information over a wireless link at various combinations of speeds, distances, and non-line-of-sight conditions. \"Mobile service provisions\" refers in part to the ability of subscribers to purchase mobile phone like services, as is often seen in co-marketing efforts between providers of landline services. It also reflects the ambition to gain wireless access on the go to voice, internet, and content/video without tethering to a network via cables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the \"reserves first\" model of money creation, a given reserve is lent out by a bank, then deposited at a bank (possibly different), which is then lent out again, the process repeating and the ultimate result being a geometric series.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 19th century, philologists devised a now classic classification of languages according to their morphology. Some languages are isolating, and have little to no morphology; others are agglutinative whose words tend to have many easily separable morphemes (such as Turkic languages); others yet are inflectional or fusional because their inflectional morphemes are \"fused\" together (like some Indo-European languages such as Pashto and Russian). That leads to one bound morpheme conveying multiple pieces of information. A standard example of an isolating language is Chinese.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics \u2014 specifically, in probability theory \u2014 the concentration dimension of a Banach space-valued random variable is a numerical measure of how \"spread out\" the random variable is compared to the norm on the space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of Wi-Fi (wireless local area networks using the IEEE 802.11b and 802.11g specification), the term beacon signifies a specific data transmission from the wireless access point (AP), which carries the SSID, the channel number and security protocols such as Wired Equivalent Privacy (WEP) or Wi-Fi Protected Access (WPA). This transmission does not contain the link layer address of another Wi-Fi device, therefore it can be received by any LAN client.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and information geometry, statistical distances measure the degree of difference between two probability distributions. There are many kinds of statistical distances, typically formalized as divergences; these allow a set of probability distributions to be understood as a geometrical object called a statistical manifold. The most elementary is the squared Euclidean distance, which is minimized by the least squares method; this is the most basic Bregman divergence. The most important in information theory is the relative entropy (Kullback\u2013Leibler divergence), which allows one to analogously study maximum likelihood estimation geometrically; this is an example of both an f-divergence and a Bregman divergence (and in fact the only example which is both). Statistical manifolds corresponding to Bregman divergences are flat manifolds in the corresponding geometry, allowing an analog of the Pythagorean theorem (which holds for squared Euclidean distance) to be used for linear inverse problems in inference by optimization theory. Other important statistical distances include the Mahalanobis distance and the energy distance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory, an area of mathematical logic, proof compression is the problem of algorithmically compressing formal proofs. The developed algorithms can be used to improve the proofs generated by automated theorem proving tools such as SAT solvers, SMT-solvers, first-order theorem provers and proof assistants.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These systems, however, gave a very poor sound quality. The first microphone that enabled proper voice telephony was the (loose-contact) carbon microphone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sound, smartphones and feature phones vary little. Some audio-quality enhancing features, such as Voice over LTE and HD Voice, have appeared and are often available on newer smartphones. Sound quality can remain a problem due to the design of the phone, the quality of the cellular network and compression algorithms used in long-distance calls. Audio quality can be improved using a VoIP application over WiFi. Cellphones have small speakers so that the user can use a speakerphone feature and talk to a person on the phone without holding it to their ear. The small speakers can also be used to listen to digital audio files of music or speech or watch videos with an audio component, without holding the phone close to the ear.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the van der Corput inequality is a corollary of the Cauchy\u2013Schwarz inequality that is useful in the study of correlations among vectors, and hence random variables. It is also useful in the study of equidistributed sequences, for example in the Weyl equidistribution estimate. Loosely stated, the van der Corput inequality asserts that if a unit vector v {\\displaystyle v} in an inner product space V {\\displaystyle V} is strongly correlated with many unit vectors u 1 , \u2026 , u n \u2208 V {\\displaystyle u_{1},\\dots ,u_{n}\\in V} , then many of the pairs u i , u j {\\displaystyle u_{i},u_{j}} must be strongly correlated with each other. Here, the notion of correlation is made precise by the inner product of the space V {\\displaystyle V}: when the absolute value of \u27e8 u , v \u27e9 {\\displaystyle \\langle u,v\\rangle } is close to 1 {\\displaystyle 1} , then u {\\displaystyle u} and v {\\displaystyle v} are considered to be strongly correlated. (More generally, if the vectors involved are not unit vectors, then strong correlation means that | \u27e8 u , v \u27e9 | \u2248 \u2016 u \u2016 \u2016 v \u2016 {\\displaystyle |\\langle u,v\\rangle |\\approx \\|u\\|\\|v\\|} .)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, a large data set leads to a large K, and storing K may become a problem. One way to deal with this is to perform clustering on the dataset, and populate the kernel with the means of those clusters. Since even this method may yield a relatively large K, it is common to compute only the top P eigenvalues and eigenvectors of the eigenvalues are calculated in this way.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some models of phonology as well as morphophonology in the field of linguistics, the underlying representation (UR) or underlying form (UF) of a word or morpheme is the abstract form that a word or morpheme is postulated to have before any phonological rules have been applied to it. In contrast, a surface representation is the phonetic representation of the word or sound. The concept of an underlying representation is central to generative grammar.If more phonological rules apply to the same underlying form, they can apply wholly independently of each other or in a feeding or counterbleeding order. The underlying representation of a morpheme is considered to be invariable across related forms (except in cases of suppletion), despite alternations among various allophones on the surface.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "+ 4! = 19. Regardless of the parity of n, the last (nth) summand, n!, is given a positive sign, the (n \u2013 1)th summand is given a negative sign, and the signs of the lower-indexed summands are alternated accordingly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Compilers were updated to take advantage of these instructions. The benefits of semantically rich instructions with compact encodings can be seen in modern processors as well, particularly in the high-performance segment where caches are a central component (as opposed to most embedded systems). This is because these fast, but complex and expensive, memories are inherently limited in size, making compact code beneficial. Of course, the fundamental reason they are needed is that main memories (i.e., dynamic RAM today) remain slow compared to a (high-performance) CPU core.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle fg=\\Lambda (f,g)+\\Lambda (g,f).} For any appropriate functions f {\\displaystyle f} and h {\\displaystyle h} with h ( 0 ) = 0 {\\displaystyle h(0)=0} , it is the case that h ( f ) = \u039b ( f , h \u2032 ( f ) ) {\\displaystyle h(f)=\\Lambda (f,h'(f))} . It should satisfy some form of the Leibniz rule.A paraproduct may also be required to satisfy some form of H\u00f6lder's inequality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, radio silence or Emissions Control (EMCON) is a status in which all fixed or mobile radio stations in an area are asked to stop transmitting for safety or security reasons. The term \"radio station\" may include anything capable of transmitting a radio signal. A single ship, aircraft, spacecraft, or group of them may also maintain radio silence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Our modified model requires us to add two more instructions to the 7 Post\u2013Turing instructions. The abbreviations that we will use are: In the cases of R, L, E, P0, and P1 after doing its task the machine continues on to the next instruction in numerical sequence; ditto for the jumps if their tests fail. But, for brevity, our examples will only use three squares.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more technical terms, let us assume that we have a theory described by a certain function Z {\\displaystyle Z} of the state variables { s i } {\\displaystyle \\{s_{i}\\}} and a certain set of coupling constants { J k } {\\displaystyle \\{J_{k}\\}} . This function may be a partition function, an action, a Hamiltonian, etc. It must contain the whole description of the physics of the system. Now we consider a certain blocking transformation of the state variables { s i } \u2192 { s ~ i } {\\displaystyle \\{s_{i}\\}\\to \\{{\\tilde {s}}_{i}\\}} , the number of s ~ i {\\displaystyle {\\tilde {s}}_{i}} must be lower than the number of s i {\\displaystyle s_{i}} . Now let us try to rewrite the Z {\\displaystyle Z} function only in terms of the s ~ i {\\displaystyle {\\tilde {s}}_{i}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On the other hand, an outcome of | \u03c8 11 \u27e9 {\\displaystyle |\\psi _{11}\\rangle } cannot possibly be observed from a qubit in state | \u03c8 01 \u27e9 {\\displaystyle |\\psi _{01}\\rangle } . Thus in the case that Bob measures in the Hadamard basis and observes state | \u03c8 11 \u27e9 {\\displaystyle |\\psi _{11}\\rangle } (and only in that case), Bob can deduce which state he was sent and therefore what the secret bit is. From the remaining k {\\displaystyle k} bits where both Bob's measurement was conclusive, Alice randomly chooses k / 2 {\\displaystyle k/2} bits and discloses her choices over the public channel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nelder (1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. See also Chrisman (1998), van den Berg (1991).The issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. \"The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations. Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer\" (Hand, 2004, p. 82).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sprint reviews can be seen as a powerful method to improve external correspondence whilst they help to share data about the features and prerequisite conditions between partners or stakeholders. Agile practices also assist in building trust between various teams associated with the process by stimulating consistent communication and conveyance of programming deliverables. As indicated by an investigation made by Passivara, Durasiewicz and, Lassenius, the software quality and correspondence are improved and communication and coordinated effort are more regular comparatively as a result of the Scrum approach utilized in the undertaking.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The multiplication axiom for integers defined this way is ( x p , x m ) \u00d7 ( y p , y m ) = ( x p \u00d7 y p + x m \u00d7 y m , x p \u00d7 y m + x m \u00d7 y p ) . {\\displaystyle (x_{p},\\,x_{m})\\times (y_{p},\\,y_{m})=(x_{p}\\times y_{p}+x_{m}\\times y_{m},\\;x_{p}\\times y_{m}+x_{m}\\times y_{p}).} The rule that \u22121 \u00d7 \u22121 = 1 can then be deduced from ( 0 , 1 ) \u00d7 ( 0 , 1 ) = ( 0 \u00d7 0 + 1 \u00d7 1 , 0 \u00d7 1 + 1 \u00d7 0 ) = ( 1 , 0 ) . {\\displaystyle (0,1)\\times (0,1)=(0\\times 0+1\\times 1,\\,0\\times 1+1\\times 0)=(1,0).} Multiplication is extended in a similar way to rational numbers and then to real numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A hash table to keep track of already defined pairs. This table is updated each time a new pair is created or removed.Since the hash table and the priority queue refer to the same elements (pairs), they can be implemented by a common data structure called PAIR with pointers for the hash table (h_next) and the priority queue (p_next and p_prev). Furthermore, each PAIR points to the beginning of the first (f_pos) and the last (b_pos) occurrences of the string represented by the PAIR in the sequence. The following picture shows an overview of this data structure. The following two pictures show an example of how these data structures look after the initialization and after applying one step of the pairing process (pointers to NULL are not displayed):", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X {\\displaystyle X} is said to be embedded in another object Y {\\displaystyle Y} , the embedding is given by some injective and structure-preserving map f: X \u2192 Y {\\displaystyle f:X\\rightarrow Y} . The precise meaning of \"structure-preserving\" depends on the kind of mathematical structure of which X {\\displaystyle X} and Y {\\displaystyle Y} are instances. In the terminology of category theory, a structure-preserving map is called a morphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Timestamps and vector clocks are often used to detect concurrency between updates. Some people use \"first writer wins\" in situations where \"last writer wins\" is unacceptable.Reconciliation of concurrent writes must occur sometime before the next read, and can be scheduled at different instants: Read repair: The correction is done when a read finds an inconsistency. This slows down the read operation. Write repair: The correction takes place during a write operation, slowing down the write operation. Asynchronous repair: The correction is not part of a read or write operation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most philosophical languages, words are constructed from a limited set of morphemes that are treated as \"elemental\" or \"fundamental\". \"Philosophical language\" is sometimes used synonymously with \"taxonomic language\". Vocabularies of oligosynthetic languages are made of compound words, which are coined from a small (theoretically minimal) set of morphemes. Languages like Toki Pona similarly use a limited set of root words but produce phrases which remain series of distinct words.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the super-logarithm is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverse functions, super-roots and super-logarithms. There are several ways of interpreting super-logarithms: As the Abel function of exponential functions, As the inverse function of tetration with respect to the height, As a generalization of Robert Munafo's large number class system,For positive integer values, the super-logarithm with base-e is equivalent to the number of times a logarithm must be iterated to get to 1 (the Iterated logarithm).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It can respond to people touching it. It's very satisfying, although we obviously have a long way to go yet.\" In his opinion, it may be possible to build an android that is indistinguishable from a human, at least during a brief encounter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle f(x)\\cdot g(x)=\\sum _{k=0}^{\\infty }\\left(\\sum _{i=0}^{k}a_{i}b_{k-i}\\right)x^{k}.} In particular, we write f 2 = f ( x ) \u22c5 f ( x ) {\\displaystyle f^{2}=f(x)\\cdot f(x)} , f 3 = f ( x ) \u22c5 f ( x ) \u22c5 f ( x ) {\\displaystyle f^{3}=f(x)\\cdot f(x)\\cdot f(x)} , and so on. In analogy to algebraic numbers, a power series f ( x ) {\\displaystyle f(x)} is called algebraic over Q ( x ) {\\displaystyle \\mathbb {Q} (x)} , if there exists a finite set of polynomials p 0 ( x ) , p 1 ( x ) , p 2 ( x ) , \u2026 , p n ( x ) {\\displaystyle p_{0}(x),p_{1}(x),p_{2}(x),\\ldots ,p_{n}(x)} each with rational coefficients such that p 0 ( x ) + p 1 ( x ) \u22c5 f + p 2 ( x ) \u22c5 f 2 + \u22ef + p n ( x ) \u22c5 f n = 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They help to describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting. The concept of logarithm as the inverse of exponentiation extends to other mathematical structures as well. However, in general settings, the logarithm tends to be a multi-valued function. For example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete logarithm is the multi-valued inverse of the exponential function in finite groups; it has uses in public-key cryptography.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A {\\displaystyle A} together with a reflexive and transitive binary relation \u2264 {\\displaystyle \\,\\leq \\,} (that is, a preorder), with the additional property that every pair of elements has an upper bound. In other words, for any a {\\displaystyle a} and b {\\displaystyle b} in A {\\displaystyle A} there must exist c {\\displaystyle c} in A {\\displaystyle A} with a \u2264 c {\\displaystyle a\\leq c} and b \u2264 c . {\\displaystyle b\\leq c.} A directed set's preorder is called a direction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and more specifically in order theory, several different types of ordered set have been studied. They include: Cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise Lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound. Many different types of lattice have been studied; see map of lattices for a list. Partially ordered sets (or posets), orderings in which some pairs are comparable and others might not be Preorders, a generalization of partial orders allowing ties (represented as equivalences and distinct from incomparabilities) Semiorders, partial orders determined by comparison of numerical values, in which values that are too close to each other are incomparable; a subfamily of partial orders with certain restrictions Total orders, orderings that specify, for every two distinct elements, which one is less than the other Weak orders, generalizations of total orders allowing ties (represented either as equivalences or, in strict weak orders, as transitive incomparabilities) Well-orders, total orders in which every non-empty subset has a least element Well-quasi-orderings, a class of preorders generalizing the well-orders", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, given a graph G {\\displaystyle G} and a specific community partition \u03c3: V ( G ) \u2192 { 1 , . . . , b } {\\displaystyle \\sigma :V(G)\\rightarrow \\{1,...,b\\}} (an assignment of a community-index \u03c3 ( v ) {\\displaystyle \\sigma (v)} (here taken as an integer from 1 {\\displaystyle 1} to b {\\displaystyle b} ) to each vertex v \u2208 V ( G ) {\\displaystyle v\\in V(G)} in the graph), the modularity measures the difference between the number of links from/to each pair of communities, from that expected in a graph that is completely random in all respects other than the set of degrees of each of the vertices (the degree sequence). In other words, the modularity contrasts the exhibited community structure in G {\\displaystyle G} with that of a null model, which in this case is the configuration model (the maximally random graph subject to a constraint on the degree of each vertex).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, bipolar encoding is a type of return-to-zero (RZ) line code, where two nonzero values are used, so that the three values are +, \u2212, and zero. Such a signal is called a duobinary signal. Standard bipolar encodings are designed to be DC-balanced, spending equal amounts of time in the + and \u2212 states. The reason why bipolar encoding is classified as a return to zero (RZ) is that when a bipolar encoded channel is idle the line is held at a constant \"zero\" level, and when it is transmitting bits the line is either in a +V or -V state corresponding to the binary bit being transmitted. Thus, the line always returns to the \"zero\" level to denote optionally a separation of bits or to denote idleness of the line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle f_{X,Y}(x,y)=f_{X}(x)f_{Y}(y).} That is, the joint distribution is equal to the product of the marginal distributions.Unless it is not clear in context, in practice the modifier \"mutual\" is usually dropped so that independence means mutual independence. A statement such as \" X, Y, Z are independent random variables\" means that X, Y, Z are mutually independent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other types of grammatical features, by contrast, may be relevant to semantics (morphosemantic features), such as tense, aspect and mood, or may only be relevant to morphology (morphological features). Inflectional class (a word's membership of a particular verb class or noun class) is a purely morphological feature, because it is only relevant to the morphological realisation of the word.In formal models of grammar, features can be represented as attribute-value pairs. For example, in Lexical functional grammar, syntactic features are represented alongside grammatical functions at the level of functional structure (f-structure), which takes the form of an attribute-value matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In symbolic logic, the universal quantifier symbol \u2200 {\\displaystyle \\forall } (a turned \"A\" in a sans-serif font, Unicode U+2200) is used to indicate universal quantification. It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's \u2203 {\\displaystyle \\exists } (turned E) notation for existential quantification and the later use of Peano's notation by Bertrand Russell.For example, if P(n) is the predicate \"2\u00b7n > 2 + n\" and N is the set of natural numbers, then \u2200 n \u2208 N P ( n ) {\\displaystyle \\forall n\\!\\in \\!\\mathbb {N} \\;P(n)} is the (false) statement \"for all natural numbers n, one has 2\u00b7n > 2 + n\".Similarly, if Q(n) is the predicate \"n is composite\", then \u2200 n \u2208 N ( Q ( n ) \u2192 P ( n ) ) {\\displaystyle \\forall n\\!\\in \\!\\mathbb {N} \\;{\\bigl (}Q(n)\\rightarrow P(n){\\bigr )}} is the (true) statement \"for all natural numbers n, if n is composite, then 2\u00b7n > 2 + n\".Several variations in the notation for quantification (which apply to all forms) can be found in the Quantifier article.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example: An isometry is an isomorphism of metric spaces. A homeomorphism is an isomorphism of topological spaces. A diffeomorphism is an isomorphism of spaces equipped with a differential structure, typically differentiable manifolds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A variety of these ways have been triedfor storing objects in a database. Some products have approached the problem from the application programming end, by making the objects manipulated by the program persistent. This typically requires the addition of some kind of query language, since conventional programming languages do not have the ability to find objects based on their information content.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sparse direct solvers, pivoting may be needed, where ultimately the resulting matrix has 2x2 blocks on the diagonal, rather than a working towards a completely pure LLH Cholesky decomposition for positive definite symmetric or Hermitian systems. Pivoting may result in unpredictable memory usage increases. For iterative solvers, only GMRES based solvers work, rather than slightly \"cheaper\" MINRES based solvers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of the TTF a testing tactic is a means to partition any test class of any operation. However, some of the testing tactics used in practice actually do not always generate a partition of some test classes. Some testing tactics originally proposed for the TTF are the following: Disjunctive Normal Form (DNF). By applying this tactic the operation is written in Disjunctive Normal Form and the test class is divided in as many test classes as terms are in the resulting operation's predicate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the formal language of first-order logic, set A {\\displaystyle A} has the property of being inhabited if \u2203 z . ( z \u2208 A ) . {\\displaystyle \\exists z. (z\\in A).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some countries, text messages can be used to contact emergency services. In the UK, text messages can be used to call emergency services only after registering with the emergency SMS service. This service is primarily aimed at people who, because of disability, are unable to make a voice call. It has recently been promoted as a means for walkers and climbers to call emergency services from areas where a voice call is not possible due to low signal strength.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(Indeed, the lower bound is easy to see: the multiset containing n \u2212 1 copies of 0 and n \u2212 1 copies of 1 contains no n-subset summing to a multiple of n.) This result is known as the Erd\u0151s\u2013Ginzburg\u2013Ziv theorem after its discoverers. It may also be deduced from the Cauchy\u2013Davenport theorem.More general results than this theorem exist, such as Olson's theorem, Kemnitz's conjecture (proved by Christian Reiher in 2003), and the weighted EGZ theorem (proved by David J. Grynkiewicz in 2005).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the bottom type is inhabited, its terms typically correspond to error conditions such as undefined behavior, infinite recursion, or unrecoverable errors. In Bounded Quantification with Bottom, Pierce says that \"Bot\" has many uses: In a language with exceptions, a natural type for the raise construct is raise \u2208 exception -> Bot, and similarly for other control structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The transition at np = 1 from giant component to small component has analogs for these graphs, but for lattices the transition point is difficult to determine. Physicists often refer to study of the complete graph as a mean field theory. Thus the Erd\u0151s\u2013R\u00e9nyi process is the mean-field case of percolation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bloomfield's \"sign base\" morpheme hypothesis: As morphemes, they are dualistic signs, since they have both (phonological) form and meaning. Bloomfield's \"lexical morpheme\" hypothesis: morphemes, affixes and roots alike are stored in the lexicon.Morpheme-based morphology comes in two flavours, one Bloomfieldian and one Hockettian. For Bloomfield, the morpheme was the minimal form with meaning, but did not have meaning itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, zero-sum Ramsey theory or zero-sum theory is a branch of combinatorics. It deals with problems of the following kind: given a combinatorial structure whose elements are assigned different weights (usually elements from an Abelian group A {\\displaystyle A} ), one seeks for conditions that guarantee the existence of certain substructure whose weights of its elements sum up to zero (in A {\\displaystyle A} ). It combines tools from number theory, algebra, linear algebra, graph theory, discrete analysis, and other branches of mathematics. The classic result in this area is the 1961 theorem of Paul Erd\u0151s, Abraham Ginzburg, and Abraham Ziv: for any 2 m \u2212 1 {\\displaystyle 2m-1} elements of Z m {\\displaystyle \\mathbb {Z} _{m}} , there is a subset of size m {\\displaystyle m} that sums to zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n \u2212 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n \u2212 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p \u2212 1 for some prime p. The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... (sequence A000043 in the OEIS) and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... (sequence A000668 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics the Function Field Sieve is one of the most efficient algorithms to solve the Discrete Logarithm Problem (DLP) in a finite field. It has heuristic subexponential complexity. Leonard Adleman developed it in 1994 and then elaborated it together with M. D. Huang in 1999.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, theory shows that collaboration emerges spontaneously in smaller groups rather than in large ones (see e.g. Dunbar's number). This explains why labor unions or charities often have a federated structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Example: SEQ x := x + 1 y := x * x PAR begins a list of expressions that may be evaluated concurrently. Example: PAR p() q() ALT specifies a list of guarded commands. The guards are a combination of a boolean condition and an input expression, both optional.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of efficient representations of graphs, J. H. Muller defined a local structure or adjacency labeling scheme for a graph G in a given family F of graphs to be an assignment of an O(log n)-bit identifier to each vertex of G, together with an algorithm (that may depend on F but is independent of the individual graph G) that takes as input two vertex identifiers and determines whether or not they are the endpoints of an edge in G. That is, this type of implicit representation is analogous to an adjacency matrix: it is straightforward to check whether two vertices are adjacent but finding the neighbors of any vertex may involve looping through all vertices and testing which ones are neighbors.Graph families with adjacency labeling schemes include: Bounded degree graphs If every vertex in G has at most d neighbors, one may number the vertices of G from 1 to n and let the identifier for a vertex be the (d + 1)-tuple of its own number and the numbers of its neighbors. Two vertices are adjacent when the first numbers in their identifiers appear later in the other vertex's identifier. More generally, the same approach can be used to provide an implicit representation for graphs with bounded arboricity or bounded degeneracy, including the planar graphs and the graphs in any minor-closed graph family. Intersection graphs An interval graph is the intersection graph of a set of line segments in the real line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psychology, semantic memory is memory for meaning \u2013 in other words, the aspect of memory that preserves only the gist, the general significance, of remembered experience \u2013 while episodic memory is memory for the ephemeral details \u2013 the individual features, or the unique particulars of experience. The term \"episodic memory\" was introduced by Tulving and Schacter in the context of \"declarative memory\", which involved simple association of factual or objective information concerning its object. Word meaning is measured by the company they keep, i.e. the relationships among words themselves in a semantic network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If \u22121 < x < 0 or 1 < x, then x3 > x. If x < \u22121 or 0 < x < 1, then x3 < x. All aforementioned properties pertain also to any higher odd power (x5, x7, ...) of real numbers. Equalities and inequalities are also true in any ordered ring.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of data management, data classification as a part of the Information Lifecycle Management (ILM) process can be defined as a tool for categorization of data to enable/help organizations to effectively answer the following questions: What data types are available? Where are certain data located? What access levels are implemented?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Artin\u2013Hasse exponential, introduced by Artin and Hasse (1928), is the power series given by E p ( x ) = exp \u2061 ( x + x p p + x p 2 p 2 + x p 3 p 3 + \u22ef ) . {\\displaystyle E_{p}(x)=\\exp \\left(x+{\\frac {x^{p}}{p}}+{\\frac {x^{p^{2}}}{p^{2}}}+{\\frac {x^{p^{3}}}{p^{3}}}+\\cdots \\right).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some real networks, the same methods as for generated networks can also be used. In many cases, however, it may not make sense to consider multiple edges between two vertices, or such information is not available. The high degree vertices (hubs) may also be an important part of the network that cannot be removed without changing other fundamental properties. To determine whether the assortativity or disassortativity of a network is of structural origin, the network can be compared with a degree-preserving randomized version of itself (without multiple edges).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1920s, Leon Chwistek and Frank P. Ramsey noticed that, if one is willing to give up the vicious circle principle, the hierarchy of levels of types in the \"ramified theory of types\" can be collapsed. The resulting restricted logic is called the theory of simple types or, perhaps more commonly, simple type theory. Detailed formulations of simple type theory were published in the late 1920s and early 1930s by R. Carnap, F. Ramsey, W.V.O. Quine, and A. Tarski.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s, Noam Chomsky formulated the generative theory of language. According to this theory, the most basic form of language is a set of syntactic rules that is universal for all humans and which underlies the grammars of all human languages. This set of rules is called Universal Grammar; for Chomsky, describing it is the primary objective of the discipline of linguistics. Thus, he considered that the grammars of individual languages are only of importance to linguistics insofar as they allow us to deduce the universal underlying rules from which the observable linguistic variability is generated.In opposition to the formal theories of the generative school, functional theories of language propose that since language is fundamentally a tool, its structures are best analyzed and understood by reference to their functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other words, it cannot be a fully conserved (i.e., invariable) site nor can it be a (singleton) site with a difference in only one sequence (as seen, for example, in single-nucleotide polymorphisms and single-nucleotide variants). In both cases, the number of character-state changes is the same regardless of the topology of the tree, equal to 0 and 1 respectively. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Estimation theory is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data. Such properties can be used to determine the best rules to use under given circumstances. However, in robust statistics, statistical theory goes on to consider the balance between having good properties, if tightly defined assumptions hold, and having less good properties that hold under wider conditions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quicksort, there is a subprocedure called partition that can, in linear time, group a list (ranging from indices left to right) into two parts: those less than a certain element, and those greater than or equal to the element. Here is pseudocode that performs a partition about the element list: function partition(list, left, right, pivotIndex) is pivotValue := list swap list and list // Move pivot to end storeIndex := left for i from left to right \u2212 1 do if list < pivotValue then swap list and list increment storeIndex swap list and list // Move pivot to its final place return storeIndex This is known as the Lomuto partition scheme, which is simpler but less efficient than Hoare's original partition scheme. In quicksort, we recursively sort both branches, leading to best-case O ( n log \u2061 n ) {\\displaystyle O(n\\log n)} time. However, when doing selection, we already know which partition our desired element lies in, since the pivot is in its final sorted position, with all those preceding it in an unsorted order and all those following it in an unsorted order.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "X is the number of faces of each dice.For example, if a game calls for a roll of d4 or 1d4, it means \"roll one 4-sided die.\" If the final number is omitted, it is typically assumed to be a six, but in some contexts, other defaults are used. 3d6 would mean \"roll three six-sided dice.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software design, model-driven integration is a subset of model-driven architecture (MDA) which focuses purely on solving Application Integration problems using executable Unified Modeling Language (UML).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In technology, living documents can be implemented using a wiki. Other common living document tools include Google Docs and Nextcloud Collabora. Living documentation is a key concept in specification by example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to be able to use the available standard indexes to locations where index data is not available we have to incorporate a new term called the Location Factor (LF) to the standard index value. It is a dimensionless value for a particular location relative to either of the above-mentioned basis. Cost in A = Cost in USGC x LF(A) where A is the location for which cost is being evaluated and LF(A) is the location factor for the location A relative to USGC Location factors are greatly influenced by currency exchange rates due to their significant effect on Index value and hence vary drastically with time. Over the past couple of decades the location factors for various locations are trending close to the value 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that the concerning interior flow is horizontal, so w = 0 {\\displaystyle w=0} at all depths, even in the boundary layers. In this case, the Navier-Stokes momentum equations, governing geophysical motion can now be reduced to: \u2212 f v = \u2212 1 \u03c1 0 \u2202 p \u2202 x + \u03bd E \u2202 2 u \u2202 z 2 , f u = \u2212 1 \u03c1 0 \u2202 p \u2202 y + \u03bd E \u2202 2 v \u2202 z 2 , 0 = \u2212 1 \u03c1 0 \u2202 p \u2202 z , {\\displaystyle {\\begin{aligned}-fv&=-{\\frac {1}{\\rho _{0}}}{\\frac {\\partial p}{\\partial x}}+\\nu _{E}{\\frac {\\partial ^{2}u}{\\partial z^{2}}},\\\\fu&=-{\\frac {1}{\\rho _{0}}}{\\frac {\\partial p}{\\partial y}}+\\nu _{E}{\\frac {\\partial ^{2}v}{\\partial z^{2}}},\\\\0&=-{\\frac {1}{\\rho _{0}}}{\\frac {\\partial p}{\\partial z}},\\end{aligned}}} Where f {\\displaystyle f} is the Coriolis parameter, \u03c1 0 {\\displaystyle \\rho _{0}} the fluid density and \u03bd E {\\displaystyle \\nu _{E}} the eddy viscosity, which are all taken as a constant here for simplicity. These parameters have a small variance on the scale of an Ekman spiral, thus this approximation will hold.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this example, all URIs, both for edges and nodes (e.g. http://schema.org/Person, http://schema.org/birthPlace, http://www.wikidata.org/entity/Q1731) can be dereferenced and will result in further RDF graphs, describing the URI, e.g. that Dresden is a city in Germany, or that a person, in the sense of that URI, can be fictional. The second graph shows the previous example, but now enriched with a few of the triples from the documents that result from dereferencing https://schema.org/Person (green edge) and https://www.wikidata.org/entity/Q1731 (blue edges). Additionally to the edges given in the involved documents explicitly, edges can be automatically inferred: the triple from the original RDFa fragment and the triple from the document at https://schema.org/Person (green edge in the figure) allow to infer the following triple, given OWL semantics (red dashed line in the second Figure):", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to connect this to tango trees, we will find an upper bound on the work done by the tango tree for a given access sequence. Our upper bound will be ( k + 1 ) O ( log \u2061 log \u2061 n ) {\\displaystyle (k+1)O(\\log \\log n)} , where k is the number of interleaves. The total cost is divided into two parts, searching for the element, and updating the structure of the tango tree to maintain the proper invariants (switching preferred children and re-arranging preferred paths).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Software has always been electronically transferred, and encryption has always been part of computing. The introduction of unified commercial software distribution catalog with a true application storefront to collectively manage and provide encryption for apps and media was a seminal invention. This is because by protecting the digital rights of artists online, the App Store provided the first viable economic and instant distribution mechanism which ultimately exploded the pace of software adoption and created an economic boom.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of constraint satisfaction problems, flexible variants exist that deal with soft constraints in a similar way to preferences in preference-based planning. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, one call-hour could be one call for an hour or two (possibly concurrent) calls for half an hour each. Call-seconds give a measure of the average number of concurrent calls. Offered load is defined as the traffic density per unit time, measured in erlangs. An erlang is defined as one call-hour per hour, or 3,600 call-seconds per hour. Hence, if one CCS is measured over a one-hour period, the offered load is 1/36 erlangs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Newton polytope is an integral polytope associated with a multivariate polynomial. It can be used to analyze the polynomial's behavior when specific variables are considered negligible relative to the others. Specifically, given a vector x = ( x 1 , \u2026 , x n ) {\\displaystyle \\mathbf {x} =(x_{1},\\ldots ,x_{n})} of variables and a finite family ( a k ) k {\\displaystyle (\\mathbf {a} _{k})_{k}} of pairwise distinct vectors from N n {\\displaystyle \\mathbb {N} ^{n}} each encoding the exponents within a monomial, consider the multivariate polynomial f ( x ) = \u2211 k c k x a k {\\displaystyle f(\\mathbf {x} )=\\sum _{k}c_{k}\\mathbf {x} ^{\\mathbf {a} _{k}}} where we use the shorthand notation ( x 1 , \u2026 , x n ) ( y 1 , \u2026 , y n ) {\\displaystyle (x_{1},\\ldots ,x_{n})^{(y_{1},\\ldots ,y_{n})}} for the monomial x 1 y 1 x 2 y 2 \u22ef x n y n {\\displaystyle x_{1}^{y_{1}}x_{2}^{y_{2}}\\cdots x_{n}^{y_{n}}} . Then the Newton polytope associated to f {\\displaystyle f} is the convex hull of the vectors a k {\\displaystyle \\mathbf {a} _{k}} ; that is Newt \u2061 ( f ) = { \u2211 k \u03b1 k a k: \u2211 k \u03b1 k = 1 & \u2200 j \u03b1 j \u2265 0 } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle p_{0}(x)+p_{1}(x)\\cdot f+p_{2}(x)\\cdot f^{2}+\\cdots +p_{n}(x)\\cdot f^{n}=0.} A context-free grammar is said to be unambiguous if every string generated by the grammar admits a unique parse tree or, equivalently, only one leftmost derivation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. This is a category because the composition of two continuous linear maps is again a continuous linear map. The category is often denoted TVect or TVS. Fixing a topological field K, one can also consider the subcategory TVectK of topological vector spaces over K with continuous K-linear maps as the morphisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1. An individual summand in a partition is called a part. The number of partitions of n is given by the partition function p(n).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is sometimes referred to as a sub-channel, but this is a misnomer because no additional channels are created. All users with different CTCSS tones on the same channel are still transmitting on the identical radio frequency, and their transmissions interfere with each other; however; the interference is masked under most conditions. The CTCSS feature also does not offer any security. A receiver with just a carrier or noise squelch does not suppress any sufficiently strong signal; in CTCSS mode it unmutes only when the signal also carries the correct sub-audible audio tone. The tones are not actually below the range of human hearing, but are poorly reproduced by most communications-grade speakers and in any event are usually filtered out before being sent to the speaker or headphone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the cuboctahedron-first parallel projection of the rectified tesseract into 3-dimensional space, the image has the following layout: The projection envelope is a cube. A cuboctahedron is inscribed in this cube, with its vertices lying at the midpoint of the cube's edges. The cuboctahedron is the image of two of the cuboctahedral cells. The remaining 6 cuboctahedral cells are projected to the square faces of the cube. The 8 tetrahedral volumes lying at the triangular faces of the central cuboctahedron are the images of the 16 tetrahedral cells, two cells to each image.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum mechanics, bra\u2013ket notation is used ubiquitously to denote quantum states. The notation uses angle brackets, \u27e8 {\\displaystyle \\langle } and \u27e9 {\\displaystyle \\rangle } , and a vertical bar | {\\displaystyle |} , to construct \"bras\" and \"kets\". A ket is of the form | v \u27e9 {\\displaystyle |v\\rangle } . Mathematically it denotes a vector, v {\\displaystyle {\\boldsymbol {v}}} , in an abstract (complex) vector space V {\\displaystyle V} , and physically it represents a state of some quantum system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Neville's algorithm is an algorithm used for polynomial interpolation that was derived by the mathematician Eric Harold Neville in 1934. Given n + 1 points, there is a unique polynomial of degree \u2264 n which goes through the given points. Neville's algorithm evaluates this polynomial. Neville's algorithm is based on the Newton form of the interpolating polynomial and the recursion relation for the divided differences. It is similar to Aitken's algorithm (named after Alexander Aitken), which is nowadays not used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a matrix is often used to represent the coefficients in a system of linear equations, and determinants can be used to solve these equations (Cramer's rule), although other methods of solution are computationally much more efficient. Determinants are used for defining the characteristic polynomial of a matrix, whose roots are the eigenvalues. In geometry, the signed n-dimensional volume of a n-dimensional parallelepiped is expressed by a determinant, and the determinant of (the matrix of) a linear transformation determines how the orientation and the n-dimensional volume are transformed. This is used in calculus with exterior differential forms and the Jacobian determinant, in particular for changes of variables in multiple integrals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the sieve of Pritchard is an algorithm for finding all prime numbers up to a specified bound. Like the ancient sieve of Eratosthenes, it has a simple conceptual basis in number theory. It is especially suited to quick hand computation for small bounds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, Sec. 204.2(d)(1) of Regulation D (FRB) previously limited withdrawals from savings accounts to six transfers or withdrawals per month, a limitation which was removed in April 2020, though some banks continue to impose a limit voluntarily as of 2021. There is no limit to the number of deposits into the account. Violations of the regulation may result in a service charge or may result in the account being changed to a checking account. Regulation D sets smaller reserve requirements for savings account balances. In addition, customers can plan withdrawals to avoid fees and earn interest, which contributes to more stable savings account balances on which banks can lend. A savings account linked to a checking account at the same financial institution can help avoid fees due to overdrafts and reduce banking costs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bob communicates over a public channel with Alice to determine which b i {\\displaystyle b_{i}} and b i \u2032 {\\displaystyle b'_{i}} are not equal. Both Alice and Bob now discard the bits in a {\\displaystyle a} and a \u2032 {\\displaystyle a'} where b {\\displaystyle b} and b \u2032 {\\displaystyle b'} do not match. From the remaining k {\\displaystyle k} bits where both Alice and Bob measured in the same basis, Alice randomly chooses k / 2 {\\displaystyle k/2} bits and discloses her choices over the public channel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre\u2013Fenchel transformation, Fenchel transformation, or Fenchel conjugate (after Adrien-Marie Legendre and Werner Fenchel). It allows in particular for a far reaching generalization of Lagrangian duality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The runtime of the algorithm is T ( n , p ) = T c o l l ( n / N , p ) + N \u2217 T s e q ( n / N ) + 2 ( N \u2212 1 ) ( T s t a r t + T b y t e ( n / N ) 2 ) {\\displaystyle T{\\mathcal {(n,p)}}=T_{coll}(n/N,p)+N*T_{seq}(n/N)+2(N-1)(T_{start}+T_{byte}(n/N)^{2})} , where T c o l l {\\displaystyle T_{coll}} is the time of the initial distribution of the matrices in the first step, T s e q {\\displaystyle T_{seq}} is the calculation of the intermediate results and T s t a r t {\\displaystyle T_{start}} and T b y t e {\\displaystyle T_{byte}} stands for the time it takes to establish a connection and transmission of byte respectively. A disadvantage of the algorithm is that there are many connection setups, with small message sizes. It would be better to be able to transmit more data in each message.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu\u2013Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff and Dimitrie Pompeiu. Informally, two sets are close in the Hausdorff distance if every point of either set is close to some point of the other set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We can't prevent aging, but we can understand its causes, take steps to limit its effects, temporarily reverse some of the damage it has caused, and prepare for the day when the software is no longer viable.\" From both an academic and industrial point of view, the software aging phenomenon has increased. Recent research has focussed on clarifying its causes and effects. Memory bloating and leaking, along with data corruption and unreleased file-locks are particular causes of software aging.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Without this property, an attacker can undermine the mechanism itself and hence violate the security policy.For example, Windows 3.x and 9x operating systems were not built with a reference monitor, whereas the Windows NT line, which also includes Windows 2000 and Windows XP, was designed to contain a reference monitor, although it is not clear that its properties (tamperproof, etc.) have ever been independently verified, or what level of computer security it was intended to provide. The claim is that a reference validation mechanism that satisfies the reference monitor concept will correctly enforce a system's access control policy, as it must be invoked to mediate all security-sensitive operations, must not be tampered with, and has undergone complete analysis and testing to verify correctness. The abstract model of a reference monitor has been widely applied to any type of system that needs to enforce access control and is considered to express the necessary and sufficient properties for any system making this security claim.According to Ross Anderson, the reference monitor concept was introduced by James Anderson in an influential 1972 paper. Peter Denning in a 2013 oral history stated that James Anderson credited the concept to a paper he and Scott Graham presented at a 1972 conference.Systems evaluated at B3 and above by the Trusted Computer System Evaluation Criteria (TCSEC) must enforce the reference monitor concept.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The original metadata schema contributed to OASIS is listed in its entirety in section 7 of the Liberty Metadata Version 1.0 specification. Similarly, the specification for Liberty Metadata Version 1.1 includes a listing of the Version 1.1 schema. Both the Version 1.0 schema and the Version 1.1 schema are linked here courtesy of the Internet Archive's Wayback Machine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics (specifically linear algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. Alternative names for this formula are the matrix inversion lemma, Sherman\u2013Morrison\u2013Woodbury formula or just Woodbury formula. However, the identity appeared in several papers before the Woodbury report.The Woodbury matrix identity is ( A + U C V ) \u2212 1 = A \u2212 1 \u2212 A \u2212 1 U ( C \u2212 1 + V A \u2212 1 U ) \u2212 1 V A \u2212 1 , {\\displaystyle \\left(A+UCV\\right)^{-1}=A^{-1}-A^{-1}U\\left(C^{-1}+VA^{-1}U\\right)^{-1}VA^{-1},} where A, U, C and V are conformable matrices: A is n\u00d7n, C is k\u00d7k, U is n\u00d7k, and V is k\u00d7n. This can be derived using blockwise matrix inversion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, it facilitates the construction of complex multi-step instructions, while simultaneously reducing the complexity of computer circuits. The act of writing microcode is often referred to as microprogramming, and the microcode in a specific processor implementation is sometimes termed a microprogram. Through extensive microprograming, microarchitectures of smaller scale and simplicity can emulate more robust architectures with wider word lengths, additional execution units, and so forth.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In planned economies, production is typically limited only to necessity, which would eliminate externalities created by overproduction. The central planner can decide to create and allocate jobs in industries that work to mitigate externalities, rather than waiting for the market to create a demand for these jobs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For our purpose it is fine to use either \u03a9 or J. However, they have a different meaning: J is contravariant and \u03a9 is covariant. The matrix \u03a9 corresponds to the Lagrange brackets of classical mechanics and J corresponds to the Poisson brackets. Note the important relation \u03a9 = J \u2212 1 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "TableSeer: In scholarly articles Tables are used to present, list, summarize, and structure important data. TableSeer automatically identifies tables in digital documents, extracts the table Metadata as well as the cells content, and stores them in such a way that allows users to either query the table content or search for tables in a large set of documents. Dataset search: ChemXSeer provides tools to incorporate datasets from different experiments sources. The system is able to manipulate results from multiple formats such as XML, Microsoft Excel, Gaussian, and CHARMM, create databases, to allow direct queries over the data, create Metadata, using an annotation tool, which will allow users to search over the datasets, as well as a way to create links among datasets and/or between datasets and documents.In addition to these tools, ChemXSeer will integrate the advances made by its sister project CiteSeerX to provide: Full text search Author, affiliation, title and venue search Citation and acknowledgement search Citation linking and statistics", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a bilinear program is a nonlinear optimization problem whose objective or constraint functions are bilinear. An example is the pooling problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of internet vigilantism, information entropy is an act intended to disrupt online services.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, for a natural number n \u2265 2 {\\displaystyle n\\geq 2} , the nth Fibonacci group, denoted F ( 2 , n ) {\\displaystyle F(2,n)} or sometimes F ( n ) {\\displaystyle F(n)} , is defined by n generators a 1 , a 2 , \u2026 , a n {\\displaystyle a_{1},a_{2},\\dots ,a_{n}} and n relations: a 1 a 2 = a 3 , {\\displaystyle a_{1}a_{2}=a_{3},} a 2 a 3 = a 4 , {\\displaystyle a_{2}a_{3}=a_{4},} \u2026 {\\displaystyle \\dots } a n \u2212 2 a n \u2212 1 = a n , {\\displaystyle a_{n-2}a_{n-1}=a_{n},} a n \u2212 1 a n = a 1 , {\\displaystyle a_{n-1}a_{n}=a_{1},} a n a 1 = a 2 {\\displaystyle a_{n}a_{1}=a_{2}} .These groups were introduced by John Conway in 1965. The group F ( 2 , n ) {\\displaystyle F(2,n)} is of finite order for n = 2 , 3 , 4 , 5 , 7 {\\displaystyle n=2,3,4,5,7} and infinite order for n = 6 {\\displaystyle n=6} and n \u2265 8 {\\displaystyle n\\geq 8} . The infinitude of F ( 2 , 9 ) {\\displaystyle F(2,9)} was proved by computer in 1990.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It has been suggested that what interrogators expect as human responses is not necessarily typical of humans. As a result, some individuals can be categorised as machines. This can therefore work in favour of a competing machine. The humans are instructed to \"act themselves\", but sometimes their answers are more like what the interrogator expects a machine to say. This raises the question of how to ensure that the humans are motivated to \"act human\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The resulting phylogeny can approximate the transmission history, and a variety of methods have been developed to adjust for confounding factors. Due to the associated stigma and the criminalization of transmission for specific infectious diseases, molecular source attribution at the level of individuals can be a controversial use of data that was originally collected in a healthcare setting, with potentially severe legal consequences for individuals who become identified as putative sources. In these contexts, the development and application of molecular source attribution techniques may involve trade-offs between public health responsibilities and individual rights to data privacy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a student is a person. Therefore, the set of students is a subset of the set of persons.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the HITS algorithm, the first step is to retrieve the most relevant pages to the search query. This set is called the root set and can be obtained by taking the top pages returned by a text-based search algorithm. A base set is generated by augmenting the root set with all the web pages that are linked from it and some of the pages that link to it. The web pages in the base set and all hyperlinks among those pages form a focused subgraph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In term logic, a \"proposition\" is simply a form of language: a particular kind of sentence, in which the subject and predicate are combined, so as to assert something true or false. It is not a thought, or an abstract entity. The word \"propositio\" is from the Latin, meaning the first premise of a syllogism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Multics operating system all files, including executables, are segments. A call to a routine not part of the current segment will cause the system to find the referenced segment, in memory or on disk, and add it to the address space of the running process. Dynamic linking is the normal method of operation, and static linking (using the binder) is the exception.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, (2 + 3) \u00d7 4 = 20 forces addition to precede multiplication, while (3 + 5)2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by brackets or braces to avoid confusion, as in  \u2212 5 = 9.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In philosophy, a process ontology refers to a universal model of the structure of the world as an ordered wholeness. Such ontologies are fundamental ontologies, in contrast to the so-called applied ontologies. Fundamental ontologies do not claim to be accessible to any empirical proof in itself but to be a structural design pattern, out of which empirical phenomena can be explained and put together consistently. Throughout Western history, the dominating fundamental ontology is the so-called substance theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In peer-to-peer networking, a supernode is any node that also serves as one of that network's relayers and proxy servers, handling data flow and connections for other users. This semi-distributed architecture allows data to be decentralized without requiring excessive overhead at every node. However, the increased workload of supernodes generally requires additional network bandwidth and central processing unit (CPU) time. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the clustering of biological information such as data from microarray experiments, the cophenetic similarity or cophenetic distance of two objects is a measure of how similar those two objects have to be in order to be grouped into the same cluster. The cophenetic distance between two objects is the height of the dendrogram where the two branches that include the two objects merge into a single branch. Outside the context of a dendrogram, it is the distance between the largest two clusters that contain the two objects individually when they are merged into a single cluster that contains both.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When applied component-wise to vectors, the discrete distance from zero behaves like a non-homogeneous \"norm\", which counts the number of non-zero components in its vector argument; again, this non-homogeneous \"norm\" is discontinuous. In signal processing and statistics, David Donoho referred to the zero \"norm\" with quotation marks. Following Donoho's notation, the zero \"norm\" of x {\\displaystyle x} is simply the number of non-zero coordinates of x , {\\displaystyle x,} or the Hamming distance of the vector from zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, latent variables (from Latin: present participle of lateo, \u201clie hidden\u201d) are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. Such latent variable models are used in many disciplines, including political science, demography, engineering, medicine, ecology, physics, machine learning/artificial intelligence, bioinformatics, chemometrics, natural language processing, management, psychology and the social sciences. Latent variables may correspond to aspects of physical reality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". should be restricted to those officials with a need for such information. These minimization requirements complement and supplement traditional standards under the Fourth Amendment to the United States Constitution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Different operating systems offer distinct methods for applications to identify their security requirements: sudo centralizes all privilege authorization information in a single configuration file, /etc/sudoers, which contains a list of users and the privileged applications and actions that those users are permitted to use. The grammar of the sudoers file is intended to be flexible enough to cover many different scenarios, such as placing restrictions on command-line parameters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of OSHA's PSM, mechanical integrity requirements apply to the following equipment: Pressure vessels and storage tanks. Piping systems (including piping components such as valves). Relief and vent systems and devices. Emergency shutdown systems. Controls (including monitoring devices and sensors, alarms, and interlocks). Pumps.In order to minimize the risk of unwanted releases of hazardous materials, companies must establish and implement adequate maintenance strategies.PSM schemes other than OSHA's usually extend this element to cover the integrity assurance of safety-critical systems in general, not just those directly responsible for fluid containment, according to a wider asset integrity management strategy that includes systems such as active and passive fire protection, fire and gas detection, sources of emergency power, etc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, many of the regulatory efforts put forth in response to predatory advertising practices, especially those involving the usage of personal data, have been spearheaded by the Federal Trade Commission. Congress too, has brought forth numerous legislative measures to address the informational asymmetry and privacy concerns of modern data-collection and advertising. Proponents of regulatory action have explained that data regulation can be exceptionally hard to craft for a number of reasons. Though many have called for greater transparency in data-collection efforts, critics claims that transparency alone falls short, as data is often repackaged and sold through many brokerage firms, leading to many uses that may not have been clearly outlined as the original purpose or intent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane. A metric may correspond to a metaphorical, rather than physical, notion of distance: for example, the set of 100-character Unicode strings can be equipped with the Hamming distance, which measures the number of characters that need to be changed to get from one string to another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, data elements (fields, columns, attributes, etc.) are sometimes \"overloaded\", meaning a given data element will have multiple potential meanings. While a known bad practice, overloading is nevertheless a very real factor or barrier to understanding what a system is doing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In salt-fingering staircases, vertical temperature and salinity fluxes are downgradient, while the vertical density flux is upgradient. This is explained by the fact that the potential energy released in transporting salt downward must exceed that expended in transporting heat upward, resulting in a net downward transport of mass. This negative diffusion sharpens the fluctuations and therefore suggests a means for generating and maintaining staircases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, OCaml uses structural typing on methods for compatibility of object types. Go uses structural typing on methods to determine compatibility of a type with an interface. C++ template functions exhibit structural typing on type arguments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This technology allows analysts to search through large volumes of recorded conversations and isolate mentions of keywords. Recordings can be indexed and analysts can run queries over the database to find conversations of interest. Some government research programs focused on intelligence applications of speech recognition, e.g. DARPA's EARS's program and IARPA's Babel program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was reported to be \"the first very deep feedforward network with hundreds of layers\". It is like an LSTM with forget gates unfolded in time, while the later Residual Nets have no equivalent of forget gates and are like the unfolded original LSTM. If the skip connections in Highway Networks are \"without gates\", or if their gates are kept open (activation 1.0) through strong positive bias weights, they become the identity skip connections in Residual Networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination). Formally, in binary logistic regression there is a single binary dependent variable, coded by an indicator variable, where the two values are labeled \"0\" and \"1\", while the independent variables can each be a binary variable (two classes, coded by an indicator variable) or a continuous variable (any real value). The corresponding probability of the value labeled \"1\" can vary between 0 (certainly the value \"0\") and 1 (certainly the value \"1\"), hence the labeling; the function that converts log-odds to probability is the logistic function, hence the name.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime. Precisely, Let p be an odd prime and a be an integer coprime to p. Then a p \u2212 1 2 \u2261 { 1 ( mod p ) if there is an integer x such that x 2 \u2261 a ( mod p ) , \u2212 1 ( mod p ) if there is no such integer. {\\displaystyle a^{\\tfrac {p-1}{2}}\\equiv {\\begin{cases}\\;\\;\\,1{\\pmod {p}}&{\\text{ if there is an integer }}x{\\text{ such that }}x^{2}\\equiv a{\\pmod {p}},\\\\-1{\\pmod {p}}&{\\text{ if there is no such integer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the standard encoding the least significant bit follows a repetitive pattern of 2 on, 2 off ( \u2026 11001100 \u2026 ); the next digit a pattern of 4 on, 4 off; the ith least significant bit a pattern of 2i on 2i off. The most significant digit is an exception to this; for an n-bit Gray code, the most significant digit follows 2n-1 on 2n-1 off, the same as for the second-most significant digit, but starting at a different point in the sequence. The four-bit version of this is shown below: For decimal 15 the code rolls over to decimal 0 with only one switch change.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a VLIW, the compiler uses heuristics or profile information to guess the direction of a branch. This allows it to move and preschedule operations speculatively before the branch is taken, favoring the most likely path it expects through the branch. If the branch takes an unexpected way, the compiler has already generated compensating code to discard speculative results to preserve program semantics. Vector processor cores (designed for large one-dimensional arrays of data called vectors) can be combined with the VLIW architecture such as in the Fujitsu FR-V microprocessor, further increasing throughput and speed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can be proven by showing that for a schema S = (D, R, h), a given set K of constants in the query expression, a tuple variable v and a header H we can construct a safe formula for every pair v.a with a in H that states that its value is in the active domain. For example, assume that K={1,2}, R={\"r\"} and h = { (\"r\", {\"a, \"b\"}) } then the corresponding safe formula for v.b is: v.b = 1 \u2228 v.b = 2 \u2228 \u2203 w ( r(w) \u2227 ( v.b = w.a \u2228 v.b = w.b ) )This formula, then, can be used to rewrite any unsafe query expression to an equivalent safe query expression by adding such a formula for every variable v and column name a in its type where it is used in the expression. Effectively this means that we let all variables range over the active domain, which, as was already explained, does not change the semantics if the expressed query is domain independent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psychometrics and psychophysics, the term accuracy is interchangeably used with validity and constant error. Precision is a synonym for reliability and variable error. The validity of a measurement instrument or psychological test is established through experiment or correlation with behavior. Reliability is established with a variety of statistical techniques, classically through an internal consistency test like Cronbach's alpha to ensure sets of related questions have related responses, and then comparison of those related question between reference and target population.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In words: A demonstration that a number is somehow apart from zero is also a demonstration that this number is non-zero. But constructively it does not follow that the doubly negative statement \u00ac ( x \u2245 0 ) {\\displaystyle \\neg (x\\cong 0)} would imply x # 0 {\\displaystyle x\\#0} . Consequently, many classically equivalent statements bifurcate into distinct statement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Operations defined on feature structures, e.g. unification, are used extensively in phrase structure grammars. In most theories (e.g. HPSG), operations are strictly speaking defined over equations describing feature structures and not over feature structures themselves, though feature structures are usually used in informal exposition. Often, feature structures are written like this:  ] {\\displaystyle {\\begin{bmatrix}{\\mbox{category}}&noun\\ phrase\\\\{\\mbox{agreement}}&{\\begin{bmatrix}{\\mbox{number}}&singular\\\\{\\mbox{person}}&third\\end{bmatrix}}\\end{bmatrix}}} Here there are the two features category and agreement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A deep result in the classification of finite semigroups is Krohn\u2013Rhodes theory, analogous to the Jordan\u2013H\u00f6lder decomposition for finite groups. Some other techniques for studying semigroups, like Green's relations, do not resemble anything in group theory. The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata via the syntactic monoid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Nirukta, written in the 6th or 5th century BCE, the Sanskrit grammarian Y\u0101ska defined four main categories of words: \u0928\u093e\u092e n\u0101ma \u2013 noun (including adjective) \u0906\u0916\u094d\u092f\u093e\u0924 \u0101khy\u0101ta \u2013 verb \u0909\u092a\u0938\u0930\u094d\u0917 upasarga \u2013 pre-verb or prefix \u0928\u093f\u092a\u093e\u0924 nip\u0101ta \u2013 particle, invariant word (perhaps preposition)These four were grouped into two larger classes: inflectable (nouns and verbs) and uninflectable (pre-verbs and particles). The ancient work on the grammar of the Tamil language, Tolk\u0101ppiyam, argued to have been written around 2nd century CE, classifies Tamil words as peyar (\u0baa\u0bc6\u0baf\u0bb0\u0bcd; noun), vinai (\u0bb5\u0bbf\u0ba9\u0bc8; verb), idai (part of speech which modifies the relationships between verbs and nouns), and uri (word that further qualifies a noun or verb).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term \"inheritance\" is loosely used for both class-based and prototype-based programming, but in narrow use the term is reserved for class-based programming (one class inherits from another), with the corresponding technique in prototype-based programming being instead called delegation (one object delegates to another). Class-modifying inheritance patterns can be pre-defined according to simple network interface parameters such that inter-language compatibility is preserved.Inheritance should not be confused with subtyping. In some languages inheritance and subtyping agree, whereas in others they differ; in general, subtyping establishes an is-a relationship, whereas inheritance only reuses implementation and establishes a syntactic relationship, not necessarily a semantic relationship (inheritance does not ensure behavioral subtyping).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The idea is that a triggering condition in the home or a desire of the user can trigger the execution of a complex process. The process is defined in the moment that it needs to be executed. It automatically composes services available on home devices and appliances.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods in primality proving. It is an idea put forward by Shafi Goldwasser and Joe Kilian in 1986 and turned into an algorithm by A. O. L. Atkin the same year. The algorithm was altered and improved by several collaborators subsequently, and notably by Atkin and Fran\u00e7ois Morain, in 1993. The concept of using elliptic curves in factorization had been developed by H. W. Lenstra in 1985, and the implications for its use in primality testing (and proving) followed quickly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Solinas prime, or generalized Mersenne prime, is a prime number that has the form f ( 2 m ) {\\displaystyle f(2^{m})} , where f ( x ) {\\displaystyle f(x)} is a low-degree polynomial with small integer coefficients. These primes allow fast modular reduction algorithms and are widely used in cryptography. They are named after Jerome Solinas. This class of numbers encompasses a few other categories of prime numbers: Mersenne primes, which have the form 2 k \u2212 1 {\\displaystyle 2^{k}-1} , Crandall or pseudo-Mersenne primes, which have the form 2 k \u2212 c {\\displaystyle 2^{k}-c} for small odd c {\\displaystyle c} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is defined by the equations: | A & B | = | A | + | B | = ( { 1 } \u00d7 | A | ) \u222a ( { 2 } \u00d7 | B | ) {\\displaystyle |{\\mathcal {A}}\\ \\&\\ {\\mathcal {B}}|=|{\\mathcal {A}}|+|{\\mathcal {B}}|=(\\{1\\}\\times |{\\mathcal {A}}|)\\cup (\\{2\\}\\times |{\\mathcal {B}}|)} (i.e. the set of tokens of A & B {\\displaystyle {\\mathcal {A}}\\ \\&\\ {\\mathcal {B}}} is the coproduct (or disjoint union) of the token sets of A {\\displaystyle {\\mathcal {A}}} and B {\\displaystyle {\\mathcal {B}}} . Tokens from differents sets are always coherent and tokens from the same set are coherent exactly when they are coherent in that set. ( 1 , \u03b1 ) \u223c A & B ( 1 , \u03b1 \u2032 ) \u27fa \u03b1 \u223c A \u03b1 \u2032 {\\displaystyle (1,\\alpha )\\sim _{{\\mathcal {A}}\\ \\&\\ {\\mathcal {B}}}(1,\\alpha ')\\iff \\alpha \\sim _{\\mathcal {A}}\\alpha '} ( 2 , \u03b2 ) \u223c A & B ( 2 , \u03b2 \u2032 ) \u27fa \u03b2 \u223c B \u03b2 \u2032 {\\displaystyle (2,\\beta )\\sim _{{\\mathcal {A}}\\ \\&\\ {\\mathcal {B}}}(2,\\beta ')\\iff \\beta \\sim _{\\mathcal {B}}\\beta '} ( 1 , \u03b1 ) \u223c A & B ( 2 , \u03b2 ) , \u2200 \u03b1 \u2208 | A | , \u03b2 \u2208 | B | {\\displaystyle (1,\\alpha )\\sim _{{\\mathcal {A}}\\ \\&\\ {\\mathcal {B}}}(2,\\beta ),\\forall \\alpha \\in |{\\mathcal {A}}|,\\beta \\in |{\\mathcal {B}}|}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function f: A \u2192 A, where A is a set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, some programming languages allow for some types to be automatically converted to other types; for example, an int can be used where the program expects a float. Dynamic typing, also called latent typing, determines the type-safety of operations at run time; in other words, types are associated with run-time values rather than textual expressions. As with type-inferred languages, dynamically-typed languages do not require the programmer to write explicit type annotations on expressions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", C n ) {\\displaystyle {\\dot {C_{i}}}={\\operatorname {d} \\!C_{i} \\over \\operatorname {d} \\!t}=f(C_{1},C_{2},...,C_{n})} which shows how the number of people in compartment C i {\\displaystyle C_{i}} changes over time. For example, in a SIR model, C 1 = S {\\displaystyle C_{1}=S} , C 2 = I {\\displaystyle C_{2}=I} , and C 3 = R {\\displaystyle C_{3}=R} . Compartmental models have a disease-free equilibrium (DFE) meaning that it is possible to find an equilibrium while setting the number of infected people to zero, I = 0 {\\displaystyle I=0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(And this principle is valid in a theory like C Z F {\\displaystyle {\\mathsf {CZF}}} . Also compare with the Replacement axiom.) That is, the mapping information exists as set and it has a pair for each element in the domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "S {\\displaystyle \\lambda :S.S^{\\prime }\\to S^{\\prime }.S} such that ( S \u2032 , \u03bb ) {\\displaystyle \\left(S^{\\prime },\\lambda \\right)} is a lax map of monads S \u2192 S {\\displaystyle S\\to S} and ( S , \u03bb ) {\\displaystyle (S,\\lambda )} is a colax map of monads S \u2032 \u2192 S \u2032 . {\\displaystyle S^{\\prime }\\to S^{\\prime }.} This is exactly the data needed to define a monad structure on S \u2032 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In informal logic this is called a counter argument. The form of an argument can be shown by the use of symbols. For each argument form, there is a corresponding statement form, called a corresponding conditional, and an argument form is valid if and only if its corresponding conditional is a logical truth.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, classification is the problem of identifying which of a set of categories (sub-populations) an observation (or observations) belongs to. Examples are assigning a given email to the \"spam\" or \"non-spam\" class, and assigning a diagnosis to a given patient based on observed characteristics of the patient (sex, blood pressure, presence or absence of certain symptoms, etc.). Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. These properties may variously be categorical (e.g. \"A\", \"B\", \"AB\" or \"O\", for blood type), ordinal (e.g. \"large\", \"medium\" or \"small\"), integer-valued (e.g. the number of occurrences of a particular word in an email) or real-valued (e.g. a measurement of blood pressure).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, apophenia is an example of a type I error \u2013 the false identification of patterns in data. It may be compared to a so-called false positive in other test situations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice the classical relational algebra described above is extended with various operations such as outer joins, aggregate functions and even transitive closure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Semantic Web approach, data from multiple websites or databases is searched via metadata. Metadata is machine-readable code, which defines the contents of the page for the program so that the comparisons between the data and the search terms are more accurate. This serves to decrease the number of results that are irrelevant or unhelpful. Some meta-data exists as definitions called ontologies, which can be tagged by either users or programs; these serve to facilitate searches by using key terms or phrases to find and return the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "N.R. Campbell and the Ferguson Committee were thus proven wrong.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This could be the set of all subsets of the array of bits that are skeletonized 4-connected (width of the font is 1). Let E X ( c , D ) {\\displaystyle EX(c,D)} be a procedure that draws an example, x {\\displaystyle x} , using a probability distribution D {\\displaystyle D} and gives the correct label c ( x ) {\\displaystyle c(x)} , that is 1 if x \u2208 c {\\displaystyle x\\in c} and 0 otherwise. Now, given 0 < \u03f5 , \u03b4 < 1 {\\displaystyle 0<\\epsilon ,\\delta <1} , assume there is an algorithm A {\\displaystyle A} and a polynomial p {\\displaystyle p} in 1 / \u03f5 , 1 / \u03b4 {\\displaystyle 1/\\epsilon ,1/\\delta } (and other relevant parameters of the class C {\\displaystyle C} ) such that, given a sample of size p {\\displaystyle p} drawn according to E X ( c , D ) {\\displaystyle EX(c,D)} , then, with probability of at least 1 \u2212 \u03b4 {\\displaystyle 1-\\delta } , A {\\displaystyle A} outputs a hypothesis h \u2208 C {\\displaystyle h\\in C} that has an average error less than or equal to \u03f5 {\\displaystyle \\epsilon } on X {\\displaystyle X} with the same distribution D {\\displaystyle D} . Further if the above statement for algorithm A {\\displaystyle A} is true for every concept c \u2208 C {\\displaystyle c\\in C} and for every distribution D {\\displaystyle D} over X {\\displaystyle X} , and for all 0 < \u03f5 , \u03b4 < 1 {\\displaystyle 0<\\epsilon ,\\delta <1} then C {\\displaystyle C} is (efficiently) PAC learnable (or distribution-free PAC learnable). We can also say that A {\\displaystyle A} is a PAC learning algorithm for C {\\displaystyle C} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the lower convex envelope f \u02d8 {\\displaystyle {\\breve {f}}} of a function f {\\displaystyle f} defined on an interval  {\\displaystyle } is defined at each point of the interval as the supremum of all convex functions that lie under that function, i.e. f \u02d8 ( x ) = sup { g ( x ) \u2223 g is convex and g \u2264 f over  } . {\\displaystyle {\\breve {f}}(x)=\\sup\\{g(x)\\mid g{\\text{ is convex and }}g\\leq f{\\text{ over }}\\}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most dialects of Lisp including Common Lisp, by convention the value NIL evaluates to the value false in a boolean expression. In Scheme, since the IEEE standard in 1991, all values except #f, including NIL's equivalent in Scheme which is written as '(), evaluate to the value true in a boolean expression. (R5RS sec. 6.3.1)Where the constant representing the boolean value of true is T in most Lisps, in Scheme it is #t.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A related result, sometimes called the second Borel\u2013Cantelli lemma, is a partial converse of the first Borel\u2013Cantelli lemma. The lemma states that, under certain conditions, an event will have probability of either zero or one. Accordingly, it is the best-known of a class of similar theorems, known as zero-one laws. Other examples include Kolmogorov's zero\u2013one law and the Hewitt\u2013Savage zero\u2013one law.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semiconductor testing, the device under test is a die on a wafer or the resulting packaged part. A connection system is used, connecting the part to automatic or manual test equipment. The test equipment then applies power to the part, supplies stimulus signals, then measures and evaluates the resulting outputs from the device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is meant to indicate that the application is temporarily unresponsive, a state from which it should recover. It may also indicate that all or part of the application has entered an unrecoverable state or an infinite loop.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, the input data may contain features that are irrelevant for comparison purposes. For example, when looking up a personal name, it may be desirable to ignore the distinction between upper and lower case letters. For such data, one must use a hash function that is compatible with the data equivalence criterion being used: that is, any two inputs that are considered equivalent must yield the same hash value. This can be accomplished by normalizing the input before hashing it, as by upper-casing all letters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In power supply networks, the power generation and the electrical load (demand) must be very close to equal every second to avoid overloading of network components, which can severely damage them. Protective relays and fuses are used to automatically detect overloads and to disconnect circuits at risk of damage. Under certain conditions, a network component shutting down can cause current fluctuations in neighboring segments of the network leading to a cascading failure of a larger section of the network. This may range from a building, to a block, to an entire city, to an entire electrical grid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In his PhD thesis, Berardi defined a cube of constructive logics akin to the lambda cube (these specifications are non-dependent). A modification of this cube was later called the L-cube by Geuvers, who in his PhD thesis extended the Curry\u2013Howard correspondence to this setting. Based on these ideas, Barthe and others defined classical pure type systems (CPTS) by adding a double negation operator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the ruler function of an integer n {\\displaystyle n} can be either of two closely related functions. One of these functions counts the number of times n {\\displaystyle n} can be evenly divided by two, which for the numbers 1, 2, 3, ... is Alternatively, the ruler function can be defined as the same numbers plus one, which for the numbers 1, 2, 3, ... produces the sequence As well as being related by adding one, these two sequences are related in a different way: the second one can be formed from the first one by removing all the zeros, and the first one can be formed from the second one by adding zeros at the start and between every pair of numbers. For either definition of the ruler function, the rising and falling patterns of the values of this function resemble the lengths of marks on rulers with traditional units such as inches. These functions should be distinguished from Thomae's function, a function on real numbers which behaves similarly to the ruler function when restricted to the dyadic rational numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, a \"300 GB\" hard drive can be expected to offer only slightly more than 300\u00d7109 = 300000000000, bytes, not 300 \u00d7 230 (which would be about 322\u00d7109 bytes or \"322 GB\"). The first terabyte (SI prefix, 1000000000000 bytes) hard disk drive was introduced in 2007. Decimal prefixes were generally used by information processing publications when comparing hard disk capacities.Users must be aware that some programs and operating systems, such as earlier versions of Microsoft Windows and MacOS, may use \"MB\" and \"GB\" to denote binary prefixes even when displaying disk drive capacities. Thus, for example, the capacity of a \"10 MB\" (decimal \"M\") disk drive could be reported as \"9.56 MB\", and that of a \"300 GB\" drive as \"279.4 GB\". Good software and documentation should specify clearly whether \"K\", \"M\", \"G\" mean binary or decimal multipliers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, transmit-after-receive time delay is the time interval from removal of RF energy at the local receiver input until the local transmitter is automatically keyed on and the transmitted rf signal amplitude has increased to 90% of its steady-state value. An Exception: High-frequency (HF) transceiver equipment is normally not designed with an interlock between receiver squelch and transmitter on-off key. The transmitter can be keyed on at any time, independent of whether or not a signal is being received at the receiver input.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following descriptions, \u03b1, \u03b2, and \u03b3 represent any string of terminals/nonterminals (including the empty string), X and Y represent single nonterminals, and a represents a terminal symbol. Earley's algorithm is a top-down dynamic programming algorithm. In the following, we use Earley's dot notation: given a production X \u2192 \u03b1\u03b2, the notation X \u2192 \u03b1 \u2022 \u03b2 represents a condition in which \u03b1 has already been parsed and \u03b2 is expected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The player with the most accurate predictions wins the top prize, or a share of it if more than one player has these predictions. In addition, there is a special \u00a33,000,000 prize or share of it for correctly predicting the nine score draws (draws of 1-1 or higher) when these are the only score draws on the coupon. Players can win large cash prizes in a variety of other ways, under a points-based scoring system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The above procedure is repeated until the solution of constraint equations, \u03c3 k ( t + \u0394 t ) {\\displaystyle \\sigma _{k}(t+\\Delta t)} , converges to a prescribed tolerance of a numerical error. Although there are a number of algorithms to compute the Lagrange multipliers, these difference is rely only on the methods to solve the system of equations. For this methods, quasi-Newton methods are commonly used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming, sequential coupling (also known as temporal coupling) is a form of coupling where a class requires its methods to be called in a particular sequence. This may be an anti-pattern, depending on context. Methods whose name starts with Init, Begin, Start, etc. may indicate the existence of sequential coupling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It provides a user interface, and reads and writes to the post office files directly in order to send, access, and manage email messages. This arrangement is called a \"shared-file mail system\" (which was also implemented later in competing products such as Microsoft Mail). This is in contrast to a \"client/server mail system\" which involves a mail client application interacting with a mail server application (the latter then being the focal point of message handling).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the four color theorem, Kempe was able to prove that all graphs necessarily have a vertex of five or less, or containing a vertex that touches five other vertices, called its neighbors. As such, to prove the four color theorem, it is sufficient to prove that vertices of five or less were all four-colorable. Kempe was able to prove the case of degree four and give a partial proof of degree five using Kempe chains.In this case, Kempe chains are used to prove the idea that no vertex has to be touching four colors different from itself, i.e., having a degree of 4. First, one can create a graph with a vertex v and four vertices as neighbors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the splitting principle is a technique used to reduce questions about vector bundles to the case of line bundles. In the theory of vector bundles, one often wishes to simplify computations, say of Chern classes. Often computations are well understood for line bundles and for direct sums of line bundles. In this case the splitting principle can be quite useful.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A positive impact of coalescing on inference graph colorability is, for example, when a node interferes with both nodes being coalesced, the degree of the node is reduced by one which leads to improving the overall colorability of the interference graph.There are several coalescing heuristics available: Aggressive coalescing it was first introduced by Chaitin original register allocator. This heuristic aims at coalescing any non-interfering, copy-related nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m. In the standard notation of modular arithmetic this congruence is written as a x \u2261 1 ( mod m ) , {\\displaystyle ax\\equiv 1{\\pmod {m}},} which is the shorthand way of writing the statement that m divides (evenly) the quantity ax \u2212 1, or, put another way, the remainder after dividing ax by the integer m is 1. If a does have an inverse modulo m, then there are an infinite number of solutions of this congruence, which form a congruence class with respect to this modulus. Furthermore, any integer that is congruent to a (i.e., in a's congruence class) has any element of x's congruence class as a modular multiplicative inverse. Using the notation of w \u00af {\\displaystyle {\\overline {w}}} to indicate the congruence class containing w, this can be expressed by saying that the modulo multiplicative inverse of the congruence class a \u00af {\\displaystyle {\\overline {a}}} is the congruence class x \u00af {\\displaystyle {\\overline {x}}} such that: a \u00af \u22c5 m x \u00af = 1 \u00af , {\\displaystyle {\\overline {a}}\\cdot _{m}{\\overline {x}}={\\overline {1}},} where the symbol \u22c5 m {\\displaystyle \\cdot _{m}} denotes the multiplication of equivalence classes modulo m. Written in this way, the analogy with the usual concept of a multiplicative inverse in the set of rational or real numbers is clearly represented, replacing the numbers by congruence classes and altering the binary operation appropriately.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social choice theory, tournaments naturally arise as majority relations of preference profiles. Let A {\\displaystyle A} be a finite set of alternatives, and consider a list P = ( \u227b 1 , \u2026 , \u227b n ) {\\displaystyle P=(\\succ _{1},\\dots ,\\succ _{n})} of linear orders over A {\\displaystyle A} . We interpret each order \u227b i {\\displaystyle \\succ _{i}} as the preference ranking of a voter i {\\displaystyle i} . The (strict) majority relation \u227b maj {\\displaystyle \\succ _{\\text{maj}}} of P {\\displaystyle P} over A {\\displaystyle A} is then defined so that a \u227b maj b {\\displaystyle a\\succ _{\\text{maj}}b} if and only if a majority of the voters prefer a {\\displaystyle a} to b {\\displaystyle b} , that is | { i \u2208 : a \u227b i b } | > | { i \u2208 : b \u227b i a } | {\\displaystyle |\\{i\\in :a\\succ _{i}b\\}|>|\\{i\\in :b\\succ _{i}a\\}|} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element of another random vector. A random vector is a random variable with multiple dimensions. Each element of the vector is a scalar random variable. Each element has either a finite number of observed empirical values or a finite or infinite number of potential values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\u03b4 i k p k M  ( l ) \u27e9 \u27e9 = ( 2 l + 2 k + 1 ) ! ! \u27e8 \u27e8 M  ( l \u2212 2 k ) \u27e9 \u27e9 {\\displaystyle {\\hat {T}}r_{1}...{\\hat {T}}r_{k}\\left\\langle \\left\\langle \\delta _{i_{1}p_{1}}...\\delta _{i_{k}p_{k}}\\mathbf {M} _{}^{(l)}\\right\\rangle \\right\\rangle =(2l+2k+1)! !\\left\\langle \\left\\langle \\mathbf {M} _{}^{(l-2k)}\\right\\rangle \\right\\rangle } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The resulting function behaves like a while or a for loop in an imperative language. Used in this way, the Y combinator implements simple recursion. In the lambda calculus, it is not possible to refer to the definition of a function inside its own body by name.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To distinguish this type of vector from those described above, it is common and useful in physics to denote an element \u03d5 {\\displaystyle \\phi } of an abstract complex vector space as a ket | \u03d5 \u27e9 {\\displaystyle |\\phi \\rangle } , to refer to it as a \"ket\" rather than as a vector, and to pronounce it \"ket- \u03d5 {\\displaystyle \\phi } \" or \"ket-A\" for |A\u27e9. Symbols, letters, numbers, or even words\u2014whatever serves as a convenient label\u2014can be used as the label inside a ket, with the | \u27e9 {\\displaystyle |\\ \\rangle } making clear that the label indicates a vector in vector space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most familiar example of a paired difference test occurs when subjects are measured before and after a treatment. Such a \"repeated measures\" test compares these measurements within subjects, rather than across subjects, and will generally have greater power than an unpaired test. Another example comes from matching cases of a disease with comparable controls.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pattern recognition, information retrieval, object detection and classification (machine learning), precision and recall are performance metrics that apply to data retrieved from a collection, corpus or sample space. Precision (also called positive predictive value) is the fraction of relevant instances among the retrieved instances. Written as a formula: r e l e v a n t _ r e t r i e v e d _ i n s t a n c e s a l l _ r e t r i e v e d _ i n s t a n c e s {\\displaystyle {\\frac {relevant\\_retrieved\\_instances}{all\\_{\\mathbf {retrieved}}\\_instances}}} . Recall (also known as sensitivity) is the fraction of relevant instances that were retrieved.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately connected to the uniform spanning tree, a model for a random tree. See also random walk for more general treatment of this topic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most models of communication protocol participants communicate through authenticated channels. This means that messages are not anonymous, and receivers know the source of every message they receive. Some models assume a stronger, transferable form of authentication, where each message is signed by the sender, so that a receiver knows not just the immediate source of every message, but the participant that initially created the message. This stronger type of authentication is achieved by digital signatures, and when this stronger form of authentication is available, protocols can tolerate a larger number of faults.The two different authentication models are often called oral communication and written communication models. In an oral communication model, the immediate source of information is known, whereas in stronger, written communication models, every step along the receiver learns not just the immediate source of the message, but the communication history of the message.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are weakly structured in common use, and become strongly structured in individual-site use. They may be abstract or concrete. They have different meanings in different social worlds but their structure is common enough to more than one world to make them recognizable, a means of translation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that in the probability inequalities above, the outcome of the protocol is understood to depend only on the random string; both strings x and y remain fixed. In other words, if R(x,y) yields g(x,y,r) when using random string r, then g(x,y,r) = f(x,y) for at least 2/3 of all choices for the string r. The randomized complexity is simply defined as the number of bits exchanged in such a protocol. Note that it is also possible to define a randomized protocol with one-sided error, and the complexity is defined similarly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Common phonological features that define the natural classes of vowels involved in vowel harmony include vowel backness, vowel height, nasalization, roundedness, and advanced and retracted tongue root. Vowel harmony is found in many agglutinative languages. The given domain of vowel harmony taking effect often spans across morpheme boundaries, and suffixes and prefixes will usually follow vowel harmony rules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories of the natural numbers\u2014specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as G\u00f6del's incompleteness theorems and Tarski's undefinability theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is still generally called the \"liar paradox\" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction. If \"this sentence is false\" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By 1963\u20131964 G\u00f6del would disavow Herbrand\u2013G\u00f6del recursion and the \u03bb-calculus in favor of the Turing machine as the definition of \"algorithm\" or \"mechanical procedure\" or \"formal system\".A hypothesis leading to a natural law? : In late 1936 Alan Turing's paper (also proving that the Entscheidungsproblem is unsolvable) was delivered orally, but had not yet appeared in print. On the other hand, Emil Post's 1936 paper had appeared and was certified independent of Turing's work.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was implemented in ECL running at 25 MHz. Major functional modules were implemented using AMCC ECL ASICs. The project grew beyond its original definition to include a front-end general purpose processor ensemble based on the multiple 68020 processors running Unix System V. The numeric processor ran a small kernel that would allow it to receive job submissions from the Unix system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the classification of programming languages, an applicative programming language is built out of functions applied to arguments. Applicative languages are functional, and applicative is often used as a synonym for functional. However, concatenative languages can be functional, while not being applicative.The semantics of applicative languages are based on beta reduction of terms, and side effects such as mutation of state are not permitted.Lisp and ML are applicative programming languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, there exist several methods to construct knowledge spaces. The most frequently used method is querying experts. There exist several querying algorithms that allow one or several experts to construct a knowledge space by answering a sequence of simple questions.Another method is to construct the knowledge space by explorative data analysis (for example by item tree analysis) from data. A third method is to derive the knowledge space from an analysis of the problem solving processes in the corresponding domain. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications networks, RANAP (Radio Access Network Application Part) is a protocol specified by 3GPP in TS 25.413 and used in UMTS for signaling between the Core Network, which can be a MSC or SGSN, and the UTRAN. RANAP is carried over Iu-interface. RANAP signalling protocol resides in the control plane of Radio network layer of Iu interface in the UMTS (Universal Mobile Telecommunication System) protocol stack. Iu interface is the interface between RNC (Radio Network Controller) and CN (Core Network).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without replacement in which each sample can be classified into two mutually exclusive categories like Pass/Fail or Employed/Unemployed. As random selections are made from the population, each subsequent draw decreases the population causing the probability of success to change with each draw. Unlike the standard hypergeometric distribution, which describes the number of successes in a fixed sample size, in the negative hypergeometric distribution, samples are drawn until r {\\displaystyle r} failures have been found, and the distribution describes the probability of finding k {\\displaystyle k} successes in such a sample. In other words, the negative hypergeometric distribution describes the likelihood of k {\\displaystyle k} successes in a sample with exactly r {\\displaystyle r} failures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the nth-term test for divergence is a simple test for the divergence of an infinite series:If lim n \u2192 \u221e a n \u2260 0 {\\displaystyle \\lim _{n\\to \\infty }a_{n}\\neq 0} or if the limit does not exist, then \u2211 n = 1 \u221e a n {\\displaystyle \\sum _{n=1}^{\\infty }a_{n}} diverges.Many authors do not name this test or give it a shorter name.When testing if a series converges or diverges, this test is often checked first due to its ease of use. In the case of p-adic analysis the term test is a necessary and sufficient condition for convergence due to the non-archimedean triangle inequality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a two-wire circuit is characterized by supporting transmission in two directions simultaneously, as opposed to four-wire circuits, which have separate pairs for transmit and receive. The subscriber local loop from the telco central office are almost all two wire for analog baseband voice calls (and some digital services like ISDN), and converted to four-wire at the line card back when telephone switching was performed on baseband audio. Today the audio is digitized and processed completely in the digital domain upstream from the local loop. The reason for using two wires rather than four is simple economics\u2014half the materials cost half as much to purchase and install.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the tent map with parameter \u03bc is the real-valued function f\u03bc defined by f \u03bc ( x ) := \u03bc min { x , 1 \u2212 x } , {\\displaystyle f_{\\mu }(x):=\\mu \\min\\{x,\\,1-x\\},} the name being due to the tent-like shape of the graph of f\u03bc. For the values of the parameter \u03bc within 0 and 2, f\u03bc maps the unit interval  into itself, thus defining a discrete-time dynamical system on it (equivalently, a recurrence relation). In particular, iterating a point x0 in  gives rise to a sequence x n {\\displaystyle x_{n}}: x n + 1 = f \u03bc ( x n ) = { \u03bc x n f o r x n < 1 2 \u03bc ( 1 \u2212 x n ) f o r 1 2 \u2264 x n {\\displaystyle x_{n+1}=f_{\\mu }(x_{n})={\\begin{cases}\\mu x_{n}&\\mathrm {for} ~~x_{n}<{\\frac {1}{2}}\\\\\\mu (1-x_{n})&\\mathrm {for} ~~{\\frac {1}{2}}\\leq x_{n}\\end{cases}}} where \u03bc is a positive real constant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to gain access to GSM services, a user needs three things: A billing relationship with a mobile phone operator. This is usually either where services are paid for in advance of them being consumed (prepaid), or where bills are issued and settled after the service has been consumed (postpaid). A mobile phone that is GSM compliant and operates at the same frequency as the operator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, time-of-check to time-of-use (TOCTOU, TOCTTOU or TOC/TOU) is a class of software bugs caused by a race condition involving the checking of the state of a part of a system (such as a security credential) and the use of the results of that check. TOCTOU race conditions are common in Unix between operations on the file system, but can occur in other contexts, including local sockets and improper use of database transactions. In the early 1990s, the mail utility of BSD 4.3 UNIX had an exploitable race condition for temporary files because it used the mktemp() function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern machines, the time to fetch a variable from the data cache is often several times longer than the time needed for basic ALU operations. A program runs faster without stalls if its memory loads can be started several cycles before the instruction that needs that variable. Complex machines can do this with a deep pipeline and \"out-of-order execution\" that examines and runs many instructions at once. Register machines can even do this with much simpler \"in-order\" hardware, a shallow pipeline, and slightly smarter compilers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A hierarchy consists of an order defined on a set. The term hierarchy is used to stress a hierarchical relation among the elements. The XML specification defines an XML document as a well-formed text if it satisfies a list of syntax rules defined in the specification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, the three brothers Faloutsos believed that the Internet had a power law degree distribution on the basis of traceroute data; however, it has been suggested that this is a layer 3 illusion created by routers, which appear as high-degree nodes while concealing the internal layer 2 structure of the ASes they interconnect. On a theoretical level, refinements to the abstract definition of scale-free have been proposed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most Unix-like systems, all processes of a pipeline are started at the same time, with their streams appropriately connected, and managed by the scheduler together with all other processes running on the machine. An important aspect of this, setting Unix pipes apart from other pipe implementations, is the concept of buffering: for example a sending program may produce 5000 bytes per second, and a receiving program may only be able to accept 100 bytes per second, but no data is lost. Instead, the output of the sending program is held in the buffer. When the receiving program is ready to read data, the next program in the pipeline reads from the buffer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We should also remember to strike out AAA; this says that since the cube of a is the identity element of G, so is the cube of the inverse of a. Under these conditions the word problem becomes easy. First reduce strings to the empty string, a, aa, A or AA. Then note that we may also multiply by aaa, so we can convert A to aa and convert AA to a. The result is that the word problem, here for the cyclic group of order three, is solvable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, simple electromagnetic analysis is not possible or does not provide enough information. Differential electromagnetic analysis (DEMA) attacks are more complex, but are effective against symmetric cryptography implementation, against which SEMA attacks are not. Additionally unlike SEMA, DEMA attacks do not require much knowledge about the device being attacked.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In that case, if it holds a \"\u2248\", then X and Y look indistinguishably equal, and if it holds a \">\", then X looks clearly more red than Y. The relation \u2265 is the disjoint union of the symmetric relation \u2248 and the transitive relation >. Using the transitivity of >, the knowledge of both f10 > d30 and d30 > b50 allows one to infer that f10 > b50. However, since \u2265 is not transitive, a \"paradoxical\" inference like \"d30 \u2265 e20 and e20 \u2265 f10, hence d30 \u2265 f10\" is no longer possible. For the same reason, e.g. \"d30 \u2248 e20 and e20 \u2248 f10, hence d30 \u2248 f10\" is no longer a valid inference. Similarly, to resolve the original heap variation of the paradox with this approach, the relation \"X grains are more a heap than Y grains\" could be considered quasitransitive rather than transitive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, the test is often retained in the original form due to Dirichlet: a piecewise monotone bounded periodic function f {\\displaystyle f} has a convergent Fourier series whose value at each point is the arithmetic mean of the left and right limits of the function. The condition of piecewise monotonicity is equivalent to having only finitely many local extrema, i.e., that the function changes its variation only finitely many times. (Dirichlet required in addition that the function have only finitely many discontinuities, but this constraint is unnecessarily stringent.) Any signal that can be physically produced in a laboratory satisfies these conditions.As in the pointwise case of the Jordan test, the condition of boundedness can be relaxed if the function is assumed to be absolutely integrable (i.e., L 1 {\\displaystyle L^{1}} ) over a period, provided it satisfies the other conditions of the test in a neighborhood of the point x {\\displaystyle x} where the limit is taken.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems engineering, information systems and software engineering, the systems development life cycle (SDLC), also referred to as the application development life cycle, is a process for planning, creating, testing, and deploying an information system. The SDLC concept applies to a range of hardware and software configurations, as a system can be composed of hardware only, software only, or a combination of both. There are usually six stages in this cycle: requirement analysis, design, development and testing, implementation, documentation, and evaluation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another Unix breakthrough was to automatically associate input and output to terminal keyboard and terminal display, respectively, by default \u2014 the program (and programmer) did absolutely nothing to establish input and output for a typical input-process-output program (unless it chose a different paradigm). In contrast, previous operating systems usually required some\u2014often complex\u2014job control language to establish connections, or the equivalent burden had to be orchestrated by the program.Since Unix provided standard streams, the Unix C runtime environment was obliged to support it as well. As a result, most C runtime environments (and C's descendants), regardless of the operating system, provide equivalent functionality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, the Foias constant is a real number named after Ciprian Foias. It is defined in the following way: for every real number x1 > 0, there is a sequence defined by the recurrence relation x n + 1 = ( 1 + 1 x n ) n {\\displaystyle x_{n+1}=\\left(1+{\\frac {1}{x_{n}}}\\right)^{n}} for n = 1, 2, 3, .... The Foias constant is the unique choice \u03b1 such that if x1 = \u03b1 then the sequence diverges to infinity. For all other values of x1, the sequence is divergent as well, but it has two accumulation points: 1 and infinity. Numerically, it is \u03b1 = 1.187452351126501 \u2026 {\\displaystyle \\alpha =1.187452351126501\\ldots } .No closed form for the constant is known. When x1 = \u03b1 then the growth rate of the sequence (xn) is given by the limit lim n \u2192 \u221e x n log \u2061 n n = 1 , {\\displaystyle \\lim _{n\\to \\infty }x_{n}{\\frac {\\log n}{n}}=1,} where \"log\" denotes the natural logarithm.The same methods used in the proof of the uniqueness of the Foias constant may also be applied to other similar recursive sequences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 3678, 13678, 34678, and 134678 are the patterns related to Braille pattern dots-2356, since the two additional dots of kantenji patterns 02356, 23567, and 023567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The M690T was followed by the M690E specifically for embedded applications which removed the TV output, which required Macrovision licensing for OEMs, and enabled native support for dual TMDS outputs, enabling dual independent DVI interfaces.In January 2011, AMD announced the AMD Embedded G-Series Accelerated Processing Unit. This was the first APU for embedded applications. These were followed by updates in 2013 and 2016.In May 2012, AMD Announced the AMD Embedded R-Series Accelerated Processing Unit. This family of products incorporates the Bulldozer CPU architecture, and Discrete-class Radeon HD 7000G Series graphics. This was followed by a system on a chip (SoC) version in 2015 which offered a faster CPU and faster graphics, with support for DDR4 SDRAM memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In residential telephony, an extension telephone is an additional telephone wired to the same telephone line as another. In middle 20th century telephone jargon, the first telephone on a line was a \"Main Station\" and subsequent ones \"Extensions\" or even called as intercom. Such extension phones allow making or receiving calls in different rooms, for example in a home, but any incoming call would ring all extensions and any one extension being in use would cause the line to be busy for all users. Some telephones intended for use as extensions have built in intercom features; a key telephone system for a small business may offer two to five lines, lamps indicating lines already in use, the ability to place calls on 'hold' and an intercom on each of the multiple extensions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Define a matrix P {\\displaystyle P} of dimension | I | \u00d7 | J | {\\displaystyle |I|\\times |J|} with entries in G 0 = G \u222a { 0 } . {\\displaystyle G^{0}=G\\cup \\{0\\}.} Then, it can be shown that every 0-simple semigroup is of the form S = ( I \u00d7 G 0 \u00d7 J ) {\\displaystyle S=(I\\times G^{0}\\times J)} with the operation ( i , a , j ) \u2217 ( k , b , n ) = ( i , a p j k b , n ) {\\displaystyle (i,a,j)*(k,b,n)=(i,ap_{jk}b,n)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public-key cryptography, the Station-to-Station (STS) protocol is a cryptographic key agreement scheme. The protocol is based on classic Diffie\u2013Hellman, and provides mutual key and entity authentication. Unlike the classic Diffie\u2013Hellman, which is not secure against a man-in-the-middle attack, this protocol assumes that the parties have signature keys, which are used to sign messages, thereby providing security against man-in-the-middle attacks. In addition to protecting the established key from an attacker, the STS protocol uses no timestamps and provides perfect forward secrecy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most of the tracks have been previously released on singles, extended plays, and via the Linkin Park Underground fan club, while other tracks are being released for the first time on this compilation. Various editions of the release were offered, including on CDs and vinyl. It was released on October 9, 2020.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a polykay, or generalised k-statistic, (denoted k r , s {\\displaystyle k_{r,s}} ) is a statistic defined as a linear combination of sample moments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to represent code points, column/line numbers are used for one-byte codes and kuten numbers are used for two-byte codes. For a way to identify a character without depending on a code, character names are used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In score voting, strategic voters who expect all other voters to be strategic will exaggerate their true preferences and use the same quasi-compromising strategy as in approval voting, above. That is, they will give all candidates either the highest possible or the lowest possible rating. This presents an additional problem as compared to the approval method if some voters give honest \"weak\" votes with middle rankings and other voters give strategic approval votes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted gcd ( x , y ) {\\displaystyle \\gcd(x,y)} . For example, the GCD of 8 and 12 is 4, that is, gcd ( 8 , 12 ) = 4 {\\displaystyle \\gcd(8,12)=4} .In the name \"greatest common divisor\", the adjective \"greatest\" may be replaced by \"highest\", and the word \"divisor\" may be replaced by \"factor\", so that other names include highest common factor (hcf), etc. Historically, other names for the same concept have included greatest common measure.This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see \u00a7 In commutative rings below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It can build self-confidence and self-esteem while enhancing skills and extending networks and social ties. Online volunteering also allows participants to adapt their program of volunteer work to their unique skills and passions.People engaged in virtual volunteering undertake a variety of activities from locations remote to the organization or people they are assisting, via a computer or other Internet-connected device, such as: researching subjects (e.g. for Wikia projects) writing software (see open-source software which is often made by volunteers) fixing software (e.g. Community patches) creating web pages editing or writing proposals, press releases, newsletter articles, etc. translating documents (e.g. Fan translations) developing material for a curriculum designing a database designing graphics scanning documents providing legal, business, medical, agricultural or any other expertise counseling people tutoring or mentoring students moderating online discussion groups writing songs creating a podcast editing a video monitoring the news internet pastoral care answering questions tagging photos and files distributed computing managing other online volunteersIn the developing world, innovative synergies between volunteerism and technology typically focus on mobile communication technologies rather than the Internet. Around 26 per cent of people worldwide had Internet access in 2009.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that property equivalence is not the same as property equality. Equivalent properties have the same \"values\" (i.e., the same property extension), but may have different intensional meaning (i.e., denote different concepts). Property equality should be expressed with the owl:sameAs construct. As this requires that properties are treated as individuals, such axioms are only allowed in OWL Full.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to guarantee safety, Gbcast defines three safety properties and ensures they hold, regardless of the pattern of failures:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Example #1 There are 5 pink marbles, 2 blue marbles, and 8 purple marbles. What are the odds in favor of picking a blue marble?Answer: The odds in favour of a blue marble are 2:13. One can equivalently say that the odds are 13:2 against.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some languages drop the copula in poetic or aphorismic contexts. Examples in English include The more, the better. Out of many, one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parametric hypothesis testing problems, a simple or point hypothesis refers to a hypothesis where the parameter's value is assumed to be a single number. In contrast, in a composite hypothesis the parameter's value is given by a set of numbers. For example, when testing the null hypothesis that a distribution is normal with a mean less than or equal to zero against the alternative that the mean is greater than zero (variance known), the null hypothesis does not specify the probability distribution of the appropriate test statistic. In the just mentioned example that would be the Z-statistic belonging to the one-sided one-sample Z-test.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, it is often necessary to compare tree structures (e.g. parse trees) for similarity. Such comparisons can be performed by computing dot products of vectors of features of the trees, but these vectors tend to be very large: NLP techniques have come to a point where a simple dependency relation over two words is encoded with a vector of several millions of features. It can be impractical to represent complex structures such as trees with features vectors. Well-designed kernels allow computing similarity over trees without explicitly computing the feature vectors of these trees. Moreover, kernel methods have been widely used in machine learning tasks ( e.g. SVM ), and thus plenty of algorithms are working natively with kernels, or have an extension that handles kernelization. An example application is classification of sentences, such as different types of questions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, the Wehrl entropy, named after Alfred Wehrl, is a classical entropy of a quantum-mechanical density matrix. It is a type of quasi-entropy defined for the Husimi Q representation of the phase-space quasiprobability distribution. See for a comprehensive review of basic properties of classical, quantum and Wehrl entropies, and their implications in statistical mechanics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance, statistical difference or variational distance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other imperative programming languages, it is possible to achieve some of the same algorithmic results as are obtained via higher-order functions by dynamically executing code (sometimes called Eval or Execute operations) in the scope of evaluation. There can be significant drawbacks to this approach: The argument code to be executed is usually not statically typed; these languages generally rely on dynamic typing to determine the well-formedness and safety of the code to be executed. The argument is usually provided as a string, the value of which may not be known until run-time. This string must either be compiled during program execution (using just-in-time compilation) or evaluated by interpretation, causing some added overhead at run-time, and usually generating less efficient code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nonparametric statistics, a kernel is a weighting function used in non-parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variables' density functions, or in kernel regression to estimate the conditional expectation of a random variable. Kernels are also used in time-series, in the use of the periodogram to estimate the spectral density where they are known as window functions. An additional use is in the estimation of a time-varying intensity for a point process where window functions (kernels) are convolved with time-series data. Commonly, kernel widths must also be specified when running a non-parametric estimation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scalar setting, McDiarmid's inequality provides one common way of bounding the differences by applying Azuma's inequality to a Doob martingale. A version of the bounded differences inequality holds in the matrix setting. Let { Z k: k = 1 , 2 , \u2026 , n } {\\displaystyle \\{Z_{k}:k=1,2,\\ldots ,n\\}} be an independent, family of random variables, and let H {\\displaystyle \\mathbf {H} } be a function that maps n {\\displaystyle n} variables to a self-adjoint matrix of dimension d {\\displaystyle d} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and particularly in number theory, N is a primary pseudoperfect number if it satisfies the Egyptian fraction equation 1 N + \u2211 p | N 1 p = 1 , {\\displaystyle {\\frac {1}{N}}+\\sum _{p\\,|\\;\\!N}{\\frac {1}{p}}=1,} where the sum is over only the prime divisors of N.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics the division polynomials provide a way to calculate multiples of points on elliptic curves and to study the fields generated by torsion points. They play a central role in the study of counting points on elliptic curves in Schoof's algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In science and engineering, the terms data processing and information systems are considered too broad, and the term data processing is typically used for the initial stage followed by a data analysis in the second stage of the overall data handling. Data analysis uses specialized algorithms and statistical calculations that are less often observed in a typical general business environment. For data analysis, software suites like SPSS or SAS, or their free counterparts such as DAP, gretl or PSPP are often used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a congruence of squares is a congruence commonly used in integer factorization algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its \"true value\" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, \"errors\" are also called disturbances.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following the majority judgment winner for the first group of voters is determined. The sorted ratings would be as follows: Result: With the votes of the first group of voters, A has the median rating of \"Excellent\" and B has the median rating of \"Fair\". Thus, A is elected majority judgment winner by the first group of voters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, Berger codes can detect any number of zero-to-one bit-flip errors, as long as no one-to-zero bit-flip errors occur in the same code word. Berger codes cannot correct any error. Like all unidirectional error detecting codes, Berger codes can also be used in delay-insensitive circuits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, every conjecture concerning the unknown probability distribution of a collection of random variables representing the observed data X {\\displaystyle X} in some study is called a statistical hypothesis. If we state one hypothesis only and the aim of the statistical test is to see whether this hypothesis is tenable, but not to investigate other specific hypotheses, then such a test is called a null hypothesis test. As our statistical hypothesis will, by definition, state some property of the distribution, the null hypothesis is the default hypothesis under which that property does not exist. The null hypothesis is typically that some parameter (such as a correlation or a difference between means) in the populations of interest is zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The technique is also known as Wiener\u2013Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov. The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate P\u00f3lya distribution (after George P\u00f3lya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector \u03b1 {\\displaystyle {\\boldsymbol {\\alpha }}} , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a cryptochannel is a complete system of crypto-communications between two or more holders or parties. It includes: (a) the cryptographic aids prescribed; (b) the holders thereof; (c) the indicators or other means of identification; (d) the area or areas in which effective; (e) the special purpose, if any, for which provided; and (f) pertinent notes as to distribution, usage, etc. A cryptochannel is analogous to a radio circuit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, in 1998, Tijn Borghuis introduced modal pure type systems (MPTS). Roorda has discussed the application of pure type systems to functional programming; and Roorda and Jeuring have proposed a programming language based on pure type systems.The systems from the lambda cube are all known to be strongly normalizing. Pure type systems in general need not be, for example System U from Girard's paradox is not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music theory, a parameter denotes an element which may be manipulated (composed), separately from the other elements. The term is used particularly for pitch, loudness, duration, and timbre, though theorists or composers have sometimes considered other musical aspects as parameters. The term is particularly used in serial music, where each parameter may follow some specified series. Paul Lansky and George Perle criticized the extension of the word \"parameter\" to this sense, since it is not closely related to its mathematical sense, but it remains common. The term is also common in music production, as the functions of audio processing units (such as the attack, release, ratio, threshold, and other variables on a compressor) are defined by parameters specific to the type of unit (compressor, equalizer, delay, etc.).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let lower case letters n , x . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical theory, the Pitman closeness criterion, named after E. J. G. Pitman, is a way of comparing two candidate estimators for the same parameter. Under this criterion, estimator A is preferred to estimator B if the probability that estimator A is closer to the true value than estimator B is greater than one half. Here the meaning of closer is determined by the absolute difference in the case of a scalar parameter, or by the Mahalanobis distance for a vector parameter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of m \u00d7 n {\\displaystyle m\\times n} matrices, and is denoted by the symbol O {\\displaystyle O} or 0 {\\displaystyle 0} followed by subscripts corresponding to the dimension of the matrix as the context sees fit. Some examples of zero matrices are 0 1 , 1 =  , 0 2 , 2 =  , 0 2 , 3 =  . {\\displaystyle 0_{1,1}={\\begin{bmatrix}0\\end{bmatrix}},\\ 0_{2,2}={\\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}},\\ 0_{2,3}={\\begin{bmatrix}0&0&0\\\\0&0&0\\end{bmatrix}}.\\ }", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Firstly, the page table walker, which uses physical addresses to access the page table and directory, can now access physical addresses greater than the 32-bit physical addresses (no PAE system). From the CR3, the page table walker can access page directories and tables that are beyond the 32-bit range. Secondly, the physical address for the data that is being accessed (stored in the page table) can be represented as a physical address that is greater than the 32-bit address (no PAE system).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model checking, a transition system is sometimes defined to include an additional labeling function for the states as well, resulting in a notion that encompasses that of Kripke structure.Action languages are extensions of transition systems, adding a set of fluents F, a set of values V, and a function that maps F \u00d7 S to V.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the \"Fall Revolution\" series of science-fiction books, author Ken Macleod riffs and puns on the expression by writing about entities composed of information actually \"wanting\", as in desiring, freedom and the machinations of several human characters with differing political and ideological agendas, to facilitate or disrupt these entities' quest for freedom. In the cyberpunk world of post-singularity transhuman culture described by Charles Stross in his books like Accelerando and Singularity Sky, the wish of information to be free is a law of nature.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Continued fractions have a number of remarkable properties related to the Euclidean algorithm for integers or real numbers. Every rational number p {\\displaystyle p} / q {\\displaystyle q} has two closely related expressions as a finite continued fraction, whose coefficients ai can be determined by applying the Euclidean algorithm to ( p , q ) {\\displaystyle (p,q)} . The numerical value of an infinite continued fraction is irrational; it is defined from its infinite sequence of integers as the limit of a sequence of values for finite continued fractions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It can also be the natural minor scale or Aeolian mode with raised third and lowered fifth intervals. It may also be derived from the Phrygian Dominant scale, but this time, the second is major, while the fifth is diminished.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In situations where software must not crash for any reason, error swallowing is a practice that a programmer can easily fall into. For example, a plugin that is running inside another application is expected to handle all errors and exceptions in such a way as to not crash the application in which it is embedded. Blanket catching of errors and exceptions is a pattern that is easy to fall into when attempting to prevent crashes at all costs, and when you combine that with poor logging tools, error swallowing can happen.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above execution scheme, the tasks which correspond to increasing job size are placed in a queue, with the tasks belonging to the largest gang scheduled first, but this method of execution tends to lead to the starvation of resources of smaller jobs and is therefore unfit to be executed in systems where the number of processors is comparatively low.The AFCFS and LGFS also have to deal with possible processor failure. In such a case, tasks executing on that processor are submitted to other processors for execution. The tasks wait in the head of the queue on these processors while the current processor is being repaired. There are two scenarios which emerge from the above issue: Blocking case: The processors assigned to the interrupted jobs are blocked and cannot execute other jobs in their queue until the jobs from the damaged processors are cleared. Non-blocking case: This case is incurred when the jobs already executing in the processors are processed early instead of waiting for the blocked jobs to resume execution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is done by treating each count within the size variable as a single sampling unit. Samples are then identified by selecting at even intervals among these counts within the size variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another example, coming from formal language theory, is the free semigroup generated by a nonempty set (an alphabet), with string concatenation as the binary operation, and the involution being the map which reverses the linear order of the letters in a string. A third example, from basic set theory, is the set of all binary relations between a set and itself, with the involution being the converse relation, and the multiplication given by the usual composition of relations. Semigroups with involution appeared explicitly named in a 1953 paper of Viktor Wagner (in Russian) as result of his attempt to bridge the theory of semigroups with that of semiheaps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent decades, the SKI combinator calculus, with only two primitive combinators, K and S, has become the canonical approach to combinatory logic. B, C, and W can be expressed in terms of S and K as follows: B = S (K S) K C = S (S (K (S (K S) K)) S) (K K) K = K W = S S (S K)Another way is, having defined B as above, to further define C = S(BBS)(KK) and W = CSI. Going the other direction, SKI can be defined in terms of B,C,K,W as: I = W K K = K S = B (B (B W) C) (B B) = B (B W) (B B C).Also of note, Y combinator has a short expression in this system, as Y = BU(CBU), where U = WI = SII is the self-application combinator. Then we have Yg = U(BgU) = BgU(BgU) = g(U(BgU)) = g(Yg).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nouns, the thematic vowel is almost always *o, and only becomes *e when there is no ending or when followed by *h\u2082 in the neuter nominative/accusative plural. Here is an example paradigm for *h\u2082\u0155\u0325t\u1e31os 'bear', a thematic animate noun, supplemented by the neuter *h\u2082\u00e9rh\u2083trom 'plough' for the nominative/accusative: Again, athematic nouns show ablaut and accent shifts, mainly between the \"strong\" cases (nominative and vocative in all numbers, and accusative singular/dual) and the \"weak\" cases (all others). A few endings are also different from the thematic paradigm; for example, the nominative/accusative neuter has *-\u2205 instead of *-m. See Athematic accent/ablaut classes of PIE nouns for examples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 21st century a rapid development of ICT services and electronical devices took place, in which the internet servers multiplied by a factor of 1000 to 395 million and its still increasing. This increase can be explained by moores law, which states, that the development of ICT increases every year by 16-20%, so it will double in numbers every four to five years. Alongside this development and the high investments in increasing demand for ICT capable products, a high environmental impact came with it. Software and Hardware development as well as production causing already in 2008 the same amount of CO2-emissions as global air travels.There are two sides of ICT, the positive environmental possibilities and the shadow side.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similar forced disclosure laws in Australia, Finland, France, and India compel individual suspects under investigation to hand over encryption keys or passwords during a criminal investigation. In the United States, the federal criminal case of United States v. Fricosu addressed whether a search warrant can compel a person to reveal an encryption passphrase or password. The Electronic Frontier Foundation (EFF) argued that this is a violation of the protection from self-incrimination given by the Fifth Amendment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These conflicts can indicate an HGT event or may be the result of uncertainty in gene tree inference. To reduce uncertainty, bipartition analyses typically focus on strongly supported bipartitions such as those associated with branches with bootstrap values or posterior probabilities above certain thresholds. Any gene family found to have one or several conflicting, but strongly supported, bipartitions is considered as an HGT candidate.Quartet decomposition Quartets are trees consisting of four leaves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Assuming that the statistical correlation function is Gaussian of the form G ( x , y ) = \u03b4 2 exp \u2061 ( \u2212 r 2 \u03c3 2 ) {\\displaystyle G(x,y)=\\delta ^{2}\\exp \\left(-{\\frac {r^{2}}{\\sigma ^{2}}}\\right)} where \u03b4 {\\displaystyle \\delta } is the root mean square height, r {\\displaystyle r} is the distance from the point ( x , y ) {\\displaystyle (x,y)} , and \u03c3 {\\displaystyle \\sigma } is the correlation length, then the Fourier transform of the correlation function is | s ( k surf ) | 2 = 1 4 \u03c0 \u03c3 2 \u03b4 2 exp \u2061 ( \u2212 \u03c3 2 k surf 2 4 ) {\\displaystyle |s(k_{\\text{surf}})|^{2}={\\frac {1}{4\\pi }}\\sigma ^{2}\\delta ^{2}\\exp \\left(-{\\frac {\\sigma ^{2}k_{\\text{surf}}^{2}}{4}}\\right)} where s {\\displaystyle s} is a measure of the amount of each spatial frequency k surf {\\displaystyle k_{\\text{surf}}} which help couple photons into a surface plasmon. If the surface only has one Fourier component of roughness (i.e. the surface profile is sinusoidal), then the s {\\displaystyle s} is discrete and exists only at k = 2 \u03c0 a {\\displaystyle k={\\frac {2\\pi }{a}}} , resulting in a single narrow set of angles for coupling. If the surface contains many Fourier components, then coupling becomes possible at multiple angles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, concentration inequalities provide bounds on how a random variable deviates from some value (typically, its expected value). The law of large numbers of classical probability theory states that sums of independent random variables are, under very mild conditions, close to their expectation with a large probability. Such sums are the most basic examples of random variables concentrated around their mean. Recent results show that such behavior is shared by other functions of independent random variables. Concentration inequalities can be sorted according to how much information about the random variable is needed in order to use them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of classical propositional logic, satisfiability is decidable for propositional formulae. In particular, satisfiability is an NP-complete problem, and is one of the most intensively studied problems in computational complexity theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a distributed-queue dual-bus network (DQDB) is a distributed multi-access network that (a) supports integrated communications using a dual bus and distributed queuing, (b) provides access to local or metropolitan area networks, and (c) supports connectionless data transfer, connection-oriented data transfer, and isochronous communications, such as voice communications. IEEE 802.6 is an example of a network providing DQDB access methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The computer designs based on this theory were called reduced instruction set computing (RISC). RISCs usually had larger numbers of registers, accessed by simpler instructions, with a few instructions specifically to load and store data to memory. The result was a very simple core CPU running at very high speed, supporting the sorts of operations the compilers were using anyway.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , 2 n } {\\displaystyle =\\{1,2,...,2n\\}} .Equivalently, haf \u2061 ( A ) = \u2211 M \u2208 M \u220f ( u , v ) \u2208 M A u , v {\\displaystyle \\operatorname {haf} (A)=\\sum _{M\\in {\\mathcal {M}}}\\prod _{\\scriptscriptstyle (u,v)\\in M}A_{u,v}} where M {\\displaystyle {\\mathcal {M}}} is the set of all 1-factors (perfect matchings) on the complete graph K 2 n {\\displaystyle K_{2n}} , namely the set of all ( 2 n ) !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs. For example, the factorial function n!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In fact, there exist instances of theoretical non-quantum correlations which, a priori, do not seem physically implausible. The aim of device-independent reconstructions is to show that all such supra-quantum examples are precluded by a reasonable physical principle. The physical principles proposed so far include no-signalling, Non-Trivial Communication Complexity, No-Advantage for Nonlocal computation, Information Causality, Macroscopic Locality, and Local Orthogonality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of d = 2 {\\displaystyle d=2} the rectangle is represented by ( ( x m i n , y m i n ) , ( x m a x , y m a x ) ) {\\displaystyle \\,((x_{min},y_{min}),(x_{max},y_{max}))} and the MBR thus four corners ( x m i n , y m i n , x m a x , y m a x ) {\\displaystyle \\,(x_{min},y_{min},x_{max},y_{max})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As well, in yes/no questions, the non-manual marking must be used over the whole utterance in order for it to be judged as a statement opposed to a question. The yes/no question is the same word order as the statement form of the sentence, with the addition of non-manual grammatical markings. This can be seen in the examples below. ASL Statement:JUAN WILL BUY SHOES TODAY \"Juan will buy shoes today\"ASL Yes/no Question:_____________________brow raise JUAN WILL BUY SHOES TODAY \"Will Juan buy shoes today?\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schr\u00f6dinger operators, and five concern operators that incorporate the Coulomb potential.In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems. Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was in fact the Cantor set, a challenge known as the \"Ten Martini Problem\" after the reward that Mark Kac offered for solving it.The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, 6G is the sixth generation mobile system standard currently under development for wireless communications technologies supporting cellular data networks. It is the planned successor to 5G and will likely be significantly faster. Like its predecessors, 6G networks will probably be broadband cellular networks, in which the service area is divided into small geographical areas called cells. Several companies (Airtel, Anritsu, Apple, Ericsson, Fly, Huawei, Jio, Keysight, LG, Nokia, NTT Docomo, Samsung, Vi, Xiaomi), research institutes (Technology Innovation Institute, the Interuniversity Microelectronics Centre) and countries (United States, countries in the European Union, Russia, China, India, Japan, South Korea, Singapore and United Arab Emirates) have shown interest in 6G networks.6G networks are expected to be even more diverse than their predecessors and are likely to support applications beyond current mobile use scenarios, such as ubiquitous instant communications, pervasive intelligence and the Internet of Things (IoT). It is expected that mobile network operators will adopt flexible decentralized business models for 6G, with local spectrum licensing, spectrum sharing, infrastructure sharing, and intelligent automated management underpinned by mobile edge computing, artificial intelligence (AI), short-packet communication and blockchain technologies.The Next G Alliance, released its report on 6G in February 2022, outlining the development roadmap of 6G. As of 2023, there is no universally-accepted government or non-government standard for what qualifies as 6G technology and it is still in the early stage of development, but expect to be deployed in 2028 as scheduled.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a composition ring, introduced in (Adler 1962), is a commutative ring (R, 0, +, \u2212, \u00b7), possibly without an identity 1 (see non-unital ring), together with an operation \u2218: R \u00d7 R \u2192 R {\\displaystyle \\circ :R\\times R\\rightarrow R} such that, for any three elements f , g , h \u2208 R {\\displaystyle f,g,h\\in R} one has ( f + g ) \u2218 h = ( f \u2218 h ) + ( g \u2218 h ) {\\displaystyle (f+g)\\circ h=(f\\circ h)+(g\\circ h)} ( f \u22c5 g ) \u2218 h = ( f \u2218 h ) \u22c5 ( g \u2218 h ) {\\displaystyle (f\\cdot g)\\circ h=(f\\circ h)\\cdot (g\\circ h)} ( f \u2218 g ) \u2218 h = f \u2218 ( g \u2218 h ) . {\\displaystyle (f\\circ g)\\circ h=f\\circ (g\\circ h).} It is not generally the case that f \u2218 g = g \u2218 f {\\displaystyle f\\circ g=g\\circ f} , nor is it generally the case that f \u2218 ( g + h ) {\\displaystyle f\\circ (g+h)} (or f \u2218 ( g \u22c5 h ) {\\displaystyle f\\circ (g\\cdot h)} ) has any algebraic relationship to f \u2218 g {\\displaystyle f\\circ g} and f \u2218 h {\\displaystyle f\\circ h} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the transfer function method is used, attention is focused on the locations in the s-plane where the transfer function is undefined (the poles) or zero (the zeroes; see Zeroes and poles). Two different transfer functions are of interest to the designer. If the feedback loops in the system are opened (that is prevented from operating) one speaks of the open-loop transfer function, while if the feedback loops are operating normally one speaks of the closed-loop transfer function. For more on the relationship between the two, see root-locus.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Conversely, the OS may deny access, and thus neither open the file nor return a handle. In a capability-based system, handles can be passed between processes, with associated access rights.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then for any observable f {\\displaystyle f} in the domain of L {\\displaystyle L} , one has L f ( \u03b7 ) = \u2211 \u039b \u222b \u03be: \u03be \u039b c = \u03b7 \u039b c c \u039b ( \u03b7 , d \u03be )  {\\displaystyle Lf(\\eta )=\\sum _{\\Lambda }\\int _{\\xi :\\xi _{\\Lambda ^{c}}=\\eta _{\\Lambda ^{c}}}c_{\\Lambda }(\\eta ,d\\xi )} . For example, for the stochastic Ising model we have G = Z d {\\displaystyle G=\\mathbb {Z} ^{d}} , S = { \u2212 1 , + 1 } {\\displaystyle S=\\{-1,+1\\}} , c \u039b = 0 {\\displaystyle c_{\\Lambda }=0} if \u039b \u2260 { i } {\\displaystyle \\Lambda \\neq \\{i\\}} for some i \u2208 G {\\displaystyle i\\in G} and c i ( \u03b7 , \u03b7 i ) = exp \u2061  {\\displaystyle c_{i}(\\eta ,\\eta ^{i})=\\exp} where \u03b7 i {\\displaystyle \\eta ^{i}} is the configuration equal to \u03b7 {\\displaystyle \\eta } except it is flipped at site i {\\displaystyle i} . \u03b2 {\\displaystyle \\beta } is a new parameter modeling the inverse temperature.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The target can be identified by an URI (e.g., fragment identifiers) and/or a selector that defines a domain-, resource- or application-specific access protocol, e.g., offset-based, XPath-based, etc. Web Annotation was standardized on February 23, 2017 with the release of three official Recommendations by the W3C Web Annotation Working Group: Web Annotation Data Model Web Annotation Vocabulary Web Annotation ProtocolThese recommendations were accompanied by additional working group notes that describe their application: Embedding Web Annotations in HTML Selectors and StatesThe Web Annotation data model is also provided in machine-readable form as the Web Annotation ontology. Note that this ontology defines the Web Annotation namespace (https://www.w3.org/ns/oa#), and that this namespace is conventionally abbreviated as oa. This is the abbreviation for Open Annotation, a W3C Community Group whose specifications formed the basis for the Web Annotation standard.Web Annotation supersedes other standardization initiatives for annotations on the web within the W3C.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Electromagnetism has been studied since ancient times. Many ancient civilizations, including the Greeks and the Mayans created wide-ranging theories to explain lightning, static electricity, and the attraction between magnetized pieces of iron ore. However, it wasn't until the late 18th century that scientists began to develop a mathematical basis for understanding the nature of electromagnetic interactions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This derived directly from the hardware design of the Intel 8086 (and, subsequently, the closely related 8088), which had exactly 20 address pins. (Both were packaged in 40-pin DIP packages; even with only 20 address lines, the address and data buses were multiplexed to fit all the address and data lines within the limited pin count.) Each segment begins at a multiple of 16 bytes, called a paragraph, from the beginning of the linear (flat) address space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values \u03bc a {\\displaystyle \\mu _{a}} and \u03bc b {\\displaystyle \\mu _{b}} and standard deviation \u03c3 a {\\displaystyle \\sigma _{a}} and \u03c3 b {\\displaystyle \\sigma _{b}} respectively is: D s n = ( \u03bc a \u2212 \u03bc b ) ( \u03c3 a + \u03c3 b ) {\\displaystyle D_{sn}={(\\mu _{a}-\\mu _{b}) \\over (\\sigma _{a}+\\sigma _{b})}} In the case of Gaussian-distributed data and unbiased class distributions, this statistic can be related to classification accuracy given an ideal linear discrimination, and a decision boundary can be derived.This distance is frequently used to identify vectors that have significant difference. One usage is in bioinformatics to locate genes that are differential expressed on microarray experiments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by Moore (1922).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the U.S., New York is the only state that does not allow peer-to-peer car rental because the owner cannot exclude him or herself from liability to a renter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first two stages of the algorithm, the time complexity is O(N2L + NL2), the space complexity is O(N2 + NL + L2). The refinement stage adds to the time complexity another term, O(N3L). MUSCLE is often used as a replacement for Clustal, since it usually (but not always) gives better sequence alignments, depending on the chosen options. is significantly faster than Clustal, more so for larger alignments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By failing to check the length of the string, it also overwrites the value of B: B's value has now been inadvertently replaced by a number formed from part of the character string. In this example \"e\" followed by a zero byte would become 25856. Writing data past the end of allocated memory can sometimes be detected by the operating system to generate a segmentation fault error that terminates the process. To prevent the buffer overflow from happening in this example, the call to strcpy could be replaced with strlcpy, which takes the maximum capacity of A (including a null-termination character) as an additional parameter and ensures that no more than this amount of data is written to A: When available, the strlcpy library function is preferred over strncpy which does not null-terminate the destination buffer if the source string's length is greater than or equal to the size of the buffer (the third argument passed to the function), therefore A may not be null-terminated and cannot be treated as a valid C-style string.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "15; 2009, c. 13; 2010, c. 15.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These applications are elaborated below. But an illustrative note bears adding here. It is sometimes claimed that what is at issue in these problems is the supervenience claim itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For a concrete example, take the universal and existential quantifiers \u2200 and \u2203, respectively. Their truth conditions can be specified as A \u22a8 \u2200 x \u03d5  \u27fa \u03d5 A , x , a \u00af \u2208 \u2200 A {\\displaystyle A\\models \\forall x\\phi \\iff \\phi ^{A,x,{\\bar {a}}}\\in \\forall _{A}} A \u22a8 \u2203 x \u03d5  \u27fa \u03d5 A , x , a \u00af \u2208 \u2203 A , {\\displaystyle A\\models \\exists x\\phi \\iff \\phi ^{A,x,{\\bar {a}}}\\in \\exists _{A},} where \u2200 A {\\displaystyle \\forall _{A}} is the singleton whose sole member is dom(A), and \u2203 A {\\displaystyle \\exists _{A}} is the set of all non-empty subsets of dom(A) (i.e. the power set of dom(A) minus the empty set).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most physical and biological sciences, the use of either quantitative or qualitative methods is uncontroversial, and each is used when appropriate. In the social sciences, particularly in sociology, social anthropology and psychology, the use of one or other type of method can be a matter of controversy and even ideology, with particular schools of thought within each discipline favouring one type of method and pouring scorn on to the other. The majority tendency throughout the history of social science, however, is to use eclectic approaches-by combining both methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Ville's inequality provides an upper bound on the probability that a supermartingale exceeds a certain value. The inequality is named after Jean Ville, who proved it in 1939. The inequality has applications in statistical testing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices, with predicates for equality and adjacency testing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some computer programming languages, the size in bits of certain data types 64-bit computing A 64-bit integer can represent up to 18,446,744,073,709,551,616 values. Base 64 is used in with Base64 encoding and other data compression formats. In 8-bit home computers, a common shorthand for the Commodore 64 The ASCII code 64 is for the @ symbol The Nintendo 64 video game console and (historically) the Commodore 64. Since 1996, the number 64 has been an abbreviation or slang for Nintendo 64 (though N64 is more common) along with the games Super Mario 64, Mario Kart 64 and more.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For the rest of the time, the mobile can carry out measurements on the network, detecting surrounding transmitters on different frequencies. This allows safe inter frequency handovers, something which is difficult in CDMA systems, not supported at all in IS-95 and supported through complex system additions in Universal Mobile Telecommunications System (UMTS). This in turn allows for co-existence of microcell layers with macrocell layers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\u03b1 \u2192 ( \u03b1 r e f ) ! : \u2200 \u03b1 . ( \u03b1 r e f ) \u2192 \u03b1 :=: \u2200 \u03b1 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times. An infinite word is recurrent if and only if it is a sesquipower.A uniformly recurrent word is a recurrent word in which for any given factor X in the sequence, there is some length nX (often much longer than the length of X) such that X appears in every block of length nX. The terms minimal sequence and almost periodic sequence (Muchnik, Semenov, Ushakov 2003) are also used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some nonlinear systems, parameters are explicit. In others they are implicit, and the system of nonlinear equations is written F ( u ) = 0 {\\displaystyle F(\\mathbf {u} )=0} where u {\\displaystyle \\mathbf {u} } is an n-vector, and its image F ( u ) {\\displaystyle F(\\mathbf {u} )} is an n-1 vector. This formulation, without an explicit parameter space is not usually suitable for the formulations in the following sections, because they refer to parameterized autonomous nonlinear dynamical systems of the form: u \u2032 = F ( u , \u03bb ) . {\\displaystyle \\mathbf {u} '=F(\\mathbf {u} ,\\lambda ).} However, in an algebraic system there is no distinction between unknowns u {\\displaystyle \\mathbf {u} } and the parameters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An advantage of these methods is that in the favorable cases it can find the exact value of the joint spectral radius and provide a certificate that this is the exact value. The second family of methods approximate the extremal norm with modern optimization techniques, such as ellipsoid norm approximation, semidefinite programming, Sum Of Squares, and conic programming. The advantage of these methods is that they are easy to implement, and in practice, they provide in general the best bounds on the joint spectral radius.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Different theorists have different categorizations and conceptualizations of defence mechanisms. Large reviews of theories of defence mechanisms are available from Paulhus, Fridhandler and Hayes (1997) and Cramer (1991). The Journal of Personality published a special issue on defence mechanisms (1998).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early decades of telegraphy, many efficiency improvements were incorporated into operations. The Morse code itself was one of these: it roughly coded more commonly used symbols into shorter keying sequences, and the rare ones into longer, thus leading to data compression online. The introduction of Morse symbols called procedural signs or prosigns was then just a logical progression. They were not defined by the inventors of Morse code, but were gradually introduced to improve the speed and accuracy of high-volume message handling, especially between professional telegraph operators operating over the time's long distance contacts, such as short wave radio and transatlantic cable. Improvements to the legibility of formal written telegraph messages (telegrams) using white space formatting were thus supported by the creation of procedure symbols. Mastery of these Morse code prosigns was important in becoming an efficient telegraph operator, as was the command of many other forms of abbreviation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most CB operators prefer to use self-assigned handles reflecting some aspect of their personality; it is generally considered a breach of CB etiquette to use real names, even that of the user. Family Radio Service and Multi-Use Radio Service have no station identification requirement, though groups of individual users have their own procedures, such as using license plates or informal callsigns (some groups within the Boy Scouts of America, for example, use the troop number followed by the scout's initials as a callsign). Wi-Fi access points are not required by law to identify (they are unlicensed transmitters) but the Wi-Fi standards include provision for an identifier called an SSID, which is transmitted as a routine part of Wi-Fi network traffic. However, since a number of standard Wi-Fi channels are shared with the amateur radio spectrum, amateur radio-operated High Speed Multimedia (HSMM), or \"hinternet\", access points usually use the call sign of the control operator as the SSID, this suffices as proper station identification for the access point being operated as an amateur radio transceiver.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern management usage, the term data is increasingly replaced by information or even knowledge in a non-technical context. Thus data management has become information management or knowledge management. This trend obscures the raw data processing and renders interpretation implicit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution, negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution, but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The need to convert a and b into Montgomery form and their product out of Montgomery form means that computing a single product by Montgomery multiplication is slower than the conventional or Barrett reduction algorithms. However, when performing many multiplications in a row, as in modular exponentiation, intermediate results can be left in Montgomery form. Then the initial and final conversions become a negligible fraction of the overall computation. Many important cryptosystems such as RSA and Diffie\u2013Hellman key exchange are based on arithmetic operations modulo a large odd number, and for these cryptosystems, computations using Montgomery multiplication with R a power of two are faster than the available alternatives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software deployment, an environment or tier is a computer system or set of systems in which a computer program or software component is deployed and executed. In simple cases, such as developing and immediately executing a program on the same machine, there may be a single environment, but in industrial use, the development environment (where changes are originally made) and production environment (what end users use) are separated, often with several stages in between. This structured release management process allows phased deployment (rollout), testing, and rollback in case of problems. Environments may vary significantly in size: the development environment is typically an individual developer's workstation, while the production environment may be a network of many geographically distributed machines in data centers, or virtual machines in cloud computing. Code, data, and configuration may be deployed in parallel, and need not connect to the corresponding tier\u2014for example, pre-production code might connect to a production database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, affricates contrast phonemically with stop\u2013fricative sequences: Polish affricate /\u0288\u0361\u0282/ in czysta 'clean (f.)' versus stop\u2013fricative /t\u0282/ in trzysta 'three hundred'. Klallam affricate /t\u0361s/ in k'\u02b7\u0259\u0301nc 'look at me' versus stop\u2013fricative /ts/ in k'\u02b7\u0259\u0301nts 'he looks at it'.The exact phonetic difference varies between languages. In stop\u2013fricative sequences, the stop has a release burst before the fricative starts; but in affricates, the fricative element is the release.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In tensor notation, the triple product is expressed using the Levi-Civita symbol: and referring to the i {\\displaystyle i} -th component of the resulting vector. This can be simplified by performing a contraction on the Levi-Civita symbols, \u03b5 i j k \u03b5 k \u2113 m = \u03b4 i j \u2113 m = \u03b4 i \u2113 \u03b4 j m \u2212 \u03b4 i m \u03b4 j \u2113 , {\\displaystyle \\varepsilon _{ijk}\\varepsilon ^{k\\ell m}=\\delta _{ij}^{\\ell m}=\\delta _{i}^{\\ell }\\delta _{j}^{m}-\\delta _{i}^{m}\\delta _{j}^{\\ell }\\,,} where \u03b4 j i {\\displaystyle \\delta _{j}^{i}} is the Kronecker delta function ( \u03b4 j i = 0 {\\displaystyle \\delta _{j}^{i}=0} when i \u2260 j {\\displaystyle i\\neq j} and \u03b4 j i = 1 {\\displaystyle \\delta _{j}^{i}=1} when i = j {\\displaystyle i=j} ) and \u03b4 i j \u2113 m {\\displaystyle \\delta _{ij}^{\\ell m}} is the generalized Kronecker delta function. We can reason out this identity by recognizing that the index k {\\displaystyle k} will be summed out leaving only i {\\displaystyle i} and j {\\displaystyle j} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the problem, each machine provides a random reward from a probability distribution specific to that machine, that is not known a-priori. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between \"exploitation\" of the machine that has the highest expected payoff and \"exploration\" to get more information about the expected payoffs of the other machines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most illustrations of the gambler's fallacy and the reverse gambler's fallacy, the trial (e.g. flipping a coin) is assumed to be fair. In practice, this assumption may not hold. For example, if a coin is flipped 21 times, the probability of 21 heads with a fair coin is 1 in 2,097,152. Since this probability is so small, if it happens, it may well be that the coin is somehow biased towards landing on heads, or that it is being controlled by hidden magnets, or similar.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proto-writing, used for inventories and the like, physical objects are represented by stylized or conventionalized pictures, or pictograms. For example, the pictorial Dongba symbols without Geba annotation cannot represent the Naxi language, but are used as a mnemonic for reciting oral literature. Some systems also use ideograms, symbols denoting abstract concepts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The problem is these samples may be biased in a way that is difficult to quantify or adjust for. For example, if interviewers decide to question the first person they see, they may oversample tall respondents (who are more easily visible from a distance), which could lead to an overestimate of average income. This non-random element is a source of uncertainty about the nature of the actual sample.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Analysis focuses not only on linguistic forms such as words, sentences, grammar, phonology, etc. but also on subtle cues such as prosody and register that signal contextual presupposition. Linguistic based analysis is not the only component that is useful for establishing instances of Interactional sociolinguistics. Culture also plays a large role in understanding this phenomenon.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution, nearest-neighbor distribution function or nearest neighbor distribution is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. More specifically, nearest neighbor functions are defined with respect to some point in the point process as being the probability distribution of the distance from this point to its nearest neighboring point in the same point process, hence they are used to describe the probability of another point existing within some distance of a point. A nearest neighbor function can be contrasted with a spherical contact distribution function, which is not defined in reference to some initial point but rather as the probability distribution of the radius of a sphere when it first encounters or makes contact with a point of a point process. Nearest neighbor function are used in the study of point processes as well as the related fields of stochastic geometry and spatial statistics, which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and directional statistics, a wrapped exponential distribution is a wrapped probability distribution that results from the \"wrapping\" of the exponential distribution around the unit circle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Both Alice and Bob announce these bits publicly and run a check to see if more than a certain number of them agree. If this check passes, Alice and Bob proceed to use privacy amplification and information reconciliation techniques to create some number of shared secret keys.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "random variables. That is, there are underlying, generally unobservable, quantities that are i.i.d. \u2013 exchangeable sequences are mixtures of i.i.d. sequences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The fact that particles can be identical has important consequences in statistical mechanics, where calculations rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The graph referred to is the graph with n vertices, with vertices i and j connected by an edge when a i j \u2260 0 {\\displaystyle a_{ij}\\neq 0} , and the degree is the degree of the vertices. A crucial aspect of such algorithms is a tie breaking strategy when there is a choice of renumbering resulting in the same degree. A version of the minimum degree algorithm was implemented in the MATLAB function symmmd (where MMD stands for multiple minimum degree), but has now been superseded by a symmetric approximate multiple minimum degree function symamd, which is faster. This is confirmed by theoretical analysis, which shows that for graphs with n vertices and m edges, MMD has a tight upper bound of O ( n 2 m ) {\\displaystyle O(n^{2}m)} on its running time, whereas for AMD a tight bound of O ( n m ) {\\displaystyle O(nm)} holds. Cummings, Fahrbach, and Fatehpuria designed an exact minimum degree algorithm with O ( n m ) {\\displaystyle O(nm)} running time, and showed that no such algorithm can exist that runs in time O ( n m 1 \u2212 \u03b5 ) {\\displaystyle O(nm^{1-\\varepsilon })} , for any \u03b5 > 0 {\\displaystyle \\varepsilon >0} , assuming the strong exponential time hypothesis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics \u2014 specifically, in ergodic theory \u2014 a maximising measure is a particular kind of probability measure. Informally, a probability measure \u03bc is a maximising measure for some function f if the integral of f with respect to \u03bc is \"as big as it can be\". The theory of maximising measures is relatively young and quite little is known about their general structure and properties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a skeleton of a category is a subcategory that, roughly speaking, does not contain any extraneous isomorphisms. In a certain sense, the skeleton of a category is the \"smallest\" equivalent category, which captures all \"categorical properties\" of the original. In fact, two categories are equivalent if and only if they have isomorphic skeletons. A category is called skeletal if isomorphic objects are necessarily identical.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In selective attention experiments, the participants may be asked to repeat aloud the content of the message they are listening to. This task is known as shadowing. As Colin Cherry (1953) found, people do not recall the shadowed message well, suggesting that most of the processing necessary to shadow the attended to message occurs in working memory and is not preserved in the long-term store. Performance on the unattended message is worse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mass spectrometry, a matrix is a compound that promotes the formation of ions. Matrix compounds are used in matrix-assisted laser desorption/ionization (MALDI), matrix-assisted ionization (MAI), and fast atom bombardment (FAB).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion. The coefficient of determination can be more (intuitively) informative than MAE, MAPE, MSE, and RMSE in regression analysis evaluation, as the former can be expressed as a percentage, whereas the latter measures have arbitrary ranges. It also proved more robust for poor fits compared to SMAPE on the test datasets in the article.When evaluating the goodness-of-fit of simulated (Ypred) vs. measured (Yobs) values, it is not appropriate to base this on the R2 of the linear regression (i.e., Yobs= m\u00b7Ypred + b). The R2 quantifies the degree of any linear correlation between Yobs and Ypred, while for the goodness-of-fit evaluation only one specific linear correlation should be taken into consideration: Yobs = 1\u00b7Ypred + 0 (i.e., the 1:1 line).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on the notion of a limit, which is in general impossible to define for a ring. Many of the properties of the derivative are true of the formal derivative, but some, especially those that make numerical statements, are not. Formal differentiation is used in algebra to test for multiple roots of a polynomial.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, Ofcom directs fixed-line telephone network providers, mobile phone providers and broadband service providers to provide number portability under the Porting Authorisation Code rules and Migration Authorisation Code code of practice respectively. As the UK was an EU member country, the Ofcom direction was intended to reflect the requirements of EU Directive 2002/22/EU.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The General Data Protection Regulation (GDPR) is an example of this. In other places, like in the United States, privacy law is argued by some to be less developed in this regard. By example, some legislation, or lack thereof, allow companies to self-regulate their collection and dissemination practices of consumer information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, ( b 1 ) 3 = b 1 \u00d7 b 1 \u00d7 b 1 = b 1 + 1 + 1 = b 3 {\\displaystyle (b^{1})^{3}=b^{1}\\times b^{1}\\times b^{1}=b^{1+1+1}=b^{3}} . Taking the cube root of both sides gives b 1 = b {\\displaystyle b^{1}=b} . The rule that multiplying makes exponents add can also be used to derive the properties of negative integer exponents.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was proven by Wassily Hoeffding in 1963.Hoeffding's inequality is a special case of the Azuma\u2013Hoeffding inequality and McDiarmid's inequality. It is similar to the Chernoff bound, but tends to be less sharp, in particular when the variance of the random variables is small. It is similar to, but incomparable with, one of Bernstein's inequalities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn. Equivalently, g(n) is the largest least common multiple (lcm) of any partition of n, or the maximum number of times a permutation of n elements can be recursively applied to itself before it returns to its starting sequence. For instance, 5 = 2 + 3 and lcm(2,3) = 6. No other partition of 5 yields a bigger lcm, so g(5) = 6.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If all numerators are 1 in a fraction written in this form, and all denominators are different from each other, the result is an Egyptian fraction representation of the number. This notation was also sometimes combined with the composite fraction notation: two composite fractions written next to each other would represent the sum of the fractions.The complexity of this notation allows numbers to be written in many different ways, and Fibonacci described several methods for converting from one style of representation to another. In particular, chapter II.7 contains a list of methods for converting an improper fraction to an Egyptian fraction, including the greedy algorithm for Egyptian fractions, also known as the Fibonacci\u2013Sylvester expansion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, compositional data are quantitative descriptions of the parts of some whole, conveying relative information. Mathematically, compositional data is represented by points on a simplex. Measurements involving probabilities, proportions, percentages, and ppm can all be thought of as compositional data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The exclusive constraint states that at most one of the causes 1 and 2 can be true, i.e. both cannot be true simultaneously. The Inclusive (at least one) constraint states that at least one of the causes 1, 2 or 3 must be true, i.e. all cannot be false simultaneously. The one and only one (OaOO or simply O) constraint states that only one of the causes 1, 2 or 3 must be true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, the Schr\u00f6der\u2013Bernstein theorem states that, if there exist injective functions f: A \u2192 B and g: B \u2192 A between the sets A and B, then there exists a bijective function h: A \u2192 B. In terms of the cardinality of the two sets, this classically implies that if |A| \u2264 |B| and |B| \u2264 |A|, then |A| = |B|; that is, A and B are equipotent. This is a useful feature in the ordering of cardinal numbers. The theorem is named after Felix Bernstein and Ernst Schr\u00f6der. It is also known as the Cantor\u2013Bernstein theorem or Cantor\u2013Schr\u00f6der\u2013Bernstein theorem, after Georg Cantor, who first published it (albeit without proof).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A tolerable idea may be given of the danger of too great a multiplicity of vulgar names, by imagining what geography would be, or, for instance, the Post-office administration, supposing every town had a totally different name in every language. Various bodies and the authors of many technical and semi-technical books do not simply adapt existing common names for various organisms; they try to coin (and put into common use) comprehensive, useful, authoritative, and standardised lists of new names. The purpose typically is: to create names from scratch where no common names exist to impose a particular choice of name where there is more than one common name to improve existing common names to replace them with names that conform more to the relatedness of the organismsOther attempts to reconcile differences between widely separated regions, traditions, and languages, by arbitrarily imposing nomenclature, often reflect narrow perspectives and have unfortunate outcomes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a microphone converts an acoustic signal to a voltage waveform, and a speaker does the reverse.Another important property of a signal is its entropy or information content. Information theory serves as the formal study of signals and their content. The information of a signal is often accompanied by noise, which primarily refers to unwanted modifications of signals, but is often extended to include unwanted signals conflicting with desired signals (crosstalk).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most of the alphabets of India and Southeast Asia, vowels are indicated through diacritics or modification of the shape of the consonant. These are called abugidas. Some abugidas, such as Ethiopic and Cree, are learned by children as syllabaries, and so are often called \"syllabics\". However, unlike true syllabaries, there is not an independent glyph for each syllable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Linux operating system, JFS is supported with the kernel module (since the kernel version 2.4.18pre9-ac4) and the complementary userspace utilities packaged under the name JFSutils. Most Linux distributions support JFS unless it is specifically removed due to space restrictions, such as on live CDs.According to benchmarks of the available filesystems for Linux, JFS is fast and reliable, with consistently good performance under different kinds of load.Actual usage of JFS in Linux is uncommon, as ext4 typically offers better performance. JFS does have a niche role in Linux: it offers a case-insensitive mount option, unlike most other Linux file systems.There are also potential problems with JFS, such as its implementation of journal writes. They can be postponed until there is another trigger\u2014potentially indefinitely, which can cause data loss over a theoretically infinite timeframe.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1950s and 1960s, travel on an \"air ferry\" was possible\u2014airplanes, often ex-military, specially equipped to take a small number of cars in addition to foot passengers. These operated various routes including between the United Kingdom and Continental Europe. Companies operating such services included Channel Air Bridge, Silver City Airways, and Corsair. The term is also applied to any \"ferrying\" by air, and is commonly used when referring to airborne military operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence ( \u2212 1 ) n \u2212 1 2 \u22c5 C n \u2212 1 2 \u2261 2 ( mod n ) , {\\displaystyle (-1)^{\\frac {n-1}{2}}\\cdot C_{\\frac {n-1}{2}}\\equiv 2{\\pmod {n}},} where Cm denotes the m-th Catalan number. The congruence also holds for every odd prime number n that justifies the name pseudoprimes for composite numbers n satisfying it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some important economic applications, the relevant change in the constraint set cannot be easily understood as an increase with respect to the strong set order and so Theorem 3 cannot be easily applied. For example, consider a consumer who maximizes a utility function u: X \u2192 R {\\displaystyle u:X\\to \\mathbb {R} } subject to a budget constraint. At price p {\\displaystyle p} in R + + n {\\displaystyle \\mathbb {R} _{++}^{n}} and wealth w > 0 {\\displaystyle w>0} , his budget set is B ( p , w ) = { x \u2208 X | p \u22c5 x \u2264 w } {\\displaystyle B(p,w)=\\{x\\in X\\ |\\ p\\cdot x\\leq w\\}} and his demand set at ( p , w ) {\\displaystyle (p,w)} is (by definition) D ( p , w ) = arg \u2061 max x \u2208 B ( p , w ) u ( x ) {\\displaystyle D(p,w)=\\arg \\max _{x\\in B(p,w)}u(x)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Doug Laney, vice president and analyst at Gartner, conducted research on Wall Street valued companies, which found that companies that had become information-centric, treating data as an asset, often had market-to-book values two to three times higher than the norm. On the topic, Laney commented: \"Even as we are in the midst of the Information Age, information simply is not valued by those in the valuation business. However, we believe that, over the next several years, those in the business of valuing corporate investments, including equity analysts, will be compelled to consider a company's wealth of information in properly valuing the company itself.\" In the latter part of the 2010s, the list of most valuable firms in the world (a list traditionally dominated by oil and energy companies) was dominated by data firms \u2013 Microsoft, Alphabet, Apple, Amazon and Facebook.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recreational mathematics, arithmetic billiards provide a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers by making use of reflections inside a rectangle whose sides are the two given numbers. This is an easy example of trajectory analysis of dynamical billiards. Arithmetic billiards have been discussed as mathematical puzzles by Hugo Steinhaus and Martin Gardner, and are known to mathematics teachers under the name 'Paper Pool'. They have been used as a source of questions in mathematical circles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term relates to the notion that the improved estimate is made closer to the value supplied by the 'other information' than the raw estimate. In this sense, shrinkage is used to regularize ill-posed inference problems. Shrinkage is implicit in Bayesian inference and penalized likelihood inference, and explicit in James\u2013Stein-type inference. In contrast, simple types of maximum-likelihood and least-squares estimation procedures do not include shrinkage effects, although they can be used within shrinkage estimation schemes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This process is known as dead reckoning. The accuracy and precision of the different PRSs is not the same.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which gk \u2261 a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n. So g is a primitive root modulo n if and only if g is a generator of the multiplicative group of integers modulo n. Gauss defined primitive roots in Article 57 of the Disquisitiones Arithmeticae (1801), where he credited Euler with coining the term. In Article 56 he stated that Lambert and Euler knew of them, but he was the first to rigorously demonstrate that primitive roots exist for a prime n. In fact, the Disquisitiones contains two proofs: The one in Article 54 is a nonconstructive existence proof, while the proof in Article 55 is constructive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, attempts to falsify a claim, by replicating an experiment, are hard and problematic for it involves tacit knowledge (i.e. unarticulated knowledge), matters of time and money and replication of exact similar conditions, which is hard. Tacit knowledge can never be fully articulated or translated into a set of rules. Some commentators have argued that Collins's \"experimenter's regress\" is foreshadowed by Sextus Empiricus' argument that \"if we shall judge the intellects by the senses, and the senses by the intellect, this involves circular reasoning inasmuch as it is required that the intellects should be judged first in order that the intellects may be tested  we possess no means by which to judge objects\" (quoted after Godin & Gingras 2002: 140). Others have extended Collins's argument to the cases of theoretical practice (\"theoretician's regress\"; Kennefick 2000) and computer simulation studies (\"simulationist's regress\"; Gelfert 2011; Tolk 2017).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, symbolic-numeric computation is the use of software that combines symbolic and numeric methods to solve problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If T denotes the entry in the table for nonterminal A and terminal a, then T contains the rule A \u2192 w if and only if a is in Fi(w) or \u03b5 is in Fi(w) and a is in Fo(A).Equivalently: T contains the rule A \u2192 w for each a \u2208 Fi(w)\u00b7Fo(A). If the table contains at most one rule in every one of its cells, then the parser will always know which rule it has to use and can therefore parse strings without backtracking. It is in precisely this case that the grammar is called an LL(1) grammar.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Depending on the context, the conditional expectation can be either a random variable or a function. The random variable is denoted E ( X \u2223 Y ) {\\displaystyle E(X\\mid Y)} analogously to conditional probability. The function form is either denoted E ( X \u2223 Y = y ) {\\displaystyle E(X\\mid Y=y)} or a separate function symbol such as f ( y ) {\\displaystyle f(y)} is introduced with the meaning E ( X \u2223 Y ) = f ( Y ) {\\displaystyle E(X\\mid Y)=f(Y)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the normal-Wishart distribution (or Gaussian-Wishart distribution) is a multivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a multivariate normal distribution with unknown mean and precision matrix (the inverse of the covariance matrix).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States and Canada, caller ID information is sent to the called party by the telephone switch as an analog data stream (similar to data passed between two modems), using Bell 202 modulation between the first and second rings, while the telephone unit is still on hook. If the telephone call is answered too quickly after the first ring, caller ID information may not be transmitted to the recipient. Also, in the United States and Canada a caller may block the display of the number they are calling from by dialling *67 before dialling the phone number. This will not work when dialling an \"800\" number, where the receiver of the call pays for the call or when 911 emergency calls are made.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Non-transparent communication systems have one or both of the following problems: user data may be incorrectly interpreted as internal commands. For example, modems with a Time Independent Escape Sequence or 20th century Signaling System No. 5 and R2 signalling telephone systems, which occasionally incorrectly interpreted user data (from a \"blue box\") as commands. output \"user data\" may not always be the same as input user data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the \"amount of information\" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected \"amount of information\" held in a random variable. Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair ( X , Y ) {\\displaystyle (X,Y)} is from the product of the marginal distributions of X {\\displaystyle X} and Y {\\displaystyle Y} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel computer architectures, a systolic array is a homogeneous network of tightly coupled data processing units (DPUs) called cells or nodes. Each node or DPU independently computes a partial result as a function of the data received from its upstream neighbours, stores the result within itself and passes it downstream. Systolic arrays were first used in Colossus, which was an early computer used to break German Lorenz ciphers during World War II. Due to the classified nature of Colossus, they were independently invented or rediscovered by H. T. Kung and Charles Leiserson who described arrays for many dense linear algebra computations (matrix product, solving systems of linear equations, LU decomposition, etc.) for banded matrices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For most common relations in mathematics, special symbols are introduced, like \"<\" for \"is less than\", and \"|\" for \"is a nontrivial divisor of\", and, most popular \"=\" for \"is equal to\". For example, \"1<3\", \"1 is less than 3\", and \"(1,3) \u2208 Rless\" mean all the same; some authors also write \"(1,3) \u2208 (<)\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Suslin tree is a tree of height \u03c91 such that every branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn tree. The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown by Kurepa (1935)) or a Suslin algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the field of number theory, the Ramanujan\u2013Nagell equation is an equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation, an equation to be solved in integers where one of the variables appears as an exponent. The equation is named after Srinivasa Ramanujan, who conjectured that it has only five integer solutions, and after Trygve Nagell, who proved the conjecture. It implies non-existence of perfect binary codes with the minimum Hamming distance 5 or 6.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Cray decided that the 8600 would include four complete CPUs sharing the main memory. To improve overall throughput, the machine could operate in a special mode that sent a single instruction to all four processors with different data. This technique, today known as SIMD, reduced the total number of memory accesses because the instruction was only read once, instead of four times.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a pseudo-finite field F is an infinite model of the first-order theory of finite fields. This is equivalent to the condition that F is quasi-finite (perfect with a unique extension of every positive degree) and pseudo algebraically closed (every absolutely irreducible variety over F has a point defined over F). Every hyperfinite field is pseudo-finite and every pseudo-finite field is quasifinite. Every non-principal ultraproduct of finite fields is pseudo-finite. Pseudo-finite fields were introduced by Ax (1968).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probabilistic combinatorics, the questions are of the following type: what is the probability of a certain property for a random discrete object, such as a random graph? For instance, what is the average number of triangles in a random graph? Probabilistic methods are also used to determine the existence of combinatorial objects with certain prescribed properties (for which explicit examples might be difficult to find) by observing that the probability of randomly selecting an object with those properties is greater than 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In project management, there are generally considered to be three constraints: time (sometimes schedule), cost (sometimes budget), and scope. (Quality is often added as a fourth constraint---represented as the middle of a triangle.) The assumption is that a change in one constraint will affect the others.Without timeboxing, projects usually work to a fixed scope, in which case when it becomes clear that some deliverables cannot be completed within the planned timescales, either the deadline has to be extended (to allow more time to complete the fixed scope) or more people are involved (to complete the fixed scope in the same time). Often both happen, resulting in delayed delivery, increased costs, and often reduced quality (as per The Mythical Man-Month principle). With timeboxing, the deadline is fixed, meaning that the scope would have to be reduced. As this means organizations have to focus on completing the most important deliverables first, timeboxing often goes hand-in-hand with a scheme for prioritizing of deliverables (such as with the MoSCoW method).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the quadratic bottleneck assignment problem (QBAP) is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research, from the category of the facilities location problems.It is related to the quadratic assignment problem in the same way as the linear bottleneck assignment problem is related to the linear assignment problem, the \"sum\" is replaced with \"max\" in the objective function. The problem models the following real-life problem: There are a set of n facilities and a set of n locations. For each pair of locations, a distance is specified and for each pair of facilities a weight or flow is specified (e.g., the amount of supplies transported between the two facilities). The problem is to assign all facilities to different locations with the goal of minimizing the maximum of the distances multiplied by the corresponding flows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Ping-Pong scheme described in Transaction Processing eliminates this problem by alternately writing the contents of said (logical) last page to two different physical pages inside the log file (the actual last page i and its empty successor i+1). Once said logical log page is no longer the last page (i.e. it is completely filled with log data), it is written one last time to the regular physical position (i) inside the log file. This scheme requires the usage of time stamps for each page in order to distinguish the most recent version of the logical last page one from its predecessor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard statement is: This law, together with its supplements, allows the easy calculation of any Legendre symbol, making it possible to determine whether there is an integer solution for any quadratic equation of the form x 2 \u2261 a mod p {\\displaystyle x^{2}\\equiv a{\\bmod {p}}} for an odd prime p {\\displaystyle p} ; that is, to determine the \"perfect squares\" modulo p {\\displaystyle p} . However, this is a non-constructive result: it gives no help at all for finding a specific solution; for this, other methods are required. For example, in the case p \u2261 3 mod 4 {\\displaystyle p\\equiv 3{\\bmod {4}}} using Euler's criterion one can give an explicit formula for the \"square roots\" modulo p {\\displaystyle p} of a quadratic residue a {\\displaystyle a} , namely, \u00b1 a p + 1 4 {\\displaystyle \\pm a^{\\frac {p+1}{4}}} indeed, ( \u00b1 a p + 1 4 ) 2 = a p + 1 2 = a \u22c5 a p \u2212 1 2 \u2261 a ( a p ) = a mod p .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the program will neither spin nor poll; thus terms like wait, hang or yield may also convey the behaviour; also in the context that it will not block other independent processes from running.) Examples (c is a variable): keyboard ?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". , x k \u2212 x k \u2212 1 ) {\\displaystyle U=(x_{2}-x_{1},x_{3}-x_{2},...,x_{k}-x_{k-1})} whose columns are the k \u2212 1 {\\displaystyle k-1} differences. Then, one computes the vector c = \u2212 U + ( x k + 1 \u2212 x k ) {\\displaystyle c=-U^{+}(x_{k+1}-x_{k})} where U + {\\displaystyle U^{+}} denotes the Moore\u2013Penrose pseudoinverse of U {\\displaystyle U} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In monotone drawing of graphs, in 2-visibility representation of graphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social network analysis, the co-stardom network represents the collaboration graph of film actors i.e. movie stars. The co-stardom network can be represented by an undirected graph of nodes and links. Nodes correspond to the movie star actors and two nodes are linked if they co-starred (performed) in the same movie. The links are un-directed, and can be weighted or not depending on the goals of study.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using the theory of elliptic functions, it can be shown that elliptic curves defined over the complex numbers correspond to embeddings of the torus into the complex projective plane. The torus is also an abelian group, and this correspondence is also a group isomorphism. Elliptic curves are especially important in number theory, and constitute a major area of current research; for example, they were used in Andrew Wiles's proof of Fermat's Last Theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A proactive fault management method to deal with the software aging incident is software rejuvenation. This method can be classified as an environment diversity technique that usually is implemented through software rejuvenation agents (SRA). The phenomenon was first identified by David Parnas, in an essay that explored what to do about it:\"Programs, like people, get old.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, whenever an ambiguity is possible, the synonym used for \"recursive language\" is Turing-decidable language, rather than simply decidable. The class of all recursive languages is often called R, although this name is also used for the class RP. This type of language was not defined in the Chomsky hierarchy of (Chomsky 1959). All recursive languages are also recursively enumerable. All regular, context-free and context-sensitive languages are recursive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis and computer science, functions which are Z-order, Lebesgue curve, Morton space-filling curve, Morton order or Morton code map multidimensional data to one dimension while preserving locality of the data points. It is named in France after Henri Lebesgue, who studied it in 1904, and named in the United States after Guy Macdonald Morton, who first applied the order to file sequencing in 1966. The z-value of a point in multidimensions is simply calculated by interleaving the binary representations of its coordinate values. Once the data are sorted into this ordering, any one-dimensional data structure can be used, such as simple one dimensional arrays, binary search trees, B-trees, skip lists or (with low significant bits truncated) hash tables. The resulting ordering can equivalently be described as the order one would get from a depth-first traversal of a quadtree or octree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This value is the average of the values of k nearest neighbors. If k = 1, then the output is simply assigned to the value of that single nearest neighbor.k-NN is a type of classification where the function is only approximated locally and all computation is deferred until function evaluation. Since this algorithm relies on distance for classification, if the features represent different physical units or come in vastly different scales then normalizing the training data can improve its accuracy dramatically.Both for classification and regression, a useful technique can be to assign weights to the contributions of the neighbors, so that the nearer neighbors contribute more to the average than the more distant ones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Structure descriptions are presented in terms of better known types of semigroups. The best known type of semigroup is the group. A (necessarily incomplete) list of various special classes of semigroups is presented below. To the extent possible the defining properties are formulated in terms of the binary operations in the semigroups. The references point to the locations from where the defining properties are sourced.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, fundamental process ontologies are becoming more important in recent times, because the progress in the discovery of the foundations of physics spurred the development of a basic concept able to integrate such boundary notions as \"energy,\" \"object\", and those of the physical dimensions of space and time. In computer science, a process ontology is a description of the components and their relationships that make up a process. A formal process ontology is an ontology in the knowledge domain of operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Various object-oriented programming languages offer similar facilities for abstraction, all to support a general strategy of polymorphism in object-oriented programming, which includes the substitution of one type for another in the same or similar role. Although not as generally supported, a configuration or image or package may predetermine a great many of these bindings at compile-time, link-time, or loadtime. This would leave only a minimum of such bindings to change at run-time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics the one-sided limit x \u2192 a+ means x approaches a from the right (i.e., right-sided limit), and x \u2192 a\u2212 means x approaches a from the left (i.e., left-sided limit). For example, 1/x \u2192 + \u221e {\\displaystyle \\infty } as x \u2192 0+ but 1/x \u2192 \u2212 \u221e {\\displaystyle \\infty } as x \u2192 0\u2212.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Define: S = { i: 1 \u2a7d i \u2a7d N , c i 1 \u2260 c i 2 } . {\\displaystyle S=\\left\\{i\\ :\\ 1\\leqslant i\\leqslant N,c_{i}^{1}\\neq c_{i}^{2}\\right\\}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, an area code split is the practice of introducing a new telephone area code by geographically dividing an existing numbering plan area (NPA), and assigning area codes to the resulting divisions, but retaining the existing area code only for one of the divisions. The purpose of this practice is to provide more central office prefixes, and therefore more telephone numbers, in an area with high demand for telephone services, and prevent a shortage of telephone numbers. An increasing demand for telephone numbers has existed since the development of automatic telephony in the early 20th century, but was spurred especially since the 1990s, with the proliferation of fax machines, pager systems, mobile telephones, computer modems, and finally smart phones. When an area code split is implemented, the telephone numbers in the affected area are typically changed to a new area code only, but this still requires the printing of new stationery, advertisements, and signage for many customers, and the dissemination of the new area code to family, friends, and customers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Return x n {\\displaystyle \\mathbf {x} _{n}} as the minimizing position and f ( x n ) {\\displaystyle f(\\mathbf {x} _{n})} as the function minimum.To assure good behavior, it is necessary that some conditions must be satisfied by p n {\\displaystyle \\mathbf {p} _{n}} . Roughly speaking p n {\\displaystyle \\mathbf {p} _{n}} should not be too far away from \u2207 f ( x n ) {\\displaystyle \\nabla f(\\mathbf {x} _{n})} . A precise version is as follows (see e.g. Bertsekas (2016)).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An arrow \u2192 in column next signifies that the rebalancing is complete with this step. If the column after determines exactly one case, this case is given as the subsequent one, otherwise there are question marks. The loop is contained in the sections \"Insert case I1\" and \"Insert case I2\", where in case I2 the problem of rebalancing is escalated \u0394 h = 2 {\\displaystyle \\Delta h=2} tree levels or 1 black level higher in the tree, in that the grandfather G becomes the new current node N. So it takes maximally h 2 {\\displaystyle {\\tfrac {h}{2}}} steps of iteration to repair the tree (where h {\\displaystyle h} is the height of the tree).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The \u03b1- series process. Given a sequence of non-negative random variables: { X k , k = 1 , 2 , \u2026 } {\\displaystyle \\{X_{k},k=1,2,\\dots \\}} , if they are independent and the cdf of X k k a {\\displaystyle {\\frac {X_{k}}{k^{a}}}} is given by F ( x ) {\\displaystyle F(x)} for k = 1 , 2 , \u2026 {\\displaystyle k=1,2,\\dots } , where a {\\displaystyle a} is a positive constant, then { X k , k = 1 , 2 , \u2026 } {\\displaystyle \\{X_{k},k=1,2,\\ldots \\}} is called an \u03b1- series process. The threshold geometric process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a layered queueing network (or rendezvous network) is a queueing network model where the service time for each job at each service node is given by the response time of a queueing network (and those service times in turn may also be determined by further nested networks). Resources can be nested and queues form along the nodes of the nesting structure. The nesting structure thus defines \"layers\" within the queueing model.Layered queueing has applications in a wide range of distributed systems which involve different master/slave, replicated services and client-server components, allowing each local node to be represented by a specific queue, then orchestrating the evaluation of these queues.For large population of jobs, a fluid limit has been shown in PEPA to be a give good approximation of performance measures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some ways it is related to the concepts of place attachment and sense of place. Place identity is largely related to the concepts of community formation because it recognizes that geographical spaces do not solely bond a community together but rather there are social bonds that account for community formation. Those social forces often are feelings of belonging and security, which involve theoretical formations of community. Theoretical formations of community, which were identified in Community: Seeking Safety in an Insecure World (Bauman, 2001) act as bonds formed by similar locality, culture, language, kinship and/or experiences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs exactly once as a factor of this product: The radical plays a central role in the statement of the abc conjecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A rival programming-language usage was pioneered by the original version of ALGOL, which was designed in 1958 and implemented in 1960. ALGOL included a relational operator that tested for equality, allowing constructions like if x = 2 with essentially the same meaning of = as the conditional usage in mathematics. The equal sign was reserved for this usage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the AGM framework, a belief set is represented by a deductively closed set of propositional formulae. While such sets are infinite, they can always be finitely representable. However, working with deductively closed sets of formulae leads to the implicit assumption that equivalent belief sets should be considered equal when revising. This is called the principle of irrelevance of syntax.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\|\\nabla v\\|_{L^{2}(\\Omega )}^{2}=\\|v\\|_{L^{p+1}(\\Omega )}^{p+1}>0.} Solutions to the original variational problem that lie in the Nehari manifold are (constrained) minimizers of the energy, and so direct methods in the calculus of variations can be brought to bear. More generally, given a suitable functional J, the associated Nehari manifold is defined as the set of functions u in an appropriate function space for which \u27e8 J \u2032 ( u ) , u \u27e9 = 0. {\\displaystyle \\langle J'(u),u\\rangle =0.} Here J\u2032 is the functional derivative of J.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, distributed version control (also known as distributed revision control) is a form of version control in which the complete codebase, including its full history, is mirrored on every developer's computer. Compared to centralized version control, this enables automatic management branching and merging, speeds up most operations (except pushing and pulling), improves the ability to work offline, and does not rely on a single location for backups. Git, the world's most popular version control system, is a distributed version control system. In 2010, software development author Joel Spolsky described distributed version control systems as \"possibly the biggest advance in software development technology in the  ten years\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some simple cases, an analysis of the recipe can reveal the maximum production rate and the rate limiting unit. In the process example above if a number of batches or lots of Product C are to be produced, it is useful to calculate the minimum time between consecutive batch starts (cycle-time). If a batch is allowed to start before the end of the prior batch the minimum cycle-time is given by the following relationship: Where CTmin is the shortest possible cycle time for a process with M unit-procedures and \u03c4j is the total duration for the jth unit-procedure. The unit-procedure with the maximum duration is sometimes referred to as the bottleneck.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most cases, place the items in order of usage, with the most-used meanings appearing at the top and less common meanings below. A recommended order is: Articles with a clarifier in parentheses (Anticipation (music)) Articles with the item as part of the name (Computer keyboard as part of a Keyboard dab page) Synonyms Larger subject articles which treat this item in a section (Medieval art from a Fresco dab page)Unless the list is quite short, separate the articles in categories (1) and (2) from those in (3) and (4), with the \"may also be\" line shown below:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable. Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible rule applications. When combined with an appropriate algorithm, however, rewrite systems can be viewed as computer programs, and several theorem provers and declarative programming languages are based on term rewriting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as \"the middle\" value. The basic feature of the median in describing data compared to the mean (often simply described as the \"average\") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe center of the income distribution because increases in the largest incomes alone have no effect on median. For this reason, the median is of central importance in robust statistics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered. Thus, for example the sequences X 1 , X 2 , X 3 , X 4 , X 5 , X 6 and X 3 , X 6 , X 1 , X 5 , X 2 , X 4 {\\displaystyle X_{1},X_{2},X_{3},X_{4},X_{5},X_{6}\\quad {\\text{ and }}\\quad X_{3},X_{6},X_{1},X_{5},X_{2},X_{4}} both have the same joint probability distribution. It is closely related to the use of independent and identically distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases of simple random sampling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x \u21a6 g ( x ) {\\displaystyle x\\mapsto g(x)} is a bijection. In case the ring is a finite field, the Dickson polynomials, which are closely related to the Chebyshev polynomials, provide examples. Over a finite field, every function, so in particular every permutation of the elements of that field, can be written as a polynomial function. In the case of finite rings Z/nZ, such polynomials have also been studied and applied in the interleaver component of error detection and correction algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Details of the history of this search, as well as the sequences leading to home primes for all other numbers through 100, are maintained at Patrick De Geest's worldofnumbers website. A wiki primarily associated with the Great Internet Mersenne Prime Search maintains the complete known data through 1000 in base 10 and also has lists for the bases 2 through 9. The primes in HP(n) are 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, 11, 223, 13, 13367, 1129, 31636373, 17, 233, 19, 3318308475676071413, 37, 211, 23, 331319, 773, 3251, 13367, 227, 29, 547, ... (sequence A037274 in the OEIS)Aside from the computational problems that have had so much time devoted to them, it appears absolute proof of existence of a home prime for any specific number might entail its effective computation. In purely heuristic terms, the existence has probability 1 for all numbers, but such heuristics make assumptions about numbers drawn from a wide variety of processes that, though they are likely correct, fall short of the standard of proof usually required of mathematical claims.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. Complex random variables can always be considered as pairs of real random variables: their real and imaginary parts. Therefore, the distribution of one complex random variable may be interpreted as the joint distribution of two real random variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, per capita income is the arithmetic average income of a nation's population. While the arithmetic mean is often used to report central tendencies, it is not a robust statistic: it is greatly influenced by outliers (values much larger or smaller than most others). For skewed distributions, such as the distribution of income for which a few people's incomes are substantially higher than most people's, the arithmetic mean may not coincide with one's notion of \"middle\". In that case, robust statistics, such as the median, may provide a better description of central tendency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a matrix of ones or all-ones matrix is a matrix where every entry is equal to one. Examples of standard notation are given below: J 2 = ( 1 1 1 1 ) ; J 3 = ( 1 1 1 1 1 1 1 1 1 ) ; J 2 , 5 = ( 1 1 1 1 1 1 1 1 1 1 ) ; J 1 , 2 = ( 1 1 ) . {\\displaystyle J_{2}={\\begin{pmatrix}1&1\\\\1&1\\end{pmatrix}};\\quad J_{3}={\\begin{pmatrix}1&1&1\\\\1&1&1\\\\1&1&1\\end{pmatrix}};\\quad J_{2,5}={\\begin{pmatrix}1&1&1&1&1\\\\1&1&1&1&1\\end{pmatrix}};\\quad J_{1,2}={\\begin{pmatrix}1&1\\end{pmatrix}}.\\quad } Some sources call the all-ones matrix the unit matrix, but that term may also refer to the identity matrix, a different type of matrix. A vector of ones or all-ones vector is matrix of ones having row or column form; it should not be confused with unit vectors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, an algorithmic technique is a general approach for implementing a process or computation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Microsoft DOS environment, daemon-like programs were implemented as terminate-and-stay-resident programs (TSR).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the subderivative, subgradient, and subdifferential generalize the derivative to convex functions which are not necessarily differentiable. Subderivatives arise in convex analysis, the study of convex functions, often in connection to convex optimization. Let f: I \u2192 R {\\displaystyle f:I\\to \\mathbb {R} } be a real-valued convex function defined on an open interval of the real line. Such a function need not be differentiable at all points: For example, the absolute value function f ( x ) = | x | {\\displaystyle f(x)=|x|} is non-differentiable when x = 0 {\\displaystyle x=0} . However, as seen in the graph on the right (where f ( x ) {\\displaystyle f(x)} in blue has non-differentiable kinks similar to the absolute value function), for any x 0 {\\displaystyle x_{0}} in the domain of the function one can draw a line which goes through the point ( x 0 , f ( x 0 ) ) {\\displaystyle (x_{0},f(x_{0}))} and which is everywhere either touching or below the graph of f. The slope of such a line is called a subderivative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a unique sink orientation is an orientation of the edges of a polytope such that, in every face of the polytope (including the whole polytope as one of the faces), there is exactly one vertex for which all adjoining edges are oriented inward (i.e. towards that vertex). If a polytope is given together with a linear objective function, and edges are oriented from vertices with smaller objective function values to vertices with larger objective values, the result is a unique sink orientation. Thus, unique sink orientations can be used to model linear programs as well as certain nonlinear programs such as the smallest circle problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There exist n-ary groups with more than one neutral element. If the set of all neutral elements of an n-ary group is non-empty it forms an n-ary subgroup.Some authors include an identity in the definition of an n-ary group but as mentioned above such n-ary operations are just repeated binary operations. Groups with intrinsically n-ary operations do not have an identity element.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Digits to the right of it are multiplied by 10 raised to a negative power or exponent. The first position to the right of the separator indicates 10\u22121 (0.1), the second position 10\u22122 (0.01), and so on for each successive position. As an example, the number 2674 in a base-10 numeral system is: (2 \u00d7 103) + (6 \u00d7 102) + (7 \u00d7 101) + (4 \u00d7 100)or (2 \u00d7 1000) + (6 \u00d7 100) + (7 \u00d7 10) + (4 \u00d7 1).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the CP/M 8-bit operating system used on early personal computers, the standard DUMP program would list a file 16 bytes per line with the hex offset at the start of the line and the ASCII equivalent of each byte at the end. Bytes outside the standard range of printable ASCII characters (20 to 7E) would be displayed as a single period for visual alignment. This same format was used to display memory when invoking the D command in the standard CP/M debugger DDT. Later incarnations of the format (e.g. in the DOS debugger DEBUG) changed the space between the 8th and 9th byte to a dash, without changing the overall width.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As such, this generalizes the same process when done with the Lyndon words. Hall trees can also be used to give a total order to the elements of a group, via the commutator collecting process, which is a special case of the general construction given below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and describes points in K2, the Cartesian product of K with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions (x, y) for: y 2 = x 3 + a x + b {\\displaystyle y^{2}=x^{3}+ax+b} for some coefficients a and b in K. The curve is required to be non-singular, which means that the curve has no cusps or self-intersections. (This is equivalent to the condition 4a3 + 27b2 \u2260 0, that is, being square-free in x.) It is always understood that the curve is really sitting in the projective plane, with the point O being the unique point at infinity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since this relaxation in US export restrictions, and because most personal computers connected to the Internet include US-sourced web browsers such as Firefox or Internet Explorer, almost every Internet user worldwide has potential access to quality cryptography via their browsers (e.g., via Transport Layer Security). The Mozilla Thunderbird and Microsoft Outlook E-mail client programs similarly can transmit and receive emails via TLS, and can send and receive email encrypted with S/MIME. Many Internet users don't realize that their basic application software contains such extensive cryptosystems. These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally don't find it practical to do much to control distribution or use of cryptography of this quality, so even when such laws are in force, actual enforcement is often effectively impossible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, call progress tones are audible tones that provide an indication of the status of a telephone call to the user. The tones are generated by a central office or a private branch exchange (PBX) to the calling party. Telecommunication equipment such as fax machines and modems are designed to recognize certain tones, such as dial tone and busy tone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the cost-to-cost method, a project's cost to date is compared to the total expected cost of the project. The costs of products already bought for a contract, but not installed, should not be added in calculating the percentage of completion (unless they were specifically obtained for that contract). Furthermore, the cost of equipment is assigned over the course of the contract, rather than directly, unless title to the supplies is being transported to the customer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, unfair coins would have p \u2260 1 / 2. {\\displaystyle p\\neq 1/2.} The Bernoulli distribution is a special case of the binomial distribution where a single trial is conducted (so n would be 1 for such a binomial distribution). It is also a special case of the two-point distribution, for which the possible outcomes need not be 0 and 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An alternative hypothesis can be defined under which each value \u03c0 i {\\displaystyle ~\\pi _{i}~} is replaced by its maximum likelihood estimate p i = x i N . {\\displaystyle ~p_{i}={\\frac {\\;x_{i}\\,}{N}}~.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a practical number or panarithmic number is a positive integer n {\\displaystyle n} such that all smaller positive integers can be represented as sums of distinct divisors of n {\\displaystyle n} . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well as these divisors themselves, we have 5 = 3 + 2, 7 = 6 + 1, 8 = 6 + 2, 9 = 6 + 3, 10 = 6 + 3 + 1, and 11 = 6 + 3 + 2. The sequence of practical numbers (sequence A005153 in the OEIS) begins Practical numbers were used by Fibonacci in his Liber Abaci (1202) in connection with the problem of representing rational numbers as Egyptian fractions. Fibonacci does not formally define practical numbers, but he gives a table of Egyptian fraction expansions for fractions with practical denominators.The name \"practical number\" is due to Srinivasan (1948).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The elements of G conventionally have circular symmetry such that E  = 0 {\\displaystyle \\mathbb {E} =0} . Inverse Complex Wishart The distribution of the inverse complex Wishart distribution of Y = S \u2212 1 {\\displaystyle \\mathbf {Y} =\\mathbf {S^{-1}} } according to Goodman, Shaman is f Y ( Y ) = | Y | \u2212 ( n + p ) e \u2212 tr \u2061 ( M Y \u2212 1 ) | M | \u2212 n \u22c5 C \u0393 ~ p ( n ) , n \u2265 p , det ( Y ) > 0 {\\displaystyle f_{Y}(\\mathbf {Y} )={\\frac {\\left|\\mathbf {Y} \\right|^{-(n+p)}e^{-\\operatorname {tr} (\\mathbf {M} \\mathbf {Y^{-1}} )}}{\\left|\\mathbf {M} \\right|^{-n}\\cdot {\\mathcal {C}}{\\widetilde {\\Gamma }}_{p}(n)}},\\;\\;\\;n\\geq p,\\;\\;\\;\\det \\left(\\mathbf {Y} \\right)>0} where M = \u0393 \u2212 1 {\\displaystyle \\mathbf {M} =\\mathbf {\\Gamma ^{-1}} } . If derived via a matrix inversion mapping, the result depends on the complex Jacobian determinant C J Y ( Y \u2212 1 ) = | Y | \u2212 2 p \u2212 2 {\\displaystyle {\\mathcal {C}}J_{Y}(Y^{-1})=\\left|Y\\right|^{-2p-2}} Goodman and others discuss such complex Jacobians.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, an M/G/k queue is a queue model where arrivals are Markovian (modulated by a Poisson process), service times have a General distribution and there are k servers. The model name is written in Kendall's notation, and is an extension of the M/M/c queue, where service times must be exponentially distributed and of the M/G/1 queue with a single server. Most performance metrics for this queueing system are not known and remain an open problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the birthday problem, neither of the two people is chosen in advance. By contrast, the probability q(n) that someone in a room of n other people has the same birthday as a particular person (for example, you) is given by q ( n ) = 1 \u2212 ( 365 \u2212 1 365 ) n {\\displaystyle q(n)=1-\\left({\\frac {365-1}{365}}\\right)^{n}} and for general d by q ( n ; d ) = 1 \u2212 ( d \u2212 1 d ) n . {\\displaystyle q(n;d)=1-\\left({\\frac {d-1}{d}}\\right)^{n}.} In the standard case of d = 365, substituting n = 23 gives about 6.1%, which is less than 1 chance in 16. For a greater than 50% chance that one person in a roomful of n people has the same birthday as you, n would need to be at least 253. This number is significantly higher than 365/2 = 182.5: the reason is that it is likely that there are some birthday matches among the other people in the room.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Web Annotation standard, n annotation is considered to be a set of connected resources, typically including a body and target, and conveys that the body is related to the target. The exact nature of this relationship changes according to the intention of the annotation, but the body is most frequently somehow \"about\" the target. (...) The (...) model supports additional functionality, enabling content to be embedded within the annotation, selecting arbitrary segments of resources, choosing the appropriate representation of a resource and providing styling hints to help clients render the annotation appropriately. The basic data structures of Web Annotation (Fig. 1) are target (the element being annotated, e.g., a web document or a part of it), body (the content of the annotation, e.g., a string value), and annotation (the element that serves to relate body and target of an annotation)The body can be a literal value or structured content (a URI).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are a number of ways to deal with this. One is to use a pseudo inverse instead of the usual matrix inverse in the above formulae. However, better numeric stability may be achieved by first projecting the problem onto the subspace spanned by \u03a3 b {\\displaystyle \\Sigma _{b}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to expose bugs, a fuzzer must be able to distinguish expected (normal) from unexpected (buggy) program behavior. However, a machine cannot always distinguish a bug from a feature. In automated software testing, this is also called the test oracle problem.Typically, a fuzzer distinguishes between crashing and non-crashing inputs in the absence of specifications and to use a simple and objective measure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The number of elements in a Tamari lattice for a sequence of n + 1 objects is the nth Catalan number Cn. The Tamari lattice can also be described in several other equivalent ways: It is the poset of sequences of n integers a1, ..., an, ordered coordinatewise, such that i \u2264 ai \u2264 n and if i \u2264 j \u2264 ai then aj \u2264 ai (Huang & Tamari 1972). It is the poset of binary trees with n leaves, ordered by tree rotation operations. It is the poset of ordered forests, in which one forest is earlier than another in the partial order if, for every j, the jth node in a preorder traversal of the first forest has at least as many descendants as the jth node in a preorder traversal of the second forest (Knuth 2005). It is the poset of triangulations of a convex n-gon, ordered by flip operations that substitute one diagonal of the polygon for another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set of tempered distributions forms a vector subspace of the space of distributions D \u2032 ( U ) {\\displaystyle {\\mathcal {D}}^{\\prime }(U)} and is thus one example of a space of distributions; there are many other spaces of distributions. There also exist other major classes of test functions that are not subsets of C c \u221e ( U ) , {\\displaystyle C_{c}^{\\infty }(U),} such as spaces of analytic test functions, which produce very different classes of distributions. The theory of such distributions has a different character from the previous one because there are no analytic functions with non-empty compact support. Use of analytic test functions leads to Sato's theory of hyperfunctions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". \", which may be denoted \"S\", between the various \"numerals\". \"We must now consider the serial character of the natural numbers in the order 0, 1, 2, 3, .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Otherwise these operations can alter the result of summation. Further, the terms of Grandi's series can be rearranged to have its accumulation points at any interval of two or more consecutive integer numbers, not only 0 or 1. For instance, the series 1 + 1 + 1 + 1 + 1 \u2212 1 \u2212 1 + 1 + 1 \u2212 1 \u2212 1 + 1 + 1 \u2212 1 \u2212 1 + 1 + 1 \u2212 \u22ef {\\displaystyle 1+1+1+1+1-1-1+1+1-1-1+1+1-1-1+1+1-\\cdots } (in which, after five initial +1 terms, the terms alternate in pairs of +1 and \u22121 terms\u2013the infinitude of both +1\u2019s and -1\u2019s allows any finite number of 1\u2019s or -1\u2019s to be prepended, by Hilbert's paradox of the Grand Hotel) is a permutation of Grandi's series in which each value in the rearranged series corresponds to a value that is at most four positions away from it in the original series; its accumulation points are 3, 4, and 5.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The overall accuracy would be 95%, but in more detail the classifier would have a 100% recognition rate (sensitivity) for the cancer class but a 0% recognition rate for the non-cancer class. F1 score is even more unreliable in such cases, and here would yield over 97.4%, whereas informedness removes such bias and yields 0 as the probability of an informed decision for any form of guessing (here always guessing cancer). According to Davide Chicco and Giuseppe Jurman, the most informative metric to evaluate a confusion matrix is the Matthews correlation coefficient (MCC).Other metrics can be included in a confusion matrix, each of them having their significance and use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 20th century, several electrical engineers intuitively recognized that Boolean algebra was analogous to the behavior of certain types of electrical circuits. Claude Shannon formally proved such behavior was logically equivalent to Boolean algebra in his 1937 master's thesis, A Symbolic Analysis of Relay and Switching Circuits. Today, all modern general purpose computers perform their functions using two-value Boolean logic; that is, their electrical circuits are a physical manifestation of two-value Boolean logic. They achieve this in various ways: as voltages on wires in high-speed circuits and capacitive storage devices, as orientations of a magnetic domain in ferromagnetic storage devices, as holes in punched cards or paper tape, and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using a pairing function on \u03c9 (such as (n,k) goes to (n2+2\u00b7n\u00b7k+k2+n+3\u00b7k)/2), we can map the powerset of \u03c9\u00d7\u03c9 into the powerset of \u03c9. And we can map the powerset of \u03c9 into the Cantor set, a subset of the real numbers. So statements about H \u2135 1 {\\displaystyle H_{\\aleph _{1}}} can be converted into statements about the reals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, a zero mode is an eigenvector with a vanishing eigenvalue. In various subfields of physics zero modes appear whenever a physical system possesses a certain symmetry. For example, normal modes of multidimensional harmonic oscillator (e.g. a system of beads arranged around the circle, connected with springs) corresponds to elementary vibrational modes of the system. In such a system zero modes typically occur and are related with a rigid rotation around the circle. The kernel of an operator consists of left zero modes, and the cokernel consists of the right zero modes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, a corpus is a set of sentences or texts, and a language model is a probability distribution over entire sentences or texts. Consequently, in NLP, the more commonly used measure is perplexity per word, defined as: where s 1 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Numbers of the form Mn = 2n \u2212 1 without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that n be prime. The smallest composite Mersenne number with prime exponent n is 211 \u2212 1 = 2047 = 23 \u00d7 89.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored according to the identity a 2 \u2212 b 2 = ( a + b ) ( a \u2212 b ) {\\displaystyle a^{2}-b^{2}=(a+b)(a-b)} in elementary algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, class variables and class methods are either statically resolved, not via dynamic dispatch, or their memory statically allocated at compile time (once for the entire class, as static variables), not dynamically allocated at run time (at every instantiation of an object). In other cases, however, either or both of these are dynamic. For example, if classes can be dynamically defined (at run time), class variables of these classes are allocated dynamically when the class is defined, and in some languages class methods are also dispatched dynamically. Thus in some languages, static member variable or static member function are used synonymously with or in place of \"class variable\" or \"class function\", but these are not synonymous across languages. These terms are commonly used in Java, C# , and C++, where class variables and class methods are declared with the static keyword, and referred to as static member variables or static member functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term subscriber trunk dialling is used in the United Kingdom, the Republic of Ireland, Australia, India and South East Asia. In the UK, the term is obsolescent, better known as the UK area codes. The introduction in the UK of subscriber dialling of long-distance calls removed the distinction that had existed between trunk and toll calls.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If N = 1, then there is roughly one recursive subroutine call for every input, but more generally there is one recursive call for (roughly) every N/2 inputs if the recursion stops at exactly n = N. By making N sufficiently large, the overhead of recursion can be made negligible (precisely this technique of a large base case for recursive summation is employed by high-performance FFT implementations). Regardless of N, exactly n\u22121 additions are performed in total, the same as for naive summation, so if the recursion overhead is made negligible then pairwise summation has essentially the same computational cost as for naive summation. A variation on this idea is to break the sum into b blocks at each recursive stage, summing each block recursively, and then summing the results, which was dubbed a \"superblock\" algorithm by its proposers. The above pairwise algorithm corresponds to b = 2 for every stage except for the last stage which is b = N.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Analytic solutions for this mechanism (also similar to the solution of Price) were presented in 2000 by Dorogovtsev, Mendes and Samukhin and independently by Krapivsky, Redner, and Leyvraz, and later rigorously proved by mathematician B\u00e9la Bollob\u00e1s. Notably, however, this mechanism only produces a specific subset of networks in the scale-free class, and many alternative mechanisms have been discovered since.The history of scale-free networks also includes some disagreement. On an empirical level, the scale-free nature of several networks has been called into question.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The trivial case is checking to see whether the return value of a function indicated success or failure, and to therefore cease further processing upon failure. This return value is actually often itself the result of a sanity check. For example, if the function attempted to open, write to, and close a file, a sanity check may be used to ensure that it did not fail on any of these actions\u2014which is a sanity check often ignored by programmers.These kinds of sanity checks may be used during development for debugging purposes and also to aid in troubleshooting software runtime errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For an n {\\displaystyle n} -card deck, the number of riffle shuffles needed grows as 1.5 log 2 \u2061 n {\\displaystyle 1.5\\log _{2}n} . The most developed theory concerns randomized algorithms for #P-Complete algorithmic counting problems such as the number of graph colorings of a given n {\\displaystyle n} vertex graph. Such problems can, for sufficiently large number of colors, be answered using the Markov chain Monte Carlo method and showing that the mixing time grows only as n log \u2061 ( n ) {\\displaystyle n\\log(n)} (Jerrum 1995).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Standard Generalized Markup Language (SGML), an entity is a primitive data type, which associates a string with either a unique alias (such as a user-specified name) or an SGML reserved word (such as #DEFAULT). Entities are foundational to the organizational structure and definition of SGML documents. The SGML specification defines numerous entity types, which are distinguished by keyword qualifiers and context. An entity string value may variously consist of plain text, SGML tags, and/or references to previously defined entities. Certain entity types may also invoke external documents. Entities are called by reference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number M(n) is the number of monotone boolean functions of n variables. Equivalently, it is the number of antichains of subsets of an n-element set, the number of elements in a free distributive lattice with n generators, and one more than the number of abstract simplicial complexes on a set with n elements. Accurate asymptotic estimates of M(n) and an exact expression as a summation are known. However Dedekind's problem of computing the values of M(n) remains difficult: no closed-form expression for M(n) is known, and exact values of M(n) have been found only for n \u2264 9 (sequence A000372 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to be able to meticulously study the English language, an annotated text corpus was much needed. The Penn Treebank was one of the most used corpora. It consisted of IBM computer manuals, transcribed telephone conversations, and other texts, together containing over 4.5 million words of American English, annotated using both part-of-speech tagging and syntactic bracketing.Japanese sentence corpora were analyzed and a pattern of log-normality was found in relation to sentence length.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C programming language, operations can be performed on a bit level using bitwise operators. Bitwise operations are contrasted by byte-level operations which characterize the bitwise operators' logical counterparts, the AND, OR, NOT operators. Instead of performing on individual bits, byte-level operators perform on strings of eight bits (known as bytes) at a time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In syllogistic logic, there are 256 possible ways to construct categorical syllogisms using the A, E, I, and O statement forms in the square of opposition. Of the 256, only 24 are valid forms. Of the 24 valid forms, 15 are unconditionally valid, and 9 are conditionally valid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In system software, a monolithic kernel is an operating system (OS) architecture where the entire OS is working in kernel space. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the derivation of the van Cittert\u2013Zernike theorem we write the direction cosines l {\\displaystyle l} and m {\\displaystyle m} as 1 2 ( x 1 + x 2 ) / R {\\displaystyle {\\frac {1}{2}}(x_{1}+x_{2})/R} and 1 2 ( y 1 + y 2 ) / R {\\displaystyle {\\frac {1}{2}}(y_{1}+y_{2})/R} . There is, however, a third direction cosine which is neglected since R \u226b 1 2 ( x 1 + x 2 ) {\\displaystyle R\\gg {\\frac {1}{2}}(x_{1}+x_{2})} and R \u226b 1 2 ( y 1 + y 2 ) {\\displaystyle R\\gg {\\frac {1}{2}}(y_{1}+y_{2})} ; under these assumptions it is very close to unity. But if the source has a large angular extent, we cannot neglect this third direction cosine and the van Cittert\u2013Zernike theorem no longer holds. Because most astronomical sources subtend very small angles on the sky (typically much less than a degree), this assumption of the theorem is easily fulfilled in the domain of radio astronomy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a maximum-entropy Markov model (MEMM), or conditional Markov model (CMM), is a graphical model for sequence labeling that combines features of hidden Markov models (HMMs) and maximum entropy (MaxEnt) models. An MEMM is a discriminative model that extends a standard maximum entropy classifier by assuming that the unknown values to be learnt are connected in a Markov chain rather than being conditionally independent of each other. MEMMs find applications in natural language processing, specifically in part-of-speech tagging and information extraction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In measurement of the I/O performance of five filesystems with five storage configurations\u2014single SSD, RAID 0, RAID 1, RAID 10, and RAID 5 it was shown that F2FS on RAID 0 and RAID 5 with eight SSDs outperforms EXT4 by 5 times and 50 times, respectively. The measurements also suggest that the RAID controller can be a significant bottleneck in building a RAID system with high speed SSDs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Francis Galton established the first tests in London for measuring IQ. He tested thousands of people, examining their physical characteristics as a basis for his results and many of the records remain today. James Cattell studied with him, and eventually worked on his own with brass instruments for evaluation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the belief revision framework, counterfactuals are treated using a formal implementation of the Ramsey test. In these systems, a counterfactual A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revision, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The formula was discovered independently by Leonhard Euler and Colin Maclaurin around 1735. Euler needed it to compute slowly converging infinite series while Maclaurin used it to calculate integrals. It was later generalized to Darboux's formula.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the output from many common PRNGs exhibit artifacts that cause them to fail statistical pattern-detection tests. These include: Shorter-than-expected periods for some seed states (such seed states may be called \"weak\" in this context); Lack of uniformity of distribution for large quantities of generated numbers; Correlation of successive values; Poor dimensional distribution of the output sequence; Distances between where certain values occur are distributed differently from those in a random sequence distribution.Defects exhibited by flawed PRNGs range from unnoticeable (and unknown) to very obvious. An example was the RANDU random number algorithm used for decades on mainframe computers. It was seriously flawed, but its inadequacy went undetected for a very long time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the output of the softargmax function can be used to represent a categorical distribution \u2013 that is, a probability distribution over K different possible outcomes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, a mistake or error may be introduced at any stage. Bugs arise from oversight or misunderstanding by a software team during specification, design, coding, configuration, data entry or documentation. For example, a relatively simple program to alphabetize a list of words, the design might fail to consider what should happen when a word contains a hyphen. Or when converting an abstract design into code, the coder might inadvertently create an off-by-one error which can be a \"<\" where \"<=\" was intended, and fail to sort the last word in a list.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Algorithms which use context-free grammars often rely on some variant of the CYK algorithm, usually with some heuristic to prune away unlikely analyses to save time. (See chart parsing.) However some systems trade speed for accuracy using, e.g., linear-time versions of the shift-reduce algorithm. A somewhat recent development has been parse reranking in which the parser proposes some large number of analyses, and a more complex system selects the best option. In natural language understanding applications, semantic parsers convert the text into a representation of its meaning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"The sky is blue\", \"grass is green\", etc. when there are actually myriad variations in hue, chroma, within these areas. In order to represent objects realistically, painters must look beyond the simplifications of local color. Demonstrations of color constancy show how flawed local color assumptions can be when the light source has a color shift. In contemporary sculpture local color is the original color of the raw material that remains unpainted in the completed work.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of harming privacy, information collection means gathering whatever information can be obtained by doing something to obtain it. Examples include surveillance and interrogation. Another example is how consumers and marketers also collect information in the business context through facial recognition which has recently caused a concern for things such as privacy. There is currently research being done related to this topic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some binary data corresponds to computer instructions, such as the data within processor registers decoded by the control unit along the fetch-decode-execute cycle. Computers rarely modify individual bits for performance reasons. Instead, data is aligned in groups of a fixed number of bits, usually 1 byte (8 bits).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While there are exponentially-many such cycles, a separation oracle that works in polynomial time can be implemented by just finding an odd cycle of minimum length, which can be done in polynomial time. The dual of the configuration linear program for the bin packing problem. It can be approximated by an LP with a constraint for each feasible configuration. While there are exponentially-many such cycles, a separation oracle that works in pseudopolynomial time can be implemented by solving a knapsack problem. This is used by the Karmarkar-Karp bin packing algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Includes user views and descriptions of how the system is expected to behave.Information viewpointMetamodel view \u2013 An abstract view that defines information model elements and their structures and relationships. Defines the classes of data that are created and managed by the system and the data architecture. Information view \u2013 Describes the actual data and information as it is realized and manipulated within the system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, an n-ary code is a code that has n significant conditions, where n is a positive integer greater than 1. The integer substituted for n indicates the specific number of significant conditions, i.e., quantization states, in the code. For example, an 8-ary code has eight significant conditions and can convey three bits per code symbol. A prefix that indicates an integer, e.g., \"bin\", \"tern,\" or \"quatern\", may be used in lieu of a numeral, to produce \"binary\", \"ternary\", or \"quaternary\" (2, 3, and 4 states respectively).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This paper also introduced concepts from convex geometry, including \"Elfving sets\" and Elfving's theorem. Being symmetric, Elfving sets are formed by the union of a set and its reflection through the origin, \u2212S \u222a S. According to Chernoff (1999, p. 204), Elfving was generous in crediting others' results: His paper in the Cram\u00e9r-festschrift acknowledged unpublished notes of L. J. Savage; Elfving was a referee for the fundamental paper on optimal designs by Kiefer and Wolfowitz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle M=B^{*}B.} A matrix is positive semi-definite if it satisfies similar equivalent conditions where \"positive\" is replaced by \"nonnegative\", \"invertible matrix\" is replaced by \"matrix\", and the word \"leading\" is removed. Positive-definite and positive-semidefinite real matrices are at the basis of convex optimization, since, given a function of several real variables that is twice differentiable, then if its Hessian matrix (matrix of its second partial derivatives) is positive-definite at a point p, then the function is convex near p, and, conversely, if the function is convex near p, then the Hessian matrix is positive-semidefinite at p. Some authors use more general definitions of definiteness, including some non-symmetric real matrices, or non-Hermitian complex ones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\sum _{k=0}^{\\infty }\\left|\\Pr(S_{n}=k)-{\\lambda _{n}^{k}e^{-\\lambda _{n}} \\over k! }\\right|<2\\left(\\sum _{i=1}^{n}p_{i}^{2}\\right).} In other words, the sum has approximately a Poisson distribution and the above inequality bounds the approximation error in terms of the total variation distance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In testing the null hypothesis that the population mean is equal to a specified value \u03bc0, one uses the statistic t = x \u00af \u2212 \u03bc 0 s / n {\\displaystyle t={\\frac {{\\bar {x}}-\\mu _{0}}{s/{\\sqrt {n}}}}} where x \u00af {\\displaystyle {\\bar {x}}} is the sample mean, s is the sample standard deviation and n is the sample size. The degrees of freedom used in this test are n \u2212 1. Although the parent population does not need to be normally distributed, the distribution of the population of sample means x \u00af {\\displaystyle {\\bar {x}}} is assumed to be normal. By the central limit theorem, if the observations are independent and the second moment exists, then t {\\displaystyle t} will be approximately normal N(0;1).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let a = ( a 1 , \u2026 , a k \u2212 1 ) {\\displaystyle \\mathbf {a} =(a_{1},\\ldots ,a_{k-1})} be a vector of positive integers and V {\\displaystyle V} be an n {\\displaystyle n} -element vertex set. We say that a family of partitions P = P ( k \u2212 1 , a ) = { P ( 1 ) \u2026 , P ( k \u2212 1 ) } {\\displaystyle {\\mathcal {P}}={\\mathcal {P}}(k-1,\\mathbf {a} )=\\{{\\mathcal {P}}^{(1)}\\,\\ldots ,{\\mathcal {P}}^{(k-1)}\\}} on V {\\displaystyle V} is ( \u03bc , \u03b4 , d , r ) {\\displaystyle (\\mu ,\\delta ,\\mathbf {d} ,r)} -equitable if it satisfies the following: P ( 1 ) = { V i: i \u2208  } {\\displaystyle {\\mathcal {P}}^{(1)}=\\{V_{i}\\colon i\\in \\}} is equitable vertex partition of V {\\displaystyle V} . That is | V 1 | \u2264 \u2026 \u2264 | V a 1 | \u2264 | V 1 | + 1 {\\displaystyle |V_{1}|\\leq \\ldots \\leq |V_{a_{1}}|\\leq |V_{1}|+1} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the area of abstract algebra known as group theory, an A-group is a type of group that is similar to abelian groups. The groups were first studied in the 1940s by Philip Hall, and are still studied today. A great deal is known about their structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Linux kernel, configfs and sysfs provide files that can be used to query the kernel for information and configure entities in the kernel. procfs maps processes and, on Linux, other operating system structures into a filespace.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is exactly the situation in computers with cache memory, one of the earliest commercial examples of which was the IBM System/360 Model 85. In the Model 85 all addresses were real addresses referring to the main core store. A semiconductor cache store, invisible to the user, held the contents of parts of the main store in use by the currently executing program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The validation sample is used to construct a classification matrix which contains the number of correctly classified and incorrectly classified cases. The percentage of correctly classified cases is called the hit ratio. Plot the results on a two dimensional map, define the dimensions, and interpret the results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music, pieces or sections which confound expectations and may be or are interpreted simultaneously in different ways are ambiguous, such as some polytonality, polymeter, other ambiguous meters or rhythms, and ambiguous phrasing, or (Stein 2005, p. 79) any aspect of music. The music of Africa is often purposely ambiguous. To quote Sir Donald Francis Tovey (1935, p. 195), \"Theorists are apt to vex themselves with vain efforts to remove uncertainty just where it has a high aesthetic value.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1950s, attempts started to apply computers to the recognition, interpretation and translation of natural languages, such as English and Russian. This requires a machine-readable description of the phrase structure of sentences, that can be used to parse and interpret them, and to generate them. Context-free grammars, a concept from structural linguistics, were adopted for this purpose; their rules can express how sentences are recursively built out of parts of speech, such as noun phrases and verb phrases, and ultimately, words, such as nouns, verbs, and pronouns. This work influenced the design and implementation of programming languages, most notably, of ALGOL 60, which introduced a syntax description in Backus\u2013Naur form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such an element is called a modular element. Even more generally, the modular law may hold for any a and a fixed pair (x, b). Such a pair is called a modular pair, and there are various generalizations of modularity related to this notion and to semimodularity. Modular lattices are sometimes called Dedekind lattices after Richard Dedekind, who discovered the modular identity in several motivating examples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Memoryless\" means that if X {\\displaystyle X} is a random variable with such a distribution, then for any numbers 0 < y < x {\\displaystyle 0 x \u2223 X > y ) = Pr ( X > x \u2212 y ) {\\displaystyle \\Pr(X>x\\mid X>y)=\\Pr(X>x-y)} . Verification of conditions of characterization theorems in practice is possible only with some error \u03f5 {\\displaystyle \\epsilon } , i.e., only to a certain degree of accuracy. Such a situation is observed, for instance, in the cases where a sample of finite size is considered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The method of casting out nines offers a quick check of decimal arithmetic computations performed by hand. It is based on modular arithmetic modulo 9, and specifically on the crucial property that 10 \u2261 1 (mod 9). Arithmetic modulo 7 is used in algorithms that determine the day of the week for a given date. In particular, Zeller's congruence and the Doomsday algorithm make heavy use of modulo-7 arithmetic. More generally, modular arithmetic also has application in disciplines such as law (e.g., apportionment), economics (e.g., game theory) and other areas of the social sciences, where proportional division and allocation of resources plays a central part of the analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Mobile UI context includes signal cues from user activity, such as the location where or the time when the device is in use, that can be observed from user interactions within a mobile app. Such context clues can be used to provide automatic suggestions when scheduling an appointment or activity or to filter a list of various services for the user. The user is often the focus of interaction with their device, and the interface entails components of both hardware and software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The owner has a distributive right to exclude others (i.e. the right to command a \"fair share\" of personal property). Private property is a social relationship between the owner and persons deprived, i.e. not a relationship between person and thing. Private property may include artifacts, factories, mines, dams, infrastructure, natural vegetation, mountains, deserts and seas\u2014these generate capital for the owner without the owner necessarily having to perform any physical labor. Conversely, those who perform labor using somebody else's private property are considered deprived of the value of their work in Marxist doctrine, and are instead given a salary that is disjointed from the value generated by the worker. In Marxist theory, private property typically refers to capital or the means of production, while personal property refers to consumer and non-capital goods and services.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, this heuristic can also produce errors. When people are asked whether there are more English words with K in the first position or with K in the third position, they use the same process. It is easy to think of words that begin with K, such as kangaroo, kitchen, or kept.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In philosophy, the term formal ontology is used to refer to an ontology defined by axioms in a formal language with the goal to provide an unbiased (domain- and application-independent) view on reality, which can help the modeler of domain- or application-specific ontologies (information science) to avoid possibly erroneous ontological assumptions encountered in modeling large-scale ontologies. By maintaining an independent view on reality a formal (upper level) ontology gains the following properties: indefinite expandability: the ontology remains consistent with increasing content. content and context independence: any kind of 'concept' can find its place. accommodate different levels of granularity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the order of a kernel is the degree of the first non-zero moment of a kernel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, allophonic palatalization developed into phonemic palatalization by phonemic split. In other languages, phonemes that were originally phonetically palatalized changed further: palatal secondary place of articulation developed into changes in manner of articulation or primary place of articulation. Phonetic palatalization of a consonant sometimes causes surrounding vowels to change by coarticulation or assimilation. In Russian, \"soft\" (palatalized) consonants are usually followed by vowels that are relatively more front (that is, closer to  or ), and vowels following \"hard\" (unpalatalized) consonants are further back. See Russian phonology \u00a7 Allophony for more information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Measurement of productivity is at its most accurate in business because of the availability of all elementary data of the quantities and prices of the inputs and the output in production. The more comprehensive the entity we want to analyse by measurements, the more data need to be aggregated. In productivity measurement, combining and aggregating the data always involves reduced measurement accuracy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the beginning, the tree is first created in time \u0398(k). In each step of merging, only the games on the path from the new element to the root need to be replayed. In each layer, only one comparison is needed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal (called the message signal or modulation signal) for the purpose of conveying information.This carrier wave usually has a much higher frequency than the message signal does. This is because it is impractical to transmit signals with low frequencies. The purpose of the carrier is usually either to transmit the information through space as an electromagnetic wave (as in radio communication), or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing (as in a cable television system). The term originated in radio communication, where the carrier wave creates the waves which carry the information (modulation) through the air from the transmitter to the receiver. The term is also used for an unmodulated emission in the absence of any modulating signal.In music production, carrier signals can be controlled by a modulating signal to change the sound property of an audio recording and add a sense of depth and movement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the rearrangement inequality states that for every choice of real numbers and every permutation y \u03c3 ( 1 ) , \u2026 , y \u03c3 ( n ) {\\displaystyle y_{\\sigma (1)},\\ldots ,y_{\\sigma (n)}} of y 1 , \u2026 , y n . {\\displaystyle y_{1},\\ldots ,y_{n}.} If the numbers x 1 , \u2026 , x n {\\displaystyle x_{1},\\ldots ,x_{n}} are different, meaning that x 1 < \u22ef < x n , {\\displaystyle x_{1}<\\cdots", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a moment matrix is a special symmetric square matrix whose rows and columns are indexed by monomials. The entries of the matrix depend on the product of the indexing monomials only (cf. Hankel matrices.) Moment matrices play an important role in polynomial fitting, polynomial optimization (since positive semidefinite moment matrices correspond to polynomials which are sums of squares) and econometrics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Haxe uses structural typing, but classes are not structurally subtyped. In languages which support subtype polymorphism, a similar dichotomy can be formed based on how the subtype relationship is defined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The notion was introduced by George E. Collins in 1975, together with an algorithm for computing it. Collins' algorithm has a computational complexity that is double exponential in n. This is an upper bound, which is reached on most entries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is possible to construct a unit distance graph efficiently, given its points. Finding all unit distances has applications in pattern matching, where it can be a first step in finding congruent copies of larger patterns. However, determining whether a given graph can be represented as a unit distance graph is NP-hard, and more specifically complete for the existential theory of the reals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Constructed languages have been included in standardized tests such as the SAT, where they were used to test the applicant's ability to infer and apply grammatical rules. By the same token, a constructed language might also be used to restrict thought, as in George Orwell's Newspeak, or to simplify thought, as in Toki Pona. However, linguists such as Steven Pinker argue that ideas exist independently of language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For specific mathematical reasons (see linear regression), this allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the independent variables take on a given set of values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1990s, MIPS began to license their designs to third-party vendors. This proved fairly successful due to the simplicity of the core, which allowed it to have many uses that would have formerly used much less able complex instruction set computer (CISC) designs of similar gate count and price; the two are strongly related: the price of a CPU is generally related to the number of gates and the number of external pins. Sun Microsystems attempted to enjoy similar success by licensing their SPARC core but was not nearly as successful. By the late 1990s, MIPS was a powerhouse in the embedded processor field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programming languages, an assignment statement returns a value, while in others it does not. In most expression-oriented programming languages (for example, C), the assignment statement returns the assigned value, allowing such idioms as x = y = a, in which the assignment statement y = a returns the value of a, which is then assigned to x. In a statement such as while ((ch = getchar()) != EOF) {\u2026}, the return value of a function is used to control a loop while assigning that same value to a variable. In other programming languages, Scheme for example, the return value of an assignment is undefined and such idioms are invalid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mechanical engineering, a key is a machine element used to connect a rotating machine element to a shaft. The key prevents relative rotation between the two parts and may enable torque transmission. For a key to function, the shaft and rotating machine element must have a keyway and a keyseat, which is a slot and pocket in which the key fits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, order of accuracy quantifies the rate of convergence of a numerical approximation of a differential equation to the exact solution. Consider u {\\displaystyle u} , the exact solution to a differential equation in an appropriate normed space ( V , | | | | ) {\\displaystyle (V,||\\ ||)} . Consider a numerical approximation u h {\\displaystyle u_{h}} , where h {\\displaystyle h} is a parameter characterizing the approximation, such as the step size in a finite difference scheme or the diameter of the cells in a finite element method. The numerical solution u h {\\displaystyle u_{h}} is said to be n {\\displaystyle n} th-order accurate if the error E ( h ) := | | u \u2212 u h | | {\\displaystyle E(h):=||u-u_{h}||} is proportional to the step-size h {\\displaystyle h} to the n {\\displaystyle n} th power: E ( h ) = | | u \u2212 u h | | \u2264 C h n {\\displaystyle E(h)=||u-u_{h}||\\leq Ch^{n}} where the constant C {\\displaystyle C} is independent of h {\\displaystyle h} and usually depends on the solution u {\\displaystyle u} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This algorithm for APR is required for some but not all forms of consumer debt in the EU. For example, this EU directive is limited to agreements of \u20ac50,000 and below and excludes all mortgages.In the Netherlands the formula above is also used for mortgages. In many cases the mortgage is not always paid back completely at the end of period N, but for instance when the borrower sells his house or dies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The English verb is to krige, and the most common noun is kriging. The word is sometimes capitalized as Kriging in the literature. Though computationally intensive in its basic formulation, kriging can be scaled to larger problems using various approximation methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer programming, index notation is used to specify the elements of an array of numbers. The formalism of how indices are used varies according to the subject. In particular, there are different methods for referring to the elements of a list, a vector, or a matrix, depending on whether one is writing a formal mathematical paper for publication, or when one is writing a computer program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Section 230 of the Communications Decency Act gives protection from any liability as a result from the publication provided by another party. Common issues include defamation, but many courts have expanded it to include other claims as well.Online communities of various kinds (social networking sites, blogs, media sharing sites, etc.) are posing new challenges for all levels of law enforcement in combating many kinds of crimes including harassment, identity theft, copyright infringement, etc. Copyright law is being challenged and debated with the shift in how individuals now disseminate their intellectual property. Individuals come together via online communities in collaborative efforts to create.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a ridge function is any function f: R d \u2192 R {\\displaystyle f:\\mathbb {R} ^{d}\\rightarrow \\mathbb {R} } that can be written as the composition of a univariate function with an affine transformation, that is: f ( x ) = g ( x \u22c5 a ) {\\displaystyle f({\\boldsymbol {x}})=g({\\boldsymbol {x}}\\cdot {\\boldsymbol {a}})} for some g: R \u2192 R {\\displaystyle g:\\mathbb {R} \\rightarrow \\mathbb {R} } and a \u2208 R d {\\displaystyle {\\boldsymbol {a}}\\in \\mathbb {R} ^{d}} . Coinage of the term 'ridge function' is often attributed to B.F. Logan and L.A. Shepp.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically abstract algebra, a square class of a field F {\\displaystyle F} is an element of the square class group, the quotient group F \u00d7 / F \u00d7 2 {\\displaystyle F^{\\times }/F^{\\times 2}} of the multiplicative group of nonzero elements in the field modulo the square elements of the field. Each square class is a subset of the nonzero elements (a coset of the multiplicative group) consisting of the elements of the form xy2 where x is some particular fixed element and y ranges over all nonzero field elements.For instance, if F = R {\\displaystyle F=\\mathbb {R} } , the field of real numbers, then F \u00d7 {\\displaystyle F^{\\times }} is just the group of all nonzero real numbers (with the multiplication operation) and F \u00d7 2 {\\displaystyle F^{\\times 2}} is the subgroup of positive numbers (as every positive number has a real square root). The quotient of these two groups is a group with two elements, corresponding to two cosets: the set of positive numbers and the set of negative numbers. Thus, the real numbers have two square classes, the positive numbers and the negative numbers.Square classes are frequently studied in relation to the theory of quadratic forms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In professional typography, the term typeface is not interchangeable with the word font (originally \"fount\" in British English, and pronounced \"font\"), because the term font has historically been defined as a given alphabet and its associated characters in a single size. For example, 8-point Caslon Italic was one font, and 10-point Caslon Italic was another. Historically, a font came from a type foundry as a set of \"sorts\", with number of copies of each character included. As the range of typeface designs increased and requirements of publishers broadened over the centuries, fonts of specific weight (blackness or lightness) and stylistic variants (most commonly regular or roman as distinct to italic, as well as condensed) have led to font families, collections of closely related typeface designs that can include hundreds of styles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Associative operations are abundant in mathematics; in fact, many algebraic structures (such as semigroups and categories) explicitly require their binary operations to be associative. However, many important and interesting operations are non-associative; some examples include subtraction, exponentiation, and the vector cross product. In contrast to the theoretical properties of real numbers, the addition of floating point numbers in computer science is not associative, and the choice of how to associate an expression can have a significant effect on rounding error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The choice of syntax is affected by both linguistic and computational concerns; for instance some parsing systems use lexical functional grammar, but in general, parsing for grammars of this type is known to be NP-complete. Head-driven phrase structure grammar is another linguistic formalism which has been popular in the parsing community, but other research efforts have focused on less complex formalisms such as the one used in the Penn Treebank. Shallow parsing aims to find only the boundaries of major constituents such as noun phrases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Characterization is not unique to mathematics, but since the science is abstract, much of the activity can be described as \"characterization\". For instance, in Mathematical Reviews, as of 2018, more than 24,000 articles contain the word in the article title, and 93,600 somewhere in the review. In an arbitrary context of objects and features, characterizations have been expressed via the heterogeneous relation aRb, meaning that object a has feature b. For example, b may mean abstract or concrete. The objects can be considered the extensions of the world, while the features are expression of the intensions. A continuing program of characterization of various objects leads to their categorization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other. A function maps elements from its domain to elements in its codomain. Given a function f: X \u2192 Y {\\displaystyle f\\colon X\\to Y}: The function is injective, or one-to-one, if each element of the codomain is mapped to by at most one element of the domain, or equivalently, if distinct elements of the domain map to distinct elements in the codomain. An injective function is also called an injection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, point-to-multipoint communication (P2MP, PTMP or PMP) is communication which is accomplished via a distinct type of one-to-many connection, providing multiple paths from a single location to multiple locations.Point-to-multipoint telecommunications is typically used in wireless Internet and IP telephony via gigahertz radio frequencies. P2MP systems have been designed with and without a return channel from the multiple receivers. A central antenna or antenna array broadcasts to several receiving antennas and the system uses a form of time-division multiplexing to allow for the return channel traffic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics the Cram\u00e9r\u2013von Mises criterion is a criterion used for judging the goodness of fit of a cumulative distribution function F \u2217 {\\displaystyle F^{*}} compared to a given empirical distribution function F n {\\displaystyle F_{n}} , or for comparing two empirical distributions. It is also used as a part of other algorithms, such as minimum distance estimation. It is defined as \u03c9 2 = \u222b \u2212 \u221e \u221e  2 d F \u2217 ( x ) {\\displaystyle \\omega ^{2}=\\int _{-\\infty }^{\\infty }^{2}\\,\\mathrm {d} F^{*}(x)} In one-sample applications F \u2217 {\\displaystyle F^{*}} is the theoretical distribution and F n {\\displaystyle F_{n}} is the empirically observed distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is still possible to check GCC-style assembly for clobber mistakes with knowledge of the instruction set.GNAT (Ada language frontend of the GCC suite), and LLVM uses the GCC syntax. The D programming language uses a DSL similar to the MSVC extension officially for x86_64, but the LLVM-based LDC also provides the GCC-style syntax on every architecture. MSVC only supports inline assembler on 32-bit x86.The Rust language has since migrated to a syntax abstracting away inline assembly options further than the LLVM (GCC-style) version. It provides enough information to allow transforming the block into an externally-assembled function if the backend could not handle embedded assembly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the calculation equals the true value. Except in some important situations, outlined later, the task has little relevance to applications of statistics since its need is avoided by standard procedures, such as the use of significance tests and confidence intervals, or by using Bayesian analysis. However, for statistical theory, it provides an exemplar problem in the context of estimation theory which is both simple to state and for which results cannot be obtained in closed form. It also provides an example where imposing the requirement for unbiased estimation might be seen as just adding inconvenience, with no real benefit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead of using all the elements contained in the selected clusters, the researcher randomly selects elements from each cluster. Constructing the clusters is the first stage. Deciding what elements within the cluster to use is the second stage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In general, however, Catalan is an SVO language. Sentences can be simple or compound, depending on whether they contain just one verb or more than one. In the sentences with more than one verb, they can be on an equal footing (juxtaposition or coordination), or there may be one main verb and other subordinate ones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"The concept of alt-metrics was introduced in 2009 by Cameron Neylon and Shirly Wu as article-level metrics. In contrast with the focus of leading metrics on journals (impact factor) or, more recently, on individual researchers (h-index), the article-level metrics makes it possible to track the circulation of individual publications: \"(an) article that used to live on a shelf now lives in Mendeley, CiteULike, or Zotero \u2013 where we can see and count it\" As such they are more compatible with the diversity of publication strategies that has characterized open science: preprints, reports or even non-textual outputs like dataset or software may also have associated metrics. In their original research proposition, Neylon and Wu favored the use of data from reference management software like Zotero or Mendeley.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Square-free factorization is the first step of the polynomial factorization algorithms that are implemented in computer algebra systems. Therefore, the algorithm of square-free factorization is basic in computer algebra. Over a field of characteristic 0, the quotient of f {\\displaystyle f} by its GCD with its derivative is the product of the a i {\\displaystyle a_{i}} in the above square-free decomposition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fair item allocation problem, there are n items and k people, each of which assigns a possibly different value to each item. The goal is to partition the items among the people in as fair way as possible. The natural generalization of the greedy number partitioning algorithm is the envy-graph algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One important principle is that if two sets X and Y have the same finite number of elements, and a function f: X \u2192 Y is known to be injective, then it is also surjective, and vice versa. A related fact is known as the pigeonhole principle, which states that if two sets X and Y have finite numbers of elements n and m with n > m, then any map f: X \u2192 Y is not injective (so there exist two distinct elements of X that f sends to the same element of Y); this follows from the former principle, since if f were injective, then so would its restriction to a strict subset S of X with m elements, which restriction would then be surjective, contradicting the fact that for x in X outside S, f(x) cannot be in the image of the restriction. Similar counting arguments can prove the existence of certain objects without explicitly providing an example. In the case of infinite sets this can even apply in situations where it is impossible to give an example.The domain of enumerative combinatorics deals with computing the number of elements of finite sets, without actually counting them; the latter usually being impossible because infinite families of finite sets are considered at once, such as the set of permutations of {1, 2, ..., n} for any natural number n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In response to enterprise environment needs, OpenSocial added support for advanced mashup scenarios. It enabled gadgets to \"securely message each other in a loosely coupled manner.\" This new feature was called Inter-Gadget Communication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Step 2: Collect \"similar\" classes into 'bundles': These above collections can be put into a \"binary relation\" (comparing for) similarity by \"equinumerosity\", symbolized here by \u2248, i.e. one-one correspondence of the elements, and thereby create Russellian classes of classes or what Russell called \"bundles\". \"We can suppose all couples in one bundle, all trios in another, and so on. In this way we obtain various bundles of collections, each bundle consisting of all the collections that have a certain number of terms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating-system-level virtualization, a physical server is virtualized at the operating system level, enabling multiple isolated and secure virtualized servers to run on a single physical server. The \"guest\" operating system environments share the same running instance of the operating system as the host system. Thus, the same operating system kernel is also used to implement the \"guest\" environments, and applications running in a given \"guest\" environment view it as a stand-alone system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The depth may also be given as the number of memory elements v in the polynomial or the maximum possible number of states of the encoder (typically: 2 v {\\displaystyle 2^{v}} ). Convolutional codes are often described as continuous. However, it may also be said that convolutional codes have arbitrary block length, rather than being continuous, since most real-world convolutional encoding is performed on blocks of data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the beginning of the COVID-19 pandemic, former US President Donald Trump delivered a very dangerous message to the public on the use of disinfectants, which was immediately rejected and refuted by health professionals. In essence, and as mentioned above, virucides are usually toxic depending on concentrations, mixture, etc., and can be deadly not just to viruses, but also if inside a human or animal body or on surface of body.With regards to the COVID-19 pandemic, some of the mentioned agents are still under research about their microbicidal activity and effectivity against SARS-CoV-2 e. g. on surfaces, as mouth-washes, hand-washing, etc. A mixture of 62\u201371% ethanol, 0.5% hydrogen peroxide or 0.1% sodium hypochlorite is found to be able to deactivate the novel Coronavirus on surfaces within 1 minute.A 2020 systematic review on hydrogen peroxide (H2O2) mouth-washes concludes, that they don't have an effect on virucidal activity, recommending that \"dental care protocols during the COVID-19 pandemic should be revised.\" Additional research with relation to the Coronavirus virucidal efficacy is on-going.Various information and overview of light-based strategies (UV-C and other types of light sources; see also Ultraviolet germicidal irradiation) to combat the COVID-19 pandemic are available.As systematic review of 16 studies by Cochrane on Antimicrobial mouthwashes (gargling) and nasal sprays concludes that \"there is currently no evidence relating to the benefits and risks of patients with COVID\u201019 using antimicrobial mouthwashes or nasal sprays.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Tikhonov regularization setting, the filter function for RLS is described below. As shown in, in this setting, c = ( K + n \u03bb I ) \u2212 1 Y {\\displaystyle c=(K+n\\lambda I)^{-1}Y} . Thus, c = ( K + n \u03bb I ) \u2212 1 Y = Q ( \u03a3 + n \u03bb I ) \u2212 1 Q T Y = \u2211 i = 1 n 1 \u03c3 i + n \u03bb < q i , Y > q i . {\\displaystyle c=(K+n\\lambda I)^{-1}Y=Q(\\Sigma +n\\lambda I)^{-1}Q^{T}Y=\\sum _{i=1}^{n}{\\frac {1}{\\sigma _{i}+n\\lambda }} q_{i}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When Mozilla redirected funding away from the project in 2020, it was forked by its original developers as Coqui STT using the same open-source license.Google Gboard supports speech recognition on all Android applications. It can be activated through the microphone icon.The commercial cloud based speech recognition APIs are broadly available. For more software resources, see List of speech recognition software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In superintuitionistic and modal logics, a logic is structurally complete if every admissible rule is derivable. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical classification, Bayes error rate is the lowest possible error rate for any classifier of a random outcome (into, for example, one of two categories) and is analogous to the irreducible error.A number of approaches to the estimation of the Bayes error rate exist. One method seeks to obtain analytical bounds which are inherently dependent on distribution parameters, and hence difficult to estimate. Another approach focuses on class densities, while yet another method combines and compares various classifiers.The Bayes error rate finds important use in the study of patterns and machine learning techniques.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Ganz factory in 1884 shipped the world's first five high-efficiency AC transformers. This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form.The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1400 V to 2000 V) than the voltage of utilization loads (100 V initially preferred). When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, a family of sets may be defined as a function from a set I {\\displaystyle I} , known as the index set, to F {\\displaystyle F} , in which case the sets of the family are indexed by members of I {\\displaystyle I} . In some contexts, a family of sets may be allowed to contain repeated copies of any given member, and in other contexts it may form a proper class. A finite family of subsets of a finite set S {\\displaystyle S} is also called a hypergraph. The subject of extremal set theory concerns the largest and smallest examples of families of sets satisfying certain restrictions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Often an adjective is added for specifying the operation, such as in additive inverse, multiplicative inverse, and functional inverse. In this case (associative operation), an invertible element is an element that has an inverse. In a ring, an invertible element, also called a unit, is an element that is invertible under multiplication (this is not ambiguous, as every element is invertible under addition).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Euclidean space, the angle \u03b8 between two Euclidean vectors u and v is related to their dot product and their lengths by the formula This formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Between any two real numbers a < b, no matter how close they are to each other, there are always infinitely many other real numbers, and Cantor showed that they are as many as those contained in the whole set of real numbers. In other words, the open interval (a,b) is equinumerous with R . {\\displaystyle \\mathbb {R} .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many of these plants do not survive long, as they are often vandalized. An estimated 10,000 plants are mutilated each week by cutting off the lower leaves for barbacoa or destroying them completely to look for the edible white grubs or ant eggs that can inhabit them.A recent series of PBS travel shows feature pulque and say that it is once again a very popular drink and that there is a retro movement leading younger people seeking to establish their Mexican heritage to drink this beverage in large quantities. It has become a trendy drink among youth and back-to-your-roots types. The prohibition on female drinkers has also been lifted and co-ed pulquerias are now the norm.Also flavored syrups, seasonings and so on are now common with one pulqueria featured in the special offering 48 separate flavors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Indeed, type T need not even have an implementation; it might be a purely abstract class. As another case in point, type Stack above is a behavioral subtype of type Bag even if type Bag's implementation exhibits FIFO behavior: what matters is that type Bag's specification does not specify which element is removed by method get. This also means that behavioral subtyping can be discussed only with respect to a particular (behavioral) specification for each type involved and that if the types involved have no well-defined behavioral specification, behavioral subtyping cannot be discussed meaningfully.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The end result of this process is to calculate a threshold value (of squared error) whereby observations with a squared error smaller than this threshold should be kept and observations with a squared error larger than this value should be removed (i.e., as an outlier). Because Peirce's criterion does not take observations, fitting parameters, or residual errors as an input, the output must be re-associated with the data. Taking the average of all the squared errors (i.e., the mean-squared error) and multiplying it by the threshold squared error (i.e., the output of this function) will result in the data-specific threshold value used to identify outliers. The following Python code returns x-squared values for a given N (first column) and n (top row) in Table 1 (m = 1) and Table 2 (m = 2) of Gould 1855. Due to the Newton-method of iteration, look-up tables, such as N versus log Q (Table III in Gould, 1855) and x versus log R (Table III in Peirce, 1852 and Table IV in Gould, 1855) are no longer necessary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any such function defines a perturbation of the initial problem. In many cases this takes the form of shifting the constraints.In some texts the value function is called the perturbation function, and the perturbation function is called the bifunction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example, the four bytes represent a KLV set where the key is one byte, the length field is one byte (or possibly BER - you cannot tell from the example), and the value is two bytes: a zero and a three. In your application you would have previously agreed to a) use one-byte keys and b) use one-byte length encoding. Also presumably the key value \"42\" would mean something to you, perhaps it indicates that the value bytes 0x00 and 0x03 are an integer representing the value of your bicycle's odometer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, biomedical research containing human subjects is governed by a baseline standard of ethics known as The Common Rule, which aims to protect a subject's privacy by requiring \"identifiers\" such as name or address to be removed from collected data. A 2012 report by the Presidential Commission for the Study of Bioethical Issues stated, however, that \"what constitutes 'identifiable' and 'de-identified' data is fluid and that evolving technologies and the increasing accessibility of data could allow de-identified data to become re-identified\". In fact, research has already shown that it is \"possible to discover a study participant's identity by cross-referencing research data about him and his DNA sequence \u2026  genetic genealogy and public-records databases\". This has led to calls for policy-makers to establish consistent guidelines and best practices for the accessibility and usage of individual genomic data collected by researchers.Privacy protections for genetic research participants were strengthened by provisions of the 21st Century Cures Act (H.R.34) passed on 7 December 2016 for which the American Society of Human Genetics (ASHG) commended Congress, Senator Warren and Senator Enzi.The Genetic Information Nondiscrimination Act of 2008 (GINA) protects the genetic privacy of the public, including research participants.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "f ( x x ) ) . {\\displaystyle {\\textsf {Y}}=\\lambda f.\\ (\\lambda x.f\\ (x\\ x))\\ (\\lambda x.f\\ (x\\ x))\\ . }: 131 In functional programming, the Y combinator can be used to formally define recursive functions in a programming language that does not support recursion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a {\\displaystyle a} , b {\\displaystyle b} , and c {\\displaystyle c} can satisfy the equation a n + b n = c n {\\displaystyle a^{n}+b^{n}=c^{n}} for any integer value of n {\\displaystyle n} greater than two. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century, and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics, and prior to its proof it was in the Guinness Book of World Records for \"most difficult mathematical problems\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In static typing, all expressions have their types determined before a program executes, typically at compile-time. For example, 1 and (2+2) are integer expressions; they cannot be passed to a function that expects a string or stored in a variable that is defined to hold dates.Statically-typed languages can be either manifestly typed or type-inferred. In the first case, the programmer must explicitly write types at certain textual positions (for example, at variable declarations). In the second case, the compiler infers the types of expressions and declarations based on context.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, a signal can mean synchronous events (sequences of samples, video frames, etc., with constant sample rate or frame rate) rather than asynchronous events, while the word event and data flow is often used for asynchronous event queues, but this is by no means universal. This language was created in the 1950s Konrad Zuse. Especially in telecommunications, electrical engineering and signal processing, a digital signal is a sampled representation of an analog physical entity. In telecommunications, the term signalling means asynchronous phone call metadata information exchange, for example of telephone numbers. One application of synchronous signal programming is observer pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Those are the only two \"tenses\" in Arabic (not counting \u0623\u064e\u0645\u0652\u0631 amr, command or imperative, which is traditionally considered as denoting future events.) To explicitly mark aspect, Arabic uses a variety of lexical and syntactic devices. Contemporary Arabic dialects are another matter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The correspondence had been described, in a rather different form, much earlier by Robinson (Robinson 1938), in an attempt to prove the Littlewood\u2013Richardson rule. The correspondence is often referred to as the Robinson\u2013Schensted algorithm, although the procedure used by Robinson is radically different from the Schensted algorithm, and almost entirely forgotten.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The compartments are not described, though it is implied that each compartment is greater than the previous one and is joined based on one's merit. The first compartment is for Jewish martyrs, the second for those who drowned, the third for \"Rabbi Johanan ben Zakkai and his disciples,\" the fourth for those whom the cloud of glory carried off, the fifth for penitents, the sixth for youths who have never sinned; and the seventh for the poor who lived decently and studied the Torah.In chapter two, Legends of the Jews gives a brief description of the lower Gan Eden. The tree of knowledge is a hedge around the tree of life, which is so vast that \"it would take a man five hundred years to traverse a distance equal to the diameter of the trunk\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, alternative hypothesis is often denoted as Ha or H1. Hypotheses are formulated to compare in a statistical hypothesis test. In the domain of inferential statistics two rival hypotheses can be compared by explanatory power and predictive power.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The concept of F-statistics was developed during the 1920s by the American geneticist Sewall Wright, who was interested in inbreeding in cattle. However, because complete dominance causes the phenotypes of homozygote dominants and heterozygotes to be the same, it was not until the advent of molecular genetics from the 1960s onwards that heterozygosity in populations could be measured. F can be used to define effective population size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 25678, 125678, 245678, and 1245678 are the patterns related to Braille pattern dots-13456, since the two additional dots of kantenji patterns 013456, 134567, and 0134567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, since only Alice knows b {\\displaystyle b} , it makes it virtually impossible for either Bob or Eve to distinguish the states of the qubits. Bob proceeds to generate a string of random bits b \u2032 {\\displaystyle b'} of the same length as b {\\displaystyle b} , and uses those bits for his choice of basis when measuring the qubits transmitted by Alice. At this point, Bob announces publicly that he has received Alice's transmission.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the max\u2013min inequality is as follows: For any function f: Z \u00d7 W \u2192 R , {\\displaystyle \\ f:Z\\times W\\to \\mathbb {R} \\ ,} sup z \u2208 Z inf w \u2208 W f ( z , w ) \u2264 inf w \u2208 W sup z \u2208 Z f ( z , w ) . {\\displaystyle \\sup _{z\\in Z}\\inf _{w\\in W}f(z,w)\\leq \\inf _{w\\in W}\\sup _{z\\in Z}f(z,w)\\ .} When equality holds one says that f, W, and Z satisfies a strong max\u2013min property (or a saddle-point property). The example function f ( z , w ) = sin \u2061 ( z + w ) {\\displaystyle \\ f(z,w)=\\sin(z+w)\\ } illustrates that the equality does not hold for every function. A theorem giving conditions on f, W, and Z which guarantee the saddle point property is called a minimax theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some languages, such as Haskell, do not substitute structurally in the case where an expected type is declared (i.e., not inferred), e.g., only substitute for functions that are signature-based polymorphic via type inference. Then it is not possible to accidentally subtype a non-inferred type, although it may still be possible to provide an explicit conversion to a non-inferred type, which is invoked implicitly. Structural subtyping is arguably more flexible than nominative subtyping, as it permits the creation of ad hoc types and protocols; in particular, it permits creation of a type which is a supertype of an existing type, without modifying the definition of the latter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Honeytokens do not necessarily prevent any tampering with the data, but instead give the administrator a further measure of confidence in the data integrity. Honeytokens are fictitious words or records that are added to legitimate databases. They allow administrators to track data in situations they wouldn't normally be able to track, such as cloud-based networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to facilitate discussion, some notational conventions need explaining. The expression \u03d5 A , x , a \u00af = { x \u2208 A: A \u22a8 \u03d5  } {\\displaystyle \\phi ^{A,x,{\\bar {a}}}=\\{x\\in A\\colon A\\models \\phi \\}} for A an L-structure (or L-model) in a language L, \u03c6 an L-formula, and a \u00af {\\displaystyle {\\bar {a}}} a tuple of elements of the domain dom(A) of A. In other words, \u03d5 A , x , a \u00af {\\displaystyle \\phi ^{A,x,{\\bar {a}}}} denotes a (monadic) property defined on dom(A). In general, where x is replaced by an n-tuple x \u00af {\\displaystyle {\\bar {x}}} of free variables, \u03d5 A , x \u00af , a \u00af {\\displaystyle \\phi ^{A,{\\bar {x}},{\\bar {a}}}} denotes an n-ary relation defined on dom(A). Each quantifier Q A {\\displaystyle Q_{A}} is relativized to a structure, since each quantifier is viewed as a family of relations (between relations) on that structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "L-matrices have the additional property that all diagonal entries are greater than zero. M-matrices have several equivalent definitions, one of which is as follows: a Z-matrix is an M-matrix if it is nonsingular and its inverse is nonnegative. All matrices that are both Z-matrices and P-matrices are nonsingular M-matrices. In the context of quantum complexity theory, these are referred to as stoquastic operators.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a \"random variable\". Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, Kr\u00fcger rejects Davidson's claim that the argument can refute the correspondence theory of truth. Stephen Neale (1995) claims, controversially, that the most compelling version was suggested by Kurt G\u00f6del (1944). These arguments are sometimes modified to support the alternative, and evidently stronger, conclusion that there is only one fact, or one true proposition, state of affairs, truth condition, truthmaker, and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the absence of all three lines of evidence mentioned above, linguistic substrata may be difficult to detect. Substantial indirect evidence is needed to infer the former existence of a substrate. The nonexistence of a substrate is difficult to show, and to avoid digressing into speculation, burden of proof must lie on the side of the scholar claiming the influence of a substrate. The principle of uniformitarianism and results from the study of human genetics suggest that many languages have formerly existed that have since then been replaced under expansive language families, such as Indo-European, Afro-Asiatic, Uralic or Bantu.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a string metric (also known as a string similarity metric or string distance function) is a metric that measures distance (\"inverse similarity\") between two text strings for approximate string matching or comparison and in fuzzy string searching. A requirement for a string metric (e.g. in contrast to string matching) is fulfillment of the triangle inequality. For example, the strings \"Sam\" and \"Samuel\" can be considered to be close. A string metric provides a number indicating an algorithm-specific indication of distance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Increment 2c: Signed in January 2009. This extended the DII footprint into the above-Secret domain to support a number of key operations and intelligence initiatives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, 5G is the fifth-generation technology standard for broadband cellular networks, which cellular phone companies began deploying worldwide in 2019, and is the successor to 4G networks which provide connectivity to most current cellphones. Like its predecessors, 5G networks are cellular networks, in which the service area is divided into small geographical areas called cells. All 5G wireless devices in a cell are connected to the Internet and telephone network by radio waves through a local antenna in the cell.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "CFA was first developed by J\u00f6reskog (1969) and has built upon and replaced older methods of analyzing construct validity such as the MTMM Matrix as described in Campbell & Fiske (1959).In confirmatory factor analysis, the researcher first develops a hypothesis about what factors they believe are underlying the measures used (e.g., \"Depression\" being the factor underlying the Beck Depression Inventory and the Hamilton Rating Scale for Depression) and may impose constraints on the model based on these a priori hypotheses. By imposing these constraints, the researcher is forcing the model to be consistent with their theory. For example, if it is posited that there are two factors accounting for the covariance in the measures, and that these factors are unrelated to each other, the researcher can create a model where the correlation between factor A and factor B is constrained to zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The speed at which an innovation spreads through a mass of people depends on how favorably an idea is perceived by the audience. Innovations that are ill matched with existing techniques are not as well accepted and diffused through the group. Social structures are naturally designed in a hierarchy; thus, different ideas follow different routes or courses in the hierarchy, depending on the type and source of an innovation.The study of the diffusion of innovations has led to advancements in awareness of three important aspects of social change: the qualities of an innovation which lead to successful diffusion, the effect of peer networking and conversations when it comes to spreading ideas, and the importance of various \"user segments\" (Robinson).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the pulse contains more than one photon, then Eve can split off the extra photons and transmit the remaining single photon to Bob. This is the basis of the photon number splitting attack, where Eve stores these extra photons in a quantum memory until Bob detects the remaining single photon and Alice reveals the encoding basis. Eve can then measure her photons in the correct basis and obtain information on the key without introducing detectable errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More precisely, subresultants are defined for polynomials over any commutative ring R, and have the following property. Let \u03c6 be a ring homomorphism of R into another commutative ring S. It extends to another homomorphism, denoted also \u03c6 between the polynomials rings over R and S. Then, if P and Q are univariate polynomials with coefficients in R such that deg \u2061 ( P ) = deg \u2061 ( \u03c6 ( P ) ) {\\displaystyle \\deg(P)=\\deg(\\varphi (P))} and deg \u2061 ( Q ) = deg \u2061 ( \u03c6 ( Q ) ) , {\\displaystyle \\deg(Q)=\\deg(\\varphi (Q)),} then the subresultant polynomials and the principal subresultant coefficients of \u03c6(P) and \u03c6(Q) are the image by \u03c6 of those of P and Q. The subresultants have two important properties which make them fundamental for the computation on computers of the GCD of two polynomials with integer coefficients. Firstly, their definition through determinants allows bounding, through Hadamard inequality, the size of the coefficients of the GCD. Secondly, this bound and the property of good specialization allow computing the GCD of two polynomials with integer coefficients through modular computation and Chinese remainder theorem (see below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The duality gap is the difference of the right and left hand sides of the inequality sup y \u2217 \u2208 Y \u2217 \u2212 F \u2217 ( 0 , y \u2217 ) \u2264 inf x \u2208 X F ( x , 0 ) . {\\displaystyle \\sup _{y^{*}\\in Y^{*}}-F^{*}\\left(0,y^{*}\\right)\\leq \\inf _{x\\in X}F(x,0).} This principle is the same as weak duality. If the two sides are equal to each other, then the problem is said to satisfy strong duality. There are many conditions for strong duality to hold such as: F = F \u2217 \u2217 {\\displaystyle F=F^{**}} where F {\\displaystyle F} is the perturbation function relating the primal and dual problems and F \u2217 \u2217 {\\displaystyle F^{**}} is the biconjugate of F {\\displaystyle F} ; the primal problem is a linear optimization problem; Slater's condition for a convex optimization problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Given these, the following program unsoundly applies a function meant for integers to a Boolean value.The above program type checks using Hindley-Milner because c is given the type \u2200 \u03b1 . ( \u03b1 \u2192 \u03b1 ) r e f {\\textstyle \\forall \\alpha . (\\alpha \\to \\alpha )\\ {\\mathtt {ref}}} , which is then instantiated to be of the type ( i n t \u2192 i n t ) r e f {\\textstyle ({\\mathtt {int}}\\to {\\mathtt {int}})\\ {\\mathtt {ref}}} when typing the assignment c := (fn x => x + 1), and ( b o o l \u2192 b o o l ) r e f {\\textstyle ({\\mathtt {bool}}\\to {\\mathtt {bool}})\\ {\\mathtt {ref}}} ref when typing the dereference !c true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Unconditionally secure ideal quantum coin flipping was shown impossible by Lo and Chau. Moreover, Lo showed that there cannot be unconditionally secure quantum protocols for one-out-of-two oblivious transfer and other secure two-party computations. However, unconditionally secure relativistic protocols for coin flipping and bit-commitment have been shown by Kent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, s ( n ) = \u2211 d | n , d \u2260 n d . {\\displaystyle s(n)=\\sum \\nolimits _{d|n,\\ d\\neq n}d.} It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the clinical evaluation, clinical features are the classification method", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite. The impolite numbers are exactly the powers of two, and the polite numbers are the natural numbers that are not powers of two. Polite numbers have also been called staircase numbers because the Young diagrams which represent graphically the partitions of a polite number into consecutive integers (in the French notation of drawing these diagrams) resemble staircases. If all numbers in the sum are strictly greater than one, the numbers so formed are also called trapezoidal numbers because they represent patterns of points arranged in a trapezoid.The problem of representing numbers as sums of consecutive integers and of counting the number of representations of this type has been studied by Sylvester, Mason, Leveque, and many other more recent authors. The polite numbers describe the possible numbers of sides of the Reinhardt polygons.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is the federal drug law that regulates manufacture, importation, possession, use, and distribution of controlled substances. The legislation classes these substances into five schedules, with varying qualifications for each schedule. The schedules are designated schedule I, schedule II, schedule III, schedule IV, and schedule V. Many drugs require a prescription, even though they are not a controlled substance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The ResNet paper, however, provided strong experimental evidence of the benefits of going deeper than 20 layers. It argued that the identity mapping without modulation is crucial and mentioned that modulation in the skip connection can still lead to vanishing signals in forward and backward propagation (Section 3 in ). This is also why the forget gates of the 2000 LSTM were initially opened through positive bias weights: as long as the gates are open, it behaves like the 1997 LSTM.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern practice, a violation of the Compulsory Process Clause leads to the reversal of a conviction unless the original error is \"harmless\". This occurs because the exclusion of defense evidence can \"significantly undermine fundamental elements of the  defense\". The remedy is not automatic reversal only because not every Sixth Amendment error is automatically a Due Process error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the incompressibility method is a proof method like the probabilistic method, the counting method or the pigeonhole principle. To prove that an object in a certain class (on average) satisfies a certain property, select an object of that class that is incompressible. If it does not satisfy the property, it can be compressed by computable coding. Since it can be generally proven that almost all objects in a given class are incompressible, the argument demonstrates that almost all objects in the class have the property involved (not just the average). To select an incompressible object is ineffective, and cannot be done by a computer program. However, a simple counting argument usually shows that almost all objects of a given class can be compressed by only a few bits (are incompressible).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the distance is Euclidean distance, the rational quadratic covariance function is also isotropic. The rational quadratic covariance between two points separated by d distance units is given by C ( d ) = ( 1 + d 2 2 \u03b1 k 2 ) \u2212 \u03b1 {\\displaystyle C(d)={\\Bigg (}1+{\\frac {d^{2}}{2\\alpha k^{2}}}{\\Bigg )}^{-\\alpha }} where \u03b1 and k are non-negative parameters of the covariance. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", A n \u22a8 C {\\displaystyle A_{1},A_{2},...,A_{n}\\models C} . In other words, a system is sound when all of its theorems are tautologies. Soundness is among the most fundamental properties of mathematical logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a block matrix pseudoinverse is a formula for the pseudoinverse of a partitioned matrix. This is useful for decomposing or approximating many algorithms updating parameters in signal processing, which are based on the least squares method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most operating systems predating Unix, programs had to explicitly connect to the appropriate input and output devices. OS-specific intricacies caused this to be a tedious programming task. On many systems it was necessary to obtain control of environment settings, access a local file table, determine the intended data set, and handle hardware correctly in the case of a punch card reader, magnetic tape drive, disk drive, line printer, card punch, or interactive terminal. One of Unix's several groundbreaking advances was abstract devices, which removed the need for a program to know or care what kind of devices it was communicating with.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social media, a story is a function in which the user tells a narrative or provides status messages and information in the form of short, time-limited clips from several automatically running sequences. A story is usually displayed on a user's profile page and thus represents an audiovisual extension to the text-based status function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n \u2192 \u221e. In practice, a limit evaluation is considered to be approximately valid for large finite sample sizes too.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first rod was then carried to the end of the third, an operation to be repeated 1,370 times. The final measurement gave the length of the base as 27,404.01 ft. (8,352 metres).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the gcd-sum function, also called Pillai's arithmetical function, is defined for every n {\\displaystyle n} by P ( n ) = \u2211 k = 1 n gcd ( k , n ) {\\displaystyle P(n)=\\sum _{k=1}^{n}\\gcd(k,n)} or equivalently P ( n ) = \u2211 d \u2223 n d \u03c6 ( n / d ) {\\displaystyle P(n)=\\sum _{d\\mid n}d\\varphi (n/d)} where d {\\displaystyle d} is a divisor of n {\\displaystyle n} and \u03c6 {\\displaystyle \\varphi } is Euler's totient function. it also can be written as P ( n ) = \u2211 d \u2223 n d \u03c4 ( d ) \u03bc ( n / d ) {\\displaystyle P(n)=\\sum _{d\\mid n}d\\tau (d)\\mu (n/d)} where, \u03c4 {\\displaystyle \\tau } is the divisor function, and \u03bc {\\displaystyle \\mu } is the M\u00f6bius function. This multiplicative arithmetical function was introduced by the Indian mathematician Subbayya Sivasankaranarayana Pillai in 1933.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If prior distributions are available, then even an underdetermined system can be solved using the Bayesian MMSE estimator. In statistics, linear least squares problems correspond to a particularly important type of statistical model called linear regression which arises as a particular form of regression analysis. One basic form of such a model is an ordinary least squares model. The present article concentrates on the mathematical aspects of linear least squares problems, with discussion of the formulation and interpretation of statistical regression models and statistical inferences related to these being dealt with in the articles just mentioned. See outline of regression analysis for an outline of the topic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fibonacci actually lists several different methods for constructing Egyptian fraction representations. He includes the greedy method as a last resort for situations when several simpler methods fail; see Egyptian fraction for a more detailed listing of these methods. As Salzer (1948) details, the greedy method, and extensions of it for the approximation of irrational numbers, have been rediscovered several times by modern mathematicians, earliest and most notably by J. J. Sylvester (1880) A closely related expansion method that produces closer approximations at each step by allowing some unit fractions in the sum to be negative dates back to Lambert (1770). The expansion produced by this method for a number x {\\displaystyle x} is called the greedy Egyptian expansion, Sylvester expansion, or Fibonacci\u2013Sylvester expansion of x {\\displaystyle x} . However, the term Fibonacci expansion usually refers, not to this method, but to representation of integers as sums of Fibonacci numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of forensic linguistics, author profiling is used to identify characteristics of the author of anonymous, pseudonymous or forged text, based on the author's use of the language. Through linguistic analysis, forensic linguists seek to identify the suspect's motivation and ideology, along with other class features, such as the suspect's ethnicity or profession. While this does not always lead to decisive author identification, such information can help law enforcement narrow the pool of suspects.In most cases, author profiling in the context of forensic linguistics involves a single text problem, in which there is either no or few comparison texts available and no external evidence that points to the author. Examples of text analysed by forensic linguists include blackmailing letters, confessions, testaments, suicide letters and plagiarised writing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "that minimizes the expected loss. This is known as a generalized Bayes rule with respect to \u03c0 ( \u03b8 ) {\\displaystyle \\pi (\\theta )\\,\\!} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A matrix is said to be d-disjunct if no set of d columns has a boolean sum which is a superset of any other single column.The following relationships are \"well-known\": Every d + 1 \u00af {\\displaystyle {\\overline {d+1}}} -separable matrix is also d {\\displaystyle d} -disjunct. Every d {\\displaystyle d} -disjunct matrix is also d \u00af {\\displaystyle {\\overline {d}}} -separable. Every d \u00af {\\displaystyle {\\overline {d}}} -separable matrix is also d {\\displaystyle d} -separable (by definition).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical physics, the ternary commutator is an additional ternary operation on a triple system defined by  = a b c \u2212 a c b \u2212 b a c + b c a + c a b \u2212 c b a . {\\displaystyle =abc-acb-bac+bca+cab-cba.\\,} Also called the ternutator or alternating ternary sum, it is a special case of the n-commutator for n = 3, whereas the 2-commutator is the ordinary commutator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This results in a total of P {\\displaystyle P} parallel block transfers. A second approach needs O ( log \u2061 ( P ) ) {\\displaystyle O(\\log(P))} parallel block transfers and an additional block for each processor. The main idea is to schedule the write operations in a binary tree fashion and gradually combine the data into a single block.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In production, research, retail, and accounting, a cost is the value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore. In business, the cost may be one of acquisition, in which case the amount of money expended to acquire it is counted as cost. In this case, money is the input that is gone in order to acquire the thing. This acquisition cost may be the sum of the cost of production as incurred by the original producer, and further costs of transaction as incurred by the acquirer over and above the price paid to the producer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, we adjust all weights W ( k ) {\\displaystyle W(k)} by multiplying it by its benchmark factor F ( C ) {\\displaystyle F(C)} , for its cell C {\\displaystyle C} . The net result is that the estimated W {\\displaystyle W}  will now equal the benchmark target total T {\\displaystyle T} . But the more important benefit is that the estimate of the total of Y {\\displaystyle Y}  will tend to be more accurate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz. The term was applied to a group of objects that arise from a common axiomatization of certain structures and split into three families, which were introduced separately: M\u00f6bius planes, Laguerre planes, and Minkowski planes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By a similar argument, b \u2212 n = 1 / b n {\\displaystyle b^{-n}=1/b^{n}} . The properties of fractional exponents also follow from the same rule. For example, suppose we consider b {\\displaystyle {\\sqrt {b}}} and ask if there is some suitable exponent, which we may call r {\\displaystyle r} , such that b r = b {\\displaystyle b^{r}={\\sqrt {b}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "February 1, 1673, at a meeting of the Royal Society of London, he demonstrated his mechanical calculator. The curator of the experiments of the Society, Robert Hooke, carefully examined the device and even removed the back cover for this.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After finding that a few other networks, including some social and biological networks, also had heavy-tailed degree distributions, Barab\u00e1si and R\u00e9ka Albert coined the term \"scale-free network\" to describe the class of networks that exhibit a power-law degree distribution. However, studying seven examples of networks in social, economic, technological, biological, and physical systems, Amaral et al. were not able to find a scale-free network among these seven examples. Only one of these examples, the movie-actor network, had degree distribution P(k) following a power law regime for moderate k, though eventually this power law regime was followed by a sharp cutoff showing exponential decay for large k.Barab\u00e1si and R\u00e9ka Albert proposed a generative mechanism to explain the appearance of power-law distributions, which they called \"preferential attachment\" and which is essentially the same as that proposed by Price.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the rise of digital distribution, distinctions have become more tenuous. The biggest digital music distributor, the iTunes Store, only accepts releases with three tracks or fewer that are less than ten minutes each as a singles (with longer releases being classified as EPs or albums). However, releases which don't fit these criteria have been promoted as singles by artists and labels elsewhere, such as on the Bandcamp storefront. Historically, when mainstream music was purchased via vinyl records, singles would be released double-sided, i.e. there was an A-side and a B-side, on which two songs would appear, one on each side.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle P=\\{~\\{1,2\\},\\{3,4\\},\\{5,6\\},\\ldots \\}.} The deleted integer topology is defined by letting X = \u22c3 n \u2208 N ( n \u2212 1 , n ) \u2286 R {\\displaystyle X={\\begin{matrix}\\bigcup _{n\\in \\mathbb {N} }(n-1,n)\\subseteq \\mathbb {R} \\end{matrix}}} and P = { ( 0 , 1 ) , ( 1 , 2 ) , ( 2 , 3 ) , \u2026 } . {\\displaystyle P={\\left\\{(0,1),(1,2),(2,3),\\ldots \\right\\}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Kleene having switched from presenting his work in the terminology of Church-Kleene lambda definability, to that of G\u00f6del-Kleene recursiveness (partial recursive functions). In this transition, Kleene modified G\u00f6del's general recursive functions to allow for proofs of the unsolvability of problems in the Intuitionism of E. J. Brouwer. In his graduate textbook on logic, \"Church's thesis\" is introduced and basic mathematical results are demonstrated to be unrealizable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Further, a mathematician's claim could be undermined by counter-claims that he had not truly invented an idea, but merely improved on someone else's idea, an improvement that required little skill, and was based on facts that were already known.A series of high-profile disputes about the scientific priority of the 17th century \u2013 the era that the American science historian D. Meli called \"the golden age of the mud-slinging priority disputes\" \u2013 is associated with the name Leibniz. The first of them occurred at the beginning of 1673, during his first visit to London, when in the presence of the famous mathematician John Pell he presented his method of approximating series by differences. To Pell's remark that this discovery had already been made by Fran\u00e7ois Regnaud and published in 1670 in Lyon by Gabriel Mouton, Leibniz answered the next day.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A call setup procedure may fail due to a number of technical reasons. Such calls are classified as failed call attempts. In many practical cases, this definition needs to be further expanded with a number of detailed specifications describing which calls exactly are counted as successfully set up and which not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So, these languages usually allow arbitrary new elements to be created at any time. This choice precludes the implementation of array types as array data structures. That is, those languages use array-like syntax to implement a more general associative array semantics, and must therefore be implemented by a hash table or some other search data structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Linear least squares problems are convex and have a closed-form solution that is unique, provided that the number of data points used for fitting equals or exceeds the number of unknown parameters, except in special degenerate situations. In contrast, non-linear least squares problems generally must be solved by an iterative procedure, and the problems can be non-convex with multiple optima for the objective function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the balanced assignment problem, both parts of the bipartite graph have the same number of vertices, denoted by n. One of the first polynomial-time algorithms for balanced assignment was the Hungarian algorithm. It is a global algorithm \u2013 it is based on improving a matching along augmenting paths (alternating paths between unmatched vertices). Its run-time complexity, when using Fibonacci heaps, is O ( m n + n 2 log \u2061 n ) {\\displaystyle O(mn+n^{2}\\log n)} , where m is a number of edges. This is currently the fastest run-time of a strongly polynomial algorithm for this problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The argument x does not belong to the function, but the two together make a whole (ib. p. 6 \" (Russell 1903:505).)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the decade preceding Unix, computers had grown enormously in power \u2013 to the point where computer operators were looking for new ways to get people to use their spare time on their machines. One of the major developments during this era was time-sharing, whereby a number of users would get small slices of computer time, at a rate at which it appeared they were each connected to their own, slower, machine.The development of time-sharing systems led to a number of problems. One was that users, particularly at universities where the systems were being developed, seemed to want to hack the system to get more CPU time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Suppose that we estimate the regression model y = \u03b2 0 + \u03b2 1 x + u , {\\displaystyle y=\\beta _{0}+\\beta _{1}x+u,\\,} and obtain from this fitted model a set of values for u ^ {\\displaystyle {\\widehat {u}}} , the residuals. Ordinary least squares constrains these so that their mean is 0 and so, given the assumption that their variance does not depend on the independent variables, an estimate of this variance can be obtained from the average of the squared values of the residuals. If the assumption is not held to be true, a simple model might be that the variance is linearly related to independent variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A function f: D \u2192 R {\\displaystyle f\\colon D\\to \\mathbb {R} } is sequentially computable if, for every n {\\displaystyle n} -tuplet ( { x i 1 } i = 1 \u221e , \u2026 { x i n } i = 1 \u221e ) {\\displaystyle \\left(\\{x_{i\\,1}\\}_{i=1}^{\\infty },\\ldots \\{x_{i\\,n}\\}_{i=1}^{\\infty }\\right)} of computable sequences of real numbers such that ( \u2200 i ) ( x i 1 , \u2026 x i n ) \u2208 D , {\\displaystyle (\\forall i)\\quad (x_{i\\,1},\\ldots x_{i\\,n})\\in D\\qquad ,} the sequence { f ( x i ) } i = 1 \u221e {\\displaystyle \\{f(x_{i})\\}_{i=1}^{\\infty }} is also computable. This article incorporates material from Computable real function on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, it is possible to exploit data transport level parallelism by scheduling several data transports in the same instruction. An addition operation can be executed in a TTA processor as follows: r1 -> ALU.operand1 r2 -> ALU.add.trigger ALU.result -> r3 The second move, a write to the second operand of the function unit called ALU, triggers the addition operation. This makes the result of addition available in the output port 'result' after the execution latency of the 'add'. The ports associated with the ALU may act as an accumulator, allowing creation of macro instructions that abstract away the underlying TTA:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spoken Welsh, the word ddim (not) often occurs with a prefixed or mutated verb form that is negative in meaning: Dydy hi ddim yma (word-for-word, \"Not-is she not here\") expresses \"She is not here\" and Chaiff Aled ddim mynd (word-for-word, \"Not-will-get Aled not go\") expresses \"Aled is not allowed to go\". Negative correlatives can also occur with already negative verb forms. In literary Welsh, the mutated verb form is caused by an initial negative particle, ni or nid. The particle is usually omitted in speech but the mutation remains:  wyddai neb (word-for-word, \" not-knew nobody\") means \"Nobody knew\" and  chaiff Aled fawr o bres (word-for-word, \" not-will-get Aled lots of money\") means \"Aled will not get much money\". This is not usually regarded as three negative markers, however, because the negative mutation is really just an effect of the initial particle on the following word.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociology, structural cohesion is the conception of a useful formal definition and measure of cohesion in social groups. It is defined as the minimal number of actors in a social network that need to be removed to disconnect the group. It is thus identical to the question of the node connectivity of a given graph in discrete mathematics. The vertex-cut version of Menger's theorem also proves that the disconnection number is equivalent to a maximally sized group with a network in which every pair of persons has at least this number of separate paths between them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a strong prime is a prime number with certain special properties. The definitions of strong primes are different in cryptography and number theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hans Moravec wrote in 1988: I am confident that this bottom-up route to artificial intelligence will one day meet the traditional top-down route more than half way, ready to provide the real-world competence and the commonsense knowledge that has been so frustratingly elusive in reasoning programs. Fully intelligent machines will result when the metaphorical golden spike is driven uniting the two efforts. However, this is disputed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scholarly and scientific publishing, altmetrics are non-traditional bibliometrics proposed as an alternative or complement to more traditional citation impact metrics, such as impact factor and h-index. The term altmetrics was proposed in 2010, as a generalization of article level metrics, and has its roots in the #altmetrics hashtag. Although altmetrics are often thought of as metrics about articles, they can be applied to people, journals, books, data sets, presentations, videos, source code repositories, web pages, etc. Altmetrics use public APIs across platforms to gather data with open scripts and algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The goal is to find a maximum profit feasible solution. Mathematically the generalized assignment problem can be formulated as an integer program: maximize \u2211 i = 1 m \u2211 j = 1 n p i j x i j . subject to \u2211 j = 1 n w i j x i j \u2264 t i i = 1 , \u2026 , m ; \u2211 i = 1 m x i j \u2264 1 j = 1 , \u2026 , n ; x i j \u2208 { 0 , 1 } i = 1 , \u2026 , m , j = 1 , \u2026 , n ; {\\displaystyle {\\begin{aligned}{\\text{maximize }}&\\sum _{i=1}^{m}\\sum _{j=1}^{n}p_{ij}x_{ij}.\\\\{\\text{subject to }}&\\sum _{j=1}^{n}w_{ij}x_{ij}\\leq t_{i}&&i=1,\\ldots ,m;\\\\&\\sum _{i=1}^{m}x_{ij}\\leq 1&&j=1,\\ldots ,n;\\\\&x_{ij}\\in \\{0,1\\}&&i=1,\\ldots ,m,\\quad j=1,\\ldots ,n;\\end{aligned}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In general, if P ( s i ) {\\displaystyle \\;P(s_{i})} is the probability that our system is in state s i {\\displaystyle \\;s_{i}} , P ( s 1 ) P ( s 2 ) = \u03a9 R ( s 1 ) \u03a9 R ( s 2 ) . {\\displaystyle {\\frac {P(s_{1})}{P(s_{2})}}={\\frac {\\Omega _{R}(s_{1})}{\\Omega _{R}(s_{2})}}.} Since the entropy of the reservoir S R = k ln \u2061 \u03a9 R {\\displaystyle \\;S_{R}=k\\ln \\Omega _{R}} , the above becomes P ( s 1 ) P ( s 2 ) = e S R ( s 1 ) / k e S R ( s 2 ) / k = e ( S R ( s 1 ) \u2212 S R ( s 2 ) ) / k .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The requirement that the convex set K {\\displaystyle K} be compact can be weakened to give the following strengthened generalization version of the theorem. The property above is sometimes called quasicompactness or convex compactness. Compactness implies convex compactness because a topological space is compact if and only if every family of closed subsets having the finite intersection property (FIP) has non-empty intersection (that is, its kernel is not empty). The definition of convex compactness is similar to this characterization of compact spaces in terms of the FIP, except that it only involves those closed subsets that are also convex (rather than all closed subsets).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical computer science, a constant-recursive sequence is an infinite sequence of numbers where each number in the sequence is equal to a fixed linear combination of one or more of its immediate predecessors. A constant-recursive sequence is also known as a linear recurrence sequence, linear-recursive sequence, linear-recurrent sequence, a C-finite sequence, or a solution to a linear recurrence with constant coefficients. The most famous example of a constant-recursive sequence is the Fibonacci sequence 0 , 1 , 1 , 2 , 3 , 5 , 8 , 13 , \u2026 {\\displaystyle 0,1,1,2,3,5,8,13,\\ldots } , in which each number is the sum of the previous two. The power of two sequence 1 , 2 , 4 , 8 , 16 , \u2026 {\\displaystyle 1,2,4,8,16,\\ldots } is also constant-recursive because each number is the sum of twice the previous number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The analysis may also show one or more exception paths. An exception path is taken as the result of a fault condition. Use cases and the resulting interactions are commonly modeled in graphical languages such as the Unified Modeling Language (UML) or SysML.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle e(g^{a},g^{b})=e(g,g)^{ab}=e(g,g^{ab}).} Thus, if h = g a b {\\displaystyle h=g^{ab}} , then the values e ( g a , g b ) {\\displaystyle e(g^{a},g^{b})} and e ( g , h ) {\\displaystyle e(g,h)} will be equal. Since this cryptographic assumption, essential to building ElGamal encryption and signatures, does not hold in this case, new assumptions are needed to build cryptography in symmetric bilinear groups. The DLIN assumption is a modification of Diffie-Hellman type assumptions to thwart the above attack.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Concrete datatypes have their representation as part of their name. Abstract datatypes are structures of concrete datatypes \u2014 with a new name assigned. For example, a list of integers could be called integer_list.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to do so, they applied the scientific method to human behavior. The first published study in the field was Norman Triplett's 1898 experiment on the phenomenon of social facilitation. These psychological experiments later went on to form the foundation of much of 20th century social psychological findings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "14. Identifying operational rules defining the use of the concept, which can be stated in a language and which cover all or most cases (material conditional). 15.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace\u2013Stieltjes transform. They were first introduced by David Cox in 1955 as distributions with rational Laplace\u2013Stieltjes transforms.The probability density function is f ( x ) = \u03b1 e x T s for x \u2265 0 {\\displaystyle f(x)=\\mathbf {\\alpha } e^{x\\,T}\\mathbf {s} {\\text{ for }}x\\geq 0} (and 0 when x < 0), and the cumulative distribution function is F ( t ) = 1 \u2212 \u03b1 e A t 1 {\\displaystyle F(t)=1-\\alpha e^{{\\textbf {A}}t}{\\textbf {1}}} where 1 is a vector of 1s and \u03b1 \u2208 R 1 \u00d7 n , T \u2208 R n \u00d7 n , s \u2208 R n \u00d7 1 . {\\displaystyle {\\begin{aligned}\\alpha &\\in \\mathbb {R} ^{1\\times n},\\\\T&\\in \\mathbb {R} ^{n\\times n},\\\\s&\\in \\mathbb {R} ^{n\\times 1}.\\end{aligned}}} There are no restrictions on the parameters \u03b1, T, s other than that they correspond to a probability distribution. There is no straightforward way to ascertain if a particular set of parameters form such a distribution. The dimension of the matrix T is the order of the matrix-exponential representation.The distribution is a generalisation of the phase-type distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Halpern\u2013L\u00e4uchli theorem is a partition result about finite products of infinite trees. Its original purpose was to give a model for set theory in which the Boolean prime ideal theorem is true but the axiom of choice is false. It is often called the Halpern\u2013L\u00e4uchli theorem, but the proper attribution for the theorem as it is formulated below is to Halpern\u2013L\u00e4uchli\u2013Laver\u2013Pincus or HLLP (named after James D. Halpern, Hans L\u00e4uchli, Richard Laver, and David Pincus), following Milliken (1979). Let d,r < \u03c9, \u27e8 T i: i \u2208 d \u27e9 {\\displaystyle \\langle T_{i}:i\\in d\\rangle } be a sequence of finitely splitting trees of height \u03c9. Let \u22c3 n \u2208 \u03c9 ( \u220f i < d T i ( n ) ) = C 1 \u222a \u22ef \u222a C r , {\\displaystyle \\bigcup _{n\\in \\omega }\\left(\\prod _{i", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, the view of the universe and its workings as the ebb and flow of information was first observed by Wheeler. Consequently, two views of the world emerged: the first one proposes that the universe is a quantum computer, while the other one proposes that the system performing the simulation is distinct from its simulation (the universe). Of the former view, quantum-computing specialist Dave Bacon wrote, In many respects this point of view may be nothing more than a result of the fact that the notion of computation is the disease of our age\u2014everywhere we look today we see examples of computers, computation, and information theory and thus we extrapolate this to our laws of physics. Indeed, thinking about computing as arising from faulty components, it seems as if the abstraction that uses perfectly operating computers is unlikely to exist as anything but a platonic ideal. Another critique of such a point of view is that there is no evidence for the kind of digitization that characterizes computers nor are there any predictions made by those who advocate such a view that have been experimentally confirmed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although more advanced algorithms such as simulated annealing or tabu search may give better results, in some situations hill climbing works just as well. Hill climbing can often produce a better result than other algorithms when the amount of time available to perform a search is limited, such as with real-time systems, so long as a small number of increments typically converges on a good solution (the optimal solution or a close approximation). At the other extreme, bubble sort can be viewed as a hill climbing algorithm (every adjacent element exchange decreases the number of disordered element pairs), yet this approach is far from efficient for even modest N, as the number of exchanges required grows quadratically. Hill climbing is an anytime algorithm: it can return a valid solution even if it's interrupted at any time before it ends.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Workshop on Mechanized Metatheory is the main meeting of researchers participating in the challenge. The design of the POPLmark benchmark is guided by features common to reasoning about programming languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a random variable Y {\\displaystyle Y} is said to be mean independent of random variable X {\\displaystyle X} if and only if its conditional mean E ( Y | X = x ) {\\displaystyle E(Y|X=x)} equals its (unconditional) mean E ( Y ) {\\displaystyle E(Y)} for all x {\\displaystyle x} such that the probability density/mass of X {\\displaystyle X} at x {\\displaystyle x} , f X ( x ) {\\displaystyle f_{X}(x)} , is not zero. Otherwise, Y {\\displaystyle Y} is said to be mean dependent on X {\\displaystyle X} . Stochastic independence implies mean independence, but the converse is not true. ; moreover, mean independence implies uncorrelatedness while the converse is not true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Latin alphabet, is a theorem from probability, and is also frequently used in analysis. Heuristically, it says that if we pick N {\\displaystyle N} complex numbers x 1 , \u2026 , x N \u2208 C {\\displaystyle x_{1},\\dots ,x_{N}\\in \\mathbb {C} } , and add them together each multiplied by a random sign \u00b1 1 {\\displaystyle \\pm 1} , then the expected value of the sum's modulus, or the modulus it will be closest to on average, will be not too far off from | x 1 | 2 + \u22ef + | x N | 2 {\\displaystyle {\\sqrt {|x_{1}|^{2}+\\cdots +|x_{N}|^{2}}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In ring theory, a branch of abstract algebra, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is a function f: R \u2192 S such that f is: addition preserving: f ( a + b ) = f ( a ) + f ( b ) {\\displaystyle f(a+b)=f(a)+f(b)} for all a and b in R,multiplication preserving: f ( a b ) = f ( a ) f ( b ) {\\displaystyle f(ab)=f(a)f(b)} for all a and b in R,and unit (multiplicative identity) preserving: f ( 1 R ) = 1 S {\\displaystyle f(1_{R})=1_{S}} .Additive inverses and the additive identity are part of the structure too, but it is not necessary to require explicitly that they too are respected, because these conditions are consequences of the three conditions above. If in addition f is a bijection, then its inverse f\u22121 is also a ring homomorphism. In this case, f is called a ring isomorphism, and the rings R and S are called isomorphic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a multiplicative partition or unordered factorization of an integer n {\\displaystyle n} is a way of writing n {\\displaystyle n} as a product of integers greater than 1, treating two products as equivalent if they differ only in the ordering of the factors. The number n {\\displaystyle n} is itself considered one of these products. Multiplicative partitions closely parallel the study of multipartite partitions, which are additive partitions of finite sequences of positive integers, with the addition made pointwise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Dow Jones Industrial Average and the S&P 500 primarily track U.S. markets, though some legacy international companies are included. The consumer price index tracks the variation in prices for different consumer goods and services over time in a constant geographical location and is integral to calculations used to adjust salaries, bond interest rates, and tax thresholds for inflation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical decision theory, where we are faced with the problem of estimating a deterministic parameter (vector) \u03b8 \u2208 \u0398 {\\displaystyle \\theta \\in \\Theta } from observations x \u2208 X , {\\displaystyle x\\in {\\mathcal {X}},} an estimator (estimation rule) \u03b4 M {\\displaystyle \\delta ^{M}\\,\\!} is called minimax if its maximal risk is minimal among all estimators of \u03b8 {\\displaystyle \\theta \\,\\!} . In a sense this means that \u03b4 M {\\displaystyle \\delta ^{M}\\,\\!} is an estimator which performs best in the worst possible case allowed in the problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the graph Fourier transform is a mathematical transform which eigendecomposes the Laplacian matrix of a graph into eigenvalues and eigenvectors. Analogously to the classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what is known as a graph Fourier basis. The Graph Fourier transform is important in spectral graph theory. It is widely applied in the recent study of graph structured learning algorithms, such as the widely employed convolutional networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other words, the \"traditional spaces\" are homogeneous spaces; but not for a uniquely determined group. Changing the group changes the appropriate geometric language. In today's language, the groups concerned in classical geometry are all very well known as Lie groups: the classical groups. The specific relationships are quite simply described, using technical language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In negotiating a connection, an RTMP client sends and receives a data stream containing multiple elements, as a single command line. An on-demand stream typically includes the following elements:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the experimental sciences, data collected from experiments are often visualized by a graph. For example, if one collects data on the speed of an object at certain points in time, one can visualize the data in a data table such as the following: Such a table representation of data is a great way to display exact values, but it can prevent the discovery and understanding of patterns in the values. In addition, a table display is often erroneously considered to be an objective, neutral collection or storage of the data (and may in that sense even be erroneously considered to be the data itself) whereas it is in fact just one of various possible visualizations of the data. Understanding the process described by the data in the table is aided by producing a graph or line chart of speed versus time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence, it is not possible to carry out this computation in polynomial time on a Turing machine, but it is possible to compute it by polynomially many arithmetic operations. However, for the first condition, there are algorithms that run in a number of Turing machine steps bounded by a polynomial in the length of binary-encoded input, but do not take a number of arithmetic operations bounded by a polynomial in the number of input numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "6. The continuous envelope Env C A {\\displaystyle {\\text{Env}}_{\\cal {C}}A} of a stereotype algebra A {\\displaystyle A} is an envelope of A {\\displaystyle A} in the category InvSteAlg {\\displaystyle {\\text{InvSteAlg}}} of all involutive stereotype algebras in the class DEpi {\\displaystyle {\\text{DEpi}}} of all dense epimorphisms in InvSteAlg {\\displaystyle {\\text{InvSteAlg}}} with respect to the class C \u2217 {\\displaystyle {\\text{C}}^{*}} of all C*-algebras: Env C A = Env C \u2217 DEpi A . {\\displaystyle {\\text{Env}}_{\\cal {C}}A={\\text{Env}}_{{\\text{C}}^{*}}^{\\text{DEpi}}A.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Mathematically, h ( p , u \u00af ) = arg \u2061 min x \u2211 i p i x i {\\displaystyle h(p,{\\bar {u}})=\\arg \\min _{x}\\sum _{i}p_{i}x_{i}} s u b j e c t t o u ( x ) \u2265 u \u00af {\\displaystyle {\\rm {subject~to}}\\ \\ u(x)\\geq {\\bar {u}}} .where h(p,u) is the Hicksian demand function, or commodity bundle demanded, at price vector p and utility level u \u00af {\\displaystyle {\\bar {u}}} . Here p is a vector of prices, and x is a vector of quantities demanded, so the sum of all pixi is total expenditure on all goods. (Note that if there is more than one vector of quantities that minimizes expenditure for the given utility, we have a Hicksian demand correspondence rather than a function.) Hicksian demand functions are useful for isolating the effect of relative prices on quantities demanded of goods, in contrast to Marshallian demand functions, which combine that with the effect of the real income of the consumer being reduced by a price increase, as explained below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Lehmer's totient problem asks whether there is any composite number n such that Euler's totient function \u03c6(n) divides n \u2212 1. This is an unsolved problem. It is known that \u03c6(n) = n \u2212 1 if and only if n is prime. So for every prime number n, we have \u03c6(n) = n \u2212 1 and thus in particular \u03c6(n) divides n \u2212 1. D. H. Lehmer conjectured in 1932 that there are no composite numbers with this property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Hausdorff distance is the longest distance you can be forced to travel by an adversary who chooses a point in one of the two sets, from where you then must travel to the other set. In other words, it is the greatest of all the distances from a point in one set to the closest point in the other set. This distance was first introduced by Hausdorff in his book Grundz\u00fcge der Mengenlehre, first published in 1914, although a very close relative appeared in the doctoral thesis of Maurice Fr\u00e9chet in 1906, in his study of the space of all continuous curves from  \u2192 R 3 {\\displaystyle \\to \\mathbb {R} ^{3}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares.Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see Ordinary least squares \u00a7 Reduced chi-squared)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Naturality here means that there are natural isomorphisms between the pair of functors C ( F \u2212 , X ): D \u2192 S e t {\\displaystyle {\\mathcal {C}}(F-,X):{\\mathcal {D}}\\to \\mathrm {Set} } and D ( \u2212 , G X ): D \u2192 S e t {\\displaystyle {\\mathcal {D}}(-,GX):{\\mathcal {D}}\\to \\mathrm {Set} } for a fixed X {\\displaystyle X} in C {\\displaystyle {\\mathcal {C}}} , and also the pair of functors C ( F Y , \u2212 ): C \u2192 S e t {\\displaystyle {\\mathcal {C}}(FY,-):{\\mathcal {C}}\\to \\mathrm {Set} } and D ( Y , G \u2212 ): C \u2192 S e t {\\displaystyle {\\mathcal {D}}(Y,G-):{\\mathcal {C}}\\to \\mathrm {Set} } for a fixed Y {\\displaystyle Y} in D {\\displaystyle {\\mathcal {D}}} . The functor F {\\displaystyle F} is called a left adjoint functor or left adjoint to G {\\displaystyle G} , while G {\\displaystyle G} is called a right adjoint functor or right adjoint to F {\\displaystyle F} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of computer technology, it is known that using one-time authorization code (OTAC) through email, in a broad sense, and using one-time authorization code (OTAC) through web-application, in a professional sense. An email is one of the common ways of using OTACs. There are two main methods used. With the first method, a service provider sends a personalised one time URL to an authenticated email address e.g. @ucl.ac.uk; when the user clicks the URL, the server authenticates the user.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and multivariate statistics, the centering matrix is a symmetric and idempotent matrix, which when multiplied with a vector has the same effect as subtracting the mean of the components of the vector from every component of that vector.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Various properties of relations are investigated. A relation R is reflexive if xRx holds for all x, and irreflexive if xRx holds for no x. It is symmetric if xRy always implies yRx, and asymmetric if xRy implies that yRx is impossible. It is transitive if xRy and yRz always implies xRz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends on the domain and other properties of the function being transformed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additional performance can be wrung from systems by examining the instructions to find ones that operate on different types of data and adding units dedicated to that sort of data; this has led to the introduction of floating point units and, more recently, single instruction, multiple data (SIMD) units. The drawback to this approach is that it makes the CPU less generic; feeding the CPU with a program that uses almost all floating point instructions, for instance, will bog the FPUs while the other units sit idle. A more recent problem in modern CPU designs is the delay talking to the registers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The comparison tree representing binary search has the fewest levels possible as every level above the lowest level of the tree is filled completely. Otherwise, the search algorithm can eliminate few elements in an iteration, increasing the number of iterations required in the average and worst case. This is the case for other search algorithms based on comparisons, as while they may work faster on some target values, the average performance over all elements is worse than binary search. By dividing the array in half, binary search ensures that the size of both subarrays are as similar as possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The implication is that it is the currency of the popularity that confers value, rather than any intrinsic quality of the music itself, or of popularity at previous times. If it is the case, a novelty in itself \u2013 though not necessarily all forms of novelty \u2013 is a key aspect of evaluation. In those cases, if a statement comparing two art forms does mention their respective states of novelty, there is no fallacy (e.g. \"Song A is currently a much better bet for your party than song B. \").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In primary-based local-write protocols, primary copy moves between processes willing to perform an update. To update a data item, a process first moves it to its location. As a result, in this approach, successive write operations can be performed locally while each process can read their local copy of data items.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If function 1 does not send data to any of the other functions, the rest of the boxes to right of function 1 would be empty. If function 2 sends data to function 3 and function 5, then the data elements would be placed in the first and third boxes to the right of function 2. If any function sends data back to a previous function, then the associated box to the left of the function would have the data elements placed in it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In survey methodology, systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equiprobability method. In this approach, progression through the list is treated circularly, with a return to the top once the list ends. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, is the sampling interval (sometimes known as the skip): this is calculated as: k = N n {\\displaystyle k={\\frac {N}{n}}} where n is the sample size, and N is the population size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, trade secrets are not protected by law in the same manner as patents or trademarks. Historically, trademarks and patents are protected under federal statutes, the Lanham Act and Patent Act, respectively, while trade secrets are usually protected under state laws, and most states have enacted the Uniform Trade Secrets Act (UTSA), except for Massachusetts, New York, and North Carolina. However, since 2016 this situation changed with the enactment of the Defend Trade Secrets Act (DTSA), making trade secrets also protectable under a federal law. One of the differences between patents and trademarks, on the one hand, and trade secrets, on the other, is that a trade secret is protected only when the owner has taken reasonable measures to protect the information as a secret (see 18 U.S.C.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is the amount by which some of the notes produced in Pythagorean tuning were flattened or sharpened to produce just minor and major thirds. In Pythagorean tuning, the only highly consonant intervals were the perfect fifth and its inversion, the perfect fourth. The Pythagorean major third (81:64) and minor third (32:27) were dissonant, and this prevented musicians from freely using triads and chords, forcing them to write music with relatively simple texture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A number of key difficulties had been methodologically analyzed in the 1990s, including gradient diminishing and weak temporal correlation structure in the neural predictive models. All these difficulties were in addition to the lack of big training data and big computing power in these early days. Most speech recognition researchers who understood such barriers hence subsequently moved away from neural nets to pursue generative modeling approaches until the recent resurgence of deep learning starting around 2009\u20132010 that had overcome all these difficulties. Hinton et al. and Deng et al. reviewed part of this recent history about how their collaboration with each other and then with colleagues across four groups (University of Toronto, Microsoft, Google, and IBM) ignited a renaissance of applications of deep feedforward neural networks to speech recognition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In medicine, the mean arterial pressure (MAP) is an average calculated blood pressure in an individual during a single cardiac cycle. Although methods of estimating MAP vary, a common calculation is to take one-third of the pulse pressure (the difference between the systolic and diastolic pressures), and add that amount to the diastolic pressure. A normal MAP is about 90 mmHg.MAP is altered by cardiac output and systemic vascular resistance. It is used clinically to estimate the risk of cardiovascular diseases, where a MAP of 90 mmHg or less is low risk, and a MAP of greater than 96 mmHg represents \"stage one hypertension\" with increased risk.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the book, Moore argued that arrogance prevents humans from recognizing their kinship with nonhuman animals and grievously mistreating them, likening their \"provincialist\" attitude to chauvinism and racism: The denial by human animals of ethical relations to the rest of the animal world is a phenomenon not differing either in character or cause from the denial of ethical relations by a tribe, people, or race of human beings to the rest of the human world. : 276 Moore criticized the anthropocentrism of human beings, who \"think of our acts toward non-human peoples  entirely from the human point of view. We never take the time to put ourselves in the places of our victims.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, deterministic parsing refers to parsing algorithms that do not backtrack. LR-parsers are an example. (This meaning of the words \"deterministic\" and \"non-deterministic\" differs from that used to describe nondeterministic algorithms.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The AI then creates and executes whatever plan is calculated to maximize the value of its objective function. For example, AlphaZero chess has a simple objective function of \"+1 if AlphaZero wins, -1 if AlphaZero loses\". During the game, AlphaZero attempts to execute whatever sequence of moves it judges most likely to give the maximum value of +1. Similarly, a reinforcement learning system can have a \"reward function\" that allows the programmers to shape the AI's desired behavior. An evolutionary algorithm's behavior is shaped by a \"fitness function\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following a brief description of applicable rules organized by source.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sensitivity (or recall) is the ability of a test to correctly identify the people with disease. Specificity is the ability of the test to correctly identify those without the disease. Now presume two tests are performed on the same group of patients.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a left-truncatable prime is a prime number which, in a given base, contains no 0, and if the leading (\"left\") digit is successively removed, then all resulting numbers are prime. For example, 9137, since 9137, 137, 37 and 7 are all prime. Decimal representation is often assumed and always used in this article. A right-truncatable prime is a prime which remains prime when the last (\"right\") digit is successively removed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It allows one to deduce many properties of concrete computational complexity measures, such as time complexity or space complexity, from properties of axiomatically defined measures. In algorithmic information theory, the Kolmogorov complexity (also called descriptive complexity, algorithmic complexity or algorithmic entropy) of a string is the length of the shortest binary program that outputs that string. Minimum message length is a practical application of this approach.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set. The IFS described is composed of contractions whose images, as a collage or union when mapping the given set, are arbitrarily close to the given set. It is typically used in fractal compression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since there are only countably many computable relations, there are also only countably many computable ordinals. Thus, \u03c9 1 C K {\\displaystyle \\omega _{1}^{CK}} is countable. The computable ordinals are exactly the ordinals that have an ordinal notation in Kleene's O {\\displaystyle {\\mathcal {O}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(See also partition function). This general result of the Gibbs algorithm is then a maximum entropy probability distribution. Statisticians identify such distributions as belonging to exponential families. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, Stone's method, also known as the strongly implicit procedure or SIP, is an algorithm for solving a sparse linear system of equations. The method uses an incomplete LU decomposition, which approximates the exact LU decomposition, to get an iterative solution of the problem. The method is named after Harold S. Stone, who proposed it in 1968. The LU decomposition is an excellent general-purpose linear equation solver.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Deutsch\u2013Jozsa problem, we are given a black box quantum computer known as an oracle that implements some function: f: { 0 , 1 } n \u2192 { 0 , 1 } {\\displaystyle f\\colon \\{0,1\\}^{n}\\rightarrow \\{0,1\\}} The function takes n-bit binary values as input and produces either a 0 or a 1 as output for each such value. We are promised that the function is either constant (0 on all inputs or 1 on all inputs) or balanced (1 for exactly half of the input domain and 0 for the other half). The task then is to determine if f {\\displaystyle f} is constant or balanced by using the oracle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Several different clustering systems based on mutual information have been proposed. One is Marina Meil\u0103's variation of information metric; another provides hierarchical clustering. Using genetic algorithms, a wide range of different fit-functions can be optimized, including mutual information. Also belief propagation, a recent development in computer science and statistical physics, has led to the creation of new types of clustering algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The data sources include, in particular: Revision Control, also known as version control. In this system every step of each individual developer is tracked for the entire life cycle of the software system. The data describes: \u201cWhich developer changed what when.\u201d This data provides a basis for answering the question, \u201cWhat effort or development cost has been invested in which areas of code?\u201d Prominent revision control systems are Subversion, Git, Perforce, Mercurial, Synergy, ClearCase, \u2026 Software Test Systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Miracle Octad Generator, or MOG, is a mathematical tool introduced by Rob T. Curtis for studying the Mathieu groups, binary Golay code and Leech lattice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When considering race as a predictor for perceived popularity by asking a class how popular and important each other person is, African American students were rated most popular by their peers. Popularity in race was found to be correlated with athleticism, and because African Americans have a stereotype of being better at sports than individuals of other races, they are viewed as more popular. Additionally, White and Hispanic children were rated as more popular the better they succeeded in school and came from a higher socioeconomic background. No single factor can explain popularity, but instead the interaction between many factors such as race and athleticism vs. academics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A Russell-style universe is a type whose terms are types. A Tarski-style universe is a type together with an interpretation operation allowing us to regard its terms as types.For example: The openendedness of Martin-L\u00f6f type theory is particularly manifest in the introduction of so-called universes. Type universes encapsulate the informal notion of reflection whose role may be explained as follows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States and Canada, callers pay the cost of connecting to the Gateway MSC of the subscriber's phone company, regardless of the actual location of the phone. As mobile numbers are given standard geographic numbers according to the North American Numbering Plan, callers pay the same to reach fixed phones and mobile phones in a given geographic area. Mobile subscribers pay for the connection time (typically using in-plan or prepaid minutes) for both incoming and outgoing calls. For outgoing calls, any long distance charges are billed as if they originate at the GMSC, even though it is the visiting MSC that completes the connection to the PSTN.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Rules come in three types: formatting rules such as hiding or coloring a control, validation rules (e.g. allow only a nine-digit number), and action rules such as setting a field's value based on other fields. Rules can be triggered either by a user action such as clicking a button or by the evaluation of various conditions such as field values. For example, a conditional rule could be: \"Set field 'Total' to 100 when field 'field1' is not blank\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of a relational database, a row\u2014also called a tuple\u2014represents a single, implicitly structured data item in a table. In simple terms, a database table can be thought of as consisting of rows and columns. Each row in a table represents a set of related data, and every row in the table has the same structure. For example, in a table that represents companies, each row would represent a single company.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The work De musica by Johannes Cotto (also known as John Cotton or Johannes Afflighemensis) was illustrated with the blacksmith scene around 1250 by an anonymous book illuminator in the Cistercian Abbey of Aldersbach.Among the medieval music theorists who told the legend of the forge according to Boethius' version, were also Juan Gil de Z\u00e1mora (Johannes Aegidius von Zamora), active in the late 13th and early 14th centuries, Johannes de Muris and Simon Tunstede in the 14th century, and Adam von Fulda on the threshold of the early modern period in the 15th century. As an opponent of the Pythagorean conception, which held that consonances were based on certain numerical ratios, Johannes de Grocheio emerged in the 13th century, starting from an Aristotelian perspective. Although he explicitly stated that Pythagoras had discovered the principles of music, and he told the legend of the forge citing Boethius, whom he considered trustworthy, he rejected the Pythagorean theory of consonance, which he wanted to reduce to a merely metaphorical expression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In paleobotany, two terms were formerly used in the codes of nomenclature, \"form genera\" and \"organ genera\", to mean groups of fossils of a particular part of a plant, such as a leaf or seed, whose parent plant is not known because the fossils were preserved unattached to the parent plant. A later term \"morphotaxa\" also allows for differences in preservational state. These three terms have been replaced as of 2011 by provisions for \"fossil-taxa\" that are more similar to the provisions for other types of plants.Names given to organ genera could only be applied to the organs in question, and could not be extended to the entire organism. Fossil-taxon names can cover several parts of an organism, or several preservational states, but do not compete for priority with any names for the same organism that are based on a non-fossil type.The part of the plant was often, but not universally, indicated by the use of a suffix in the generic name: wood fossils may have generic names ending in -xylon leaf fossils generic names ending in -phyllum fruit fossils generic names ending in -carpon, -carpum or -carpus pollen fossils generic names ending in -pollis or -pollenoides.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physical security and information security, access control (AC) is the selective restriction of access to a place or other resource, while access management describes the process. The act of accessing may mean consuming, entering, or using. Permission to access a resource is called authorization. Locks and login credentials are two analogous mechanisms of access control.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and econometrics, a distributed lag model is a model for time series data in which a regression equation is used to predict current values of a dependent variable based on both the current values of an explanatory variable and the lagged (past period) values of this explanatory variable.The starting point for a distributed lag model is an assumed structure of the form y t = a + w 0 x t + w 1 x t \u2212 1 + w 2 x t \u2212 2 + . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the ARM processor architecture, 26-bit refers to the design used in the original ARM processors where the Program Counter (PC) and Processor Status Register (PSR) were combined into one 32-bit register (R15), the status flags filling the high 6 bits and the Program Counter taking up the lower 26 bits. In fact, because the program counter is always word-aligned the lowest two bits are always zero which allowed the designers to reuse these two bits to hold the processor's mode bits too. The four modes allowed were USR26, SVC26, IRQ26, FIQ26; contrast this with the 32 possible modes available when the program status was separated from the program counter in more recent ARM architectures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is no specific requirement for any particular transmission mode on the older bands, but in practice many legacy phones also have digital features such as DSSS and FHSS. Some cordless phones formerly advertised as 5.8 GHz actually transmit from base to phone on 5.8 GHz and transmit from phone to base on 2.4 GHz or 900 MHz, to conserve battery life. The 1.9 GHz band is used by the DECT 6.0 phone standard and is considered more secure than the other shared frequencies. The vast majority of new cordless phone devices sold in North America, whether connected by landline or to mobile phones (usually via Bluetooth), now use DECT 6.0. However, DECT 6.0's late start compared to DECT elsewhere has led to a large installed base of legacy cordless phones using other frequencies, many of which remain in use today despite increasingly common interference with the ever growing use of Wi-Fi, Bluetooth and other unlicensed digital radio standards, especially at 2.4 GHz and 5.8 GHz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. Any connected graph without simple cycles is a tree. A tree data structure simulates a hierarchical tree structure with a set of linked nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A 1983 anthology edited by Peter Achinstein provided a concise presentation by prominent philosophers on scientific evidence, including Carl Hempel (on the logic of confirmation), R. B. Braithwaite (on the structure of a scientific system), Norwood Russell Hanson (on the logic of discovery), Nelson Goodman (of grue fame, on a theory of projection), Rudolf Carnap (on the concept of confirming evidence), Wesley C. Salmon (on confirmation and relevance), and Clark Glymour (on relevant evidence). In 1990, William Bechtel provided four factors (clarity of the data, replication by others, consistency with results arrived at by alternative methods, and consistency with plausible theories of mechanisms) that biologists used to settle controversies about procedures and reliability of evidence.In 2001, Achinstein published his own book on the subject titled The Book of Evidence, in which, among other topics, he distinguished between four concepts of evidence: epistemic-situation evidence (evidence relative to a given epistemic situation), subjective evidence (considered to be evidence by a particular person at a particular time), veridical evidence (a good reason to believe that a hypothesis is true), and potential evidence (a good reason to believe that a hypothesis is highly probable). Achinstein defined all his concepts of evidence in terms of potential evidence, since any other kind of evidence must at least be potential evidence, and he argued that scientists mainly seek veridical evidence but they also use the other concepts of evidence, which rely on a distinctive concept of probability, and Achinstein contrasted this concept of probability with previous probabilistic theories of evidence such as Bayesian, Carnapian, and frequentist.Simplicity is one common philosophical criterion for scientific theories.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, Kruskal's most influential work is his seminal contribution to the formulation of multidimensional scaling. In computer science, his best known work is Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph. The algorithm first orders the edges by weight and then proceeds through the ordered list adding an edge to the partial MST provided that adding the new edge does not create a cycle. Minimal spanning trees have applications to the construction and pricing of communication networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The UNIVAC 1050 was an internally programmed computer with up to 32K of six-bit character memory, which was introduced in 1963. It was a one-address machine with 30-bit instructions, had a 4K operating system and was programmed in the PAL assembly language. The 1050 was used extensively by the U.S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory\u2014an active mathematical discipline\u2014studies groups in their own right. To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2368, 12368, 23468, and 123468 are the patterns related to Braille pattern dots-1256, since the two additional dots of kantenji patterns 01256, 12567, and 012567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural and social science research, a protocol is most commonly a predefined procedural method in the design and implementation of an experiment. Protocols are written whenever it is desirable to standardize a laboratory method to ensure successful replication of results by others in the same laboratory or by other laboratories. Additionally, and by extension, protocols have the advantage of facilitating the assessment of experimental results through peer review. In addition to detailed procedures, equipment, and instruments, protocols will also contain study objectives, reasoning for experimental design, reasoning for chosen sample sizes, safety precautions, and how results were calculated and reported, including statistical analysis and any rules for predefining and documenting excluded data to avoid bias.Similarly, a protocol may refer to the procedural methods of health organizations, commercial laboratories, manufacturing plants, etc. to ensure their activities (e.g., blood testing at a hospital, testing of certified reference materials at a calibration laboratory, and manufacturing of transmission gears at a facility) are consistent to a specific standard, encouraging safe use and accurate results.Finally, in the field of social science, a protocol may also refer to a \"descriptive record\" of observed events or a \"sequence of behavior\" of one or more organisms, recorded during or immediately after an activity (e.g., how an infant reacts to certain stimuli or how gorillas behave in natural habitat) to better identify \"consistent patterns and cause-effect relationships.\" These protocols may take the form of hand-written journals or electronically documented media, including video and audio capture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most practical cases, the stated prior data or testable information is given by a set of conserved quantities (average values of some moment functions), associated with the probability distribution in question. This is the way the maximum entropy principle is most often used in statistical thermodynamics. Another possibility is to prescribe some symmetries of the probability distribution. The equivalence between conserved quantities and corresponding symmetry groups implies a similar equivalence for these two ways of specifying the testable information in the maximum entropy method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Semantic technologies are \"meaning-centered\". They involve but are not limited to the following areas of application: encoding/decoding of semantic representation, knowledge graphs of entities and their interrelationships, auto-recognition of topics and concepts, information and meaning extraction, semantic data integration, and taxonomies/classification.Given a question, semantic technologies can directly search topics, concepts, associations that span a vast number of sources. Semantic technologies provide an abstraction layer above existing IT technologies that enables bridging and interconnection of data, content, and processes. Second, from the portal perspective, semantic technologies can be thought of as a new level of depth that provides far more intelligent, capable, relevant, and responsive interaction than with information technologies alone. Semantic technologies would often leverage natural language processing and machine learning in order to extract topics, concepts, and associations between concepts in text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to improve performance in a new instruction set architecture, the Cydrome processors were based on a very long instruction word (VLIW) containing instructions from parallel operations. Software pipelining in a custom Fortran compiler generated code that would run efficiently. The numeric processor used a 256 bit-wide instruction word with seven \"fields\". In most cases the compiler would find instructions that could run in parallel and place them together in a single word.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some functional programming languages make explicit use of type constructors. A notable example is Haskell, in which all data type declarations are considered to declare type constructors, and basic types (or nullary type constructors) are called type constants. Type constructors may also be considered as parametric polymorphic data types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Internet of things (IoT), 3GPP is going to submit evolution of NB-IoT and eMTC (LTE-M) as 5G technologies for the LPWA (Low Power Wide Area) use case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fermat's Last Theorem states that x k + y k = z k {\\displaystyle x^{k}+y^{k}=z^{k}} is impossible in positive integers with k>2. The equation of a superellipse is | x / a | k + | y / b | k = 1 {\\displaystyle |x/a|^{k}+|y/b|^{k}=1} . The squircle is the case k = 4 , a = b {\\displaystyle k=4,a=b} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A named identifier of each of the entities and their attributes that are represented in a database. A basic unit of information built on standard structures having a unique meaning and distinct units or values. In electronic record-keeping, a combination of characters or bytes referring to one separate item of information, such as name, address, or age.In the areas of databases and data systems more generally a data element is a concept forming part of a data model. As an element of data representation, a collection of data elements forms a data structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to understand a text, it is usually necessary to understand the spoken language associated with that text. In this way, writing systems are distinguished from many other symbolic communication systems. Once established, writing systems on the whole change more slowly than their spoken counterparts, and often preserve features and expressions which are no longer current in the spoken language. The great benefit of writing systems is their ability to maintain a persistent record of information expressed in a language, which can be retrieved independently of the initial act of formulation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, noncommutative projective geometry is a noncommutative analog of projective geometry in the setting of noncommutative algebraic geometry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, South West Trains and Northern Rail have issued BlackBerry devices to guards in order to improve the communication between control, guards and passengers.In Canada, Toronto and many other municipalities within Canada have issued BlackBerry devices to most of its employees including but not limited to transportation, technical, water and operations inspection staff and all management staff in order to improve the communication between contracted construction companies, its winter maintenance operations and to assist and successfully organize multimillion-dollar contracts. The devices are the standard mobile device to receive e-mail redirected from GroupWise. As part of their Internet of Things endeavours, the company announced plans of moving into the shipping industry by adapting the smartphones devices to the communication necessities of freight containers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of control engineering, a map-based controller is a controller whose outputs are based on values derived from a pre-defined lookup table. The inputs to the controller are usually values taken from one or more sensors and are used to index the output values in the lookup table. By effectively placing the transfer function as discrete entries within a lookup table, engineers free to modify smaller sections or update the whole list of entries as required. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel corpora single sentences in one language can be found translated into several sentences in the other and vice versa. Long sentences may be broken up, short sentences may be merged. There are even some languages that use writing systems without clear indication of a sentence end (for example, Thai). Sentence aligning can be performed through the Gale-Church alignment algorithm. Through this and other mathematical models efficient search and retrieval of the highest scoring sentence alignment is possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, these models are derived under the concept that the respondent obtains some utility for each possible answer and gives the answer that provides the greatest utility. It might be more natural to think that the respondent has some latent measure or index associated with the question and answers in response to how high this measure is. Ordered logit and ordered probit models are derived under this concept.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, \u22121 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (\u22122) and less than 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To receive the inversion of any prime, each number value is subtracted from 12 and the resulting number placed in the corresponding matrix cell (see twelve-tone technique). The retrograde inversion is the values of the inversion numbers read backwards. Therefore: A given prime zero (derived from the notes of Anton Webern's Concerto): 0, 11, 3, 4, 8, 7, 9, 5, 6, 1, 2, 10 The retrograde: 10, 2, 1, 6, 5, 9, 7, 8, 4, 3, 11, 0 The inversion: 0, 1, 9, 8, 4, 5, 3, 7, 6, 11, 10, 2 The retrograde inversion: 2, 10, 11, 6, 7, 3, 5, 4, 8, 9, 1, 0 More generally, a musical permutation is any reordering of the prime form of an ordered set of pitch classes or, with respect to twelve-tone rows, any ordering at all of the set consisting of the integers modulo 12.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and coding theory, a Hamming space (named after American mathematician Richard Hamming) is usually the set of all 2 N {\\displaystyle 2^{N}} binary strings of length N. It is used in the theory of coding signals and transmission. More generally, a Hamming space can be defined over any alphabet (set) Q as the set of words of a fixed length N with letters from Q. If Q is a finite field, then a Hamming space over Q is an N-dimensional vector space over Q. In the typical, binary case, the field is thus GF(2) (also denoted by Z2).In coding theory, if Q has q elements, then any subset C (usually assumed of cardinality at least two) of the N-dimensional Hamming space over Q is called a q-ary code of length N; the elements of C are called codewords. In the case where C is a linear subspace of its Hamming space, it is called a linear code. A typical example of linear code is the Hamming code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practical use, inline assembly operating on values is rarely standalone as free-floating code. Since the programmer cannot predict what register a variable is assigned to, compilers typically provide a way to substitute them in as an extension. There are, in general, two types of inline assembly supported by C/C++ compilers: asm (or __asm__) in GCC. GCC uses a direct extension of the ISO rules: assembly code template is written in strings, with inputs, outputs, and clobbered registers specified after the strings in colons.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical learning models, the training sample ( x i , y i ) {\\displaystyle (x_{i},y_{i})} are assumed to have been drawn from the true distribution p ( x , y ) {\\displaystyle p(x,y)} and the objective is to minimize the expected \"risk\" I  = E  = \u222b V ( f ( x ) , y ) d p ( x , y ) . {\\displaystyle I=\\mathbb {E} =\\int V(f(x),y)\\,dp(x,y)\\ .} A common paradigm in this situation is to estimate a function f ^ {\\displaystyle {\\hat {f}}} through empirical risk minimization or regularized empirical risk minimization (usually Tikhonov regularization).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to decrypt, we turn the ciphertext back into a vector, then simply multiply by the inverse matrix of the key matrix (IFK/VIV/VMI in letters). We find that, modulo 26, the inverse of the matrix used in the previous example is: ( 6 24 1 13 16 10 20 17 15 ) \u2212 1 ( mod 26 ) \u2261 ( 8 5 10 21 8 21 21 12 8 ) {\\displaystyle {\\begin{pmatrix}6&24&1\\\\13&16&10\\\\20&17&15\\end{pmatrix}}^{-1}{\\pmod {26}}\\equiv {\\begin{pmatrix}8&5&10\\\\21&8&21\\\\21&12&8\\end{pmatrix}}} Taking the previous example ciphertext of 'POH', we get: ( 8 5 10 21 8 21 21 12 8 ) ( 15 14 7 ) = ( 260 574 539 ) \u2261 ( 0 2 19 ) ( mod 26 ) {\\displaystyle {\\begin{pmatrix}8&5&10\\\\21&8&21\\\\21&12&8\\end{pmatrix}}{\\begin{pmatrix}15\\\\14\\\\7\\end{pmatrix}}={\\begin{pmatrix}260\\\\574\\\\539\\end{pmatrix}}\\equiv {\\begin{pmatrix}0\\\\2\\\\19\\end{pmatrix}}{\\pmod {26}}} which gets us back to 'ACT', as expected. Two complications exist in picking the encrypting matrix: Not all matrices have an inverse. The matrix will have an inverse if and only if its determinant is not zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, inter-rater reliability (also called by various similar names, such as inter-rater agreement, inter-rater concordance, inter-observer reliability, inter-coder reliability, and so on) is the degree of agreement among independent observers who rate, code, or assess the same phenomenon. Assessment tools that rely on ratings must exhibit good inter-rater reliability, otherwise they are not valid tests. There are a number of statistics that can be used to determine inter-rater reliability. Different statistics are appropriate for different types of measurement. Some options are joint-probability of agreement, such as Cohen's kappa, Scott's pi and Fleiss' kappa; or inter-rater correlation, concordance correlation coefficient, intra-class correlation, and Krippendorff's alpha.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This notion has relevance in pure mathematics, as well as in any other field that uses classical logic. Outside of mathematics, statements which can be characterized informally as vacuously true can be misleading. Such statements make reasonable assertions about qualified objects which do not actually exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, transparency can refer to: The property of an entity that allows another entity to pass through it without altering either of the entities. The property that allows a transmission system or channel to accept, at its input, unmodified user information, and deliver corresponding user information at its output, unchanged in form or information content. The user information may be changed internally within the transmission system, but it is restored to its original form prior to the output without the involvement of the user. The quality of a data communications system or device that uses a bit-oriented link protocol that does not depend on the bit sequence structure used by the data source.Some communication systems are not transparent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, if a VLIW device has five execution units, then a VLIW instruction for the device has five operation fields, each field specifying what operation should be done on that corresponding execution unit. To accommodate these operation fields, VLIW instructions are usually at least 64 bits wide, and far wider on some architectures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, all five inferences involving A and B and any of the five values of C may be replaced by the single descriptive inference \"(A and B) implies the particular value of D\". To establish that the prime implicants or descriptive inferences derived from the data by the QCA method are causal requires establishing the existence of causal mechanism using another method such as process tracing, formal logic, intervening variables, or established multidisciplinary knowledge. The method is used in social science and is based on the binary logic of Boolean algebra, and attempts to ensure that all possible combinations of variables that can be made across the cases under investigation are considered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They prepare the next generation for school, work, and decision-making. The way in which a child is nurtured at a young age and through adolescence has both psychological and developmental effects that effect their future.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a hyper-finite field is an uncountable field similar in many ways to finite fields. More precisely a field F is called hyper-finite if it is uncountable and quasi-finite, and for every subfield E, every absolutely entire E-algebra (regular field extension of E) of smaller cardinality than F can be embedded in F. They were introduced by Ax (1968). Every hyper-finite field is a pseudo-finite field, and is in particular a model for the first-order theory of finite fields.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case that p = 3 the following three matrices H m {\\displaystyle \\mathbf {H} _{m}} can be chosen H 1 = ( 0 0 0 0 0 \u2212 1 0 1 0 ) {\\displaystyle \\mathbf {H} _{1}={\\begin{pmatrix}0&0&0\\\\0&0&-1\\\\0&1&0\\end{pmatrix}}} , H 2 = ( 0 0 1 0 0 0 \u2212 1 0 0 ) {\\displaystyle \\mathbf {H} _{2}={\\begin{pmatrix}0&0&1\\\\0&0&0\\\\-1&0&0\\end{pmatrix}}} , H 3 = ( 0 \u2212 1 0 1 0 0 0 0 0 ) . {\\displaystyle \\mathbf {H} _{3}={\\begin{pmatrix}0&-1&0\\\\1&0&0\\\\0&0&0\\end{pmatrix}}.} In this particular case, the homogeneous linear equations can be written as 0 =  \u00d7 A y k {\\displaystyle \\mathbf {0} =_{\\times }\\,\\mathbf {A} \\,\\mathbf {y} _{k}} for k = 1 , \u2026 , N {\\displaystyle \\,k=1,\\ldots ,N} where  \u00d7 {\\displaystyle _{\\times }} is the matrix representation of the vector cross product.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Because the \"dits\" are created automatically by the pendulum mechanism, but the \"dahs\" are keyed the old-fashioned way, the keys are called \"semi-automatic\". (Modern electronic keyers create both the \"dits\" and the \"dahs\" automatically, as long as one of the switches is in contact, and are called \"fully-automatic\".)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, one may describe the distribution of a random variable as belonging to a family of probability distributions, distinguished from each other by the values of a finite number of parameters. For example, one talks about \"a Poisson distribution with mean value \u03bb\". The function defining the distribution (the probability mass function) is: f ( k ; \u03bb ) = e \u2212 \u03bb \u03bb k k ! .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle k!} permutations so P k n = C k n \u00d7 k ! {\\displaystyle P_{k}^{n}=C_{k}^{n}\\times k!}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such mixture problem are often formulated with normalized constraints, so that the nonnegative components sum to one, in which case the feasible region forms a simplex. The quality of the bread mixtures can be estimated using response surface methodology, and then a local maximum can be computed using a nonlinear programming method, such as sequential quadratic programming. In operations research, linear programming problems can be solved by the simplex algorithm of George Dantzig.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a nonempty collection of sets is called a \ud835\udf0e-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a chaos machine is a class of algorithms constructed on the base of chaos theory (mainly deterministic chaos) to produce pseudo-random oracle. It represents the idea of creating a universal scheme with modular design and customizable parameters, which can be applied wherever randomness and sensitiveness is needed.Theoretical model was published in early 2015 by Maciej A. Czyzewski. It was designed specifically to combine the benefits of hash function and pseudo-random function. However, it can be used to implement many cryptographic primitives, including cryptographic hashes, message authentication codes and randomness extractors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen\u2013Fox\u2013Lyndon theorem states that the Lyndon words furnish a factorisation. The Sch\u00fctzenberger theorem relates the definition in terms of a multiplicative property to an additive property.Let A* be the free monoid on an alphabet A. Let Xi be a sequence of subsets of A* indexed by a totally ordered index set I. A factorisation of a word w in A* is an expression w = x i 1 x i 2 \u22ef x i n {\\displaystyle w=x_{i_{1}}x_{i_{2}}\\cdots x_{i_{n}}\\ } with x i j \u2208 X i j {\\displaystyle x_{i_{j}}\\in X_{i_{j}}} and i 1 \u2265 i 2 \u2265 \u2026 \u2265 i n {\\displaystyle i_{1}\\geq i_{2}\\geq \\ldots \\geq i_{n}} . Some authors reverse the order of the inequalities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plane geometry the Kovner\u2013Besicovitch measure is a number defined for any bounded convex set describing how close to being centrally symmetric it is. It is the fraction of the area of the set that can be covered by its largest centrally symmetric subset.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimension. Matrices are used in most areas of mathematics and most scientific fields, either directly, or through their use in geometry and numerical analysis. Matrix theory is the branch of mathematics that focuses on the study of matrices. It was initially a sub-branch of linear algebra, but soon grew to include subjects related to graph theory, algebra, combinatorics and statistics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other allowed signs are 1010 (A) and 1110 (E) for positive and 1011 (B) for negative. IBM System/360 processors will use the 1010 (A) and 1011 (B) signs if the A bit is set in the PSW, for the ASCII-8 standard that never passed. Most implementations also provide unsigned BCD values with a sign nibble of 1111 (F).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, i was coded as \"2\", but d was coded as \"222\". Myer's 1866 manual also includes a 3-element fixed length code using four elements, and the 1872 manual has a 3-element fixed length code using three elements. There is little sign that these codes were widely used. The 1872 manual includes a variable length code using four elements which Myer says was used by the Army, but is superseded.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the notion of a divisor originally arose within the context of arithmetic of whole numbers. With the development of abstract rings, of which the integers are the archetype, the original notion of divisor found a natural extension. Divisibility is a useful concept for the analysis of the structure of commutative rings because of its relationship with the ideal structure of such rings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In state space search, a state space is formally represented as a tuple S: \u27e8 S , A , A c t i o n ( s ) , R e s u l t ( s , a ) , C o s t ( s , a ) \u27e9 {\\displaystyle S:\\langle S,A,Action(s),Result(s,a),Cost(s,a)\\rangle } , in which: S {\\displaystyle S} is the set of all possible states; A {\\displaystyle A} is the set of possible actions, not related to a particular state but regarding all the state space; A c t i o n ( s ) {\\displaystyle Action(s)} is the function that establish which action is possible to perform in a certain state; R e s u l t ( s , a ) {\\displaystyle Result(s,a)} is the function that returns the state reached performing action a {\\displaystyle a} in state s {\\displaystyle s} C o s t ( s , a ) {\\displaystyle Cost(s,a)} is the cost of performing an action a {\\displaystyle a} in state s {\\displaystyle s} . In many state spaces a is a constant, but this is not always true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fourth standard, \"unification criteria for maintaining compatibility with previous standards\" (\u904e\u53bb\u306e\u898f\u683c\u3068\u306e\u4e92\u63db\u6027\u3092\u7dad\u6301\u3059\u308b\u305f\u3081\u306e\u5305\u6442\u898f\u6e96, kako no kikaku to no gokansei wo iji suru tame no h\u014dsetsu kijun) is defined. Their application is limited to 29 code points whose glyphs vary greatly between the standards JIS C 6226-1983 on and after and JIS C 6226-1978. For those 29 code points, the glyphs from JIS C 6226-1983 on and after are displayed as \"A\", and the glyphs from JIS C 6226-1978 as \"B\". On each of them, both \"A\" and \"B\" glyphs may be applied. However, in order to claim compatibility with the standard, whether the \"A\" or \"B\" form has been used for each code point must be explicitly noted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering and development, a software metric is a standard of measure of a degree to which a software system or process possesses some property. Even if a metric is not a measurement (metrics are functions, while measurements are the numbers obtained by the application of metrics), often the two terms are used as synonyms. Since quantitative measurements are essential in all sciences, there is a continuous effort by computer science practitioners and theoreticians to bring similar approaches to software development. The goal is obtaining objective, reproducible and quantifiable measurements, which may have numerous valuable applications in schedule and budget planning, cost estimation, quality assurance, testing, software debugging, software performance optimization, and optimal personnel task assignments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some parts of the world, such as the UK and Commonwealth countries, 999 (pronounced as 9-9-9) is the emergency telephone number. 999 was a London punk band active during the 1970s. 999 is also the short name for the visual novel Nine Hours, Nine Persons, Nine Doors. 999 is the last 3 digit number. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence, \"binary data\" in computers are actually sequences of bytes. On a higher level, data is accessed in groups of 1 word (4 bytes) for 32-bit systems and 2 words for 64-bit systems. In applied computer science and in the information technology field, the term binary data is often specifically opposed to text-based data, referring to any sort of data that cannot be interpreted as text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the notation above, P is the set X, Q is a collection S of subsets of X, R is the binary relation \"is contained in\" between elements and subsets, and R\u22121 restricted to Q \u00d7 P* is the function \"contains\" from subsets to selected elements. Whereas an exact cover problem involves selecting subsets and the relation \"contains\" from subsets to elements, an exact hitting set problem involves selecting elements and the relation \"is contained in\" from elements to subsets. In a sense, an exact hitting set problem is the inverse of the exact cover problem involving the same set and collection of subsets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Religious vows are of two varieties: simple vows and solemn vows. The highest level of commitment is exemplified by those who have taken their solemn, perpetual vows. There once were significant technical differences between them in canon law; but these differences were suppressed by the current Code of Canon Law in 1983, although the nominal distinction is maintained.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of the molecule.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Yet the output is: i=54, a=1.000000 Another example is: Take 2 numbers: 2.56 \u00d7 10 0 {\\displaystyle 2.56\\times 10^{0}} and 2.34 \u00d7 10 2 {\\displaystyle 2.34\\times 10^{2}} we bring the first number to the same power of 10 {\\displaystyle 10} as the second one: 0.0256 \u00d7 10 2 {\\displaystyle 0.0256\\times 10^{2}} The addition of the 2 numbers is: 0.0256*10^2 2.3400*10^2 + ____________ 2.3656*10^2 After padding the second number (i.e., 2.34 \u00d7 10 2 {\\displaystyle 2.34\\times 10^{2}} ) with two 0 {\\displaystyle 0} s, the bit after 4 {\\displaystyle 4} is the guard digit, and the bit after is the round digit. The result after rounding is 2.37 {\\displaystyle 2.37} as opposed to 2.36 {\\displaystyle 2.36} , without the extra bits (guard and round bits), i.e., by considering only 0.02 + 2.34 = 2.36 {\\displaystyle 0.02+2.34=2.36} . The error therefore is 0.01 {\\displaystyle 0.01} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But all nullary constructors, thus all monomorphic types, have the same, simplest kind; namely \u2217 {\\displaystyle *} . Since higher-order type operators are uncommon in programming languages, in most programming practice, kinds are used to distinguish between data types and the types of constructors which are used to implement parametric polymorphism. Kinds appear, either explicitly or implicitly, in languages whose type systems account for parametric polymorphism in a programmatically accessible way, such as C++, Haskell and Scala.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the latter case, it may use either a transport layer virtual circuit protocol such as the TCP protocol, allowing data to be delivered in order. Although the lower-layer switching is connectionless, or it may be a data link layer or network layer switching mode, where all data packets belonging to the same traffic stream are delivered over the same path, and traffic flows are identified by some connection identifier reducing the overhead of routing decisions on a packet-by-packet basis for the network. Connection-oriented protocol services are often, but not always, reliable network services that provide acknowledgment after successful delivery and automatic repeat request functions in case of missing or corrupted data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing (NLP), a word embedding is a representation of a word. The embedding is used in text analysis. Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that words that are closer in the vector space are expected to be similar in meaning. Word embeddings can be obtained using language modeling and feature learning techniques, where words or phrases from the vocabulary are mapped to vectors of real numbers. Methods to generate this mapping include neural networks, dimensionality reduction on the word co-occurrence matrix, probabilistic models, explainable knowledge base method, and explicit representation in terms of the context in which words appear.Word and phrase embeddings, when used as the underlying input representation, have been shown to boost the performance in NLP tasks such as syntactic parsing and sentiment analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psychology, cognitive science, and in neuroscience, there have been two main approaches for describing how humans perceive and classify emotion: continuous or categorical. The continuous approach tends to use dimensions such as negative vs. positive, calm vs. aroused. The categorical approach tends to use discrete classes such as happy, sad, angry, fearful, surprise, disgust. Different kinds of machine learning regression and classification models can be used for having machines produce continuous or discrete labels. Sometimes models are also built that allow combinations across the categories, e.g. a happy-surprised face or a fearful-surprised face.The following sections consider many of the kinds of input data used for the task of emotion recognition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, there are Hands-Free Profile (HFP) 1.5 implementations using both Bluetooth 2.0 and Bluetooth 1.2 core specifications. The way a device uses Bluetooth depends on its profile capabilities. The profiles provide standards that manufacturers follow to allow devices to use Bluetooth in the intended manner.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, it may be necessary to regularize the whitened STA, since whitening amplifies noise along stimulus dimensions that are poorly explored by the stimulus (i.e., axes along which the stimulus has low variance). A common approach to this problem is ridge regression. The regularized STA, computed using ridge regression, can be written S T A r i d g e = T n s p ( X T X + \u03bb I ) \u2212 1 X T y , {\\displaystyle \\mathrm {STA} _{ridge}={\\tfrac {T}{n_{sp}}}\\left(X^{T}X+\\lambda I\\right)^{-1}X^{T}\\mathbf {y} ,} where I {\\displaystyle I} denotes the identity matrix and \u03bb {\\displaystyle \\lambda } is the ridge parameter controlling the amount of regularization. This procedure has a simple Bayesian interpretation: ridge regression is equivalent to placing a prior on the STA elements that says they are drawn i.i.d. from a zero-mean Gaussian prior with covariance proportional to the identity matrix. The ridge parameter sets the inverse variance of this prior, and is usually fit by cross-validation or empirical Bayes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The branch operated for some time. On 1 September 1932, 27-year-old Polish mathematician Marian Rejewski and two fellow Pozna\u0144 University mathematics graduates, Henryk Zygalski and Jerzy R\u00f3\u017cycki, joined the Bureau full-time and moved to Warsaw. Their first task was to reconstruct a four-letter German naval cipher.Near the end of 1932 Rejewski was asked to work a couple of hours a day on breaking the Enigma.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The stream nomenclature alludes to a physical setup in which the observers are physically separated and have no control over the emitted events from the subject/stream source. This pattern thus suits any process by which data arrives from some input that is not available to the CPU at startup, but instead arrives seemingly at random (HTTP requests, GPIO data, user input from peripherals, distributed databases and blockchains, etc.). Most modern programming languages comprise built-in event constructs implementing the observer-pattern components. While not mandatory, most observer implementations use background threads listening for subject events and other support mechanisms provided by the kernel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the decision-making process, optimisation is almost always intractable in any implementation, whether machine or neural. Because of this, defined parameters or boundaries must be implemented in the process in order to achieve an acceptable outcome. This method is known as applying bounded rationality, where an individual makes a collective and rational choice that considers \u201cthe limits of human capability to calculate, the severe deficiencies of human knowledge about the consequences of choice, and the limits of human ability to adjudicate among multiple goals\u201d. They are essentially incorporating a series of criteria, referred to as alternatives for choice. These alternatives are often not initially given to the decision maker, so a theory of search is also incorporated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the signature defect of a singularity measures the correction that a singularity contributes to the signature theorem. Hirzebruch (1973) introduced the signature defect for the cusp singularities of Hilbert modular surfaces. Michael Francis Atiyah, H. Donnelly, and I. M. Singer (1983) defined the signature defect of the boundary of a manifold as the eta invariant, the value as s = 0 of their eta function, and used this to show that Hirzebruch's signature defect of a cusp of a Hilbert modular surface can be expressed in terms of the value at s = 0 or 1 of a Shimizu L-function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sometimes only constraints on distribution are known; one can then use the principle of maximum entropy to determine a single distribution, the one with the greatest entropy given the constraints. (Analogously, in the specific context of a dynamic Bayesian network, the conditional distribution for the hidden state's temporal evolution is commonly specified to maximize the entropy rate of the implied stochastic process.) Often these conditional distributions include parameters that are unknown and must be estimated from data, e.g., via the maximum likelihood approach.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Euler's totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime, then \u03c6(mn) = \u03c6(m)\u03c6(n). This function gives the order of the multiplicative group of integers modulo n (the group of units of the ring Z / n Z {\\displaystyle \\mathbb {Z} /n\\mathbb {Z} } ). It is also used for defining the RSA encryption system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally, a PIT algorithm is given an arithmetic circuit that computes a polynomial p in a field, and decides whether p is the zero polynomial. Determining the computational complexity required for polynomial identity testing is one of the most important open problems in algebraic computing complexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a monolithic application is a single unified software application which is self-contained and independent from other applications, but typically lacks flexibility. There are advantages and disadvantages of building applications in a monolithic style of software architecture, depending on requirements. Alternative styles to monolithic applications include multitier architectures, distributed computing and microservices. The design philosophy is that the application is responsible not just for a particular task, but can perform every step needed to complete a particular function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In its simplest and most na\u00efve form, this way of analyzing word forms, called \"item-and-arrangement\", treats words as if they were made of morphemes put after each other (\"concatenated\") like beads on a string. More recent and sophisticated approaches, such as distributed morphology, seek to maintain the idea of the morpheme while accommodating non-concatenated, analogical, and other processes that have proven problematic for item-and-arrangement theories and similar approaches. Morpheme-based morphology presumes three basic axioms: Baudouin's \"single morpheme\" hypothesis: Roots and affixes have the same status as morphemes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as \"given any\", \"for all\", or \"for any\". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , m i n d \u2212 1 , m i n d \u2212 1 } {\\displaystyle k_{min}=\\{min_{0},min_{0},min_{1},min_{1},...,min_{d-1},min_{d-1}\\}} k m a x = { m a x 0 , m a x 0 , m a x 1 , m a x 1 , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The doubly extreme case ' \u22a2 ', where both the antecedent and consequent lists of formulas are empty is \"not satisfiable\". In this case, the meaning of the sequent is effectively ' \u22a4 \u22a2 \u22a5 '. This is equivalent to the sequent ' \u22a2 \u22a5 ', which clearly cannot be valid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a semigroupoid (also called semicategory, naked category or precategory) is a partial algebra that satisfies the axioms for a small category, except possibly for the requirement that there be an identity at each object. Semigroupoids generalise semigroups in the same way that small categories generalise monoids and groupoids generalise groups. Semigroupoids have applications in the structural theory of semigroups. Formally, a semigroupoid consists of: a set of things called objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These curves are defined to satisfy conformal invariance and a domain Markov property. It was discovered by Oded Schramm (2000) as a conjectured scaling limit of the planar uniform spanning tree (UST) and the planar loop-erased random walk (LERW) probabilistic processes, and developed by him together with Greg Lawler and Wendelin Werner in a series of joint papers. Besides UST and LERW, the Schramm\u2013Loewner evolution is conjectured or proven to describe the scaling limit of various stochastic processes in the plane, such as critical percolation, the critical Ising model, the double-dimer model, self-avoiding walks, and other critical statistical mechanics models that exhibit conformal invariance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more formal probability theory, a random variable is a function X defined from a sample space \u03a9 to a measurable space called the state space. If an element in \u03a9 is mapped to an element in state space by X, then that element in state space is a realization. Elements of the sample space can be thought of as all the different possibilities that could happen; while a realization (an element of the state space) can be thought of as the value X attains when one of the possibilities did happen. Probability is a mapping that assigns numbers between zero and one to certain subsets of the sample space, namely the measurable subsets, known here as events. Subsets of the sample space that contain only one element are called elementary events. The value of the random variable (that is, the function) X at a point \u03c9 \u2208 \u03a9, x = X ( \u03c9 ) {\\displaystyle x=X(\\omega )} is called a realization of X.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the article A Universal Data Compression System, Rissanen introduced a consistent algorithm to estimate the probabilistic context tree that generates the data. This algorithm's function can be summarized in two steps: Given the sample produced by a chain with memory of variable length, we start with the maximum tree whose branches are all the candidates to contexts to the sample; The branches in this tree are then cut until you obtain the smallest tree that's well adapted to the data. Deciding whether or not shortening the context is done through a given gain function, such as the ratio of the log-likelihood.Be X 0 , \u2026 , X n \u2212 1 {\\displaystyle X_{0},\\ldots ,X_{n-1}} a sample of a finite probabilistic tree ( \u03c4 , p ) {\\displaystyle (\\tau ,p)} . For any sequence x \u2212 j \u2212 1 {\\displaystyle x_{-j}^{-1}} with j \u2264 n {\\displaystyle j\\leq n} , it is possible to denote by N n ( x \u2212 j \u2212 1 ) {\\displaystyle N_{n}(x_{-j}^{-1})} the number of occurrences of the sequence in the sample, i.e., N n ( x \u2212 j \u2212 1 ) = \u2211 t = 0 n \u2212 j 1 { X t t + j \u2212 1 = x \u2212 j \u2212 1 } {\\displaystyle N_{n}(x_{-j}^{-1})=\\sum _{t=0}^{n-j}\\mathbf {1} \\left\\{X_{t}^{t+j-1}=x_{-j}^{-1}\\right\\}} Rissanen first built a context maximum candidate, given by X n \u2212 K ( n ) n \u2212 1 {\\displaystyle X_{n-K(n)}^{n-1}} , where K ( n ) = C log \u2061 n {\\displaystyle K(n)=C\\log {n}} and C {\\displaystyle C} is an arbitrary positive constant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed. Smith numbers were named by Albert Wilansky of Lehigh University, as he noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith: 4937775 = 3 \u00b7 5 \u00b7 5 \u00b7 65837while 4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + (6 + 5 + 8 + 3 + 7)in base 10.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In technical communication, topic-based authoring is a modular approach to content creation where content is structured around topics that can be mixed and reused in different contexts. It is defined in contrast with book-oriented or narrative content, written in the linear structure of written books.Topic-based authoring is popular in the technical publications and documentation arenas, as it is especially suitable for technical documentation. Tools supporting this approach typically store content in XHTML or other XML formats and support content reuse, management, and the dynamic assembly of personalized information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied (\"scaled\") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sepp Hochreiter analyzed the vanishing gradient problem in 1991 and attributed to it the reason why deep learning did not work well. To overcome this problem, Long Short-Term Memory (LSTM) recurrent neural networks had skip connections or residual connections with a weight of 1.0 in every LSTM cell (called the constant error carrousel) to compute y t + 1 = F ( x t ) + x t {\\textstyle y_{t+1}=F(x_{t})+x_{t}} . During backpropagation through time, this becomes the above-mentioned residual formula y = F ( x ) + x {\\textstyle y=F(x)+x} for feedforward neural networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 25, 125, 245, and 1245 are the patterns related to Braille pattern dots-14, since the two additional dots of kantenji patterns 014, 147, and 0147 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Hua's lemma, named for Hua Loo-keng, is an estimate for exponential sums. It states that if P is an integral-valued polynomial of degree k, \u03b5 {\\displaystyle \\varepsilon } is a positive real number, and f a real function defined by f ( \u03b1 ) = \u2211 x = 1 N exp \u2061 ( 2 \u03c0 i P ( x ) \u03b1 ) , {\\displaystyle f(\\alpha )=\\sum _{x=1}^{N}\\exp(2\\pi iP(x)\\alpha ),} then \u222b 0 1 | f ( \u03b1 ) | \u03bb d \u03b1 \u226a P , \u03b5 N \u03bc ( \u03bb ) {\\displaystyle \\int _{0}^{1}|f(\\alpha )|^{\\lambda }d\\alpha \\ll _{P,\\varepsilon }N^{\\mu (\\lambda )}} ,where ( \u03bb , \u03bc ( \u03bb ) ) {\\displaystyle (\\lambda ,\\mu (\\lambda ))} lies on a polygonal line with vertices ( 2 \u03bd , 2 \u03bd \u2212 \u03bd + \u03b5 ) , \u03bd = 1 , \u2026 , k . {\\displaystyle (2^{\\nu },2^{\\nu }-\\nu +\\varepsilon ),\\quad \\nu =1,\\ldots ,k.} == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The multinomial distribution models the outcome of n experiments, where the outcome of each trial has a categorical distribution, such as rolling a k-sided die n times. Let k be a fixed finite number. Mathematically, we have k possible mutually exclusive outcomes, with corresponding probabilities p1, ..., pk, and n independent trials.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Third, find all covers of cardinality k {\\displaystyle k} that do not violate the budget. Using these covers of cardinality k {\\displaystyle k} as starting points, apply the modified greedy algorithm, maintaining the best cover found so far. Call this cover H 2 {\\displaystyle H_{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consequently, a random integer with at most 2n digits (for large enough n) is about half as likely to be prime as a random integer with at most n digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime (log(101000) \u2248 2302.6), whereas among positive integers of at most 2000 digits, about one in 4600 is prime (log(102000) \u2248 4605.2). In other words, the average gap between consecutive prime numbers among the first N integers is roughly log(N).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In technology, agile development involves teams self-managing to a large extent (though agile development is commonly still practiced within a hierarchical organization, which means that certain types of decisions such as hiring, firing, and pay raises remain the prerogative of managers). In scrum, an agile framework, team members assign work to be done among themselves, either by free choice or by consensus. The scrum master role in scrum is not a management role as such, but is a role that involves helping remove obstacles to progress and ensuring that the basic scrum framework is adhered to by all parties, inside and outside the team - both aspects of the role being more akin to facilitation than to top-down micromanagement. Agile frameworks such as scrum have also begun being used in non-technology companies and organizations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on n {\\displaystyle n} -dimensional Euclidean space R n {\\displaystyle \\mathbb {R} ^{n}} by the Euclidean metric.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, to indicate the product of binomials, parentheses are usually used, thus: ( 2 x + 3 ) ( 3 x + 4 ) {\\displaystyle (2x+3)(3x+4)} . But if one of the binomials itself contains parentheses, as in ( 2 ( a + b ) + 3 ) {\\displaystyle (2(a+b)+3)} one or more pairs of parentheses may be replaced by brackets, thus:   {\\displaystyle } . Beyond elementary mathematics, brackets are mostly used for other purposes, e.g. to denote a closed interval, or an equivalence class, so they appear rarely for grouping.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In organization development, the initial phase within the Cognitive work analysis (CWA) framework is Work Domain Analysis. It provides a description of the constraints that govern the purpose and the function of the systems under analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a Lindstr\u00f6m quantifier is a generalized polyadic quantifier. Lindstr\u00f6m quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindstr\u00f6m in 1966. They were later studied for their applications in logic in computer science and database query languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, CI/CD or CICD is the combined practices of continuous integration (CI) and continuous delivery (CD) or, less often, continuous deployment. They are sometimes referred to collectively as continuous development or continuous software development.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Elkies trinomial curves are certain hyperelliptic curves constructed by Noam Elkies which have the property that rational points on them correspond to trinomial polynomials giving an extension of Q with particular Galois groups. One curve, C168, gives Galois group PSL(2,7) from a polynomial of degree seven, and the other, C1344, gives Galois group AL(8), the semidirect product of a 2-elementary group of order eight acted on by PSL(2, 7), giving a transitive permutation subgroup of the symmetric group on eight roots of order 1344. The equation of the curve C168 is: y 2 = x ( 81 x 5 + 396 x 4 + 738 x 3 + 660 x 2 + 269 x + 48 ) {\\displaystyle y^{2}=x(81x^{5}+396x^{4}+738x^{3}+660x^{2}+269x+48)} The curve is a plane algebraic curve model for a Galois resolvent for the trinomial polynomial equation x7 + bx + c = 0. If there exists a point (x, y) on the (projectivized) curve, there is a corresponding pair (b, c) of rational numbers, such that the trinomial polynomial either factors or has Galois group PSL(2,7), the finite simple group of order 168.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel computing, the fork\u2013join model is a way of setting up and executing parallel programs, such that execution branches off in parallel at designated points in the program, to \"join\" (merge) at a subsequent point and resume sequential execution. Parallel sections may fork recursively until a certain task granularity is reached. Fork\u2013join can be considered a parallel design pattern. : 209 ff. It was formulated as early as 1963.By nesting fork\u2013join computations recursively, one obtains a parallel version of the divide and conquer paradigm, expressed by the following generic pseudocode: solve(problem): if problem is small enough: solve problem directly (sequential algorithm) else: for part in subdivide(problem) fork subtask to solve(part) join all subtasks spawned in previous loop return combined results", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\|B\\|=\\sup\\{|B(x_{1},x_{2})|:\\|x_{i}\\|_{\\infty }\\leq 1\\}.} The exponent 4/3 is optimal, i.e., cannot be improved by a smaller exponent. It is also known that for real scalars the aforementioned constant is sharp.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As of April 2011 O2 will unlock any of their pay-monthly phones for free, even if they're still in contract, with the exception of handsets made exclusively for them, such as their Palm devices.Carphone Warehouse, one of the largest UK phone retailers, offers unlocked phones with most PAYG deals. As of January 1, 2014, all phones sold by 3 UK are unlocked. Phones bought before this date will be unlocked for free.On 17 December 2019, Ofcom announced that it would explore a mandate banning SIM locking. On 27 October 2020, The UK's mobile networks are to be forbidden from selling phones locked to their services from December 2021.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a totative of a given positive integer n is an integer k such that 0 < k \u2264 n and k is coprime to n. Euler's totient function \u03c6(n) counts the number of totatives of n. The totatives under multiplication modulo n form the multiplicative group of integers modulo n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages, ad hoc polymorphism is a kind of polymorphism in which polymorphic functions can be applied to arguments of different types, because a polymorphic function can denote a number of distinct and potentially heterogeneous implementations depending on the type of argument(s) to which it is applied. When applied to object-oriented or procedural concepts, it is also known as function overloading or operator overloading. The term ad hoc in this context is not intended to be pejorative; it refers simply to the fact that this type of polymorphism is not a fundamental feature of the type system. This is in contrast to parametric polymorphism, in which polymorphic functions are written without mention of any specific type, and can thus apply a single abstract implementation to any number of types in a transparent way. This classification was introduced by Christopher Strachey in 1967.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, the generalized integer gamma distribution (GIG) is the distribution of the sum of independent gamma distributed random variables, all with integer shape parameters and different rate parameters. This is a special case of the generalized chi-squared distribution. A related concept is the generalized near-integer gamma distribution (GNIG).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented. Other categorizations have been proposed. For example, Mosteller and Tukey (1977) distinguished grades, ranks, counted fractions, counts, amounts, and balances.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In computer-assisted translation, a technique called fuzzy matching is used to find the most likely translation of a piece of text, using previous translated texts as a basis. In hypnotherapy, fuzzy language is deliberately used for the purpose of trance induction. Hypnotic suggestions are often couched in a somewhat vague, general or ambiguous language requiring interpretation by the subject.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By dividing a high-rate data stream into numerous low-rate data streams, OFDM enables longer duration symbols. A cyclic prefix (CP) may be inserted to create a (time) guard interval that prevents ISI entirely.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the distributed memory model, each processing entity has its own memory. Because of this, processing entities must send and receive messages to each other to share its local data or get access to remote data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first stage logico-linguistic modeling uses SSM for systems analysis. This stage seeks to structure the problem in the client organization by identifying stakeholders, modelling organizational objectives and discussing possible solutions. At this stage it not assumed that a KBS will be a solution and logico-linguistic modeling often produces solutions that do not require a computerized KBS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In RLNC, it will randomly choose two coding coefficients, d 1 {\\displaystyle d_{1}} and d 2 {\\displaystyle d_{2}} in the example. The node will multiply each symbol of packet f {\\displaystyle f} by d 1 {\\displaystyle d_{1}} , and each symbol of packet e {\\displaystyle e} by d 2 {\\displaystyle d_{2}} . Then, it will add the results symbol-wise to produce the new coded data. It will perform the same operations of multiplication and addition to the coding coefficients of the coded packets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for the whole system to work, one has to postulate that: \u2200 m \u2208 M , I D \u2208 { 0 , 1 } \u2217: D e c r y p t ( E x t r a c t ( P , K m , I D ) , P , E n c r y p t ( P , m , I D ) ) = m {\\displaystyle \\forall m\\in {\\mathcal {M}},ID\\in \\left\\{0,1\\right\\}^{*}:\\mathrm {Decrypt} \\left(\\mathrm {Extract} \\left({\\mathcal {P}},K_{m},ID\\right),{\\mathcal {P}},\\mathrm {Encrypt} \\left({\\mathcal {P}},m,ID\\right)\\right)=m}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The constrained optimization leads to the Marshallian demand function: x \u2217 ( p 1 , p 2 , I ) = ( \u03b1 I ( \u03b1 + \u03b2 ) p 1 , \u03b2 I ( \u03b1 + \u03b2 ) p 2 ) . {\\displaystyle x^{*}(p_{1},p_{2},I)=\\left({\\frac {\\alpha I}{(\\alpha +\\beta )p_{1}}},{\\frac {\\beta I}{(\\alpha +\\beta )p_{2}}}\\right).} 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "High-performance FFT implementations make many modifications to the implementation of such an algorithm compared to this simple pseudocode. For example, one can use a larger base case than N=1 to amortize the overhead of recursion, the twiddle factors exp \u2061  {\\displaystyle \\exp} can be precomputed, and larger radices are often used for cache reasons; these and other optimizations together can improve the performance by an order of magnitude or more. (In many textbook implementations the depth-first recursion is eliminated in favor of a nonrecursive breadth-first approach, although depth-first recursion has been argued to have better memory locality.) Several of these ideas are described in further detail below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory, proof nets are a geometrical method of representing proofs that eliminates two forms of bureaucracy that differentiate proofs: (A) irrelevant syntactical features of regular proof calculi, and (B) the order of rules applied in a derivation. In this way, the formal properties of proof identity correspond more closely to the intuitively desirable properties. Proof nets were introduced by Jean-Yves Girard. This distinguishes proof nets from regular proof calculi such as the natural deduction calculus and the sequent calculus, where these phenomena are present. For instance, these two linear logic proofs are identical: And their corresponding nets will be the same.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mobile telephony GSM 03.38 or 3GPP 23.038 is a character encoding used in GSM networks for SMS (Short Message Service), CB (Cell Broadcast) and USSD (Unstructured Supplementary Service Data). The 3GPP TS 23.038 standard (originally GSM recommendation 03.38) defines GSM 7-bit default alphabet which is mandatory for GSM handsets and network elements, but the character set is suitable only for English and a number of Western-European languages. Languages such as Chinese, Korean or Japanese must be transferred using the 16-bit UCS-2 character encoding. A limited number of languages, like Portuguese, Spanish, Turkish and a number of languages used in India written with a Brahmic scripts may use 7-bit encoding with national language shift table defined in 3GPP 23.038. For binary messages, 8-bit encoding is used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent times, cache control instructions have become less popular as increasingly advanced application processor designs from Intel and ARM devote more transistors to accelerating code written in traditional languages, e.g., performing automatic prefetch, with hardware to detect linear access patterns on the fly. However the techniques may remain valid for throughput-oriented processors, which have a different throughput vs latency tradeoff, and may prefer to devote more area to execution units.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As regards English, there are many verb forms and constructions which combine time reference with continuous and/or perfect aspect, and with indicative, subjunctive or conditional mood. Particularly in some English language teaching materials, some or all of these forms can be referred to simply as tenses (see below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a sketch can be used to speed up explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numerical linear algebra algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of Wireless Communications one main application is to facilitate wireless access, such as 5G and WiFi simultaneously from the same antenna. In other words, radio signals are carried over fiber-optic cable. Thus, a single antenna can receive any and all radio signals (5G, Wifi, cell, etc..) carried over a single-fiber cable to a central location where equipment then converts the signals; this is opposed to the traditional way where each protocol type (5G, WiFi, cell) requires separate equipment at the location of the antenna.Although radio transmission over fiber is used for multiple purposes, such as in cable television (CATV) networks and in satellite base stations, the term RoF is usually applied when this is done for wireless access. In RoF systems, wireless signals are transported in optical form between a central station and a set of base stations before being radiated through the air.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "c_cc is zero and c_cc is non-zero In this case, the data in the buffer are \"available for reading\" after the specified number of characters have been received in the buffer. In other words, read() waits for a minimum amount of data (which may be larger than what the caller is prepared to read in the system call), will not return zero data, and may wait indefinitely. c_cc and c_cc are both non-zero In this case, the data in the buffer are \"available for reading\" after the specified number of characters have been received in the buffer or the timeout has expired since the last character was entered. There is no timeout for the very first character. In other words, read() waits for a minimum amount of data (which may be larger than what the caller is prepared to read in the system call), will not return zero data, may wait indefinitely, but won't wait longer than the specified timeout if at least one character is in the buffer to be read.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Also, having chosen such e {\\displaystyle e} , it is simpler to test whether gcd ( e , p \u2212 1 ) = 1 {\\displaystyle \\gcd(e,p-1)=1} and gcd ( e , q \u2212 1 ) = 1 {\\displaystyle \\gcd(e,q-1)=1} while generating and testing the primes in step 1 of the key generation. Values of p {\\displaystyle p} or q {\\displaystyle q} that fail this test can be rejected there and then. (Even better: if e is prime and greater than 2, then the test p mod e \u2260 1 {\\displaystyle p{\\bmod {e}}\\neq 1} can replace the more expensive test gcd ( p \u2212 1 , e ) = 1 {\\displaystyle \\gcd(p-1,e)=1} .)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, the Boolean is the type with two values. The unit type is implemented in most functional programming languages. The void type that is used in some imperative programming languages serves some of its functions, but because its carrier set is empty, it has some limitations (as detailed below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain (PID) can be uniquely decomposed in much the same way that integers have a prime factorization. The result provides a simple framework to understand various canonical form results for square matrices over fields.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Oltra-Massuet and Arregi (2005) argue that the metrical structure, as well, makes reference to hierarchical syntactic structure in Spanish. The extent of the interaction between the syntax and phonology at the interface is a matter of current debate. == Notes ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode: if error is True then set x to 0 In guarded command language: if error \u2192 x := 0 \u25a1 \u00ac {\\displaystyle \\neg } error \u2192 skip fi If the second guard is omitted and error is False, the result is abort.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The earliest uses of the method of infinite descent appear in Euclid's Elements. A typical example is Proposition 31 of Book 7, in which Euclid proves that every composite integer is divided (in Euclid's terminology \"measured\") by some prime number.The method was much later developed by Fermat, who coined the term and often used it for Diophantine equations. Two typical examples are showing the non-solvability of the Diophantine equation r 2 + s 4 = t 4 {\\displaystyle r^{2}+s^{4}=t^{4}} and proving Fermat's theorem on sums of two squares, which states that an odd prime p can be expressed as a sum of two squares when p \u2261 1 ( mod 4 ) {\\displaystyle p\\equiv 1{\\pmod {4}}} (see Modular arithmetic and proof by infinite descent).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In short, a network is in system optimum (SO) when the total system cost is the minimum among all possible assignments. System Optimum is based on the assumption that routes of all vehicles would be controlled by the system, and that rerouting would be based on maximum utilization of resources and minimum total system cost. (Cost can be interpreted as travel time.) Hence, in a System Optimum routing algorithm, all routes between a given OD pair have the same marginal cost.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the worst case, merge sort uses approximately 39% fewer comparisons than quicksort does in its average case, and in terms of moves, merge sort's worst case complexity is O(n log n) - the same complexity as quicksort's best case.Merge sort is more efficient than quicksort for some types of lists if the data to be sorted can only be efficiently accessed sequentially, and is thus popular in languages such as Lisp, where sequentially accessed data structures are very common. Unlike some (efficient) implementations of quicksort, merge sort is a stable sort. Merge sort's most common implementation does not sort in place; therefore, the memory size of the input must be allocated for the sorted output to be stored in (see below for variations that need only n/2 extra spaces).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Notably, the addition operation, logadd (for multiple terms, LogSumExp) can be viewed as a deformation of maximum or minimum. The log semiring has applications in mathematical optimization, since it replaces the non-smooth maximum and minimum by a smooth operation. The log semiring also arises when working with numbers that are logarithms (measured on a logarithmic scale), such as decibels (see Decibel \u00a7 Addition), log probability, or log-likelihoods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In such systems, a central complexity measure is the number of synchronous communication rounds required to complete the task.This complexity measure is closely related to the diameter of the network. Let D be the diameter of the network. On the one hand, any computable problem can be solved trivially in a synchronous distributed system in approximately 2D communication rounds: simply gather all information in one location (D rounds), solve the problem, and inform each node about the solution (D rounds).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This results in P ( A \u2223 B ) = P ( A \u2229 B ) / P ( B ) {\\textstyle P(A\\mid B)=P(A\\cap B)/P(B)} whenever P(B) > 0 and 0 otherwise.This approach results in a probability measure that is consistent with the original probability measure and satisfies all the Kolmogorov axioms. This conditional probability measure also could have resulted by assuming that the relative magnitude of the probability of A with respect to X will be preserved with respect to B (cf. a Formal Derivation below). The wording \"evidence\" or \"information\" is generally used in the Bayesian interpretation of probability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the binary case, the correlation function between the variables X n {\\displaystyle X_{n}} and X k {\\displaystyle X_{k}} of the chain depends on the distance n \u2212 k {\\displaystyle n-k} only. It is defined as follows: K ( r ) = \u27e8 ( X n \u2212 X \u00af ) ( X n + r \u2212 X \u00af ) \u27e9 = \u27e8 X n X n + r \u27e9 \u2212 X \u00af 2 , {\\displaystyle K(r)=\\langle (X_{n}-{\\bar {X}})(X_{n+r}-{\\bar {X}})\\rangle =\\langle X_{n}X_{n+r}\\rangle -{\\bar {X}}^{2},} where the symbol \u27e8 \u22ef \u27e9 {\\displaystyle \\langle \\cdots \\rangle } denotes averaging over all n. By definition, K ( \u2212 r ) = K ( r ) , K ( 0 ) = X \u00af ( 1 \u2212 X \u00af ) . {\\displaystyle K(-r)=K(r),K(0)={\\bar {X}}(1-{\\bar {X}}).} There is a relation between the memory function and the correlation function of the binary additive Markov chain: K ( r ) = \u2211 s = 1 m K ( r \u2212 s ) F ( s ) , r = 1 , 2 , \u2026 . {\\displaystyle K(r)=\\sum _{s=1}^{m}K(r-s)F(s),\\,\\,\\,\\,r=1,2,\\dots \\,.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first three examples possess simple parametric representations, which is not true for the fourth and fifth examples. The fifth example shows the possibly complicated geometric structure of an implicit curve. The implicit function theorem describes conditions under which an equation F ( x , y ) = 0 {\\displaystyle F(x,y)=0} can be solved implicitly for x and/or y \u2013 that is, under which one can validly write x = g ( y ) {\\displaystyle x=g(y)} or y = f ( x ) {\\displaystyle y=f(x)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to create specialized packet processing platforms, a variety of technologies have been developed and deployed. These technologies, which span the breadth of hardware and software, have all been designed with the aim of maximizing speed and throughput while minimizing latency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first round P {\\displaystyle P} processors combine their blocks into P / 2 {\\displaystyle P/2} blocks. Then P / 2 {\\displaystyle P/2} processors combine the P / 2 {\\displaystyle P/2} blocks into P / 4 {\\displaystyle P/4} . This procedure is continued until all the data is combined in one block.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, data compaction is the reduction of the number of data elements, bandwidth, cost, and time for the generation, transmission, and storage of data without loss of information by eliminating unnecessary redundancy, removing irrelevancy, or using special coding. Examples of data compaction methods are the use of fixed-tolerance bands, variable-tolerance bands, slope-keypoints, sample changes, curve patterns, curve fitting, variable-precision coding, frequency analysis, and probability analysis. Simply squeezing noncompacted data into a smaller space, for example by increasing packing density by transferring images from newsprint to microfilm or by transferring data on punched cards onto magnetic tape, is not data compaction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of continuous optimization, individual learning exists in the form of local heuristics or conventional exact enumerative methods. Examples of individual learning strategies include the hill climbing, Simplex method, Newton/Quasi-Newton method, interior point methods, conjugate gradient method, line search, and other local heuristics. Note that most of the common individual learning methods are deterministic. In combinatorial optimization, on the other hand, individual learning methods commonly exist in the form of heuristics (which can be deterministic or stochastic) that are tailored to a specific problem of interest. Typical heuristic procedures and schemes include the k-gene exchange, edge exchange, first-improvement, and many others.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By symmetry, for only successes, the 95% confidence interval is . The rule is useful in the interpretation of clinical trials generally, particularly in phase II and phase III where often there are limitations in duration or statistical power. The rule of three applies well beyond medical research, to any trial done n times. If 300 parachutes are randomly tested and all open successfully, then it is concluded with 95% confidence that fewer than 1 in 100 parachutes with the same characteristics (3/300) will fail.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Primality testing is a field that has been around since the time of Fermat, in whose time most algorithms were based on factoring, which become unwieldy with large input; modern algorithms treat the problems of determining whether a number is prime and what its factors are separately. It became of practical importance with the advent of modern cryptography. Although many current tests result in a probabilistic output (N is either shown composite, or probably prime, such as with the Baillie\u2013PSW primality test or the Miller\u2013Rabin test), the elliptic curve test proves primality (or compositeness) with a quickly verifiable certificate.Previously-known prime-proving methods such as the Pocklington primality test required at least partial factorization of N \u00b1 1 {\\displaystyle N\\pm 1} in order to prove that N {\\displaystyle N} is prime. As a result, these methods required some luck and are generally slow in practice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These are also sometimes called canonical maps. A canonical isomorphism is a canonical map that is also an isomorphism (i.e., invertible). In some contexts, it might be necessary to address an issue of choices of canonical maps or canonical isomorphisms; for a typical example, see prestack. For a discussion of the problem of defining a canonical map see Kevin Buzzard's talk at the 2022 Grothendieck conference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A researcher may request outputs which breach the 'rules of thumb' as long as (1) they are non-disclosive (2) they are important and (3) this is an exceptional request. It is up to the researcher to prove that any 'unsafe' outputs are non-disclosive, but the checker has the final say. Since there are no hard rules, this requires knowledge on disclosure risks and judgment from both the researcher and the checker. It requires training and an understanding of statistics and data analysis, although it has been argued that this can be used to make the process more efficient than a rules-based model. The UK Data Service employs a principles-based approach to statistical disclosure control from its Secure Data Service.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This method was proposed in Shannon's \"A Mathematical Theory of Communication\" (1948), his article introducing the field of information theory. Fano's method divides the source symbols into two sets (\"0\" and \"1\") with probabilities as close to 1/2 as possible. Then those sets are themselves divided in two, and so on, until each set contains only one symbol.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model theory, an atomic formula is satisfiable if there is a collection of elements of a structure that render the formula true. If A is a structure, \u03c6 is a formula, and a is a collection of elements, taken from the structure, that satisfy \u03c6, then it is commonly written that A \u22a7 \u03c6 If \u03c6 has no free variables, that is, if \u03c6 is an atomic sentence, and it is satisfied by A, then one writes A \u22a7 \u03c6In this case, one may also say that A is a model for \u03c6, or that \u03c6 is true in A. If T is a collection of atomic sentences (a theory) satisfied by A, one writes A \u22a7 T", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following table, each row shows undisputed Greek cognates sharing the three ablaut grades of a root. The four sonorants and the two semivowels are represented as individual letters, other consonants as C and the vowel or its absence as (V). The reconstructed PIE e grade and zero grade of the above roots may be arranged as follows: An extension of the table to PIE roots ending in presumed laryngeals allows many Greek cognates to follow a regular ablaut pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most parliamentary democracies, members of a parliament can propose a motion of confidence or of no confidence in the government or executive. The results of such motions show how much support the government currently has in parliament. Should a motion of confidence fail, or a motion of no confidence pass, the government will usually either resign and allow other politicians to form a new government, or call an election.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to generate a Janet basis, a ranking of derivatives must be defined. It is a total ordering such that for any derivatives \u03b4 {\\displaystyle \\delta } , \u03b4 1 {\\displaystyle \\delta _{1}} and \u03b4 2 {\\displaystyle \\delta _{2}} , and any derivation operator \u03b8 {\\displaystyle \\theta } the relations \u03b4 \u2aaf \u03b8 \u03b4 {\\displaystyle \\delta \\preceq \\theta \\delta } , and \u03b4 1 \u2aaf \u03b4 2 \u2192 \u03b4 \u03b4 1 \u2aaf \u03b4 \u03b4 2 {\\displaystyle \\delta _{1}\\preceq \\delta _{2}\\rightarrow \\delta \\delta _{1}\\preceq \\delta \\delta _{2}} are valid. Here graded lexicographic term orderings g r l e x {\\displaystyle grlex} are applied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These were not merely binary-coded decimal (BCD). Most machines had ten vacuum tubes per digit in each processor register.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example green edges are being evaluated by the algorithm and red edges have been deleted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a formal calculation, or formal operation, is a calculation that is systematic but without a rigorous justification. It involves manipulating symbols in an expression using a generic substitution without proving that the necessary conditions hold. Essentially, it involves the form of an expression without considering its underlying meaning. This reasoning can either serve as positive evidence that some statement is true when it is difficult or unnecessary to provide proof or as an inspiration for the creation of new (completely rigorous) definitions. However, this interpretation of the term formal is not universally accepted, and some consider it to mean quite the opposite: a completely rigorous argument, as in formal mathematical logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that, at first glance, suggest the possibility of communication faster-than-light. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics, such as the EPR paradox, or violations of local realism obtained in tests of Bell's theorem. In these experiments, the no-communication theorem shows that failure of local realism does not lead to what could be referred to as \"spooky communication at a distance\" (in analogy with Einstein's labeling of quantum entanglement as requiring \"spooky action at a distance\" on the assumption of QM's completeness).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, net gain is the overall gain of a transmission circuit. Net gain is measured by applying a test signal at an appropriate power level at the input port of a circuit and measuring the power delivered at the output port. The net gain in dB is calculated by taking 10 times the common logarithm of the ratio of the output power to the input power. The net gain expressed in dB may be positive or negative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Execute test suites of test cases. Generate associated test reports.These individual objectives may be fulfilled by unit test framework tools, stubs or drivers.A test harness may provide some of the following benefits: Increased productivity due to automation of the testing process. Increased probability that regression testing will occur.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of n distinct objects is n factorial, usually written as n!, which means the product of all positive integers less than or equal to n. Technically, a permutation of a set S is defined as a bijection from S to itself. That is, it is a function from S to S for which every element occurs exactly once as an image value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fantasy role-playing game Dungeons & Dragons, an Outer Plane is one of a number of general types of planes of existence. They can also be referred to as godly planes, spiritual planes or divine planes. The Outer Planes are home to beings such as deities and their servants such as demons, celestials and devils. Each Outer Plane is usually the physical manifestation of a particular moral and ethical alignment and the entities that dwell there often embody the traits related to that alignment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In prior iterations of Visual Basic, all statements in a condition would have been evaluated even if the outcome of the condition could be determined before evaluating a condition. For example: This was not only inefficient, but could lead to unexpected results for any person used to another language. In Visual Basic .NET, the new AndAlso and OrElse operators have been added to provide short-circuit evaluation like many other languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The logistic regression model itself simply models probability of output in terms of input and does not perform statistical classification (it is not a classifier), though it can be used to make a classifier, for instance by choosing a cutoff value and classifying inputs with probability greater than the cutoff as one class, below the cutoff as the other; this is a common way to make a binary classifier. Analogous linear models for binary variables with a different sigmoid function instead of the logistic function (to convert the linear combination to a probability) can also be used, most notably the probit model; see \u00a7 Alternatives. The defining characteristic of the logistic model is that increasing one of the independent variables multiplicatively scales the odds of the given outcome at a constant rate, with each independent variable having its own parameter; for a binary dependent variable this generalizes the odds ratio.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States only, the two largest carriers are instead implementing 4G LTE in the 700 MHz band, which was reallocated from TV broadcasting during the DTV transition. TV stations were forced to move to lower UHF and even far worse VHF frequencies with poorer mobile TV and even regular terrestrial TV performance, because the 700 MHz band has better radio propagation characteristics that allow mobile phone signal to penetrate deeper into buildings with less attenuation than the 1700 MHz or 2100 MHz bands.AT&T Mobility devices use former TV channel 53 and 54 nationwide and has purchased spectrum from former TV channel 55 nationwide (purchased from Qualcomm's defunct MediaFLO pay TV service), and also channel 56 in densely populated areas such as California and the Northeast Corridor. Verizon Wireless formerly held frequencies just above TV channel 51, which is still in use, causing adjacent-channel interference that is preventing the carrier from using them until the planned top-down spectrum repacking occurs. The channel 52 spectrum was later purchased by T-Mobile US who now uses this spectrum for their network. Verizon now uses higher blocks within the former TV band (channels 60 and 61).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a minimal counterexample is the smallest example which falsifies a claim, and a proof by minimal counterexample is a method of proof which combines the use of a minimal counterexample with the ideas of proof by induction and proof by contradiction. More specifically, in trying to prove a proposition P, one first assumes by contradiction that it is false, and that therefore there must be at least one counterexample. With respect to some idea of size (which may need to be chosen carefully), one then concludes that there is such a counterexample C that is minimal. In regard to the argument, C is generally something quite hypothetical (since the truth of P excludes the possibility of C), but it may be possible to argue that if C existed, then it would have some definite properties which, after applying some reasoning similar to that in an inductive proof, would lead to a contradiction, thereby showing that the proposition P is indeed true.If the form of the contradiction is that we can derive a further counterexample D, that is smaller than C in the sense of the working hypothesis of minimality, then this technique is traditionally called proof by infinite descent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "COBOL-74 added subprograms, giving programmers the ability to control the data each part of the program could access. COBOL-85 then added nested subprograms, allowing programmers to hide subprograms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Northern hemisphere, characteristic dominant broadleaf trees in this biome include oaks (Quercus spp. ), beeches (Fagus spp. ), maples (Acer spp. ), or birches (Betula spp.).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The most common such robust statistics are the interquartile range (IQR) and the median absolute deviation (MAD). These are contrasted with conventional or non-robust measures of scale, such as sample standard deviation, which are greatly influenced by outliers. These robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency on contaminated data, at the cost of inferior efficiency on clean data from distributions such as the normal distribution. To illustrate robustness, the standard deviation can be made arbitrarily large by increasing exactly one observation (it has a breakdown point of 0, as it can be contaminated by a single point), a defect that is not shared by robust statistics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational algebra, a projection is a unary operation written as \u03a0 a 1 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In renewal-anomalous files, a random period is taken independently from a waiting time probability density function (WT-PDF; see Continuous-time Markov process for more information) of the form: \u03c8 \u03b1 ( t ) \u223c k ( k t ) \u2212 1 \u2212 \u03b1 , 0 < \u03b1 \u2264 1 {\\displaystyle \\psi _{\\alpha }(t)\\sim k(kt)^{-1-\\alpha },0<\\alpha \\leq 1} , where k is a parameter. Then, all the particles in the file stand still for this random period, where afterwards, all the particles attempt jumping in accordance with the rules of the file. This procedure is carried on over and over again. The equation of motion for the particles\u2019 PDF in a renewal-anomalous file is obtained when convoluting the equation of motion for a Brownian file with a kernel k \u03b1 ( t ) {\\displaystyle k_{\\alpha }(t)}: Here, the kernel k \u03b1 ( t ) {\\displaystyle k_{\\alpha }(t)} and the WT-PDF \u03c8 \u03b1 ( t ) {\\displaystyle \\psi _{\\alpha }(t)} are related in Laplace space, k \u00af \u03b1 ( s ) = s \u03c8 \u00af \u03b1 ( s ) 1 \u2212 \u03c8 \u00af \u03b1 ( s ) {\\displaystyle {\\bar {k}}_{\\alpha }(s)={\\frac {s{\\bar {\\psi }}_{\\alpha }(s)}{1-{\\bar {\\psi }}_{\\alpha }(s)}}} . (The Laplace transform of a function f ( t ) {\\displaystyle f(t)} reads, f \u00af ( s ) = \u222b 0 \u221e f ( t ) e \u2212 s t d t {\\displaystyle {\\bar {f}}(s)=\\int _{0}^{\\infty }f(t)e^{-st}\\,dt} .) The reflecting boundary conditions accompanied Eq. (8) are obtained when convoluting the boundary conditions of a Brownian file with the kernel k \u03b1 ( t ) {\\displaystyle k_{\\alpha }(t)} , where here and in a Brownian file the initial conditions are identical.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems such as CGA or SFS and most cryptographic peer-to-peer networks, fingerprints are embedded into pre-existing address and name formats (such as IPv6 addresses, file names or other identification strings). If addresses and names are already being exchanged through trusted channels, this approach allows fingerprints to piggyback on them.In PGP, most keys are created in such a way that what is called the \"key ID\" is equal to the lower 32 or 64 bits respectively of a key fingerprint.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Character sets that may be available in one system may not be so in others. In other cases, one or more of the following transformation types may be required to meet the business and technical needs of the server or data warehouse: Selecting only certain columns to load: (or selecting null columns not to load). For example, if the source data has three columns (aka \"attributes\"), roll_no, age, and salary, then the selection may take only roll_no and salary. Or, the selection mechanism may ignore all those records where salary is not present (salary = null). Translating coded values: (e.g., if the source system codes male as \"1\" and female as \"2\", but the warehouse codes male as \"M\" and female as \"F\") Encoding free-form values: (e.g., mapping \"Male\" to \"M\") Deriving a new calculated value: (e.g., sale_amount = qty * unit_price) Sorting or ordering the data based on a list of columns to improve search performance Joining data from multiple sources (e.g., lookup, merge) and deduplicating the data Aggregating (for example, rollup \u2014 summarizing multiple rows of data \u2014 total sales for each store, and for each region, etc.) Generating surrogate-key values Transposing or pivoting (turning multiple columns into multiple rows or vice versa) Splitting a column into multiple columns (e.g., converting a comma-separated list, specified as a string in one column, into individual values in different columns) Disaggregating repeating columns Looking up and validating the relevant data from tables or referential files Applying any form of data validation; failed validation may result in a full rejection of the data, partial rejection, or no rejection at all, and thus none, some, or all of the data is handed over to the next step depending on the rule design and exception handling; many of the above transformations may result in exceptions, e.g., when a code translation parses an unknown code in the extracted data", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical finite group theory, an N-group is a group all of whose local subgroups (that is, the normalizers of nontrivial p-subgroups) are solvable groups. The non-solvable ones were classified by Thompson during his work on finding all the minimal finite simple groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages, an abstract type is a type in a nominative type system that cannot be instantiated directly; a type that is not abstract \u2013 which can be instantiated \u2013 is called a concrete type. Every instance of an abstract type is an instance of some concrete subtype. Abstract types are also known as existential types.An abstract type may provide no implementation, or an incomplete implementation. In some languages, abstract types with no implementation (rather than an incomplete implementation) are known as protocols, interfaces, signatures, or class types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 8-bit versions, while running, the CP/M operating system loaded into memory had three components: Basic Input/Output System (BIOS), Basic Disk Operating System (BDOS), Console Command Processor (CCP).The BIOS and BDOS were memory-resident, while the CCP was memory-resident unless overwritten by an application, in which case it was automatically reloaded after the application finished running. A number of transient commands for standard utilities were also provided. The transient commands resided in files with the extension .COM on disk. The BIOS directly controlled hardware components other than the CPU and main memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, call control refers to the software within a telephone switch that supplies its central function. Call control decodes addressing information and routes telephone calls from one end point to another. It also creates the features that can be used to adapt standard switch operation to the needs of users.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to strengthen parity protection for the sound samples, the parity bit is calculated on only the top six bits of each NICAM sample. Early BBC NICAM research showed that uncorrected errors in the least significant four bits were preferable to the reduced overall protection offered by parity-protecting all ten bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the System/360, other than the 360/67, and System/370 architectures, the general-purpose registers were 32 bits wide, the machine did 32-bit arithmetic operations, and addresses were always stored in 32-bit words, so the architecture was considered 32-bit, but the machines ignored the top 8 bits of the address resulting in 24-bit addressing. Much of System/360's and System/370's large installed code base relied on a 24-bit logical address; In particular, a heavily used machine instruction, LA, Load Address, explicitly cleared the top eight bits of the address being placed in a register. If the 24-bit limit were to be removed, this would create migration problems for existing software. This was addressed by adding an addressing mode bit to the Program Status Word controlling whether the program runs in 24-bit mode, in which the top eight bits of virtual addresses are ignored, or 31-bit mode, in which only the uppermost bit of virtual addresses are ignored.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The 8-bit ISO 8859-2 (Latin-2) standard was developed by ISO. MS-DOS introduced 8-bit encoding CP852 for Central European languages, disregarding the ISO standard. Microsoft Windows spread yet another 8-bit encoding called CP1250, which had a few letters mapped one-to-one with ISO 8859-2, but also had some mapped elsewhere.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The fork operation creates a separate address space for the child. The child process has an exact copy of all the memory segments of the parent process. In modern UNIX variants that follow the virtual memory model from SunOS-4.0, copy-on-write semantics are implemented and the physical memory need not be actually copied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers. It is an instance of a scheme for numbering permutations and is an example of an inversion table. The Lehmer code is named in reference to Derrick Henry Lehmer, but the code had been known since 1888 at least.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to apply backtracking to a specific class of problems, one must provide the data P for the particular instance of the problem that is to be solved, and six procedural parameters, root, reject, accept, first, next, and output. These procedures should take the instance data P as a parameter and should do the following: root(P): return the partial candidate at the root of the search tree. reject(P,c): return true only if the partial candidate c is not worth completing. accept(P,c): return true if c is a solution of P, and false otherwise. first(P,c): generate the first extension of candidate c. next(P,s): generate the next alternative extension of a candidate, after the extension s. output(P,c): use the solution c of P, as appropriate to the application.The backtracking algorithm reduces the problem to the call backtrack(root(P)), where backtrack is the following recursive procedure: procedure backtrack(P, c) is if reject(P, c) then return if accept(P, c) then output(P, c) s \u2190 first(P, c) while s \u2260 NULL do backtrack(P, s) s \u2190 next(P, s)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a pepper which is unique to each user, the tradeoff is gaining extra security at the cost of storing more information securely. Compromising one password hash and revealing its secret pepper will have no effect on other password hashes and their secret pepper, so each pepper must be individually discovered, which greatly increases the time taken to attack the password hashes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the aforementioned interview, Vass also described their plans for the company's first multi-user computer, based on a CP/M-derived executive that they called AMEX (Altos Multiuser Executive). Their new design planned to support up to four users, by providing each user with its own 48 KB of dedicated program memory (addressable by the 8-bit Z80 processor through bank switching), while the 16 KB of memory for the operating system's image could be shared by all users. An advertisement for the \"Sun-Series ACS8000-6\" sold under Altos' own brand appeared in the November 1979 issue of Byte, and indeed promised to support up to four users by means of its AMEX kernel, and supporting a maximum system memory of 208 KB. The ACS 8000 could run at least three multi-user operating systems: Altos' own AMEX, Oasis, or MP/M.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a rational reciprocity law is a reciprocity law involving residue symbols that are related by a factor of +1 or \u20131 rather than a general root of unity. As an example, there are rational biquadratic and octic reciprocity laws. Define the symbol (x|p)k to be +1 if x is a k-th power modulo the prime p and -1 otherwise. Let p and q be distinct primes congruent to 1 modulo 4, such that (p|q)2 = (q|p)2 = +1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this case, positive numbers always have a most significant digit between 0 and 4 (inclusive), while negative numbers are represented by the 10's complement of the corresponding positive number. As a result, this system allows for 32-bit packed BCD numbers to range from \u221250,000,000 to +49,999,999, and \u22121 is represented as 99999999. (As with two's complement binary numbers, the range is not symmetric about zero.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, scale analysis is a set of methods to analyze survey data, in which responses to questions are combined to measure a latent variable. These items can be dichotomous (e.g. yes/no, agree/disagree, correct/incorrect) or polytomous (e.g. disagree strongly/disagree/neutral/agree/agree strongly). Any measurement for such data is required to be reliable, valid, and homogeneous with comparable results over different studies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Outliers, being the most extreme observations, may include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum are not always outliers because they may not be unusually far from other observations. Naive interpretation of statistics derived from data sets that include outliers may be misleading.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is x, and the most common symbol for the output is y; the function itself is commonly written y = f(x).It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and y are independent variables. Functions with multiple outputs are often referred to as vector-valued functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Take for example the following exchange: A (to passerby): I am out of gas. B: There is a gas station 'round the corner.Here, B does not say, but conversationally implicates, that the gas station is open, because otherwise his utterance would not be relevant in the context. Conversational implicatures are classically seen as contrasting with entailments: They are not necessary or logical consequences of what is said, but are defeasible (cancellable). So, B could continue without contradiction: B: But unfortunately it's closed today.An example of a conventional implicature is \"Donovan is poor but happy\", where the word \"but\" implicates a sense of contrast between being poor and being happy.Later linguists introduced refined and different definitions of the term, leading to somewhat different ideas about which parts of the information conveyed by an utterance are actually implicatures and which are not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Out-of-order delivery When a collection of related packets is routed through a network, different packets may take different routes, each resulting in a different delay. The result is that the packets arrive in a different order than they were sent. This problem requires special additional protocols for rearranging out-of-order packets. The reordering process requires additional buffering at the receiver, and, as with packet delay variation, increases the overall latency for the stream.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Stern\u2013Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree. The Stern\u2013Brocot tree was introduced independently by Moritz Stern (1858) and Achille Brocot (1861). Stern was a German number theorist; Brocot was a French clockmaker who used the Stern\u2013Brocot tree to design systems of gears with a gear ratio close to some desired value by finding a ratio of smooth numbers near that value. The root of the Stern\u2013Brocot tree corresponds to the number 1. The parent-child relation between numbers in the Stern\u2013Brocot tree may be defined in terms of continued fractions or mediants, and a path in the tree from the root to any other number q provides a sequence of approximations to q with smaller denominators than q. Because the tree contains each positive rational number exactly once, a breadth first search of the tree provides a method of listing all positive rationals that is closely related to Farey sequences. The left subtree of the Stern\u2013Brocot tree, containing the rational numbers in the range (0,1), is called the Farey tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice many channels have memory. Namely, at time i {\\displaystyle i} the channel is given by the conditional probability P ( y i | x i , x i \u2212 1 , x i \u2212 2 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When this group has order 16, Dummit and Foote refer to this group as the \"modular group of order 16\", as its lattice of subgroups is modular. In this article this group will be called the modular maximal-cyclic group of order 2 n {\\displaystyle 2^{n}} . Its presentation is: \u27e8 r , s \u2223 r 2 n \u2212 1 = s 2 = 1 , s r s = r 2 n \u2212 2 + 1 \u27e9 {\\displaystyle \\langle r,s\\mid r^{2^{n-1}}=s^{2}=1,\\ srs=r^{2^{n-2}+1}\\rangle \\,\\!}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to achieve optimal place and routing for partitioned designs, the engineer must focus on FPGA pin count and inter-FPGA signals. After partitioning the design into separate FPGAs, the number of inter-FPGA signals must not to exceed the pin count on the FPGA. This is very difficult to avoid when circuit designs are immense, thus signals must utilize strategies such as time-division multiplexing (TDM) which multiple signals can be transferred over a single line. These multiple signals, called sub-channels, take turns being transferred over the line over a time slot. When the TDM ratio is high, the bus clock frequency has to be reduced to accommodate time slots for each sub-channel. By reducing the clock frequency the throughput of the system is hindered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, neither instrument used electricity as a sound-source. The first electric synthesizer was invented in 1876 by Elisha Gray. The \"Musical Telegraph\" was a chance by-product of his telephone technology when Gray discovered that he could control sound from a self-vibrating electromagnetic circuit and so invented a basic oscillator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When personal confidential information is shared between healthcare workers, consent is taken as implied. If a patient doesn't want a healthcare worker to share confidential health information, they need to make this clear and discuss the matter with healthcare staff. Patients have the right, in most situations, to refuse permission for a health care professional to share their information with another healthcare professional, even one giving them care\u2014but are advised, where appropriate, about the dangers of this course of action, due to possible drug interactions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages multi-level breaks are also possible. For handling exceptional situations, specialized exception handling constructs were added, such as try/catch/finally in Java. The throw-catch exception handling mechanisms can also be easily abused to create non-transparent control structures, just like goto can be abused.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to prove a lower bound for the distance of a code C \u2217 {\\displaystyle C^{*}} we prove that the Hamming distance of an arbitrary but distinct pair of codewords has a lower bound. So let \u0394 ( c 1 , c 2 ) {\\displaystyle \\Delta (c^{1},c^{2})} be the Hamming distance of two codewords c 1 {\\displaystyle c^{1}} and c 2 {\\displaystyle c^{2}} . For any given m 1 \u2260 m 2 \u2208 ( F q k ) K , {\\displaystyle m_{1}\\neq m_{2}\\in \\left(\\mathbb {F} _{q^{k}}\\right)^{K},} we want a lower bound for \u0394 ( C \u2217 ( m 1 ) , C \u2217 ( m 2 ) ) . {\\displaystyle \\Delta (C^{*}(m_{1}),C^{*}(m_{2})).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(also shortest addition chain, 5 multiplications).On the other hand, the determination of a shortest addition chain is hard: no efficient optimal methods are currently known for arbitrary exponents, and the related problem of finding a shortest addition chain for a given set of exponents has been proven NP-complete. Even given a shortest chain, addition-chain exponentiation requires more memory than the binary method, because it must potentially store many previous exponents from the chain. So in practice, shortest addition-chain exponentiation is primarily used for small fixed exponents for which a shortest chain can be pre-computed and is not too large.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way). The concept of a group was elaborated for handling, in a unified way, many mathematical structures such as numbers, geometric shapes and polynomial roots.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1). Years 6, 12 and 23 of the cycle are common years beginning on Monday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Monday.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, version control (also known as revision control, source control, or source code management) is a class of systems responsible for managing changes to computer programs, documents, large web sites, or other collections of information. Version control is a component of software configuration management.Changes are usually identified by a number or letter code, termed the \"revision number\", \"revision level\", or simply \"revision\". For example, an initial set of files is \"revision 1\". When the first change is made, the resulting set is \"revision 2\", and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Arf semigroups are certain subsets of the non-negative integers closed under addition, that were studied by Cahit Arf (1948). They appeared as the semigroups of values of Arf rings. A subset of the integers forms a monoid if it includes zero, and if every two elements in the subset have a sum that also belongs to the subset. In this case, it is called a \"numerical semigroup\". A numerical semigroup is called an Arf semigroup if, for every three elements x, y, and z with z = min(x, y, and z), the semigroup also contains the element x + y \u2212 z. For instance, the set containing zero and all even numbers greater than 10 is an Arf semigroup.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Overfilling a buffer on the stack is more likely to derail program execution than overfilling a buffer on the heap because the stack contains the return addresses for all active function calls. A stack buffer overflow can be caused deliberately as part of an attack known as stack smashing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is a copy of the pids array in all 11 processes, but only in the parent is it complete - the copy in each child will be missing the lower-numbered child PIDs, and have zero for its own PID. (Not that this really matters, as only the parent process actually uses this array.) The second loop executes only in the parent process (because all of the children have exited before this point), and waits for each child to exit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two competing notational conventions split the field of matrix calculus into two separate groups. The two groups can be distinguished by whether they write the derivative of a scalar with respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be treated as column vectors when combined with matrices (rather than row vectors).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Policy formulation \u2013 Involves exploring a variation of options or alternative courses of action available for addressing the problem. (appraisal, dialogue, formulation, and consolidation) Decision-making \u2013 Government decides on an ultimate course of action, whether to perpetuate the policy status quo or alter it. (Decision could be 'positive', 'negative', or 'no-action') Implementation \u2013 The ultimate decision made earlier will be put into practice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This tactic applies only to VIS' variables of type Z {\\displaystyle \\mathbb {Z} } (or its \"subtype\" N {\\displaystyle \\mathbb {N} } ). It consists in associating a range to a variable and deriving test classes by comparing the variable with the limits of the range in some ways. More formally, let n be a variable of type Z {\\displaystyle \\mathbb {Z} } and let  {\\displaystyle } be the associated range.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1880s, German scientist Herman Von Helmholtz derived the equation for the maximum work which can be reversibly obtained from a closed system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the support of a probability distribution can be loosely thought of as the closure of the set of possible values of a random variable having that distribution. There are, however, some subtleties to consider when dealing with general distributions defined on a sigma algebra, rather than on a topological space. More formally, if X: \u03a9 \u2192 R {\\displaystyle X:\\Omega \\to \\mathbb {R} } is a random variable on ( \u03a9 , F , P ) {\\displaystyle (\\Omega ,{\\mathcal {F}},P)} then the support of X {\\displaystyle X} is the smallest closed set R X \u2286 R {\\displaystyle R_{X}\\subseteq \\mathbb {R} } such that P ( X \u2208 R X ) = 1. {\\displaystyle P\\left(X\\in R_{X}\\right)=1.} In practice however, the support of a discrete random variable X {\\displaystyle X} is often defined as the set R X = { x \u2208 R: P ( X = x ) > 0 } {\\displaystyle R_{X}=\\{x\\in \\mathbb {R} :P(X=x)>0\\}} and the support of a continuous random variable X {\\displaystyle X} is defined as the set R X = { x \u2208 R: f X ( x ) > 0 } {\\displaystyle R_{X}=\\{x\\in \\mathbb {R} :f_{X}(x)>0\\}} where f X ( x ) {\\displaystyle f_{X}(x)} is a probability density function of X {\\displaystyle X} (the set-theoretic support).Note that the word support can refer to the logarithm of the likelihood of a probability density function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Fermi\u2013Dirac prime is a prime power whose exponent is a power of two. These numbers are named from an analogy to Fermi\u2013Dirac statistics in physics based on the fact that each integer has a unique representation as a product of Fermi\u2013Dirac primes without repetition. Each element of the sequence of Fermi\u2013Dirac primes is the smallest number that does not divide the product of all previous elements. Srinivasa Ramanujan used the Fermi\u2013Dirac primes to find the smallest number whose number of divisors is a given power of two.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then T {\\displaystyle T} is the number of linear codes C i n i , i \u2208 S {\\displaystyle C_{in}^{i},i\\in S} having the distance H q \u2212 1 ( 1 2 \u2212 \u03b5 ) \u22c5 2 k . {\\displaystyle H_{q}^{-1}\\left({\\tfrac {1}{2}}-\\varepsilon \\right)\\cdot 2k.} Now we want to estimate | S | .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical modeling (especially process modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example, graph H is a minor of graph G: H. G. The following diagram illustrates this. First construct a subgraph of G by deleting the dashed edges (and the resulting isolated vertex), and then contract the gray edge (merging the two vertices it connects):", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the bin covering problem, the bin size is bounded from below: the goal is to maximize the number of bins used such that the total size in each bin is at least a given threshold. In the fair indivisible chore allocation problem (a variant of fair item allocation), the items represent chores, and there are different people each of whom attributes a different difficulty-value to each chore. The goal is to allocate to each person a set of chores with an upper bound on its total difficulty-value (thus, each person corresponds to a bin). Many techniques from bin packing are used in this problem too.In the guillotine cutting problem, both the items and the \"bins\" are two-dimensional rectangles rather than one-dimensional numbers, and the items have to be cut from the bin using end-to-end cuts. In the selfish bin packing problem, each item is a player who wants to minimize its cost.There is also a variant of bin packing in which the cost that should be minimized is not the number of bins, but rather a certain concave function of the number of items in each bin.Other variants are two-dimensional bin packing, three-dimensional bin packing, bin packing with delivery,", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x\u22121, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of computational biology, a planted motif search (PMS) also known as a (l, d)-motif search (LDMS) is a method for identifying conserved motifs within a set of nucleic acid or peptide sequences. PMS is known to be NP-complete. The time complexities of most of the planted motif search algorithms depend exponentially on the alphabet size and l. The PMS problem was first introduced by Keich and Pevzner.The problem of identifying meaningful patterns (e.g., motifs) from biological data has been studied extensively since they play a vital role in understanding gene function, human disease, and may serve as therapeutic drug targets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In that paper, a \"similarity ratio\" is given over bitmaps, where each bit of a fixed-size array represents the presence or absence of a characteristic in the plant being modelled. The definition of the ratio is the number of common bits, divided by the number of bits set (i.e. nonzero) in either sample. Presented in mathematical terms, if samples X and Y are bitmaps, X i {\\displaystyle X_{i}} is the ith bit of X, and \u2227 , \u2228 {\\displaystyle \\land ,\\lor } are bitwise and, or operators respectively, then the similarity ratio T s {\\displaystyle T_{s}} is T s ( X , Y ) = \u2211 i ( X i \u2227 Y i ) \u2211 i ( X i \u2228 Y i ) {\\displaystyle T_{s}(X,Y)={\\frac {\\sum _{i}(X_{i}\\land Y_{i})}{\\sum _{i}(X_{i}\\lor Y_{i})}}} If each sample is modelled instead as a set of attributes, this value is equal to the Jaccard coefficient of the two sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F242 of 24-bit words such that any two distinct elements of W differ in at least 8 coordinates. W is called a linear code because it is a vector space. In all, W comprises 4096 = 212 elements. The elements of W are called code words.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the diagram above (Oxelheim, 1990), the options are: Option (a): A stable exchange rate and free capital flows (but not an independent monetary policy because setting a domestic interest rate that is different from the world interest rate would undermine a stable exchange rate due to appreciation or depreciation pressure on the domestic currency). Option (b): An independent monetary policy and free capital flows (but not a stable exchange rate). Option (c): A stable exchange rate and independent monetary policy (but no free capital flows, which would require the use of capital controls).Currently, Eurozone members have chosen the first option (a) after the introduction of the euro.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Designers also experimented with using large sets of internal registers. The goal was to cache intermediate results in the registers under the control of the compiler. This also reduced the number of addressing modes and orthogonality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the presence of the axiom of choice, any cardinal number can be well-ordered, and then the following are equivalent for a cardinal \u03ba {\\displaystyle \\kappa }: \u03ba {\\displaystyle \\kappa } is a regular cardinal. If \u03ba = \u2211 i \u2208 I \u03bb i {\\displaystyle \\kappa =\\sum _{i\\in I}\\lambda _{i}} and \u03bb i < \u03ba {\\displaystyle \\lambda _{i}<\\kappa } for all i {\\displaystyle i} , then | I | \u2265 \u03ba {\\displaystyle |I|\\geq \\kappa } . If S = \u22c3 i \u2208 I S i {\\displaystyle S=\\bigcup _{i\\in I}S_{i}} , and if | I | < \u03ba {\\displaystyle |I|<\\kappa } and | S i | < \u03ba {\\displaystyle |S_{i}|<\\kappa } for all i {\\displaystyle i} , then | S | < \u03ba {\\displaystyle |S|<\\kappa } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Apple's Macintosh Central European encoding does not include the entire Gaj's Latin alphabet. Instead, a separate codepage, called MacCroatian encoding, is used. EBCDIC also has a Latin-2 encoding.The preferred character encoding for Croatian today is either the ISO 8859-2, or the Unicode encoding UTF-8 (with two bytes or 16 bits necessary to use the letters with diacritics). However, as of 2010, one can still find programs as well as databases that use CP1250, CP852 or even CROSCII. Digraphs \u27e8d\u017e\u27e9, \u27e8lj\u27e9 and \u27e8nj\u27e9 in their upper case, title case and lower case forms have dedicated Unicode code points as shown in the table below, However, these are included chiefly for backwards compatibility with legacy encodings which kept a one-to-one correspondence with Cyrillic; modern texts use a sequence of characters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many choices made at software design time cannot be directly expressed in today's implementation languages like C# and Java. These design choices (known by names like Design Pattern, Design Contract, Refactoring, Effective Programming Idioms, Blueprints, etc.) must be implemented via programming and naming conventions, because they go beyond the built-in functionality of production programming languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Personal information such as contact numbers of friends and family can also be stored on the SIM by the subscriber.After subscribers sign up, information about their identity (telephone number) and what services they are allowed to access are stored in a \"SIM record\" in the Home Location Register (HLR). Once the SIM card is loaded into the phone and the phone is powered on, it will search for the nearest mobile phone mast (also called a Base Transceiver Station/BTS) with the strongest signal in the operator's frequency band. If a mast can be successfully contacted, then there is said to be coverage in the area.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically in linear algebra, the spark of a m \u00d7 n {\\displaystyle m\\times n} matrix A {\\displaystyle A} is the smallest integer k {\\displaystyle k} such that there exists a set of k {\\displaystyle k} columns in A {\\displaystyle A} which are linearly dependent. If all the columns are linearly independent, s p a r k ( A ) {\\displaystyle \\mathrm {spark} (A)} is usually defined to be 1 more than the number of rows. The concept of matrix spark finds applications in error-correction codes, compressive sensing, and matroid theory, and provides a simple criterion for maximal sparsity of solutions to a system of linear equations. The spark of a matrix is NP-hard to compute.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of classical computer vision, scale-space theory has established itself as a theoretical framework for early vision, with Gaussian derivatives constituting a canonical model for the first layer of receptive fields. With the introduction of deep learning, there has also been work on also using Gaussian derivatives or Gaussian kernels as a general basis for receptive fields in deep networks. Using the transformation properties of the Gaussian derivatives and Gaussian kernels under scaling transformations, it is in this way possible to obtain scale covariance/equivariance and scale invariance of the deep network to handle image structures at different scales in a theoretically well-founded manner. There have also been approaches developed to obtain scale covariance/equivariance and scale invariance by learned filters combined with multiple scale channels. Specifically, using the notions of scale covariance/equivariance and scale invariance, it is possible to make deep networks operate robustly at scales not spanned by the training data, thus enabling scale generalization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, particularly when considering data analysis, it is common to use the term \"categorical data\" to apply to data sets that, while containing some categorical variables, may also contain non-categorical variables. A categorical variable that can take on exactly two values is termed a binary variable or a dichotomous variable; an important special case is the Bernoulli variable. Categorical variables with more than two possible values are called polytomous variables; categorical variables are often assumed to be polytomous unless otherwise specified.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These segments had to be contiguous when resident in RAM, requiring additional computation and movement to remedy fragmentation.Ferranti's Atlas, and the Atlas Supervisor developed at the University of Manchester, (1962), was the first system to implement memory paging. Subsequent early machines, and their operating systems, supporting paging include the IBM M44/44X and its MOS operating system (1964),, the SDS 940 and the Berkeley Timesharing System (1966), a modified IBM System/360 Model 40 and the CP-40 operating system (1967), the IBM System/360 Model 67 and operating systems such as TSS/360 and CP/CMS (1967), the RCA 70/46 and the Time Sharing Operating System (1967), the GE 645 and Multics (1969), and the PDP-10 with added BBN-designed paging hardware and the TENEX operating system (1969). Those machines, and subsequent machines supporting memory paging, use either a set of page address registers or in-memory page tables to allow the processor to operate on arbitrary pages anywhere in RAM as a seemingly contiguous logical address space. These pages became the units exchanged between disk and RAM.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of group theory, a sequence G 0 \u2192 f 1 G 1 \u2192 f 2 G 2 \u2192 f 3 \u22ef \u2192 f n G n {\\displaystyle G_{0}\\;{\\xrightarrow {\\ f_{1}\\ }}\\;G_{1}\\;{\\xrightarrow {\\ f_{2}\\ }}\\;G_{2}\\;{\\xrightarrow {\\ f_{3}\\ }}\\;\\cdots \\;{\\xrightarrow {\\ f_{n}\\ }}\\;G_{n}} of groups and group homomorphisms is said to be exact at G i {\\displaystyle G_{i}} if im \u2061 ( f i ) = ker \u2061 ( f i + 1 ) {\\displaystyle \\operatorname {im} (f_{i})=\\ker(f_{i+1})} . The sequence is called exact if it is exact at each G i {\\displaystyle G_{i}} for all 1 \u2264 i < n {\\displaystyle 1\\leq i", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Usually only rules that are recursive are important; i.e. rules such that there is an effective procedure for determining whether any given formula is the conclusion of a given set of formulae according to the rule. An example of a rule that is not effective in this sense is the infinitary \u03c9-rule.Popular rules of inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical quantifiers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the benefit is that minimal functionality is still possible on hosts that otherwise would be unable to support HID. The only devices supported in boot protocol are Keyboard \u2013 Any of the first 256 key codes (\"Usages\") defined in the HID Usage Tables, Usage Page 7 can be reported by a keyboard using the boot protocol, but most systems only handle a subset of these keys. Most systems support all 104 keys on the IBM AT-101 layout, plus the three extra keys designed for Microsoft Windows 95 (the left and right Windows key, and the Menu key).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that this terminology is not standardized and some authors will use rate where this article uses order (e.g., ). In practice, the rate and order of convergence provide useful insights when using iterative methods for calculating numerical approximations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are constants C 1 , C 2 > 0 {\\displaystyle C_{1},C_{2}>0} so that the following two conditions are satisfied: For all n, \u2016 p n \u2016 \u2265 C 1 \u2016 \u2207 f ( x n ) \u2016 {\\displaystyle \\|\\mathbf {p} _{n}\\|\\geq C_{1}\\,\\|\\nabla f(\\mathbf {x} _{n})\\|} . Here, \u2016 y \u2016 {\\displaystyle \\|y\\|} is the Euclidean norm of y {\\displaystyle y} . (This assures that if p n = 0 {\\displaystyle \\mathbf {p} _{n}=0} , then also \u2207 f ( x n ) = 0 {\\displaystyle \\nabla f(\\mathbf {x} _{n})=0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nevertheless, most of the interesting results on cardinality and its arithmetic can be expressed merely with =c. The goal of a cardinal assignment is to assign to every set A a specific, unique set that is only dependent on the cardinality of A. This is in accordance with Cantor's original vision of cardinals: to take a set and abstract its elements into canonical \"units\" and collect these units into another set, such that the only thing special about this set is its size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most typed functional programming languages implement tuples directly as product types, tightly associated with algebraic data types, pattern matching, and destructuring assignment. Many programming languages offer an alternative to tuples, known as record types, featuring unordered elements accessed by label. A few programming languages combine ordered tuple product types and unordered record types into a single construct, as in C structs and Haskell records. Relational databases may formally identify their rows (records) as tuples. Tuples also occur in relational algebra; when programming the semantic web with the Resource Description Framework (RDF); in linguistics; and in philosophy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to mitigate risk on vulnerable clients, some WPA2-enabled Wi-Fi access points have configuration options that can disable EAPOL-Key frame re-transmission during key installation. Attackers cannot cause re-transmissions with a delayed frame transmission, thereby denying them access to the network, provided TDLS is not enabled. One disadvantage of this method is that, with poor connectivity, key reinstallation failure may cause failure of the Wi-Fi link.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming for telephony, concatenation is used to provide dynamic audio feedback to a user. For example, in a \"time of day\" speaking clock, concatenation is used to give the correct time by playing the appropriate recordings concatenated together. For example: \"At the tone the time will be\" \"Eight\" \"Thirty\" \"Five\" \"and\" \"Twenty\" \"Five\" \"Seconds\"The recordings themselves exist separately, but playing them one after the other provides a grammatically correct sentence to the listener.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The composition of two ring homomorphisms is a ring homomorphism. It follows that the class of all rings forms a category with ring homomorphisms as the morphisms (cf. the category of rings). In particular, one obtains the notions of ring endomorphism, ring isomorphism, and ring automorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first fifty nonhypotenuse numbers are: 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 23, 24, 27, 28, 31, 32, 33, 36, 38, 42, 43, 44, 46, 47, 48, 49, 54, 56, 57, 59, 62, 63, 64, 66, 67, 69, 71, 72, 76, 77, 79, 81, 83, 84 (sequence A004144 in the OEIS)Although nonhypotenuse numbers are common among small integers, they become more-and-more sparse for larger numbers. Yet, there are infinitely many nonhypotenuse numbers, and the number of nonhypotenuse numbers not exceeding a value x scales asymptotically with x/\u221alog x.The nonhypotenuse numbers are those numbers that have no prime factors of the form 4k+1. Equivalently, they are the number that cannot be expressed in the form K ( m 2 + n 2 ) {\\displaystyle K(m^{2}+n^{2})} where K, m, and n are all positive integers. A number whose prime factors are not all of the form 4k+1 cannot be the hypotenuse of a primitive integer right triangle (one for which the sides do not have a nontrivial common divisor), but may still be the hypotenuse of a non-primitive triangle.The nonhypotenuse numbers have been applied to prove the existence of addition chains that compute the first n {\\displaystyle n} square numbers using only n + o ( n ) {\\displaystyle n+o(n)} additions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an interprime is the average of two consecutive odd primes. For example, 9 is an interprime because it is the average of 7 and 11. The first interprimes are: 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, ... (sequence A024675 in the OEIS)Interprimes cannot be prime themselves (otherwise the primes would not have been consecutive).There are infinitely many primes and therefore also infinitely many interprimes. The largest known interprime as of 2018 may be the 388342-digit n = 2996863034895 \u00b7 21290000, where n + 1 is the largest known twin prime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regions such as North America and Europe, Musa fruits offered for sale can be divided into \"bananas\" and \"plantains\" (cooking banana), based on their intended use as food. Thus the banana producer and distributor Chiquita produces publicity material for the American market which says that \"a plantain is not a banana\". The stated differences are that plantains are more starchy and less sweet; they are eaten cooked rather than raw; they have thicker skin, which may be green, yellow or black; and they can be used at any stage of ripeness.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation (cognitive psychology).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let A be a set of probability distributions over an alphabet X, and let q be an arbitrary distribution over X (where q may or may not be in A). Suppose we draw n i.i.d. samples from q, represented by the vector x n = x 1 , x 2 , \u2026 , x n {\\displaystyle x^{n}=x_{1},x_{2},\\ldots ,x_{n}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Events can be both mutually exclusive and collectively exhaustive. In the case of flipping a coin, flipping a head and flipping a tail are also mutually exclusive events. Both outcomes cannot occur for a single trial (i.e., when a coin is flipped only once). The probability of flipping a head and the probability of flipping a tail can be added to yield a probability of 1: 1/2 + 1/2 =1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In stochastic (or \"on-line\") gradient descent, the true gradient of Q ( w ) {\\displaystyle Q(w)} is approximated by a gradient at a single sample: w := w \u2212 \u03b7 \u2207 Q i ( w ) . {\\displaystyle w:=w-\\eta \\nabla Q_{i}(w).} As the algorithm sweeps through the training set, it performs the above update for each training sample. Several passes can be made over the training set until the algorithm converges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such address translations are carried out by the segmentation unit of the CPU. The last segment, FFFFh (65535), begins at linear address FFFF0h (1048560), 16 bytes before the end of the 20 bit address space, and thus, can access, with an offset of up to 65,536 bytes, up to 65,520 (65536\u221216) bytes past the end of the 20 bit 8088 address space. On the 8088, these address accesses were wrapped around to the beginning of the address space such that 65535:16 would access address 0 and 65533:1000 would access address 952 of the linear address space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory, lazy evaluation, or call-by-need, is an evaluation strategy which delays the evaluation of an expression until its value is needed (non-strict evaluation) and which also avoids repeated evaluations (by the use of sharing).The benefits of lazy evaluation include: The ability to define control flow (structures) as abstractions instead of primitives. The ability to define potentially infinite data structures. This allows for more straightforward implementation of some algorithms. The ability to define partially-defined data structures where some elements are errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Whenever the data changes from one address to another address, from an address to a command, or from one command to another command, the data frames must be separated by at least 6 clear zero crossings (or \"000000\"). The sequence of six zeros resets the device decoder hardware.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the algebraic theory of semigroups, in constructing special classes, attention is focused only on those properties, restrictions and conditions which can be expressed in terms of the binary operations in the semigroups and occasionally on the cardinality and similar properties of subsets of the underlying set. The underlying sets are not assumed to carry any other mathematical structures like order or topology. As in any algebraic theory, one of the main problems of the theory of semigroups is the classification of all semigroups and a complete description of their structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the method is applied to a sufficient number of people over the course of a project, the objections raised above become addressed: The sample size ceases to be small and usability problems that arise with only occasional users are found. The value of the method lies in the fact that specific design problems, once encountered, are never seen again because they are immediately eliminated, while the parts that appear successful are tested over and over. While it's true that the initial problems in the design may be tested by only five users, when the method is properly applied, the parts of the design that worked in that initial test will go on to be tested by 50 to 100 people.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1990s, US social economist James D. Montgomery contributed to economic theories of network structures in the labour market. In 1991, Montgomery incorporated network structures in an adverse selection model to analyze the effects of social networks on labour market outcomes. In 1992, Montgomery explored the role of \"weak ties\", which he defined as non-frequent and transitory social relations in the labour market. He demonstrated that weak ties are positively correlated with higher wages and higher aggregate employment rates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Special values, where all contributing Catalan numbers equal 1, are  s n ( x ) = ( \u2212 1 ) n 2 n . {\\displaystyle s_{n}(x)={\\frac {(-1)^{n}}{2^{n}}}.} s n ( x ) = ( \u2212 1 ) n n ( n \u2212 1 ) ( n \u2212 2 ) 2 n .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, legal rules sometimes exempt people from the obligation to give evidence and legal rules disqualify people from serving as witnesses under some circumstances. Privilege rules give the holder of the privilege a right to prevent a witness from giving testimony. These privileges are ordinarily (but not always) designed to protect socially valued types of confidential communications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of backpropagation based artificial neural networks or perceptrons, the type of decision boundary that the network can learn is determined by the number of hidden layers the network has. If it has no hidden layers, then it can only learn linear problems. If it has one hidden layer, then it can learn any continuous function on compact subsets of Rn as shown by the universal approximation theorem, thus it can have an arbitrary decision boundary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It guarantees that the allocation is envy-free up to at most one item (EF1). Moreover, if the instance is ordered (- all agents rank the items in the same order), then the outcome is EFX, and guarantees to each agent at least 2 n 3 n \u2212 1 {\\displaystyle {\\frac {2n}{3n-1}}} of his maximin share. If the items are chores, then a similar algorithm guarantees 4 n \u2212 1 3 n {\\displaystyle {\\frac {4n-1}{3n}}} MMS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In record-oriented file systems files are stored as a collection of records. They are typically associated with mainframe and minicomputer operating systems. Programs read and write whole records, rather than bytes or arbitrary byte ranges, and can seek to a record boundary but not within records.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, a bug bash is a procedure where all the developers, testers, program managers, usability researchers, designers, documentation folks, and even sometimes marketing people, put aside their regular day-to-day duties and \"pound on the product\"\u2014that is, each exercises the product in every way they can think of. Because each person will use the product in slightly different (or very different) ways, and the product is getting a great deal of use in a short amount of time, this approach may reveal bugs relatively quickly.The use of bug-bashing sessions is one possible tool in the testing methodology TMap (test management approach). Bug-bashing sessions are usually announced to the organization some days or weeks ahead of time. The test management team may specify that only some parts of the product need testing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Tables exist. \"Both of these propositions are a posteriori: any justification of them would require one's experience.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the conditional probability that someone unwell (sick) is coughing might be 75%, in which case we would have that P(Cough) = 5% and P(Cough|Sick) = 75 %. Although there is a relationship between A and B in this example, such a relationship or dependence between A and B is not necessary, nor do they have to occur simultaneously. P(A|B) may or may not be equal to P(A), i.e., the unconditional probability or absolute probability of A. If P(A|B) = P(A), then events A and B are said to be independent: in such a case, knowledge about either event does not alter the likelihood of each other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Cantor mentioned the ternary construction only in passing, as an example of a more general idea, that of a perfect set that is nowhere dense. More generally, in topology, a Cantor space is a topological space homeomorphic to the Cantor ternary set (equipped with its subspace topology). By a theorem of L. E. J. Brouwer, this is equivalent to being perfect nonempty, compact metrizable and zero dimensional.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is usually denoted by the turned A (\u2200) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier (\"\u2200x\", \"\u2200(x)\", or sometimes by \"(x)\" alone). Universal quantification is distinct from existential quantification (\"there exists\"), which only asserts that the property or relation holds for at least one member of the domain. Quantification in general is covered in the article on quantification (logic). The universal quantifier is encoded as U+2200 \u2200 FOR ALL in Unicode, and as \\forall in LaTeX and related formula editors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hill climbing finds optimal solutions for convex problems \u2013 for other problems it will find only local optima (solutions that cannot be improved upon by any neighboring configurations), which are not necessarily the best possible solution (the global optimum) out of all possible solutions (the search space). Examples of algorithms that solve convex problems by hill-climbing include the simplex algorithm for linear programming and binary search. : 253 To attempt to avoid getting stuck in local optima, one could use restarts (i.e. repeated local search), or more complex schemes based on iterations (like iterated local search), or on memory (like reactive search optimization and tabu search), or on memory-less stochastic modifications (like simulated annealing).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, property equivalence is the statement that two properties have the same property extension or values. This usually (but not always) implies that the two properties have the same semantics or meaning. Technically it only implies that the data elements have the same values. Property equivalence is one of the three ways that a metadata registry can store equivalence mappings to other metadata registries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systemic functional grammar (SFG), a nominal group is a group of words that represents or describes an entity, for example The nice old English police inspector who was sitting at the table with Mr Morse. Grammatically, the wording \"The nice old English police inspector who was sitting at the table with Mr Morse\" can be understood as a nominal group (a description of someone), which functions as the subject of the information exchange and as the person being identified as \"Mr Morse\". A nominal group is widely regarded as synonymous with noun phrase in other grammatical models. However, there are two major differences between the functional notion of a nominal group and the formal notion of a noun phrase that must be taken into account.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and particularly general topology, the half-disk topology is an example of a topology given to the set X {\\displaystyle X} , given by all points ( x , y ) {\\displaystyle (x,y)} in the plane such that y \u2265 0 {\\displaystyle y\\geq 0} . The set X {\\displaystyle X} can be termed the closed upper half plane. To give the set X {\\displaystyle X} a topology means to say which subsets of X {\\displaystyle X} are \"open\", and to do so in a way that the following axioms are met: The union of open sets is an open set. The finite intersection of open sets is an open set. The set X {\\displaystyle X} and the empty set \u2205 {\\displaystyle \\emptyset } are open sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, humans routinely make conceptual, linguistic, and probabilistic generalizations from small amounts of data. There is some debate about the utility of various tools of statistical inference in understanding the mind, but it is commonly accepted that the human mind is somehow an exceptionally apt prediction machine, and that action-oriented processes underlying this phenomenon, whatever they might entail, are at the core of cognition. Probabilistic inferences and generalization play central roles in concepts and categories and language learning, and infant studies are commonly used to understand the developmental trajectory of humans' intuitive statistical toolkit(s).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1980s the term FCAPS was introduced within the first Working Drafts (N1719) of ISO 10040, the Open Systems Interconnection (OSI) Systems Management Overview (SMO) standard. At that time the intention was to define five separate protocol standards, one for each functional area. Since initial experiences showed that these protocols would become very similar, the ISO working group responsible for the development of these protocols (ISO/TC97/SC16/WG4, later renamed into ISO-IEC/JTC1/SC21/WG4) decided to create a single protocol for all five areas instead. This protocol is called common management information protocol (CMIP). In the 1990s the ITU-T, as part of their work on Telecommunications Management Network (TMN), further refined the FCAPS as part of the TMN recommendation on Management Functions (M.3400). The idea of FCAPS turned out to be very useful for teaching network management functions; most textbooks therefore start with a section that explains the FCAPS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The associativity and precedence of an operator is a part of the definition of the programming language; different programming languages may have different associativity and precedence for the same type of operator. Consider the expression a ~ b ~ c. If the operator ~ has left associativity, this expression would be interpreted as (a ~ b) ~ c. If the operator has right associativity, the expression would be interpreted as a ~ (b ~ c). If the operator is non-associative, the expression might be a syntax error, or it might have some special meaning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If so, it then attempts to expand the macro, treating the items in the tail of the s-expression as arguments without compiling code to evaluate them, and this process is repeated recursively until no macro invocations remain. If it is not a syntactic keyword, the compiler compiles code to evaluate the arguments in the tail of the s-expression and then to evaluate the variable represented by the symbol at the head of the s-expression and call it as a procedure with the evaluated tail expressions passed as arguments to it. Most Scheme implementations also provide additional macro systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For infinite sets, the picture is more complicated, leading to the concept of cardinal number\u2014a way to distinguish the various sizes of infinite sets. A bijective function from a set to itself is also called a permutation, and the set of all permutations of a set forms the symmetric group. Bijective functions are essential to many areas of mathematics including the definitions of isomorphisms, homeomorphisms, diffeomorphisms, permutation groups, and projective maps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to generate the Google matrix G, we must first generate an adjacency matrix A which represents the relations between pages or nodes. Assuming there are N pages, we can fill out A by doing the following: A matrix element A i , j {\\displaystyle A_{i,j}} is filled with 1 if node j {\\displaystyle j} has a link to node i {\\displaystyle i} , and 0 otherwise; this is the adjacency matrix of links. A related matrix S corresponding to the transitions in a Markov chain of given network is constructed from A by dividing the elements of column \"j\" by a number of k j = \u03a3 i = 1 N A i , j {\\displaystyle k_{j}=\\Sigma _{i=1}^{N}A_{i,j}} where k j {\\displaystyle k_{j}} is the total number of outgoing links from node j to all other nodes. The columns having zero matrix elements, corresponding to dangling nodes, are replaced by a constant value 1/N.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Events are also represented as terms. The effects of events are given using the predicates Initiates and Terminates. In particular, I n i t i a t e s ( e , f , t ) {\\displaystyle {\\mathit {Initiates}}(e,f,t)} means that, if the event represented by the term e is executed at time t, then the fluent f will be true after t. The Terminates predicate has a similar meaning, with the only difference being that f will be false after t.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Our hypothesis might specify the probability distribution of X {\\displaystyle X} precisely, or it might only specify that it belongs to some class of distributions. Often, we reduce the data to a single numerical statistic, e.g., T {\\displaystyle T} , whose marginal probability distribution is closely connected to a main question of interest in the study. The p-value is used in the context of null hypothesis testing in order to quantify the statistical significance of a result, the result being the observed value of the chosen statistic T {\\displaystyle T} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that element in the multiset. As a consequence, an infinite number of multisets exist which contain only elements a and b, but vary in the multiplicities of their elements: The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset. In the multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above moment-cumulant formula E \u2061 ( X 1 \u22ef X n ) = \u2211 \u03c0 \u220f B \u2208 \u03c0 \u03ba ( X i: i \u2208 B ) {\\displaystyle \\operatorname {E} (X_{1}\\cdots X_{n})=\\sum _{\\pi }\\prod _{B\\,\\in \\,\\pi }\\kappa (X_{i}:i\\in B)} for joint cumulants, one sums over all partitions of the set { 1, ..., n }. If instead, one sums only over the noncrossing partitions, then, by solving these formulae for the \u03ba {\\displaystyle \\kappa } in terms of the moments, one gets free cumulants rather than conventional cumulants treated above. These free cumulants were introduced by Roland Speicher and play a central role in free probability theory. In that theory, rather than considering independence of random variables, defined in terms of tensor products of algebras of random variables, one considers instead free independence of random variables, defined in terms of free products of algebras.The ordinary cumulants of degree higher than 2 of the normal distribution are zero. The free cumulants of degree higher than 2 of the Wigner semicircle distribution are zero. This is one respect in which the role of the Wigner distribution in free probability theory is analogous to that of the normal distribution in conventional probability theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "1997 nr 89 poz. 555.) provides means of protecting against self-incrimination, including lack of penalization for refusing to answer any question which would enable law enforcement agencies to obtain access to potential evidence, which could be used against testifying person.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Often the principal components with higher variances (the ones based on eigenvectors corresponding to the higher eigenvalues of the sample variance-covariance matrix of the explanatory variables) are selected as regressors. However, for the purpose of predicting the outcome, the principal components with low variances may also be important, in some cases even more important.One major use of PCR lies in overcoming the multicollinearity problem which arises when two or more of the explanatory variables are close to being collinear. PCR can aptly deal with such situations by excluding some of the low-variance principal components in the regression step.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It can be accomplished by planting a significant news story indirectly in the media, or presenting it favorably through press releases or corporate anniversary parties. Examples include newspaper and magazine articles, TVs and radio presentations, charitable contributions, speeches, issue advertising, seminars. Word of mouth is also a type of publicity, which transform from the person-to-person storytelling to social media influencers, or bloggers promotions today.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to handle such conflicts correctly, the pipeline must be provided with extra circuitry or logic that detects them and takes the appropriate action. Strategies for doing so include: Stalling: Every affected stage, such as A, is halted until the dependency is resolved\u2014that is, until the required information is available and/or the required state has been achieved. Reordering items: Instead of stalling, stage A may put item Y aside and look for any subsequent item Z in its input stream that does not have any dependencies pending with any earlier item.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the definitions provided below, let \u03c9 {\\displaystyle \\omega } denote the set of natural numbers ( N {\\displaystyle \\mathbb {N} } ) and A , B . . . {\\displaystyle A,B...} denote subsets of \u03c9 {\\displaystyle \\omega } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consequently, lawmakers aim to devise definitions and categories which are sufficiently precise, so that they are not open to different interpretations. For this purpose, it is critically important to remove fuzziness, and differences of interpretation are typically resolved through a court ruling based on evidence. Alternatively, some other procedure is devised which permits the correct distinction to be discovered and made. In administration, archiving and accounting, fuzziness problems in interpretation and boundary problems can arise, because it is not clear to what category exactly a case, item, document, transaction or piece of data belongs. In principle, each case, event or item must be allocated to the correct category in a procedure, but it may be, that it is difficult to make the appropriate or relevant distinctions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of Java (before the HotSpot VM was implemented in Java 1.3 in 2000) there were some criticisms of performance. Benchmarks typically reported Java as being about 50% slower than C (a language which compiles to native code).Java's performance has improved substantially since the early versions. Performance of JIT compilers relative to native compilers has in some optimized tests been shown to be quite similar.Java bytecode can either be interpreted at run time by a virtual machine, or it can be compiled at load time or runtime into native code which runs directly on the computer's hardware. Interpretation is slower than native execution, and compilation at load time or runtime has an initial performance penalty for the compilation. Modern performant JVM implementations all use the compilation approach, so after the initial startup time the performance is equivalent to native code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties. Without such an axiom, such a set might not provably exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, even elements always commute. Odd elements, on the other hand, always anticommute.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the false fame experiment, participants are presented with a list of non-famous names. Later, they are presented with the same names as before, with new non-famous and famous people. The participants then have to determine which names are famous, and the typical finding is that the old non-famous names are often misidentified as famous.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In symmetric-key schemes, the encryption and decryption keys are the same. Communicating parties must have the same key in order to achieve secure communication. The German Enigma Machine utilized a new symmetric-key each day for encoding and decoding messages. In public-key encryption schemes, the encryption key is published for anyone to use and encrypt messages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the basic five-bit biquinary code of the UNIVAC-LARC, 15 combinations are allowed, any one of which may be stored may be stored in any digit position in storage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation: X n + Y n = Z n . {\\displaystyle X^{n}+Y^{n}=Z^{n}.\\ } Therefore, in terms of the affine plane its equation is: x n + y n = 1. {\\displaystyle x^{n}+y^{n}=1.\\ } An integer solution to the Fermat equation would correspond to a nonzero rational number solution to the affine equation, and vice versa. But by Fermat's Last Theorem it is now known that (for n > 2) there are no nontrivial integer solutions to the Fermat equation; therefore, the Fermat curve has no nontrivial rational points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, version control is a class of systems responsible for managing changes to computer programs or other collections of information such that revisions have a logical and consistent organization. The following tables include general and technical information on notable version control and software configuration management (SCM) software. For SCM software not suitable for source code, see Comparison of open-source configuration management software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In project management, a schedule is a listing of a project's milestones, activities, and deliverables. Usually dependencies and resources are defined for each task, then start and finish dates are estimated from the resource allocation, budget, task duration, and scheduled events. A schedule is commonly used in the project planning and project portfolio management parts of project management. Elements on a schedule may be closely related to the work breakdown structure (WBS) terminal elements, the Statement of work, or a Contract Data Requirements List.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that if X and X1, X2, ... are random variables corresponding to these distribution functions, then the Helly\u2013Bray theorem does not imply that E(Xn) \u2192 E(X), since g(x) = x is not a bounded function. In fact, a stronger and more general theorem holds. Let P and P1, P2, ... be probability measures on some set S. Then Pn converges weakly to P if and only if \u222b S g d P n \u2192 n \u2192 \u221e \u222b S g d P , {\\displaystyle \\int _{S}g\\,dP_{n}\\quad {\\xrightarrow{}}\\quad \\int _{S}g\\,dP,} for all bounded, continuous and real-valued functions on S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to guarantee safety (also called \"consistency\"), Paxos defines three properties and ensures the first two are always held, regardless of the pattern of failures: Validity (or non-triviality) Only proposed values can be chosen and learned. Agreement (or consistency, or safety) No two distinct learners can learn different values (or there can't be more than one decided value) Termination (or liveness) If value C has been proposed, then eventually learner L will learn some value (if sufficient processors remain non-faulty).Note that Paxos is not guaranteed to terminate, and thus does not have the liveness property. This is supported by the Fischer Lynch Paterson impossibility result (FLP) which states that a consistency protocol can only have two of safety, liveness, and fault tolerance. As Paxos's point is to ensure fault tolerance and it guarantees safety, it cannot also guarantee liveness.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, string literals may contain placeholders referring to variables or expressions in the current context, which are evaluated (usually at run time). This is referred to as variable interpolation, or more generally string interpolation. Languages that support interpolation generally distinguish strings literals that are interpolated from ones that are not. For example, in sh-compatible Unix shells (as well as Perl and Ruby), double-quoted (quotation-delimited, \") strings are interpolated, while single-quoted (apostrophe-delimited, ') strings are not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus for S = a \u22c5 10 2 n {\\displaystyle S=a\\cdot 10^{2n}}: S \u2248 ( \u2212 190 a + 20 + 10 ) \u22c5 10 n {\\displaystyle {\\sqrt {S}}\\approx \\left({\\frac {-190}{a+20}}+10\\right)\\cdot 10^{n}} The floating division need be accurate to only one decimal digit, because the estimate overall is only that accurate, and can be done mentally. A hyperbolic estimate is better on average than scalar or linear estimates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Software developers can use these models as a basis for the implementation of software architectures and applications. This approach to domain analysis is sometimes called model-driven engineering. In information science, the term \"domain analysis\" was suggested in 1995 by Birger Hj\u00f8rland and H. Albrechtsen.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The in situ in ISCR is just Latin for \"in place\", signifying that ISCR is a chemical reduction reaction that occurs at the site of the contamination. Like ISCO, it is able to decontaminate many compounds, and, in theory, ISCR could be more effective in ground water remediation than ISCO. Chemical reduction is one half of a redox reaction, which results in the gain of electrons. One of the reactants in the reaction becomes oxidized, or loses electrons, while the other reactant becomes reduced, or gains electrons. In ISCR, reducing compounds, compounds that accept electrons given by other compounds in a reaction, are used to change the contaminants into harmless compounds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Important algorithms in computational group theory include: the Schreier\u2013Sims algorithm for finding the order of a permutation group the Todd\u2013Coxeter algorithm and Knuth\u2013Bendix algorithm for coset enumeration the product-replacement algorithm for finding random elements of a groupTwo important computer algebra systems (CAS) used for group theory are GAP and Magma. Historically, other systems such as CAS (for character theory) and Cayley (a predecessor of Magma) were important. Some achievements of the field include: complete enumeration of all finite groups of order less than 2000 computation of representations for all the sporadic groups", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development has been motivated by descriptive complexity theory and their relationship to database query languages, in particular to Datalog. Least fixed-point logic was first studied systematically by Yiannis N. Moschovakis in 1974, and it was introduced to computer scientists in 1979, when Alfred Aho and Jeffrey Ullman suggested fixed-point logic as an expressive database query language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The genitive plural, however is hjartna showing a-breaking instead of u-breaking. Some borrowings may exhibit similar behaviour, e.g, singular drama, plural dr\u00f6mu. Most of these are words for organs.An almost exhaustive list of neuter weak nouns follows: auga (eye) bj\u00faga (a type of sausage) eista (testicle) eyra (ear) hjarta (heart) hno\u00f0a (a woollen ball, most often encountered in fairy-tales) lunga (lung) milta (spleen) n\u00fdra (kidney)Then there are a small number of borrowings like firma, drama, \u00feema etc. none of which require translation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Tamari lattice, introduced by Dov Tamari (1962), is a partially ordered set in which the elements consist of different ways of grouping a sequence of objects into pairs using parentheses; for instance, for a sequence of four objects abcd, the five possible groupings are ((ab)c)d, (ab)(cd), (a(bc))d, a((bc)d), and a(b(cd)). Each grouping describes a different order in which the objects may be combined by a binary operation; in the Tamari lattice, one grouping is ordered before another if the second grouping may be obtained from the first by only rightward applications of the associative law (xy)z = x(yz). For instance, applying this law with x = a, y = bc, and z = d gives the expansion (a(bc))d = a((bc)d), so in the ordering of the Tamari lattice (a(bc))d \u2264 a((bc)d).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the push\u2013relabel algorithm (alternatively, preflow\u2013push algorithm) is an algorithm for computing maximum flows in a flow network. The name \"push\u2013relabel\" comes from the two basic operations used in the algorithm. Throughout its execution, the algorithm maintains a \"preflow\" and gradually converts it into a maximum flow by moving flow locally between neighboring nodes using push operations under the guidance of an admissible network maintained by relabel operations. In comparison, the Ford\u2013Fulkerson algorithm performs global augmentations that send flow following paths from the source all the way to the sink.The push\u2013relabel algorithm is considered one of the most efficient maximum flow algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, many functions of interest are computable by machines that always halt. A machine that uses only finite memory on any particular input can be forced to halt for every input by restricting its flow control capabilities so that no input will ever cause the machine to enter an infinite loop. As a trivial example, a machine implementing a finitary decision tree will always halt. It is not required that the machine be entirely free of looping capabilities, however, to guarantee halting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A positive voltage is applied to the anode. This voltage, combined with the high magnetic field between the tips of the internal and external cathodes allow a plasma to start. Ions from the plasma are repelled by the anode electric field. This creates an ion beam.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From the universal algebra viewpoint, most structures can be divided into varieties and quasivarieties depending on the axioms used. Some axiomatic formal systems that are neither varieties nor quasivarieties, called nonvarieties, are sometimes included among the algebraic structures by tradition. Concrete examples of each structure will be found in the articles listed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of one continuous (or at least with bounded variation) compactly supported scaling function with orthogonal shifts, one may make a number of deductions. The proof of existence of this class of functions is due to Ingrid Daubechies. Assuming the scaling function has compact support, then V 0 \u2282 V \u2212 1 {\\displaystyle V_{0}\\subset V_{-1}} implies that there is a finite sequence of coefficients a k = 2 \u27e8 \u03d5 ( x ) , \u03d5 ( 2 x \u2212 k ) \u27e9 {\\displaystyle a_{k}=2\\langle \\phi (x),\\phi (2x-k)\\rangle } for | k | \u2264 N {\\displaystyle |k|\\leq N} , and a k = 0 {\\displaystyle a_{k}=0} for | k | > N {\\displaystyle |k|>N} , such that \u03d5 ( x ) = \u2211 k = \u2212 N N a k \u03d5 ( 2 x \u2212 k ) . {\\displaystyle \\phi (x)=\\sum _{k=-N}^{N}a_{k}\\phi (2x-k).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1999, MIPS Technologies replaced the previous versions of the MIPS architecture with two architectures, the 32-bit MIPS32 (based on MIPS II with some added features from MIPS III, MIPS IV, and MIPS V) and the 64-bit MIPS64 (based on MIPS V) for licensing. Nippon Electric Corporation (NEC), Toshiba, and SiByte (later acquired by Broadcom) each obtained licenses for the MIPS64 as soon as it was announced.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the HPCC implementation, by default, most ECL constructs will execute in parallel across the hardware being used. Many of the primitives also have a LOCAL option to specify that the operation is to occur locally on each node.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The system used a third-party service to identify content being distributed illegally. Users were then informed that their accounts were being used for possible copyright infringement and were provided with information about ways to get authorized content online. Users who received multiple notices of infringement faced \"mitigations measures,\" such as temporary slowing of their Internet service, but the system did not include termination of subscriber accounts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A similar result also holds in some closed networks. Examples of product-form networks where the arrival theorem does not hold include reversible Kingman networks and networks with a delay protocol.Mitrani offers the intuition that \"The state of node i as seen by an incoming job has a different distribution from the state seen by a random observer. For instance, an incoming job can never see all 'k jobs present at node i, because it itself cannot be among the jobs already present.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The benchmark visible when pH7CMS is on the development mode. Better search experiences with the new SISE (Smart Intuitive Search Engine) and better translation are now done.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The iterations converge to the fixed point of the IFS. Whenever x0 belongs to the attractor of the IFS, all iterations xk stay inside the attractor and, with probability 1, form a dense set in the latter. The \"chaos game\" method plots points in random order all over the attractor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics a quasi-maximum likelihood estimate (QMLE), also known as a pseudo-likelihood estimate or a composite likelihood estimate, is an estimate of a parameter \u03b8 in a statistical model that is formed by maximizing a function that is related to the logarithm of the likelihood function, but in discussing the consistency and (asymptotic) variance-covariance matrix, we assume some parts of the distribution may be mis-specified. In contrast, the maximum likelihood estimate maximizes the actual log likelihood function for the data and model. The function that is maximized to form a QMLE is often a simplified form of the actual log likelihood function. A common way to form such a simplified function is to use the log-likelihood function of a misspecified model that treats certain data values as being independent, even when in actuality they may not be.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In online analytical processing (OLAP), data cubes are a common arrangement of business data suitable for analysis from different perspectives through operations like slicing, dicing, pivoting, and aggregation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We want to give unit A a 20% probability of selection, unit B a 40% probability, and so on up to unit E (100%). Assuming we maintain alphabetical order, we allocate each unit to the following interval: A: 0 to 0.2 B: 0.2 to 0.6 (= 0.2 + 0.4) C: 0.6 to 1.2 (= 0.6 + 0.6) D: 1.2 to 2.0 (= 1.2 + 0.8) E: 2.0 to 3.0 (= 2.0 + 1.0) If our random start was 0.156, we would first select the unit whose interval contains this number (i.e. A). Next, we would select the interval containing 1.156 (element C), then 2.156 (element E). If instead our random start was 0.350, we would select from points 0.350 (B), 1.350 (D), and 2.350 (E).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, Searle's main interlocutor on issues of social ontology has been Tony Lawson. Although their accounts of social reality are similar, there are important differences. Lawson emphasizes the notion of social totality whereas Searle prefers to refer to institutional facts. Furthermore, Searle believes that emergence implies causal reduction whereas Lawson argues that social totalities cannot be completely explained by the causal powers of their components. Searle also places language at the foundation of the construction of social reality, while Lawson believes that community formation necessarily precedes the development of language and, therefore, there must be the possibility for non-linguistic social structure formation. The debate is ongoing and takes place additionally through regular meetings of the Centre for Social Ontology at the University of California, Berkeley and the Cambridge Social Ontology Group at the University of Cambridge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A Boolean function with multiple outputs, f: { 0 , 1 } k \u2192 { 0 , 1 } m {\\displaystyle f:\\{0,1\\}^{k}\\to \\{0,1\\}^{m}} with m > 1 {\\displaystyle m>1} is a vectorial or vector-valued Boolean function (an S-box in symmetric cryptography).There are 2 2 k {\\displaystyle 2^{2^{k}}} different Boolean functions with k {\\displaystyle k} arguments; equal to the number of different truth tables with 2 k {\\displaystyle 2^{k}} entries. Every k {\\displaystyle k} -ary Boolean function can be expressed as a propositional formula in k {\\displaystyle k} variables x 1 , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a management review is defined by the IEEE as: A systematic evaluation of a software acquisition, supply, development, operation, or maintenance process performed by or on behalf of management ...  to monitor progress, determine the status of plans and schedules, confirm requirements and their system allocation, or evaluate the effectiveness of management approaches used to achieve fitness for purpose. Management reviews support decisions about corrective actions, changes in the allocation of resources, or changes to the scope of the project. Management reviews are carried out by, or on behalf of, the management personnel having direct responsibility for the system. Management reviews identify consistency with and deviations from plans, or adequacies and inadequacies of management procedures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When a process calls fork, it is deemed the parent process and the newly created process is its child. After the fork, both processes not only run the same program, but they resume execution as though both had called the system call. They can then inspect the call's return value to determine their status, child or parent, and act accordingly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to implement 802.11i, one must first make sure both that the router/access point(s), as well as all client devices are indeed equipped to support the network encryption. If this is done, a server such as RADIUS, ADS, NDS, or LDAP needs to be integrated. This server can be a computer on the local network, an access point / router with integrated authentication server, or a remote server. AP's/routers with integrated authentication servers are often very expensive and specifically an option for commercial usage like hot spots.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In patient care, authorised users have the ability to override masking and access restrictions under emergency circumstances. If a patient is in a critical health state and treatment is urgently required, physicians are provided with the right to access all required information within the EHR. This mechanism is known as \"breaking the glass.\" Any unmasking of a patient's EHR is audited, and a sufficient reason for access is generally required.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank (with the largest example having rank 1). This can markedly improve the fit over a simple power-law relationship (see references below). In the Laherr\u00e8re/Deheuvels paper below, examples include galaxy sizes (ordered by luminosity), towns (in the USA, France, and world), spoken languages (by number of speakers) in the world, and oil fields in the world (by size). They also mention utility for this distribution in fitting seismic events (no example).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Social media influencers can be defined as \"regular\" individuals who have accrued a large number of followers across multiple social media platforms as a result of the content they post. For the most part, social media influencers focus their content on one subject area, like food or fashion. Social media influencers have become their own kind of \"internet celebrities\" and their followers value and trust their opinions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are several different ways to express reciprocity laws. The early reciprocity laws found in the 19th century were usually expressed in terms of a power residue symbol (p/q) generalizing the quadratic reciprocity symbol, that describes when a prime number is an nth power residue modulo another prime, and gave a relation between (p/q) and (q/p). Hilbert reformulated the reciprocity laws as saying that a product over p of Hilbert symbols (a,b/p), taking values in roots of unity, is equal to 1. Artin's reformulated reciprocity law states that the Artin symbol from ideals (or ideles) to elements of a Galois group is trivial on a certain subgroup. Several more recent generalizations express reciprocity laws using cohomology of groups or representations of adelic groups or algebraic K-groups, and their relationship with the original quadratic reciprocity law can be hard to see.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of algorithms that run over the very long term (servers, cloud...), the computer architecture evolves over time. However, it is preferable not to have to design a new algorithm each time. An extremely important parameter of a load balancing algorithm is therefore its ability to adapt to scalable hardware architecture. This is called the scalability of the algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each guard for which the condition is true and the input channel is ready is successful. One of the successful alternatives is selected for execution. Example: ALT count1 < 100 & c1 ?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Recall the definition of SVD: S V D ( T ) = U \u039b V T {\\displaystyle \\mathrm {SVD} ({\\mathcal {T}})=U\\Lambda V^{T}} It is the decomposition of the transformation, T {\\displaystyle {\\mathcal {T}}} , into a rotation in the source domain (i.e. the ellipsoid surface), V T {\\displaystyle V^{T}} , a scaling along the basis, \u039b {\\displaystyle \\Lambda } , and a subsequent second rotation, U {\\displaystyle U} . For understanding distortion, the first rotation is irrelevant, as it rotates the axes of the circle but has no bearing on the final orientation of the ellipse. The next operation, represented by the diagonal singular value matrix, scales the circle along its axes, deforming it to an ellipse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Through various implementations, the MPIC was included in PowerPC reference designs and some retail computers. IBM used a MPIC based on OpenPIC 1.0 in their RS/6000 F50 and one based on OpenPIC 1.2 in their RS/6000 S70. Both of these systems also used a dual 8259 on their PCI-ISA bridges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the tensor product (TP) model transformation was proposed by Baranyi and Yam as key concept for higher-order singular value decomposition of functions. It transforms a function (which can be given via closed formulas or neural networks, fuzzy logic, etc.) into TP function form if such a transformation is possible. If an exact transformation is not possible, then the method determines a TP function that is an approximation of the given function. Hence, the TP model transformation can provide a trade-off between approximation accuracy and complexity.A free MATLAB implementation of the TP model transformation can be downloaded at  or an old version of the toolbox is available at MATLAB Central .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where each N i {\\displaystyle \\textstyle {N}_{i}} is a Poisson point process, then the resulting process N {\\displaystyle \\textstyle {N}} is also a Poisson point process with mean intensity \u039b = \u2211 i = 1 \u221e \u039b i . {\\displaystyle \\Lambda =\\sum \\limits _{i=1}^{\\infty }\\Lambda _{i}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the class means and covariances are not known. They can, however, be estimated from the training set. Either the maximum likelihood estimate or the maximum a posteriori estimate may be used in place of the exact value in the above equations. Although the estimates of the covariance may be considered optimal in some sense, this does not mean that the resulting discriminant obtained by substituting these values is optimal in any sense, even if the assumption of normally distributed classes is correct.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the compilation of high-level programming languages, pathwidth arises in the problem of reordering sequences of straight-line code (that is, code with no control flow branches or loops) in such a way that all the values computed in the code can be placed in machine registers instead of having to be spilled into main memory. In this application, one represents the code to be compiled as a directed acyclic graph in which the nodes represent the input values to the code and the values computed by the operations within the code. An edge from node x to node y in this DAG represents the fact that value x is one of the inputs to operation y. A topological ordering of the vertices of this DAG represents a valid reordering of the code, and the number of registers needed to evaluate the code in a given ordering is given by the vertex separation number of the ordering.For any fixed number w of machine registers, it is possible to determine in linear time whether a piece of straight-line code can be reordered in such a way that it can be evaluated with at most w registers. For, if the vertex separation number of a topological ordering is at most w, the minimum vertex separation among all orderings can be no larger, so the undirected graph formed by ignoring the orientations of the DAG described above must have pathwidth at most w. It is possible to test whether this is the case, using the known fixed-parameter-tractable algorithms for pathwidth, and if so to find a path-decomposition for the undirected graph, in linear time given the assumption that w is a constant. Once a path decomposition has been found, a topological ordering of width w (if one exists) can be found using dynamic programming, again in linear time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In much the same way as the IA is difficult to define, it can be utilised in a range of contexts by the information professional, from complying with freedom of information legislation to identifying any existing gaps, duplications, bottlenecks or other inefficiencies in information flows and to understand how existing channels can be used for knowledge transfer In 2007 Buchanan and Gibb developed upon their 1998 examination of the IA process by outlining a summary of its main objectives: To identify an organisation\u2019s information resource To identify an organisation\u2019s information needsFurthermore, Buchanan and Gibb went on to state that the IA also had to meet the following additional objectives: To identify the cost/benefits of information resources To identify the opportunities to use the information resources for strategic competitive advantage To integrate IT investment with strategic business initiatives To identify information flow and processes To develop an integrated information strategy and/or policy To create an awareness of the importance of Information Resource Management (IRM) To monitor/evaluate conformance to information related standards, legislations, policy and guidelines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical test theory, the notion of a statistical error is an integral part of hypothesis testing. The test goes about choosing about two competing propositions called null hypothesis, denoted by H0 and alternative hypothesis, denoted by H1. This is conceptually similar to the judgement in a court trial. The null hypothesis corresponds to the position of the defendant: just as he is presumed to be innocent until proven guilty, so is the null hypothesis presumed to be true until the data provide convincing evidence against it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in the area of algebra known as group theory, the term Z-group refers to a number of distinct types of groups: in the study of finite groups, a Z-group is a finite group whose Sylow subgroups are all cyclic. in the study of infinite groups, a Z-group is a group which possesses a very general form of central series. in the study of ordered groups, a Z-group or Z {\\displaystyle \\mathbb {Z} } -group is a discretely ordered abelian group whose quotient over its minimal convex subgroup is divisible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In planar directed graphs, the feedback arc set problem obeys a min-max theorem: the minimum size of a feedback arc set equals the maximum number of edge-disjoint directed cycles that can be found in the graph. This is not true for some other graphs; for instance the first illustration shows a directed version of the non-planar graph K 3 , 3 {\\displaystyle K_{3,3}} in which the minimum size of a feedback arc set is two, while the maximum number of edge-disjoint directed cycles is only one. Every tournament graph has a Hamiltonian path, and the Hamiltonian paths correspond one-for-one with minimal feedback arc sets, disjoint from the corresponding path. The Hamiltonian path for a feedback arc set is found by reversing its arcs and finding a topological order of the resulting acyclic tournament.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle =efg.} The relation above shows that /ef equals the number g of prime factors of p in OL. By the orbit-stabilizer formula this number is also equal to |G|/|DPj| for every j, where DPj, the decomposition group of Pj, is the subgroup of elements of G sending a given Pj to itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, exact recovery can be solved in its feasible range using maximum likelihood, but this amounts to solving a constrained or regularized cut problem such as minimum bisection that is typically NP-complete. Hence, no known efficient algorithms will correctly compute the maximum-likelihood estimate in the worst case. However, a wide variety of algorithms perform well in the average case, and many high-probability performance guarantees have been proven for algorithms in both the partial and exact recovery settings. Successful algorithms include spectral clustering of the vertices, semidefinite programming, forms of belief propagation, and community detection among others.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The USPA protocol for training students is called the \"Integrated Student Program\" (ISP). The ISP is separated into categories, each with targeted learning objectives that must be met before the student progresses to the next level. Static Line, AFF, and Tandem Progression all follow the same categories, but use different methods to train within each category.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above example, each vertex of H has exactly 2 preimages in C. Hence C is a 2-fold cover or a double cover of H. For any graph G, it is possible to construct the bipartite double cover of G, which is a bipartite graph and a double cover of G. The bipartite double cover of G is the tensor product of graphs G \u00d7 K2: If G is already bipartite, its bipartite double cover consists of two disjoint copies of G. A graph may have many different double covers other than the bipartite double cover.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In processor mode cores are on and executing code from the system memory and programmed I/O (inputs and outputs) through the system which is connected to the system board FPGA. Loading memory and configuring the processor for bootstrapping (sustaining after the initial load) is currently done by software running on the SCC's management console that's embedded in the chip.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle (\\phi ,\\psi )\\cdot f=\\psi ^{-1}\\circ f\\circ \\phi .} Under this action we see that the map germs f , g: ( M , x ) \u2192 ( N , y ) {\\displaystyle f,g:(M,x)\\to (N,y)} are A {\\displaystyle {\\mathcal {A}}} -equivalent if, and only if, g {\\displaystyle g} lies in the orbit of f {\\displaystyle f} , i.e. g \u2208 orb G ( f ) {\\displaystyle g\\in {\\mbox{orb}}_{G}(f)} (or vice versa). A map germ is called stable if its orbit under the action of G := diff ( M x ) \u00d7 diff ( N y ) {\\displaystyle G:={\\mbox{diff}}(M_{x})\\times {\\mbox{diff}}(N_{y})} is open relative to the Whitney topology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Call this number \u03a9 R ( s 1 ) {\\displaystyle \\;\\Omega _{R}(s_{1})} . By assumption, the combined system (of the system we are interested in and the reservoir) is isolated, so all microstates are equally probable. Therefore, for instance, if \u03a9 R ( s 1 ) = 2 \u03a9 R ( s 2 ) {\\displaystyle \\;\\Omega _{R}(s_{1})=2\\;\\Omega _{R}(s_{2})} , we can conclude that our system is twice as likely to be in state s 1 {\\displaystyle \\;s_{1}} than s 2 {\\displaystyle \\;s_{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For many distributions, the kernel can be written in closed form, but not the normalization constant. An example is the normal distribution. Its probability density function is p ( x | \u03bc , \u03c3 2 ) = 1 2 \u03c0 \u03c3 2 e \u2212 ( x \u2212 \u03bc ) 2 2 \u03c3 2 {\\displaystyle p(x|\\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}} and the associated kernel is p ( x | \u03bc , \u03c3 2 ) \u221d e \u2212 ( x \u2212 \u03bc ) 2 2 \u03c3 2 {\\displaystyle p(x|\\mu ,\\sigma ^{2})\\propto e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}} Note that the factor in front of the exponential has been omitted, even though it contains the parameter \u03c3 2 {\\displaystyle \\sigma ^{2}} , because it is not a function of the domain variable x {\\displaystyle x} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These evaluations are then transferred to the linguistic feature. An observer's attention may be drawn to a target as a result of certain general features of that target. These features include: General object attributes \u2013 vivid colors, object's proximity to observer Difference between object attribute and its immediate environment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regression analysis, plotting is a more natural way to view the overall trend of the whole data. The mean of the distance from each point to the predicted regression model can be calculated, and shown as the mean squared error. The squaring is critical to reduce the complexity with negative signs. To minimize MSE, the model could be more accurate, which would mean the model is closer to actual data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "First, define a modified greedy algorithm, that selects the set S i {\\displaystyle S_{i}} that has the best ratio of weighted uncovered elements to cost. Second, among covers of cardinality 1 , 2 , . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The longer, e.g. a sentence (measured in terms of the number of clauses) the shorter the clauses (measured in terms of the number of words), or: the longer a word (in syllables or morphs) the shorter the syllables or words in sounds). Law of diversification: If linguistic categories such as parts-of-speech or inflectional endings appear in various forms it can be shown that the frequencies of their occurrences in texts are controlled by laws. Martin's law: This law concerns lexical chains which are obtained by looking up the definition of a word in a dictionary, then looking up the definition of the definition just obtained etc. Finally, all these definitions form a hierarchy of more and more general meanings, whereby the number of definitions decreases with increasing generality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proved numerous times by many different methods \u2013 possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This yields one scalar equation for x 1 {\\displaystyle x_{1}}: As such, we find: The implementation in Dev-C++ without preserving the coefficient vectors: In both cases the auxiliary systems to be solved are genuinely tri-diagonal, so the overall computational complexity of solving system A x = d {\\displaystyle Ax=d} remains linear with the respect to the dimension of the system n {\\displaystyle n} , that is O ( n ) {\\displaystyle O(n)} arithmetic operations. In other situations, the system of equations may be block tridiagonal (see block matrix), with smaller submatrices arranged as the individual elements in the above matrix system (e.g., the 2D Poisson problem). Simplified forms of Gaussian elimination have been developed for these situations.The textbook Numerical Mathematics by Quarteroni, Sacco and Saleri, lists a modified version of the algorithm which avoids some of the divisions (using instead multiplications), which is beneficial on some computer architectures. Parallel tridiagonal solvers have been published for many vector and parallel architectures, including GPUsFor an extensive treatment of parallel tridiagonal and block tridiagonal solvers see", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, the term can be defined as: The ability to provide services to and accept services from other systems, and to use the services exchanged to enable them to operate effectively together. ITU-T provides standards for international telecommunications. The condition achieved among communications-electronics systems or items of communications-electronics equipment when information or services can be exchanged directly and satisfactorily between them and/or their users. The degree of interoperability should be defined when referring to specific cases.In two-way radio, interoperability is composed of three dimensions: compatible communications paths (compatible frequencies, equipment and signaling), radio system coverage or adequate signal strength, and; scalable capacity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical computation, pseudocode often consists of mathematical notation, typically from set and matrix theory, mixed with the control structures of a conventional programming language, and perhaps also natural language descriptions. This is a compact and often informal notation that can be understood by a wide range of mathematically trained people, and is frequently used as a way to describe mathematical algorithms. For example, the sum operator (capital-sigma notation) or the product operator (capital-pi notation) may represent a for-loop and a selection structure in one expression: Return \u2211 k \u2208 S x k {\\displaystyle \\sum _{k\\in S}x_{k}} Normally non-ASCII typesetting is used for the mathematical equations, for example by means of markup languages, such as TeX or MathML, or proprietary formula editors. Mathematical style pseudocode is sometimes referred to as pidgin code, for example pidgin ALGOL (the origin of the concept), pidgin Fortran, pidgin BASIC, pidgin Pascal, pidgin C, and pidgin Lisp.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the analysis of algorithms on graphs, the distinction between a graph and its complement is an important one, because a sparse graph (one with a small number of edges compared to the number of pairs of vertices) will in general not have a sparse complement, and so an algorithm that takes time proportional to the number of edges on a given graph may take a much larger amount of time if the same algorithm is run on an explicit representation of the complement graph. Therefore, researchers have studied algorithms that perform standard graph computations on the complement of an input graph, using an implicit graph representation that does not require the explicit construction of the complement graph. In particular, it is possible to simulate either depth-first search or breadth-first search on the complement graph, in an amount of time that is linear in the size of the given graph, even when the complement graph may have a much larger size. It is also possible to use these simulations to compute other properties concerning the connectivity of the complement graph. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a latent class model (LCM) relates a set of observed (usually discrete) multivariate variables to a set of latent variables. It is a type of latent variable model. It is called a latent class model because the latent variable is discrete.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a branch of mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it. The special number field sieve is efficient for integers of the form re \u00b1 s, where r and s are small (for instance Mersenne numbers). Heuristically, its complexity for factoring an integer n {\\displaystyle n} is of the form: exp \u2061 ( ( 1 + o ( 1 ) ) ( 32 9 log \u2061 n ) 1 / 3 ( log \u2061 log \u2061 n ) 2 / 3 ) = L n  {\\displaystyle \\exp \\left(\\left(1+o(1)\\right)\\left({\\tfrac {32}{9}}\\log n\\right)^{1/3}\\left(\\log \\log n\\right)^{2/3}\\right)=L_{n}\\left} in O and L-notations. The SNFS has been used extensively by NFSNet (a volunteer distributed computing effort), NFS@Home and others to factorise numbers of the Cunningham project; for some time the records for integer factorization have been numbers factored by SNFS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In penetration testing, black-box testing refers to a method where an ethical hacker has no knowledge of the system being attacked. The goal of a black-box penetration test is to simulate an external hacking or cyber warfare attack.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the concept hierarchy derivation step, the OL system tries to arrange the extracted concepts in a taxonomic structure. This is mostly achieved with unsupervised hierarchical clustering methods. Because the result of such methods is often noisy, a supervision step, e.g., user evaluation, is added.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "First, geometric structures such as that of a differentiable manifold or a scheme can be expressed in terms of a sheaf of rings on the space. In such contexts, several geometric constructions such as vector bundles or divisors are naturally specified in terms of sheaves. Second, sheaves provide the framework for a very general cohomology theory, which encompasses also the \"usual\" topological cohomology theories such as singular cohomology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which culminated with the classification of finite simple groups, completed in 2004. Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become an active area in group theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications and computer networking, connection-oriented communication is a communication protocol where a communication session or a semi-permanent connection is established before any useful data can be transferred. The established connection ensures that data is delivered in the correct order to the upper communication layer. The alternative is called connectionless communication, such as the datagram mode communication used by Internet Protocol (IP) and User Datagram Protocol, where data may be delivered out of order, since different network packets are routed independently and may be delivered over different paths. Connection-oriented communication may be implemented with a circuit switched connection, or a packet-mode virtual circuit connection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cram\u00e9r bound, which may decay faster than exponential (e.g. sub-Gaussian). It is especially useful for sums of independent random variables, such as sums of Bernoulli random variables.The bound is commonly named after Herman Chernoff who described the method in a 1952 paper, though Chernoff himself attributed it to Herman Rubin. In 1938 Harald Cram\u00e9r had published an almost identical concept now known as Cram\u00e9r's theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "ALGOL's key ideas were continued, producing ALGOL 68: syntax and semantics became even more orthogonal, with anonymous routines, a recursive typing system with higher-order functions, etc.; not only the context-free part, but the full language syntax and semantics were defined formally, in terms of Van Wijngaarden grammar, a formalism designed specifically for this purpose.ALGOL 68's many little-used language features (for example, concurrent and parallel blocks) and its complex system of syntactic shortcuts and automatic type coercions made it unpopular with implementers and gained it a reputation of being difficult. Niklaus Wirth actually walked out of the design committee to create the simpler Pascal language. Some notable languages that were developed in this period include:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There were also around 188 million AXE lines in place or on order in 117 countries. Telecom and chip companies worked in the 1990s to provide Internet access over mobile telephones. Early versions such as Wireless Application Protocol (WAP) used packet data over the existing GSM network, in a form known as GPRS (General Packet Radio Service), but these services, known as 2.5G, were fairly rudimentary and did not achieve much mass-market success.The International Telecommunication Union (ITU) had prepared the specifications for a 3G mobile service that included several technologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the absence of empirical algorithmics, analyzing the complexity of an algorithm can involve various theoretical methods applicable to various situations in which the algorithm may be used. Memory and cache considerations are often significant factors to be considered in the theoretical choice of a complex algorithm, or the approach to its optimization, for a given purpose. Performance profiling is a dynamic program analysis technique typically used for finding and analyzing bottlenecks in an entire application's code or for analyzing an entire application to identify poorly performing code. A profiler can reveal the code most relevant to an application's performance issues.A profiler may help to determine when to choose one algorithm over another in a particular situation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The morphisms take one from one object to another, and form a dependent family of types, thus morphisms might be typed g: A \u2192 B {\\displaystyle g:A\\rightarrow B} , h: B \u2192 C {\\displaystyle h:B\\rightarrow C} , say. Composition is then a total function: \u2218: ( B \u2192 C ) \u2192 ( A \u2192 B ) \u2192 A \u2192 C {\\displaystyle \\circ :(B\\rightarrow C)\\rightarrow (A\\rightarrow B)\\rightarrow A\\rightarrow C} , so that h \u2218 g: A \u2192 C {\\displaystyle h\\circ g:A\\rightarrow C} . Special cases include: Setoids: sets that come with an equivalence relation, G-sets: sets equipped with an action of a group G {\\displaystyle G} .Groupoids are often used to reason about geometrical objects such as manifolds. Heinrich Brandt (1927) introduced groupoids implicitly via Brandt semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is no undisputed winner by only looking at the pairwise differences here. Now the strongest paths have to be identified. To help visualize the strongest paths, the set of pairwise preferences is depicted in the diagram on the right in the form of a directed graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is related to the rearrangement of the elements of S in which each element s is replaced by the corresponding f(s). For example, the permutation (3, 1, 2) mentioned above is described by the function \u03b1 {\\displaystyle \\alpha } defined as \u03b1 ( 1 ) = 3 , \u03b1 ( 2 ) = 1 , \u03b1 ( 3 ) = 2 {\\displaystyle \\alpha (1)=3,\\quad \\alpha (2)=1,\\quad \\alpha (3)=2} .The collection of all permutations of a set form a group called the symmetric group of the set. The group operation is the composition (performing two given rearrangements in succession), which results in another rearrangement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L\u221e metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. It is named after Pafnuty Chebyshev. It is also known as chessboard distance, since in the game of chess the minimum number of moves needed by a king to go from one square on a chessboard to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to the edges of the board. For example, the Chebyshev distance between f6 and e2 equals 4.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a wholly textual search, the first step in classifying web pages is to find an \u2018index item\u2019 that might relate expressly to the \u2018search term.\u2019 In the past, search engines began with a small list of URLs as a so-called seed list, fetched the content, and parsed the links on those pages for relevant information, which subsequently provided new links. The process was highly cyclical and continued until enough pages were found for the searcher's use. These days, a continuous crawl method is employed as opposed to an incidental discovery based on a seed list.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1950s, Alick Glennie developed Autocode, possibly the first compiled programming language, at the University of Manchester. In 1954, a second iteration of the language, known as the \"Mark 1 Autocode,\" was developed for the Mark 1 by R. A. Brooker. Brooker, with the University of Manchester, also developed an autocode for the Ferranti Mercury in the 1950s.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the other developers check out the new code without being aware of the problem, their work may grind to a halt while they wait for the problem to be fixed (or try to fix it themselves, which can be even more problematic, if multiple developers attempt to fix the issue at the same time). This naturally can result in a significant loss of productivity. Neutral builds are important for software development processes running at high loads with short schedules (see extreme programming, startup). Not having them means that any build that needs to be created for the software quality assurance department will use code that may be in the middle of major modifications, and which is therefore best left out of a build intended for independent validation \u2013 particularly a build being evaluated for possible release.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Cram\u00e9r\u2013Wold theorem in measure theory states that a Borel probability measure on R k {\\displaystyle \\mathbb {R} ^{k}} is uniquely determined by the totality of its one-dimensional projections. It is used as a method for proving joint convergence results. The theorem is named after Harald Cram\u00e9r and Herman Ole Andreas Wold. Let X n = ( X n 1 , \u2026 , X n k ) {\\displaystyle {X}_{n}=(X_{n1},\\dots ,X_{nk})} and X = ( X 1 , \u2026 , X k ) {\\displaystyle \\;{X}=(X_{1},\\dots ,X_{k})} be random vectors of dimension k. Then X n {\\displaystyle {X}_{n}} converges in distribution to X {\\displaystyle {X}} if and only if: \u2211 i = 1 k t i X n i \u2192 n \u2192 \u221e D \u2211 i = 1 k t i X i . {\\displaystyle \\sum _{i=1}^{k}t_{i}X_{ni}{\\overset {D}{\\underset {n\\rightarrow \\infty }{\\rightarrow }}}\\sum _{i=1}^{k}t_{i}X_{i}.} for each ( t 1 , \u2026 , t k ) \u2208 R k {\\displaystyle (t_{1},\\dots ,t_{k})\\in \\mathbb {R} ^{k}} , that is, if every fixed linear combination of the coordinates of X n {\\displaystyle {X}_{n}} converges in distribution to the correspondent linear combination of coordinates of X {\\displaystyle {X}} .If X n {\\displaystyle {X}_{n}} takes values in R + k {\\displaystyle \\mathbb {R} _{+}^{k}} , then the statement is also true with ( t 1 , \u2026 , t k ) \u2208 R + k {\\displaystyle (t_{1},\\dots ,t_{k})\\in \\mathbb {R} _{+}^{k}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of rental harmony (envy-free division of rooms and rent), the following results are known. Unanimous envy-freeness (called strong envy-freeness in the paper) may not exist when the cost-sharing policy is equal or proportional, but always exists with free cost-sharing policy. Moreover, a unanimously-envy-free allocation with free cost-sharing that maximizes the total rent can be found in polynomial time. With ad-hoc groups, unanimous envy-freeness exists even with equal cost-sharing policy. Average envy-freeness (called aggregate envy-freeness in the paper) always exists when the cost-sharing policy is equal or proportional or free.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Private (optional) \u2013 indicates that the function procedure is accessible only to other procedures in the module where it is declared. Friend (optional) \u2013 used only in a class module. Indicates that the Function procedure is visible throughout the project, but not visible to a controller of an instance of an object.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The soundness property provides the initial reason for counting a logical system as desirable. The completeness property means that every validity (truth) is provable. Together they imply that all and only validities are provable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, given a field F {\\displaystyle \\mathbb {F} } , nonnegative integers m , n {\\displaystyle m,n} , and a matrix A \u2208 F m \u00d7 n {\\displaystyle A\\in \\mathbb {F} ^{m\\times n}} , a rank decomposition or rank factorization of A is a factorization of A of the form A = CF, where C \u2208 F m \u00d7 r {\\displaystyle C\\in \\mathbb {F} ^{m\\times r}} and F \u2208 F r \u00d7 n {\\displaystyle F\\in \\mathbb {F} ^{r\\times n}} , where r = rank \u2061 A {\\displaystyle r=\\operatorname {rank} A} is the rank of A {\\displaystyle A} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the decision-making process, when faced with uncertainty, a subject can make two possible errors: type I or type II. A type I error is a false positive, thinking that an effect is there, when it is not. For example, acting on a fire alarm that turns out to be false. When someone infers sexual interest, where there is none, then a false-positive error has occurred.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel programming, the code is divided into threads. The read-write conflicting variables are split between threads and each thread has a copy of them. Data structures like linked lists, trees, hash tables etc. have data variables that are linked and cannot be split between threads and hence implementing parallelism is very difficult. To improve the efficiency of implementing data structures multiple operations like insertion, deletion, search need to be executed in parallel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Durrett and Steif (1993) and Steif (1994) show that for large radii there is a critical value \u03b8 c {\\displaystyle \\theta _{c}} such that if \u03b8 > \u03b8 c {\\displaystyle \\theta >\\theta _{c}} most individuals never change, and for \u03b8 \u2208 ( 1 / 2 , \u03b8 c ) {\\displaystyle \\theta \\in (1/2,\\theta _{c})} in the limit most sites agree. (Both of these results assume the probability of \u03be 0 ( x ) = 1 {\\displaystyle \\xi _{0}(x)=1} is one half.) This process has a natural generalization to more dimensions, some results for this are discussed in Durrett and Steif (1993).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Following a failure, the failover mechanism is tested to ensure that data is not lost or corrupted and that any agreed service levels are maintained (e.g., function availability or response times). Type or extent of recovery is specified in the requirement specifications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Complex craters have uplifted centers, and they have typically broad flat shallow crater floors, and terraced walls. At the largest sizes, one or more exterior or interior rings may appear, and the structure may be labeled an impact basin rather than an impact crater. Complex-crater morphology on rocky planets appears to follow a regular sequence with increasing size: small complex craters with a central topographic peak are called central peak craters, for example Tycho; intermediate-sized craters, in which the central peak is replaced by a ring of peaks, are called peak-ring craters, for example Schr\u00f6dinger; and the largest craters contain multiple concentric topographic rings, and are called multi-ringed basins, for example Orientale. On icy (as opposed to rocky) bodies, other morphological forms appear that may have central pits rather than central peaks, and at the largest sizes may contain many concentric rings. Valhalla on Callisto is an example of this type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the significance level, alpha (\u03b1), is 0.05, and only reject the null hypothesis if the p-value is less than or equal to 0.05, then the hypothesis test will indeed have a significance level (maximal type 1 error rate) of 0.05. As Neyman wrote: \u201cThe error that a practising statistician would consider the more important to avoid (which is a subjective judgment) is called the error of the first kind. The first demand of the mathematical theory is to deduce such test criteria as would ensure that the probability of committing an error of the first kind would equal (or approximately equal, or not exceed) a preassigned number \u03b1, such as \u03b1 = 0.05 or 0.01, etc. This number is called the level of significance\u201d; Neyman 1976, p.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Small farmers in Colombia grow a much wider range of cultivars than large commercial plantations. A study of these cultivars showed that they could be placed into at least three groups based on their characteristics: dessert bananas, non-plantain cooking bananas, and plantains, although there were overlaps between dessert and cooking bananas.In Southeast Asia\u2014the center of diversity for bananas, both wild and cultivated\u2014the distinction between \"bananas\" and \"plantains\" does not work, according to Valmayor et al. Many bananas are used both raw and cooked. There are starchy cooking bananas which are smaller than those eaten raw.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is also known as the log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplace distribution). It is related to the Gompertz distribution: when its density is first reflected about the origin and then restricted to the positive half line, a Gompertz function is obtained.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In radio, for example, a very narrow band will carry Morse code, a broader band will carry speech, and a still broader band will carry music without losing the high audio frequencies required for realistic sound reproduction. This broad band is often divided into channels or \"frequency bins\" using passband techniques to allow frequency-division multiplexing instead of sending a higher-quality signal. In data communications, a 56k modem will transmit a data rate of 56 kilobits per second (kbit/s) over a 4-kilohertz-wide telephone line (narrowband or voiceband).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "H D ( x , R ) {\\displaystyle H_{D}(x,R)} is a good measure for local complexity. Entropy only measures the statistic of the local attribute. It does not measure the spatial arrangement of the local attribute.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formal theories of grammar seek to define the different elements of language and describe the way they relate to each other as systems of formal rules or operations, while functional theories seek to define the functions performed by language and then relate them to the linguistic elements that carry them out. The framework of cognitive linguistics interprets language in terms of the concepts (which are sometimes universal, and sometimes specific to a particular language) which underlie its forms. Cognitive linguistics is primarily concerned with how the mind creates meaning through language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples of this include the failure to account for measurement error, or the failure to adequately control experiments for any parameters being measured. Fabrication can also occur in the context of undergraduate or graduate studies wherein a student fabricates a laboratory or homework assignment. Such cheating, when discovered, is usually handled within the institution, and does not become a scandal within the larger academic community (as cheating by students seldom has any academic significance).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the circle group, denoted by T {\\displaystyle \\mathbb {T} } or S 1 {\\displaystyle \\mathbb {S} ^{1}} , is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C \u00d7 {\\displaystyle \\mathbb {C} ^{\\times }} , the multiplicative group of all nonzero complex numbers. Since C \u00d7 {\\displaystyle \\mathbb {C} ^{\\times }} is abelian, it follows that T {\\displaystyle \\mathbb {T} } is as well. A unit complex number in the circle group represents a rotation of the complex plane about the origin and can be parametrized by the angle measure \u03b8 {\\displaystyle \\theta }: This is the exponential map for the circle group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that \"division\" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. A quasigroup with an identity element is called a loop.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages with Hindley-Milner type inference and imperative features, in particular the ML programming language family, the value restriction means that declarations are only polymorphically generalized if they are syntactic values (also called non-expansive). The value restriction prevents reference cells from holding values of different types and preserves type safety.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Increasing return loss corresponds to lower SWR. Return loss is a measure of how well devices or lines are matched. A match is good if the return loss is high.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Among popular ones are syntactic closures, explicit renaming macros and define-macro, a non-hygienic macro system similar to defmacro system provided in Common Lisp. The inability to specify whether or not a macro is hygienic is one of the shortcomings of the macro system. Alternative models for expansion such as scope sets provide a potential solution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Lagrange's theorem is a statement named after Joseph-Louis Lagrange about how frequently a polynomial over the integers may evaluate to a multiple of a fixed prime. More precisely, it states that if p is a prime number, x \u2208 Z / p Z {\\displaystyle x\\in \\mathbb {Z} /p\\mathbb {Z} } , and f ( x ) \u2208 Z  {\\displaystyle \\textstyle f(x)\\in \\mathbb {Z} } is a polynomial with integer coefficients, then either: every coefficient of f(x) is divisible by p, or f(x) \u2261 0 (mod p) has at most deg f(x) solutionswhere deg f(x) is the degree of f(x). If the modulus is not prime, then it is possible for there to be more than deg f(x) solutions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of text indexing, RMQs can be used to find the LCP (longest common prefix), where LCPT(i, j) computes the LCP of the suffixes that start at indexes i and j in T. To do this we first compute the suffix array A, and the inverse suffix array A\u22121. We then compute the LCP array H giving the LCP of adjacent suffixes in A. Once these data structures are computed, and RMQ preprocessing is complete, the length of the general LCP can be computed in constant time by the formula: LCP(i, j) = RMQH(A-1 + 1, A-1), where we assume for simplicity that A-1 + 1 <= A-1 (otherwise swap).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Dimensionality reduction using PCA has also been explored.Another line of approximate solution techniques for solving POMDPs relies on using (a subset of) the history of previous observations, actions and rewards up to the current time step as a pseudo-state. Usual techniques for solving MDPs based on these pseudo-states can then be used (e.g. Q-learning). Ideally the pseudo-states should contain the most important information from the whole history (to reduce bias) while being as compressed as possible (to reduce overfitting).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other languages which use writing systems with lowercases and uppercases, adjectives derived from proper nouns are commonly not capitalized.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The tee symbol \u22a4 {\\displaystyle \\top } is sometimes used to denote an arbitrary tautology, with the dual symbol \u22a5 {\\displaystyle \\bot } (falsum) representing an arbitrary contradiction; in any symbolism, a tautology may be substituted for the truth value \"true\", as symbolized, for instance, by \"1\".Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A key property of tautologies in propositional logic is that an effective method exists for testing whether a given formula is always satisfied (equiv., whether its negation is unsatisfiable). The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers\u2014a feature absent from sentences of propositional logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sometimes, a set is endowed with more than one feature simultaneously, which allows mathematicians to study the interaction between the different structures more richly. For example, an ordering imposes a rigid form, shape, or topology on the set, and if a set has both a topology feature and a group feature, such that these two features are related in a certain way, then the structure becomes a topological group.Mappings between sets which preserve structures (i.e., structures in the domain are mapped to equivalent structures in the codomain) are of special interest in many fields of mathematics. Examples are homomorphisms, which preserve algebraic structures; homeomorphisms, which preserve topological structures; and diffeomorphisms, which preserve differential structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory: Branching process, a Markov process that models a population Diffusion process, a solution to a stochastic differential equation Empirical process, a stochastic process that describes the proportion of objects in a system in a given state L\u00e9vy process, a stochastic process with independent, stationary increments Poisson process, a point process consisting of randomly located points on some underlying space Predictable process, a stochastic process whose value is knowable Stochastic process, a random process, as opposed to a deterministic process Wiener process, a continuous-time stochastic process Process calculus, a diverse family of related approaches for formally modeling concurrent systems Process function, a mathematical concept used in thermodynamics", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the It\u00f4 isometry, named after Kiyoshi It\u00f4, is a crucial fact about It\u00f4 stochastic integrals. One of its main applications is to enable the computation of variances for random variables that are given as It\u00f4 integrals. Let W:  \u00d7 \u03a9 \u2192 R {\\displaystyle W:\\times \\Omega \\to \\mathbb {R} } denote the canonical real-valued Wiener process defined up to time T > 0 {\\displaystyle T>0} , and let X:  \u00d7 \u03a9 \u2192 R {\\displaystyle X:\\times \\Omega \\to \\mathbb {R} } be a stochastic process that is adapted to the natural filtration F \u2217 W {\\displaystyle {\\mathcal {F}}_{*}^{W}} of the Wiener process. Then E \u2061  = E \u2061  , {\\displaystyle \\operatorname {E} \\left=\\operatorname {E} \\left,} where E {\\displaystyle \\operatorname {E} } denotes expectation with respect to classical Wiener measure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum theory, an experimental setup is described by the observable A {\\displaystyle A} to be measured, and the state \u03c3 {\\displaystyle \\sigma } of the system. The expectation value of A {\\displaystyle A} in the state \u03c3 {\\displaystyle \\sigma } is denoted as \u27e8 A \u27e9 \u03c3 {\\displaystyle \\langle A\\rangle _{\\sigma }} . Mathematically, A {\\displaystyle A} is a self-adjoint operator on a Hilbert space. In the most commonly used case in quantum mechanics, \u03c3 {\\displaystyle \\sigma } is a pure state, described by a normalized vector \u03c8 {\\displaystyle \\psi } in the Hilbert space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the BB84 scheme, Alice wishes to send a private key to Bob. She begins with two strings of bits, a {\\displaystyle a} and b {\\displaystyle b} , each n {\\displaystyle n} bits long. She then encodes these two strings as a tensor product of n {\\displaystyle n} qubits: | \u03c8 \u27e9 = \u2a02 i = 1 n | \u03c8 a i b i \u27e9 , {\\displaystyle |\\psi \\rangle =\\bigotimes _{i=1}^{n}|\\psi _{a_{i}b_{i}}\\rangle ,} where a i {\\displaystyle a_{i}} and b i {\\displaystyle b_{i}} are the i {\\displaystyle i} -th bits of a {\\displaystyle a} and b {\\displaystyle b} respectively. Together, a i b i {\\displaystyle a_{i}b_{i}} give us an index into the following four qubit states: | \u03c8 00 \u27e9 = | 0 \u27e9 , {\\displaystyle |\\psi _{00}\\rangle =|0\\rangle ,} | \u03c8 10 \u27e9 = | 1 \u27e9 , {\\displaystyle |\\psi _{10}\\rangle =|1\\rangle ,} | \u03c8 01 \u27e9 = | + \u27e9 = 1 2 | 0 \u27e9 + 1 2 | 1 \u27e9 , {\\displaystyle |\\psi _{01}\\rangle =|+\\rangle ={\\frac {1}{\\sqrt {2}}}|0\\rangle +{\\frac {1}{\\sqrt {2}}}|1\\rangle ,} | \u03c8 11 \u27e9 = | \u2212 \u27e9 = 1 2 | 0 \u27e9 \u2212 1 2 | 1 \u27e9 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "16 \u00d7 8 equals 128, therefore, each module has two ranks of 64 bits each. So, from the MCH point of view there are four 1 GB modules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More generally, a linear differential operator of order k, sending sections of a vector bundle E \u2192 M {\\displaystyle E\\rightarrow M} to sections of another bundle F \u2192 M {\\displaystyle F\\rightarrow M} is seen to be an R {\\displaystyle \\mathbb {R} } -linear map \u0394: \u0393 ( E ) \u2192 \u0393 ( F ) {\\displaystyle \\Delta :\\Gamma (E)\\to \\Gamma (F)} between the associated modules, such that for any k + 1 {\\displaystyle k+1} elements f 0 , \u2026 , f k \u2208 A {\\displaystyle f_{0},\\ldots ,f_{k}\\in A}: where the bracket : \u0393 ( E ) \u2192 \u0393 ( F ) {\\displaystyle :\\Gamma (E)\\to \\Gamma (F)} is defined as the commutator Denoting the set of k {\\displaystyle k} th order linear differential operators from an A {\\displaystyle A} -module P {\\displaystyle P} to an A {\\displaystyle A} -module Q {\\displaystyle Q} with D i f f k ( P , Q ) {\\displaystyle \\mathrm {Diff} _{k}(P,Q)} we obtain a bi-functor with values in the category of A {\\displaystyle A} -modules. Other natural concepts of calculus such as jet spaces, differential forms are then obtained as representing objects of the functors D i f f k {\\displaystyle \\mathrm {Diff} _{k}} and related functors. Seen from this point of view calculus may in fact be understood as the theory of these functors and their representing objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sometimes, the components of the covector v \u22c5 {\\displaystyle \\mathbf {v} \\ \\cdot } are referred to as the covariant components of v {\\displaystyle \\mathbf {v} } , although this is potentially misleading, (due to a vector having components that always vary in the contravariant sense). Despite potential confusion, this is what will be meant when the \"covariant components of a vector\" are referred to herein. The gradient is often cited as an example of a covector, but this is incorrect.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "G L 4 ( F 2 ) {\\displaystyle 2^{4\\,. }\\mathrm {GL} _{4}(\\mathbb {F} _{2})} is a maximal subgroup of the sporadic Conway group Co3. The nonsplit extension 2 5 . G L 5 ( F 2 ) {\\displaystyle 2^{5\\,. }\\mathrm {GL} _{5}(\\mathbb {F} _{2})} is a maximal subgroup of the Thompson sporadic group Th.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a special case, for C = \u03c0/2, then cos C = 0, and one obtains the spherical analogue of the Pythagorean theorem: If the law of cosines is used to solve for c, the necessity of inverting the cosine magnifies rounding errors when c is small. In this case, the alternative formulation of the law of haversines is preferable.A variation on the law of cosines, the second spherical law of cosines, (also called the cosine rule for angles) states: where A and B are the angles of the corners opposite to sides a and b, respectively. It can be obtained from consideration of a spherical triangle dual to the given one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All registered healthcare professionals must abide by these standards and if they are found to have breached confidentiality, they can face disciplinary action. A healthcare worker shares confidential information with someone else who is, or is about to, provide the patient directly with healthcare to make sure they get the best possible treatment. They only share information that is relevant to their care in that instance, and with consent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A related concept is the role of \"recommendation engines\", which give a user recommendations based on his/her previous online activity. Discoverability applies to computers and devices that can access the Internet, including various console video game systems and mobile devices such as tablets and smartphones. When producers make an effort to promote content (e.g., a TV show, film, song, or video game), they can use traditional marketing (billboards, TV ads, radio ads) and digital ads (pop-up ads, pre-roll ads, etc.), or a mix of traditional and digital marketing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are debates if increasing the number of taxa sampled improves phylogenetic accuracy more than increasing the number of genes sampled per taxon. Differences in each method's sampling impact the number of nucleotide sites utilized in a sequence alignment, which may contribute to disagreements. For example, phylogenetic trees constructed utilizing a more significant number of total nucleotides are generally more accurate, as supported by phylogenetic trees' bootstrapping replicability from random sampling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 67, 167, 467, and 1467 are the patterns related to Braille pattern dots-35, since the two additional dots of kantenji patterns 035, 357, and 0357 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In processor design, microcode serves as an intermediary layer situated between the central processing unit (CPU) hardware and the programmer-visible instruction set architecture of a computer. It consists of a set of hardware-level instructions that implement higher-level machine code instructions or control internal finite-state machine sequencing in many digital processing components. While microcode is utilized in general-purpose CPUs in contemporary desktops, it also functions as a fallback path for scenarios that the faster hardwired control unit is unable to manage.Housed in special high-speed memory, microcode translates machine instructions, state machine data, or other input into sequences of detailed circuit-level operations. It separates the machine instructions from the underlying electronics, thereby enabling greater flexibility in designing and altering instructions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following piece of Java code, the Java keyword synchronized makes the method thread-safe: In the C programming language, each thread has its own stack. However, a static variable is not kept on the stack; all threads share simultaneous access to it. If multiple threads overlap while running the same function, it is possible that a static variable might be changed by one thread while another is midway through checking it. This difficult-to-diagnose logic error, which may compile and run properly most of the time, is called a race condition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In priority-based scheduling algorithms, a major problem is indefinite block, or starvation. A process that is ready to run but waiting for the CPU can be considered blocked. A priority scheduling algorithm can leave some low-priority processes waiting indefinitely. A steady stream of higher-priority processes can prevent a low-priority process from ever getting the CPU.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although the distance update is still correct with the help of synchronization, the resource is wasted. In fact, to find the vertices for the next frontier, each unvisited vertex only need to check if any its neighbor vertex is in the frontier. This is also the core idea for direction optimization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead, the method of assessment should be changed so that this requirement is met, in the same way that a weighing scale should be rectified if it gives different comparisons between objects upon separate measurements of the objects. Data analysed using the model are usually responses to conventional items on tests, such as educational tests with right/wrong answers. However, the model is a general one, and can be applied wherever discrete data are obtained with the intention of measuring a quantitative attribute or trait.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance (ANOVA). They can be used for ascertaining which statistic should appear in the denominator in an F-test for testing a null hypothesis that a particular effect is absent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the category of sets, the coequalizer of two functions f, g: X \u2192 Y is the quotient of Y by the smallest equivalence relation \u223c {\\displaystyle \\sim } such that for every x \u2208 X {\\displaystyle x\\in X} , we have f ( x ) \u223c g ( x ) {\\displaystyle f(x)\\sim g(x)} . In particular, if R is an equivalence relation on a set Y, and r1, r2 are the natural projections (R \u2282 Y \u00d7 Y) \u2192 Y then the coequalizer of r1 and r2 is the quotient set Y/R. (See also: quotient by an equivalence relation.) The coequalizer in the category of groups is very similar.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence if it's possible to polynomial-time assign weights from a field of characteristic 2 to a digraph's arcs that make its weighted adjacency matrix unitary and having a non-zero Hamiltonian cycle polynomial then the digraph is Hamiltonian. Therefore the Hamiltonian cycle problem is computable on such graphs in polynomial time. In characteristic 2, the Hamiltonian cycle polynomial of an n\u00d7n-matrix is zero if n > 2k where k is its rank or if it's involutory and n > 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Annotea is an extensible standard and is designed to work with other W3C standards when possible. For instance, Annotea uses an RDF Schema for describing annotations as metadata and XPointer for locating the annotations in the annotated document. Similarly a bookmark schema describes the bookmark and topic metadata.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, static typing does imply static name resolution. Static name resolution catches, at compile time, use of variables that are not in scope; preventing programmer errors. Languages with dynamic scope resolution sacrifice this safety for more flexibility; they can typically set and get variables in the same scope at runtime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Base vector, the new metrics User Interaction (UI) and Privileges Required (PR) were added to help distinguish vulnerabilities that required user interaction or user or administrator privileges to be exploited. Previously, these concepts were part of the Access Vector metric of CVSSv2. The Base vector also saw the introduction of the new Scope (S) metric, which was designed to make clear which vulnerabilities may be exploited and then used to attack other parts of a system or network. These new metrics allow the Base vector to more clearly express the type of vulnerability being evaluated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As in prior designs, instructions were \"stuffed\" into words, with each instruction taking up either 16- or 32-bits (up from 15/30). The 8600 no longer used the A or B registers as in previous designs, and included a set of 16 general-purpose X registers instead.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model. The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution function at neighbouring data points. The concept underlying the method is based on the probability integral transform, in that a set of independent random samples derived from any random variable should on average be uniformly distributed with respect to the cumulative distribution function of the random variable. The MPS method chooses the parameter values that make the observed data as uniform as possible, according to a specific quantitative measure of uniformity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example: The code rate of a convolutional code will typically be 1\u20442, 2\u20443, 3\u20444, 5\u20446, 7\u20448, etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that 204 \u2212 188 = 16 redundant octets (or bytes) are added to each block of 188 octets of useful information. A few error correction codes do not have a fixed code rate\u2014rateless erasure codes. Note that bit/s is a more widespread unit of measurement for the information rate, implying that it is synonymous with net bit rate or useful bit rate exclusive of error-correction codes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. For example, the integers are nowhere dense among the reals, whereas the interval (0, 1) is not nowhere dense. A countable union of nowhere dense sets is called a meagre set. Meagre sets play an important role in the formulation of the Baire category theorem, which is used in the proof of several fundamental results of functional analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The denominator is the sample size reduced by the number of model parameters estimated from the same data, (n\u2212p) for p regressors or (n\u2212p\u22121) if an intercept is used (see errors and residuals in statistics for more details). Although the MSE (as defined in this article) is not an unbiased estimator of the error variance, it is consistent, given the consistency of the predictor. In regression analysis, \"mean squared error\", often referred to as mean squared prediction error or \"out-of-sample mean squared error\", can also refer to the mean value of the squared deviations of the predictions from the true values, over an out-of-sample test space, generated by a model estimated over a particular sample space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order of increasing strength, i.e., decreasing sets of pairs, three of the possible orders on the Cartesian product of two totally ordered sets are: Lexicographical order: (a,b) \u2264 (c,d) if and only if a < c or (a = c and b \u2264 d). This is a total order. (a,b) \u2264 (c,d) if and only if a \u2264 c and b \u2264 d (the product order). This is a partial order.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of 3 events\u2014A, B, and C\u2014it can be shown that:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In territories such as the UK a core function of a DMS has always been to support safe switching and work on the networks. Control engineers prepare switching schedules to isolate and make safe a section of network before work is carried out, and the DMS validates these schedules using its network model. Switching schedules can combine telecontrolled and manual (on-site) switching operations. When the required section has been made safe, the DMS allows a Pemit To Work (PTW) document to be issued.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Marcinkiewicz\u2013Zygmund inequality, named after J\u00f3zef Marcinkiewicz and Antoni Zygmund, gives relations between moments of a collection of independent random variables. It is a generalization of the rule for the sum of variances of independent random variables to moments of arbitrary order. It is a special case of the Burkholder-Davis-Gundy inequality in the case of discrete-time martingales.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A lockstep fault-tolerant machine uses replicated elements operating in parallel. At any time, all the replications of each element should be in the same state. The same inputs are provided to each replication, and the same outputs are expected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the primitive recursive functionals are a generalization of primitive recursive functions into higher type theory. They consist of a collection of functions in all pure finite types. The primitive recursive functionals are important in proof theory and constructive mathematics. They are a central part of the Dialectica interpretation of intuitionistic arithmetic developed by Kurt G\u00f6del. In recursion theory, the primitive recursive functionals are an example of higher-type computability, as primitive recursive functions are examples of Turing computability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation on a set is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in algebraic topology and algebraic geometry, an inverse image functor is a contravariant construction of sheaves; here \u201ccontravariant\u201d in the sense given a map f: X \u2192 Y {\\displaystyle f:X\\to Y} , the inverse image functor is a functor from the category of sheaves on Y to the category of sheaves on X. The direct image functor is the primary operation on sheaves, with the simplest definition. The inverse image exhibits some relatively subtle features.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems, memory management is the function responsible for managing the computer's primary memory. : 105\u2013208 The memory management function keeps track of the status of each memory location, either allocated or free. It determines how memory is allocated among competing processes, deciding which gets memory, when they receive it, and how much they are allowed. When memory is allocated it determines which memory locations will be assigned. It tracks when memory is freed or unallocated and updates the status. This is distinct from application memory management, which is how a process manages the memory assigned to it by the operating system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A weaker three-sigma rule can be derived from Chebyshev's inequality, stating that even for non-normally distributed variables, at least 88.8% of cases should fall within properly calculated three-sigma intervals. For unimodal distributions, the probability of being within the interval is at least 95% by the Vysochanskij\u2013Petunin inequality. There may be certain assumptions for a distribution that force this probability to be at least 98%.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes). It is a weakened form of Goldbach's conjecture, which states that every even number is the sum of two primes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a greatest common divisor matrix (sometimes abbreviated as GCD matrix) is a matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the bin covering problem, there are n items with different sizes. The goal is to pack the items into a maximum number of bins, where each bin should contain at least B. A natural configuration LP for this problem could be: maximize 1 \u22c5 x s.t. A x \u2264 n and x \u2265 0 {\\displaystyle {\\text{maximize}}~~\\mathbf {1} \\cdot \\mathbf {x} ~~~{\\text{s.t. }}~~A\\mathbf {x} \\leq \\mathbf {n} ~~~{\\text{and}}~~\\mathbf {x} \\geq 0} where A represents all configurations of items with sum at least B (one can take only the inclusion-minimal configurations).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a congruence is an equivalence relation on the integers. The following sections list important or interesting prime-related congruences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one. For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution. In Bayes' theorem, a normalizing constant is used to ensure that the sum of all possible hypotheses equals 1. Other uses of normalizing constants include making the value of a Legendre polynomial at 1 and in the orthogonality of orthonormal functions. A similar concept has been used in areas other than probability, such as for polynomials.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Factorization was first considered by ancient Greek mathematicians in the case of integers. They proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church-Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding. In the untyped lambda calculus the only primitive data type is the function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If at phase i, V has an incorrect value for f i \u2212 1 ( r 1 , \u2026 ) {\\displaystyle f_{i-1}(r_{1},\\dots )} then f i ( r 1 , \u2026 , 0 ) {\\displaystyle f_{i}(r_{1},\\dots ,0)} and f i ( r 1 , \u2026 , 1 ) {\\displaystyle f_{i}(r_{1},\\dots ,1)} will likely also be incorrect, and so forth. The probability for P ~ {\\displaystyle {\\tilde {P}}} to get lucky on some random r is at most the degree of the polynomial divided by the field size: n / n 4 {\\displaystyle n/n^{4}} . The protocol runs through O(n2) phases, so the probability that P ~ {\\displaystyle {\\tilde {P}}} gets lucky at some phase is \u2264 1/n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But the CFC industry did not give up that easily. As late as 1986, the Alliance for Responsible CFC Policy (an association representing the CFC industry founded by DuPont) was still arguing that the science was too uncertain to justify any action. In 1987, DuPont testified before the US Congress that \"We believe there is no imminent crisis that demands unilateral regulation.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\mathbb {R} \\cup \\left\\{-\\infty ,+\\infty \\right\\}.} It is the Dedekind\u2013MacNeille completion of the real numbers. When the meaning is clear from context, the symbol + \u221e {\\displaystyle +\\infty } is often written simply as \u221e . {\\displaystyle \\infty .} There is also the projectively extended real line where + \u221e {\\displaystyle +\\infty } and \u2212 \u221e {\\displaystyle -\\infty } are not distinguished so the infinity is denoted by only \u221e {\\displaystyle \\infty } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects). For example, the ordered triple (a,b,c) can be defined as (a, (b,c)), i.e., as one pair nested in another. In the ordered pair (a, b), the object a is called the first entry, and the object b the second entry of the pair. Alternatively, the objects are called the first and second components, the first and second coordinates, or the left and right projections of the ordered pair. Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs, cf. picture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Chebyshev's inequality (also called the Bienaym\u00e9\u2013Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1/k2 of the distribution's values can be k or more standard deviations away from the mean (or equivalently, at least 1 \u2212 1/k2 of the distribution's values are less than k standard deviations away from the mean). The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms. Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1st edition of his well-known work, Phaselock Techniques, Floyd M. Gardner introduced a lock-in concept: If, for some reason, the frequency difference between input and VCO is less than the loop bandwidth, the loop will lock up almost instantaneously without slipping cycles. The maximum frequency difference for which this fast acquisition is possible is called the lock-in frequency. His notion of the lock-in frequency and corresponding definition of the lock-in range have become popular and nowadays are given in various engineering publications. However, since even for zero frequency difference there may exist initial states of loop such that cycle slipping may take place during the acquisition process, the consideration of initial state of the loop is of utmost importance for the cycle slip analysis and, therefore, Gardner\u2019s concept of lock-in frequency lacked rigor and required clarification. In the 2nd edition of his book, Gardner stated: \"there is no natural way to define exactly any unique lock-in frequency\", and he wrote that \"despite its vague reality, lock-in range is a useful concept\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hilbert projection theorem is a famous result of convex analysis that says that for every vector x {\\displaystyle x} in a Hilbert space H {\\displaystyle H} and every nonempty closed convex C \u2286 H , {\\displaystyle C\\subseteq H,} there exists a unique vector m \u2208 C {\\displaystyle m\\in C} for which \u2016 c \u2212 x \u2016 {\\displaystyle \\|c-x\\|} is minimized over the vectors c \u2208 C {\\displaystyle c\\in C} ; that is, such that \u2016 m \u2212 x \u2016 \u2264 \u2016 c \u2212 x \u2016 {\\displaystyle \\|m-x\\|\\leq \\|c-x\\|} for every c \u2208 C . {\\displaystyle c\\in C.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a dial plan (or dialing plan) establishes the permitted sequences of digits dialed by telephone subscriber and the manner in which a telephone switch interprets these digits within the definitions of the prevailing telephone numbering plan. Dial plans in the public switched telephone network referred to as dialing procedures.The collection of permissible digit patterns, so called digit-maps, for a private telephone system or for customer premise equipment, such as an analog telephone adapter (ATA) or an IP phone, is sometimes also called dial plan. A pattern may be as short as a single digit, e.g. for reaching an operator, or as long as a complete international telephone number, including trunk prefixes and international prefixes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The method became known as the Diffie-Hellman key exchange. RSA (Rivest\u2013Shamir\u2013Adleman) is another notable public-key cryptosystem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each time this (latter) magnitude comprises a half, a third, or a quarter of the given magnitude (of the unit), or, compared with (the unit), comprises three, five, or three-fifths, it is a rational magnitude. And, in general, each magnitude that corresponds to this magnitude (i.e. to the unit), as one number to another, is rational. If, however, a magnitude cannot be represented as a multiple, a part (1/n), or parts (m/n) of a given magnitude, it is irrational, i.e. it cannot be expressed other than by means of roots.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of machine learning and specifically the problem of statistical classification, a confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one; in unsupervised learning it is usually called a matching matrix. Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa \u2013 both variants are found in the literature. The name stems from the fact that it makes it easy to see whether the system is confusing two classes (i.e. commonly mislabeling one as another). It is a special kind of contingency table, with two dimensions (\"actual\" and \"predicted\"), and identical sets of \"classes\" in both dimensions (each combination of dimension and class is a variable in the contingency table).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature. F-algebras can also be used to represent data structures used in programming, such as lists and trees. The main related concepts are initial F-algebras which may serve to encapsulate the induction principle, and the dual construction F-coalgebras.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Faraday created this concept by impression of Roger Boscovich, a physicist that impacted Maxwell's work as well. In 1856, he published his 1st paper in electromagnetism: On Faraday's Lines of Force. He tried to use the analogy of incompressible fluid flow to model the magnetic lines of forces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. A simple random sample is an unbiased sampling technique. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, an n-Kn\u00f6del number for a given positive integer n is a composite number m with the property that each i < m coprime to m satisfies i m \u2212 n \u2261 1 ( mod m ) {\\displaystyle i^{m-n}\\equiv 1{\\pmod {m}}} . The concept is named after Walter Kn\u00f6del.The set of all n-Kn\u00f6del numbers is denoted Kn. The special case K1 is the Carmichael numbers. There are infinitely many n-Kn\u00f6del numbers for a given n. Due to Euler's theorem every composite number m is an n-Kn\u00f6del number for n = m \u2212 \u03c6 ( m ) {\\displaystyle n=m-\\varphi (m)} where \u03c6 {\\displaystyle \\varphi } is Euler's totient function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of digital privacy, information privacy is the idea that individuals should have the freedom to determine how their digital information is collected and used. This is particularly relevant for personally identifiable information. The concept of information privacy has evolved in parallel to the evolution of the field of Information Technology (IT). The rise of networking and computing led to the dramatic change in the ways of information exchange.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical hypothesis testing, a null result occurs when an experimental result is not significantly different from what is to be expected under the null hypothesis; its probability (under the null hypothesis) does not exceed the significance level, i.e., the threshold set prior to testing for rejection of the null hypothesis. The significance level varies, but common choices include 0.10, 0.05, and 0.01.As an example in physics, the results of the Michelson\u2013Morley experiment were of this type, as it did not detect the expected velocity relative to the postulated luminiferous aether. This experiment's famous failed detection, commonly referred to as the null result, contributed to the development of special relativity. The experiment did appear to measure a non-zero \"drift\", but the value was far too small to account for the theoretically expected results; it is generally thought to be inside the noise level of the experiment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In engineering there are multiple types of failure based upon the application of the material. In many machine applications any change in the part due to yielding will result in the machine piece needing to be replaced. Although this deformation or weakening of the material is not the technical definition of ultimate failure, the piece has failed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . \u03b4 i k p k M  ( l \u2212 2 ) \u27e9 \u27e9 {\\displaystyle {\\hat {T}}r\\left\\langle \\left\\langle \\delta _{i_{1}p_{1}}...\\delta _{i_{k}p_{k}}\\mathbf {M} _{i_{1}p_{1}}^{(l)}\\right\\rangle \\right\\rangle =(2l+2k+1)\\left\\langle \\left\\langle \\delta _{i_{2}p_{2}}...\\delta _{i_{k}p_{k}}\\mathbf {M} _{}^{(l-2)}\\right\\rangle \\right\\rangle } .Calculating the trace reduces the number of the Kronecker symbols by one, and the rank of the harmonic tensor on the right-hand side of the equation decreases by two.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and especially general topology, the interlocking interval topology is an example of a topology on the set S := R+ \\ Z+, i.e. the set of all positive real numbers that are not positive whole numbers. To give the set S a topology means to say which subsets of S are \"open\", and to do so in a way that the following axioms are met: The union of open sets is an open set. The finite intersection of open sets is an open set. S and the empty set \u2205 are open sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, gender is determined by strictly semantic criteria, but in other languages, semantic criteria only partially determine gender.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to effectively manage all the documentation required to care for collections, organized systems are necessary. In the early days of museum registration simple paper ledgers were used to track objects, and documentation was stored in file cabinets. Since computers became more commonplace however, practices have evolved and very technologically advanced systems now exist to manage all aspects of collection management in one place.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Primary rules require individuals to act or not act in certain ways and create duties for the governed to obey. Secondary rules are rules that confer authority to create new primary rules or modify existing ones. Secondary rules are divided into rules of adjudication (how to resolve legal disputes), rules of change (how laws are amended), and the rule of recognition (how laws are identified as valid).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nursing, a study has been conducted of the impact of interruptions on nurses in a trauma center. Another study has been done on the interruption rates of nurses and doctors.Interruption caused by smartphone use in health-care settings can be deadly. Hence, it may be worthwhile for health care organizations to craft effective cellphone usage policies to maximize technological benefits and minimize unnecessary distraction associated with smartphone use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The elements l i \u2208 D {\\displaystyle l_{i}\\in {\\mathcal {D}}} are applied to a single differential indeterminate z {\\displaystyle z} . In this way the ideal I = \u27e8 l 1 , l 2 , \u2026 \u27e9 {\\displaystyle I=\\langle l_{1},l_{2},\\ldots \\rangle } corresponds to the system of PDEs l 1 z = 0 {\\displaystyle l_{1}z=0} , l 2 z = 0 , \u2026 {\\displaystyle l_{2}z=0,\\ldots } for the single function z {\\displaystyle z} . The generators of an ideal are highly non-unique; its members may be transformed in infinitely many ways by taking linear combinations of them or its derivatives without changing the ideal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From this matrix, the probability of being in a particular state n steps in the future can be calculated. A Markov chain's state space can be partitioned into communicating classes that describe which states are reachable from each other (in one transition or in many). Each state can be described as transient or recurrent, depending on the probability of the chain ever returning to that state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum neural networks programmed on gate-model quantum computers, based on quantum perceptrons instead of variational quantum circuits, the non-linearity of the activation function can be implemented with no need of measuring the output of each perceptron at each layer. The quantum properties loaded within the circuit such as superposition can be preserved by creating the Taylor series of the argument computed by the perceptron itself, with suitable quantum circuits computing the powers up to a wanted approximation degree. Because of the flexibility of such quantum circuits, they can be designed in order to approximate any arbitrary classical activation function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although not perfect, these frequencies can usually provide some clues about the topic of the document. And sometimes it is also useful to weight the term frequencies by the inverse document frequencies. See tf-idf for detailed discussions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, communications protection is the application of communications security (COMSEC) measures to telecommunications systems in order to: (a) deny unauthorized access to sensitive unclassified information of value, (b) prevent disruption of telecommunications services, or (c) ensure the authenticity of information handled by telecommunications systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, researchers attempt to fit appropriate model parameters to the data corpus using one of several heuristics for maximum likelihood fit. A survey by D. Blei describes this suite of algorithms. Several groups of researchers starting with Papadimitriou et al. have attempted to design algorithms with provable guarantees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, the no-broadcasting theorem is a result of quantum information theory. In the case of pure quantum states, it is a corollary of the no-cloning theorem. The no-cloning theorem for pure states says that it is impossible to create two copies of an unknown state given a single copy of the state. Since quantum states cannot be copied in general, they cannot be broadcast.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, the Extract Class refactoring is applied when a class becomes overweight with too many methods and its purpose becomes unclear. Extract Class refactoring involves creating a new class and moving methods and/or data to the new class.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In situation theory, situation semantics (pioneered by Jon Barwise and John Perry in the early 1980s) attempts to provide a solid theoretical foundation for reasoning about common-sense and real world situations, typically in the context of theoretical linguistics, theoretical philosophy, or applied natural language processing,", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions. Comparison of sum-of-squares with degrees-of-freedom is no longer meaningful, and software may report certain fractional 'degrees of freedom' in these cases. Such numbers have no genuine degrees-of-freedom interpretation, but are simply providing an approximate chi-squared distribution for the corresponding sum-of-squares. The details of such approximations are beyond the scope of this page.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, seven frequency bands have been allocated by the Federal Communications Commission for uses that include cordless phones. These are: 1.7 MHz (1.665\u20131.770 MHz, narrow-band FM) Cordless phones manufactured after October 1, 1984, are not allowed to use this band and were required to use the newer (higher) 43-50 MHz frequencies, although older telephones, on the older frequency pairs, could still be used. 27 MHz, near the Citizens Band (CB) Radio service with some frequencies being 26.010, 26.050, 26.380, 26.419 and 27.095 MHz. These were initially paired with the 1.7 MHz frequencies, then, later, with the 49 MHz frequencies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Among other things, the use of serializing tokens prevents many of the situations that could result in deadlocks and priority inversions when using mutexes, as well as greatly simplifying the design and implementation of a many-step procedure that would require a resource to be shared among multiple threads. The serializing token code is evolving into something quite similar to the \"Read-copy-update\" feature now available in Linux. Unlike Linux's current RCU implementation, DragonFly's is being implemented such that only processors competing for the same token are affected rather than all processors in the computer.DragonFly switched to multiprocessor safe slab allocator, which requires neither mutexes nor blocking operations for memory assignment tasks. It was eventually ported into standard C library in the userland, where it replaced FreeBSD's malloc implementation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In organizational development (OD), performance can be thought of as Actual Results vs Desired Results. Any discrepancy, where Actual is less than Desired, could constitute the performance improvement zone. Performance management and improvement can be thought of as a cycle: Performance planning where goals and objectives are established Performance coaching where a manager intervenes to give feedback and adjust performance Performance appraisal where individual performance is formally documented and feedback deliveredA performance problem is any gap between Desired Results and Actual Results. Performance improvement is any effort targeted at closing the gap between Actual Results and Desired Results.Other organizational development definitions are slightly different. The U.S. Office of Personnel Management (OPM) indicates that Performance Management consists of a system or process whereby: Work is planned and expectations are set Performance of work is monitored Staff ability to perform is developed and enhanced Performance is rated or measured and the ratings summarized Top performance is rewarded.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, even if an artifact or process is protected by trade secrets, reverse-engineering the artifact or process is often lawful if it has been legitimately obtained.Reverse engineering of computer software often falls under both contract law as a breach of contract as well as any other relevant laws. That is because most end-user license agreements specifically prohibit it, and US courts have ruled that if such terms are present, they override the copyright law that expressly permits it (see Bowers v. Baystate Technologies). According to Section 103(f) of the Digital Millennium Copyright Act (17 U.S.C. \u00a7 1201 (f)), a person in legal possession of a program may reverse-engineer and circumvent its protection if that is necessary to achieve \"interoperability\", a term that broadly covers other devices and programs that can interact with it, make use of it, and to use and transfer data to and from it in useful ways. A limited exemption exists that allows the knowledge thus gained to be shared and used for interoperability purposes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the quantum world, however, the conservation of quantum information should mean that information cannot be created nor destroyed. This concept stems from two fundamental theorems of quantum mechanics: the no-cloning theorem and the no-deleting theorem. But the no-hiding theorem is a more general proof of conservation of quantum information which originates from the proof of conservation of wave function in quantum theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These facilities tend to vary drastically between languages, but in general each can achieve anything that is possible with any of the others. A great many operation overloads, data type by data type, can have the same effect at compile-time as any degree of inheritance or other means to achieve polymorphism. The class notation is simply a coder's convenience.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Within the PBX, the user merely dials the extension number to reach any other user directly. For inbound calls, a switchboard operator or automated attendant may request the number of the desired extension or the call may be completed with direct inbound dialing, if outside numbers are assigned to individual extensions. An off-premises extension, where a worker at a remote location employs a telephone configured to appear as if it were an extension located at the main business site, may be created in analog telephony by using a leased line to connect the extension to the main enterprise system. Voice over IP makes the creation of off-premises extensions inexpensive and trivial as broadband Internet and virtual private networking can extend local network access anywhere in the world. In either system, an off-premises extension is reachable from within the same enterprise simply by calling its extension number directly; for inbound and outgoing calls, it functions as if it were located at the main place of business.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Turing test, the conversation is conducted via keyboards and the challenge for the AI community is to produce a computer that can give answers that are indistinguishable from those produced by a real human. Given that such interactions are by their very nature open-ended and context-dependent Collins argues that only a fully socialised intelligence will be able to respond appropriately to any of the new and potentially unknown sentences directed to it. Although the argument was not made in these terms at the time, the concept of interactional expertise is important here.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The H-ternary code has also timing superiority compared to similar ternary codes. Other ternary line code such as alternate mark inversion (AMI) also lacks the timing information when a run of zeros needs to be transmitted. This drawback is partly overcome by its modified version the high density bipolar with three zeros substitution (HDB3). On the other hand, the new code has a smaller bandwidth in comparison with the polar RZ code. The latter has its frequency spectral components concentrated at twice the original binary data rate because the polar RZ code has a pulse duty cycle of 50 percent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one of the earliest studies involving misattribution, the Canadian cognitive psychologist Bruce Whittlesea presented subjects with a list of common words. Each word was briefly displayed to the subject. The task required the subject to judge whether a target word was semantically related to any word in the list. Unlike Whittlesea's first experiment involving the recognition of target words, this study involved the manipulation of processing fluency through the conceptual context of the target word, rather than the physical context.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Release Management capabilities give teams the ability to perform a controlled, workflow (provided by Windows Workflow Foundation) driven release to development, test and production environments and provides dashboards for monitoring the progress of one or more releases. Microsoft has rebuilt Release Management for Visual Studio Team Services and on-premises version of TFS with the new changes in 2015 Update 2. The new version of Release Management leverages the web browser as the client and relies on the same agent architecture as Team Foundation Build. Release Management enables DevOps capabilities for Azure DevOps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An alternative way to express this is to assume one or more solutions or examples exists, from which a smallest solution or example\u2014a minimal counterexample\u2014can then be inferred. Once there, one would try to prove that if a smallest solution exists, then it must imply the existence of a smaller solution (in some sense), which again proves that the existence of any solution would lead to a contradiction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Double extension set theory (DEST) is an axiomatic set theory proposed by Andrzej Kisielewicz consisting of two separate membership relations on the universe of sets, denoted here by \u2208 {\\displaystyle \\in } and \u03b5 {\\displaystyle \\varepsilon } , and a set of axioms relating the two. The intention behind defining the two membership relations is to avoid the usual paradoxes of set theory, without substantially weakening the axiom of unrestricted comprehension. Intuitively, in DEST, comprehension is used to define the elements of a set under one membership relation using formulas that involve only the other membership relation. Let \u03d5 ( x ) {\\displaystyle \\phi (x)} be a first-order formula with free variable x {\\displaystyle x} in the language of DEST not involving the membership relation \u03b5 {\\displaystyle \\varepsilon } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence the expression, \"counted with multiplicity\". If multiplicity is ignored, this may be emphasized by counting the number of distinct elements, as in \"the number of distinct roots\". However, whenever a set (as opposed to multiset) is formed, multiplicity is automatically ignored, without requiring use of the term \"distinct\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The study of unattested substrata often begins from the study of substrate words, which lack a clear etymology. Such words can in principle still be native inheritance, lost everywhere else in the language family; but they might in principle also originate from a substrate. The sound structure of words of unknown origin \u2014 their phonology and morphology \u2014 can often suggest hints in either direction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Strahler number or Horton\u2013Strahler number of a mathematical tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology, as a way of measuring the complexity of rivers and streams, by Robert E. Horton (1945) and Arthur Newell Strahler (1952, 1957). In this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributaries. The same numbers also arise in the analysis of L-systems and of hierarchical biological structures such as (biological) trees and animal respiratory and circulatory systems, in register allocation for compilation of high-level programming languages and in the analysis of social networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is symmetric as two equal mathematical objects are equal regardless of their order.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of generics the two languages show a superficial syntactical similarity, but they have deep underlying differences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance). It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order to transform one input string into another. Simplistic string metrics such as Levenshtein distance have expanded to include phonetic, token, grammatical and character-based methods of statistical comparisons. String metrics are used heavily in information integration and are currently used in areas including fraud detection, fingerprint analysis, plagiarism detection, ontology merging, DNA analysis, RNA analysis, image analysis, evidence-based machine learning, database data deduplication, data mining, incremental search, data integration, malware detection, and semantic knowledge integration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These are then, however, not real time capable (except one uses a really big buffer, that lowers the throughput dramatically) anymore and only sufficient for post processing. Other variants do several passes to yield a rough estimate first and then refine it by the following passes, which is inspired by video editing/transcoding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of mathematical analysis, an interpolation inequality is an inequality of the form \u2016 u 0 \u2016 0 \u2264 C \u2016 u 1 \u2016 1 \u03b1 1 \u2016 u 2 \u2016 2 \u03b1 2 \u2026 \u2016 u n \u2016 n \u03b1 n , n \u2265 2 , {\\displaystyle \\|u_{0}\\|_{0}\\leq C\\|u_{1}\\|_{1}^{\\alpha _{1}}\\|u_{2}\\|_{2}^{\\alpha _{2}}\\dots \\|u_{n}\\|_{n}^{\\alpha _{n}},\\quad n\\geq 2,} where for 0 \u2264 k \u2264 n {\\displaystyle 0\\leq k\\leq n} , u k {\\displaystyle u_{k}} is an element of some particular vector space X k {\\displaystyle X_{k}} equipped with norm \u2016 \u22c5 \u2016 k {\\displaystyle \\|\\cdot \\|_{k}} and \u03b1 k {\\displaystyle \\alpha _{k}} is some real exponent, and C {\\displaystyle C} is some constant independent of u 0 , . . , u n {\\displaystyle u_{0},..,u_{n}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following the Kemeny-Young winner for the first group of voters is determined. The Kemeny\u2013Young method arranges the pairwise comparison counts in the following tally table: The ranking scores of all possible rankings are: Result: The ranking A > B > C has the highest ranking score. Thus, A wins ahead of B and C.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to disinfect water, such as chlorine, chlorine dioxide, and ozone are introduced which kill microorganisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many older pianos only have 85 keys (seven octaves from A0 to A7). Some piano manufacturers have extended the range further in one or both directions. For example, the Imperial B\u00f6sendorfer has nine extra keys at the bass end, giving a total of 97 keys and an eight octave range.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "IPS are usually defined via their Markov generator giving rise to a unique Markov process using Markov semigroups and the Hille-Yosida theorem. The generator again is given via so-called transition rates c \u039b ( \u03b7 , \u03be ) > 0 {\\displaystyle c_{\\Lambda }(\\eta ,\\xi )>0} where \u039b \u2282 G {\\displaystyle \\Lambda \\subset G} is a finite set of sites and \u03b7 , \u03be \u2208 \u03a9 {\\displaystyle \\eta ,\\xi \\in \\Omega } with \u03b7 i = \u03be i {\\displaystyle \\eta _{i}=\\xi _{i}} for all i \u2209 \u039b {\\displaystyle i\\notin \\Lambda } . The rates describe exponential waiting times of the process to jump from configuration \u03b7 {\\displaystyle \\eta } into configuration \u03be {\\displaystyle \\xi } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and optimization, a pseudo-Boolean function is a function of the form f: B n \u2192 R , {\\displaystyle f:\\mathbf {B} ^{n}\\to \\mathbb {R} ,} where B = {0, 1} is a Boolean domain and n is a nonnegative integer called the arity of the function. A Boolean function is then a special case, where the values are also restricted to 0 or 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More specifically, ground truth may refer to a process in which \"pixels\" on a satellite image are compared to what is imaged (at the time of capture) in order to verify the contents of the \"pixels\" in the image (noting that the concept of \"pixel\" is imaging-system-dependent). In the case of a classified image, supervised classification can help to determine the accuracy of the classification by the remote sensing system which can minimize error in the classification. Ground truth is usually done on site, correlating what is known with surface observations and measurements of various properties of the features of the ground resolution cells under study in the remotely sensed digital image.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In general terms the size of the CPU die has remained largely the same over time, while the size of the units within the CPU has grown much smaller as more and more units were added. That means that the relative distance between any one function unit and the global register file has grown over time. Once introduced in order to avoid delays in talking to main memory, the global register file has itself become a delay that is worth avoiding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The machine had a two-stage assembler (SAAL \u2013 Single Address Assembly Language) which was its primary assembler; it also had a three-stage card based compiler for a programming language called SARGE. 1005s were used as some nodes on Autodin. There were actually two versions of the 1005.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The family of all rotations and their partial order can be constructed in polynomial time, leading to polynomial time solutions for other problems on stable matching including the minimum or maximum weight stable matching. The Gale\u2013Shapley algorithm can be used to construct two special lattice elements, its top and bottom element.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for a CDSS to offer value, it must demonstrably improve clinical workflow or outcome. Evaluation of CDSS quantifies its value to improve a system's quality and measure its effectiveness. Because different CDSSs serve different purposes, no generic metric applies to all such systems; however, attributes such as consistency (with and with experts) often apply across a wide spectrum of systems.The evaluation benchmark for a CDSS depends on the system's goal: for example, a diagnostic decision support system may be rated based upon the consistency and accuracy of its classification of disease (as compared to physicians or other decision support systems). An evidence-based medicine system might be rated based upon a high incidence of patient improvement or higher financial reimbursement for care providers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The second mechanism is the balancing of power generation, which is coordinated by the TSO. Depending on the energy lacks and surplus (e.g. due to power plant failures or to intermittence in the case of wind power installations), the TSO determines the penalties that will be paid by IPPs who missed in their obligations. In some cases, an intra-day market is also present, in order to take corrective actions.In order to illustrate this electricity market mechanism, consider the Dutch electricity market.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practical electric circuits electrical breakdown is usually an unwanted occurrence, a failure of insulating material causing a short circuit, possibly resulting in a catastrophic failure of the equipment. In power circuits, the sudden drop in resistance causes a high current to flow through the material, beginning an electric arc, and if safety devices do not interrupt the current quickly the sudden extreme Joule heating may cause the insulating material or other parts of the circuit to melt or vaporize explosively, damaging the equipment and creating a fire hazard. However, external protective devices in the circuit such as circuit breakers and current limiting can prevent the high current; and the breakdown process itself is not necessarily destructive and may be reversible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Euclidean algorithm or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements (c. 300 BC). It is one of the oldest algorithms in common use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nuclear strategy, a first strike or preemptive strike is a preemptive surprise attack employing overwhelming force. First strike capability is a country's ability to defeat another nuclear power by destroying its arsenal to the point where the attacking country can survive the weakened retaliation while the opposing side is left unable to continue war. The preferred methodology is to attack the opponent's strategic nuclear weapon facilities (missile silos, submarine bases, bomber airfields), command and control sites, and storage depots first. The strategy is called counterforce.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sachs was interested in them for their self-complementarity properties, while Erd\u0151s and R\u00e9nyi studied their symmetries. Paley digraphs are directed analogs of Paley graphs that yield antisymmetric conference matrices. They were introduced by Graham & Spencer (1971) (independently of Sachs, Erd\u0151s, and R\u00e9nyi) as a way of constructing tournaments with a property previously known to be held only by random tournaments: in a Paley digraph, every small subset of vertices is dominated by some other vertex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases morphemes have effectively fused and will not be recognizable as being composed of two separate morphemes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operator theory, a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix. It was first introduced by James Mercer in the early 20th century, in the context of solving integral operator equations. Since then, positive-definite functions and their various analogues and generalizations have arisen in diverse parts of mathematics. They occur naturally in Fourier analysis, probability theory, operator theory, complex function-theory, moment problems, integral equations, boundary-value problems for partial differential equations, machine learning, embedding problem, information theory, and other areas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the Brownian web is an uncountable collection of one-dimensional coalescing Brownian motions, starting from every point in space and time. It arises as the diffusive space-time scaling limit of a collection of coalescing random walks, with one walk starting from each point of the integer lattice Z at each time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The best-known algorithms are Shor's algorithm for factoring and Grover's algorithm for searching an unstructured database or an unordered list. Shor's algorithms runs much (almost exponentially) faster than the best-known classical algorithm for factoring, the general number field sieve. Grover's algorithm runs quadratically faster than the best possible classical algorithm for the same task, a linear search.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the phrase complete partial order is variously used to refer to at least three similar, but distinct, classes of partially ordered sets, characterized by particular completeness properties. Complete partial orders play a central role in theoretical computer science: in denotational semantics and domain theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The reason for this deviation is that standard upper limits based on a most powerful test necessarily produce empty intervals with some fixed probability when the parameter value is zero, and this property is considered undesirable by most physicists and statisticians.Upper limits derived with the CLs method always contain the zero value of the parameter and hence the coverage probability at this point is always 100%. The definition of CLs does not follow from any precise theoretical framework of statistical inference and is therefore described sometimes as ad hoc. It has however close resemblance to concepts of statistical evidence proposed by the statistician Allan Birnbaum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first contribution to the Lagrangian is the entropy: L e n t = \u2212 \u2211 k = 1 K \u2211 n = 0 N p n k ln \u2061 ( p n k ) {\\displaystyle {\\mathcal {L}}_{ent}=-\\sum _{k=1}^{K}\\sum _{n=0}^{N}p_{nk}\\ln(p_{nk})} The log-likelihood is: \u2113 = \u2211 k = 1 K \u2211 n = 0 N \u0394 ( n , y k ) ln \u2061 ( p n k ) {\\displaystyle \\ell =\\sum _{k=1}^{K}\\sum _{n=0}^{N}\\Delta (n,y_{k})\\ln(p_{nk})} Assuming the multinomial logistic function, the derivative of the log-likelihood with respect the beta coefficients was found to be: \u2202 \u2113 \u2202 \u03b2 n m = \u2211 k = 1 K ( p n k x m k \u2212 \u0394 ( n , y k ) x m k ) {\\displaystyle {\\frac {\\partial \\ell }{\\partial \\beta _{nm}}}=\\sum _{k=1}^{K}(p_{nk}x_{mk}-\\Delta (n,y_{k})x_{mk})} A very important point here is that this expression is (remarkably) not an explicit function of the beta coefficients. It is only a function of the probabilities pnk and the data. Rather than being specific to the assumed multinomial logistic case, it is taken to be a general statement of the condition at which the log-likelihood is maximized and makes no reference to the functional form of pnk.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages that have associative arrays or comparable data structures, such as Python, Perl, PHP or Objective-C, it is idiomatic to use them to implement conditional assignment. In languages that have anonymous functions or that allow a programmer to assign a named function to a variable reference, conditional flow can be implemented by using a hash as a dispatch table.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Costa et al. write that \"the case p = 5 {\\displaystyle p=5} is trivial\", and credit the observation that 13 is a Wilson prime to Mathews (1892). Early work on these numbers included searches by N. G. W. H. Beeger and Emma Lehmer, but 563 was not discovered until the early 1950s, when computer searches could be applied to the problem. If any others exist, they must be greater than 2 \u00d7 1013.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets , braces { } and angle brackets \u27e8 \u27e9, are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take precedence over those surrounding it. Sometimes, for the clarity of reading, different kinds of brackets are used to express the same meaning of precedence in a single expression with deep nesting of sub-expressions.Historically, other notations, such as the vinculum, were similarly used for grouping. In present-day use, these notations all have specific meanings. The earliest use of brackets to indicate aggregation (i.e. grouping) was suggested in 1608 by Christopher Clavius, and in 1629 by Albert Girard.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045 {\\displaystyle 9045} would be 9 + 0 + 4 + 5 = 18. {\\displaystyle 9+0+4+5=18.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, per-comparison error rate (PCER) is the probability of a Type I error in the absence of any multiple hypothesis testing correction. This is a liberal error rate relative to the false discovery rate and family-wise error rate, in that it is always less than or equal to those rates. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the chi-squared distribution (also chi-square or \u03c7 2 {\\displaystyle \\chi ^{2}} -distribution) with k {\\displaystyle k} degrees of freedom is the distribution of a sum of the squares of k {\\displaystyle k} independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals. This distribution is sometimes called the central chi-squared distribution, a special case of the more general noncentral chi-squared distribution. The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also use this distribution, such as Friedman's analysis of variance by ranks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of union by size, a node stores its size, which is simply its number of descendants (including the node itself). When the trees with roots x and y are merged, the node with more descendants becomes the parent. If the two nodes have the same number of descendants, then either one can become the parent. In both cases, the size of the new parent node is set to its new total number of descendants. function Union(x, y) is // Replace nodes by roots x := Find(x) y := Find(y) if x = y then return // x and y are already in the same set end if // If necessary, swap variables to ensure that // x has at least as many descendants as y if x.size < y.size then (x, y) := (y, x) end if // Make x the new root y.parent := x // Update the size of x x.size := x.size + y.size end function The number of bits necessary to store the size is clearly the number of bits necessary to store n. This adds a constant factor to the forest's required storage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Commercial Privacy Bill of Rights Act of 2011 (Not Passed): Established parameters on the purposes for which data could be collected and placed further limitations on the length of time that data could be retained. Also established and FTC protocol that would require covered entities (those collection data on 5000+ U.S. citizens in the span of any year) to: 1) Give individuals notice about the use and storage of their personal information; 2) Provide individuals opportunities to \"opt-out\" of data collection, especially as used in behavioral advertising; 3) Provide avenues to fix inaccurate information; 4) Allow data points with personally identifiable characteristics to be rendered. Data Broker Accountability and Transparency Act of 2019 (Not Passed): Established requirements for entities that engage in the collections of personal data for the purposes of re-sale to third party entities. Also required that individuals be granted access to the information that is collected about themselves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Section 4 of this act called for testing of chemicals to determine any detrimental impacts that could come as a result. A sector of the EPA focused on \"compliance monitoring,\" which ensures that companies are following the guidelines that have been put in place by the TSCA. PCBs have been found in de-dusting agents, so the TCSA has proven important in the mitigation of this chemical in household cleaning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This RBM is a generative stochastic feedforward neural network that can learn a probability distribution over its set of inputs. Once sufficiently many layers have been learned, the deep architecture may be used as a generative model by reproducing the data when sampling down the model (an \"ancestral pass\") from the top level feature activations. In 2012, Andrew Ng and Jeff Dean created an FNN that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from YouTube videos.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1870s, Georg Cantor started to develop set theory and, in 1874, published a paper proving that the algebraic numbers could be put in one-to-one correspondence with the set of natural numbers, and thus that the set of transcendental numbers must be uncountable. Later, in 1891, Cantor used his more familiar diagonal argument to prove the same result. While Cantor's result is often quoted as being purely existential and thus unusable for constructing a single transcendental number, the proofs in both the aforementioned papers give methods to construct transcendental numbers.While Cantor used set theory to prove the plenitude of transcendental numbers, a recent development has been the use of model theory in attempts to prove an unsolved problem in transcendental number theory. The problem is to determine the transcendence degree of the field K = Q ( x 1 , \u2026 , x n , e x 1 , \u2026 , e x n ) {\\displaystyle K=\\mathbb {Q} (x_{1},\\ldots ,x_{n},e^{x_{1}},\\ldots ,e^{x_{n}})} for complex numbers x1, ..., xn that are linearly independent over the rational numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Guide to Legal Writing Style (2007) also does not directly address this topic.Some legal style guides do provide guidance on sentence spacing, such as the 2009 edition of the AP Stylebook and Briefing on Media Law, and the 2006 edition of The Redbook: A Manual on Legal Style\u2014both of which state that a single space follows terminal punctuation. The Redbook provides further details on the use of this convention: \"The custom during the reign of the typewriter was to insert two spaces between sentences\" due to the use by typewriters of monospaced fonts that are not effective at creating readable text. It indicates that users could continue the use of two spaces if using a typewriter \"or the Courier font\", and espouses the advantages of widely available proportional fonts which are degraded by the use of two spaces after terminal punctuation. Of the legal style guides listed in this section, all use proportional fonts with a single space between sentences in their text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics applied to analysis of social structures, homogeneity blockmodeling is an approach in blockmodeling, which is best suited for a preliminary or main approach to valued networks, when a prior knowledge about these networks is not available. This is due to the fact, that homogeneity blockmodeling emphasizes the similarity of link (tie) strengths within the blocks over the pattern of links. In this approach, tie (link) values (or statistical data computed on them) are assumed to be equal (homogenous) within blocks.This approach to the generalized blockmodeling of valued networks was first proposed by Ale\u0161 \u017diberna in 2007 with the basic idea, \"that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values\". The newly\u2013formed ideal blocks, which are appropriate for blockmodeling of valued networks, are then presented together with the definitions of their block inconsistencies. Similar approach to the homogeneity blockmodeling, dealing with direct approach for structural equivalence, was previously suggested by Stephen P. Borgatti and Martin G. Everett (1992).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1980s, significant uncertainties surrounded the RISC concept. One concern involved the use of memory; a single instruction from a traditional processor like the Motorola 68k may be written out as perhaps a half dozen of the simpler RISC instructions. In theory, this could slow the system down as it spent more time fetching instructions from memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Search models illustrate how best to balance the cost of delay against the value of the option to try again. Mathematically, search models are optimal stopping problems. Macroeconomists have extended search theory by studying general equilibrium models in which one or more types of searchers interact. These macroeconomic theories have been called 'matching theory', or 'search and matching theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The relevant ambiguity can be resolved by establishing a higher level of linguistic analysis. At this higher level, the two items can be clearly shown having two different structural interpretations. In this way, constructional homonymities at the phonemic level can be resolved by establishing the level of morphology, and so forth.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociology, a social organization is a pattern of relationships between and among individuals and social groups.Characteristics of social organization can include qualities such as sexual composition, spatiotemporal cohesion, leadership, structure, division of labor, communication systems, and so on.And because of these characteristics of social organization, people can monitor their everyday work and involvement in other activities that are controlled forms of human interaction. These interactions include: affiliation, collective resources, substitutability of individuals and recorded control. These interactions come together to constitute common features in basic social units such as family, enterprises, clubs, states, etc. These are social organizations.Common examples of modern social organizations are government agencies, NGO's and corporations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a special case, an even delta-matroid is a delta-matroid in which either all sets have even number of elements, or all sets have an odd number of elements. If a constraint satisfaction problem has a Boolean variable on each edge of a planar graph, and if the variables of the edges incident to each vertex of the graph are constrained to belong to an even delta-matroid (possibly a different even delta-matroid for each vertex), then the problem can be solved in polynomial time. This result plays a key role in a characterization of the planar Boolean constraint satisfaction problems that can be solved in polynomial time. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each of the standards has been placed in one of four fundamental categories to promote educational evaluations that are proper, useful, feasible, and accurate. In these sets of standards, validity and reliability considerations are covered under the accuracy topic. For example, the student accuracy standards help ensure that student evaluations will provide sound, accurate, and credible information about student learning and performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Asynchronous Transfer Mode, Frame Relay and MPLS are examples of a connection-oriented, unreliable protocol. SMTP is an example of a connection-oriented protocol in which if a message is not delivered, an error report is sent to the sender which makes SMTP a reliable protocol. Because they can keep track of a conversation, connection-oriented protocols are sometimes described as stateful.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In symmetric key cryptography, both parties must possess a secret key which they must exchange prior to using any encryption. Distribution of secret keys has been problematic until recently, because it involved face-to-face meeting, use of a trusted courier, or sending the key through an existing encryption channel. The first two are often impractical and always unsafe, while the third depends on the security of a previous key exchange. In public key cryptography, the key distribution of public keys is done through public key servers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to ensure and increase the 'conformance quality' of services, that is, service delivery happening as designed, various methods are available. Some of these include Guaranteeing; Mystery Shopping; Recovering; Setting standards and measuring; Statistical process control and Customer involvement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Humphry Davy would go on to create Decomposition Tables from his preliminary experiments on Electrolysis. The Decomposition Tables would give insight on the energies needed to break apart certain compounds.In 1817 Johan August Arfwedson determined there was another element, lithium, in some of his samples; however, he could not isolate the component. It was not until 1821 that William Thomas Brande used electrolysis to single it out.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory and quantum optics, the Schr\u00f6dinger\u2013HJW theorem is a result about the realization of a mixed state of a quantum system as an ensemble of pure quantum states and the relation between the corresponding purifications of the density operators. The theorem is named after physicists and mathematicians Erwin Schr\u00f6dinger, Lane P. Hughston, Richard Jozsa and William Wootters. The result was also found independently (albeit partially) by Nicolas Gisin, and by Nicolas Hadjisavvas building upon work by Ed Jaynes, while a significant part of it was likewise independently discovered by N. David Mermin. Thanks to its complicated history, it is also known by various other names such as the GHJW theorem, the HJW theorem, and the purification theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the mean signed difference (MSD), also known as mean signed deviation and mean signed error, is a sample statistic that summarises how well a set of estimates \u03b8 ^ i {\\displaystyle {\\hat {\\theta }}_{i}} match the quantities \u03b8 i {\\displaystyle \\theta _{i}} that they are supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error. For example, suppose a linear regression model has been estimated over a sample of data, and is then used to extrapolate predictions of the dependent variable out of sample after the out-of-sample data points have become available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Otherwise the gap is strictly positive and weak duality holds.In general given two dual pairs separated locally convex spaces ( X , X \u2217 ) {\\displaystyle \\left(X,X^{*}\\right)} and ( Y , Y \u2217 ) {\\displaystyle \\left(Y,Y^{*}\\right)} . Then given the function f: X \u2192 R \u222a { + \u221e } {\\displaystyle f:X\\to \\mathbb {R} \\cup \\{+\\infty \\}} , we can define the primal problem by inf x \u2208 X f ( x ) . {\\displaystyle \\inf _{x\\in X}f(x).\\,} If there are constraint conditions, these can be built into the function f {\\displaystyle f} by letting f = f + I constraints {\\displaystyle f=f+I_{\\text{constraints}}} where I {\\displaystyle I} is the indicator function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "History monoids were first presented by M.W. Shields.History monoids are isomorphic to trace monoids (free partially commutative monoids) and to the monoid of dependency graphs. As such, they are free objects and are universal. The history monoid is a type of semi-abelian categorical product in the category of monoids.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nonetheless, CI techniques are considered the more modern approach. CI jobs are often run on isolated virtual machines, and typically include automated testing as well. When someone says a developer \"broke the build\", they are effectively saying that a developer checked in code which might very well have compiled (and hopefully also run properly) in their account, but does not compile (and therefore, cannot be run) in anyone else's account.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the term \"vector\" is used for an element of any vector space. In physics, however, the term \"vector\" tends to refer almost exclusively to quantities like displacement or velocity, which have components that relate directly to the three dimensions of space, or relativistically, to the four of spacetime. Such vectors are typically denoted with over arrows ( r \u2192 {\\displaystyle {\\vec {r}}} ), boldface ( p {\\displaystyle \\mathbf {p} } ) or indices ( v \u03bc {\\displaystyle v^{\\mu }} ). In quantum mechanics, a quantum state is typically represented as an element of a complex Hilbert space, for example, the infinite-dimensional vector space of all possible wavefunctions (square integrable functions mapping each point of 3D space to a complex number) or some more abstract Hilbert space constructed more algebraically.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a polymatroid is a polytope associated with a submodular function. The notion was introduced by Jack Edmonds in 1970. It is also described as the multiset analogue of the matroid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the cancellation property asserts that from an equality of the form a\u00b7b = a\u00b7c, where \u00b7 is a binary operation, one can cancel the element a and deduce the equality b = c. In this case the element being cancelled out is appearing as the left factors of a\u00b7b and a\u00b7c and hence it is a case of the left cancellation property. The right cancellation property can be defined analogously.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other languages, verbification is a more regular process. However, such processes often do not qualify as conversion, as they involve changes in the form of the word. For example, in Esperanto, any word can be transformed into a verb, either by altering its ending to -i, or by applying suffixes such as -igi and -i\u011di; and in Semitic languages, the process often involves changes of internal vowels, such as the Hebrew word \"\u05d2\u05d2\u05dc\" (Gig\u00e9l, \"He/it googled\"), from the proper noun \u05d2\u05d5\u05d2\u05dc (Google). In Toki Pona, any content word may function as a noun, verb or adjective depending on syntax. For example, moku may either mean food or to eat.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to store volumes (axis-aligned hyper-boxes) as keys, implementations typically use corner representation which converts the two d {\\displaystyle d} -dimensional minimum and maximum corners of a box into a single key with 2 \u2217 d {\\displaystyle 2*d} dimensions, for example by interleaving them: k = { m i n 0 , m a x 0 , m i n 1 , m a x 1 , . . . , m i n d \u2212 1 , m a x d \u2212 1 } {\\displaystyle k=\\{min_{0},max_{0},min_{1},max_{1},...,min_{d-1},max_{d-1}\\}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a cwatset is a set of bitstrings, all of the same length, which is closed with a twist. If each string in a cwatset, C, say, is of length n, then C will be a subset of Z 2 n {\\displaystyle \\mathbb {Z} _{2}^{n}} . Thus, two strings in C are added by adding the bits in the strings modulo 2 (that is, addition without carry, or exclusive disjunction). The symmetric group on n letters, Sym ( n ) {\\displaystyle {\\text{Sym}}(n)} , acts on Z 2 n {\\displaystyle \\mathbb {Z} _{2}^{n}} by bit permutation: p ( ( c 1 , \u2026 , c n ) ) = ( c p ( 1 ) , \u2026 , c p ( n ) ) , {\\displaystyle p((c_{1},\\ldots ,c_{n}))=(c_{p(1)},\\ldots ,c_{p(n)}),} where c = ( c 1 , \u2026 , c n ) {\\displaystyle c=(c_{1},\\ldots ,c_{n})} is an element of Z 2 n {\\displaystyle \\mathbb {Z} _{2}^{n}} and p is an element of Sym ( n ) {\\displaystyle {\\text{Sym}}(n)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Starting from the root node, the left or right subtrees are traversed depending on whether the target value is less or more than the node under consideration.In the worst case, binary search makes \u230a log 2 \u2061 ( n ) + 1 \u230b {\\textstyle \\lfloor \\log _{2}(n)+1\\rfloor } iterations of the comparison loop, where the \u230a \u230b {\\textstyle \\lfloor \\rfloor } notation denotes the floor function that yields the greatest integer less than or equal to the argument, and log 2 {\\textstyle \\log _{2}} is the binary logarithm. This is because the worst case is reached when the search reaches the deepest level of the tree, and there are always \u230a log 2 \u2061 ( n ) + 1 \u230b {\\textstyle \\lfloor \\log _{2}(n)+1\\rfloor } levels in the tree for any binary search. The worst case may also be reached when the target element is not in the array.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The next generation of microprocessors incorporated the clock generation on chip. The 8080 uses a 2 MHz clock but the processing throughput is similar to the 1 MHz 6800. The 8080 requires more clock cycles to execute a processor instruction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, function composition is an operation \u2218 that takes two functions f and g, and produces a function h = g \u2218 f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f: X \u2192 Y and g: Y \u2192 Z are composed to yield a function that maps x in domain X to g(f(x)) in codomain Z. Intuitively, if z is a function of y, and y is a function of x, then z is a function of x. The resulting composite function is denoted g \u2218 f: X \u2192 Z, defined by (g \u2218 f )(x) = g(f(x)) for all x in X.The notation g \u2218 f is read as \"g of f \", \"g after f \", \"g circle f \", \"g round f \", \"g about f \", \"g composed with f \", \"g following f \", \"f then g\", or \"g on f \", or \"the composition of g and f \". Intuitively, composing functions is a chaining process in which the output of function f feeds the input of function g. The composition of functions is a special case of the composition of relations, sometimes also denoted by \u2218 {\\displaystyle \\circ } . As a result, all properties of composition of relations are true of composition of functions, such as the property of associativity. Composition of functions is different from multiplication of functions (if defined at all), and has some quite different properties; in particular, composition of functions is not commutative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After a model is obtained using the data collected, conditional probability is formed for each target contained in the training database. In this example, there are M blocks of data. This will result in a collection of M probabilities for each target in the database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of this article, a metric is a measurement. A metric that evaluates machine translation output represents the quality of the output. The quality of a translation is inherently subjective, there is no objective or quantifiable \"good.\" Therefore, any metric must assign quality scores so they correlate with the human judgment of quality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In addition, the semantic web approach is still considered an emerging technology and is not in wide-scale use at this time.One of the current applications of ontology-based search in the biomedical sciences is GoPubMed, which searches the PubMed database of scientific literature. Another use of ontologies is within databases such as SwissProt, Ensembl and TrEMBL, which use this technology to search through the stores of human proteome-related data for tags related to the search term.Some of the research in this field has focused on creating new and specific ontologies. Other researchers have worked on verifying the results of existing ontologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alice and Bob agree that the output of the toss d is the xor of the bits a {\\displaystyle a} and b, d = a \u2295 b {\\displaystyle d=a\\oplus b} . Alice and Bob agree on advance on the values of t0 and t1 in a common reference frame, in such a way that |t0 - t1| < t. Thus, from the principle of no superluminal signalling, at receiving a {\\displaystyle a} from A0, B0 cannot send any signal that arrives to B1 before B1 gives b to A1. Therefore, Alice is guaranteed that the bit b is chosen by Bob independently of the bit a {\\displaystyle a} chosen by her.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". , k } , \u2200 i \u2208 { 1 , 2 , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The commitment made selecting one or another ontology can produce a sharply different view of the task at hand. Consider the difference that arises in selecting the lumped element view of a circuit rather than the electrodynamic view of the same device. As a second example, medical diagnosis viewed in terms of rules (e.g., MYCIN) looks substantially different from the same task viewed in terms of frames (e.g., INTERNIST). Where MYCIN sees the medical world as made up of empirical associations connecting symptom to disease, INTERNIST sees a set of prototypes, in particular prototypical diseases, to be matched against the case at hand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Class B \u2013 Any single vehicle which has a gross vehicle weight rating or gross vehicle weight of 26,001 pounds (11,794 kilograms) or more, or any such vehicle towing a vehicle with a gross vehicle weight rating or gross vehicle weight that does not exceed 10,000 pounds (4,536 kilograms). Class C \u2013 Any single vehicle, or combination of vehicles, that does not meet the definition of Class A or Class B, but is either designed to transport 16 or more passengers, including the driver or is transporting material that has been designated as hazardous under 49 U.S.C. 5103 and is required to be placarded under subpart F of 49 CFR Part 172 or is transporting any quantity of a material listed as a select agent or toxin in 42 CFR Part 73.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a redundant proof is a proof that has a subset that is a shorter proof of the same result. In other words, a proof is redundant if it has more proof steps than are actually necessary to prove the result. Formally, a proof \u03c8 {\\displaystyle \\psi } of \u03ba {\\displaystyle \\kappa } is considered redundant if there exists another proof \u03c8 \u2032 {\\displaystyle \\psi ^{\\prime }} of \u03ba \u2032 {\\displaystyle \\kappa ^{\\prime }} such that \u03ba \u2032 \u2286 \u03ba {\\displaystyle \\kappa ^{\\prime }\\subseteq \\kappa } (i.e. \u03ba \u2032 subsumes \u03ba {\\displaystyle \\kappa ^{\\prime }\\;{\\text{subsumes}}\\;\\kappa } ) and | \u03c8 \u2032 | < | \u03c8 | {\\displaystyle |\\psi ^{\\prime }|<|\\psi |} where | \u03c6 | {\\displaystyle |\\varphi |} is the number of nodes in \u03c6 {\\displaystyle \\varphi } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Intel said that the approach Digital Research wished to take in emulating 8086 software in protected mode differed from the original specifications; nevertheless they incorporated into the E-2 step minor changes in the microcode that allowed Digital Research to run emulation mode much faster (see LOADALL). These same limitations affected FlexOS 286 version 1.x, a reengineered derivation of Concurrent DOS 286, which was developed by Digital Research's new Flexible Automation Business Unit in Monterey, California, since 1986. Later versions added compatibility with PC DOS 2.x and 3.x. Known versions include: Concurrent DOS 286 1.0 (1985) Concurrent DOS 286 1.1 (1986-01-07) Concurrent DOS 286 1.2 (1986) FlexOS 286 1.3 (November 1986) FlexOS 286 1.31 (May 1987)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the decade after Richards' publication, advances in the theory of distributed circuits took place mostly in Japan. K. Kuroda published these identities in 1955 in his Ph.D thesis. However, they did not appear in English until 1958 in a paper by Ozaki and Ishii on stripline filters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In addition to placing and receiving cellular calls, the touchscreen-equipped Simon could send and receive faxes and emails. It included an address book, calendar, appointment scheduler, calculator, world time clock, and notepad, as well as other visionary mobile applications such as maps, stock reports and news.The IBM Simon was manufactured by Mitsubishi Electric, which integrated features with its own cellular radio technologies. It featured a liquid-crystal display (LCD) and PC Card support. The Simon was commercially unsuccessful, particularly due to its bulky form factor and limited battery life, using NiCad batteries rather than the nickel\u2013metal hydride batteries commonly used in mobile phones in the 1990s, or lithium-ion batteries used in modern smartphones.The term \"smart phone\" was not coined until a year after the introduction of the Simon, appearing in print as early as 1995, describing AT&T's PhoneWriter Communicator. The term \"smartphone\" was first used by Ericsson in 1997 to describe a new device concept, the GS88.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the use of upper camel case data element names is a convention used in many standard but is not specified by the XML Schema specification. Naming and Design Rules have become an important aspect of each organizations data exchange standards. Within the United States, Naming and Design Rules standards are recommended for each federal and state agency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern sources, the Adian\u2013Rabin theorem is usually stated as follows:Let P be a Markov property of finitely presentable groups. Then there does not exist an algorithm that, given a finite presentation G = \u27e8 X \u2223 R \u27e9 {\\displaystyle G=\\langle X\\mid R\\rangle } , decides whether or not the group G {\\displaystyle G} defined by this presentation has property P. The word 'algorithm' here is used in the sense of recursion theory. More formally, the conclusion of Adian\u2013Rabin theorem means that set of all finite presentations \u27e8 x 1 , x 2 , x 3 , \u22ef \u2223 R \u27e9 {\\displaystyle \\langle x_{1},x_{2},x_{3},\\dots \\mid R\\rangle } (where x 1 , x 2 , x 3 , \u2026 {\\displaystyle x_{1},x_{2},x_{3},\\dots } is a fixed countably infinite alphabet, and R {\\displaystyle R} is a finite set of relations in these generators and their inverses) defining groups with property P, is not a recursive set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming, string concatenation generally occurs at run time, as string values are typically not known until run time. However, in the case of string literals, the values are known at compile time, and thus string concatenation can be done at compile time, either via string literal concatenation or via constant folding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Concurrent Read Exclusive Write (CREW): The same block in main memory can be read by multiple processors concurrently. Only one processor can write to a block at a time. Exclusive Read Exclusive Write (EREW): The same block in main memory cannot be read or written by multiple processors concurrently.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of linguistics, specifically in syntax, phonetic form (PF), also known as phonological form or the articulatory-perceptual (A-P) system, is a certain level of mental representation of a linguistic expression, derived from surface structure, and related to Logical Form. Phonetic form is the level of representation wherein expressions, or sentences, are assigned a phonetic representation, which is then pronounced by the speaker. Phonetic form takes surface structure as its input, and outputs an audible (or visual, in the case of sign languages), pronounced sentence.This is part of the Y- or T-model of grammar within minimalist grammar, wherein the syntactic structure is constructed and then transferred (called spell-out) to both the Phonetic Form and the Logical Form. Operations in this branch of the model (between spell-out and pronunciation), the syntax-phonology interface, affect the pronunciation of the utterance but not its meaning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to the Gumbel distribution. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, Exponentiation stands for repeated application of the group operation Juxtaposition stands for multiplication on the set of congruence classes or application of the group operation (as applicable) Subtraction stands for subtraction on the set of congruence classes M \u2208 { 0 , 1 } \u2217 {\\displaystyle M\\in \\{0,1\\}^{*}} , the set of finite bit strings s , e , e v \u2208 Z q {\\displaystyle s,e,e_{v}\\in \\mathbb {Z} _{q}} , the set of congruence classes modulo q {\\displaystyle q} x , k \u2208 Z q \u00d7 {\\displaystyle x,k\\in \\mathbb {Z} _{q}^{\\times }} , the multiplicative group of integers modulo q {\\displaystyle q} (for prime q {\\displaystyle q} , Z q \u00d7 = Z q \u2216 0 \u00af q {\\displaystyle \\mathbb {Z} _{q}^{\\times }=\\mathbb {Z} _{q}\\setminus {\\overline {0}}_{q}} ) y , r , r v \u2208 G {\\displaystyle y,r,r_{v}\\in G} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, a leaky abstraction is an abstraction that leaks details that it is supposed to abstract away.As coined by Joel Spolsky, the Law of Leaky Abstractions states: All non-trivial abstractions, to some degree, are leaky. This statement highlights a particularly problematic cause of software defects: the reliance of the software developer on an abstraction's infallibility. Spolsky's article gives examples of an abstraction that works most of the time, but where a detail of the underlying complexity cannot be ignored, thus leaking complexity out of the abstraction back into the software that uses the abstraction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, least squares function approximation applies the principle of least squares to function approximation, by means of a weighted sum of other functions. The best approximation can be defined as that which minimizes the difference between the original function and the approximation; for a least-squares approach the quality of the approximation is measured in terms of the squared differences between the two.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a pseudoprime is called an elliptic pseudoprime for (E, P), where E is an elliptic curve defined over the field of rational numbers with complex multiplication by an order in Q ( \u2212 d ) {\\displaystyle \\mathbb {Q} {\\big (}{\\sqrt {-d}}{\\big )}} , having equation y2 = x3 + ax + b with a, b integers, P being a point on E and n a natural number such that the Jacobi symbol (\u2212d | n) = \u22121, if (n + 1)P \u2261 0 (mod n). The number of elliptic pseudoprimes less than X is bounded above, for large X, by X / exp \u2061 ( ( 1 / 3 ) log \u2061 X log \u2061 log \u2061 log \u2061 X / log \u2061 log \u2061 X ) . {\\displaystyle X/\\exp((1/3)\\log X\\log \\log \\log X/\\log \\log X)\\ .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a Hagelbarger code is a convolutional code that enables error bursts to be corrected provided that there are relatively long error-free intervals between the error bursts. In the Hagelbarger code, inserted parity check bits are spread out in time so that an error burst is not likely to affect more than one of the groups in which parity is checked.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is idempotent under the ring's multiplication. Inductively then, one can also conclude that a = a2 = a3 = a4 = ... = an for any positive integer n. For example, an idempotent element of a matrix ring is precisely an idempotent matrix. For general rings, elements idempotent under multiplication are involved in decompositions of modules, and connected to homological properties of the ring. In Boolean algebra, the main objects of study are rings in which all elements are idempotent under both addition and multiplication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to verify the monotonicity property, we set E 1 = A {\\displaystyle E_{1}=A} and E 2 = B \u2216 A {\\displaystyle E_{2}=B\\setminus A} , where A \u2286 B {\\displaystyle A\\subseteq B} and E i = \u2205 {\\displaystyle E_{i}=\\varnothing } for i \u2265 3 {\\displaystyle i\\geq 3} . From the properties of the empty set ( \u2205 {\\displaystyle \\varnothing } ), it is easy to see that the sets E i {\\displaystyle E_{i}} are pairwise disjoint and E 1 \u222a E 2 \u222a \u22ef = B {\\displaystyle E_{1}\\cup E_{2}\\cup \\cdots =B} . Hence, we obtain from the third axiom that P ( A ) + P ( B \u2216 A ) + \u2211 i = 3 \u221e P ( E i ) = P ( B ) . {\\displaystyle P(A)+P(B\\setminus A)+\\sum _{i=3}^{\\infty }P(E_{i})=P(B).} Since, by the first axiom, the left-hand side of this equation is a series of non-negative numbers, and since it converges to P ( B ) {\\displaystyle P(B)} which is finite, we obtain both P ( A ) \u2264 P ( B ) {\\displaystyle P(A)\\leq P(B)} and P ( \u2205 ) = 0 {\\displaystyle P(\\varnothing )=0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Fermat\u2013Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture, hence the name. The conjecture states that the equation has only finitely many solutions (a,b,c,m,n,k) with distinct triplets of values (am, bn, ck) where a, b, c are positive coprime integers and m, n, k are positive integers satisfying The inequality on m, n, and k is a necessary part of the conjecture. Without the inequality there would be infinitely many solutions, for instance with k = 1 (for any a, b, m, and n and with c = am + bn) or with m, n, and k all equal to two (for the infinitely many known Pythagorean triples).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. This article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square matrices, matrices with the same number of rows and columns, play a major role in matrix theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, Kendall's notation (or sometimes Kendall notation) is the standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/c in 1953 where A denotes the time between arrivals to the queue, S the service time distribution and c the number of service channels open at the node. It has since been extended to A/S/c/K/N/D where K is the capacity of the queue, N is the size of the population of jobs to be served, and D is the queueing discipline.When the final three parameters are not specified (e.g. M/M/1 queue), it is assumed K = \u221e, N = \u221e and D = FIFO.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An 8086 system, including coprocessors such as 8087 and 8089, and simpler Intel-specific system chips, was thereby described as an iAPX 86 system. There were also terms iRMX (for operating systems), iSBC (for single-board computers), and iSBX (for multimodule boards based on the 8086-architecture), all together under the heading Microsystem 80.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus f0 is the truth value of \u03c8. In order to arithmetize \u03c8 we must use the following rules: f i ( a 1 , \u2026 , a i ) = { f i + 1 ( a 1 , \u2026 , a i , 0 ) \u22c5 f i + 1 ( a 1 , \u2026 , a i , 1 ) Q i + 1 = \u2200 f i + 1 ( a 1 , \u2026 , a i , 0 ) \u2217 f i + 1 ( a 1 , \u2026 , a i , 1 ) Q i + 1 = \u2203 {\\displaystyle f_{i}(a_{1},\\dots ,a_{i})={\\begin{cases}f_{i+1}(a_{1},\\dots ,a_{i},0)\\cdot f_{i+1}(a_{1},\\dots ,a_{i},1)&{\\mathsf {Q}}_{i+1}=\\forall \\\\f_{i+1}(a_{1},\\dots ,a_{i},0)*f_{i+1}(a_{1},\\dots ,a_{i},1)&{\\mathsf {Q}}_{i+1}=\\exists \\end{cases}}} where as before we define x \u2217 y = 1 \u2212 (1 \u2212 x)(1 \u2212 y). By using the method described in #SAT, we must face a problem that for any fi the degree of the resulting polynomial may double with each quantifier. In order to prevent this, we must introduce a new reduction operator R which will reduce the degrees of the polynomial without changing their behavior on Boolean inputs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public key infrastructure (PKI) systems, a certificate signing request (also CSR or certification request) is a message sent from an applicant to a certificate authority of the public key infrastructure in order to apply for a digital identity certificate. The CSR usually contains the public key for which the certificate should be issued, identifying information (such as a domain name) and a proof of authenticity including integrity protection (e.g., a digital signature). The most common format for CSRs is the PKCS #10 specification; others include the more capable CRMF and the Signed Public Key and Challenge SPKAC format generated by some web browsers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to prevent such elaborate attacks, different modes of operation were introduced: tweakable narrow-block encryption (LRW and XEX) and wide-block encryption (CMC and EME). Whereas a purpose of a usual block cipher E K {\\displaystyle E_{K}} is to mimic a random permutation for any secret key K {\\displaystyle K} , the purpose of tweakable encryption E K T {\\displaystyle E_{K}^{T}} is to mimic a random permutation for any secret key K {\\displaystyle K} and any known tweak T {\\displaystyle T} . The tweakable narrow-block encryption (LRW) is an instantiation of the mode of operations introduced by Liskov, Rivest, and Wagner (see Theorem 2). This mode uses two keys: K {\\displaystyle K} is the key for the block cipher and F {\\displaystyle F} is an additional key of the same size as block.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the book Secretum de thesauro experimentorum ymaginationis hominum (Secret of the treasure-room of experiments in man's imagination), written ca. 1430, Fontana described mnemonic machines, written in his cypher. At least Bellicorum instrumentorum liber and this book used a cryptographic system, described as a simple, rational cipher, based on signs without letters or numbers. It has been suggested that some illustrations slightly resemble Voynich illustrations. During this time he also met with the Count of Carmagnola.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using the Chinese remainder theorem, it suffices to evaluate f {\\displaystyle f} modulo different primes p 1 , \u2026 , p \u2113 {\\displaystyle p_{1},\\dots ,p_{\\ell }} with a product at least M {\\displaystyle M} . Each prime can be taken to be roughly log \u2061 M = O ( d m log \u2061 q ) {\\displaystyle \\log M=O(dm\\log q)} , and the number of primes needed, \u2113 {\\displaystyle \\ell } , is roughly the same. Doing this process recursively, we can get the primes as small as log \u2061 log \u2061 q {\\displaystyle \\log \\log q} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An example 3\u00d73 polynomial matrix, degree 2: P = ( 1 x 2 x 0 2 x 2 3 x + 2 x 2 \u2212 1 0 ) = ( 1 0 0 0 0 2 2 \u2212 1 0 ) + ( 0 0 1 0 2 0 3 0 0 ) x + ( 0 1 0 0 0 0 0 1 0 ) x 2 . {\\displaystyle P={\\begin{pmatrix}1&x^{2}&x\\\\0&2x&2\\\\3x+2&x^{2}-1&0\\end{pmatrix}}={\\begin{pmatrix}1&0&0\\\\0&0&2\\\\2&-1&0\\end{pmatrix}}+{\\begin{pmatrix}0&0&1\\\\0&2&0\\\\3&0&0\\end{pmatrix}}x+{\\begin{pmatrix}0&1&0\\\\0&0&0\\\\0&1&0\\end{pmatrix}}x^{2}.} We can express this by saying that for a ring R, the rings M n ( R  ) {\\displaystyle M_{n}(R)} and ( M n ( R ) )  {\\displaystyle (M_{n}(R))} are isomorphic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In C#, reification is used to make parametric polymorphism implemented in the form of generics as a first-class feature of the language. In the Java programming language, there exist \"reifiable types\" that are \"completely available at run time\" (i.e. their information is not erased during compilation).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early years of the 21st century class browsers began to morph into modeling tools, where programmers could not only visualize their class hierarchy as a diagram, but also add classes to their code by adding them to the diagram. Most of these visualization systems have been based on some form of the Unified Modeling Language (UML).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem. An optimization problem is defined using an objective function to minimize or maximize, and a set of constraints g 1 ( x ) \u2265 0 , \u2026 , g k ( x ) \u2265 0 {\\displaystyle g_{1}(x)\\geq 0,\\dots ,g_{k}(x)\\geq 0} that define the feasible region, that is, the set of all x to search for the optimal solution. Given a point x {\\displaystyle x} in the feasible region, a constraint g i ( x ) \u2265 0 {\\displaystyle g_{i}(x)\\geq 0} is called active at x 0 {\\displaystyle x_{0}} if g i ( x 0 ) = 0 {\\displaystyle g_{i}(x_{0})=0} , and inactive at x {\\displaystyle x} if g i ( x 0 ) > 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The numbers that can be represented with four bits are shown in the comparison table below. The range of numbers that can be represented is asymmetric. If the word has an even number of bits, the magnitude of the largest negative number that can be represented is twice as large as the largest positive number that can be represented, and vice versa if the word has an odd number of bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, in general, the average number at distance d {\\displaystyle d} can be written as: c d = ( c 2 c 1 ) d \u2212 1 c 1 . {\\displaystyle c_{d}=\\left({\\frac {c_{2}}{c_{1}}}\\right)^{d-1}c_{1}.} Which implies that if the ratio of c 2 c 1 {\\displaystyle {\\frac {c_{2}}{c_{1}}}} is larger than one, then the network can have a giant component.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The strength of a path is the strength of its weakest link. For each pair of candidates X and Y, the following table shows the strongest path from candidate X to candidate Y in red, with the weakest link underlined. Now the output of the Schulze method can be determined. For example, when comparing A and B, since ( 28 = ) p  > p  ( = 25 ) {\\displaystyle (28=)p>p(=25)} , for the Schulze method candidate A is better than candidate B. Another example is that ( 31 = ) p  > p  ( = 24 ) {\\displaystyle (31=)p>p(=24)} , so candidate E is better than candidate D. Continuing in this way, the result is that the Schulze ranking is E > A > C > B > D {\\displaystyle E>A>C>B>D} , and E wins. In other words, E wins since p  \u2265 p  {\\displaystyle p\\geq p} for every other candidate X.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a finite field or Galois field (so-named in honor of \u00c9variste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod p when p is a prime number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bob now knows that the state of his qubit was one of the two states indicated by Alice. To determine the secret bit, Bob must distinguish between the two candidate states. For each qubit, Bob can check to see whether his measurement is consistent with either possible state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public policy, authorization is a feature of trusted systems used for security or social control.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Amateur radio requires the call sign to be stated at the end of a communication and every ten minutes during (some hams use countdown clocks to remind them to identify); modes such as packet radio and fast-scan television often have a provision for automatic identification, either including it as part of a digital data stream or overlaying it over an analog picture. Repeaters are often designed to automatically transmit the repeater's callsign, usually in Morse code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one L 1 = 253.5 cm {\\displaystyle L_{1}=253.5\\,{\\text{cm}}} long and the other L 2 = 252.5 cm {\\displaystyle L_{2}=252.5\\,{\\text{cm}}} long, and they are measured with a ruler that is good only to the centimeter, then the approximations could come out to be L ~ 1 = 254 cm {\\displaystyle {\\tilde {L}}_{1}=254\\,{\\text{cm}}} and L ~ 2 = 252 cm {\\displaystyle {\\tilde {L}}_{2}=252\\,{\\text{cm}}} . These may be good approximations, in relative error, to the true lengths: the approximations are in error by less than 2% of the true lengths, | L 1 \u2212 L ~ 1 | / | L 1 | < 2 % {\\displaystyle |L_{1}-{\\tilde {L}}_{1}|/|L_{1}|<2\\%} . However, if the approximate lengths are subtracted, the difference will be L ~ 1 \u2212 L ~ 2 = 254 cm \u2212 252 cm = 2 cm {\\displaystyle {\\tilde {L}}_{1}-{\\tilde {L}}_{2}=254\\,{\\text{cm}}-252\\,{\\text{cm}}=2\\,{\\text{cm}}} , even though the true difference between the lengths is L 1 \u2212 L 2 = 253.5 cm \u2212 252.5 cm = 1 cm {\\displaystyle L_{1}-L_{2}=253.5\\,{\\text{cm}}-252.5\\,{\\text{cm}}=1\\,{\\text{cm}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this way Fermat was able to show the non-existence of solutions in many cases of Diophantine equations of classical interest (for example, the problem of four perfect squares in arithmetic progression). In some cases, to the modern eye, his \"method of infinite descent\" is an exploitation of the inversion of the doubling function for rational points on an elliptic curve E. The context is of a hypothetical non-trivial rational point on E. Doubling a point on E roughly doubles the length of the numbers required to write it (as number of digits), so that a \"halving\" a point gives a rational with smaller terms. Since the terms are positive, they cannot decrease forever.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a differential field K is differentially closed if every finite system of differential equations with a solution in some differential field extending K already has a solution in K. This concept was introduced by Robinson (1959). Differentially closed fields are the analogues for differential equations of algebraically closed fields for polynomial equations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Assuming that the data were actually generated by the model in question, they try to design algorithms that probably find the model that was used to create the data. Techniques used here include singular value decomposition (SVD) and the method of moments. In 2012 an algorithm based upon non-negative matrix factorization (NMF) was introduced that also generalizes to topic models with correlations among topics.In 2018 a new approach to topic models was proposed: it is based on stochastic block model", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a required bit rate, delay, delay variation, packet loss or bit error rates may be guaranteed. Quality of service is important for real-time streaming multimedia applications such as voice over IP, multiplayer online games and IPTV, since these often require fixed bit rate and are delay sensitive. Quality of service is especially important in networks where the capacity is a limited resource, for example in cellular data communication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "indegree (followers count) retweet count mention countAn initial analysis of the three aforementioned metrics showed that the users with the highest indegrees and the users with the highest retweet/mention counts were not the same. The top 1% of users by indegree are shown to have very low correlation with the same percentile of users by retweets and by mentions. This implies that follower count is not useful in determining whether a user's tweets get retweeted or whether the other users engage with them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, just what constitutes \"structure\" vs. non-structure can vary. In a book specifically about typography, tagging something as \"italic\" or \"bold\" may well be the whole point. For example, a discussion of when to use particular styles will likely want to give examples and counter-examples, which would no longer make sense if the rendering is not in sync with the prose. Similarly, a particular edition of a document may be of interest not only for its content but for its typographic practice as well, in which case describing that practice is not only desirable but necessary. This problem is not unique to document structure, however; it also arises in grammar when discussing grammar, and in many other cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the optimal number of populations or topics is not known beforehand. It can be estimated by approximation of the posterior distribution with reversible-jump Markov chain Monte Carlo.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A problem that arose in the 16th century was creating a general formula using radicals to express the solution of any polynomial equation of fixed degree k, where k \u2265 5. In the 1820s, the Abel\u2013Ruffini theorem (also known as Abel's impossibility theorem) showed this to be impossible, using concepts such as solvable groups from Galois theory\u2014a new sub-field of abstract algebra. Some of the most important proofs of impossibility found in the 20th century were those related to undecidability, which showed that there are problems that cannot be solved in general by any algorithm, with one of the more prominent ones being the halting problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The baseline for this concept was put forward in the late 1940s, and the third era of privacy development began in the 1990s.The European Union has various privacy laws that dictate how information may be collected and used by companies. Some of those laws are written to give agency to the preferences of individuals/consumers in how their data is used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Wolstenholme prime is a special type of prime number satisfying a stronger version of Wolstenholme's theorem. Wolstenholme's theorem is a congruence relation satisfied by all prime numbers greater than 3. Wolstenholme primes are named after mathematician Joseph Wolstenholme, who first described this theorem in the 19th century.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in group theory, the direct product is an operation that takes two groups G and H and constructs a new group, usually denoted G \u00d7 H. This operation is the group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics. In the context of abelian groups, the direct product is sometimes referred to as the direct sum, and is denoted G \u2295 H {\\displaystyle G\\oplus H} . Direct sums play an important role in the classification of abelian groups: according to the fundamental theorem of finite abelian groups, every finite abelian group can be expressed as the direct sum of cyclic groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following summations, n P k {\\displaystyle {}_{n}P_{k}} is the number of k-permutations of n. \u2211 i = 0 n i P k ( n i ) = n P k ( 2 n \u2212 k ) {\\displaystyle \\sum _{i=0}^{n}{}_{i}P_{k}{n \\choose i}={}_{n}P_{k}(2^{n-k})} \u2211 i = 1 n i + k P k + 1 = \u2211 i = 1 n \u220f j = 0 k ( i + j ) = ( n + k + 1 ) ! ( n \u2212 1 ) ! ( k + 2 ) {\\displaystyle \\sum _{i=1}^{n}{}_{i+k}P_{k+1}=\\sum _{i=1}^{n}\\prod _{j=0}^{k}(i+j)={\\frac {(n+k+1)!}{(n-1)!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1920s the German military began using a 3-rotor Enigma, whose security was increased in 1930 by the addition of a plugboard. The Polish Cipher Bureau sought to break it due to the threat that Poland faced from Germany, but its early attempts did not succeed. Near the beginning of 1929, the Polish Cipher Bureau realized that mathematicians may make good codebreakers; the bureau invited math students at Pozna\u0144 University to take a class on cryptology. After the class, the Bureau recruited some students to work part-time at a Bureau branch set up in Pozna\u0144 for the students.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to recognize a pedestrian, the computational system uses AI pattern recognition technology that typically uses machine learning and deep convolutional neural networks based on millions of images. In a simplified description, images from the car's camera and radar are compared to the prototypes stored in the computer. If a match is made and confirmed, the other systems in the PCAM are invoked. PCAM technologies can be improved with additional information from connected vehicles. A thorough description of the processes for pedestrian detection in about 2010 is provided in . AI technologies have improved dramatically since then, as can be seen in an update in May 2016.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Under computer control, dots would be activated to create tactile patterns of highs and lows representing the information to be read. Visual and tactile impressions of a virtual surface are displayed by a high resolution tactile display, a so-called \"artificial skin\" (Fig. 6).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most object-oriented languages, objects can be referred to using references. Some examples of such languages are Java, C++, C#, VB.NET, and many scripting languages, such as Perl, Python, and Ruby. In this case, it matters whether the state of an object can vary when objects are shared via references.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one type of generalization of the matrix singular value decomposition. It has applications in computer vision, computer graphics, machine learning, scientific computing, and signal processing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to take advantage of the above described representations of elements with their traces and furthermore ensure sufficient security, that will be discussed below, we need to find primes p {\\displaystyle p} and q {\\displaystyle q} , where p {\\displaystyle p} denotes the characteristic of the field G F ( p 6 ) {\\displaystyle GF(p^{6})} with p \u2261 2 mod 3 {\\displaystyle p\\equiv 2\\ {\\text{mod}}\\ 3} and q {\\displaystyle q} is the size of the subgroup, such that q {\\displaystyle q} divides p 2 \u2212 p + 1 {\\displaystyle p^{2}-p+1} . We denote with P {\\displaystyle P} and Q {\\displaystyle Q} the sizes of p {\\displaystyle p} and q {\\displaystyle q} in bits. To achieve security comparable to 1024-bit RSA, we should choose 6 P {\\displaystyle 6P} about 1024, i.e. P \u2248 170 {\\displaystyle P\\approx 170} and Q {\\displaystyle Q} can be around 160. A first easy algorithm to compute such primes p {\\displaystyle p} and q {\\displaystyle q} is the next Algorithm A: Algorithm A Find r \u2208 Z {\\displaystyle r\\in \\mathbb {Z} } such that q = r 2 \u2212 r + 1 {\\displaystyle q=r^{2}-r+1} is a Q {\\displaystyle Q} -bit prime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In routers and switches, active queue management (AQM) is the policy of dropping packets inside a buffer associated with a network interface controller (NIC) before that buffer becomes full, often with the goal of reducing network congestion or improving end-to-end latency. This task is performed by the network scheduler, which for this purpose uses various algorithms such as random early detection (RED), Explicit Congestion Notification (ECN), or controlled delay (CoDel). RFC 7567 recommends active queue management as a best practice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-agent reinforcement learning experiments, researchers try to optimize the performance of a learning agent on a given task, in cooperation or competition with one or more agents. These agents learn by trial-and-error, and researchers may choose to have the learning algorithm play the role of two or more of the different agents. When successfully executed, this technique has a double advantage: It provides a straightforward way to determine the actions of the other agents, resulting in a meaningful challenge. It increases the amount of experience that can be used to improve the policy, by a factor of two or more, since the viewpoints of each of the different agents can be used for learning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The case (x, y, z) = (2l, 2m, n) and all its permutations were proven for l, m \u2265 5 primes and n = 3, 5, 7, 11 by Anni and Siksek. The case (x, y, z) = (2l, 2m, 13) and all its permutations were proven for l, m \u2265 5 primes by Billerey, Chen, Demb\u00e9l\u00e9, Dieulefait, Freitas. The case (x, y, z) = (3l, 3m, n) is direct for l, m \u2265 2 and n \u2265 3 from work by Kraus.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 2007, AMD added the AMD Athlon, AMD Turion, and Mobile AMD Sempron processors to its embedded product line. Leveraging the same 64-bit instruction set and Direct Connect Architecture as the AMD Opteron but at lower power levels, these processors were well suited to a variety of traditional embedded applications. Throughout 2007 and into 2008, AMD has continued to add both single-core Mobile AMD Sempron and AMD Athlon processors and dual-core AMD Athlon X2 and AMD Turion processors to its embedded product line and now offers embedded 64-bit solutions starting with 8 W TDP Mobile AMD Sempron and AMD Athlon processors for fan-less designs up to multi-processor systems leveraging multi-core AMD Opteron processors all supporting longer than standard availability.The ATI acquisition in 2006 included the Imageon and Xilleon product lines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The entropy of a closed system, determined relative to this zero point, is then the absolute entropy of that system. Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant kB = 1.38\u00d710\u221223 J K\u22121.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some payphones were altered to accept tokens, while others have been designed to use telephone cards. For example, in St Petersburg, payment for payphones can be made with metro tokens. In some regions, calls from public phones are free of charge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hermite constant, named after Charles Hermite, determines how long a shortest element of a lattice in Euclidean space can be. The constant \u03b3n for integers n > 0 is defined as follows. For a lattice L in Euclidean space Rn with unit covolume, i.e. vol(Rn/L) = 1, let \u03bb1(L) denote the least length of a nonzero element of L. Then \u221a\u03b3n is the maximum of \u03bb1(L) over all such lattices L. The square root in the definition of the Hermite constant is a matter of historical convention. Alternatively, the Hermite constant \u03b3n can be defined as the square of the maximal systole of a flat n-dimensional torus of unit volume.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, logistic regression is a type of regression analysis used for predicting the outcome of a categorical dependent variable (with a limited number of categories) or dichotomic dependent variable based on one or more predictor variables. The probabilities describing the possible outcome of a single trial are modeled, as a function of explanatory (independent) variables, using a logistic function or multinomial distribution. Logistic regression measures the relationship between a categorical or dichotomic dependent variable and usually a continuous independent variable (or several), by converting the dependent variable to probability scores. The probabilities can be retrieved using the logistic function or the multinomial distribution, while those probabilities, like in probability theory, takes on values between zero and one: So the model tested can be defined by: whereas yi is the category of the dependent variable for the i-th observation and xij is the j independent variable (j=1,2,...k) for that observation, \u03b2j is the j-th coefficient of xij and indicates its influence on and expected from the fitted model . Note: independent variables in logistic regression can also be continuous.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If there is branching, so multiple future revisions are based on a past revision, or undoing, so a revision can depend on a revision older than its immediate predecessor, then the resulting graph is instead a directed tree (each node can have more than one child), and has multiple tips, corresponding to the revisions without children (\"latest revision on each branch\"). In principle the resulting tree need not have a preferred tip (\"main\" latest revision) \u2013 just various different revisions \u2013 but in practice one tip is generally identified as HEAD. When a new revision is based on HEAD, it is either identified as the new HEAD, or considered a new branch.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Kernel methods have the advantage of having convex loss functions, with no local minima, and of being only moderately complex to implement. Because high-dimensional feature space is linear, kernel adaptive filters can be thought of as a generalization of linear adaptive filters. As with linear adaptive filters, there are two general approaches to adapting a filter: the least mean squares filter (LMS) and the recursive least squares filter (RLS).Self organising kernel adaptive filters that use iteration to achieve convex LMS error minimisation address some of the statistical and practical issues of non-linear models that do not arise in the linear case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle p_{t}-p_{t-1}=0\\quad {\\text{for all present and future }}t.} The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering. If a system is in a steady state, then the recently observed behavior of the system will continue into the future.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems that use virtual memory, every process is given the impression that it is working with large, contiguous sections of memory. Physically, the memory of each process may be dispersed across different areas of physical memory, or may have been moved (paged out) to secondary storage, typically to a hard disk drive (HDD) or solid-state drive (SSD). When a process requests access to data in its memory, it is the responsibility of the operating system to map the virtual address provided by the process to the physical address of the actual memory where that data is stored. The page table is where the operating system stores its mappings of virtual addresses to physical addresses, with each mapping also known as a page table entry (PTE).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This suggests that the nucleoprotein assembly is sequential in the PriA, DnaD, DnaB order. The preferred DNA substrate mimics an arrested DNA replication fork with unreplicated lagging strand, structurally identical to a product of recombinational repair of a stalled replication fork. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the relationship square is a graphical representation for use in the factorial analysis of a table individuals x variables. This representation completes classical representations provided by principal component analysis (PCA) or multiple correspondence analysis (MCA), namely those of individuals, of quantitative variables (correlation circle) and of the categories of qualitative variables (at the centroid of the individuals who possess them). It is especially important in factor analysis of mixed data (FAMD) and in multiple factor analysis (MFA).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Beyond that, operations like the converse of a relation and the composition of relations are available, satisfying the laws of a calculus of relations, for which there are textbooks by Ernst Schr\u00f6der, Clarence Lewis, and Gunther Schmidt. A deeper analysis of relations involves decomposing them into subsets called concepts, and placing them in a complete lattice. In some systems of axiomatic set theory, relations are extended to classes, which are generalizations of sets. This extension is needed for, among other things, modeling the concepts of \"is an element of\" or \"is a subset of\" in set theory, without running into logical inconsistencies such as Russell's paradox. The terms correspondence, dyadic relation and two-place relation are synonyms for binary relation, though some authors use the term \"binary relation\" for any subset of a Cartesian product X \u00d7 Y {\\displaystyle X\\times Y} without reference to X and Y, and reserve the term \"correspondence\" for a binary relation with reference to X and Y.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, let G = ( V , E ) {\\displaystyle G=(V,E)} be an arbitrary graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically in functional analysis, a K-space is an F-space V {\\displaystyle V} such that every extension of F-spaces (or twisted sum) of the form is equivalent to the trivial one where R {\\displaystyle \\mathbb {R} } is the real line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It has also been reported that Stuxnet and associated variants have infected more than 30,000 systems and had a lasting presence which was extremely difficult to eradicate and purify. Both malicious programs exploited Zero-Day attacks on Windows-based operating systems.As computing crosses the cyber-physical barrier, there is significant effort spent on 'smart' systems, for instance smart cities, smart homes, smart manufacturing and smart vehicles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle M(x)=M(\\lfloor x\\rfloor ).} Less formally, M ( x ) {\\displaystyle M(x)} is the count of square-free integers up to x that have an even number of prime factors, minus the count of those that have an odd number. The first 143 M(n) values are (sequence A002321 in the OEIS) The Mertens function slowly grows in positive and negative directions both on average and in peak value, oscillating in an apparently chaotic manner passing through zero when n has the values 2, 39, 40, 58, 65, 93, 101, 145, 149, 150, 159, 160, 163, 164, 166, 214, 231, 232, 235, 236, 238, 254, 329, 331, 332, 333, 353, 355, 356, 358, 362, 363, 364, 366, 393, 401, 403, 404, 405, 407, 408, 413, 414, 419, 420, 422, 423, 424, 425, 427, 428, ... (sequence A028442 in the OEIS).Because the M\u00f6bius function only takes the values \u22121, 0, and +1, the Mertens function moves slowly, and there is no x such that |M(x)| > x. H. Davenport demonstrated that, for any fixed h, \u2211 n = 1 x \u03bc ( n ) exp \u2061 ( i 2 \u03c0 n \u03b8 ) = O ( x log h \u2061 x ) {\\displaystyle \\sum _{n=1}^{x}\\mu (n)\\exp(i2\\pi n\\theta )=O\\left({\\frac {x}{\\log ^{h}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states, a set \u03a3 called the input alphabet, and a function T: Q \u00d7 \u03a3 \u2192 Q called the transition function. Associated with any semiautomaton is a monoid called the characteristic monoid, input monoid, transition monoid or transition system of the semiautomaton, which acts on the set of states Q. This may be viewed either as an action of the free monoid of strings in the input alphabet \u03a3, or as the induced transformation semigroup of Q. In older books like Clifford and Preston (1967) semigroup actions are called \"operands\". In category theory, semiautomata essentially are functors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or \u22121. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N that is its inverse (these are equivalent under Cramer's rule). Thus every equation Mx = b, where M and b both have integer components and M is unimodular, has an integer solution. The n \u00d7 n unimodular matrices form a group called the n \u00d7 n general linear group over Z {\\displaystyle \\mathbb {Z} } , which is denoted GL n \u2061 ( Z ) {\\displaystyle \\operatorname {GL} _{n}(\\mathbb {Z} )} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean \u03bc and variance \u03c32, and Y is exponential of rate \u03bb. It has a characteristic positive skew from the exponential component. It may also be regarded as a weighted function of a shifted exponential with the weight being a function of the normal distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, this can occur recursively, with processing objects calling higher-up processing objects with commands that attempt to solve some smaller part of the problem; in this case recursion continues until the command is processed, or the entire tree has been explored. An XML interpreter might work in this manner. This pattern promotes the idea of loose coupling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The outcome of this approach was revolutionary at the time; it suggested that the search terms be left in their original format, what would today be known as a natural language query.Another major change was how the results were judged. In the original tests, a success occurred only if the index returned the exact document that had been used to generate the search. However, this was not typical of an actual query; a user looking for information on aircraft landing gear might be happy with any of the collection's many papers on the topic, but Cranfield 1 would consider such a result a failure in spite of returning relevant materials. In the second series, the results were judged by 3rd parties who gave a qualitative answer on whether the query generated a relevant set of papers, as opposed to returning a specified original document.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a preordered class is a class equipped with a preorder.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see Lubotzky & Segal 2003).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It also had a special mode where each of the operations could be executed sequentially. It implemented register rotation to aid in software pipelining of loops. There was an instruction cache only, since it was felt that a data cache would be inefficient on sparse array operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, time code ambiguity is the shortest interval between successive repetitions of the same time code value. For example, in a time code in which year-of-century (the '72' in 10/04/72) is the most slowly changing field, the time code ambiguity would be 100 years; it is ambiguous whether this value refers to a date in 1872, 1972 or some other century. For a digital clock in which hours and minutes up to a maximum of 11:59 are displayed, the time code ambiguity would be 12 hours. The Year 2000 problem is an example of the pitfalls of time code ambiguity. Very often dates are now recorded with 4 digit years (10/04/1972). Assuming that the use of a 4-digit year field would continue, even in the far future, this would change the time code ambiguity from 100 years to 10 000 years.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The file size distribution of publicly available audio and video data files (MIME types) follows a log-normal distribution over five orders of magnitude. File sizes of 140 million files on personal computers running the Windows OS, collected in 1999. Sizes of text-based emails (1990s) and multimedia-based emails (2000s).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Conversely, in the languages of Western Europe, the dot on a lower-case \u27e8i\u27e9 is not a glyph in because it does not convey any distinction, and an \u27e8\u0131\u27e9 in which the dot has been accidentally omitted is still likely to be recognized correctly. However, in Turkish and adjacent languages, this dot is a glyph because that language has two distinct versions of the letter i, with and without a dot. In Japanese syllabaries, some of the characters are made up of more than one separate mark, but in general these separate marks are not glyphs because they have no meaning by themselves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most designs the 56000 is dedicated to one single task, because digital signal processing using special hardware is mostly real-time and does not allow any interruption. For less demanding tasks which are not time-critical, designers normally use a separate CPU or MCU. The 56000 can execute a 1024-point complex Fast Fourier transform (FFT) in 59,898 clock cycles, taking 1.8 ms at 33 MHz, or a rate of just over 555 operations per second, allowing both realtime decoding and encoding of reasonably advanced audio codecs such as MP3 for direct-to-disc recording purposes.The addition of SIMD instructions to most desktop computer CPUs have meant that dedicated DSP chips like the 56000 have partly disappeared from some application fields, but they continue to be used widely in communications and other professional uses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Common practical digital signals are represented as 8-bit (256 levels), 16-bit (65,536 levels), 24-bit (16.8 million levels), and 32-bit (4.3 billion levels) using pulse-code modulation where the number of quantization levels is not necessarily limited to powers of two. A floating point representation is used in many DSP applications. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the TV series Person of Interest, bluesnarfing, often mistakenly referred to as bluejacking in the show and at other times forced pairing and phone cloning, is a common element in the show used to spy on and track the people the main characters are trying to save or stop.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Davenport\u2013Erd\u0151s theorem states that, for sets of multiples of integers, several different notions of density are equivalent.Let A = a 1 , a 2 , \u2026 {\\displaystyle A=a_{1},a_{2},\\dots } be a sequence of positive integers. Then the multiples of A {\\displaystyle A} are another set M ( A ) {\\displaystyle M(A)} that can be defined as the set M ( A ) = { k a \u2223 k \u2208 N , a \u2208 A } {\\displaystyle M(A)=\\{ka\\mid k\\in \\mathbb {N} ,a\\in A\\}} of numbers formed by multiplying members of A {\\displaystyle A} by arbitrary positive integers.According to the Davenport\u2013Erd\u0151s theorem, for a set M ( A ) {\\displaystyle M(A)} , the following notions of density are equivalent, in the sense that they all produce the same number as each other for the density of M ( A ) {\\displaystyle M(A)}: The lower natural density, the inferior limit as n {\\displaystyle n} goes to infinity of the proportion of members of M ( A ) {\\displaystyle M(A)} in the interval  {\\displaystyle } . The logarithmic density or multiplicative density, the weighted proportion of members of M ( A ) {\\displaystyle M(A)} in the interval  {\\displaystyle } , again in the limit, where the weight of an element a {\\displaystyle a} is 1 / a {\\displaystyle 1/a} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For this reason, in a quantum algorithm there is no way to deterministically put bits in a specific prescribed state unless one is given access to bits whose original state is known in advance. Such bits, whose values are known a priori, are known as ancilla bits in a quantum or reversible computing task. A trivial use for ancilla bits is downgrading complicated quantum gates into simple gates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Salt baths can be used as an antiseptic and fungicide, and will not damage beneficial bacteria, though ordinary table salt may contain additives which can harm fish. Alternatives include aquarium salt, Kosher salt or rock salt. Gradually raising the temperature of the tank may kill certain parasites, though some diseased fish may be harmed and certain species can not tolerate high temperatures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of size measure, the two most common cases are the largest-area empty rectangle and largest-perimeter empty rectangle.Another major classification is whether the rectangle is sought among axis-oriented or arbitrarily oriented rectangles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is conjectured that MLPT has the same approximation ratio for more general cardinality constraints (c>3). Currently, it is known that the approximation ratio of MLPT for general c>3 is at most 2. Chen, He and Lin show that, for the same problem, MLPT attains at least ( 3 m \u2212 1 ) / ( 4 m \u2212 2 ) {\\displaystyle (3m-1)/(4m-2)} of the maximum smallest sum, which is again the same ratio that LPT attains for the unconstrained problem.Another constraint is that the number of jobs on all machines should be n / m {\\displaystyle n/m} rounded either up or down.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The notation a \u2264T b indicates there is a set in degree b that computes a set in degree a. Equivalently, a \u2264T b holds if and only if every set in b computes every set in a. A function f from the natural numbers to the natural numbers is said to be diagonally nonrecursive (DNR) if, for all n, f ( n ) \u2260 \u03d5 n ( n ) {\\displaystyle f(n)\\not =\\phi _{n}(n)} (here inequality holds by definition if \u03d5 n ( n ) {\\displaystyle \\phi _{n}(n)} is undefined). If the range of f is the set {0,1} then f is a DNR2 function. It is known that there are DNR functions that do not compute any DNR2 function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to implement the MinHash scheme as described above, one needs the hash function h to define a random permutation on n elements, where n is the total number of distinct elements in the union of all of the sets to be compared. But because there are n! different permutations, it would require \u03a9(n log n) bits just to specify a truly random permutation, an infeasibly large number for even moderate values of n. Because of this fact, by analogy to the theory of universal hashing, there has been significant work on finding a family of permutations that is \"min-wise independent\", meaning that for any subset of the domain, any element is equally likely to be the minimum. It has been established that a min-wise independent family of permutations must include at least lcm \u2061 ( 1 , 2 , \u22ef , n ) \u2265 e n \u2212 o ( n ) {\\displaystyle \\operatorname {lcm} (1,2,\\cdots ,n)\\geq e^{n-o(n)}} different permutations, and therefore that it needs \u03a9(n) bits to specify a single permutation, still infeasibly large.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semantics, research into linguistic universals has taken place in a number of ways. Some linguists, starting with Gottfried Leibniz, have pursued the search for a hypothetic irreducible semantic core of all languages. A modern variant of this approach can be found in the natural semantic metalanguage of Anna Wierzbicka and associates. See, for example, and Other lines of research suggest cross-linguistic tendencies to use body part terms metaphorically as adpositions, or tendencies to have morphologically simple words for cognitively salient concepts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Heawood number of a surface is an upper bound for the number of colors that suffice to color any graph embedded in the surface. In 1890 Heawood proved for all surfaces except the sphere that no more than H ( S ) = \u230a 7 + 49 \u2212 24 e ( S ) 2 \u230b = \u230a 7 + 1 + 48 g ( S ) 2 \u230b {\\displaystyle H(S)=\\left\\lfloor {\\frac {7+{\\sqrt {49-24e(S)}}}{2}}\\right\\rfloor =\\left\\lfloor {\\frac {7+{\\sqrt {1+48g(S)}}}{2}}\\right\\rfloor } colors are needed to color any graph embedded in a surface of Euler characteristic e ( S ) {\\displaystyle e(S)} , or genus g ( S ) {\\displaystyle g(S)} for an orientable surface. The number H ( S ) {\\displaystyle H(S)} became known as Heawood number in 1976.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 678, 1678, 4678, and 14678 are the patterns related to Braille pattern dots-356, since the two additional dots of kantenji patterns 0356, 3567, and 03567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the number system and its notational conventions, while primality is independent of such concerns. The first few decimal palindromic primes are: 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, \u2026 (sequence A002385 in the OEIS)Except for 11, all palindromic primes have an odd number of digits, because the divisibility test for 11 tells us that every palindromic number with an even number of digits is a multiple of 11. It is not known if there are infinitely many palindromic primes in base 10. The largest known as of October 2021 is 101888529 - 10944264 - 1.which has 1,888,529 digits, and was found on 18 October 2021 by Ryan Propper and Serge Batalov. On the other hand, it is known that, for any base, almost all palindromic numbers are composite, i.e. the ratio between palindromic composites and all palindromes less than n tends to 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The sum of distances is widely used in applications such as the facility location problem. The proposed algorithm uses Lloyd-style iteration which alternates between an expectation (E) and maximization (M) step, making this an expectation\u2013maximization algorithm. In the E step, all objects are assigned to their nearest median. In the M step, the medians are recomputed by using the median in each single dimension.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language semantics, normalisation by evaluation (NBE) is a style of obtaining the normal form of terms in the \u03bb-calculus by appealing to their denotational semantics. A term is first interpreted into a denotational model of the \u03bb-term structure, and then a canonical (\u03b2-normal and \u03b7-long) representative is extracted by reifying the denotation. Such an essentially semantic, reduction-free, approach differs from the more traditional syntactic, reduction-based, description of normalisation as reductions in a term rewrite system where \u03b2-reductions are allowed deep inside \u03bb-terms. NBE was first described for the simply typed lambda calculus. It has since been extended both to weaker type systems such as the untyped lambda calculus using a domain theoretic approach, and to richer type systems such as several variants of Martin-L\u00f6f type theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If N {\\displaystyle N} is V, then \u03ba {\\displaystyle \\kappa } (the critical point of j {\\displaystyle j} ) is always a measurable cardinal, i.e. an uncountable cardinal number \u03ba such that there exists a \u03ba {\\displaystyle \\kappa } -complete, non-principal ultrafilter over \u03ba {\\displaystyle \\kappa } . Specifically, one may take the filter to be { A \u2223 A \u2286 \u03ba \u2227 \u03ba \u2208 j ( A ) } {\\displaystyle \\{A\\mid A\\subseteq \\kappa \\land \\kappa \\in j(A)\\}} . Generally, there will be many other <\u03ba-complete, non-principal ultrafilters over \u03ba {\\displaystyle \\kappa } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As part of Schmidt's proof, he proves that a finite p-group is a modular group if and only if every subgroup is permutable, by (Schmidt 1994, Lemma 2.3.2, p. 55). Every subgroup of a finite p-group is subnormal, and those finite groups in which subnormality and permutability coincide are called PT-groups. In other words, a finite p-group is an Iwasawa group if and only if it is a PT-group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, groups of individual data points may be classified as belonging to any of various statistical data types, e.g. categorical (\"red\", \"blue\", \"green\"), real number (1.68, -5, 1.7e+6), odd number (1,3,5) etc. The data type is a fundamental component of the semantic content of the variable, and controls which sorts of probability distributions can logically be used to describe the variable, the permissible operations on the variable, the type of regression analysis used to predict the variable, etc. The concept of data type is similar to the concept of level of measurement, but more specific: For example, count data require a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale). Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one transformation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in group theory, the Pr\u00fcfer p-group or the p-quasicyclic group or p\u221e-group, Z(p\u221e), for a prime number p is the unique p-group in which every element has p different p-th roots. The Pr\u00fcfer p-groups are countable abelian groups that are important in the classification of infinite abelian groups: they (along with the group of rational numbers) form the smallest building blocks of all divisible groups. The groups are named after Heinz Pr\u00fcfer, a German mathematician of the early 20th century.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, generalized iterative scaling (GIS) and improved iterative scaling (IIS) are two early algorithms used to fit log-linear models, notably multinomial logistic regression (MaxEnt) classifiers and extensions of it such as MaxEnt Markov models and conditional random fields. These algorithms have been largely surpassed by gradient-based methods such as L-BFGS and coordinate descent algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the EOQ model, it is assumed that the orders are received all at once. However, in the EBQ model, this assumption is relaxed.There are two types of costs: those which increase with the batch size such as working capital investment in materials and labor, cost of handling and storing materials, insurance and tax charges, interest on capital investment, etc., and those which decrease with the batch size such as cost (per unit) of setting up machines, cost of preparing paper work that enters and controls the production of the order, etc. These costs, i.e., (a) and (b) are plotted and added graphically (figure). The figure graphs the holding cost and ordering cost per year equations. The third line is the addition of these two equations, which generates the total inventory cost per year.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The functional dependencies, along with the attribute domains, are selected so as to generate constraints that would exclude as much data inappropriate to the user domain from the system as possible. A notion of logical implication is defined for functional dependencies in the following way: a set of functional dependencies \u03a3 {\\displaystyle \\Sigma } logically implies another set of dependencies \u0393 {\\displaystyle \\Gamma } , if any relation R satisfying all dependencies from \u03a3 {\\displaystyle \\Sigma } also satisfies all dependencies from \u0393 {\\displaystyle \\Gamma } ; this is usually written \u03a3 \u22a8 \u0393 {\\displaystyle \\Sigma \\models \\Gamma } . The notion of logical implication for functional dependencies admits a sound and complete finite axiomatization, known as Armstrong's axioms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another proof, which is a simplification of Lambert's proof, is due to Mikl\u00f3s Laczkovich. Many of these are proofs by contradiction. In 1882, Ferdinand von Lindemann proved that \u03c0 {\\displaystyle \\pi } is not just irrational, but transcendental as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and related subjects, understanding a mathematical expression depends on an understanding of symbols of grouping, such as parentheses (), brackets , and braces {}. These same symbols are also used in ways where they are not symbols of grouping. For example, in the expression 3(x+y) the parentheses are symbols of grouping, but in the expression (3, 5) the parentheses may indicate an open interval. The most common symbols of grouping are the parentheses and the brackets, and the brackets are usually used to avoid too many repeated parentheses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The radical of an ideal in a commutative ring. In geometry, the convex hull of a set S of points is the smallest convex set of which S is a subset. In formal languages, the Kleene closure of a language can be described as the set of strings that can be made by concatenating zero or more strings from that language. In group theory, the conjugate closure or normal closure of a set of group elements is the smallest normal subgroup containing the set. In mathematical analysis and in probability theory, the closure of a collection of subsets of X under countably many set operations is called the \u03c3-algebra generated by the collection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space. Vector spaces generalize Euclidean vectors, which allow modeling of physical quantities, such as forces and velocity, that have not only a magnitude, but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Zorn ring is an alternative ring in which for every non-nilpotent x there exists an element y such that xy is a non-zero idempotent (Kaplansky 1968, pages 19, 25). Kaplansky (1951) named them after Max August Zorn, who studied a similar condition in (Zorn 1941). For associative rings, the definition of Zorn ring can be restated as follows: the Jacobson radical J(R) is a nil ideal and every right ideal of R which is not contained in J(R) contains a nonzero idempotent. Replacing \"right ideal\" with \"left ideal\" yields an equivalent definition. Left or right Artinian rings, left or right perfect rings, semiprimary rings and von Neumann regular rings are all examples of associative Zorn rings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical finance, if security weights maximize the expected geometric growth rate (which is equivalent to maximizing log wealth), then a portfolio is growth optimal. Computations of growth optimal portfolios can suffer tremendous garbage in, garbage out problems. For example, the cases below take as given the expected return and covariance structure of assets, but these parameters are at best estimates or models that have significant uncertainty.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, during marine transfer operations when flammable products are transferred between the marine terminal and tanker ships or barges, two-way radio communication needs to be constantly maintained in case the transfer needs to stop for unforeseen reasons such as a spill. The United States Coast Guard requires that the two way radio must be certified as intrinsically safe. Another example is intrinsically safe or explosion-proof mobile phones used in explosive atmospheres, such as refineries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory \u2014 specifically, in stochastic analysis \u2014 a killed process is a stochastic process that is forced to assume an undefined or \"killed\" state at some (possibly random) time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is used as an optimality criterion in parameter selection and model selection. In general, total sum of squares = explained sum of squares + residual sum of squares. For a proof of this in the multivariate ordinary least squares (OLS) case, see partitioning in the general OLS model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "b  {\\displaystyle z\\neq x\\ \\to (\\lambda z.b)=\\lambda z.b} This is to stop bound variables with the same name being substituted. This would not have occurred in a canonically renamed lambda expression. For example the previous rules would have wrongly translated, ( \u03bb x .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matrix theory, Sylvester's determinant identity is an identity useful for evaluating certain types of determinants. It is named after James Joseph Sylvester, who stated this identity without proof in 1851.Given an n-by-n matrix A {\\displaystyle A} , let det ( A ) {\\displaystyle \\det(A)} denote its determinant. Choose a pair u = ( u 1 , \u2026 , u m ) , v = ( v 1 , \u2026 , v m ) \u2282 ( 1 , \u2026 , n ) {\\displaystyle u=(u_{1},\\dots ,u_{m}),v=(v_{1},\\dots ,v_{m})\\subset (1,\\dots ,n)} of m-element ordered subsets of ( 1 , \u2026 , n ) {\\displaystyle (1,\\dots ,n)} , where m \u2264 n. Let A v u {\\displaystyle A_{v}^{u}} denote the (n\u2212m)-by-(n\u2212m) submatrix of A {\\displaystyle A} obtained by deleting the rows in u {\\displaystyle u} and the columns in v {\\displaystyle v} . Define the auxiliary m-by-m matrix A ~ v u {\\displaystyle {\\tilde {A}}_{v}^{u}} whose elements are equal to the following determinants ( A ~ v u ) i j := det ( A v  u  ) , {\\displaystyle ({\\tilde {A}}_{v}^{u})_{ij}:=\\det(A_{v}^{u}),} where u  {\\displaystyle u} , v  {\\displaystyle v} denote the m\u22121 element subsets of u {\\displaystyle u} and v {\\displaystyle v} obtained by deleting the elements u i {\\displaystyle u_{i}} and v j {\\displaystyle v_{j}} , respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This trick is mentioned by Kleene (1952) p. 223. The problem arises when the number to be created exhausts the number of instructions available to the finite state machine; there is always a bigger constant than the number of instructions available to the finite state machine.Unbounded numbers of registers versus bounded state-machine instructions: This is more severe than the first problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The number 1 is then appended to the end of c {\\displaystyle c} , and the extrapolated limit is s = X c \u2211 i = 1 k c i , {\\displaystyle s={Xc \\over \\sum _{i=1}^{k}c_{i}},} where X = ( x 2 , x 3 , . . . , x k + 1 ) {\\displaystyle X=(x_{2},x_{3},...,x_{k+1})} is the matrix whose columns are the k {\\displaystyle k} iterates starting at 2. The following 4 line MATLAB code segment implements the MPE algorithm: == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sequential search, a consumer looks for a product or service one at a time until they find it, McCall J.J. introduced this type of search to economics. In economics, the sequential search model is used to examine how consumers choose which goods or services to purchase when they have asymmetrical information (incomplete)of those goods' quality. Consumers in sequential search models must choose whether to stop looking for a better good or service or to buy what they have found so far.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use: With a shape parameter k {\\displaystyle k} and a scale parameter \u03b8 {\\displaystyle \\theta } . With a shape parameter \u03b1 = k {\\displaystyle \\alpha =k} and an inverse scale parameter \u03b2 = 1 / \u03b8 {\\displaystyle \\beta =1/\\theta } , called a rate parameter.In each of these forms, both parameters are positive real numbers. The gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and a 1 / x {\\displaystyle 1/x} base measure) for a random variable X {\\displaystyle X} for which E = k\u03b8 = \u03b1/\u03b2 is fixed and greater than zero, and E = \u03c8(k) + ln(\u03b8) = \u03c8(\u03b1) \u2212 ln(\u03b2) is fixed (\u03c8 is the digamma function).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The value associated with the largest identifier in that majority is V2, so it must propose it. This Proposer then gets all Acceptors to accept V2, achieving consensus. Proposer Acceptor Learner | | | | | | | | | | | X--------------->|->|->|->|->| | | Prepare(1) |<---------------X--X--X--X--X | | Promise(1,{null,null,null,null,null}) x--------------->| | | | | | | Accept!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This fact is called weak duality. In general, the optimal values of the primal and dual problems need not be equal. Their difference is called the duality gap. For convex optimization problems, the duality gap is zero under a constraint qualification condition. This fact is called strong duality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is a standard, ETSI ES 202 130, that covers European languages and other languages used in Europe, published by the independent ETSI organisation in 2003 and updated in 2007. Work describing some principles of the standard is available.Since many newer smartphones, such as the Palm Treo and BlackBerry, have full alphanumeric keyboards instead of the traditional telephone keypads, the user must execute additional steps to dial a number containing convenience letters. On certain BlackBerry devices, a user can press the Alt key, followed by the desired letter, and the device will generate the appropriate DTMF tone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Egalitarian zero The index I(x) is zero in the egalitarian case, when all values xi are equal. Bounded above by maximum inequality The index I(x) attains its maximum value for maximum inequality. (all xi are zero except one) This value is usually unity as the number of agents n approaches infinity. Subgroup decomposabilityThis property states that if a set of agents x is divided into two disjoint subsets (y and z) then the I(x) is expressible as: where \u03bc(x) and \u03bc(y) are the mean incomes of x and y. and the w functions are scalar weighting function of the sets y and z. In a stronger statement, wy = \u03bcy / \u03bcx and wz = \u03bcz / \u03bcx.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But they will not be maintained. Another issue is that an XML document can be transcoded from one encoding to another during transport. When the XML document is converted to a more limited character set, such as ASCII, characters that can no longer be represented are converted to nnn; character references for a lossless conversion. But within a CDATA section, these characters can not be represented at all, and have to be removed or converted to some equivalent, altering the content of the CDATA section.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most wireless ad hoc networks, the nodes compete for access to shared wireless medium, often resulting in collisions (interference). Collisions can be handled using centralized scheduling or distributed contention access protocols. Using cooperative wireless communications improves immunity to interference by having the destination node combine self-interference and other-node interference to improve decoding of the desired signals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to adapt to the changes, the Linuxtag focused on the core issue of the professional use of open source software in 2014. Therefore, LinuxTag started a strategic partnership with the droidcon. The 20th LinuxTag took place between 8 and 10 May 2014 in the STATION Berlin. In spatial and temporal proximity were the Media Convention Berlin (May 6 to 7), the re: publica (6 to 8 May) and the droidcon (8 to 10 May 2014). All events aimed towards a close relationship in order to achieve a high level of appreciation of the combined effort.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The framework is developed and supported by the Science of High-Performance Computing (SHPC) group of the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin and the Matthews Research Group at Southern Methodist University. BLIS yields high performance on many current CPU microarchitectures in both single-threaded and multithreaded modes of execution. BLIS also offers competitive performance for some cases of matrix multiplication in which one or more matrix operands are unusually skinny and/or small.The framework achieves high performance by employing specialized kernels (typically written in GNU extended inline assembly syntax) along with cache and register blocking through matrix operands. BLIS also works on processors for which custom kernels have not yet been written; in those cases, the framework relies upon portable kernel implementations that perform at a lower rate of computation. BLIS is sometimes described as a refactoring of GotoBLAS2, which was created by Kazushige Goto at the Texas Advanced Computing Center.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics, bootstrap percolation is a percolation process in which a random initial configuration of active cells is selected from a lattice or other space, and then cells with few active neighbors are successively removed from the active set until the system stabilizes. The order in which this removal occurs makes no difference to the final stable state.When the threshold of active neighbors needed for an active cell to survive is high enough (depending on the lattice), the only stable states are states with no active cells, or states in which every cluster of active cells is infinitely large. For instance, on the square lattice with the von Neumann neighborhood, there are finite clusters with at least two active neighbors per cluster cell, but when three or four active neighbors are required, any stable cluster must be infinite. With three active neighbors needed to stay active, an infinite cluster must stretch infinitely in three or four of the possible cardinal directions, and any finite holes it contains will necessarily be rectangular.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most commonly however, these white spaces exist naturally between used channels, since assigning nearby transmissions to immediately adjacent channels will cause destructive interference to both. In addition to white space assigned for technical reasons, there is also unused radio spectrum which has either never been used, or is becoming free as a result of technical changes. In particular, the switchover to digital television frees up large areas between about 50 MHz and 700 MHz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to achieve a linear improvement in usefulness over time it is necessary to have an exponential increase in technology over time. Moore's law delivers an exponential increase in technology, and so when Claasen's law is combined with Moore's law it implies a linear improvement in usefulness over time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, Zadeh's rule (also known as the least-entered rule) is an algorithmic refinement of the simplex method for linear optimization. The rule was proposed around 1980 by Norman Zadeh (son of Lotfi A. Zadeh), and has entered the folklore of convex optimization since then.Zadeh offered a reward of $1,000 to anyone who can show that the rule admits polynomially many iterations or to prove that there is a family of linear programs on which the pivoting rule requires subexponentially many iterations to find the optimum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, any arbitrary boolean function, including addition, multiplication, and other mathematical functions, can be built up from a functionally complete set of logic operators. In 1987, Conway's Game of Life became one of the first examples of general-purpose computing using an early stream processor called a blitter to invoke a special sequence of logical operations on bit vectors.General-purpose computing on GPUs became more practical and popular after about 2001, with the advent of both programmable shaders and floating point support on graphics processors. Notably, problems involving matrices and/or vectors \u2013 especially two-, three-, or four-dimensional vectors \u2013 were easy to translate to a GPU, which acts with native speed and support on those types. A significant milestone for GPGPU was the year 2003 when two research groups independently discovered GPU-based approaches for the solution of general linear algebra problems on GPUs that ran faster than on CPUs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The notation J represents the part of the correlations that can be attributed to classical correlations and varies in dependence on the chosen eigenbasis; therefore, in order for the quantum discord to reflect the purely nonclassical correlations independently of basis, it is necessary that J first be maximized over the set of all possible projective measurements onto the eigenbasis: D A ( \u03c1 ) = I ( \u03c1 ) \u2212 max { \u03a0 j A } J { \u03a0 j A } ( \u03c1 ) = S ( \u03c1 A ) \u2212 S ( \u03c1 ) + min { \u03a0 j A } S ( \u03c1 B | { \u03a0 j A } ) {\\displaystyle {\\mathcal {D}}_{A}(\\rho )=I(\\rho )-\\max _{\\{\\Pi _{j}^{A}\\}}J_{\\{\\Pi _{j}^{A}\\}}(\\rho )=S(\\rho _{A})-S(\\rho )+\\min _{\\{\\Pi _{j}^{A}\\}}S(\\rho _{B|\\{\\Pi _{j}^{A}\\}})} Nonzero quantum discord indicates the presence of correlations that are due to noncommutativity of quantum operators. For pure states, the quantum discord becomes a measure of quantum entanglement, more specifically, in that case it equals the entropy of entanglement.Vanishing quantum discord is a criterion for the pointer states, which constitute preferred effectively classical states of a system. It could be shown that quantum discord must be non-negative and that states with vanishing quantum discord can in fact be identified with pointer states.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the PKCS#1 standard, the random oracles are identical. The PKCS#1 standard further requires that the random oracles be MGF1 with an appropriate hash function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the deviation is reckoned from the central value, being construed as some type of average, most often the median or sometimes the mean of the data set: where Di is the absolute deviation, xi is the data element, m(X) is the chosen measure of central tendency of the data set\u2014sometimes the mean ( x \u00af {\\displaystyle {\\overline {x}}} ), but most often the median.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At a minimum, each profile specification contains information on the following topics: Dependencies on other formats Suggested user interface formats Specific parts of the Bluetooth protocol stack used by the profile. To perform its task, each profile uses particular options and parameters at each layer of the stack. This may include an outline of the required service record, if appropriate.This article summarizes the current definitions of profiles defined and adopted by the Bluetooth SIG and possible applications of each profile.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Social networks like Facebook, Twitter and Ning allow learners, once they move beyond the personal connections, to embrace a community where they can learn from each other. Social interaction is an important part of the learning process. As technology has grown and become an integral part of the lives of children, teens, and young adults, older adults have been forced to adapt.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The B5000 was designed in 1961, long before the term RISC was invented. The architecture puts six 8-bit instructions in a 48-bit word, and was a precursor to very long instruction word (VLIW) design (see below: 1990 to today). The Burroughs architecture was one of the inspirations for Charles H. Moore's programming language Forth, which in turn inspired his later MISC chip designs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization and related fields, relaxation is a modeling strategy. A relaxation is an approximation of a difficult problem by a nearby problem that is easier to solve. A solution of the relaxed problem provides information about the original problem. For example, a linear programming relaxation of an integer programming problem removes the integrality constraint and so allows non-integer rational solutions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The distribution was first introduced in a more general context and is an example of the vine copula, an approach to constrained high-dimensional probability distributions. It has been implemented as part of the Stan probabilistic programming language and as a library linked to the Turing.jl probabilistic programming library in Julia. The distribution has a single shape parameter \u03b7 {\\displaystyle \\eta } and the probability density function for a d \u00d7 d {\\displaystyle d\\times d} matrix R {\\displaystyle \\mathbf {R} } is p ( R ; \u03b7 ) = C \u00d7  \u03b7 \u2212 1 {\\displaystyle p(\\mathbf {R} ;\\eta )=C\\times ^{\\eta -1}} with normalizing constant C = 2 \u2211 k = 1 d ( 2 \u03b7 \u2212 2 + d \u2212 k ) ( d \u2212 k ) \u220f k = 1 d \u2212 1  d \u2212 k {\\displaystyle C=2^{\\sum _{k=1}^{d}(2\\eta -2+d-k)(d-k)}\\prod _{k=1}^{d-1}\\left^{d-k}} , a complicated expression including a product over Beta functions. For \u03b7 = 1 {\\displaystyle \\eta =1} , the distribution is uniform over the space of all correlation matrices; i.e. the space of positive definite matrices with unit diagonal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This design enabled more efficient program execution, as the Program Counter and status flags could be saved and restored with a single operation. This resulted in faster subroutine calls and interrupt response than traditional designs, which would have to do two register loads or saves when calling or returning from a subroutine. Despite having a 32-bit ALU and word-length, processors based on ARM architecture version 1 and 2 had only a 26-bit PC and address bus, and were consequently limited to 64 MiB of addressable memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This leads to faster convergence in terms of basis set size than pure gaussian-type basis set, but requires calculation of more complex integrals. To simplify them, interelectron distances are expanded into a series making for simpler integrals. The idea of R12 methods is quite old, but practical implementations begun to appear only recently.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Swapping conflict: a swapping conflict is the case in which two agents exchange their position, passing on the same edge at the same time in two different directions. It is expressed as \u03c0 i  = \u03c0 j  {\\displaystyle \\pi _{i}=\\pi _{j}} and \u03c0 j  = \u03c0 i  {\\displaystyle \\pi _{j}=\\pi _{i}} .When formalizing a MAPF problem, it is possible to decide which conflicts are allowed and which are forbidden. A unified standard about permitted and denied conflicts does not exist, however vertex and edge conflicts are usually not allowed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The dispute had several levels, some technical (sockets vs. streams, BSD tty vs. System V termio) and some cultural. The divide was roughly between longhairs and shorthairs; programmers and technical people tended to line up with Berkeley and BSD, more business-oriented types with AT&T and System V. While HP, IBM and others chose System V as the basis for their Unix offerings, other vendors such as Sun Microsystems and DEC extended BSD. Throughout its development, though, System V was infused with features from BSD, while BSD variants such as DEC's Ultrix received System V features. AT&T and Sun Microsystems worked together to merge System V with BSD-based SunOS to produce Solaris, one of the primary System V descendants still in use today. Since the early 1990s, due to standardization efforts such as POSIX and the success of Linux, the division between System V and BSD has become less important.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The rank of a free abelian group is the cardinality of a basis; every two bases for the same group give the same rank, and every two free abelian groups with the same rank are isomorphic. Every subgroup of a free abelian group is itself free abelian; this fact allows a general abelian group to be understood as a quotient of a free abelian group by \"relations\", or as a cokernel of an injective homomorphism between free abelian groups. The only free abelian groups that are free groups are the trivial group and the infinite cyclic group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the late 1980s, the European standardization group GSM who worked on the Pan-European Digital mobile communication system GSM greatly expanded the use of ALOHA channels for access to radio channels in mobile telephony. In addition, SMS message texting was implemented in 2G mobile phones. In the early 2000s additional ALOHA channels were added to 2.5G and 3G mobile phones with the widespread introduction of General Packet Radio Service (GPRS), using a slotted-ALOHA random-access channel combined with a version of the Reservation ALOHA scheme first analyzed by a group at BBN Technologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This leads to the notion of \"genetic distance\", which is a measure of recombination frequency averaged over a (suitably large) sample of pedigrees. Loosely speaking, one may say that this is because recombination is greatly influenced by the proximity of one gene to another. If two genes are located close together on a chromosome, the likelihood that a recombination event will separate these two genes is less than if they were farther apart.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the present context, our system is assumed to have the energy levels \u03b5 i {\\displaystyle \\varepsilon _{i}} with degeneracies g i {\\displaystyle g_{i}} . As before, we would like to calculate the probability that our system has energy \u03b5 i {\\displaystyle \\varepsilon _{i}} . If our system is in state s 1 {\\displaystyle \\;s_{1}} , then there would be a corresponding number of microstates available to the reservoir.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly computational algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields). The algorithm consists mainly of matrix reduction and polynomial GCD computations. It was invented by Elwyn Berlekamp in 1967. It was the dominant algorithm for solving the problem until the Cantor\u2013Zassenhaus algorithm of 1981. It is currently implemented in many well-known computer algebra systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This theorem is useful in searching for cycles of the permutation, since an efficient search can look only at multiples of divisors of MN\u22121 (Brenner, 1973). Laflin & Brebner (1970) pointed out that the cycles often come in pairs, which is exploited by several algorithms that permute pairs of cycles at a time. In particular, let s be the smallest element of some cycle C of length k. It follows that MN\u22121\u2212s is also an element of a cycle of length k (possibly the same cycle).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the discrete formulation of the pursuit\u2013evasion problem, the environment is modeled as a graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Musser reported that on a median-of-3 killer sequence of 100,000 elements, introsort's running time was 1/200 that of median-of-3 quicksort. Musser also considered the effect on caches of Sedgewick's delayed small sorting, where small ranges are sorted at the end in a single pass of insertion sort. He reported that it could double the number of cache misses, but that its performance with double-ended queues was significantly better and should be retained for template libraries, in part because the gain in other cases from doing the sorts immediately was not great.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This definition encompasses most curves that are studied in mathematics; notable exceptions are level curves (which are unions of curves and isolated points), and algebraic curves (see below). Level curves and algebraic curves are sometimes called implicit curves, since they are generally defined by implicit equations. Nevertheless, the class of topological curves is very broad, and contains some curves that do not look as one may expect for a curve, or even cannot be drawn.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The nines' complement of a number given in decimal representation is formed by replacing each digit with nine minus that digit. To subtract a decimal number y (the subtrahend) from another number x (the minuend) two methods may be used: In the first method the nines' complement of x is added to y. Then the nines' complement of the result obtained is formed to produce the desired result. In the second method the nines' complement of y is added to x and one is added to the sum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set. The larger set is then said to be generated by the smaller set. It is commonly the case that the generating set has a simpler set of properties than the generated set, thus making it easier to discuss and examine. It is usually the case that properties of the generating set are in some way preserved by the act of generation; likewise, the properties of the generated set are often reflected in the generating set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A 6600/7600 Peripheral Processor system was used for I/O, largely unchanged. Some effort was made to help compatibility between the older machines and the 8600, but the change in word length made this difficult. Instead, floating point formats were retained, allowing Fortran code to port directly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multivariate statistics, random matrices were introduced by John Wishart, who sought to estimate covariance matrices of large samples. Chernoff-, Bernstein-, and Hoeffding-type inequalities can typically be strengthened when applied to the maximal eigenvalue (i.e. the eigenvalue of largest magnitude) of a finite sum of random Hermitian matrices. Random matrix theory is used to study the spectral properties of random matrices\u2014such as sample covariance matrices\u2014which is of particular interest in high-dimensional statistics. Random matrix theory also saw applications in neuronal networks and deep learning, with recent work utilizing random matrices to show that hyper-parameter tunings can be cheaply transferred between large neural networks without the need for re-training.In numerical analysis, random matrices have been used since the work of John von Neumann and Herman Goldstine to describe computation errors in operations such as matrix multiplication. Although random entries are traditional \"generic\" inputs to an algorithm, the concentration of measure associated with random matrix distributions implies that random matrices will not test large portions of an algorithm's input space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The second phase requires choosing an ontology by which to organize categories of things. Temporal expressions and some numerical expressions (e.g., money, percentages, etc.) may also be considered as named entities in the context of the NER task. While some instances of these types are good examples of rigid designators (e.g., the year 2001) there are also many invalid ones (e.g., I take my vacations in \u201cJune\u201d).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the balanced partition problem, there are constraints on the number of jobs that can be assigned to each machine. A simple constraint is that each machine can process at most c jobs. The LPT rule assigns each job to the machine with the smallest load from among those with fewer than c jobs. This rule is called modified LPT or MLPT.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Porter's constant C arises in the study of the efficiency of the Euclidean algorithm. It is named after J. W. Porter of University College, Cardiff. Euclid's algorithm finds the greatest common divisor of two positive integers m and n. Hans Heilbronn proved that the average number of iterations of Euclid's algorithm, for fixed n and averaged over all choices of relatively prime integers m < n, is 12 ln \u2061 2 \u03c0 2 ln \u2061 n + o ( ln \u2061 n ) . {\\displaystyle {\\frac {12\\ln 2}{\\pi ^{2}}}\\ln n+o(\\ln n).} Porter showed that the error term in this estimate is a constant, plus a polynomially-small correction, and Donald Knuth evaluated this constant to high accuracy. It is: C = 6 ln \u2061 2 \u03c0 2  \u2212 1 2 = 6 ln \u2061 2 ( ( 48 ln \u2061 A ) \u2212 ( ln \u2061 2 ) \u2212 ( 4 ln \u2061 \u03c0 ) \u2212 2 ) \u03c0 2 \u2212 1 2 = 1.4670780794 \u2026 {\\displaystyle {\\begin{aligned}C&={{6\\ln 2} \\over {\\pi ^{2}}}\\left-{{1} \\over {2}}\\\\&={{{6\\ln 2}((48\\ln A)-(\\ln 2)-(4\\ln \\pi )-2)} \\over {\\pi ^{2}}}-{{1} \\over {2}}\\\\&=1.4670780794\\ldots \\end{aligned}}} where \u03b3 {\\displaystyle \\gamma } is the Euler\u2013Mascheroni constant \u03b6 {\\displaystyle \\zeta } is the Riemann zeta function A {\\displaystyle A} is the Glaisher\u2013Kinkelin constant(sequence A086237 in the OEIS) \u2212 \u03b6 \u2032 ( 2 ) = \u03c0 2 6  = \u2211 k = 2 \u221e ln \u2061 k k 2 {\\displaystyle -\\zeta ^{\\prime }(2)={{\\pi ^{2}} \\over 6}\\left=\\sum _{k=2}^{\\infty }{{\\ln k} \\over {k^{2}}}} {\\displaystyle }", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As with the analogous operation on the real numbers, a fundamental use of this operation is in solving, when possible, linear congruences of the form a x \u2261 b ( mod m ) . {\\displaystyle ax\\equiv b{\\pmod {m}}.} Finding modular multiplicative inverses also has practical applications in the field of cryptography, e.g. public-key cryptography and the RSA algorithm. A benefit for the computer implementation of these applications is that there exists a very fast algorithm (the extended Euclidean algorithm) that can be used for the calculation of modular multiplicative inverses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to expose an application's geographic data with GML, a community or organization creates an XML schema specific to the application domain of interest (the application schema). This schema describes the object types whose data the community is interested in and which community applications must expose. For example, an application for tourism may define object types including monuments, places of interest, museums, road exits, and viewpoints in its application schema.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, reads by Illumina\u2019s sequencing technology capture reads of 100-mers. However, the problem with the sequencing is that only small fractions out of all the possible 100-mers that are present in the genome are actually generated. This is due to read errors, but more importantly, just simple coverage holes that occur during sequencing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, a Highway Net whose gates are opened through strongly positive bias weights behaves like a ResNet. The skip connections used in modern neural networks (e.g., Transformers) are dominantly identity mappings. DenseNets in 2016 were designed as deep neural networks that attempt to connect each layer to every other layer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In previous decades, multilevel security (MLS) technologies were developed and implemented that enabled objective and deterministic security, but left little wiggle room for subjective and discretionary interpretation. These enforced mandatory access control (MAC) with near certainty. This rigidity prevented simpler solutions that would seem acceptable on the surface. Automated information systems have enabled extensive information sharing that is sometimes contrary to the need to avoid sharing secrets with adversaries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The orders of the full symmetry groups are twice as much again (24, 48, and 120). See (Coxeter 1973) for a derivation of these facts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Connecting elements into a pipeline is analogous to function composition. Narrowly speaking, a pipeline is linear and one-directional, though sometimes the term is applied to more general flows. For example, a primarily one-directional pipeline may have some communication in the other direction, known as a return channel or backchannel, as in the lexer hack, or a pipeline may be fully bi-directional. Flows with one-directional tree and directed acyclic graph topologies behave similarly to (linear) pipelines \u2013 the lack of cycles makes them simple \u2013 and thus may be loosely referred to as \"pipelines\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a colored matroid is a matroid whose elements are labeled from a set of colors, which can be any set that suits the purpose, for instance the set of the first n positive integers, or the sign set {+, \u2212}. The interest in colored matroids is through their invariants, especially the colored Tutte polynomial, which generalizes the Tutte polynomial of a signed graph of Kauffman (1989).There has also been study of optimization problems on matroids where the objective function of the optimization depends on the set of colors chosen as part of a matroid basis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1998 book Vectorproducts and Applications, Sz\u00e9p presented a new approach to system theory that contained a summary of his results from research between 1990 and 1995 as well as the applications of multiplicative structures in coding theory, game theory, and distribution vectors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Algorithms that push content based on user search histories, frequent clicks and paid advertising leads to unbalanced, poorly sourced, and actively misleading information. It is also highly profitable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Philips, LSI Logic and Integrated Device Technology (IDT) have since joined them. Today, the MIPS cores are one of the most-used \"heavyweight\" cores in the market for computer-like devices: handheld PCs, set-top boxes, etc. Since the MIPS architecture is licensable, it has attracted several processor start-up companies over the years. One of the first start-ups to design MIPS processors was Quantum Effect Devices (see next section).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The variables \u03b5 i {\\displaystyle \\varepsilon _{i}} are random variables, which in standard linear regression are distributed according to a standard normal distribution; they express the influence of any unknown factors on the outcome. This makes it possible to find optimal coefficients through the method of least squares using simple matrix operations. In particular, the optimal coefficients \u03b2 ^ {\\displaystyle {\\boldsymbol {\\hat {\\beta }}}} as estimated by least squares can be written as follows: \u03b2 ^ = ( X T X ) \u2212 1 X T y .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the animated short cartoon The Bowling Alley-Cat (1942), cat and mouse Tom and Jerry do battle inside a bowling center.In Dreamer (1979), Tim Matheson plays a man aspiring to be a professional bowler who faces a challenger played by Dick Weber.In Greedy (1994), Michael J. Fox plays an \"honest but luckless pro bowler with a bad wrist and a good woman. \"The Farrelly brothers' comedy Kingpin (1996) is a bowling comedy about which Randy Quaid said in an interview, \"If we can't laugh at bowling, what can we laugh at? \"In the Coen Brothers' The Big Lebowski (1998), \"the Dude\" (Jeff Bridges), a \"slacker's slacker\", hangs out with his buddies at a bowling alley, in which John Goodman's character pulls out a gun to threaten a competitor who stepped over the foul line and refused to accept the mandatory zero score for the shot.In the Disney Channel's Alley Cats Strike (2000), high school students engage in a bowling rivalry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the original subroutine call instructions BAL, Branch and Link, and its register-register equivalent, BALR, Branch and Link Register, store certain status information, the instruction length code, the condition code and the program mask, in the top byte of the return address. A BAS, Branch and Save, instruction was added to allow 31-bit return addresses. BAS, and its register-register equivalent, BASR, Branch and Save Register, was part of the instruction set of the 360/67, which was the only System/360 model to allow addresses longer than 24 bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Schwartz\u2013Zippel lemma (also called the DeMillo\u2013Lipton\u2013Schwartz\u2013Zippel lemma) is a tool commonly used in probabilistic polynomial identity testing, i.e. in the problem of determining whether a given multivariate polynomial is the 0-polynomial (or identically equal to 0). It was discovered independently by Jack Schwartz, Richard Zippel, and Richard DeMillo and Richard J. Lipton, although DeMillo and Lipton's version was shown a year prior to Schwartz and Zippel's result. The finite field version of this bound was proved by \u00d8ystein Ore in 1922.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(We use the transitive closure of {x} rather than of x itself to avoid confusing the elements of x with elements of its elements or whatever.) A code includes that information identifying x and also information about the particular injection from X into \u03c9 which was used to create E. The extra information about the injection is non-essential, so there are many codes for the same set which are equally useful. So codes are a way of mapping H \u2135 1 {\\displaystyle H_{\\aleph _{1}}} into the powerset of \u03c9\u00d7\u03c9.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\nabla \\cdot \\mathbf {H} (x)=0.} as H {\\displaystyle \\mathbf {H} } contains similar terms. The expression \u2207 \u00d7 E ( x ) {\\displaystyle \\nabla \\times \\mathbf {E} (x)} contains terms of the form p \u00d7 \u03f5 1 ( p ) {\\displaystyle \\mathbf {p} \\times \\mathbf {\\epsilon ^{1}} (\\mathbf {p} )} while \u2202 H ( x ) / \u2202 t {\\displaystyle \\partial \\mathbf {H} (x)/\\partial t} contains terms of form i p 0 \u03f5 1 ( p ) {\\displaystyle ip_{0}\\mathbf {\\epsilon ^{1}} (\\mathbf {p} )} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum error correction, CSS codes, named after their inventors, Robert Calderbank, Peter Shor and Andrew Steane, are a special type of stabilizer code constructed from classical codes with some special properties. An example of a CSS code is the Steane code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is exactly analogous to G\u00fcntsch's system, designed as a means to improve performance, rather than to solve the problems involved in multi-programming. The first true virtual memory system was that implemented at the University of Manchester to create a one-level storage system as part of the Atlas Computer. It used a paging mechanism to map the virtual addresses available to the programmer onto the real memory that consisted of 16,384 words of primary core memory with an additional 98,304 words of secondary drum memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The codeword for that symbol is the string of \"0\"s and \"1\"s that records which half of the divides it fell on. This method was proposed in a later (in print) technical report by Fano (1949).Shannon\u2013Fano codes are suboptimal in the sense that they do not always achieve the lowest possible expected codeword length, as Huffman coding does. However, Shannon\u2013Fano codes have an expected codeword length within 1 bit of optimal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to interpret the credible sets as confidence sets, a Bernstein\u2013von Mises theorem is needed. In case of the Dirichlet process we compare the posterior distribution with the empirical process P n = 1 n \u2211 i = 1 n \u03b4 X i {\\displaystyle \\mathbb {P} _{n}={\\frac {1}{n}}\\sum _{i=1}^{n}\\delta _{X_{i}}} . Suppose F {\\displaystyle {\\mathcal {F}}} is a P 0 {\\displaystyle P_{0}} -Donsker class, i.e. ( n ) ( P n \u2212 P 0 ) \u21dd G P 0 {\\displaystyle {\\begin{aligned}{\\sqrt {(}}n)\\left(\\mathbb {P} _{n}-P_{0}\\right)\\rightsquigarrow G_{P_{0}}\\end{aligned}}} for some Brownian Bridge G P 0 {\\displaystyle G_{P_{0}}} . Suppose also that there exists a function F {\\displaystyle F} such that F ( x ) \u2265 sup f \u2208 F f ( x ) {\\displaystyle F(x)\\geq \\sup _{f\\in {\\mathcal {F}}}f(x)} such that \u222b F 2 d H < \u221e {\\displaystyle \\int F^{2}\\mathrm {d} H<\\infty } , then, P 0 {\\displaystyle P_{0}} almost surely n ( P \u2212 P n ) | X 1 , \u22ef , X n \u21dd G P 0 . {\\displaystyle {\\sqrt {n}}\\left(P-\\mathbb {P} _{n}\\right)|X_{1},\\cdots ,X_{n}\\rightsquigarrow G_{P_{0}}.} This implies that credible sets you construct are asymptotic confidence sets, and the Bayesian inference based on the Dirichlet process is asymptotically also valid frequentist inference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scholarly and academic publishing, scientific and non-fiction books that are released serially (in successive parts) once a year, or less often, are also called a series. (Publications that are released more often than once a year are known as periodicals.) The connection among books belonging to such a series can be by discipline, focus, approach, type of work, or geographic location. Examples of such series include the \"Antwerp Working Papers in Linguistics\", \"Early English Manuscripts in Facsimile\", \"Garland Reference Library\", \"Canterbury Tales Project\", \"Early English Text Society\", and \"Cambridge Companions to Music\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If this is done, the data can be shuffled for each pass to prevent cycles. Typical implementations may use an adaptive learning rate so that the algorithm converges.In pseudocode, stochastic gradient descent can be presented as: A compromise between computing the true gradient and the gradient at a single sample is to compute the gradient against more than one training sample (called a \"mini-batch\") at each step. This can perform significantly better than \"true\" stochastic gradient descent described, because the code can make use of vectorization libraries rather than computing each step separately as was first shown in where it was called \"the bunch-mode back-propagation algorithm\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, proof compression by RecycleUnits is a method for compressing propositional logic resolution proofs. Its main idea is to make use of intermediate (e.g. non input) proof results being unit clauses, i.e. clauses containing only one literal. Certain proof nodes can be replaced with the nodes representing these unit clauses. After this operation the obtained graph is transformed into a valid proof. The output proof is shorter than the original while being equivalent or stronger.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plant anatomy, tissues are categorized broadly into three tissue systems: the epidermis, the ground tissue, and the vascular tissue. Epidermis \u2013 Cells forming the outer surface of the leaves and of the young plant body. Vascular tissue \u2013 The primary components of vascular tissue are the xylem and phloem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hardy\u2013Ramanujan theorem, proved by Ramanujan and checked by Hardy states that the normal order of the number \u03c9(n) of distinct prime factors of a number n is log(log(n)). Roughly speaking, this means that most numbers have about this number of distinct prime factors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle (n,m)\\in \\times \\,.} This defines a permutation on the numbers a = 0 , \u2026 , M N \u2212 1 {\\displaystyle a=0,\\ldots ,MN-1} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Addresses in the process VAS are mapped to bytes in the exe file. The OS manages the mapping: 0 4 GiB VAS |---vvv----------------------------------------| mapping ||| file bytes app The v's are values from bytes in the mapped file. Then, required DLL files are mapped (this includes custom libraries as well as system ones such as kernel32.dll and user32.dll): 0 4 GiB VAS |---vvv--------vvvvvv---vvvv-------------------| mapping ||| |||||| |||| file bytes app kernel user The process then starts executing bytes in the EXE file.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are similar arguments for a Sanskrit substrate, a Greek one, and a substrate underlying the Sami languages. Relatively clear examples are the Finno-Ugric languages of the Chude and the \"Volga Finns\" (Merya, Muromian, and Meshcheran): while unattested, their existence has been noted in medieval chronicles, and one or more of them have left substantial influence in the Northern Russian dialects. By contrast more contentious cases are the Vasconic substratum theory and Old European hydronymy, which hypothesize large families of substrate languages across western Europe.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Early batch systems gave the currently running job the entire computer; program decks and tapes had to include what we would now think of as operating system code to talk to I/O devices and do whatever other housekeeping was needed. Midway through the batch period, after 1957, various groups began to experiment with so-called \"load-and-go\" systems. These used a monitor program which was always resident on the computer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the Markov\u2013Krein theorem gives the best upper and lower bounds on the expected values of certain functions of a random variable where only the first moments of the random variable are known. The result is named after Andrey Markov and Mark Krein.The theorem can be used to bound average response times in the M/G/k queueing system. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages\u2014particularly, those without garbage collection\u2014the Treiber stack can be at risk for the ABA problem. When a process is about to remove an element from the stack (just before the compare and set in the pop routine below) another process can change the stack such that the head is the same, but the second element is different. The compare and swap will set the head of the stack to the old second element in the stack mixing up the complete data structure. However, the Java version on this page is not subject to this problem, because of the stronger guarantees offered by the Java runtime (it is impossible for a newly created, unaliased object reference to be reference-equal to any other reachable object.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In an 8-bit code, this allowed the entire range from 0xA0 to 0xFF to be used for graphical characters. Use of 96-code sets also meant that the meaning of the bytes 0x20 and 0x7F in the corresponding 7-bit code could differ from \"Space\" and \"Delete\", unless the code was in the Shift In state. Using 96-code sets for the G0 (Shift In) set was not made possible.In accordance with this revised 8-bit ISO 2022 code structure, ISO 8859 defines sets of characters to be encoded over 0xA0\u2013FF, in combination with the ASCII graphical characters over 0x20\u20137E, and reserves the bytes outside of these ranges for use as non-graphical codes by other specifications such as ISO/IEC 6429. Unicode inherits its first 256 code points from ISO 8859-1, hence also incorporating a range reserved for a C1 control code set, although it mostly leaves their function to be defined by higher level protocols, with ISO/IEC 6429 suggested as a default.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If P ~ {\\displaystyle {\\tilde {P}}} is never lucky, then V will reject at phase k+1. Since we have now shown that both IP \u2286 PSPACE and PSPACE \u2286 IP, we can conclude that IP = PSPACE as desired. Moreover, we have shown that any IP algorithm may be taken to be public-coin, since the reduction from PSPACE to IP has this property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and more particularly in number theory, primorial, denoted by \"#\", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers. The name \"primorial\", coined by Harvey Dubner, draws an analogy to primes similar to the way the name \"factorial\" relates to factors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The integers 7 and 10 are coprime, and \u03c6 ( 10 ) = 4 {\\displaystyle \\varphi (10)=4} . So Euler's theorem yields 7 4 \u2261 1 ( mod 10 ) {\\displaystyle 7^{4}\\equiv 1{\\pmod {10}}} , and we get 7 222 \u2261 7 4 \u00d7 55 + 2 \u2261 ( 7 4 ) 55 \u00d7 7 2 \u2261 1 55 \u00d7 7 2 \u2261 49 \u2261 9 ( mod 10 ) {\\displaystyle 7^{222}\\equiv 7^{4\\times 55+2}\\equiv (7^{4})^{55}\\times 7^{2}\\equiv 1^{55}\\times 7^{2}\\equiv 49\\equiv 9{\\pmod {10}}} . In general, when reducing a power of a {\\displaystyle a} modulo n {\\displaystyle n} (where a {\\displaystyle a} and n {\\displaystyle n} are coprime), one needs to work modulo \u03c6 ( n ) {\\displaystyle \\varphi (n)} in the exponent of a {\\displaystyle a}: if x \u2261 y ( mod \u03c6 ( n ) ) {\\displaystyle x\\equiv y{\\pmod {\\varphi (n)}}} , then a x \u2261 a y ( mod n ) {\\displaystyle a^{x}\\equiv a^{y}{\\pmod {n}}} .Euler's theorem underlies the RSA cryptosystem, which is widely used in Internet communications. In this cryptosystem, Euler's theorem is used with n being a product of two large prime numbers, and the security of the system is based on the difficulty of factoring such an integer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern computers, binary data refers to any data represented in binary form rather than interpreted on a higher level or converted into some other form. At the lowest level, bits are stored in a bistable device such as a flip-flop. While most binary data has symbolic meaning (except for don't cares) not all binary data is numeric.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Before System/360, each computer model often had its own specific devices and programs that could not be used with other systems. Buying a bigger CPU also meant buying new printers, card readers, tape drives, etc. In addition, customers would have to rewrite their programs to run on the new CPU, something customers often balked at. With the S/360, IBM wanted to offer a huge range of computer systems, all sharing a single processor architecture, instruction set, I/O interface, and operating system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "5 of the 9 symbols got erased by the channel. The decoder is still able to reconstruct the message, i.e. the whole puzzle. Note that the symbols sent over the channel are not binary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It starts with a peripheral node and then generates levels R i {\\displaystyle R_{i}} for i = 1 , 2 , . . {\\displaystyle i=1,2,..} until all nodes are exhausted. The set R i + 1 {\\displaystyle R_{i+1}} is created from set R i {\\displaystyle R_{i}} by listing all vertices adjacent to all nodes in R i {\\displaystyle R_{i}} . These nodes are ordered according to predecessors and degree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since the 1970s, the subject has been shaped decisively by Saharon Shelah's stability theory. Compared to other areas of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit to classical mathematics. This has prompted the comment that \"if proof theory is about the sacred, then model theory is about the profane\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, such as the evaporation of spherical liquid droplets in air, the following correlation is used: N u D = 2 + 0.4 R e D 1 / 2 P r 1 / 3 {\\displaystyle \\mathrm {Nu} _{D}\\ ={2}+0.4\\,\\mathrm {Re} _{D}^{1/2}\\,\\mathrm {Pr} ^{1/3}\\,}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This had been solved earlier by Monroe Donsker and Srinivasa Varadhan using a probabilistic path integral method. In another work with Herm Brascamp in 1976, Lieb extended the Pr\u00e9kopa-Leindler inequality to other types of convex combinations of two positive functions. He strengthened the inequality and the Brunn-Minkowski inequality by introducing the notion of essential addition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model theory, a branch of mathematical logic, the \u0141o\u015b\u2013Vaught test is a criterion for a theory to be complete, unable to be augmented without becoming inconsistent. For theories in classical logic, this means that for every sentence, the theory contains either the sentence or its negation but not both.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "According to Music Week the song sold a total of 30,830 equivalent units, placing it at number four on the UK Singles Downloads Chart, and number 28 on the Official Audio Streaming Chart. It had sharp drops down the chart and was present in the top 100 for just six weeks. In France, the track debuted at number one on the French Singles Chart.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Diplomatic sources include charters and other legal documents which usually follow a set format. Social documents are records created by organizations, such as registers of births and tax records.In historiography, when the study of history is subject to historical scrutiny, a secondary source becomes a primary source. For a biography of a historian, that historian's publications would be primary sources.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the final analytical step the team discusses its results with management to confirm (or refute) assumptions, provide missing information, reveal deficiencies in the organization and establish future priorities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some games, extra limitations are added; for instance: The associations between words must be strictly obvious, rather than the usual \"first word that comes to mind\", which can often require explaining to see how it is connected with the previous word. If played in-person, a time limit of two or three seconds can be placed to make a very fast-paced game, often combined with the previous rule of an 'explicit' connection, and extra emphasis on the idea that a previously used word cannot be repeated. Word Disassociation (sometimes called Dissociation) is sometimes played. In this game, the aim is to say a word that is as unrelated as possible to the previous one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A client may then receive a \"Level 2 OpLock\" from the server. A Level 2 OpLock allows the caching of read requests but excludes write caching. Filter OpLocks Added in Windows NT 4.0, Filter Oplocks are similar to Level 2 OpLocks but prevent sharing-mode violations between file open and lock reception.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the gradient of the least-squares regression best-fitting line for a given sample of data may be written as: m = r s y s x {\\displaystyle m={\\frac {rs_{y}}{s_{x}}}} ,This quantity m is called as the regression slope for the line y = m x + c {\\displaystyle y=mx+c} . The quantity r {\\displaystyle r} is Pearson's correlation coefficient, s y {\\displaystyle s_{y}} is the standard deviation of the y-values and s x {\\displaystyle s_{x}} is the standard deviation of the x-values. This may also be written as a ratio of covariances: m = cov \u2061 ( Y , X ) cov \u2061 ( X , X ) {\\displaystyle m={\\frac {\\operatorname {cov} (Y,X)}{\\operatorname {cov} (X,X)}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In contrast to quantum key distribution where unconditional security can be achieved based only on the laws of quantum physics, in the case of various tasks in mistrustful cryptography there are no-go theorems showing that it is impossible to achieve unconditionally secure protocols based only on the laws of quantum physics. However, some of these tasks can be implemented with unconditional security if the protocols not only exploit quantum mechanics but also special relativity. For example, unconditionally secure quantum bit commitment was shown impossible by Mayers and by Lo and Chau.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The stack must be depth shallow enough for the CPU's available copy instructions. Hand-written stack code often uses this approach, and achieves speeds like general-purpose register machines. Unfortunately, algorithms for optimal \"stack scheduling\" are not in wide use by programming languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a preradical is a subfunctor of the identity functor in the category of left modules over a ring with identity. The class of all preradicals over R-mod is denoted by R-pr. There is a natural order in R-pr given by, for any two preradicals \u03c3 {\\displaystyle \\sigma } and \u03c4 {\\displaystyle \\tau } , \u03c3 \u2264 \u03c4 {\\displaystyle \\sigma \\leq \\tau } , if for any left R-module M, \u03c3 M \u2264 \u03c4 M {\\displaystyle \\sigma M\\leq \\tau M} . With this order R-pr becomes a big lattice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to access a record with key c {\\displaystyle c} , a family of hash functions, called collectively a dynamic hash function is applied to the key c {\\displaystyle c} . At any time, at most two hash functions h i {\\displaystyle h_{i}} and h i + 1 {\\displaystyle h_{i+1}} are used. A typical example uses the division modulo x operation. If the original number of buckets is N {\\displaystyle N} , then the family of hash functions is h i ( c ) \u21a6 c ( mod N \u22c5 2 i ) {\\displaystyle h_{i}(c)\\mapsto c{\\pmod {N\\cdot 2^{i}}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One attempt by Germain to prove Fermat\u2019s Last Theorem was to let p be a prime number of the form 8k + 7 and to let n = p \u2013 1. In this case, x n + y n = z n {\\displaystyle x^{n}+y^{n}=z^{n}} is unsolvable. Germain\u2019s proof, however, remained unfinished.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Furthermore, insofar as it would be featureless, it could neither be encountered by the senses, nor could its supposition lend additional explanatory power. Hero of Alexandria challenged the theory in the first century AD, but his attempts to create an artificial vacuum failed. The theory was debated in the context of 17th-century fluid mechanics, by Thomas Hobbes and Robert Boyle, among others, and through the early 18th century by Sir Isaac Newton and Gottfried Leibniz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "( x x ) {\\displaystyle \\lambda x.\\! (x\\;x)} can be assigned the type ( ( \u03b1 \u2192 \u03b2 ) \u2229 \u03b1 ) \u2192 \u03b2 {\\displaystyle ((\\alpha \\to \\beta )\\cap \\alpha )\\to \\beta } in most intersection type systems, assuming for the term variable x {\\displaystyle x} both the function type \u03b1 \u2192 \u03b2 {\\displaystyle \\alpha \\to \\beta } and the corresponding argument type \u03b1 {\\displaystyle \\alpha } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and more particularly in set theory, a cover (or covering) of a set X {\\displaystyle X} is a family of subsets of X {\\displaystyle X} whose union is all of X {\\displaystyle X} . More formally, if C = { U \u03b1: \u03b1 \u2208 A } {\\displaystyle C=\\lbrace U_{\\alpha }:\\alpha \\in A\\rbrace } is an indexed family of subsets U \u03b1 \u2282 X {\\displaystyle U_{\\alpha }\\subset X} (indexed by the set A {\\displaystyle A} ), then C {\\displaystyle C} is a cover of X {\\displaystyle X} if \u22c3 \u03b1 \u2208 A U \u03b1 = X {\\displaystyle \\bigcup _{\\alpha \\in A}U_{\\alpha }=X} . Thus the collection { U \u03b1: \u03b1 \u2208 A } {\\displaystyle \\lbrace U_{\\alpha }:\\alpha \\in A\\rbrace } is a cover of X {\\displaystyle X} if each element of X {\\displaystyle X} belongs to at least one of the subsets U \u03b1 {\\displaystyle U_{\\alpha }} . A subcover of a cover of a set is a subset of the cover that also covers the set. A cover is called an open cover if each of its elements is an open set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The conditions of additivity and homogeneity are often combined in the superposition principle f ( \u03b1 x + \u03b2 y ) = \u03b1 f ( x ) + \u03b2 f ( y ) {\\displaystyle f(\\alpha x+\\beta y)=\\alpha f(x)+\\beta f(y)} An equation written as f ( x ) = C {\\displaystyle f(x)=C} is called linear if f ( x ) {\\displaystyle f(x)} is a linear map (as defined above) and nonlinear otherwise. The equation is called homogeneous if C = 0 {\\displaystyle C=0} and f ( x ) {\\displaystyle f(x)} is a homogeneous function. The definition f ( x ) = C {\\displaystyle f(x)=C} is very general in that x {\\displaystyle x} can be any sensible mathematical object (number, vector, function, etc.), and the function f ( x ) {\\displaystyle f(x)} can literally be any mapping, including integration or differentiation with associated constraints (such as boundary values). If f ( x ) {\\displaystyle f(x)} contains differentiation with respect to x {\\displaystyle x} , the result will be a differential equation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are guidelines for notification depending on type; these types include: mail, phone, facsimile, e-mail, media. Instructions and mechanics are information provided to the consumer regarding appropriate action for the recall. The instructions include if the product is to be returned, and if so, where and how they should return the product. It is important to consider the recalled drug\u2019s place in the market, should the recall lead to market shortages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Resource productivity of the EU is expressed by the amount of gross domestic product (GDP) generated per unit of material consumed (Domestic Material Consumption, see below), in other words GDP / DMC in euro per kg. This means that less material was consumed in order to produce the same amount of products in the EU. However, breaking down the components of the index it is seen that both GDP and DMC are increasing, only not equally fast.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Typically, multidimensional signal processing is directly associated with digital signal processing because its complexity warrants the use of computer modelling and computation. A multidimensional signal is similar to a single dimensional signal as far as manipulations that can be performed, such as sampling, Fourier analysis, and filtering. The actual computations of these manipulations grow with the number of dimensions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, from 64 bits in the page table entry, 12 low-order and 12 high-order bits have other uses, leaving 40 bits (bits 12 though 51) for the physical page number. Combined with 12 bits of \"offset within page\" from the linear address, a maximum of 52 bits are available to address physical memory. This allows a maximum RAM configuration of 252 bytes, or 4 petabytes (about 4.5\u00d71015 bytes).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where two objects are traveling in parallel directions, the relativistic formula for relative velocity is similar in form to the formula for addition of relativistic velocities. v \u2192 B | A = v \u2192 B \u2212 v \u2192 A 1 \u2212 v \u2192 A v \u2192 B c 2 {\\displaystyle {\\vec {v}}_{\\mathrm {B|A} }={\\frac {{\\vec {v}}_{\\mathrm {B} }-{\\vec {v}}_{\\mathrm {A} }}{1-{\\frac {{\\vec {v}}_{\\mathrm {A} }{\\vec {v}}_{\\mathrm {B} }}{c^{2}}}}}} The relative speed is given by the formula: v B | A = | v \u2192 B \u2212 v \u2192 A | 1 \u2212 v \u2192 A v \u2192 B c 2 {\\displaystyle v_{\\mathrm {B|A} }={\\frac {\\left|{\\vec {v}}_{\\mathrm {B} }-{\\vec {v}}_{\\mathrm {A} }\\right|}{1-{\\frac {{\\vec {v}}_{\\mathrm {A} }{\\vec {v}}_{\\mathrm {B} }}{c^{2}}}}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Even though the units are initially chosen with known probabilities, the nonresponse mechanisms are unknown. For surveys with substantial nonresponse, statisticians have proposed statistical models with which the data sets are analyzed. Issues related to survey sampling are discussed in several sources, including Salant and Dillman (1994).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is possible to use segmentation in 32-bit protected mode as well (resulting in 48-bit pointers) and there exist C language compilers which support that. However segmentation in 32-bit mode does not allow to access a larger address space than what a single segment would cover, unless some segments are not always present in memory and the linear address space is just used as a cache over a larger segmented virtual space. It allows better protection for access to various objects (areas up to 1 MB long can benefit from a one-byte access protection granularity, versus the coarse 4 KiB granularity offered by sole paging), and is therefore only used in specialized applications, like telecommunications software. Technically, the \"flat\" 32-bit address space is a \"tiny\" memory model for the segmented address space. Under both reigns all four segment registers contain one and the same value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Prototypical examples of cancellative semigroups are the positive integers under addition or multiplication. Cancellative semigroups are considered to be very close to being groups because cancellability is one of the necessary conditions for a semigroup to be embeddable in a group. Moreover, every finite cancellative semigroup is a group. One of the main problems associated with the study of cancellative semigroups is to determine the necessary and sufficient conditions for embedding a cancellative semigroup in a group. The origins of the study of cancellative semigroups can be traced to the first substantial paper on semigroups, (Suschkewitsch 1928).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical group theory, the Hall\u2013Higman theorem, due to Philip Hall and Graham Higman (1956, Theorem B), describes the possibilities for the minimal polynomial of an element of prime power order for a representation of a p-solvable group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mobile cellular telephony networks like GSM and UMTS the SS7 application MAP is used. Voice connections are Circuit Switched (CS) and data connections are Packet Switched (PS) applications. Some of the GSM/UMTS Circuit Switched interfaces in the Mobile Switching Center (MSC) transported over SS7 include the following: B -> VLR (uses MAP/B). Most MSCs are associated with a Visitor Location Register (VLR), making the B interface \"internal\". C -> HLR (uses MAP/C) Messages between MSC to HLR handled by C Interface D -> HLR (uses MAP/D) for attaching to the CS network and location update E -> MSC (uses MAP/E) for inter-MSC handover F -> EIR (uses MAP/F) for equipment identity check H -> SMS-G (uses MAP/H) for Short Message Service (SMS) over CS I -> ME (uses MAP/I) Messages between MSC to ME handled by I Interface J -> SCF (uses MAP/J) Messages between HLR to gsmSCF handled by J Interface There are also several GSM/UMTS PS interfaces in the Serving GPRS Support Node (SGSN) transported over SS7: Gr -> HLR for attaching to the PS network and location update Gd -> SMS-C for SMS over PS Gs -> MSC for combined CS+PS signaling over PS Ge -> Charging for Customised Applications for Mobile networks Enhanced Logic (CAMEL) prepaid charging Gf -> EIR for equipment identity check == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the cake number, denoted by Cn, is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly n planes. The cake number is so-called because one may imagine each partition of the cube by a plane as a slice made by a knife through a cube-shaped cake. It is the 3D analogue of the lazy caterer's sequence. The values of Cn for n = 0, 1, 2, ... are given by 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, ... (sequence A000125 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following simple stack implementation in Java, each element popped from the stack becomes semantic garbage once there are no outside references to it: This is because elements still contains a reference to the object, but the object will never be accessed again through this reference, because elements is private to the class and the pop method only returns references to elements it has not already popped. (After it decrements size, this class will never access that element again.) However, knowing this requires analysis of the code of the class, which is undecidable in general. If a later push call re-grows the stack to the previous size, overwriting this last reference, then the object will become syntactic garbage, because it can never be accessed again, and will be eligible for garbage collection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to acquire the world's demand for wood, it is suggested that high yielding forest plantations are suitable according to forest writers Botkins and Sedjo. Plantations that yield 10 cubic meters per hectare a year would supply enough wood for trading of 5% of the world's existing forestland. By contrast, natural forests produce about 1\u20132 cubic meters per hectare; therefore, 5\u201310 times more forestland would be required to meet demand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1, 2, ..., n} then Sym(M) is usually denoted by Sn, and may be called the symmetric group on n letters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Coset enumeration is usually considered to be one of the fundamental problems in computational group theory. The original algorithm for coset enumeration was invented by John Arthur Todd and H. S. M. Coxeter. Various improvements to the original Todd\u2013Coxeter algorithm have been suggested, notably the classical strategies of V. Felsch and HLT (Haselgrove, Leech and Trotter).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof by contradiction, also known by the Latin phrase reductio ad absurdum (by reduction to the absurd), it is shown that if some statement is assumed true, a logical contradiction occurs, hence the statement must be false. A famous example involves the proof that 2 {\\displaystyle {\\sqrt {2}}} is an irrational number: Suppose that 2 {\\displaystyle {\\sqrt {2}}} were a rational number. Then it could be written in lowest terms as 2 = a b {\\displaystyle {\\sqrt {2}}={a \\over b}} where a and b are non-zero integers with no common factor. Thus, b 2 = a {\\displaystyle b{\\sqrt {2}}=a} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to address the issues presented by memorization and security many businesses and internet sites have turned to accepting different types of authentication. This authentication could be a single use password, non-text based, Biometric, a 2D key, multi-factor authentication, or Cognitive Passwords that are question based. Many of these options are more expensive, time consuming or still require some form of memorization. Thus, most businesses and individuals still use the common format of single word and text-based passwords as security protection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In specifying a regular expression, alternate delimiters may also be used to simplify the syntax for match and substitution operations in Perl.For example, a simple match operation may be specified in Perl with the following syntax: The syntax is flexible enough to specify match operations with alternate delimiters, making it easy to avoid delimiter collision:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Cello, another early browser, also had bookmarking features. With the advent of social bookmarking, shared bookmarks have become a means for users sharing similar interests to pool web resources, or to store their bookmarks in such a way that they are not tied to one specific computer or browser. Web-based bookmarking services let users save bookmarks on a remote web server, accessible from anywhere.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In fact, Turing's machine does this\u2014it prints on alternate squares, leaving blanks between figures so it can print locator symbols. Turing always left alternate squares blank so his machine could place a symbol to the left of a figure (or a letter if the machine is the universal machine and the scanned square is actually in the \u201cprogram\u201d). In our little example we will forego this and just put symbols ( ) around the scanned symbol, as follows: Let us write a simple program: start: P1, R, P1, R, P1, H Remember that we always start with blank tape.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "itself. This check can be restricted to seeds involved by s, i.e. this drawback can be avoided by requiring that the distribution of { Z 1 , \u2026 , Z m | S = s } {\\displaystyle \\{Z_{1},\\ldots ,Z_{m}|S=s\\}} is independent of ?. An easy way to check this property is by mapping seed specifications into x i {\\displaystyle x_{i}} s specifications. The mapping of course depends on ?, but the distribution of { X 1 , \u2026 , X m | S = s } {\\displaystyle \\{X_{1},\\ldots ,X_{m}|S=s\\}} will not depend on ?, if the above seed independence holds \u2013 a condition that looks like a local sufficiency of the statistic S.The remainder of the present article is mainly concerned with the context of data mining procedures applied to statistical inference and, in particular, to the group of computationally intensive procedure that have been called algorithmic inference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, R ( x ) {\\displaystyle R({\\textbf {x}})} may be one or more linear combinations of x {\\displaystyle {\\textbf {x}}} . A dimension reduction R ( x ) {\\displaystyle R({\\textbf {x}})} is said to be sufficient if the distribution of y \u2223 R ( x ) {\\displaystyle y\\mid R({\\textbf {x}})} is the same as that of y \u2223 x {\\displaystyle y\\mid {\\textbf {x}}} . In other words, no information about the regression is lost in reducing the dimension of x {\\displaystyle {\\textbf {x}}} if the reduction is sufficient.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one dimension, generalized balanced ternary is equivalent to standard balanced ternary, with three digits (0, 1, and -1). B {\\displaystyle B} is a 1 \u00d7 1 {\\displaystyle 1\\times 1} matrix, and the digits D i {\\displaystyle D_{i}} are length-1 vectors, so they appear here without the extra brackets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface\u2014the smaller the differences, the better the model fits the data. The resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At this point, the above equation looks like this: ln \u2061 ( \u220f k \u2208 K \u2282 Z 0 + 1 + 2 \u2212 k ) = \u2211 k \u2208 K \u2282 Z 0 + ln \u2061 ( 1 + 2 \u2212 k ) {\\displaystyle \\ln \\left(\\prod _{k\\in K\\subset \\mathbb {Z} _{0}^{+}}1+2^{-k}\\right)=\\sum _{k\\in K\\subset \\mathbb {Z} _{0}^{+}}\\ln(1+2^{-k})} This choice of a k {\\displaystyle a_{k}} reduces the computational complexity of the product from repeated multiplication to simple addition and bit-shifting depending on the implementation. Finally, by storing the values ln \u2061 ( 1 + 2 \u2212 k ) {\\displaystyle \\ln(1+2^{-k})} in a table, calculating the solution is also a simple matter of addition. Iteratively, this gives us two separate sequences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an information source is a sequence of random variables ranging over a finite alphabet \u0393, having a stationary distribution. The uncertainty, or entropy rate, of an information source is defined as H { X } = lim n \u2192 \u221e H ( X n | X 0 , X 1 , \u2026 , X n \u2212 1 ) {\\displaystyle H\\{\\mathbf {X} \\}=\\lim _{n\\to \\infty }H(X_{n}|X_{0},X_{1},\\dots ,X_{n-1})} where X 0 , X 1 , \u2026 , X n {\\displaystyle X_{0},X_{1},\\dots ,X_{n}} is the sequence of random variables defining the information source, and H ( X n | X 0 , X 1 , \u2026 , X n \u2212 1 ) {\\displaystyle H(X_{n}|X_{0},X_{1},\\dots ,X_{n-1})} is the conditional information entropy of the sequence of random variables. Equivalently, one has H { X } = lim n \u2192 \u221e H ( X 0 , X 1 , \u2026 , X n \u2212 1 , X n ) n + 1 . {\\displaystyle H\\{\\mathbf {X} \\}=\\lim _{n\\to \\infty }{\\frac {H(X_{0},X_{1},\\dots ,X_{n-1},X_{n})}{n+1}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For a hyperedge E \u2208 E {\\displaystyle E\\in {\\mathcal {E}}} , set \u03c7 ( E ) := \u2211 v \u2208 E \u03c7 ( v ) . {\\displaystyle \\chi (E):=\\sum _{v\\in E}\\chi (v).} The discrepancy of H {\\displaystyle {\\mathcal {H}}} with respect to \u03c7 {\\displaystyle \\chi } and the discrepancy of H {\\displaystyle {\\mathcal {H}}} are defined by disc \u2061 ( H , \u03c7 ) := max E \u2208 E | \u03c7 ( E ) | , {\\displaystyle \\operatorname {disc} ({\\mathcal {H}},\\chi ):=\\;\\max _{E\\in {\\mathcal {E}}}|\\chi (E)|,} disc \u2061 ( H ) := min \u03c7: V \u2192 { \u2212 1 , + 1 } disc \u2061 ( H , \u03c7 ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With this strategy, if A ranks ahead of B and C (which compare equal) which are both ranked ahead of D, then A gets ranking number 1 (\"first\") and D gets ranking number 4 (\"fourth\"), and either B gets ranking number 2 (\"second\") and C gets ranking number 3 (\"third\") or C gets ranking number 2 (\"second\") and B gets ranking number 3 (\"third\"). In computer data processing, ordinal ranking is also referred to as \"row numbering\". This method corresponds to the \"first\", \"last\", and \"random\" methods in the R programming language to handle ties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "MIPS cores can be found in newer Cisco, Linksys and Mikrotik's routerboard routers, cable modems and asymmetric digital subscriber line (ADSL) modems, smartcards, laser printer engines, set-top boxes, robots, and hand-held computers. In cellphones and PDAs, MIPS has been largely unable to displace the incumbent, competing ARM architecture. MIPS architecture processors include: IDT RC32438; ATI/AMD Xilleon; Alchemy Au1000, 1100, 1200; Broadcom Sentry5; RMI XLR7xx, Cavium Octeon CN30xx, CN31xx, CN36xx, CN38xx and CN5xxx; Infineon Technologies EasyPort, Amazon, Danube, ADM5120, WildPass, INCA-IP, INCA-IP2; Microchip Technology PIC32; NEC EMMA and EMMA2, NEC VR4181A, VR4121, VR4122, VR4181A, VR4300, VR5432, VR5500; Oak Technologies Generation; PMC-Sierra RM11200; QuickLogic QuickMIPS ESP; Toshiba Donau, Toshiba TMPR492x, TX4925, TX9956, TX7901; KOMDIV-32, KOMDIV-64, ELVEES Multicore from Russia.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a paired disparity code is a line code in which at least one of the data characters is represented by two codewords of opposite disparity that are used in sequence so as to minimize the total disparity of a longer sequence of digits. A particular codeword of any line code can either have no disparity (the average weight of the codeword is zero), negative disparity (the average weight of the codeword is negative), or positive disparity (the average weight of the codeword is positive). In a paired disparity code, every codeword that averages to a negative level (negative disparity) is paired with some other codeword that averages to a positive level (positive disparity). In a system that uses a paired disparity code, the transmitter must keep track of the running DC buildup \u2013 the running disparity \u2013 and always pick the codeword that pushes the DC level back towards zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. Combinatorial explosion is sometimes used to justify the intractability of certain problems. Examples of such problems include certain mathematical functions, the analysis of some puzzles and games, and some pathological examples which can be modelled as the Ackermann function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern computing practice, Unicode is the standard and default method for character encoding. However, Unicode itself and many legacy applications have echoes of earlier practices. Furthermore, the limited character set provided by computer keyboards has also required practical and pragmatic adjustments. These issues are detailed below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Also P ( R n \u2223 W ) {\\displaystyle P(R_{n}\\mid W)} is the probability that player 1 experiences gambler's ruin having started with n + 1 {\\displaystyle n+1} amount of money: P ( R n + 1 ) {\\displaystyle P(R_{n+1})} ; and P ( R n \u2223 W \u00af ) {\\displaystyle P(R_{n}\\mid {\\bar {W}})} is the probability that player 1 experiences gambler's ruin having started with n \u2212 1 {\\displaystyle n-1} amount of money: P ( R n \u2212 1 ) {\\displaystyle P(R_{n-1})} . Denoting q n = P ( R n ) {\\displaystyle q_{n}=P(R_{n})} , we get the linear homogeneous recurrence relation q n = q n + 1 p + q n \u2212 1 q , {\\displaystyle q_{n}=q_{n+1}p+q_{n-1}q,} which we can solve using the fact that q 0 = 1 {\\displaystyle q_{0}=1} (i.e. the probability of gambler's ruin given that player 1 starts with no money is 1), and q n 1 + n 2 = 0 {\\displaystyle q_{n_{1}+n_{2}}=0} (i.e. the probability of gambler's ruin given that player 1 starts with all the money is 0.) For a more detailed description of the method see e.g. Feller (1970), An introduction to probability theory and its applications, 3rd ed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of the LF logical framework, the meta-language is the \u03bb\u03a0-calculus. This is a system of first-order dependent function types which are related by the propositions as types principle to first-order minimal logic. The key features of the \u03bb\u03a0-calculus are that it consists of entities of three levels: objects, types and kinds (or type classes, or families of types). It is predicative, all well-typed terms are strongly normalizing and Church-Rosser and the property of being well-typed is decidable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777\u20131855).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A move defines endpoints for a data transport taking place in a transport bus. For instance, a move can state that a data transport from function unit F, port 1, to register file R, register index 2, should take place in bus B1. In case there are multiple buses in the target processor, each bus can be utilized in parallel in the same clock cycle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In technical terms, palatalization refers to the secondary articulation of consonants by which the body of the tongue is raised toward the hard palate and the alveolar ridge during the articulation of the consonant. Such consonants are phonetically palatalized. \"Pure\" palatalization is a modification to the articulation of a consonant, where the middle of the tongue is raised, and nothing else. It may produce a laminal articulation of otherwise apical consonants such as /t/ and /s/.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most applications of protocol spoofing, a communications device such as a modem or router simulates (\"spoofs\") the remote endpoint of a connection to a locally attached host, while using a more appropriate protocol to communicate with a compatible remote device that performs the equivalent spoof at the other end of the communications link.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This specification is long, however 2 key points relating to the tree structure of an XML document are: The begin, end, and empty-element tags that delimit the elements are correctly nested, with none missing and none overlapping A single \"root\" element contains all the other elementsThese features resemble those of trees, in that there is a single root node, and an order to the elements. XML has appeared as a first-class data type in other languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When thus organized, residuated lattices form an equational class or variety, whose homomorphisms respect the residuals as well as the lattice and monoid operations. Note that distributivity x\u2022(y \u2228 z) = (x\u2022y) \u2228 (x\u2022z) and x\u20220 = 0 are consequences of these axioms and so do not need to be made part of the definition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sequence modeling, the graph of interest is usually a chain graph. An input sequence of observed variables X {\\displaystyle X} represents a sequence of observations and Y {\\displaystyle Y} represents a hidden (or unknown) state variable that needs to be inferred given the observations. The Y i {\\displaystyle Y_{i}} are structured to form a chain, with an edge between each Y i \u2212 1 {\\displaystyle Y_{i-1}} and Y i {\\displaystyle Y_{i}} . As well as having a simple interpretation of the Y i {\\displaystyle Y_{i}} as \"labels\" for each element in the input sequence, this layout admits efficient algorithms for: model training, learning the conditional distributions between the Y i {\\displaystyle Y_{i}} and feature functions from some corpus of training data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, bridge weight limits for trucks and other heavy vehicles may be expressed in terms of gross vehicle weight or empty weight.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\mu _{R_{0}}^{\\text{g}}(\\mathbf {x} -{\\hat {\\mathbf {x} }}_{j})={\\frac {1}{(2\\pi R_{0}^{2})^{3/2}}}\\,\\exp \\left(-{\\frac {(\\mathbf {x} -{\\hat {\\mathbf {x} }}_{j})^{2}}{2R_{0}^{2}}}\\right).} Choosing one or another distribution \u03bc R 0 ( x \u2212 x ^ j ) {\\displaystyle \\mu _{R_{0}}(\\mathbf {x} -{\\hat {\\mathbf {x} }}_{j})} does not affect significantly the predictions of the model, as long as the same value for R 0 {\\displaystyle R_{0}} is considered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases the iterates converge but do not converge as quickly as promised. In these cases simpler methods converge just as quickly as Newton's method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the calculus of variations and classical mechanics, the Euler\u2013Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange. Because a differentiable functional is stationary at its local extrema, the Euler\u2013Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information, the diamond norm, also known as completely bounded trace norm, is a norm on the space of quantum operations, or more generally on any linear map that acts on complex matrices. Its main application is to measure the \"single use distinguishability\" of two quantum channels. If an agent is randomly given one of two quantum channels, permitted to pass one state through the unknown channel, and then measures the state in an attempt to determine which operation they were given, then their maximal probability of success is determined by the diamond norm of the difference of the two channels. Although the diamond norm can be efficiently computed via semidefinite programming, it is in general difficult to obtain analytical expressions and those are known only for a few particular cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The base code rate is typically given as n / k {\\displaystyle n/k} , where n is the raw input data rate and k is the data rate of output channel encoded stream. n is less than k because channel coding inserts redundancy in the input bits. The memory is often called the \"constraint length\" K, where the output is a function of the current input as well as the previous K \u2212 1 {\\displaystyle K-1} inputs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "First, it takes up the idea of considering the event giving rise to the right to compensation, starting from the nature of the interest affected. Moreover, there is an astonishing resemblance between the respective formulations: \u00a7 823 paragraph 1 BGB is supposed to protect the integrity of property and persons by granting protection \"to life, body, health, freedom, to property\". Starck, for his part, claims \"a right to life, to bodily integrity and to the material integrity of the objects belonging to us\". Finally, on both sides, it is with the same arguments, such as the need to protect the freedom to act, that a less intense protection of purely economic and moral interests is justified. Nevertheless, Boris Starck departs from the German model by raising the protection of physical integrity by a notch, believing that the only breach here generates a right to compensation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The predicate added to each new test class is the precondition of one of the terms in the operation's predicate. Standard Partitions (SP).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the final step, the linguist checks to see how the proto-phonemes fit the known typological constraints. For example, a hypothetical system, has only one voiced stop, *b, and although it has an alveolar and a velar nasal, *n and *\u014b, there is no corresponding labial nasal. However, languages generally maintain symmetry in their phonemic inventories. In this case, a linguist might attempt to investigate the possibilities that either what was earlier reconstructed as *b is in fact *m or that the *n and *\u014b are in fact *d and *g. Even a symmetrical system can be typologically suspicious.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Zn\u00e1m's problem asks which sets of integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Zn\u00e1m's problem is named after the Slovak mathematician \u0160tefan Zn\u00e1m, who suggested it in 1972, although other mathematicians had considered similar problems around the same time. The initial terms of Sylvester's sequence almost solve this problem, except that the last chosen term equals one plus the product of the others, rather than being a proper divisor. Sun (1983) showed that there is at least one solution to the (proper) Zn\u00e1m problem for each k \u2265 5 {\\displaystyle k\\geq 5} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension. For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical physics, phase transitions can only appear in many particle systems. Though phase transitions are well known in network science, in single networks they are second order only. With the introduction of internetwork dependency, first order transitions emerge. This is a new phenomenon and one with profound implications for systems engineering. Where system dissolution takes place after steady (if steep) degradation for second order transitions, the existence of a first order transition implies that the system can go from a relatively healthy state to complete collapse with no advanced warning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other variations on the concept include being able to listen to the past but not view it. One reason authors may choose to write about time viewers rather than time machines is to circumvent the issue of temporal paradoxes. Recurring applications include studying history, solving crimes, and entertainment in the form of displaying historic events to an audience.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical linear algebra, an incomplete LU factorization (abbreviated as ILU) of a matrix is a sparse approximation of the LU factorization often used as a preconditioner.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consequently, apart from the provisions of this Convention, the extent of protection, as well as the means of redress afforded to the author to protect his rights, shall be governed exclusively by the laws of the country where protection is claimed. \u2014 Berne Convention, article 5(2). This specifies national treatment, and also makes the existence of copyright on a work in one country independent from the existence of copyright on the work in other countries (lex loci protectionis). A WIPO study in 2011 recommended that \u00abThe difficulty of the rule of the comparison of terms applicable to the duration for protection, as provided by Article 7(8) of the Berne Convention, should at least be assessed\u00bb.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Beyond the cardinalities given by each of the natural numbers, there is an infinite hierarchy of infinite cardinalities, although only very few such cardinalities occur in ordinary mathematics (that is, outside set theory that explicitly studies possible cardinalities). Counting, mostly of finite sets, has various applications in mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In representation theory, a branch of mathematics, the Kostant partition function, introduced by Bertram Kostant (1958, 1959), of a root system \u0394 {\\displaystyle \\Delta } is the number of ways one can represent a vector (weight) as a non-negative integer linear combination of the positive roots \u0394 + \u2282 \u0394 {\\displaystyle \\Delta ^{+}\\subset \\Delta } . Kostant used it to rewrite the Weyl character formula as a formula (the Kostant multiplicity formula) for the multiplicity of a weight of an irreducible representation of a semisimple Lie algebra. An alternative formula, that is more computationally efficient in some cases, is Freudenthal's formula. The Kostant partition function can also be defined for Kac\u2013Moody algebras and has similar properties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "0 3 8 1 6 11 4 9 2 7 0 4 8 | 0 4 8 0 4 8 0 4 8 0 4 8 0 3 9 | 0 3 6 9 0 3 6 9 0 3 6 9 0 2 10 | 0 2 4 6 8 10 0 2 4 6 8 10 0 1 11 | 0 1 2 3 4 5 6 7 8 9 10 11 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 Source:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most popular programming languages, source code is delivered and deployed in granules of functionality which we will here call packages; actual terminology for this concept varies between language. Each package may contain multiple type, value, and function definitions, packages are often compiled separately in languages with a compilation step, and a non-cyclical dependency relationship may exist. A complete program is a set of packages, with a main package which may depend on several other packages, and the whole program consisting of the transitive closure of the dependency relationship. The so-called expression problem relates to the ability for code in a depending package to extend behaviors (functions or datatypes) defined in a base package from within an including package, without modifying the source to the base package.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Information on virulence factors can be obtained from the usage of the provided browser tool. Once the browser tool is used, the results are returned as a readable table that is organized by ascending E-Values, each of which are hyperlinked to their related page. MvirDB is implemented in an Oracle 10g relational database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "UWs are intended to represent universal concepts, but are expressed in English words or in any other natural language in order to be humanly readable. They consist of a \"headword\" (the UW root) and a \"constraint list\" (the UW suffix between parentheses), where the constraints are used to disambiguate the general concept conveyed by the headword. The set of UWs is organized in the UNL Ontology, in which high-level concepts are related to lower-level ones through the relations \"icl\" (= is a kind of), \"iof\" (= is an instance of) and \"equ\" (= is equal to).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, optimization (and searching, and learning) problems are often NP-hard, complex, and time-consuming. Two major approaches are traditionally used to tackle these problems: exact methods and metaheuristics. Exact methods allow to find exact solutions but are often impractical as they are extremely time-consuming for real-world problems (large dimension, hardly constrained, multimodal, time-varying, epistatic problems). Conversely, metaheuristics provide sub-optimal (sometimes optimal) solutions in a reasonable time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Forester Chad Oliver has suggested a forest mosaic with high-yield forest lands interspersed with conservation land.Plantation forests cover about 131 million ha, which is 3 percent of the global forest area and 45 percent of the total area of planted forests.Globally, planted forests increased from 4.1% to 7.0% of the total forest area between 1990 and 2015. Plantation forests made up 280 million ha in 2015, an increase of about 40 million ha in the last ten years. Globally, planted forests consist of about 18% exotic or introduced species while the rest are species native to the country where they are planted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A logical system L {\\displaystyle {\\mathcal {L}}} is represented by its signature which assigns kinds and types to a finite set of constants that represents its syntax, its judgements and its rule schemes. An object-logic's rules and proofs are seen as primitive proofs of hypothetico-general judgements \u039b x \u2208 C .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However this theoretical approach was widely considered unattainable, since the Taniyama\u2013Shimura conjecture was itself widely seen as completely inaccessible to proof with current knowledge. For example, Wiles' ex-supervisor John Coates states that it seemed \"impossible to actually prove\", and Ken Ribet considered himself \"one of the vast majority of people who believed  was completely inaccessible\".Hearing of the 1986 proof of the epsilon conjecture, Wiles decided to begin researching exclusively towards a proof of the Taniyama\u2013Shimura conjecture. Ribet later commented that \"Andrew Wiles was probably one of the few people on earth who had the audacity to dream that you can actually go and prove .\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, local carriers have been responsible for distributing telephone numbers to individuals and businesses since AT&T split up into local and long-distance carriers as a result of demonopolization. Orders to change long-distance carriers would be submitted to them, and the local carrier would make the change. In the most common scenario regarding slamming, an employee of a telephone company (usually a telemarketer making outbound calls to prospective clients) would submit an order to change carriers to the local exchange carrier without the approval of the customer. In the United Kingdom, landline telecommunications services were provided exclusively by BT until 1984 when the industry was demonopolized, and the number of independent operators providing fixed-line domestic telephone services increased.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Older operating systems forced upon the programmer a record structure and frequently non-orthogonal data semantics and device control. Unix eliminated this complexity with the concept of a data stream: an ordered sequence of data bytes which can be read until the end of file. A program may also write bytes as desired and need not, and cannot easily declare their count or grouping.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not. For example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up. One example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, a data element definition is a human readable phrase or sentence associated with a data element within a data dictionary that describes the meaning or semantics of a data element. Data element definitions are critical for external users of any data system. Good definitions can dramatically ease the process of mapping one set of data into another set of data. This is a core feature of distributed computing and intelligent agent development. There are several guidelines that should be followed when creating high-quality data element definitions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "C++ is an example of a language that supports both inner classes and inner types (via typedef declarations).Another type is a local class, which is a class defined within a procedure or function. This limits references to the class name to within the scope where the class is declared. Depending on the semantic rules of the language, there may be additional restrictions on local classes compared to non-local ones. One common restriction is to disallow local class methods to access local variables of the enclosing function. For example, in C++, a local class may refer to static variables declared within its enclosing function, but may not access the function's automatic variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function. Factorization systems are a generalization of this situation in category theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the announcement for Shindig's first code commit, four primary features of Shindig were cited: Gadget Container JavaScript\u2014core JavaScript foundation for general gadget functionality. This JavaScript manages security, communication, UI layout, and feature extensions, such as the OpenSocial API. Gadget Server\u2014an open source version of gmodules.com, which is used to render the gadget XML into JavaScript and HTML for the container to expose via the container JavaScript.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most logical systems, one proves a statement of the form \"P iff Q\" by proving either \"if P, then Q\" and \"if Q, then P\", or \"if P, then Q\" and \"if not-P, then not-Q\". Proving these pairs of statements sometimes leads to a more natural proof, since there are not obvious conditions in which one would infer a biconditional directly. An alternative is to prove the disjunction \"(P and Q) or (not-P and not-Q)\", which itself can be inferred directly from either of its disjuncts\u2014that is, because \"iff\" is truth-functional, \"P iff Q\" follows if P and Q have been shown to be both true, or both false.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an extreme point of a convex set S {\\displaystyle S} in a real or complex vector space is a point in S {\\displaystyle S} which does not lie in any open line segment joining two points of S . {\\displaystyle S.} In linear programming problems, an extreme point is also called vertex or corner point of S . {\\displaystyle S.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the design of experiments, consecutive sampling, also known as total enumerative sampling, is a sampling technique in which every subject meeting the criteria of inclusion is selected until the required sample size is achieved. Along with convenience sampling and snowball sampling, consecutive sampling is one of the most commonly used kinds of nonprobability sampling. Consecutive sampling is typically better than convenience sampling in controlling sampling bias.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This process of converting a raw score into a standard score is called standardizing or normalizing (however, \"normalizing\" can refer to many types of ratios; see Normalization for more). Standard scores are most commonly called z-scores; the two terms may be used interchangeably, as they are in this article. Other equivalent terms in use include z-value, z-statistic, normal score, standardized variable and pull in high energy physics.Computing a z-score requires knowledge of the mean and standard deviation of the complete population to which a data point belongs; if one only has a sample of observations from the population, then the analogous computation using the sample mean and sample standard deviation yields the t-statistic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While the probability of \"netshop\" is extremely low, since \"netshop\" isn't currently a compound or phrase in English, and \"sweatshop\" also seems contextually improbable, \"pet shop\" is a good fit because it is a common phrase and is also related to the word \"dog\".Moreover, an utterance can have different meanings depending on how it is split into words. A popular example, often quoted in the field, is the phrase \"How to wreck a nice beach\", which sounds very similar to \"How to recognize speech\". As this example shows, proper lexical segmentation depends on context and semantics which draws on the whole of human knowledge and experience, and would thus require advanced pattern recognition and artificial intelligence technologies to be implemented on a computer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On calculators, it is printed as \"log\", but mathematicians usually mean natural logarithm (logarithm with base e \u2248 2.71828) rather than common logarithm when they write \"log\". To mitigate this ambiguity, the ISO 80000 specification recommends that log10 (x) should be written lg(x), and loge (x) should be ln(x). Before the early 1970s, handheld electronic calculators were not available, and mechanical calculators capable of multiplication were bulky, expensive and not widely available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For a simple hypothesis, \u03b1 = P ( test rejects H 0 \u2223 H 0 ) . {\\displaystyle \\alpha =P({\\text{test rejects }}H_{0}\\mid H_{0}).} In the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as \u03c6 ( n ) {\\displaystyle \\varphi (n)} or \u03d5 ( n ) {\\displaystyle \\phi (n)} , and may also be called Euler's phi function. In other words, it is the number of integers k in the range 1 \u2264 k \u2264 n for which the greatest common divisor gcd(n, k) is equal to 1. The integers k of this form are sometimes referred to as totatives of n. For example, the totatives of n = 9 are the six numbers 1, 2, 4, 5, 7 and 8. They are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, since gcd(9, 3) = gcd(9, 6) = 3 and gcd(9, 9) = 9.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-broadcast multiple-access network(NBMA), neighbor adjacency is formed with unicast packets to remote host. A network may have more than two routers, but is no broadcast support. IP 192.0.2.1 > 192.0.2.2: OSPFv2, hello IP 192.0.2.2 > 192.0.2.1: OSPFv2, hello IP 192.0.2.1 > 192.0.2.2: OSPFv2, database description IP 192.0.2.2 > 192.0.2.1: OSPFv2, database description Types of Non-broadcast networks: X.25 Public data network Wireguard Serial interface Requires all routers to be able to communicate directly, on the same network. Designated Router is elected for the network. LSA is generated for the network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most cases, Java support is unnecessary in Web browsers, and security experts recommend that it not be run in a browser unless absolutely necessary. It was suggested that, if Java is required by a few Web sites, users should have a separate browser installation specifically for those sites.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi systems, LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen as a tool for studying natural deduction in first-order logic (in classical and intuitionistic versions, respectively). Gentzen's so-called \"Main Theorem\" (Hauptsatz) about LK and LJ was the cut-elimination theorem, a result with far-reaching meta-theoretic consequences, including consistency. Gentzen further demonstrated the power and flexibility of this technique a few years later, applying a cut-elimination argument to give a (transfinite) proof of the consistency of Peano arithmetic, in surprising response to G\u00f6del's incompleteness theorems. Since this early work, sequent calculi, also called Gentzen systems, and the general concepts relating to them, have been widely applied in the fields of proof theory, mathematical logic, and automated deduction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They argue that unrestricted use of digital resources can cause an overproduction of redundant data which causes noise and corrupts communication channels within the digital environment. Others argue that the pollution caused by the overuse of digital resources also causes pollution in the physical environment. They argue that unrestricted use of digital resources causes misinformation, fake news, crime, and terrorism, as well as problems of a different nature such as confusion, manipulation, insecurity, and loss of confidence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Under the integrability condition that E \u2016 X \u2016 L 2 2 {\\displaystyle \\mathbb {E} \\|X\\|_{L^{2}}^{2}} is finite, the covariance operator of X {\\displaystyle X} is a linear operator C: H \u2192 H {\\displaystyle {\\mathcal {C}}:H\\to H} that is uniquely defined by the relation C h = E  , h \u2208 H , {\\displaystyle {\\mathcal {C}}h=\\mathbb {E} ,\\qquad h\\in H,} or, in tensor form, C = E  {\\displaystyle {\\mathcal {C}}=\\mathbb {E} } . The spectral theorem allows to decompose X {\\displaystyle X} as the Karhunen-Lo\u00e8ve decomposition X = \u03bc + \u2211 i = 1 \u221e \u27e8 X , \u03c6 i \u27e9 \u03c6 i , {\\displaystyle X=\\mu +\\sum _{i=1}^{\\infty }\\langle X,\\varphi _{i}\\rangle \\varphi _{i},} where \u03c6 i {\\displaystyle \\varphi _{i}} are eigenvectors of C {\\displaystyle {\\mathcal {C}}} , corresponding to the nonnegative eigenvalues of C {\\displaystyle {\\mathcal {C}}} , in a non-increasing order. Truncating this infinite series to a finite order underpins functional principal component analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a hyperexponential distribution is a continuous probability distribution whose probability density function of the random variable X is given by f X ( x ) = \u2211 i = 1 n f Y i ( x ) p i , {\\displaystyle f_{X}(x)=\\sum _{i=1}^{n}f_{Y_{i}}(x)\\;p_{i},} where each Yi is an exponentially distributed random variable with rate parameter \u03bbi, and pi is the probability that X will take on the form of the exponential distribution with rate \u03bbi. It is named the hyperexponential distribution since its coefficient of variation is greater than that of the exponential distribution, whose coefficient of variation is 1, and the hypoexponential distribution, which has a coefficient of variation smaller than one. While the exponential distribution is the continuous analogue of the geometric distribution, the hyperexponential distribution is not analogous to the hypergeometric distribution. The hyperexponential distribution is an example of a mixture density. An example of a hyperexponential random variable can be seen in the context of telephony, where, if someone has a modem and a phone, their phone line usage could be modeled as a hyperexponential distribution where there is probability p of them talking on the phone with rate \u03bb1 and probability q of them using their internet connection with rate \u03bb2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The FETI-DP method is hybrid between a dual and a primal method. Non-overlapping domain decomposition methods are also called iterative substructuring methods. Mortar methods are discretization methods for partial differential equations, which use separate discretization on nonoverlapping subdomains.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Kronecker's congruence, introduced by Kronecker, states that \u03a6 p ( x , y ) \u2261 ( x \u2212 y p ) ( x p \u2212 y ) mod p , {\\displaystyle \\Phi _{p}(x,y)\\equiv (x-y^{p})(x^{p}-y){\\bmod {p}},} where p is a prime and \u03a6p(x,y) is the modular polynomial of order p, given by \u03a6 n ( x , j ) = \u220f \u03c4 ( x \u2212 j ( \u03c4 ) ) {\\displaystyle \\Phi _{n}(x,j)=\\prod _{\\tau }(x-j(\\tau ))} for j the elliptic modular function and \u03c4 running through classes of imaginary quadratic integers of discriminant n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Clearly, we don't want to integrate a mixed loss when the less is significantly larger than the gain. This is often referred to as a \"silver lining\", a reference to the folk maxim \"every cloud has a silver lining\". When the loss is just barely larger than the gain, integration may be preferred.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Coastal flood hazards have been mapped by a similar approach that includes the relevant physical processes. Most areas where serious floods can occur in the United States have been mapped consistently in this manner.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, an overline sometimes indicates a vector, although boldface and arrows are also commonly used: x \u00af = | x | x ^ {\\displaystyle {\\overline {x}}=|x|{\\hat {x}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The opposite of embarrassingly parallel problems are inherently serial problems, which cannot be parallelized at all. A common example of an embarrassingly parallel problem is 3D video rendering handled by a graphics processing unit, where each frame (forward method) or pixel (ray tracing method) can be handled with no interdependency. Some forms of password cracking are another embarrassingly parallel task that is easily distributed on central processing units, CPU cores, or clusters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following case, one Proposer achieves acceptance of value V1 of two Acceptors before failing. A new Proposer may start another round, but it is now impossible for that proposer to prepare a majority that doesn't include at least one Acceptor that has accepted V1. As such, even though the Proposer doesn't see the existing consensus, the Proposer's only option is to propose the value already agreed upon. New Proposers can continually increase the identifier to restart the process, but the consensus can never be changed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, a variety of machine learning techniques have been used in record linkage. It has been recognized that the classic Fellegi-Sunter algorithm for probabilistic record linkage outlined above is equivalent to the Naive Bayes algorithm in the field of machine learning, and suffers from the same assumption of the independence of its features (an assumption that is typically not true). Higher accuracy can often be achieved by using various other machine learning techniques, including a single-layer perceptron, random forest, and SVM. In conjunction with distributed technologies, accuracy and scale for record linkage can be improved further.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Abstract object theory is a discipline that studies the nature and role of abstract objects. It holds that properties can be related to objects in two ways: through exemplification and through encoding. Concrete objects exemplify their properties while abstract objects merely encode them. This approach is also known as the dual copula strategy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Without an online connection to a licensing server to verify the licensing status every two weeks (four weeks since version 9.0.0), the software would fall back to the functionality of the freeware version. This caused an uproar in the user community, in particular among those who work in secure or remote environments without direct Internet access and users for whom it is mandatory to be able to gain full access to their designs even after extended periods of time (several years up to decades) without depending on third-parties such as Autodesk to allow reactivation (who may no longer be around or support the product by then). Many users have indicated they would refuse to upgrade under a subscription model and rather migrate to other electronic design applications such as KiCad.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years more advanced strategies have been proposed, they all rely on machine learning and attempt to merge the content and collaborative information in a single model. One example of this approaches is called attribute to feature mapping which is tailored to matrix factorization algorithms. The basic idea is the following. A matrix factorization model represents the user-item interactions as the product of two rectangular matrices whose content is learned using the known interactions via machine learning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the X Window System, every individual, physical key is associated a number in the range 8\u2013255, called its keycode. A keycode only identifies a key, not a particular character or term (e.g., \"Page Up\") among the ones that may be printed on the key. Each one of these characters or terms is instead identified by a keysym. While a keycode only depends on the actual key that is pressed, a keysym may depend, for example, on whether the Shift key or another modifier was also pressed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The rest of the numbers are counted half-step-wise such that: B = 0, C = 1, C\u266f/D\u266d = 2, D = 3, D\u266f/E\u266d = 4, E = 5, F = 6, F\u266f/G\u266d = 7, G = 8, G\u266f/A\u266d = 9, A = 10, and A\u266f/B\u266d = 11. Prime zero is retrieved entirely by choice of the composer. To receive the retrograde of any given prime, the numbers are simply rewritten backwards.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this case, the metacharacter character ($) (not to be confused with the sigil in the variable assignment statement) is interpreted to indicate variable interpolation, and requires some escaping if it needs to be outputted literally. This should be contrasted with the printf function, which produces the same output using notation such as: but does not perform interpolation: the %s is a placeholder in a printf format string, but the variables themselves are outside the string. This is contrasted with \"raw\" strings: which produce output like: $name said $greeting to the crowd of people. Here the $ characters are not metacharacters, and are not interpreted to have any meaning other than plain text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the craps principle is a theorem about event probabilities under repeated iid trials. Let E 1 {\\displaystyle E_{1}} and E 2 {\\displaystyle E_{2}} denote two mutually exclusive events which might occur on a given trial. Then the probability that E 1 {\\displaystyle E_{1}} occurs before E 2 {\\displaystyle E_{2}} equals the conditional probability that E 1 {\\displaystyle E_{1}} occurs given that E 1 {\\displaystyle E_{1}} or E 2 {\\displaystyle E_{2}} occur on the next trial, which is P \u2061  = P \u2061  = P \u2061  P \u2061  + P \u2061  {\\displaystyle \\operatorname {P} =\\operatorname {P} \\left={\\frac {\\operatorname {P} }{\\operatorname {P} +\\operatorname {P} }}} The events E 1 {\\displaystyle E_{1}} and E 2 {\\displaystyle E_{2}} need not be collectively exhaustive (if they are, the result is trivial).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This recursive process ends when the entropy is zero so that either all pixels in that subset are corners or non-corners. This generated decision tree can then be converted into programming code, such as C and C++, which is just a bunch of nested if-else statements. For optimization purpose, profile-guided optimization is used to compile the code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Max pooling layers are located after the second, the forth and the fifth convolution layer. A Global average pooling is also applied before the output. All convolution layers use Leaky ReLU nonlinearity activation function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UK, the spoofed number is called the \"presentation number\". This must be either allocated to the caller, or if allocated to a third party, it is only to be used with the third party's explicit permission.Starting 2016, direct marketing companies are obliged to display their phone numbers. Any offending companies can be fined up to \u00a32 million by Ofcom.In 2021, Huw Saunders, a director at Ofcom, the UK regulator, said the current UK phone network (Public Switched Telephone Network) is being updated to a new system (Voice Over Internet Protocol), which should be in place by 2025. Saunders said, \"It's only when the vast majority of people are on the new technology (VOIP) that we can implement a new patch to address this problem .\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of population genetics, LDA was proposed by J. K. Pritchard, M. Stephens and P. Donnelly in 2000.LDA was applied in machine learning by David Blei, Andrew Ng and Michael I. Jordan in 2003.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Once all missing values have been imputed, the data set can then be analysed using standard techniques for complete data. There have been many theories embraced by scientists to account for missing data but the majority of them introduce bias. A few of the well known attempts to deal with missing data include: hot deck and cold deck imputation; listwise and pairwise deletion; mean imputation; non-negative matrix factorization; regression imputation; last observation carried forward; stochastic imputation; and multiple imputation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The English verb is to krige and the most common noun is Kriging; both are often pronounced with a hard \"g\", following the pronunciation of the name \"Krige\". Advantages Very good in local and global estimates. Geological knowledge is captured in variogram.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The data protection legislation requires that the collection and processing of personal data be fair, lawful and transparent. This means that the collection and processing of data as defined by data protection legislation must always have a valid lawful basis and must also meet the requirements of the CLDC. In the China, Article 18 of the \"National Health Care Big Data Standards, Security and Services Management Measures (for Trial Implementation)\" (National Health Planning and Development (2018) No. 23) promulgated by the National Health Care Commission in 2018 states, \"The responsible unit shall adopt measures such as data classification, important data backup, and encryption authentication to guarantee the security of health care big data.\" However, the scope and definition of important data are not covered. Although the \"Information Security Technology-Healthcare Data Security Guide\" (the \"Guide\") issued by the National Standardization Committee also proposes that important data should be evaluated and approved in accordance with the regulations, there is likewise no definition of the connotation and definition of important data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Initially, this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained wide acceptance since then, although some doubters remain.The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken after many false proofs and counterexamples (unlike the five color theorem, proved in the 1800s, which states that five colors are enough to color a map). To dispel any remaining doubts about the Appel\u2013Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas. In 2005, the theorem was also proved by Georges Gonthier with general-purpose theorem-proving software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a Kaniadakis distribution (also known as \u03ba-distribution) is a statistical distribution that emerges from the Kaniadakis statistics. There are several families of Kaniadakis distributions related to different constraints used in the maximization of the Kaniadakis entropy, such as the \u03ba-Exponential distribution, \u03ba-Gaussian distribution, Kaniadakis \u03ba-Gamma distribution and \u03ba-Weibull distribution. The \u03ba-distributions have been applied for modeling a vast phenomenology of experimental statistical distributions in natural or artificial complex systems, such as, in epidemiology, quantum statistics, in astrophysics and cosmology, in geophysics, in economy, in machine learning.The \u03ba-distributions are written as function of the \u03ba-deformed exponential, taking the form f i = exp \u03ba \u2061 ( \u2212 \u03b2 E i + \u03b2 \u03bc ) {\\displaystyle f_{i}=\\exp _{\\kappa }(-\\beta E_{i}+\\beta \\mu )} enables the power-law description of complex systems following the consistent \u03ba-generalized statistical theory., where exp \u03ba \u2061 ( x ) = ( 1 + \u03ba 2 x 2 + \u03ba x ) 1 / \u03ba {\\displaystyle \\exp _{\\kappa }(x)=({\\sqrt {1+\\kappa ^{2}x^{2}}}+\\kappa x)^{1/\\kappa }} is the Kaniadakis \u03ba-exponential function. The \u03ba-distribution becomes the common Boltzmann distribution at low energies, while it has a power-law tail at high energies, the feature of high interest of many researchers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The error terms, which are not directly observed in data and are often denoted using the scalar e i {\\displaystyle e_{i}} .In various fields of application, different terminologies are used in place of dependent and independent variables. Most regression models propose that Y i {\\displaystyle Y_{i}} is a function (regression function) of X i {\\displaystyle X_{i}} and \u03b2 {\\displaystyle \\beta } , with e i {\\displaystyle e_{i}} representing an additive error term that may stand in for un-modeled determinants of Y i {\\displaystyle Y_{i}} or random statistical noise: Y i = f ( X i , \u03b2 ) + e i {\\displaystyle Y_{i}=f(X_{i},\\beta )+e_{i}} The researchers' goal is to estimate the function f ( X i , \u03b2 ) {\\displaystyle f(X_{i},\\beta )} that most closely fits the data. To carry out regression analysis, the form of the function f {\\displaystyle f} must be specified.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Quoting Shaler, \"We have two opinions in this case. That, in essence, is a 50 percent error rate. \"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In certain types of programmable logic arrays and read-only memory, a bit may be represented by the presence or absence of a conducting path at a certain point of a circuit. In optical discs, a bit is encoded as the presence or absence of a microscopic pit on a reflective surface. In one-dimensional bar codes, bits are encoded as the thickness of alternating black and white lines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There will be N + 1 {\\displaystyle N+1} possible values of the categorical variable y ranging from 0 to N. Let pn(x) be the probability, given explanatory variable vector x, that the outcome will be y = n {\\displaystyle y=n} . Define p n k = p n ( x k ) {\\displaystyle p_{nk}=p_{n}({\\boldsymbol {x}}_{k})} which is the probability that for the k-th measurement, the categorical outcome is n. The Lagrangian will be expressed as a function of the probabilities pnk and will minimized by equating the derivatives of the Lagrangian with respect to these probabilities to zero. An important point is that the probabilities are treated equally and the fact that they sum to unity is part of the Lagrangian formulation, rather than being assumed from the beginning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a rational monoid is a monoid, an algebraic structure, for which each element can be represented in a \"normal form\" that can be computed by a finite transducer: multiplication in such a monoid is \"easy\", in the sense that it can be described by a rational function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, truth is reducible to this process of verification. According to perspectivism and relativism, a proposition is only true relative to a particular perspective. Roughly, a proposition is true relative to a perspective if and only if it is accepted, endorsed, or legitimated by that perspective.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accuracy computations more easily. Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical data analysis the total sum of squares (TSS or SST) is a quantity that appears as part of a standard way of presenting results of such analyses. For a set of observations, y i , i \u2264 n {\\displaystyle y_{i},i\\leq n} , it is defined as the sum over all squared differences between the observations and their overall mean y \u00af {\\displaystyle {\\bar {y}}} . : T S S = \u2211 i = 1 n ( y i \u2212 y \u00af ) 2 {\\displaystyle \\mathrm {TSS} =\\sum _{i=1}^{n}\\left(y_{i}-{\\bar {y}}\\right)^{2}} For wide classes of linear models, the total sum of squares equals the explained sum of squares plus the residual sum of squares. For proof of this in the multivariate OLS case, see partitioning in the general OLS model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matroid theory, a binary matroid is a matroid that can be represented over the finite field GF(2). That is, up to isomorphism, they are the matroids whose elements are the columns of a (0,1)-matrix and whose sets of elements are independent if and only if the corresponding columns are linearly independent in GF(2).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some verbs, the past tense, past participle, or both are identical in form to the basic (infinitive) form of the verb. This is the case with certain strong verbs, where historical sound changes have led to a leveling of the vowel modifications: for example, let has both past tense and past participle identical to the infinitive, while come has the past participle identical (but a different past tense, came). The same is true of the verbs listed above under \u00a7 Weak verbs as having undergone coalescence of final consonants (and without other irregularities such as vowel shortening or devoicing of the ending): bet, bid, etc. (these verbs have infinitive, past tense and past participle all identical, although some of them also have alternative regular forms in -ed).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, International Standard Book Number (ISBN) uses modulo 11 (for 10 digit ISBN) or modulo 10 (for 13 digit ISBN) arithmetic for error detection. Likewise, International Bank Account Numbers (IBANs), for example, make use of modulo 97 arithmetic to spot user input errors in bank account numbers. In chemistry, the last digit of the CAS registry number (a unique identifying number for each chemical compound) is a check digit, which is calculated by taking the last digit of the first two parts of the CAS registry number times 1, the previous digit times 2, the previous digit times 3 etc., adding all these up and computing the sum modulo 10.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This report consolidated many ideas circulating at the time and featured three key language innovations: nested block structure: code sequences and associated declarations could be grouped into blocks without having to be turned into separate, explicitly named procedures; lexical scoping: a block could have its own private variables, procedures and functions, invisible to code outside that block, that is, information hiding.Another innovation, related to this, was in how the language was described: a mathematically exact notation, Backus\u2013Naur form (BNF), was used to describe the language's syntax. Nearly all subsequent programming languages have used a variant of BNF to describe the context-free portion of their syntax.ALGOL 60 was particularly influential in the design of later languages, some of which soon became more popular. The Burroughs large systems were designed to be programmed in an extended subset of ALGOL.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in the fields of universal algebra and graph theory, a graph algebra is a way of giving a directed graph an algebraic structure. It was introduced by McNulty and Shallon, and has seen many uses in the field of universal algebra since then.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Parameters on which items are characterized include their difficulty (known as \"location\" for their location on the difficulty range); discrimination (slope or correlation), representing how steeply the rate of success of individuals varies with their ability; and a pseudoguessing parameter, characterising the (lower) asymptote at which even the least able persons will score due to guessing (for instance, 25% for a pure chance on a multiple choice item with four possible responses). In the same manner, IRT can be used to measure human behavior in online social networks. The views expressed by different people can be aggregated to be studied using IRT. Its use in classifying information as misinformation or true information has also been evaluated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The conversion of letter case in a string is common practice in computer applications, for instance to make case-insensitive comparisons. Many high-level programming languages provide simple methods for case conversion, at least for the ASCII character set. Whether or not the case variants are treated as equivalent to each other varies depending on the computer system and context. For example, user passwords are generally case sensitive in order to allow more diversity and make them more difficult to break. In contrast, case is often ignored in keyword searches in order to ignore insignificant variations in keyword capitalisation both in queries and queried material.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here, Z/pZ denotes the cyclic group of order p (or equivalently the integers mod p), and the superscript notation means the n-fold direct product of groups.In general, a (possibly infinite) elementary abelian p-group is a direct sum of cyclic groups of order p. (Note that in the finite case the direct product and direct sum coincide, but this is not so in the infinite case.) In the rest of this article, all groups are assumed finite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Multiple combinations of centralized and decentralized systems exist. Another classification of sensor configuration refers to the coordination of information flow between sensors. These mechanisms provide a way to resolve conflicts or disagreements and to allow the development of dynamic sensing strategies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to illustrate Generalized Paxos, the example below shows a message flow between two concurrently executing clients and a replicated state machine implementing read/write operations over two distinct registers A and B. Note that in this table indicates operations which are non-commutative. A possible sequence of operations: <1:Read(A), 2:Read(B), 3:Write(B), 4:Read(B), 5:Read(A), 6:Write(A)> Since 5:Read(A) commutes with both 3:Write(B) and 4:Read(B), one possible permutation equivalent to the previous order is the following: <1:Read(A), 2:Read(B), 5:Read(A), 3:Write(B), 4:Read(B), 6:Write(A)> In practice, a commute occurs only when operations are proposed concurrently.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a natural and geometric way such a presentation. A very closely related topic is geometric group theory, which today largely subsumes combinatorial group theory, using techniques from outside combinatorics besides. It also comprises a number of algorithmically insoluble problems, most notably the word problem for groups; and the classical Burnside problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Increased quality of software components and application. Repeatability of subsequent test runs. Offline testing (e.g. at times that the office is not staffed, like overnight). Access to conditions and/or use cases that are otherwise difficult to simulate (load, for example).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of Oracle Databases, a schema object is a logical data storage structure.An Oracle database associates a separate schema with each database user. A schema comprises a collection of schema objects. Examples of schema objects include: tables views sequences synonyms indexes clusters database links snapshots procedures functions packagesOn the other hand, non-schema objects may include: users roles contexts directory objectsSchema objects do not have a one-to-one correspondence to physical files on disk that store their information. However, Oracle databases store schema objects logically within a tablespace of the database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the FHS, all files and directories appear under the root directory /, even if they are stored on different physical or virtual devices. Some of these directories only exist in a particular system if certain subsystems, such as the X Window System, are installed. Most of these directories exist in all Unix-like operating systems and are generally used in much the same way; however, the descriptions here are those used specifically for the FHS and are not considered authoritative for platforms other than Linux.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the first uncountable ordinal, traditionally denoted by \u03c9 1 {\\displaystyle \\omega _{1}} or sometimes by \u03a9 {\\displaystyle \\Omega } , is the smallest ordinal number that, considered as a set, is uncountable. It is the supremum (least upper bound) of all countable ordinals. When considered as a set, the elements of \u03c9 1 {\\displaystyle \\omega _{1}} are the countable ordinals (including finite ordinals), of which there are uncountably many.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If most, or a weighted most, of the \u03c6's are satisfied by one unique object y, then y is the referent of 'X'. If the vote yields no unique object, 'X' does not refer. The statement, 'If X exists, then X has most of the \u03c6's' is known a priori by the speaker.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pure mathematics, modular arithmetic is one of the foundations of number theory, touching on almost every aspect of its study, and it is also used extensively in group theory, ring theory, knot theory, and abstract algebra. In applied mathematics, it is used in computer algebra, cryptography, computer science, chemistry and the visual and musical arts. A very practical application is to calculate checksums within serial number identifiers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The two ends of a line segment determine the points in between: in vector terms the segment from v to w consists of the \u03bbv + (1 \u2212 \u03bb)w with 0 \u2264 \u03bb \u2264 1. The classical result of Hermann Minkowski says that in Euclidean space, a bounded, closed convex set C is the convex hull of its extreme point set E, so that any c in C is a (finite) convex combination of points e of E. Here E may be a finite or an infinite set. In vector terms, by assigning non-negative weights w(e) to the e in E, almost all 0, we can represent any c in C as with In any case the w(e) give a probability measure supported on a finite subset of E. For any affine function f on C, its value at the point c is In the infinite dimensional setting, one would like to make a similar statement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This leads to the important fact that entire programs (which are just lists of these instructions) can be represented as lists of numbers and can themselves be manipulated inside the computer in the same way as numeric data. The fundamental concept of storing programs in the computer's memory alongside the data they operate on is the crux of the von Neumann, or stored program, architecture. In some cases, a computer might store some or all of its program in memory that is kept separate from the data it operates on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The infiltration of state organizations can provide subversive groups the opportunity to do many things to achieve their goals. The infiltration of security forces can provide information about the government's capabilities and how they plan to address the group's activities. Infiltration also provides the opportunity to plant false information, lead the government to misallocate resources, to steal funds, weapons, equipment, and other resources, and ultimately aid in weakening and delegitimizing the government.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the U.S., Federal Communications Commission (FCC) regulations prohibit the use of mobile phones aboard aircraft in flight. Contrary to popular misconception, the Federal Aviation Administration (FAA) does not actually prohibit the use of personal electronic devices (including cell phones) on aircraft. Paragraph (b)(5) of 14 CFR 91.21 permits airlines to determine if devices can be used in flight, allowing use of \"any other portable electronic device that the operator of the aircraft has determined will not cause interference with the navigation or communication system of the aircraft on which it is to be used. \"In Europe, regulations and technology have allowed the limited introduction of the use of passenger mobile phones on some commercial flights, and elsewhere in the world many airlines are moving towards allowing mobile phone use in flight.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Finding such an inequality is the separation problem, and such an inequality is a cut. A cut can be added to the relaxed linear program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even\u2014as the last digit of any even number is 0, 2, 4, 6, or 8. The same idea will work using any even base. In particular, a number expressed in the binary numeral system is odd if its last digit is 1; and it is even if its last digit is 0. In an odd base, the number is even according to the sum of its digits\u2014it is even if and only if the sum of its digits is even.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Resource-leveling can take the \"work demand\" and balance it against the resource pool availability for the given week. The goal is to create this weekly schedule in advance of performing the work. Without resource-leveling the organization (planner, scheduler, supervisor) is most likely performing subjective selection. For the most part, when it comes to maintenance scheduling, there is less, if any, task interdependence, and therefore less need to calculate critical path and total float.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Linguists and typologists such as Joseph Greenberg have suggested that specific count-classifiers are semantically \"redundant\", repeating information present within the noun. Count-classifiers can be used stylistically, though, and can also be used to clarify or limit a speaker's intended meaning when using a vague or ambiguous noun; for example, the noun \u8bfe k\u00e8 \"class\" can refer to courses in a semester or specific class periods during a day, depending on whether the classifier \u95e8 (\u9580) m\u00e9n or \u8282 (\u7bc0) ji\u00e9 is used.One proposed explanation for the existence of count-classifiers is that they serve more of a cognitive purpose than a practical one: in other words, they provide a linguistic way for speakers to organize or categorize real objects. An alternative account is that they serve more of a discursive and pragmatic function (a communicative function when people interact) rather than an abstract function within the mind. Specifically, it has been proposed that count-classifiers might be used to mark new or unfamiliar objects within a discourse, to introduce major characters or items in a story or conversation, or to foreground important information and objects by making them bigger and more salient. In this way, count-classifiers might not serve an abstract grammatical or cognitive function, but may help in communication by making important information more noticeable and drawing attention to it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sampling is a foundation of hip hop music, which emerged when producers in the 1980s began sampling funk and soul records, particularly drum breaks. It has influenced many other genres of music, particularly electronic music and pop. Samples such as the Amen break, the \"Funky Drummer\" drum break and the orchestra hit have been used in thousands of recordings, and James Brown, Loleatta Holloway, Fab Five Freddy and Led Zeppelin are among the most sampled artists.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof compression, an area of mathematical logic, LowerUnivalents is an algorithm used for the compression of propositional resolution proofs. LowerUnivalents is a generalised algorithm of the LowerUnits, and it is able to lower not only units but also subproofs of non-unit clauses, provided that they satisfy some additional conditions. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The proposed new branch of scientific exploration admits many different forms of scientific production. For instance, qualitative classifications are often the results of initial forays into the computational jungle. On the other hand, explicit proofs that certain systems compute this or that function are also admissible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Part of the settlement agreement for this case, Mink v. University of Chicago, attorneys for the plaintiffs negotiated for the university to provide free medical exams for all offspring exposed to DES in utero during the 1950 experiments as well as treat the daughters of any women involved who develop DES-associated vaginal or cervical cancer.As of February 1991, there were over a thousand pending legal actions against DES manufacturers. There are over 300 companies that manufactured DES according to the same formula and the largest barrier to recovery is determining which manufacturer supplied the drug in each particular case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Once a system has been commissioned it should be either put immediately into service or drained down and dried. If either of these options is not possible then the system should be flushed though regularly until it is put into use. It should not be left to stand for more than a week.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Moser\u2013de Bruijn sequence is an integer sequence named after Leo Moser and Nicolaas Govert de Bruijn, consisting of the sums of distinct powers of 4. Equivalently, they are the numbers whose binary representations are nonzero only in even positions. The Moser\u2013de Bruijn numbers in this sequence grow in proportion to the square numbers. They are the squares for a modified form of arithmetic without carrying.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication contracts it is frequent the practice to lock the use of a sim card of one operator with a phone acquired through the same mobile operator. Obstructing the unlocking of the phone may be illegal if the consumer is entitled to it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The intangible and esoteric Outer Planes\u2014the realms of ideals, philosophies, and gods\u2014stand in contrast to the Inner Planes, which compose the material building blocks of reality and the realms of energy and matter. All Outer Planes are spatially infinite but are composed of features and locations of finite scope. Many of these planes are often split into a collection of further infinites called layers, which are essentially sub-planes that represent one particular facet or theme of the plane.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral \u03c7 2 {\\displaystyle \\chi ^{2}} distribution) is a noncentral generalization of the chi-squared distribution. It often arises in the power analysis of statistical tests in which the null distribution is (perhaps asymptotically) a chi-squared distribution; important examples of such tests are the likelihood-ratio tests.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such a core ontology is a key pre-requisite to a more complete foundation ontology, or a more general philosophical sense of ontology. Most applicable to teaching, e.g. the Longmans defining dictionary of the simplest meanings of 2,000 English words is used to define the 4,000 most basic English idioms\u2014this is a core glossary of the English language, which permits access to the core ontology (the idioms). Core ontologies is a concept that is used in information science as well. For example, CIDOC-CRM and CORA are considered as core ontologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Changing the sign of any number is encoded by generating its complement, which can be done by a very simple and efficient algorithm. This method was commonly used in mechanical calculators and is still used in modern computers. The generalized concept of the radix complement (as described below) is also valuable in number theory, such as in Midy's theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some models of smartphones allow the user to enter letters into the device\u2019s dialing window to allow the completion of phonewords. Numerous Blackberry models allow this feature by using the ALT key when pressing a key to select the letter, and not the number on the key. On older landline telephones, the O, Q and Z sometimes vary in placement or are omitted entirely; this is not an issue for most mobile telephones as all 26 letters must be provided to support short message service transmission. The dialing of 1 or 0 instead of I or O in phonewords can lead to misdialed calls; one such typosquatting incident targeted 1-800-HOLIDAY (+1-800-465-4329, the toll-free direct reservations line for Holiday Inn) by subscribing 1-800-H0LIDAY (+1-800-405-4329, the same number with 'o' replaced by 'zero') to a rival vendor which stood to collect a profitable travel agent's commission.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other classifiers work by comparing observations to previous observations by means of a similarity or distance function. An algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term \"classifier\" sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a proper linear model is a linear regression model in which the weights given to the predictor variables are chosen in such a way as to optimize the relationship between the prediction and the criterion. Simple regression analysis is the most common example of a proper linear model. Unit-weighted regression is the most common example of an improper linear model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nonrelativistic classical mechanics, a closed system is a physical system that doesn't exchange any matter with its surroundings, and isn't subject to any net force whose source is external to the system. A closed system in classical mechanics would be equivalent to an isolated system in thermodynamics. Closed systems are often used to limit the factors that can affect the results of a specific problem or experiment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While performing these operations, there may be scenarios where the same element is being searched by one thread and is being deleted by another. In such cases, the output may be erroneous. The thread searching the element may have a hit, whereas the other thread may delete it just after that time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the classical setting, we aim at partitioning the vertices of a hypergraph H = ( V , E ) {\\displaystyle {\\mathcal {H}}=(V,{\\mathcal {E}})} into two classes in such a way that ideally each hyperedge contains the same number of vertices in both classes. A partition into two classes can be represented by a coloring \u03c7: V \u2192 { \u2212 1 , + 1 } {\\displaystyle \\chi \\colon V\\rightarrow \\{-1,+1\\}} . We call \u22121 and +1 colors. The color-classes \u03c7 \u2212 1 ( \u2212 1 ) {\\displaystyle \\chi ^{-1}(-1)} and \u03c7 \u2212 1 ( + 1 ) {\\displaystyle \\chi ^{-1}(+1)} form the corresponding partition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a of a group, is thus the smallest positive integer m such that am = e, where e denotes the identity element of the group, and am denotes the product of m copies of a. If no such m exists, the order of a is infinite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known accuracy, a device generating the quantity to be measured such as a voltage, a sound tone, or a physical artifact, such as a meter ruler. The outcome of the comparison can result in one of the following: no significant error being noted on the device under test a significant error being noted but no adjustment made an adjustment made to correct the error to an acceptable levelStrictly speaking, the term \"calibration\" means just the act of comparison and does not include any subsequent adjustment. The calibration standard is normally traceable to a national or international standard held by a metrology body.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Step 8: For every class of equinumerous classes, create its successor. Step 9: Order the numbers: The process of creating a successor requires the relation \" . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\max _{\\left\\{c_{t}\\right\\}_{t=0}^{\\infty }}\\mathbb {E} {\\bigg (}\\sum _{t=0}^{\\infty }\\beta ^{t}u({\\color {OliveGreen}c_{t}}){\\bigg )}.} The expectation E {\\displaystyle \\mathbb {E} } is taken with respect to the appropriate probability measure given by Q on the sequences of r's. Because r is governed by a Markov process, dynamic programming simplifies the problem significantly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This representation was translated to a computational model and an anytime algorithm for belief revision was developed.Ginsberg\u2013Fagin\u2013Ullman\u2013Vardi the maximal subsets of K \u222a { P } {\\displaystyle K\\cup \\{P\\}} that are consistent and contain P {\\displaystyle P} are combined by disjunction;Nebel similar to the above, but a priority among formulae can be given, so that formulae with higher priority are less likely to being retracted than formulae with lower priority.A different realization of the foundational approach to belief revision is based on explicitly declaring the dependences among beliefs. In the truth maintenance systems, dependence links among beliefs can be specified. In other words, one can explicitly declare that a given fact is believed because of one or more other facts; such a dependency is called a justification. Beliefs not having any justifications play the role of non-derived beliefs in the non-deductively closed knowledge base approach.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fix an integer m. Let ej denote the number of units in the right order of Ij and let Bij denote the number of \u03b1 in Ij\u22121Ii with reduced norm N(\u03b1) equal to mN(Ii)/N(Ij). The Brandt matrix B(m) is the H\u00d7H matrix with entries Bij. Up to conjugation by a permutation matrix it is independent of the choice of representatives Ij; it is dependent only on the level of the order O.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In structured programming, stack resource management is done simply by nesting code sufficiently to handle all cases. This requires only a single return at the end of the code, and can result in heavily nested code if many resources must be acquired, which is considered an anti-pattern by some \u2013 the Arrow Anti Pattern, due to the triangular shape from the successive nesting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This structure is specified, e.g., in a file format or protocol and distinguishes valid from invalid input. An effective fuzzer generates semi-valid inputs that are \"valid enough\" in that they are not directly rejected by the parser, but do create unexpected behaviors deeper in the program and are \"invalid enough\" to expose corner cases that have not been properly dealt with. For the purpose of security, input that crosses a trust boundary is often the most useful. For example, it is more important to fuzz code that handles the upload of a file by any user than it is to fuzz the code that parses a configuration file that is accessible only to a privileged user.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Maximum weighted matchings do not have to be stable, but in some applications a maximum weighted matching is better than a stable one. The matching with contracts problem is a generalization of matching problem, in which participants can be matched with different terms of contracts. An important special case of contracts is matching with flexible wages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Extensions that were busy or rang \u201cno answer\u201d would forward to the message center onto a device called a \u201ccall director\u201d. The call director had a button for each extension in the company which would flash when that person's extension forwarded to the message center. A little label next to the button told the operator whose extension it was. As wireless communication technologies increased in the late 1980s, the Pager service providers created a subscription service offered in a variety of plans and options to meet the needs of a subscriber and the type of device used. In general, all pagers are given unique telephone numbers so that callers could dial in and send a numeric message, such as their callback number or a numerically coded special message, such as room numbers to report to, etc. However, alphanumeric pagers could only receive text messages when the message sender had installed software on their PC to dial into the publicly accessible modems operated by the paging service provider to then transmit their message over-the-air through the network of radio towers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If S {\\displaystyle S} is also separable, then P ( S ) {\\displaystyle {\\mathcal {P}}(S)} is metrizable and separable, for example by the L\u00e9vy\u2013Prokhorov metric. If S {\\displaystyle S} is also compact or Polish, so is P ( S ) {\\displaystyle {\\mathcal {P}}(S)} . If S {\\displaystyle S} is separable, it naturally embeds into P ( S ) {\\displaystyle {\\mathcal {P}}(S)} as the (closed) set of Dirac measures, and its convex hull is dense. There are many \"arrow notations\" for this kind of convergence: the most frequently used are P n \u21d2 P {\\displaystyle P_{n}\\Rightarrow P} , P n \u21c0 P {\\displaystyle P_{n}\\rightharpoonup P} , P n \u2192 w P {\\displaystyle P_{n}\\xrightarrow {w} P} and P n \u2192 D P {\\displaystyle P_{n}\\xrightarrow {\\mathcal {D}} P} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s, an epidemic of \"cloning\" cost the cellular carriers millions of dollars. An eavesdropper with specialized equipment could intercept a handset's ESN (Electronic Serial Number) and MDN or CTN (Mobile Directory Number or Cellular Telephone Number). The Electronic Serial Number, a 12-digit number sent by the handset to the cellular system for billing purposes, uniquely identified that phone on the network. The system then allowed or disallowed calls and/or features based on its customer file.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the background of the technology looked to address the following issues: The development of non-removable SIM technology - a new generation of SIM-cards like MFF which are soldered into the device. The appearance and support by mobile operators of the concept of ABC (always best connected) \u2013 the opportunity get quality connections from any mobile operator at any point in time. The explosive growth of the Internet of Things (IoT) - according to Gartner about 8.4 billion connections in 2017 (up 31% from 2016). The cost and effort required to swap a SIM in a device that has been deployed in the field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The main criteria included: A large selection of publication items (journal articles, books, dataset, software) that agree with the writing and reading practices of scientific communities. Fully documented data sources. Transparent and reproducible process for the calculation of the metrics and other indices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programming languages, e.g. Java, the term conditional operator refers to short circuit boolean operators && and ||. The second expression is evaluated only when the first expression is not sufficient to determine the value of the whole expression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Harvey writes that the asymptotic time complexity of this algorithm is O(n2 log(n)2 + \u03b5) and claims that this implementation is significantly faster than implementations based on other methods. Using this implementation Harvey computed Bn for n = 108. Harvey's implementation has been included in SageMath since version 3.1. Prior to that, Bernd Kellner computed Bn to full precision for n = 106 in December 2002 and Oleksandr Pavlyk for n = 107 with Mathematica in April 2008. * Digits is to be understood as the exponent of 10 when Bn is written as a real number in normalized scientific notation.A possible algorithm for computing Bernoulli numbers in the Julia programming language is given by", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The example C code below illustrates how structure objects are dynamically allocated and referenced. The standard C library provides the function malloc() for allocating memory blocks from the heap. It takes the size of an object to allocate as a parameter and returns a pointer to a newly allocated block of memory suitable for storing the object, or it returns a null pointer if the allocation failed. The code below illustrates how memory objects are dynamically deallocated, i.e., returned to the heap or free store. The standard C library provides the function free() for deallocating a previously allocated memory block and returning it back to the heap.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although she developed many techniques for establishing the non-consecutivity condition, she did not succeed in her strategic goal. She also worked to set lower limits on the size of solutions to Fermat's equation for a given exponent p {\\displaystyle p} , a modified version of which was published by Adrien-Marie Legendre.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the beginning there was Sendmail and many other mail delivery agents soon followed (Postfix etc.) Once email spam and computer virus problems started becoming prevalent in the early 1990s. These critical Internet infrastructure systems had to be patched and the underlying protocols changed -or in some cases ignored- to deal with these issues. Thus was born the messaging platform. Large telecommunication operators and internet service providers needed flexible, easily deployed and scaled messaging systems for quickly growing messaging services and cell phone networks (for examples see SMS and BlackBerry.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the area of the four triangles removed from both side of the equation what remains is a 2 + b 2 = c 2 . {\\displaystyle a^{2}+b^{2}=c^{2}.} In another proof rectangles in the second box can also be placed such that both have one corner that correspond to consecutive corners of the square.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "He follows a similar method for the other eleven categories, then represents them in the following table: These categories, then, are the fundamental, primary, or native concepts of the understanding. These flow from, or constitute the mechanism of understanding and its nature, and are inseparable from its activity. Therefore, for human thought, they are universal and necessary, or a priori.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This filter prevents payloads such as and its URI-encoded form %3Cscript%3Ealert%281%29%3C%2Fscript%3E. However, %253Cscript%253Ealert%25281%2529%253C%252Fscript%253E, which is the double-URI-encoded form of , will bypass this filter. When double-URI-encoded payload %253Cscript%253Ealert%25281%2529%253C%252Fscript%253E is used, the value of $_GET will be %3Cscript%3Ealert%281%29%3C%2Fscript%3E which doesn't contain any illegal character and thus passes through the htmlentities function without any change and will be given to the urldecode function which returns , resulting in a successful attack.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In medicine (oncology and other fields), performance status is an attempt to quantify cancer patients' general well-being and activities of daily life. This measure is used to determine whether they can receive chemotherapy, whether dose adjustment is necessary, and as a measure for the required intensity of palliative care. It is also used in oncological randomized controlled trials as a measure of quality of life.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, the elements of the set being permuted will be compared with each other. This requires that the set S has a total order so that any two elements can be compared. The set {1, 2, ..., n} is totally ordered by the usual \"\u2264\" relation and so it is the most frequently used set in these applications, but in general, any totally ordered set will do. In these applications, the ordered arrangement view of a permutation is needed to talk about the positions in a permutation. There are a number of properties that are directly related to the total ordering of S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, in the Euclidean case, squares of distances are used to avoid computing square roots and to simplify relevant theorems and algorithms. Euclidean distance matrices are closely related to Gram matrices (matrices of dot products, describing norms of vectors and angles between them). The latter are easily analyzed using methods of linear algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It can be extended to infinite-dimensional vector spaces as the L2 norm or L2 distance. The Euclidean distance gives Euclidean space the structure of a topological space, the Euclidean topology, with the open balls (subsets of points at less than a given distance from a given point) as its neighborhoods.Other common distances on Euclidean spaces and low-dimensional vector spaces include: Chebyshev distance, which measures distance assuming only the most significant dimension is relevant. Manhattan distance, which measures distance following only axis-aligned directions. Minkowski distance, a generalization that unifies Euclidean distance, Manhattan distance, and Chebyshev distance.For points on surfaces in three dimensions, the Euclidean distance should be distinguished from the geodesic distance, the length of a shortest curve that belongs to the surface. In particular, for measuring great-circle distances on the earth or other spherical or near-spherical surfaces, distances that have been used include the haversine distance giving great-circle distances between two points on a sphere from their longitudes and latitudes, and Vincenty's formulae also known as \"Vincent distance\" for distance on a spheroid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "n 1 ! \u22c5 ( N \u2212 n 1 ) ! ( N \u2212 n 1 \u2212 n 2 ) !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to split a secret into several shares, Blakley's scheme specifies the secret as a point in n-dimensional space, and gives out shares that correspond to hyperplanes that intersect the secret point. Any n such hyperplanes will specify the point, while fewer than n hyperplanes will leave at least one degree of freedom, and thus leave the point unspecified.In contrast, Shamir's secret sharing scheme represents the secret as the y-intercept of an n-degree polynomial, and shares correspond to points on the polynomial.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, for all t \u2265 0 {\\displaystyle t\\geq 0} Pr { \u03bb max ( H ( z ) \u2212 E H ( z ) ) \u2265 t } \u2264 d \u22c5 e \u2212 t 2 / 8 \u03c3 2 , {\\displaystyle \\Pr \\left\\{\\lambda _{\\text{max}}\\left(\\mathbf {H} (\\mathbf {z} )-\\mathbb {E} \\,\\mathbf {H} (\\mathbf {z} )\\right)\\geq t\\right\\}\\leq d\\cdot e^{-t^{2}/8\\sigma ^{2}},} where z = ( Z 1 , \u2026 , Z n ) {\\displaystyle \\mathbf {z} =(Z_{1},\\ldots ,Z_{n})} . An improvement of this result was established in (Paulin, Mackey & Tropp 2013) (see also (Paulin, Mackey & Tropp 2016)): for all t \u2265 0 {\\displaystyle t\\geq 0} Pr { \u03bb max ( H ( z ) \u2212 E H ( z ) ) \u2265 t } \u2264 d \u22c5 e \u2212 t 2 / \u03c3 2 , {\\displaystyle \\Pr \\left\\{\\lambda _{\\text{max}}\\left(\\mathbf {H} (\\mathbf {z} )-\\mathbb {E} \\,\\mathbf {H} (\\mathbf {z} )\\right)\\geq t\\right\\}\\leq d\\cdot e^{-t^{2}/\\sigma ^{2}},} where z = ( Z 1 , \u2026 , Z n ) {\\displaystyle \\mathbf {z} =(Z_{1},\\ldots ,Z_{n})} and \u03c3 2 = \u2016 \u2211 k A k 2 \u2016 . {\\displaystyle \\sigma ^{2}={\\bigg \\Vert }\\sum _{k}\\mathbf {A} _{k}^{2}{\\bigg \\Vert }.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In polymer chemistry, the term prepolymer or pre-polymer, refers to a monomer or system of monomers that have been reacted to an intermediate-molecular mass state. This material is capable of further polymerization by reactive groups to a fully cured, high-molecular-mass state. As such, mixtures of reactive polymers with un-reacted monomers may also be referred to as pre-polymers. The term \"pre-polymer\" and \"polymer precursor\" may be interchanged.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, in the term ( \u03bb x . x \u03a9 ) ( \u03bb y . I ) {\\displaystyle (\\lambda x.x\\Omega )(\\lambda y.I)} with \u03a9 , I {\\displaystyle \\Omega ,I} defined here, the leftmost redex of the in-order traversal is \u03a9 {\\displaystyle \\Omega } while the leftmost-outermost redex is the entire expression.Applicative order reduction refers to leftmost-innermost reduction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and probability, the Borell\u2013TIS inequality is a result bounding the probability of a deviation of the uniform norm of a centered Gaussian stochastic process above its expected value. The result is named for Christer Borell and its independent discoverers Boris Tsirelson, Ildar Ibragimov, and Vladimir Sudakov. The inequality has been described as \"the single most important tool in the study of Gaussian processes.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to at least k connected components. These edges are referred to as k-cut. The goal is to find the minimum-weight k-cut. This partitioning can have applications in VLSI design, data-mining, finite elements and communication in parallel computing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Symbols are concatenated together according to recursive rules, in order to construct strings to which truth-values will be assigned. The rules specify how the operators, function and predicate symbols, and quantifiers are to be concatenated with other strings. A proposition is then a string with a specific form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regular English verbs, the past tense and past participle have the same form. This is also true of most irregular verbs that follow a variation of the weak conjugation, as can be seen in the list below. Differences between the past tense and past participle (as in sing\u2013sang\u2013sung, rise\u2013rose\u2013risen) generally appear in the case of verbs that continue the strong conjugation, or in a few cases weak verbs that have acquired strong-type forms by analogy\u2014as with show (regular past tense showed, strong-type past participle shown). However, even some strong verbs have identical past tense and participle, as in cling\u2013clung\u2013clung.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a superabundant number (sometimes abbreviated as SA) is a certain kind of natural number. A natural number n is called superabundant precisely when, for all m < n \u03c3 ( m ) m < \u03c3 ( n ) n {\\displaystyle {\\frac {\\sigma (m)}{m}}<{\\frac {\\sigma (n)}{n}}} where \u03c3 denotes the sum-of-divisors function (i.e., the sum of all positive divisors of n, including n itself). The first few superabundant numbers are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... (sequence A004394 in the OEIS). For example, the number 5 is not a superabundant number because for 1, 2, 3, 4, and 5, the sigma is 1, 3, 4, 7, 6, and 7/4 > 6/5.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To express the constraint that all items must be allocated, add an n-ary constraint for each item (where n is the number of agents), with an infinite cost if no variable related to this item is \"1\".The problem can be solved using the following local search algorithm. All agents are ordered lexicographically (e.g. by their name or index). Each agent also orders its variables lexicographically.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a call-second is a unit used to measure communications traffic density, equivalent to one call with a duration of one second. Traffic is measured independent of users. For example, one user making two 75-second calls is equivalent to two users each making one 75-second call, as each case produces 150 call-seconds of traffic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "During the Vedic period, gods aid humans against demons. By that, gods secure their own place in heaven, using humans as tools to defeat their cosmic enemies.Asura, in the earliest hymns of the Rigveda, originally meant any supernatural spirit, either good or bad. Since the /s/ of the Indic linguistic branch is cognate with the /h/ of the Early Iranian languages, the word asura, representing a category of celestial beings, is a cognate with Old Persian Ahura.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Feature vectors are often combined with weights using a dot product in order to construct a linear predictor function that is used to determine a score for making a prediction. The vector space associated with these vectors is often called the feature space. In order to reduce the dimensionality of the feature space, a number of dimensionality reduction techniques can be employed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of computer science recently more specific types of modeling languages have emerged.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1920s, William Giauque and Herrick L. Johnston discovered the stable isotopes of oxygen. Isotopes were not well understood at the time; James Chadwick would not discover the neutron until 1932. Two systems were in use for classifying them, based on chemical and physical properties. The latter was determined using the mass spectrograph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of process-driven applications, three categories of process exist:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The protection thus granted has proven to be incomplete. Consequently, over the course of the 20th century, case law has extended liability for recklessness to other cases, in particular by admitting that \u00a7 823 paragraph 1 BGB aims to protect a \"general right to personality\" and a \"right to the company\" or by recognising, alongside tort liability, the theory of culpa in contrahendo. Although Boris Starck makes no express reference to it, there are serious reasons to think that this right strongly inspired him in his elaboration of the theory of the guarantee.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These numbers may surprise many, because the market is perceived as desktop computers. x86 designs dominate desktop and notebook computer sales, but such computers are only a tiny fraction of the computers now sold. Most people in industrialised countries own more computers in embedded systems in their car and house, than on their desks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Facebook estimated the existence of up to 60 million troll bots actively spreading misinformation on their platform, and has taken measures to stop the spread of misinformation, resulting in a decrease, though misinformation continues to exist on the platform. A research report by NewsGuard found there is a very high level (~20% in their probes of videos about relevant topics) of online misinformation delivered \u2013 to a mainly young user base \u2013 with TikTok, whose (essentially unregulated) usage is increasing as of 2022.Spontaneous spread of misinformation on social media usually occurs from users sharing posts from friends or mutually-followed pages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some disadvantages are that the datasets are often huge and difficult to keep up to date. Another problem with this method is that it is costly to compile such a warehouse.Standardized formats for different types of data (ex: protein data) are now emerging due to the influence of groups like the Proteomics Standards Initiative (PSI). Some data warehousing projects even require the submission of data in one of these new formats.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, multidimensional empirical mode decomposition (multidimensional EMD) is an extension of the one-dimensional (1-D) EMD algorithm to a signal encompassing multiple dimensions. The Hilbert\u2013Huang empirical mode decomposition (EMD) process decomposes a signal into intrinsic mode functions combined with the Hilbert spectral analysis, known as the Hilbert\u2013Huang transform (HHT). The multidimensional EMD extends the 1-D EMD algorithm into multiple-dimensional signals. This decomposition can be applied to image processing, audio signal processing, and various other multidimensional signals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The effect is that i2 uses the correct (the more recent) value of Register 1: the commit/store was made immediately and not pipelined. With forwarding enabled, the Instruction Decode/Execution (ID/EX) stage of the pipeline now has two inputs: the value read from the register specified (in this example, the value 6 from Register 1), and the new value of Register 1 (in this example, this value is 3) which is sent from the next stage Instruction Execute/Memory Access (EX/MEM). Added control logic is used to determine which input to use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, simply typed lambda calculus can be seen as a language with a single non-basic type constructor\u2014the function type constructor. Product types can generally be considered \"built-in\" in typed lambda calculi via currying. Abstractly, a type constructor is an n-ary type operator taking as argument zero or more types, and returning another type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "stock market is too narrow, omitting all sorts of other domestic and international asset classes. Thus another occasional choice would be the use of international indexes, such as the MSCI EAFE. However, even these indexes have returns that are surprisingly similar to the stock market.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Key relevance is the measure of similarity between the key and the optimal size needed to fit the lock, or it is the similarity between a duplicate key and the original it is seeking to replicate. Key relevance cannot be deduced from a key code, since the key code merely refers to a central authoritative source for designed shapes and sizes of keys. Typical modern keys require a key relevance of approximately 0.03 millimetres (0.0012 in) to 0.07 millimetres (0.0028 in) (accuracy within 0.75% to 1.75%) in order to operate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a perfect matrix is an m-by-n binary matrix that has no possible k-by-k submatrix K that satisfies the following conditions: k > 3 the row and column sums of K are each equal to b, where b \u2265 2 there exists no row of the (m \u2212 k)-by-k submatrix formed by the rows not included in K with a row sum greater than b.The following is an example of a K submatrix where k = 5 and b = 2:  . {\\displaystyle {\\begin{bmatrix}1&1&0&0&0\\\\0&1&1&0&0\\\\0&0&1&1&0\\\\0&0&0&1&1\\\\1&0&0&0&1\\end{bmatrix}}.} == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reporting result of horse races winning margins are commonly abbreviated:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group.Let G {\\displaystyle G} be a finitely generated group. Then, for each integer n {\\displaystyle n} define a n ( G ) {\\displaystyle a_{n}(G)} to be the number of subgroups H {\\displaystyle H} of index n {\\displaystyle n} in G {\\displaystyle G} . Similarly, if G {\\displaystyle G} is a topological group, s n ( G ) {\\displaystyle s_{n}(G)} denotes the number of open subgroups U {\\displaystyle U} of index n {\\displaystyle n} in G {\\displaystyle G} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The correct proof was published in May 1995. The proof uses many techniques from algebraic geometry and number theory, and has many ramifications in these branches of mathematics. It also uses standard constructions of modern algebraic geometry, such as the category of schemes and Iwasawa theory, and other 20th-century techniques not available to Fermat.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These are for informational purposes only, and are called by a variety of names, such as Lot Book Report, Plat Certificate, 300-foot Radius Report, Ownership & Lien Report and others. These informational searches are used mainly in two instances: Ownership & Lien Report. Is informational, coming from examining the current owner's vesting deed forward and examining: owed taxes, new encumbrances on record, name searches on parties in title.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The parameters of a logistic regression are most commonly estimated by maximum-likelihood estimation (MLE). This does not have a closed-form expression, unlike linear least squares; see \u00a7 Model fitting. Logistic regression by MLE plays a similarly basic role for binary or categorical responses as linear regression by ordinary least squares (OLS) plays for scalar responses: it is a simple, well-analyzed baseline model; see \u00a7 Comparison with linear regression for discussion. The logistic regression as a general statistical model was originally developed and popularized primarily by Joseph Berkson, beginning in Berkson (1944), where he coined \"logit\"; see \u00a7 History.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Now supporting VESA Local Bus and using the Am486 with up to 100 MHz clock speed. A SC450 with 33 MHze.g. was used in the Nokia 9000 Communicator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At the Center for Group Dynamics at the University of Michigan, Dorwin Cartwright and Harary generalized Fritz Heider's psychological theory of balance in triangles of sentiments to a psychological theory of balance in signed graphs.Signed graphs have been rediscovered many times because they come up naturally in many unrelated areas. For instance, they enable one to describe and analyze the geometry of subsets of the classical root systems. They appear in topological graph theory and group theory. They are a natural context for questions about odd and even cycles in graphs. They appear in computing the ground state energy in the non-ferromagnetic Ising model; for this one needs to find a largest balanced edge set in \u03a3. They have been applied to data classification in correlation clustering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of games for many 8-bit computers, users could load games into memory and, before launching them, modify specific memory addresses in order to cheat, getting an unlimited number of lives, immunity, invisibility, etc. Such modifications were performed using POKE statements. The Commodore 64, ZX Spectrum and Amstrad CPC also allowed players with one of the relevant cartridges (such as Action Replay or Multiface) to freeze the running program, enter POKEs, and resume. For example, in Knight Lore for the ZX Spectrum, immunity can be achieved with the following command: In this case, the value 201 corresponds to a RET instruction, so that the game returns from a subroutine early before triggering collision detection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the System/360, other than the 360/67, and early System/370 architectures, the general-purpose registers were 32 bits wide, the machine did 32-bit arithmetic operations, and addresses were always stored in 32-bit words, so the architecture was considered 32-bit, but the machines ignored the top 8 bits of the address resulting in 24-bit addressing. With the System/370-XA architecture and the IBM Enterprise Systems Architecture, in addition to a 24-bit addressing mode for compatibility with older applications, there is a 31-bit addressing mode, in which only the high order bit (bit 0) in the word is ignored for addressing. An exception is that mode-switching instructions also use bit 0. There were at least two reasons that IBM did not implement the 32-bit addressing of the 360/67 The loop control instructions BXH and BXLE did signed comparisons. Much of the existing software used bit 0 as an end-of-list indicator.The 64-bit z/Architecture also supports 24-bit and 31-bit addressing modes for compatibility with older applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a *-ring is a ring with a map *: A \u2192 A that is an antiautomorphism and an involution. More precisely, * is required to satisfy the following properties: (x + y)* = x* + y* (x y)* = y* x* 1* = 1 (x*)* = xfor all x, y in A. This is also called an involutive ring, involutory ring, and ring with involution. The third axiom is implied by the second and fourth axioms, making it redundant. Elements such that x* = x are called self-adjoint.Archetypical examples of a *-ring are fields of complex numbers and algebraic numbers with complex conjugation as the involution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If some processors in a large grid of processors fail (become inactive), then it may also be necessary to inactivate other processors with too few active neighbors, in order to preserve the high connectivity of the remaining network. The analysis of bootstrap percolation can be used to determine the failure probability that can be tolerated by the system. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Convolutionally encoded block codes typically employ termination. The arbitrary block length of convolutional codes can also be contrasted to classic block codes, which generally have fixed block lengths that are determined by algebraic properties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, cousin primes are prime numbers that differ by four. Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences OEIS: A023200 and OEIS: A046132 in OEIS) below 1000 are: (3, 7), (7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), (79, 83), (97, 101), (103, 107), (109, 113), (127, 131), (163, 167), (193, 197), (223, 227), (229, 233), (277, 281), (307, 311), (313, 317), (349, 353), (379, 383), (397, 401), (439, 443), (457, 461), (463,467), (487, 491), (499, 503), (613, 617), (643, 647), (673, 677), (739, 743), (757, 761), (769, 773), (823, 827), (853, 857), (859, 863), (877, 881), (883, 887), (907, 911), (937, 941), (967, 971)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another example would be to measure the productivity of a software development team in terms of lines of source code written. This approach can easily add large amounts of dubious code, thereby inflating the line count but adding little value in terms of systemic improvement. A similar problem arises when a footballer kicks a ball uselessly to build up their statistics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 17th century, the method of exhaustion led to the rectification by geometrical methods of several transcendental curves: the logarithmic spiral by Evangelista Torricelli in 1645 (some sources say John Wallis in the 1650s), the cycloid by Christopher Wren in 1658, and the catenary by Gottfried Leibniz in 1691. In 1659, Wallis credited William Neile's discovery of the first rectification of a nontrivial algebraic curve, the semicubical parabola. The accompanying figures appear on page 145. On page 91, William Neile is mentioned as Gulielmus Nelius.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In search engines, autocomplete user interface features provide users with suggested queries or results as they type their query in the search box. This is also commonly called autosuggest or incremental search. This type of search often relies on matching algorithms that forgive entry errors such as phonetic Soundex algorithms or the language independent Levenshtein algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In symbolic programming languages, it is easy to have patterns as arguments to functions or as elements of data structures. A consequence of this is the ability to use patterns to declaratively make statements about pieces of data and to flexibly instruct functions how to operate. For instance, the Mathematica function Compile can be used to make more efficient versions of the code. In the following example the details do not particularly matter; what matters is that the subexpression {{com, Integer}} instructs Compile that expressions of the form com can be assumed to be integers for the purposes of compilation: Mailboxes in Erlang also work this way. The Curry\u2013Howard correspondence between proofs and programs relates ML-style pattern matching to case analysis and proof by exhaustion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to state the paradox it is necessary to understand that the cardinal numbers are totally ordered, so that one can speak about one being greater or less than another. Then Cantor's paradox is: This fact is a direct consequence of Cantor's theorem on the cardinality of the power set of a set. Another consequence of Cantor's theorem is that the cardinal numbers constitute a proper class. That is, they cannot all be collected together as elements of a single set. Here is a somewhat more general result.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plant biology, the perforations in a perforate leaf are also described as fenestrae, and the leaf is called a fenestrate leaf. The leaf window is also known as a fenestra, and is a translucent structure that transmits light, as in Fenestraria. Examples of fenestrate structures in the fungal kingdom include the symmetrically arranged gaps in the indusium (\"skirt\") of the mushroom Phallus duplicatus, and the thallus of the coral lichen Pulchrocladia retipora.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the contexts of software architecture, service-orientation and service-oriented architecture, the term service refers to a software functionality, or a set of software functionalities (such as the retrieval of specified information or the execution of a set of operations) with a purpose that different clients can reuse for different purposes, together with the policies that should control its usage (based on the identity of the client requesting the service, for example). OASIS defines a service as \"a mechanism to enable access to one or more capabilities, where the access is provided using a prescribed interface and is exercised consistent with constraints and policies as specified by the service description\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Reduced heat production and lower overheating risk Redesigned pipeline, supporting faster clock speeds (target up to 1 GHz) Longer: 8 (vs 5) stages Out-of-order completion for some operations (e.g., stores) Dynamic branch prediction/folding (like XScale) Cache misses don't block execution of non-dependent instructions. Load/store parallelism ALU parallelism 64-bit data pathsJTAG debug support (for halting, stepping, breakpoints, and watchpoints) was simplified. The EmbeddedICE module was replaced with an interface which became part of the ARMv7 architecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C programming language, the standard input, output, and error streams are attached to the existing Unix file descriptors 0, 1 and 2 respectively. In a POSIX environment the definitions STDIN_FILENO, STDOUT_FILENO or STDERR_FILENO should be used instead rather than magic numbers. File pointers stdin, stdout, and stderr are also provided. Ken Thompson (designer and implementer of the original Unix operating system) modified sort in Version 5 Unix to accept \"-\" as representing standard input, which spread to other utilities and became a part of the operating system as a special file in Version 8. Diagnostics were part of standard output through Version 6, after which Dennis M. Ritchie created the concept of standard error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Erd\u0151s\u2013R\u00e9nyi model, the average degree \u27e8 k \u27e9 {\\displaystyle \\langle k\\rangle } of a graph with n vertices and N edges is given by \u27e8 k \u27e9 = 2 N n {\\displaystyle \\langle k\\rangle ={\\frac {2N}{n}}} . The condition for the emergence of a giant component is: \u27e8 k \u27e9 = 1 {\\displaystyle {\\left\\langle k\\right\\rangle =1}} . Thus, one link is sufficient for its emergence of the giant component. If expressing the condition in terms of p {\\displaystyle {p}} , one obtains: P c = 1 N \u2212 1 \u2248 1 N {\\displaystyle {P_{c}={\\frac {1}{N-1}}\\approx {\\frac {1}{N}}}} (1) Where N {\\displaystyle {N}} is the number of nodes, P c {\\displaystyle {P_{c}}} is the probability of clustering. Therefore, the larger a network, the smaller p {\\displaystyle {p}} is sufficient for the giant component.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real mode each logical address points directly into a physical memory location, every logical address consists of two 16 bit parts: The segment part of the logical address contains the base address of a segment with a granularity of 16 bytes, i.e. a segment may start at physical address 0, 16, 32, ..., 220-16. The offset part of the logical address contains an offset inside the segment, i.e. the physical address can be calculated as physical_address: = segment_part \u00d7 16 + offset (if the address line A20 is enabled), respectively (segment_part \u00d7 16 + offset) mod 220 (if A20 is off) Every segment has a size of 216 bytes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In peer-to-peer file sharing, the strength of a swarm depends on user behaviour, as peers ideally upload more than they download. This is done by seeding, and there are different motivations to do this. There are two popular motivations to seed, of which one is the reputation-based incentive mechanism and the other is the tit for tat mechanism. As the name reveals, the former is based on the reputation of a peer, meaning that those peers who have a good reputation will get a better treatment from the uploader.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first year 24 technical standards committees were created. A year later, AENOR assumed the representation of Spain before the European organizations (CENELEC, ETSI) and international (ISO, IEC). Nowadays, AENOR has more than 200 technical standards committees involving nearly 6,000 experts in the field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, the hybrid (H-) ternary line code is a line code that operates on a hybrid principle combining the binary non-return-to-zero-level (NRZL) and the polar return-to-zero (RZ) codes. The H-ternary code has three levels for signal representation; these are positive (+), zero (0), and negative (\u2212). These three levels are represented by three states. The state of the line code could be in any one of these three states.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most territories, access to mobile satellite service is managed by traditional telecom companies and specialized resellers which market hardware, software and network access to end users, although occasionally some constellation operators also market service directly to end users. Some companies providing commercial access: Avanti Globalsat Group Iridium Communications Inmarsat Telespazio Thuraya Vizada", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Operator error and a faulty shutdown system led to a sudden, massive spike in the neutron multiplication rate, a sudden decrease in the neutron period, and a consequent increase in neutron population; thus, core heat flux increased rapidly beyond the design limits of the reactor. This caused the water coolant to flash to steam, causing a sudden overpressure within the reactor core (the first of the two major explosions that occurred), leading to granulation of the upper portion of the core and the ejection of the upper biological shield atop the core along with core debris from the reactor building in a widely dispersed pattern. The lower portion of the reactor remained somewhat intact; the graphite neutron moderator was exposed to oxygen-containing air; heat from the power excursion in addition to residual heat flux from the remaining fuel rods left without coolant induced oxidation in the moderator and in the opened fuel rods; this in turn evolved more heat and contributed to the melting of more of the fuel rods and the outgassing of the fission products contained therein.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to determine where each channel is located in the stream of data being received, each set of 24 channels is aligned in a frame. The frame is 192 bits long (8 * 24), and is terminated with a 193rd bit, the framing bit, which is used to find the end of the frame. In order for the framing bit to be located by receiving equipment, a predictable pattern is sent on this bit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs. One of them is a random greedy algorithm which was proposed by Joel Spencer. He used a branching process to formally prove the optimal achievable bound under some side conditions. The other algorithm is called the R\u00f6dl nibble and was proposed by Vojt\u011bch R\u00f6dl et al. They showed that the achievable packing by the R\u00f6dl nibble is in some sense close to that of the random greedy algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Reduction of surface tension increases cavitation, so the solution usually contains a good wetting agent (surfactant). Aqueous cleaning solutions contain detergents, wetting agents and other components, which have a large influence on the cleaning process. The correct composition of the solution is very dependent upon the item cleaned.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fair item allocation problem, classic allocation procedures such as adjusted winner and envy-graph are not RM. Moreover, even the Nash-optimal rule, which is RM in cake-cutting, is not RM in item allocation. In contrast, round-robin item allocation is RM. Moreover, round-robin can be adapted to yield picking sequences appropriate for agents with different entitlements; all these picking sequences are RM too.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most functional programming languages, such as Scheme, nested functions are a common way of implementing algorithms with loops in them. A simple (tail) recursive inner function is created, which behaves as the algorithm's main loop, while the outer function performs startup actions that only need to be done once. In more complex cases, a number of mutually recursive functions may be created as inner functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, if tones x, y, and z form a rising sequence of tones, then the measure of the interval from x to y plus the measure of the interval from y to z should equal the measure of the interval from x to z. Such a measure is given by the cent, which divides the octave into 1200 equal intervals (12 semitones of 100 cents each). Mathematically, given tones with frequencies f1 and f2, the number of cents in the interval from f1 to f2 is | 1200 log 2 \u2061 f 1 f 2 | . {\\displaystyle \\left|1200\\log _{2}{\\frac {f_{1}}{f_{2}}}\\right|.} The millioctave is defined in the same way, but with a multiplier of 1000 instead of 1200.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The axiom schema of Replacement can also be formulated in terms of the ranges of such set functions. If both the domain A {\\displaystyle A} and choosen codomain C {\\displaystyle C} are sets, then the above predicate only involves bounded quantifiers. Common notions such as injectivity and surjectivity can be expressed in a bounded fashion as well, and thus so is bijectivity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the earliest non-electronic information processing devices, such as Jacquard's loom or Babbage's Analytical Engine, a bit was often stored as the position of a mechanical lever or gear, or the presence or absence of a hole at a specific point of a paper card or tape. The first electrical devices for discrete logic (such as elevator and traffic light control circuits, telephone switches, and Konrad Zuse's computer) represented bits as the states of electrical relays which could be either \"open\" or \"closed\". When relays were replaced by vacuum tubes, starting in the 1940s, computer builders experimented with a variety of storage methods, such as pressure pulses traveling down a mercury delay line, charges stored on the inside surface of a cathode-ray tube, or opaque spots printed on glass discs by photolithographic techniques. In the 1950s and 1960s, these methods were largely supplanted by magnetic storage devices such as magnetic-core memory, magnetic tapes, drums, and disks, where a bit was represented by the polarity of magnetization of a certain area of a ferromagnetic film, or by a change in polarity from one direction to the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In six columns the classes of traffic handled at the station was shown as follows:Column 1 - G = Goods Traffic Column 1 - G* = Coal Class, Mineral and Station-to-Station Traffic in Truck Loads. Column 2 - P = Passenger, Parcels & Miscellaneous Traffic. Column 2 - P* = Passenger, but not Parcels & Miscellaneous Traffic. Column 2 - P\u2020 = Parcels & Miscellaneous Traffic (i.e. not Passengers).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\lambda _{\\text{piv}}={\\sqrt {\\frac {\\int e(\\lambda )\\lambda \\,\\mathrm {d} \\lambda }{\\int e(\\lambda )\\lambda ^{-1}\\,\\mathrm {d} \\lambda }}}.} For a response function expressed in the quantum-efficiency convention, it is: \u03bb piv = \u222b e ( \u03bb ) d \u03bb \u222b e ( \u03bb ) \u03bb \u2212 2 d \u03bb . {\\displaystyle \\lambda _{\\text{piv}}={\\sqrt {\\frac {\\int e(\\lambda )\\,\\mathrm {d} \\lambda }{\\int e(\\lambda )\\lambda ^{-2}\\,\\mathrm {d} \\lambda }}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Supported modulation formats on the PDSCH are QPSK, 16QAM and 64QAM. The Physical Multicast Channel (PMCH) is used for broadcast transmission using a Single Frequency Network The Physical Broadcast Channel (PBCH) is used to broadcast the basic system information within the cellAnd the following signals: The synchronization signals (PSS and SSS) are meant for the UE to discover the LTE cell and do the initial synchronization. The reference signals (cell specific, MBSFN, and UE specific) are used by the UE to estimate the DL channel. Positioning reference signals (PRS), added in release 9, meant to be used by the UE for OTDOA positioning (a type of multilateration)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following examples indentation and formatting are critical for parsing the code: expressions are terminated by the end of the line, lists of expressions need to be on the same level of indentation. This feature, named the off-side rule, is also found in other languages such as Haskell and Python. Communication between processes work through named channels. One process outputs data to a channel via !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 3567, 13567, 34567, and 134567 are the patterns related to Braille pattern dots-2345, since the two additional dots of kantenji patterns 02345, 23457, and 023457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism (or arrow) R: A \u2192 B in this category is a relation between the sets A and B, so R \u2286 A \u00d7 B. The composition of two relations R: A \u2192 B and S: B \u2192 C is given by (a, c) \u2208 S o R \u21d4 for some b \u2208 B, (a, b) \u2208 R and (b, c) \u2208 S.Rel has also been called the \"category of correspondences of sets\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some publications, the author responsible for new names and nomenclatural acts is not stated directly in the original source, but can sometimes be inferred from reliable external evidence. Recommendation 51D of the Code states: \"...if the authorship is known or inferred from external evidence, the name of the author, if cited, should be enclosed in square brackets to show the original anonymity\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In diagnostic labs, MIC test results are used to grade microbes as \"S\" (susceptible or responding to a standard dosing regimen), \"I\" (intermediate or requiring increased exposure) or \"R\" (resistant). These grades are assigned based on agreed upon values called breakpoints. Breakpoints are published by standards development organizations such as the U.S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order theory it is common to define a pointwise partial order on functions. With A, B posets, the set of functions A \u2192 B can be ordered by f \u2264 g if and only if (\u2200x \u2208 A) f(x) \u2264 g(x). Pointwise orders also inherit some properties of the underlying posets. For instance if A and B are continuous lattices, then so is the set of functions A \u2192 B with pointwise order. Using the pointwise order on functions one can concisely define other important notions, for instance: A closure operator c on a poset P is a monotone and idempotent self-map on P (i.e. a projection operator) with the additional property that idA \u2264 c, where id is the identity function. Similarly, a projection operator k is called a kernel operator if and only if k \u2264 idA.An example of an infinitary pointwise relation is pointwise convergence of functions\u2014a sequence of functions with converges pointwise to a function f {\\displaystyle f} if for each x {\\displaystyle x} in X {\\displaystyle X}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In text-based indexing or large vocabulary continuous speech recognition (LVCSR), the audio file is first broken down into recognizable phonemes. It is then run through a dictionary that can contain several hundred thousand entries and matched with words and phrases to produce a full text transcript. A user can then simply search a desired word term and the relevant portion of the audio content will be returned. If the text or word could not be found in the dictionary, the system will choose the next most similar entry it can find. The system uses a language understanding model to create a confidence level for its matches. If the confidence level be below 100 percent, the system will provide options of all the found matches.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The quantity \u00bd(b \u2212 a)=0.125 is then added to the horizontal side of the square and subtracted from the vertical side. The resulting line segments are the sides of the desired rectangle.One difficulty in reconstructing Old Babylonian geometric diagrams is that known tablets never include diagrams in solutions\u2014even in geometric solutions where explicit constructions are described in text\u2014although diagrams are often included in formulations of problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\forall x\\forall y(x+y\\leq z)\\to \\forall x\\forall y(x+y=0).} This formula has one free variable, z.The axioms for ordered abelian groups can be expressed as a set of sentences in the language. For example, the axiom stating that the group is commutative is usually written ( \u2200 x ) ( \u2200 y )  . {\\displaystyle (\\forall x)(\\forall y).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a semi-infinite programming (SIP) problem is an optimization problem with a finite number of variables and an infinite number of constraints. The constraints are typically parameterized. In a generalized semi-infinite programming (GSIP) problem, the feasible set of the parameters depends on the variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In which case, there may be multiple and more complex ways to structure the argument of the proof. The assumption that if there is a counterexample, there is a minimal counterexample, is based on a well-ordering of some kind. The usual ordering on the natural numbers is clearly possible, by the most usual formulation of mathematical induction; but the scope of the method can include well-ordered induction of any kind.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Geometry paper, set on the second morning of the papers for candidates for the Gold Medal in the General Examination of the University of Dublin in October 1820, the following three problems appear. Question 10. Three equilateral triangles are thus constructed on the sides of a given triangle, A, B, D, the lines joining their centres, C, C', C\" form an equilateral triangle. Question 11.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The result was documented in CSC-STD-004-85. Two relatively independent components of robustness were defined: Assurance Level and Functionality. Both were specified with a degree of precision that warranted significant confidence in certifications based on these criteria.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang\u2013C model: 495 ) is a multi-server queueing model. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a Poisson process, there are c servers, and job service times are exponentially distributed. It is a generalisation of the M/M/1 queue which considers only a single server. The model with infinitely many servers is the M/M/\u221e queue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis. Prediction intervals are used in both frequentist statistics and Bayesian statistics: a prediction interval bears the same relationship to a future observation that a frequentist confidence interval or Bayesian credible interval bears to an unobservable population parameter: prediction intervals predict the distribution of individual future points, whereas confidence intervals and credible intervals of parameters predict the distribution of estimates of the true population mean or other quantity of interest that cannot be observed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years most of the technology used in the various MIPS generations has been offered as semiconductor intellectual property cores (IP cores), as building blocks for embedded processor designs. Both 32-bit and 64-bit basic cores are offered, known as the 4K and 5K. These cores can be mixed with add-in units such as floating-point units (FPU), single instruction, multiple data (SIMD) systems, various input/output (I/O) devices, etc. MIPS cores have been commercially successful, now having many consumer and industrial uses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the data stream model, some or all of the input is represented as a finite sequence of integers (from some finite domain) which is generally not available for random access, but instead arrives one at a time in a \"stream\". If the stream has length n and the domain has size m, algorithms are generally constrained to use space that is logarithmic in m and n. They can generally make only some small constant number of passes over the stream, sometimes just one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then Pr  \u2265 ( \u2211 i = 1 n Pr  ) 2 \u2211 i = 1 n \u2211 j = 1 n Pr  . {\\displaystyle \\Pr\\geq {\\frac {\\left(\\sum _{i=1}^{n}\\Pr\\right)^{2}}{\\sum _{i=1}^{n}\\sum _{j=1}^{n}\\Pr}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the alphabetic sequence c is identical either to k (in front of a, o, u or consonant or as the last letter of the word) or to z (in front of e or i). The letter y is identical to i.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This also is a known, computed quantity, and it varies by sample and by out-of-sample test space. In the context of gradient descent algorithms, it is common to introduce a factor of 1 / 2 {\\displaystyle 1/2} to the MSE for ease of computation after taking the derivative. So a value which is technically half the mean of squared errors may be called the MSE.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Impossibility theorems are usually expressible as negative existential propositions or universal propositions in logic. The irrationality of the square root of 2 is one of the oldest proofs of impossibility.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The arithmetical hierarchy and polynomial hierarchy classify the degree to which problems are respectively computable and computable in polynomial time. For instance, the level \u03a3 0 0 = \u03a0 0 0 = \u0394 0 0 {\\displaystyle \\Sigma _{0}^{0}=\\Pi _{0}^{0}=\\Delta _{0}^{0}} of the arithmetical hierarchy classifies computable, partial functions. Moreover, this hierarchy is strict such that at any other class in the arithmetic hierarchy classifies strictly uncomputable functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Legendre symbol is a multiplicative function with values 1, \u22121, 0 that is a quadratic character modulo of an odd prime number p: its value at a (nonzero) quadratic residue mod p is 1 and at a non-quadratic residue (non-residue) is \u22121. Its value at zero is 0. The Legendre symbol was introduced by Adrien-Marie Legendre in 1798 in the course of his attempts at proving the law of quadratic reciprocity. Generalizations of the symbol include the Jacobi symbol and Dirichlet characters of higher order. The notational convenience of the Legendre symbol inspired introduction of several other \"symbols\" used in algebraic number theory, such as the Hilbert symbol and the Artin symbol.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems engineering, dependability is a measure of a system's availability, reliability, maintainability, and in some cases, other characteristics such as durability, safety and security. In real-time computing, dependability is the ability to provide services that can be trusted within a time-period. The service guarantees must hold even when the system is subject to attacks or natural failures. The International Electrotechnical Commission (IEC), via its Technical Committee TC 56 develops and maintains international standards that provide systematic methods and tools for dependability assessment and management of equipment, services, and systems throughout their life cycles. The IFIP Working Group 10.4 on \"Dependable Computing and Fault Tolerance\" plays a role in synthesizing the technical community's progress in the field and organizes two workshops each year to disseminate the results. Dependability can be broken down into three elements: Attributes - a way to assess the dependability of a system Threats - an understanding of the things that can affect the dependability of a system Means - ways to increase a system's dependability", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Prediction: For every state in S(k) of the form (X \u2192 \u03b1 \u2022 Y \u03b2, j) (where j is the origin position as above), add (Y \u2192 \u2022 \u03b3, k) to S(k) for every production in the grammar with Y on the left-hand side (Y \u2192 \u03b3). Scanning: If a is the next symbol in the input stream, for every state in S(k) of the form (X \u2192 \u03b1 \u2022 a \u03b2, j), add (X \u2192 \u03b1 a \u2022 \u03b2, j) to S(k+1). Completion: For every state in S(k) of the form (Y \u2192 \u03b3 \u2022, j), find all states in S(j) of the form (X \u2192 \u03b1 \u2022 Y \u03b2, i) and add (X \u2192 \u03b1 Y \u2022 \u03b2, i) to S(k).Duplicate states are not added to the state set, only new ones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the true working-correlation is known, consistency does not require MCAR. Huber-White standard errors improve the efficiency of Liang Zeger GEE in the absence of serial Autocorrelation but may remove the marginal interpretation. GEE estimates the average response over the population (\"population-averaged\" effects) with Liang Zeger Standard Errors, and in individuals using Huber White Standard Errors also known as \"robust standard error\" or \"sandwich variance\" estimates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In radio systems, TDMA is usually used alongside frequency-division multiple access (FDMA) and frequency-division duplex (FDD); the combination is referred to as FDMA/TDMA/FDD. This is the case in both GSM and IS-136 for example. Exceptions to this include the DECT and Personal Handy-phone System (PHS) micro-cellular systems, UMTS-TDD UMTS variant, and China's TD-SCDMA, which use time-division duplexing, where different time slots are allocated for the base station and handsets on the same frequency. A major advantage of TDMA is that the radio part of the mobile only needs to listen and broadcast for its own time slot.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, effective dimension is a modification of Hausdorff dimension and other fractal dimensions that places it in a computability theory setting. There are several variations (various notions of effective dimension) of which the most common is effective Hausdorff dimension. Dimension, in mathematics, is a particular way of describing the size of an object (contrasting with measure and other, different, notions of size).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0. The concept is analogous to the concept of \"almost everywhere\" in measure theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Crashes can be easily identified and might indicate potential vulnerabilities (e.g., denial of service or arbitrary code execution). However, the absence of a crash does not indicate the absence of a vulnerability. For instance, a program written in C may or may not crash when an input causes a buffer overflow.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In singularity theory the general phenomenon of points and sets of singularities is studied, as part of the concept that manifolds (spaces without singularities) may acquire special, singular points by a number of routes. Projection is one way, very obvious in visual terms when three-dimensional objects are projected into two dimensions (for example in one of our eyes); in looking at classical statuary the folds of drapery are amongst the most obvious features. Singularities of this kind include caustics, very familiar as the light patterns at the bottom of a swimming pool. Other ways in which singularities occur is by degeneration of manifold structure. The presence of symmetry can be good cause to consider orbifolds, which are manifolds that have acquired \"corners\" in a process of folding up, resembling the creasing of a table napkin.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for a game to be in normal form, we are provided with the following data: There is a finite set I of players, each player is denoted by i. Each player i has a finite k number of pure strategies S i = { 1 , 2 , \u2026 , k } . {\\displaystyle S_{i}=\\{1,2,\\ldots ,k\\}.} A pure strategy profile is an association of strategies to players, that is an I-tuple s \u2192 = ( s 1 , s 2 , \u2026 , s I ) {\\displaystyle {\\vec {s}}=(s_{1},s_{2},\\ldots ,s_{I})} such that s 1 \u2208 S 1 , s 2 \u2208 S 2 , \u2026 , s I \u2208 S I {\\displaystyle s_{1}\\in S_{1},s_{2}\\in S_{2},\\ldots ,s_{I}\\in S_{I}} A payoff function is a function u i: S 1 \u00d7 S 2 \u00d7 \u2026 \u00d7 S I \u2192 R . {\\displaystyle u_{i}:S_{1}\\times S_{2}\\times \\ldots \\times S_{I}\\rightarrow \\mathbb {R} .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The relationship between the two covariant return types is usually one which allows substitution of the one type with the other, following the Liskov substitution principle. This usually implies that the return types of the overriding methods will be subtypes of the return type of the overridden method. The above example specifically illustrates such a case. If substitution is not allowed, the return type is invariant and causes a compile error. Another example of covariance with the help of built in Object and String class of Java:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, the 'cake' to be divided has a negative value. For example, it might be piece of lawn that has to be mowed, or a piece of wasteland that has to be cleaned. Then, the cake is a 'heterogeneous bad' rather than a 'heterogeneous good'. Some procedures for envy-free cake-cutting can be adapted to work for a bad cake, but the adaptation is often not trivial. See envy-free chore division for more details.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a similar fashion, cross-multiplier 2 states that fPC = (1/2) \u2014while cross-multiplier 3 states that fPD = (1/2)  . Returning to the first multiplier, it can now be seen also to be fPQ = (1/2) , which, after substituting multipliers 2 and 3, resumes its original form. In much of the following, the grand-parental generation is referred to as (t-2) , the parent generation as (t-1) , and the \"target\" generation as t.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Fermat number, named after Pierre de Fermat, the first known to have studied them, is a positive integer of the form F n = 2 2 n + 1 , {\\displaystyle F_{n}=2^{2^{n}}+1,} where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ... (sequence A000215 in the OEIS).If 2k + 1 is prime and k > 0, then k itself must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023, the only known Fermat primes are F0 = 3, F1 = 5, F2 = 17, F3 = 257, and F4 = 65537 (sequence A019434 in the OEIS); heuristics suggest that there are no more.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then it checks if p ( r 1 , \u2026 , r m ) = f k ( r 1 , \u2026 , r m ) {\\displaystyle p(r_{1},\\dots ,r_{m})=f_{k}(r_{1},\\dots ,r_{m})} If they are equal then V accepts, otherwise V rejects.This is the end of the protocol description. If \u03c8 is true then V will accept when P follows the protocol. Likewise if P ~ {\\displaystyle {\\tilde {P}}} is a malicious prover which lies, and if \u03c8 is false, then P ~ {\\displaystyle {\\tilde {P}}} will need to lie at phase 0 and send some value for f0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the PEM model, there is no direct communication network between the P processors. The processors have to communicate indirectly over the main memory. If multiple processors try to access the same block in main memory concurrently read/write conflicts occur. Like in the PRAM model, three different variations of this problem are considered: Concurrent Read Concurrent Write (CRCW): The same block in main memory can be read and written by multiple processors concurrently.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "He named them after his advisor Wolfgang Gr\u00f6bner. In 2007, Buchberger received the Association for Computing Machinery's Paris Kanellakis Theory and Practice Award for this work. However, the Russian mathematician Nikolai G\u00fcnther had introduced a similar notion in 1913, published in various Russian mathematical journals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since many users do not have unlimited web space, either as a paid service, or through an ISP offering, video hosting services are becoming increasingly popular, especially with the explosion in popularity of blogs, internet forums and other interactive pages. The mass market for camera phones and smartphones has increased the supply of user-generated video. Traditional methods of personal video distribution, such as making a DVD to show to friends at home, are unsuited to the low resolution and high volume of camera phone clips. In contrast, current broadband Internet connections are well suited to serving the quality of video shot on mobile phones. Most people do not own web servers, and this has created demand for user-generated video content hosting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, the '1' flag bits indicate the beginning of each segment. 1 2 3 4 5 6 input 1 0 0 1 0 1 flag bits 1 3 6 4 9 6 segmented scan + {\\displaystyle {\\begin{array}{|rrrrrr|l|}1&2&3&4&5&6&{\\text{input}}\\\\\\hline 1&0&0&1&0&1&{\\text{flag bits}}\\\\\\hline 1&3&6&4&9&6&{\\text{segmented scan +}}\\\\\\end{array}}} Group11 = 1 3 = 1 + 2 6 = 1 + 2 + 3Group24 = 4 9 = 4 + 5Group36 = 6An alternative method used by High Performance Fortran is to begin a new segment at every transition of flag value. An advantage of this representation is that it is useful with both prefix and suffix (backwards) scans without changing its interpretation. In HPF, Fortran logical data type is used to represent segments. So the equivalent flag array for the above example would be as follows: 1 2 3 4 5 6 input T T T F F T flag values 1 3 6 4 9 6 segmented scan + {\\displaystyle {\\begin{array}{|rrrrrr|l|}1&2&3&4&5&6&{\\text{input}}\\\\\\hline T&T&T&F&F&T&{\\text{flag values}}\\\\\\hline 1&3&6&4&9&6&{\\text{segmented scan +}}\\\\\\end{array}}} == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a square-difference-free set is a set of natural numbers, no two of which differ by a square number. Hillel Furstenberg and Andr\u00e1s S\u00e1rk\u00f6zy proved in the late 1970s the Furstenberg\u2013S\u00e1rk\u00f6zy theorem of additive number theory showing that, in a certain sense, these sets cannot be very large. In the game of subtract a square, the positions where the next player loses form a square-difference-free set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A person intercepting an ESN/MDN pair could clone the combination onto a different phone and use it in other areas for making calls without paying. Cellular phone cloning became possible with off-the-shelf technology in the 1990s. Would-be cloners required three key items: A radio receiver, such as the Icom PCR-1000, that could tune into the Reverse Channel (the frequency on which AMPS phones transmit data to the tower) A PC with a sound card and a software program called Banpaia A phone that could easily be used for cloning, such as the Oki 900The radio, when tuned to the proper frequency, would receive the signal transmitted by the cell phone to be cloned, containing the phone's ESN/MDN pair.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems, feedback vertex sets play a prominent role in the study of deadlock recovery. In the wait-for graph of an operating system, each directed cycle corresponds to a deadlock situation. In order to resolve all deadlocks, some blocked processes have to be aborted. A minimum feedback vertex set in this graph corresponds to a minimum number of processes that one needs to abort.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is often denoted Hom(V, k), or, when the field k is understood, V \u2217 {\\displaystyle V^{*}} ; other notations are also used, such as V \u2032 {\\displaystyle V'} , V # {\\displaystyle V^{\\#}} or V \u2228 . {\\displaystyle V^{\\vee }.} When vectors are represented by column vectors (as is common when a basis is fixed), then linear functionals are represented as row vectors, and their values on specific vectors are given by matrix products (with the row vector on the left).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Prolog syntactical convention a symbol starting with an upper case letter is a variable name; a symbol that starts with a lowercase letter is a function symbol; the comma is used as the logical and operator. For mathematical notation, x,y,z are used as variables, f,g as function symbols, and a,b as constants. The most general unifier of a syntactic first-order unification problem of size n may have a size of 2n. For example, the problem ( ( ( a \u2217 z ) \u2217 y ) \u2217 x ) \u2217 w \u2250 w \u2217 ( x \u2217 ( y \u2217 ( z \u2217 a ) ) ) {\\displaystyle (((a*z)*y)*x)*w\\doteq w*(x*(y*(z*a)))} has the most general unifier { z \u21a6 a , y \u21a6 a \u2217 a , x \u21a6 ( a \u2217 a ) \u2217 ( a \u2217 a ) , w \u21a6 ( ( a \u2217 a ) \u2217 ( a \u2217 a ) ) \u2217 ( ( a \u2217 a ) \u2217 ( a \u2217 a ) ) } {\\displaystyle \\{z\\mapsto a,y\\mapsto a*a,x\\mapsto (a*a)*(a*a),w\\mapsto ((a*a)*(a*a))*((a*a)*(a*a))\\}} , cf. picture. In order to avoid exponential time complexity caused by such blow-up, advanced unification algorithms work on directed acyclic graphs (dags) rather than trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the second method, a service provider sends a personalised OTAC (e.g. an enciphered token) to an authenticated email address; when the user types the OTAC into the website, the server authenticates the user. A web application can generate a unique personal identification number (PIN) that the user can input into the desktop client, the desktop client, in turn, uses that code to authenticate itself to the web application. This form of authentication is particularly useful in web applications that do not have an internal username/password store but instead use SAML for authentication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These identifications are routinely done in mathematics. They can be expressed formally in Cartesian coordinates as with basis vectors in the tangent spaces defined by Here p and q are any two events and the second basis vector identification is referred to as parallel transport. The first identification is the canonical identification of vectors in the tangent space at any point with vectors in the space itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , \u2212 \u221e , m i n d \u2212 1 } {\\displaystyle k_{min}=\\{-\\infty ,min_{0},-\\infty ,min_{1},...,-\\infty ,min_{d-1}\\}} k m a x = { m a x 0 , + \u221e , m a x 1 , + \u221e , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Decimal megabytes were used for disk capacity by the CDC in 1974. The Seagate ST-412, one of several types installed in the IBM PC/XT, had a capacity of 10027008 bytes when formatted as 306 \u00d7 4 tracks and 32 256-byte sectors per track, which was quoted as \"10 MB\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the application of the Strahler stream order to hydrology, each segment of a stream or river within a river network is treated as a node in a tree, with the next segment downstream as its parent. When two first-order streams come together, they form a second-order stream. When two second-order streams come together, they form a third-order stream. Streams of lower order joining a higher order stream do not change the order of the higher stream.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most computer programming, a programmer keeps a program's intended results in mind and painstakingly constructs a program to achieve those results. Inferential programming refers to (still mostly hypothetical) techniques and technologies enabling the inverse. This would allow describing an intended result to a computer, using a metaphor such as a fitness function, a test specification, or a logical specification, and then the computer, on its own, would construct a program needed to meet the supplied criteria.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, axiomatization is the process of taking a body of knowledge and working backwards towards its axioms. It is the formulation of a system of statements (i.e. axioms) that relate a number of primitive terms \u2014 in order that a consistent body of propositions may be derived deductively from these statements. Thereafter, the proof of any proposition should be, in principle, traceable back to these axioms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, computer science, telecommunication, information theory, and searching theory, error-correcting codes with feedback are error correcting codes designed to work in the presence of feedback from the receiver to the sender.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Owen, New York: Marcel Dekker, pp. 149\u2013193. See also \"Confusion Over Measures of Evidence (p's) Versus Errors (a's) in Classical Statistical Testing,\" Raymond Hubbard and M. J. Bayarri, The American Statistician, August 2003, Vol.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of national or homeland security, law enforcement, or social control policy, trusted systems provide conditional prediction about the behavior of people or objects prior to authorizing access to system resources. For example, trusted systems include the use of \"security envelopes\" in national security and counterterrorism applications, \"trusted computing\" initiatives in technical systems security, and credit or identity scoring systems in financial and anti-fraud applications. In general, they include any system in which probabilistic threat or risk analysis is used to assess \"trust\" for decision-making before authorizing access or for allocating resources against likely threats (including their use in the design of systems constraints to control behavior within the system); or deviation analysis or systems surveillance is used to ensure that behavior within systems complies with expected or authorized parameters.The widespread adoption of these authorization-based security strategies (where the default state is DEFAULT=DENY) for counterterrorism, anti-fraud, and other purposes is helping accelerate the ongoing transformation of modern societies from a notional Beccarian model of criminal justice based on accountability for deviant actions after they occur to a Foucauldian model based on authorization, preemption, and general social compliance through ubiquitous preventative surveillance and control through system constraints.In this emergent model, \"security\" is not geared towards policing but to risk management through surveillance, information exchange, auditing, communication, and classification. These developments have led to general concerns about individual privacy and civil liberty, and to a broader philosophical debate about appropriate social governance methodologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-canonical mode, data are accumulated in a buffer (which may or may not be the line editing buffer \u2014 some implementations having separate \"processed input\" and \"raw input\" queues) and become \"available for reading\" according to the values of two input control parameters, the c_cc and c_cc members of the termios data structure. Both are unsigned quantities (because cc_t is required to be an alias for an unsigned type). The former specifies a minimum number of characters, and the latter specifies a timeout in tenths of a second.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Common types of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental, and used in virtually every branch of modern mathematics. The study of topological spaces in their own right is called point-set topology or general topology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, many government regulations simply have categories for \"off-highway vehicles\" which are loosely defined and often result in SUVs (along with pick-up trucks and minivans) being classified as light trucks. For example, corporate average fuel economy (CAFE) regulations previously included \"permit greater cargo-carrying capacity than passenger carrying volume\" in the definition for trucks, resulting in SUVs being classified as light trucks.This classification as trucks allowed SUVs to be regulated less strictly than passenger cars under the Energy Policy and Conservation Act for fuel economy, and the Clean Air Act for emissions. However, from 2004 onwards, the United States Environmental Protection Agency (EPA) began to hold sport utility vehicles to the same tailpipe emissions standards as cars for criteria pollutants, though not greenhouse gas emissions standards as they were not set until 2010. In 2011, the CAFE regulations were changed to classify small, two-wheel-drive SUVs as passenger cars.However, the licensing and traffic enforcement regulations in the United States vary from state to state, and an SUV may be classified as a car in some states but as a truck in others.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In several Linux operating systems, the Software Updater program updates installed software and their associated packages with important software updates for security or with recommended patches. It also informs users when updates are available, listing them in alphabetical order for users to choose which updates to install, if any. It was originally written for Ubuntu, although it is now part of other APT-based systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It turns out that one can define simple formulas for P and its inverse (Cate & Twigg, 1977). First: P ( a ) = { M N \u2212 1 if a = M N \u2212 1 , N a mod ( M N \u2212 1 ) otherwise , {\\displaystyle P(a)={\\begin{cases}MN-1&{\\text{if }}a=MN-1,\\\\Na{\\bmod {(}}MN-1)&{\\text{otherwise}},\\end{cases}}} where \"mod\" is the modulo operation. Second, the inverse permutation is given by: P \u2212 1 ( a \u2032 ) = { M N \u2212 1 if a \u2032 = M N \u2212 1 , M a \u2032 mod ( M N \u2212 1 ) otherwise .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The active set at x 0 {\\displaystyle x_{0}} is made up of those constraints g i ( x 0 ) {\\displaystyle g_{i}(x_{0})} that are active at the current point (Nocedal & Wright 2006, p. 308). The active set is particularly important in optimization theory, as it determines which constraints will influence the final result of optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, consider the plaintext: crypto is short for cryptography. \"crypto\" is a repeated string, and the distance between the occurrences is 20 characters. If we line up the plaintext with a 6-character keyword \"abcdef\" (6 does not divide into 20): abcdefabcdefabcdefabcdefabcdefabc crypto is short for cryptography.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the support function hA of a non-empty closed convex set A in R n {\\displaystyle \\mathbb {R} ^{n}} describes the (signed) distances of supporting hyperplanes of A from the origin. The support function is a convex function on R n {\\displaystyle \\mathbb {R} ^{n}} . Any non-empty closed convex set A is uniquely determined by hA. Furthermore, the support function, as a function of the set A, is compatible with many natural geometric operations, like scaling, translation, rotation and Minkowski addition. Due to these properties, the support function is one of the most central basic concepts in convex geometry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In protected mode a segment cannot be both writable and executable. Therefore, when implementing the Tiny memory model the code segment register must point to the same physical address and have the same limit as the data segment register. This defeated one of the features of the 80286, which makes sure data segments are never executable and code segments are never writable (which means that self-modifying code is never allowed). However, on the 80386, with its paged memory management unit it is possible to protect individual memory pages against writing.Memory models are not limited to 16-bit programs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An ideal network structure has a vine and cluster structure, providing access to many different clusters and structural holes.Networks rich in structural holes are a form of social capital in that they offer information benefits. The main player in a network that bridges structural holes is able to access information from diverse sources and clusters. For example, in business networks, this is beneficial to an individual's career because he is more likely to hear of job openings and opportunities if his network spans a wide range of contacts in different industries/sectors. This concept is similar to Mark Granovetter's theory of weak ties, which rests on the basis that having a broad range of contacts is most effective for job attainment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Less common are unilateral contracts, in which one party makes a promise, but the other side does not promise anything. In these cases, those accepting the offer are not required to communicate their acceptance to the offeror. In a reward contract, for example, a person who has lost a dog could promise a reward if the dog is found, through publication or orally.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More generally the transition rates are given in form of a finite measure c \u039b ( \u03b7 , d \u03be ) {\\displaystyle c_{\\Lambda }(\\eta ,d\\xi )} on S \u039b {\\displaystyle S^{\\Lambda }} . The generator L {\\displaystyle L} of an IPS has the following form. First, the domain of L {\\displaystyle L} is a subset of the space of \"observables\", that is, the set of real valued continuous functions on the configuration space \u03a9 {\\displaystyle \\Omega } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are many key distribution schemes in the literature that are designed to maintain an easy and at the same time secure communication among sensor nodes. The most accepted method of key distribution in WSNs is key predistribution, where secret keys are placed in sensor nodes before deployment. When the nodes are deployed over the target area, the secret keys are used to create the network. For more info see: key distribution in wireless sensor networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example expressed in C, a program has two variables which are adjacent in memory: an 8-byte-long string buffer, A, and a two-byte big-endian integer, B. Initially, A contains nothing but zero bytes, and B contains the number 1979. Now, the program attempts to store the null-terminated string \"excessive\" with ASCII encoding in the A buffer. \"excessive\" is 9 characters long and encodes to 10 bytes including the null terminator, but A can take only 8 bytes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Woodall's conjecture, an unsolved problem in this area, states that in any directed graph the minimum number of edges in a dicut (the unweighted minimum closure) equals the maximum number of disjoint dijoins that can be found in the graph (a packing of dijoins). A fractional weighted version of the conjecture, posed by Jack Edmonds and Rick Giles, was refuted by Alexander Schrijver. In the other direction, the Lucchesi\u2013Younger theorem states that the minimum size of a dijoin equals the maximum number of disjoint dicuts that can be found in a given graph. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Stanis\u0142aw Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of a solution, direct methods may be used to compute the solution to desired accuracy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fall of 2004, the exam became computerized; the MAT is now solely a computer-based test (CBT).Out of the 120 questions, only 100 count in the test-taker's score. The remaining 20 questions are experimental. There is no way for test-takers to identify any of the 20 experimental questions on a given test form, as the two types of questions are intermingled. Tests taken before October 2004 were scored simply by the number of questions the test-taker answered correctly, with a range from 0-100.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, most failures can be traced back to some type of human error, for example in: Management decisions (e.g. in budgeting, timing, and required tasks) Systems Engineering: Use studies (load cases) Systems Engineering: Requirement analysis / setting Systems Engineering: Configuration control Assumptions Calculations / simulations / FEM analysis Design Design drawings Testing (e.g. incorrect load settings or failure measurement) Statistical analysis Manufacturing Quality control Maintenance Maintenance manuals Training Classifying and ordering of information Feedback of field information (e.g. incorrect or too vague) etc.However, humans are also very good at detecting such failures, correcting for them, and improvising when abnormal situations occur. Therefore, policies that completely rule out human actions in design and production processes to improve reliability may not be effective. Some tasks are better performed by humans and some are better performed by machines.Furthermore, human errors in management; the organization of data and information; or the misuse or abuse of items, may also contribute to unreliability. This is the core reason why high levels of reliability for complex systems can only be achieved by following a robust systems engineering process with proper planning and execution of the validation and verification tasks. This also includes careful organization of data and information sharing and creating a \"reliability culture\", in the same way that having a \"safety culture\" is paramount in the development of safety critical systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can be used to handle queries in the following fashion: when we look up cell T for some k, we can check if k is in the range {1, ..., m}: if it is not, then T is uninitialized. Otherwise, we check V], and verify that the first component of this pair is equal to k. If it is not, then T is uninitialized (and just happened by accident to fall in the range {1, ..., m}). Otherwise, we know that T is indeed one of the initialized cells, and the corresponding value is the second component of the pair.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form lim m \u2192 \u221e lim n \u2192 \u221e a n , m = lim m \u2192 \u221e ( lim n \u2192 \u221e a n , m ) {\\displaystyle \\lim _{m\\to \\infty }\\lim _{n\\to \\infty }a_{n,m}=\\lim _{m\\to \\infty }\\left(\\lim _{n\\to \\infty }a_{n,m}\\right)} , lim y \u2192 b lim x \u2192 a f ( x , y ) = lim y \u2192 b ( lim x \u2192 a f ( x , y ) ) {\\displaystyle \\lim _{y\\to b}\\lim _{x\\to a}f(x,y)=\\lim _{y\\to b}\\left(\\lim _{x\\to a}f(x,y)\\right)} ,or other similar forms. An iterated limit is only defined for an expression whose value depends on at least two variables. To evaluate such a limit, one takes the limiting process as one of the two variables approaches some number, getting an expression whose value depends only on the other variable, and then one takes the limit as the other variable approaches some number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The definition of the term named entity is therefore not strict and often has to be explained in the context in which it is used.Certain hierarchies of named entity types have been proposed in the literature. BBN categories, proposed in 2002, is used for question answering and consists of 29 types and 64 subtypes. Sekine's extended hierarchy, proposed in 2002, is made of 200 subtypes. More recently, in 2011 Ritter used a hierarchy based on common Freebase entity types in ground-breaking experiments on NER over social media text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more recent years, since the development of the top-down methodologies, IA have been used as a basis for the development of a knowledge audit, which itself in-turn contributes to an organisation's knowledge management strategy. Once complete, the IA allows examination into where knowledge is produced, where there may be need for further input and where knowledge transfer is required. Furthermore, this analysis develops strategy for knowledge capture, access, storage, dissemination and validation. Dissimilarly to the IA, the objectives of the knowledge audit are to identify any people-related issues which impact the ways in which knowledge is created, transferred and shared and to identify where knowledge could be captured, where it is required and then determine how best to undertake a knowledge transfer as \"unlike information, knowledge is bound to a person, organisation or community.\" Similarities between the knowledge and information audit methodologies can be noted however, as questionnaires, the development of an inventory, analysis of flow and a data map are here again used. The importance of this audit therefore is to understand the strategic significance of an organisation's knowledge assets to ensure management is focused to those areas it is specifically required.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psychology and sociology, a trust metric is a measurement or metric of the degree to which one social actor (an individual or a group) trusts another social actor. Trust metrics may be abstracted in a manner that can be implemented on computers, making them of interest for the study and engineering of virtual communities, such as Friendster and LiveJournal. Trust escapes a simple measurement because its meaning is too subjective for universally reliable metrics, and the fact that it is a mental process, unavailable to instruments. There is a strong argument against the use of simplistic metrics to measure trust due to the complexity of the process and the 'embeddedness' of trust that makes it impossible to isolate trust from related factors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Now, \u03b8 \u02d8 j = h \u2212 1 ( s , z \u02d8 1 j , \u2026 , z \u02d8 m j ) {\\displaystyle {\\breve {\\theta }}_{j}=h^{-1}(s,{\\breve {z}}_{1}^{j},\\ldots ,{\\breve {z}}_{m}^{j})} is a solution of (1) with the seed { z \u02d8 1 j , \u2026 , z \u02d8 m j } {\\displaystyle \\{{\\breve {z}}_{1}^{j},\\ldots ,{\\breve {z}}_{m}^{j}\\}} . Since the seeds are equally distributed, the sole caveat comes from their independence or, conversely from their dependence on ?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in number theory, Gauss composition law is a rule, invented by Carl Friedrich Gauss, for performing a binary operation on integral binary quadratic forms (IBQFs). Gauss presented this rule in his Disquisitiones Arithmeticae, a textbook on number theory published in 1801, in Articles 234 - 244. Gauss composition law is one of the deepest results in the theory of IBQFs and Gauss's formulation of the law and the proofs its properties as given by Gauss are generally considered highly complicated and very difficult. Several later mathematicians have simplified the formulation of the composition law and have presented it in a format suitable for numerical computations. The concept has also found generalisations in several directions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other words, if a model defines type COLOUR ::= red | blue | green and some operation uses c of type COLOUR, then by applying this tactic each test class will by divided into three new test classes: one in which c equals red, the other in which c equals blue, and the third where c equals green. Proper Subset of Set Extension (PSSE). This tactic uses the same concept of ISE but applied to set inclusions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Mood can be bound up with tense, aspect, or both, in particular verb forms. Hence, certain languages are sometimes analysed as having a single tense\u2013aspect\u2013mood (TAM) system, without separate manifestation of the three categories. The term tense, then, particularly in less formal contexts, is sometimes used to denote any combination of tense proper, aspect, and mood.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Storable resources remain available unless depleted by usage, and may be replenished by project tasks that produce them. Nonstorable resources must be renewed for each time period, even if not used in previous periods.Resource scheduling, availability, and optimisation are considered key to successful project management.Allocation of limited resources is based on the priority given to each of the project activities. Their priorities are calculated using the critical path method and heuristic analysis. For a case with a constraint on the available resources, the objective is to create the most efficient schedule possible - minimising project duration and maximising the use of the resources available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case r=2, the hypergraph becomes a bipartite graph, and the conjecture becomes \u03c4 ( H ) \u2264 \u03bd ( H ) {\\displaystyle \\tau (H)\\leq \\nu (H)} . This is known to be true by K\u0151nig's theorem. In the case r=3, the conjecture has been proved by Ron Aharoni. The proof uses the Aharoni-Haxell theorem for matching in hypergraphs. In the cases r=4 and r=5, the following weaker version has been proved by Penny Haxell and Scott: there exists some \u03b5 > 0 such that \u03c4 ( H ) \u2264 ( r \u2212 \u03b5 ) \u22c5 \u03bd ( H ) {\\displaystyle \\tau (H)\\leq (r-\\varepsilon )\\cdot \\nu (H)} .Moreover, in the cases r=4 and r=5, Ryser's conjecture has been proved by Tuza (1978) in the special case \u03bd ( H ) = 1 {\\displaystyle \\nu (H)=1} , i.e.: \u03bd ( H ) = 1 \u27f9 \u03c4 ( H ) \u2264 r \u2212 1 {\\displaystyle \\nu (H)=1\\implies \\tau (H)\\leq r-1} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the entropy influence conjecture is a statement about Boolean functions originally conjectured by Ehud Friedgut and Gil Kalai in 1996.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and in particular model theory, a prime model is a model that is as simple as possible. Specifically, a model P {\\displaystyle P} is prime if it admits an elementary embedding into any model M {\\displaystyle M} to which it is elementarily equivalent (that is, into any model M {\\displaystyle M} satisfying the same complete theory as P {\\displaystyle P} ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Euler's sum of powers conjecture (disproved) concerns situations in which the sum of n integers, each a kth power of an integer, equals another kth power. The Fermat-Catalan conjecture asks whether there are an infinitude of examples in which the sum of two coprime integers, each a power of an integer, with the powers not necessarily equal, can equal another integer that is a power, with the reciprocals of the three powers summing to less than 1. Beal's conjecture concerns the question of whether the sum of two coprime integers, each a power greater than 2 of an integer, with the powers not necessarily equal, can equal another integer that is a power greater than 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead, the receiving 'client' (object or function) is provided with its dependencies by external code (an 'injector'), which it is not aware of. Dependency injection makes implicit dependencies explicit and helps solve the following problems: How can a class be independent from the creation of the objects it depends on? How can an application, and the objects it uses support different configurations?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The record size is stored on a file-by-file basis in special entries in the directory table. Sequential access methods for IBM's z/OS and z/VSE mainframe operating systems: Basic Sequential Access Method (BSAM), Basic Partitioned Access Method (BPAM) and Queued Sequential Access Method (QSAM); see Access methods and Data set (IBM mainframe) for more examples Pick Operating System \u2013 A record-oriented filesystem and database that uses hash-coding to store data. Shared File System (SFS) for IBM's VM Virtual Storage Access Method (VSAM) \u2013 for IBM's z/OS and z/VSE mainframe operating systems", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof, a kind of proof whose semantic properties are exposed. When all the theorems of a logic formalised in a structural proof theory have analytic proofs, then the proof theory can be used to demonstrate such things as consistency, provide decision procedures, and allow mathematical or computational witnesses to be extracted as counterparts to theorems, the kind of task that is more often given to model theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The dual graph of a directed graph, embedded in the plane, is a graph with a vertex for each face of the given graph, and a dual edge between two dual vertices when the corresponding two faces are separated by an edge. Each dual edge crosses one of the original graph edges, turned by 90\u00b0 clockwise. For a dicut in the given graph, the duals of the edges that cross the dicut form a directed cycle in the dual graph, and vice versa.A dijoin can be defined as a set of edges that crosses all dicuts; when the edges of a dijoin are contracted, the result is a strongly connected graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: x 2 \u2261 q ( mod n ) . {\\displaystyle x^{2}\\equiv q{\\pmod {n}}.} Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical classification, the Bayes classifier minimizes the probability of misclassification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is some centralization (a general assembly) and some central decision (over local decision): there is no choice of \"each room decision\" or \"each regulars' community decision\". So it is a central decision. The subsidiarity principle can be applied: there is an \"embryonic local governance\" connecting the cyclists, and the other people (voters) of the condominium recognise the group, transferring some (little) responsibility to them (the keys of the gym room and right to advocate their cycling activities to other residents).There is no \"enforced minoritarianism\"; it seems a legitimate characterization of a relevant (and not dominant) minority. This is a tyranny of the majority situation because: there is a little \"global gain\" in a global decision (where X wins), and a good \"local gain\" in local decision (local Y preference); there is relevant voting for a local decision: 6 voters (46%) are gym room regulars, 5 that voted Y. The majority of them (83%) voted Y.In this situation, even with no formal federation structure, the minority and a potential local governance emerged: the tyranny perception arrives with it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Neyman\u2013Pearson lemma was introduced by Jerzy Neyman and Egon Pearson in a paper in 1933. The Neyman-Pearson lemma is part of the Neyman-Pearson theory of statistical testing, which introduced concepts like errors of the second kind, power function, and inductive behavior. The previous Fisherian theory of significance testing postulated only one hypothesis. By introducing a competing hypothesis, the Neyman-Pearsonian flavor of statistical testing allows investigating the two types of errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In stack-oriented programming languages (and concatenative ones, most of which are stack based), point-free methods are commonly used. For example, a procedure to compute the Fibonacci numbers might look like the following in PostScript:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to effectively implement variables of such types as array structures (with indexing done by pointer arithmetic), many languages restrict the indices to integer data types (or other types that can be interpreted as integers, such as bytes and enumerated types), and require that all elements have the same data type and storage size. Most of those languages also restrict each index to a finite interval of integers, that remains fixed throughout the lifetime of the array variable. In some compiled languages, in fact, the index ranges may have to be known at compile time. On the other hand, some programming languages provide more liberal array types, that allow indexing by arbitrary values, such as floating-point numbers, strings, objects, references, etc.. Such index values cannot be restricted to an interval, much less a fixed interval.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition includes all positive rational numbers with this property.The sequence of (integer) congruent numbers starts with 5, 6, 7, 13, 14, 15, 20, 21, 22, 23, 24, 28, 29, 30, 31, 34, 37, 38, 39, 41, 45, 46, 47, 52, 53, 54, 55, 56, 60, 61, 62, 63, 65, 69, 70, 71, 77, 78, 79, 80, 84, 85, 86, 87, 88, 92, 93, 94, 95, 96, 101, 102, 103, 109, 110, 111, 112, 116, 117, 118, 119, 120, ... (sequence A003273 in the OEIS) For example, 5 is a congruent number because it is the area of a (20/3, 3/2, 41/6) triangle. Similarly, 6 is a congruent number because it is the area of a (3,4,5) triangle. 3 and 4 are not congruent numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In philosophy, ontological maximalism (or metaontological maximalism) is a ontological realist position that asserts, \"whatever can exist does in some sense exist\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a natural number n is a Blum integer if n = p \u00d7 q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes. This means that the factors of a Blum integer are Gaussian primes with no imaginary part. The first few Blum integers are 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 341, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, ... (sequence A016105 in the OEIS)The integers were named for computer scientist Manuel Blum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Georg Cantor, the inventor of set theory, showed in 1874 that there is more than one kind of infinity, specifically that the collection of all natural numbers and the collection of all real numbers, while both infinite, are not equinumerous (see Cantor's first uncountability proof). In his controversial 1878 paper, Cantor explicitly defined the notion of \"power\" of sets and used it to prove that the set of all natural numbers and the set of all rational numbers are equinumerous (an example where a proper subset of an infinite set is equinumerous to the original set), and that the Cartesian product of even a countably infinite number of copies of the real numbers is equinumerous to a single copy of the real numbers. Cantor's theorem from 1891 implies that no set is equinumerous to its own power set (the set of all its subsets).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This recovers both the inclusion of finite sets in sets (where a cogenerator is the set of two elements), and also the inclusion of finite-dimensional vector spaces in vector spaces (where the cogenerator is the ground field). Sipo\u015f showed that the algebras over the codensity monad of the inclusion of finite sets (regarded as discrete topological spaces) into topological spaces are equivalent to Stone spaces. Avery shows that the Giry monad arises as the codensity monad of natural forgetful functors between certain categories of convex vector spaces to measurable spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A theory consists of some basis statements called axioms, and some deducing rules (sometimes included in the axioms). The theorems of the theory are the statements that can be derived from the axioms by using the deducing rules. This formalization led to proof theory, which allows proving general theorems about theorems and proofs. In particular, G\u00f6del's incompleteness theorems show that every consistent theory containing the natural numbers has true statements on natural numbers that are not theorems of the theory (that is they cannot be proved inside the theory). As the axioms are often abstractions of properties of the physical world, theorems may be considered as expressing some truth, but in contrast to the notion of a scientific law, which is experimental, the justification of the truth of a theorem is purely deductive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here the matrix completion problem does not obey the restricted isometry property (RIP). For matrices, the RIP would assume that the sampling operator obeys ( 1 \u2212 \u03b4 ) \u2016 X \u2016 F 2 \u2264 1 p \u2016 P \u03a9 ( X ) \u2016 F 2 \u2264 ( 1 + \u03b4 ) \u2016 X \u2016 F 2 {\\displaystyle (1-\\delta )\\|X\\|_{F}^{2}\\leq {\\frac {1}{p}}\\|P_{\\Omega }(X)\\|_{F}^{2}\\leq (1+\\delta )\\|X\\|_{F}^{2}} for all matrices X {\\displaystyle X} with sufficiently small rank and \u03b4 < 1 {\\displaystyle \\delta <1} sufficiently small. The methods are also applicable to sparse signal recovery problems in which the RIP does not hold.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the definitions above, the functions T(x), \u03b7(\u03b8), and A(\u03b7) were arbitrary. However, these functions have important interpretations in the resulting probability distribution. T(x) is a sufficient statistic of the distribution. For exponential families, the sufficient statistic is a function of the data that holds all information the data x provides with regard to the unknown parameter values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a byproduct of this latter work, she proved Sophie Germain's theorem, which verified the first case of Fermat's Last Theorem (namely, the case in which p {\\displaystyle p} does not divide x y z {\\displaystyle xyz} ) for every odd prime exponent less than 270 {\\displaystyle 270} , and for all primes p {\\displaystyle p} such that at least one of 2 p + 1 {\\displaystyle 2p+1} , 4 p + 1 {\\displaystyle 4p+1} , 8 p + 1 {\\displaystyle 8p+1} , 10 p + 1 {\\displaystyle 10p+1} , 14 p + 1 {\\displaystyle 14p+1} and 16 p + 1 {\\displaystyle 16p+1} is prime (specially, the primes p {\\displaystyle p} such that 2 p + 1 {\\displaystyle 2p+1} is prime are called Sophie Germain primes). Germain tried unsuccessfully to prove the first case of Fermat's Last Theorem for all even exponents, specifically for n = 2 p {\\displaystyle n=2p} , which was proved by Guy Terjanian in 1977. In 1985, Leonard Adleman, Roger Heath-Brown and \u00c9tienne Fouvry proved that the first case of Fermat's Last Theorem holds for infinitely many odd primes p {\\displaystyle p} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It implies a coarse-grained authentication, given that domains appear on the right part of email addresses, after the at sign. Fine-grain authentication, at user level, can be achieved by other means, such as Pretty Good Privacy and S/MIME. At present, digital identity needs to be managed by each individual.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a member of the (a, b, 0) class of distributions is any distribution of a discrete random variable N whose values are nonnegative integers whose probability mass function satisfies the recurrence formula p k p k \u2212 1 = a + b k , k = 1 , 2 , 3 , \u2026 {\\displaystyle {\\frac {p_{k}}{p_{k-1}}}=a+{\\frac {b}{k}},\\qquad k=1,2,3,\\dots } for some real numbers a and b, where p k = P ( N = k ) {\\displaystyle p_{k}=P(N=k)} . Only the Poisson, binomial and negative binomial distributions satisfy the full form of this relationship. These are also the three discrete distributions among the six members of the natural exponential family with quadratic variance functions (NEF\u2013QVF). More general distributions can be defined by fixing some initial values of pj and applying the recursion to define subsequent values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The n-dimensional parallelotope spanned by the rows of an n\u00d7n Hadamard matrix has the maximum possible n-dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value by 1. Equivalently, a Hadamard matrix has maximal determinant among matrices with entries of absolute value less than or equal to 1 and so is an extremal solution of Hadamard's maximal determinant problem. Certain Hadamard matrices can almost directly be used as an error-correcting code using a Hadamard code (generalized in Reed\u2013Muller codes), and are also used in balanced repeated replication (BRR), used by statisticians to estimate the variance of a parameter estimator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An alternative way to compute C X {\\displaystyle {\\textbf {C}}_{X}} , is by using the N \u2032 \u00d7 M {\\displaystyle N'\\times M} \"trajectory matrix\" D {\\displaystyle {\\textbf {D}}} that is formed by M {\\displaystyle M} lag-shifted copies of X ( t ) {\\displaystyle {\\it {X(t)}}} , which are N \u2032 = N \u2212 M + 1 {\\displaystyle N'=N-M+1} long; then C X = 1 N \u2032 D t D . {\\displaystyle {\\textbf {C}}_{X}={\\frac {1}{N'}}{\\textbf {D}}^{\\rm {t}}{\\textbf {D}}.} The M {\\displaystyle M} eigenvectors E k {\\displaystyle {\\textbf {E}}_{k}} of the lag-covariance matrix C X {\\displaystyle {\\textbf {C}}_{X}} are called temporal empirical orthogonal functions (EOFs).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In technical applications of 3D computer graphics (CAx) such as computer-aided design and computer-aided manufacturing, surfaces are one way of representing objects. The other ways are wireframe (lines and curves) and solids. Point clouds are also sometimes used as temporary ways to represent an object, with the goal of using the points to create one or more of the three permanent representations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-Germanic Indo-European languages, past marking is typically combined with a distinction between perfective and imperfective aspect, with the former reserved for single completed actions in the past. French for instance, has an imperfect tense form similar to that of German but used only for past habitual or past progressive contexts like \"I used to...\" or \"I was doing...\". Similar patterns extend across most languages of the Indo-European family right through to the Indic languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The discovery of deuterium stood, however.Urey and Washburn attempted to use electrolysis to create pure heavy water. Their technique was sound, but they were beaten to it in 1933 by Lewis, who had the resources of the University of California at his disposal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software architecture, a service mesh is a dedicated infrastructure layer for facilitating service-to-service communications between services or microservices using a proxy.A dedicated communication layer can provide numerous benefits, such as providing observability into communications, providing secure connections or automating retries and backoff for failed requests.A service mesh consists of network proxies paired with each service in an application and a set of task-management processes. The proxies are called the data plane and the management processes are called the control plane. The data plane intercepts calls between different services and processes them; the control plane is the brain of the mesh that coordinates the behavior of proxies and provides APIs for operations and maintenance personnel to manipulate and observe the entire network.The service mesh architecture is implemented by software products such as Istio, Cilium, Linkerd, Consul, AWS App Mesh, Kuma, Traefik Mesh, Greymatter.io and Open Service Mesh. Many service meshes use the Envoy proxy on the data plane.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusually large number of proofs. Several hundred proofs of the law of quadratic reciprocity have been published.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Bauer\u2013Fike theorem is a standard result in the perturbation theory of the eigenvalue of a complex-valued diagonalizable matrix. In its substance, it states an absolute upper bound for the deviation of one perturbed matrix eigenvalue from a properly chosen eigenvalue of the exact matrix. Informally speaking, what it says is that the sensitivity of the eigenvalues is estimated by the condition number of the matrix of eigenvectors. The theorem was proved by Friedrich L. Bauer and C. T. Fike in 1960.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(Gauss' conjecture was proven more than one hundred years later by Kurt Heegner, Alan Baker and Harold Stark.) However, this was understood (only) in the language of equivalence classes of quadratic forms, so that in particular the analogy between quadratic forms and the Fermat equation seems not to have been perceived.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They may also be used for ordering (as in \"this is the third largest city in the country\"), in which case they serve as ordinal numbers. Natural numbers are sometimes used as labels, known as nominal numbers, having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers).The natural numbers form a set, often symbolized as N {\\textstyle \\mathbb {N} } . Many other number sets are built by successively extending the set of natural numbers: the integers, by including an additive identity 0 (if not yet in) and an additive inverse \u2212n for each nonzero natural number n; the rational numbers, by including a multiplicative inverse 1 / n {\\displaystyle 1/n} for each nonzero integer n (and also the product of these inverses by integers); the real numbers by including the limits of Cauchy sequences of rationals; the complex numbers, by adjoining to the real numbers a square root of \u22121 (and also the sums and products thereof); and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle 0,1,2,3,\\ldots ,n,\\ldots ;\\aleph _{0},\\aleph _{1},\\aleph _{2},\\ldots ,\\aleph _{\\alpha },\\ldots .\\ } This sequence starts with the natural numbers including zero (finite cardinals), which are followed by the aleph numbers. The aleph numbers are indexed by ordinal numbers. If the axiom of choice is true, this transfinite sequence includes every cardinal number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, although it is easy to score a phylogenetic tree (by counting the number of character-state changes), there is no algorithm to quickly generate the most-parsimonious tree. Instead, the most-parsimonious tree must be sought in \"tree space\" (i.e., amongst all possible trees). For a small number of taxa (i.e., fewer than nine) it is possible to do an exhaustive search, in which every possible tree is scored, and the best one is selected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a cardinal function (or cardinal invariant) is a function that returns cardinal numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to demonstrate that IP \u2286 PSPACE, we present a simulation of an interactive proof system by a polynomial space machine. Now, we can define: Pr  = max P Pr  {\\displaystyle \\Pr=\\max \\nolimits _{P}\\Pr \\left} and for every 0 \u2264 j \u2264 p and every message history Mj, we inductively define the function NMj: N M j = { 0 j = p and m p = reject 1 j = p and m p = accept max m j + 1 N M j + 1 j < p and j is odd wt-avg m j + 1 N M j + 1 j < p and j is even {\\displaystyle N_{M_{j}}={\\begin{cases}0&j=p{\\text{ and }}m_{p}={\\text{reject}}\\\\1&j=p{\\text{ and }}m_{p}={\\text{accept}}\\\\\\max _{m_{j+1}}N_{M_{j+1}}&j", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since Alice chooses a {\\displaystyle a} randomly, and since b is independent of a {\\displaystyle a} , Alice is guaranteed that the bit d = a \u2295 b {\\displaystyle d=a\\oplus b} is random. With similar arguments, Bob is also guaranteed that the bit d is random. Variations of coin tossing have been investigated in relativistic cryptography by Colbeck and Kent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although many functions do not have an inverse, every relation does have a unique converse. The unary operation that maps a relation to the converse relation is an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or, more generally, induces a dagger category on the category of relations as detailed below. As a unary operation, taking the converse (sometimes called conversion or transposition) commutes with the order-related operations of the calculus of relations, that is it commutes with union, intersection, and complement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let T 1 {\\displaystyle T_{1}} be a theory obtained from T {\\displaystyle T} by extending its language with new constants a 1 , \u2026 , a m {\\displaystyle a_{1},\\ldots ,a_{m}} and adding a new axiom \u03c6 ( a 1 , \u2026 , a m ) {\\displaystyle \\varphi (a_{1},\\ldots ,a_{m})} .Then T 1 {\\displaystyle T_{1}} is a conservative extension of T {\\displaystyle T} , which means that the theory T 1 {\\displaystyle T_{1}} has the same set of theorems in the original language (i.e., without constants a i {\\displaystyle a_{i}} ) as the theory T {\\displaystyle T} . Such a theory can also be conservatively extended by introducing a new functional symbol:Suppose that a closed formula \u2200 x \u2192 \u2203 y \u03c6 ( y , x \u2192 ) {\\displaystyle \\forall {\\vec {x}}\\,\\exists y\\,\\!\\,\\varphi (y,{\\vec {x}})} is a theorem of a first-order theory T {\\displaystyle T} , where we denote x \u2192 := ( x 1 , \u2026 , x n ) {\\displaystyle {\\vec {x}}:=(x_{1},\\ldots ,x_{n})} . Let T 1 {\\displaystyle T_{1}} be a theory obtained from T {\\displaystyle T} by extending its language with a new functional symbol f {\\displaystyle f} (of arity n {\\displaystyle n} ) and adding a new axiom \u2200 x \u2192 \u03c6 ( f ( x \u2192 ) , x \u2192 ) {\\displaystyle \\forall {\\vec {x}}\\,\\varphi (f({\\vec {x}}),{\\vec {x}})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the digital imaging community the term annotation is commonly used for visible metadata superimposed on an image without changing the underlying master image, such as sticky notes, virtual laser pointers, circles, arrows, and black-outs (cf. redaction).In the medical imaging community, an annotation is often referred to as a region of interest and is encoded in DICOM format.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, quantum channels, or quantum operations, are defined to be completely positive maps between C*-algebras. Being a classification for all such maps, Stinespring's theorem is important in that context. For example, the uniqueness part of the theorem has been used to classify certain classes of quantum channels. For the comparison of different channels and computation of their mutual fidelities and information another representation of the channels by their \"Radon\u2013Nikodym\" derivatives introduced by Belavkin is useful.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The ability to perform economical maximum likelihood soft decision decoding is one of the major benefits of convolutional codes. This is in contrast to classic block codes, which are generally represented by a time-variant trellis and therefore are typically hard-decision decoded. Convolutional codes are often characterized by the base code rate and the depth (or memory) of the encoder  {\\displaystyle } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Page faults are not only used for memory protection. The operating system may manage the page table in such a way that a reference to a page that has been previously paged out to secondary storage causes a page fault. The operating system intercepts the page fault, loads the required memory page, and the application continues as if no fault had occurred.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of mathematics called combinatorial optimization, the method of symmetry-breaking constraints can be used to take advantage of symmetries in many constraint satisfaction and optimization problems, by adding constraints that eliminate symmetries and reduce the search space size. Symmetries in a combinatorial problem increase the size of the search space and therefore, time is wasted in visiting new solutions which are symmetric to the already visited solutions. The solution time of a combinatorial problem can be reduced by adding new constraints, referred as symmetry breaking constraints, such that some of the symmetric solutions are eliminated from the search space while preserving the existence of at least one solution.Symmetry is common in many real-life combinatorial problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recursive function theory, double recursion is an extension of primitive recursion which allows the definition of non-primitive recursive functions like the Ackermann function. Raphael M. Robinson called functions of two natural number variables G(n, x) double recursive with respect to given functions, if G(0, x) is a given function of x. G(n + 1, 0) is obtained by substitution from the function G(n, \u00b7) and given functions. G(n + 1, x + 1) is obtained by substitution from G(n + 1, x), the function G(n, \u00b7) and given functions.Robinson goes on to provide a specific double recursive function (originally defined by R\u00f3zsa P\u00e9ter) G(0, x) = x + 1 G(n + 1, 0) = G(n, 1) G(n + 1, x + 1) = G(n, G(n + 1, x))where the given functions are primitive recursive, but G is not primitive recursive. In fact, this is precisely the function now known as the Ackermann function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the average case, if the input numbers are distributed uniformly in , then the largest sum in an LPT schedule satisfies the following properties: The expected largest sum for m=2 machines is at least n 4 + 1 4 n + 4 {\\displaystyle {\\frac {n}{4}}+{\\frac {1}{4n+4}}} and at most n 4 + e 2 n + 2 {\\displaystyle {\\frac {n}{4}}+{\\frac {e}{2n+2}}} , where n is the number of inputs. The largest sum is at most 1 + O ( log \u2061 log \u2061 n / n ) {\\displaystyle 1+O(\\log {\\log {n}}/n)} times the optimum almost surely, and 1 + O ( 1 / n ) {\\displaystyle 1+O(1/n)} in expectation, where n {\\displaystyle n} is the number of inputs. The difference between the LPT largest sum and the optimal largest sum is at most O ( log \u2061 n / n ) {\\displaystyle O(\\log {n}/n)} almost surely (for uniform or negative exponential distributions), and at most O ( m 2 / n ) {\\displaystyle O(m^{2}/n)} in expectation (for uniform distribution). These results hold also for machines with different speeds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Very long numbers can be further grouped by doubling up separators. Typically decimal numbers (base-10) are grouped in three digit groups (representing one of 1000 possible values), binary numbers (base-2) in four digit groups (one nibble, representing one of 16 possible values), and hexadecimal numbers (base-16) in two digit groups (each digit is one nibble, so two digits are one byte, representing one of 256 possible values). Numbers from other systems (such as id numbers) are grouped following whatever convention is in use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, the following properties hold: P i 2 = 1 , i = 1 , 2 , . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems theory, the black box is an abstraction representing a class of concrete open system which can be viewed solely in terms of its stimuli inputs and output reactions: The constitution and structure of the box are altogether irrelevant to the approach under consideration, which is purely external or phenomenological. In other words, only the behavior of the system will be accounted for. The understanding of a black box is based on the \"explanatory principle\", the hypothesis of a causal relation between the input and the output. This principle states that input and output are distinct, that the system has observable (and relatable) inputs and outputs and that the system is black to the observer (non-openable).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Now operator decides the number of vehicles(N), which use alternative route. The optimal number of vehicles (N) can be obtained by calculus of variation, to make marginal cost of each route equal. Thus, optimal condition is T0 = T1 + \u22061.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. Depending upon the application involved, the distance being used to define this matrix may or may not be a metric. If there are N elements, this matrix will have size N\u00d7N. In graph-theoretic applications, the elements are more often referred to as points, nodes or vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The process was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and insurance mathematics.The Poisson point process is often defined on the real line, where it can be considered as a stochastic process. In this setting, it is used, for example, in queueing theory to model random events, such as the arrival of customers at a store, phone calls at an exchange or occurrence of earthquakes, distributed in time. In the plane, the point process, also known as a spatial Poisson process, can represent the locations of scattered objects such as transmitters in a wireless network, particles colliding into a detector, or trees in a forest.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In printing and publishing, proofs are the preliminary versions of publications meant for review by authors, editors, and proofreaders, often with extra-wide margins. Galley proofs may be uncut and unbound, or in some cases electronically transmitted. They are created for proofreading and copyediting purposes, but may also be used for promotional and review purposes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, on a social platform a supplier of sports gear promises the first 20 callers a free bicycle helmet. The lapse of this information is significant. Then, after the 20th reader has called, the information value drops down to zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the eIDAS Regulation trust services are defined as electronic services, normally provided by TSPs, which consist of electronic signatures, electronic seals, electronic time stamps, electronic registered delivery services and website authentication.In essence, the eIDAS Regulation provides a framework to promote: Transparency and accountability: well-defined minimal obligations for TSPs and liability. Guarantee of trustworthiness of the services together with security requirements for TSPs. Technological neutrality: avoiding requirements which could only be met by a specific technology. Market rules and standardization certainty.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic and computer science, some type theories and type systems include a top type that is commonly denoted with top or the symbol \u22a4. The top type is sometimes called also universal type, or universal supertype as all other types in the type system of interest are subtypes of it, and in most cases, it contains every possible object of the type system. It is in contrast with the bottom type, or the universal subtype, which every other type is supertype of and it is often that the type contains no members at all.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order theory, an embedding of partially ordered sets is a function F {\\displaystyle F} between partially ordered sets X {\\displaystyle X} and Y {\\displaystyle Y} such that \u2200 x 1 , x 2 \u2208 X: x 1 \u2264 x 2 \u27fa F ( x 1 ) \u2264 F ( x 2 ) . {\\displaystyle \\forall x_{1},x_{2}\\in X:x_{1}\\leq x_{2}\\iff F(x_{1})\\leq F(x_{2}).} Injectivity of F {\\displaystyle F} follows quickly from this definition. In domain theory, an additional requirement is that \u2200 y \u2208 Y: { x \u2223 F ( x ) \u2264 y } {\\displaystyle \\forall y\\in Y:\\{x\\mid F(x)\\leq y\\}} is directed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory, the POPLmark challenge (from \"Principles of Programming Languages benchmark\", formerly Mechanized Metatheory for the Masses!) (Aydemir, 2005) is a set of benchmarks designed to evaluate the state of automated reasoning (or mechanization) in the metatheory of programming languages, and to stimulate discussion and collaboration among a diverse cross section of the formal methods community. Very loosely speaking, the challenge is about measurement of how well programs may be proven to match a specification of how they are intended to behave (and the many complex issues that this involves). The challenge was initially proposed by the members of the PL club at the University of Pennsylvania, in association with collaborators around the world.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "First, one typically starts by defining a term as follows: A variable, or A function symbol applied to the number of terms required by the function symbol's arity.For example, if + is a binary function symbol and x, y, and z are variables, then x+(y+z) is a term, which might be written with the symbols in various orders. Once a term is defined, a proposition can then be defined as follows: A predicate symbol applied to the number of terms required by its arity, or An operator applied to the number of propositions required by its arity, or A quantifier applied to a proposition.For example, if = is a binary predicate symbol and \u2200 is a quantifier, then \u2200x,y,z  is a proposition. This more complex structure of propositions allows these logics to make finer distinctions between inferences, i.e., to have greater expressive power.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Stone functor is a functor S: Topop \u2192 Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras and Boolean homomorphisms. It assigns to each topological space X the Boolean algebra S(X) of its clopen subsets, and to each morphism fop: X \u2192 Y in Topop (i.e., a continuous map f: Y \u2192 X) the homomorphism S(f): S(X) \u2192 S(Y) given by S(f)(Z) = f\u22121.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The human body, being a physiological universal, provides an ideal domain for research into semantic and lexical universals. In a seminal study, Cecil H. Brown (1976) proposed a number of universals in the semantics of body part terminology, including the following: in any language, there will be distinct terms for BODY, HEAD, ARM, EYES, NOSE, and MOUTH; if there is a distinct term for FOOT, there will be a distinct term for HAND; similarly, if there are terms for INDIVIDUAL TOES, then there are terms for INDIVIDUAL FINGERS. Subsequent research has shown that most of these features have to be considered cross-linguistic tendencies rather than true universals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, using the properties of the cumulant generating function, E \u2061 ( T j ) = \u2202 A ( \u03b7 ) \u2202 \u03b7 j {\\displaystyle \\operatorname {E} (T_{j})={\\frac {\\partial A(\\eta )}{\\partial \\eta _{j}}}} and cov \u2061 ( T i , T j ) = \u2202 2 A ( \u03b7 ) \u2202 \u03b7 i \u2202 \u03b7 j . {\\displaystyle \\operatorname {cov} \\left(T_{i},\\ T_{j}\\right)={\\frac {\\partial ^{2}A(\\eta )}{\\partial \\eta _{i}\\,\\partial \\eta _{j}}}.} The first two raw moments and all mixed second moments can be recovered from these two identities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct elements; that is, x1 \u2260 x2 implies f(x1) \u2260 f(x2). (Equivalently, f(x1) = f(x2) implies x1 = x2 in the equivalent contrapositive statement.) In other words, every element of the function's codomain is the image of at most one element of its domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, the mediator pattern defines an object that encapsulates how a set of objects interact. This pattern is considered to be a behavioral pattern due to the way it can alter the program's running behavior. In object-oriented programming, programs often consist of many classes. Business logic and computation are distributed among these classes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Different theoretical explanations of these inconsistencies are discussed later in the article. There are various types of phrase in which the ordering of head and complement(s) may be considered when attempting to determine the head directionality of a language, including: Verb Phrase: the head of verb phrase (VP) is a verb, and the complement(s) are most commonly objects of various types. The ordering here is related to one of the chief questions in the word order typology of languages, namely the normal order of subject, verb and object within a clause (languages are classed on this basis as SVO, SOV, VSO, etc.).Noun Phrase: the head of a noun phrase (NP) is a noun; various kinds of complementizer phrases (CPs) and adpositional phrases (PPs) can be complements.Adjective Phrase: the head of an adjective phrase (AP) is an adjective, which can take as a complement, for example, an adverbial phrase or adpositional phrase (PP).Adpositional Phrase: the head of an adpositional phrase (PP) is an apposition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the CC4 network, which is a three-stage network, the number of input nodes is one more than the size of the training vector, with the extra node serving as the biasing node whose input is always 1. For binary input vectors, the weights from the input nodes to the hidden neuron (say of index j) corresponding to the trained vector is given by the following formula: w i j = { \u2212 1 , for x i = 0 + 1 , for x i = 1 r \u2212 s + 1 , for i = n + 1 {\\displaystyle w_{ij}={\\begin{cases}-1,&{\\mbox{for }}x_{i}=0\\\\+1,&{\\mbox{for }}x_{i}=1\\\\r-s+1,&{\\mbox{for }}i=n+1\\end{cases}}} where r {\\displaystyle r} is the radius of generalization and s {\\displaystyle s} is the Hamming weight (the number of 1s) of the binary sequence. From the hidden layer to the output layer the weights are 1 or -1 depending on whether the vector belongs to a given output class or not. The neurons in the hidden and output layers output 1 if the weighted sum to the input is 0 or positive and 0, if the weighted sum to the input is negative: y = { 1 if \u2211 x i \u2265 0 0 if \u2211 x i < 0 {\\displaystyle y=\\left\\{{\\begin{matrix}1&{\\mbox{if }}\\sum x_{i}\\geq 0\\\\0&{\\mbox{if }}\\sum x_{i}<0\\end{matrix}}\\right.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Camel case is sometimes used for abbreviated names of certain neighborhoods, e.g. New York City neighborhoods SoHo (South of Houston Street) and TriBeCa (Triangle Below Canal Street) and San Francisco's SoMa (South of Market). Such usages erode quickly, so the neighborhoods are now typically rendered as Soho, Tribeca, and Soma. Internal capitalization has also been used for other technical codes like HeLa (1983).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of education, one-to-one computing (sometimes abbreviated as \"1:1\") refers to academic institutions, such as schools or colleges, that allow each enrolled student to use an electronic device in order to access the Internet, digital course materials, and digital textbooks. The concept has been actively explored and sporadically implemented since the late 1990s. One-to-one computing used to be contrasted with a policy of \"bring your own device\" (BYOD), which encourages or requires students to use their own laptops, smartphones or other electronic devices in class.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Rather than a complicated script running a set of unit tests, if this simple programme fails to compile or execute, it proves that the supporting environment likely has a configuration problem that will prevent any code from compiling or executing. But if \"Hello world\" executes, then any problems experienced with other programmes likely can be attributed to errors in that application's code rather than the environment. The Association for Computing Machinery, and software projects such as Android, MediaWiki and Twitter, discourage use of the phrase sanity check in favour of other terms such as confidence test, coherence check, or simply test, as part of a wider attempt to avoid ableist language and increase inclusivity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, matrices will be indicated by indexed variables. \"Subject\" indices will be indicated using letters a {\\displaystyle a} , b {\\displaystyle b} and c {\\displaystyle c} , with values running from 1 {\\displaystyle 1} to p {\\displaystyle p} which is equal to 10 {\\displaystyle 10} in the above example. \"Factor\" indices will be indicated using letters p {\\displaystyle p} , q {\\displaystyle q} and r {\\displaystyle r} , with values running from 1 {\\displaystyle 1} to k {\\displaystyle k} which is equal to 2 {\\displaystyle 2} in the above example. \"Instance\" or \"sample\" indices will be indicated using letters i {\\displaystyle i} , j {\\displaystyle j} and k {\\displaystyle k} , with values running from 1 {\\displaystyle 1} to N {\\displaystyle N} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example S = {e,f} with the equalities given, S is a semigroup. It demonstrates the possibility for (S, \u2217) to have several left identities. In fact, every element can be a left identity. In a similar manner, there can be several right identities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1881, the company changed its name to the Champion Bridge Company in 1881 and began to also manufacture farm implements, iron fences, and some machinery. In 1893, the company moved to its present location on East Sugartree Street in Wilmington. The company was among the first to use and promote steel for the construction of smaller highway bridges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In video gaming, players may be given a ranking. To \"rank up\" is to achieve a higher ranking relative to other players, especially with strategies that do not depend on the player's skill.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is also difficult to tell when exactly a grammatical structure has been learned, as learners may use structures correctly in some situations but not in others. Thus it is more accurate to speak of sequences of acquisition, in which specific grammatical features in a language are acquired before or after certain others but the overall order of acquisition is less rigid. For example, if neither feature B nor feature D can be acquired until feature A has been acquired (feature B and D depend on A) and feature C depends on B, but D does not depend on B (or, therefore, on C), then acquisition orders (A, B, C, D) and (A, D, B, C) are possible, as they are both valid topological orderings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case n = 6, the unique optimal polygon is not regular. The solution to this case was published in 1975 by Ronald Graham, answering a question posed in 1956 by Hanfried Lenz; it takes the form of an irregular equidiagonal pentagon with an obtuse isosceles triangle attached to one of its sides, with the distance from the apex of the triangle to the opposite pentagon vertex equal to the diagonals of the pentagon. Its area is 0.674981.... (sequence A111969 in the OEIS), a number that satisfies the equation 4096 x10 +8192x9 \u2212 3008x8 \u2212 30848x7 + 21056x6 + 146496x5 \u2212 221360x4 + 1232x3 + 144464x2 \u2212 78488x + 11993 = 0.Graham conjectured that the optimal solution for the general case of even values of n consists in the same way of an equidiagonal (n \u2212 1)-gon with an isosceles triangle attached to one of its sides, its apex at unit distance from the opposite (n \u2212 1)-gon vertex. In the case n = 8 this was verified by a computer calculation by Audet et al. Graham's proof that his hexagon is optimal, and the computer proof of the n = 8 case, both involved a case analysis of all possible n-vertex thrackles with straight edges. The full conjecture of Graham, characterizing the solution to the biggest little polygon problem for all even values of n, was proven in 2007 by Foster and Szabo.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory and proof theory, the Curry\u2013Howard correspondence (also known as the Curry\u2013Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and the logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer\u2013Heyting\u2013Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry\u2013Howard\u2013Lambek correspondence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The distinction came into prominence on modern character displays.The digit 0 with a dot in the centre seems to have originated as an option on IBM 3270 displays. Its appearance has continued with Taligent's command line typeface Andal\u00e9 Mono. One variation used a short vertical bar instead of the dot.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis and linear algebra, lower\u2013upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a filter on a set X {\\displaystyle X} informally gives a notion of which subsets A \u2286 X {\\displaystyle A\\subseteq X} are \"large\". Filter quantifiers are a type of logical quantifier which, informally, say whether or not a statement is true for \"most\" elements of X . {\\displaystyle X.} Such quantifiers are often used in combinatorics, model theory (such as when dealing with ultraproducts), and in other fields of mathematical logic where (ultra)filters are used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some drawbacks of writing use cases include the fact that each action, by the actor or the world, consist of little detail, and is simply a small action. This may possibly lead to further imagination and different interpretation of action from different designers. Also, during the process, it is really easy to oversimplify a task, since a small task derived from a larger task may still consist of even smaller tasks which were missed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fe'i bananas, grown and eaten in the islands of the Pacific, are derived from entirely different wild species than traditional bananas and plantains. Most Fe'i bananas are cooked, but Karat bananas, which are short and squat with bright red skins, very different from the usual yellow dessert bananas, are eaten raw.In the Spanish market, the distinction is among pl\u00e1tano, applied to the Cavendish cultivars produced in the Spanish Canary Islands under the protected geographical indication pl\u00e1tano de Canarias, banana, applied to dessert imports from Africa and the Americas, and pl\u00e1tano macho (literally, \"male banana\"), applied to imports that are to be cooked.In summary, in commerce in Europe and the Americas (although not in small-scale cultivation), it is possible to distinguish between \"bananas\", which are eaten raw, and \"plantains\", which are cooked. In other regions of the world, particularly India, Southeast Asia and the islands of the Pacific, there are many more kinds of banana and the two-fold distinction is not useful and not made in local languages. Plantains are one of many kinds of cooking bananas, which are not always distinct from dessert bananas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The thirteenth loaf is called the vantage loaf because it is considered advantageous overall to get 13 loaves for the price of 12.In Arthurian legend, which was recorded in Medieval texts, King Arthur is resting in Avalon with the twelve greatest knights of the Round Table, totalling 13, and will return when his country is in peril.The Thirteen Treasures of Britain are a series of magical items listed in late Medieval texts. The Thirteen Postures of Tai Chi are thirteen postures (consisting of Eight Gates and Five Steps) which are considered to be of fundamental importance in the practice of Tai Chi.In astronomy there are 13 star constellations in the zodiac (including Ophiuchus); this can be compared with astrology where there are 12 signs of the zodiac. In Judaism, 13 signifies the age at which a boy matures and becomes a Bar Mitzvah, i.e., a full member of the Jewish faith (counts as a member of Minyan).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point). Fermat's theorem is a theorem in real analysis, named after Pierre de Fermat. By using Fermat's theorem, the potential extrema of a function f {\\displaystyle \\displaystyle f} , with derivative f \u2032 {\\displaystyle \\displaystyle f'} , are found by solving an equation in f \u2032 {\\displaystyle \\displaystyle f'} . Fermat's theorem gives only a necessary condition for extreme function values, as some stationary points are inflection points (not a maximum or minimum). The function's second derivative, if it exists, can sometimes be used to determine whether a stationary point is a maximum or minimum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ": xiv The maximum possible clock rate is capped by the logic path with the longest propagation delay, called the critical path. Because of that, the paths that may operate quickly are idle most of the time. A widely distributed clock network dissipates a lot of useful power and must run whether the circuit is receiving inputs or not. Because of this level of complexity, testing and debugging takes over half of development time in all dimensions for synchronous circuits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above UML class diagram, the Caretaker class refers to the Originator class for saving (createMemento()) and restoring (restore(memento)) originator's internal state. The Originator class implements (1) createMemento() by creating and returning a Memento object that stores originator's current internal state and (2) restore(memento) by restoring state from the passed in Memento object. The UML sequence diagram shows the run-time interactions: (1) Saving originator's internal state: The Caretaker object calls createMemento() on the Originator object, which creates a Memento object, saves its current internal state (setState()), and returns the Memento to the Caretaker. (2) Restoring originator's internal state: The Caretaker calls restore(memento) on the Originator object and specifies the Memento object that stores the state that should be restored. The Originator gets the state (getState()) from the Memento to set its own state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Th\u0101bit derived an equation for determining amicable numbers. His proof of this rule is presented in the Treatise on the Derivation of the Amicable Numbers in an Easy Way. This was done while writing on the theory of numbers, extending their use to describe the ratios between geometrical quantities, a step which the Greeks did not take. Th\u0101bit's work on amicable numbers and number theory helped him to invest more heavily into the Geometrical relations of numbers establishing his Transversal (geometry) theorem.Th\u0101bit described a generalized proof of the Pythagorean theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, guard intervals are used to ensure that distinct transmissions do not interfere with one another, or otherwise cause overlapping transmissions. These transmissions may belong to different users (as in TDMA) or to the same user (as in OFDM). The purpose of the guard interval is to introduce immunity to propagation delays, echoes and reflections, to which digital data is normally very sensitive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, when j = 3 {\\displaystyle j=3} , the quantity d ( G ( 3 ) | Q ( 2 ) ) {\\displaystyle d({\\mathcal {G}}^{(3)}\\vert \\mathbf {Q} ^{(2)})} is equal to the fraction of triangles formed by 2-edges in the subhypergraph that are 3-edges. Definition . For j \u2265 3 {\\displaystyle j\\geq 3} , fix some classes V i 1 , \u2026 , V i j {\\displaystyle V_{i_{1}},\\ldots ,V_{i_{j}}} of G ( 1 ) {\\displaystyle {\\mathcal {G}}^{(1)}} with 1 \u2264 i 1 < \u2026 < i j \u2264 l {\\displaystyle 1\\leq i_{1}<\\ldots 0 {\\displaystyle \\mu >0} be a real number, r \u2265 1 {\\displaystyle r\\geq 1} be an integer, and \u03b4 = ( \u03b4 2 , \u2026 , \u03b4 k \u2212 1 ) {\\displaystyle \\delta =(\\delta _{2},\\ldots ,\\delta _{k-1})} , d = ( d 2 , \u2026 , d k \u2212 1 ) {\\displaystyle \\mathbf {d} =(d_{2},\\ldots ,d_{k-1})} be vectors of positive reals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and data mining, X-means clustering is a variation of k-means clustering that refines cluster assignments by repeatedly attempting subdivision, and keeping the best resulting splits, until a criterion such as the Akaike information criterion (AIC) or Bayesian information criterion (BIC) is reached.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of Combinatorial game theory, which typically studies sequential games with perfect information, a game tree is a graph representing all possible game states within such a game. Such games include well-known ones such as chess, checkers, Go, and tic-tac-toe. This can be used to measure the complexity of a game, as it represents all the possible ways a game can pan out.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first version in 2003, North Eastern Scotland (which then included part of Moray) was coded UKM1, and Highlands and Islands was coded UKM4. The current NUTS level 1 codes start with \"C\" (following \"UK\") rather than \"1\" because the new list reflected the revised regions of England and local government changes throughout the UK; \"1\" to \"B\" had been used for the 11 regions in the previous coding system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Also, the fact that Q ( t ) {\\displaystyle Q(t)} is random with probability density given by the square modulus of \u03c8 ( t , \u22c5 ) {\\displaystyle \\psi (t,\\cdot )} implies that the conditional probability density of Q I ( t ) {\\displaystyle Q^{\\text{I}}(t)} given Q II ( t ) {\\displaystyle Q^{\\text{II}}(t)} is given by the square modulus of the (normalized) conditional wavefunction \u03c8 I ( t , \u22c5 ) {\\displaystyle \\psi ^{\\text{I}}(t,\\cdot )} (in the terminology of D\u00fcrr et al. this fact is called the fundamental conditional probability formula). Unlike the universal wavefunction, the conditional wavefunction of a subsystem does not always evolve by the Schr\u00f6dinger equation, but in many situations it does. For instance, if the universal wavefunction factors as \u03c8 ( t , q I , q II ) = \u03c8 I ( t , q I ) \u03c8 II ( t , q II ) , {\\displaystyle \\psi (t,q^{\\text{I}},q^{\\text{II}})=\\psi ^{\\text{I}}(t,q^{\\text{I}})\\psi ^{\\text{II}}(t,q^{\\text{II}}),} then the conditional wavefunction of subsystem (I) is (up to an irrelevant scalar factor) equal to \u03c8 I {\\displaystyle \\psi ^{\\text{I}}} (this is what standard quantum theory would regard as the wavefunction of subsystem (I)).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically number theory, Granville numbers, also known as S {\\displaystyle {\\mathcal {S}}} -perfect numbers, are an extension of the perfect numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following examples, the natural numbers refer to the set of positive integers. The equation x = ( y 1 + 1 ) ( y 2 + 1 ) {\\displaystyle x=(y_{1}+1)(y_{2}+1)} is an example of a Diophantine equation with a parameter x and unknowns y1 and y2. The equation has a solution in y1 and y2 precisely when x can be expressed as a product of two integers greater than 1, in other words x is a composite number. Namely, this equation provides a Diophantine definition of the set {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ...}consisting of the composite numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multitype branching processes, individuals are not identical, but can be classified into n types. After each time step, an individual of type i will produce individuals of different types, and X i {\\displaystyle \\mathbf {X} _{i}} , a random vector representing the numbers of children in different types, satisfies a probability distribution on N n {\\displaystyle \\mathbb {N} ^{n}} . For example, consider the population of cancer stem cells (CSCs) and non-stem cancer cells (NSCCs). After each time interval, each CSC has probability p 1 {\\displaystyle p_{1}} to produce two CSCs (symmetric division), probability p 2 {\\displaystyle p_{2}} to produce one CSC and one NSCC (asymmetric division), probability p 3 {\\displaystyle p_{3}} to produce one CSC (stagnation), and probability 1 \u2212 p 1 \u2212 p 2 \u2212 p 3 {\\displaystyle 1-p_{1}-p_{2}-p_{3}} to produce nothing (death); each NSCC has probability p 4 {\\displaystyle p_{4}} to produce two NSCCs (symmetric division), probability p 5 {\\displaystyle p_{5}} to produce one NSCC (stagnation), and probability 1 \u2212 p 4 \u2212 p 5 {\\displaystyle 1-p_{4}-p_{5}} to produce nothing (death).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The systems are similar in that they were all produced in the same way. This infinite sequence is an ensemble.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Bertrand's postulate (actually now a theorem) states that for each n \u2265 2 {\\displaystyle n\\geq 2} there is a prime p {\\displaystyle p} such that n < p < 2 n {\\displaystyle n", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A daemon is usually created either by a process forking a child process and then immediately exiting, thus causing init to adopt the child process, or by the init process directly launching the daemon. In addition, a daemon launched by forking and exiting typically must perform other operations, such as dissociating the process from any controlling terminal (tty).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of DIKW, data is conceived of as symbols or signs, representing stimuli or signals, that are \"of no use until ... in a usable (that is, relevant) form\". Zeleny characterized this non-usable characteristic of data as \"know-nothing\".In some cases, data is understood to refer not only to symbols, but also to signals or stimuli referred to by said symbols\u2014what Zins terms subjective data. Where universal data, for Zins, are \"the product of observation\" (italics in original), subjective data are the observations. This distinction is often obscured in definitions of data in terms of \"facts\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, Moreover, since s \u00d7 s will never exceed M2 < 22p, this simple technique converges in at most 1 p-bit addition (and possibly a carry from the pth bit to the 1st bit), which can be done in linear time. This algorithm has a small exceptional case. It will produce 2n\u22121 for a multiple of the modulus rather than the correct value of 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, differential Galois theory studies the Galois groups of differential equations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result, different parameterized types are implemented by the same class or interface at run time. All invocations of a given generic type declaration share a single run-time implementation. This results in the possibility of heap pollution.Under certain conditions, a variable of a parameterized type may refer to an object that is not of that parameterized type. The variable will always refer to an object that is an instance of a class that implements the parameterized type. Heap Pollution in a non-varargs context", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed.The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alcohol-based hand sanitizers are almost entirely ineffective against norovirus (or Norwalk) type viruses, the most common cause of contagious gastroenteritis.US Centers for Disease Control and Prevention recommend hand washing with soap over hand sanitizer rubs, particularly when hands are visibly dirty. The increasing use of these agents is based on their ease of use and rapid killing activity against micro-organisms; however, they should not serve as a replacement for proper hand washing unless soap and water are unavailable. Despite their effectiveness, non-water agents do not cleanse the hands of organic material, but simply disinfect them. It is for this reason that hand sanitizers are not as effective as soap and water at preventing the spread of many pathogens, since the pathogens remain on the hands.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Drupal community, \"core\" refers to the collaboratively built codebase that can be extended through contributory modules and\u2014for versions prior to Drupal 8\u2014is kept outside of the \"sites\" folder of a Drupal installation. (Starting with version 8, the core is kept in its own 'core' sub-directory.) Drupal core is the stock element of Drupal. Common Drupal-specific libraries, as well as the bootstrap process, are defined as Drupal core; all other functionality is defined as Drupal modules including the system module itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the multiplicative digital root of a natural number n {\\displaystyle n} in a given number base b {\\displaystyle b} is found by multiplying the digits of n {\\displaystyle n} together, then repeating this operation until only a single-digit remains, which is called the multiplicative digital root of n {\\displaystyle n} . The multiplicative digital root for the first few positive integers are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 0, 3, 6, 9, 2, 5, 8, 2, 8, 4, 0. (sequence A031347 in the OEIS)Multiplicative digital roots are the multiplicative equivalent of digital roots.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Division in semigroups (or in monoids) is not possible in general. The formal study of semigroups began in the early 20th century. Early results include a Cayley theorem for semigroups realizing any semigroup as transformation semigroup, in which arbitrary functions replace the role of bijections from group theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The graphic presented in Taxon Sampling, Bioinformatics, and Phylogenomics, compares the correctness of phylogenetic trees generated using fewer taxa and more sites per taxon on the x-axis to more taxa and fewer sites per taxon on the y-axis. With fewer taxa, more genes are sampled amongst the taxonomic group; in comparison, with more taxa added to the taxonomic sampling group, fewer genes are sampled. Each method has the same total number of nucleotide sites sampled.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following case, one of the (redundant) Learners fails, but the Basic Paxos protocol still succeeds. Client Proposer Acceptor Learner | | | | | | | X-------->| | | | | | Request | X--------->|->|->| | | Prepare(1) | |<---------X--X--X | | Promise(1,{Va,Vb,Vc}) | X--------->|->|->| | | Accept! (1,V) | |<---------X--X--X------>|->| Accepted(1,V) | | | | | | ! !! FAIL !! |<---------------------------------X Response | | | | | |", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a player whose score is three strokes over par after a given hole would appear as \"+3\" on the scoreboard. If two or more players have the same number of strokes, it may be desired to determine an outright winner. Two of the more common methods are a playoff and scorecard count back.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors\u2014that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle h_{ji}={\\begin{cases}{\\boldsymbol {v}}_{j}^{\\mathrm {T} }{\\boldsymbol {Av}}_{i}&{\\text{if }}j\\leq i{\\text{,}}\\\\\\lVert {\\boldsymbol {w}}_{i+1}\\rVert _{2}&{\\text{if }}j=i+1{\\text{,}}\\\\0&{\\text{if }}j>i+1{\\text{. }}\\end{cases}}} When applying the Arnoldi iteration to solving linear systems, one starts with r 0 = b \u2212 A x 0 {\\displaystyle {\\boldsymbol {r}}_{0}={\\boldsymbol {b}}-{\\boldsymbol {Ax}}_{0}} , the residual corresponding to an initial guess x 0 {\\displaystyle {\\boldsymbol {x}}_{0}} . After each step of iteration, one computes y i = H i \u2212 1 ( \u2016 r 0 \u2016 2 e 1 ) {\\displaystyle {\\boldsymbol {y}}_{i}={\\boldsymbol {H}}_{i}^{-1}(\\lVert {\\boldsymbol {r}}_{0}\\rVert _{2}{\\boldsymbol {e}}_{1})} and the new iterate x i = x 0 + V i y i {\\displaystyle {\\boldsymbol {x}}_{i}={\\boldsymbol {x}}_{0}+{\\boldsymbol {V}}_{i}{\\boldsymbol {y}}_{i}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s, software engineers needed language support to break large projects down into modules. One obvious feature was to decompose large projects physically into separate files. A less obvious feature was to decompose large projects logically into abstract datatypes. At the time, languages supported concrete (scalar) datatypes like integer numbers, floating-point numbers, and strings of characters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Constructivism is a mathematical philosophy that rejects all proof methods that involve the existence of objects that are not explicitly built. This excludes, in particular, the use of the law of the excluded middle, the axiom of infinity, and the axiom of choice, and induces a different meaning for some terminology (for example, the term \"or\" has a stronger meaning in constructive mathematics than in classical).Some non-constructive proofs show that if a certain proposition is false, a contradiction ensues; consequently the proposition must be true (proof by contradiction). However, the principle of explosion (ex falso quodlibet) has been accepted in some varieties of constructive mathematics, including intuitionism. Constructive proofs can be seen as defining certified mathematical algorithms: this idea is explored in the Brouwer\u2013Heyting\u2013Kolmogorov interpretation of constructive logic, the Curry\u2013Howard correspondence between proofs and programs, and such logical systems as Per Martin-L\u00f6f's intuitionistic type theory, and Thierry Coquand and G\u00e9rard Huet's calculus of constructions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, an arbitrary permutation of the elements of a set X is an automorphism. The automorphism group of X is also called the symmetric group on X. In elementary arithmetic, the set of integers, Z, considered as a group under addition, has a unique nontrivial automorphism: negation. Considered as a ring, however, it has only the trivial automorphism. Generally speaking, negation is an automorphism of any abelian group, but not of a ring or field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Euclidean field is an ordered field K for which every non-negative element is a square: that is, x \u2265 0 in K implies that x = y2 for some y in K. The constructible numbers form a Euclidean field. It is the smallest Euclidean field, as every Euclidean field contains it as an ordered subfield. In other words, the constructible numbers form the Euclidean closure of the rational numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Once we have determined which case we are in, instead of using division polynomials, we are able to work with a polynomial that has lower degree than the corresponding division polynomial: O ( l ) {\\displaystyle O(l)} rather than O ( l 2 ) {\\displaystyle O(l^{2})} . For efficient implementation, probabilistic root-finding algorithms are used, which makes this a Las Vegas algorithm rather than a deterministic algorithm. Under the heuristic assumption that approximately half of the primes up to an O ( log \u2061 q ) {\\displaystyle O(\\log q)} bound are Elkies primes, this yields an algorithm that is more efficient than Schoof's, with an expected running time of O ( log 6 \u2061 q ) {\\displaystyle O(\\log ^{6}q)} using naive arithmetic, and O ~ ( log 4 \u2061 q ) {\\displaystyle {\\tilde {O}}(\\log ^{4}q)} using fast arithmetic. Although this heuristic assumption is known to hold for most elliptic curves, it is not known to hold in every case, even under the GRH.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Linux kernel, the fat, hfs, hpfs, ntfs, and udf file system drivers support a umask mount option, which controls how the disk information is mapped to permissions. This is not the same as the per-process mask described above, although the permissions are calculated in a similar way. Some of these file system drivers also support separate masks for files and directories, using mount options such as fmask.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Every tree of fixed size occurs linearly many times. Critical p \u2248 1 / n {\\displaystyle p\\approx 1/n} The largest connected component has a number of vertices proportional to n 2 / 3 {\\displaystyle n^{2/3}} . There may exist several other large components; however, the total number of vertices in non-tree components is again proportional to n 2 / 3 {\\displaystyle n^{2/3}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are numerous special classes of semigroups, semigroups with additional properties, which appear in particular applications. Some of these classes are even closer to groups by exhibiting some additional but not all properties of a group. Of these we mention: regular semigroups, orthodox semigroups, semigroups with involution, inverse semigroups and cancellative semigroups. There are also interesting classes of semigroups that do not contain any groups except the trivial group; examples of the latter kind are bands and their commutative subclass\u2014semilattices, which are also ordered algebraic structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are two ways this is represented in the IPA: (a) the same way as ejectives, with an apostrophe; or, (b) more properly with a superscript glottal stop or with an under-tilde for creaky voice. For example, the Yapese word for sick with a glottalized m could be transcribed ,  or . (In some conventions, the apostrophe can occur above the em.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such sets can be either disjoint or non-disjoint sets. Spatially near sets are also descriptively near sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An important property of the Pearson correlation is that it is invariant to application of separate linear transformations to the two variables being compared. Thus, if we are correlating X and Y, where, say, Y = 2X + 1, the Pearson correlation between X and Y is 1 \u2014 a perfect correlation. This property does not make sense for the ICC, since there is no basis for deciding which transformation is applied to each value in a group. However, if all the data in all groups are subjected to the same linear transformation, the ICC does not change.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Ordinary consumer machines and game consoles began to have parallel processors like the Intel Core, AMD K10, and Cell. Graphics card companies like Nvidia and AMD began introducing large parallel systems like CUDA and OpenCL. It appears, however, that these new technologies do not cite FGCS research.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages (especially functional programming languages) and type theory, an option type or maybe type is a polymorphic type that represents encapsulation of an optional value; e.g., it is used as the return type of functions which may or may not return a meaningful value when they are applied. It consists of a constructor which either is empty (often named None or Nothing), or which encapsulates the original data type A (often written Just A or Some A). A distinct, but related concept outside of functional programming, which is popular in object-oriented programming, is called nullable types (often expressed as A?). The core difference between option types and nullable types is that option types support nesting (e.g. Maybe (Maybe String) \u2260 Maybe String), while nullable types do not (e.g.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In an undirected simple graph of order n, the maximum degree of each vertex is n \u2212 1 and the maximum size of the graph is n(n \u2212 1)/2. The edges of an undirected simple graph permitting loops G {\\displaystyle G} induce a symmetric homogeneous relation \u223c {\\displaystyle \\sim } on the vertices of G {\\displaystyle G} that is called the adjacency relation of G {\\displaystyle G} . Specifically, for each edge ( x , y ) {\\displaystyle (x,y)} , its endpoints x {\\displaystyle x} and y {\\displaystyle y} are said to be adjacent to one another, which is denoted x \u223c y {\\displaystyle x\\sim y} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other operators run their own speaking clocks, with broadly similar formats, or redirect to BT's service. Virgin Media have their own service available by dialling 123 from a Virgin Media line. Sky also have their own service accessible by dialling 123 from a Sky telephone line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming, a class is an extensible program-code-template for creating objects, providing initial values for state (member variables) and implementations of behavior (member functions or methods). In many languages, the class name is used as the name for the class (the template itself), the name for the default constructor of the class (a subroutine that creates objects), and as the type of objects generated by instantiating the class; these distinct concepts are easily conflated. Although, to the point of conflation, one could argue that is a feature inherent in a language because of its polymorphic nature and why these languages are so powerful, dynamic and adaptable for use compared to languages without polymorphism present. Thus they can model dynamic systems (i.e. the real world, machine learning, AI) more easily.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). In other words, the values that the noise can take are Gaussian-distributed. The probability density function p {\\displaystyle p} of a Gaussian random variable z {\\displaystyle z} is given by: \u03c6 ( z ) = 1 \u03c3 2 \u03c0 e \u2212 ( z \u2212 \u03bc ) 2 / ( 2 \u03c3 2 ) {\\displaystyle \\varphi (z)={\\frac {1}{\\sigma {\\sqrt {2\\pi }}}}e^{-(z-\\mu )^{2}/(2\\sigma ^{2})}} where z {\\displaystyle z} represents the grey level, \u03bc {\\displaystyle \\mu } the mean grey value and \u03c3 {\\displaystyle \\sigma } its standard deviation.A special case is white Gaussian noise, in which the values at any pair of times are identically distributed and statistically independent (and hence uncorrelated). In communication channel testing and modelling, Gaussian noise is used as additive white noise to generate additive white Gaussian noise. In telecommunications and computer networking, communication channels can be affected by wideband Gaussian noise coming from many natural sources, such as the thermal vibrations of atoms in conductors (referred to as thermal noise or Johnson\u2013Nyquist noise), shot noise, black-body radiation from the earth and other warm objects, and from celestial sources such as the Sun.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If A m > T {\\displaystyle A_{m}>T} , set R {\\displaystyle R} to m \u2212 1 {\\displaystyle m-1} . Else, A m \u2264 T {\\displaystyle A_{m}\\leq T} ; set L {\\displaystyle L} to m {\\displaystyle m} . Now L = R {\\displaystyle L=R} , the search is done. If A L = T {\\displaystyle A_{L}=T} , return L {\\displaystyle L} . Otherwise, the search terminates as unsuccessful.Where ceil is the ceiling function, the pseudocode for this version is: function binary_search_alternative(A, n, T) is L := 0 R := n \u2212 1 while L != R do m := ceil((L + R) / 2) if A > T then R := m \u2212 1 else: L := m if A = T then return L return unsuccessful", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most forms of Latin scribal abbreviation, an overline or macron indicates omitted letters similar to use of apostrophes in English contractions. Letters with macrons or overlines continue to be used in medical abbreviations in various European languages, particularly for prescriptions. Common examples include a, a\u0305, or \u0101 for ante (\"before\") c, c\u0305, or c\u0304 for cum (\"with\") p, p\u0305, or p\u0304 for post (\"after\") q, q\u0305, or q\u0304 for quisque and its inflections (\"every\", \"each\") s, s\u0305, or s\u0304 for sine (\"without\") x, x\u0305, or x\u0304 for exceptus and its inflections (\"except\")Note, however, that abbreviations involving the letter h take their macron halfway up the ascending line rather than at the normal height for Unicode overlines and macrons: \u0127. This is separately encoded in Unicode with the symbols using bar diacritics and appears shorter than other overlines in many fonts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The contents of the Posterior Analytics may be summarised as follows: All demonstration must be founded on principles already known. The principles on which it is founded must either themselves be demonstrable, or be so-called first principles, which cannot be demonstrated, nor need to be, being evident in themselves (\"nota per se\"). We cannot demonstrate things in a circular way, supporting the conclusion by the premises, and the premises by the conclusion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case when the factor graph is a tree, the belief propagation algorithm will compute the exact marginals. Furthermore, with proper scheduling of the message updates, it will terminate after two full passes through the tree. This optimal scheduling can be described as follows: Before starting, the graph is oriented by designating one node as the root; any non-root node which is connected to only one other node is called a leaf.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Appropriate for their use hardware resources, such as computers, mobile phones and pagers.As its core, the provisioning process monitors access rights and privileges to ensure the security of an enterprise's resources and user privacy. As a secondary responsibility, it ensures compliance and minimizes the vulnerability of systems to penetration and abuse. As a tertiary responsibility, it tries to reduce the amount of custom configuration using boot image control and other methods that radically reduce the number of different configurations involved.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, censoring is a condition in which the value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is at least 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In microscopy, negative staining is an established method, often used in diagnostic microscopy, for contrasting a thin specimen with an optically opaque fluid. In this technique, the background is stained, leaving the actual specimen untouched, and thus visible. This contrasts with positive staining, in which the actual specimen is stained.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value,: pp. 160 is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0). For a system of order k (the number of time lags in discrete time, or the order of the largest derivative in continuous time) and dimension n (that is, with n different evolving variables, which together can be denoted by an n-dimensional coordinate vector), generally nk initial conditions are needed in order to trace the system's variables forward through time. In both differential equations in continuous time and difference equations in discrete time, initial conditions affect the value of the dynamic variables (state variables) at any future time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions with support on (0,\u221e). Its probability density function is given by f ( x ; \u03bc , \u03bb ) = \u03bb 2 \u03c0 x 3 exp \u2061 ( \u2212 \u03bb ( x \u2212 \u03bc ) 2 2 \u03bc 2 x ) {\\displaystyle f(x;\\mu ,\\lambda )={\\sqrt {\\frac {\\lambda }{2\\pi x^{3}}}}\\exp {\\biggl (}-{\\frac {\\lambda (x-\\mu )^{2}}{2\\mu ^{2}x}}{\\biggr )}} for x > 0, where \u03bc > 0 {\\displaystyle \\mu >0} is the mean and \u03bb > 0 {\\displaystyle \\lambda >0} is the shape parameter.The inverse Gaussian distribution has several properties analogous to a Gaussian distribution. The name can be misleading: it is an \"inverse\" only in that, while the Gaussian describes a Brownian motion's level at a fixed time, the inverse Gaussian describes the distribution of the time a Brownian motion with positive drift takes to reach a fixed positive level.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the event a radio is stolen, or a user's permission to access the radio system is revoked, a data packet can be sent to the radio's ID to disable the radio. This prevents the radio from transmitting or receiving until either an un-inhibit packet is sent to the radio or in some cases re-programmed using the appropriate service software. Some literature refers to this feature as 'stunning' and 'un-stunning' the radio, or a 'radiokill'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit. The test was used by Gottfried Leibniz and is sometimes known as Leibniz's test, Leibniz's rule, or the Leibniz criterion. The test is only sufficient, not necessary, so some convergent alternating series may fail the first part of the test.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this sense a feature structure is a list of key-value pairs. The value might be atomic or another feature structure. This leads to another notation for feature structures: the use of trees. In fact, some systems (such as PATR-II) use S-expressions to represent feature structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using the FEE, it is possible to prove the following theorem: Theorem: Let y = f ( x ) {\\displaystyle y=f(x)} be an elementary transcendental function, that is the exponential function, or a trigonometric function, or an elementary algebraic function, or their superposition, or their inverse, or a superposition of the inverses. Then s f ( n ) = O ( M ( n ) log 2 \u2061 n ) . {\\displaystyle s_{f}(n)=O(M(n)\\log ^{2}n).\\,} Here s f ( n ) {\\displaystyle s_{f}(n)} is the complexity of computation (bit) of the function f ( x ) {\\displaystyle f(x)} with accuracy up to n {\\displaystyle n} digits, M ( n ) {\\displaystyle M(n)} is the complexity of multiplication of two n {\\displaystyle n} -digit integers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Java computer programming language, an annotation is a form of syntactic metadata that can be added to Java source code. Classes, methods, variables, parameters and Java packages may be annotated. Like Javadoc tags, Java annotations can be read from source files.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software testing, error guessing is a test method in which test cases used to find bugs in programs are established based on experience in prior testing. The scope of test cases usually rely on the software tester involved, who uses past experience and intuition to determine what situations commonly cause software failure, or may cause errors to appear. Typical errors include divide by zero, null pointers, or invalid parameters. Error guessing has no explicit rules for testing; test cases can be designed depending on the situation, either drawing from functional documents or when an unexpected/undocumented error is found while testing operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In native vocabulary, the fricatives  and  are allophones of a single phoneme /\u03b8/. is used morpheme-initially, as in \u00feak  ('roof'), and before a voiceless consonant, as in ma\u00f0kur  ('worm'). is used intervocalically, as in i\u00f0a  ('vortex') and word-finally, as in ba\u00f0  ('bath'), although it is devoiced to  before pause. Some loanwords (mostly from Classical Greek) have introduced the phone  in intervocalic environments, as in A\u00feena  ('Athens').The phone  is actually a laminal voiceless alveolar non-sibilant fricative . The corresponding voiced phone  is similar, but is apical rather than laminal (Ladefoged & Maddieson 1996).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They were Mode 5 stone tools, or microliths. He mentions neither Westropp nor the Mesolithic, however.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This reduces the complexity to O(p2 log p log log p) or \u00d5(p2). An even more efficient multiplication algorithm, F\u00fcrer's algorithm, only needs p log \u2061 p 2 O ( log \u2217 \u2061 p ) {\\displaystyle p\\log p\\ 2^{O(\\log ^{*}p)}} time to multiply two p-bit numbers. By comparison, the most efficient randomized primality test for general integers, the Miller\u2013Rabin primality test, requires O(k n2 log n log log n) bit operations using FFT multiplication for an n-digit number, where k is the number of iterations and is related to the error rate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process, which means that its future evolution is independent of its history. It is named after the Russian mathematician Andrey Markov. The term strong Markov property is similar to the Markov property, except that the meaning of \"present\" is defined in terms of a random variable known as a stopping time. The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the second place, the functional notion of nominal group differs from the formal notion of noun phrase because the first is anchored on the thing being described whereas the second is anchored on word classes. For that reason, one can analyse the nominal groups some friends and a couple of friends very similarly in terms of function: a thing/entity quantified in an imprecise fashion; whereas one must recognise some friends as being a simple noun phrase and a couple of friends as being a noun phrase embedded in another noun phrase (one noun phrase per noun). In short, these notions are different even if formalists do not perceive them as different.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ": 255 R. M. W. Dixon has defined four criteria for determining whether a construction is a passive: It applies to underlying transitive clauses and forms a derived intransitive. The entity that is the patient or the object of the transitive verb in the underlying representation (indicated as O in linguistic terminology) becomes the core argument of the clause (indicated as S, since the core argument is the subject of an intransitive). The agent in the underlying representation (indicated as A) becomes a ch\u00f4meur, a noun in the periphery that is not a core argument. It is marked by a non-core case or becomes part of an adpositional phrase, etc. This can be omitted, but there is always the option of including it. There is some explicit marking of the construction.Dixon acknowledges that this excludes some constructions labeled as passive by some linguists.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In solving an underdetermined system of linear equations, the regularization term for the parameter vector is expressed in terms of the \u2113 1 {\\displaystyle \\ell _{1}} norm (taxicab geometry) of the vector. This approach appears in the signal recovery framework called compressed sensing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Access to information is only possible if patients have given their prior consent. Patients can view their medical records online (authentication takes place via eID) and allow access to the care providers.Critics in the Netherlands see the risk of abuse and invasion of privacy in the event of burglary of the system by crackers. In that case, very sensitive medical information can be exposed. Such information is highly sensitive to privacy and can cause major harm to victims.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But most of the knowledge on this topic is not older than circa 1965 and the first computer algebra systems: When the long-known finite step algorithms were first put on computers, they turned out to be highly inefficient. The fact that almost any uni- or multivariate polynomial of degree up to 100 and with coefficients of a moderate size (up to 100 bits) can be factored by modern algorithms in a few minutes of computer time indicates how successfully this problem has been attacked during the past fifteen years. (Erich Kaltofen, 1982) Nowadays, modern algorithms and computers can quickly factor univariate polynomials of degree more than 1000 having coefficients with thousands of digits. For this purpose, even for factoring over the rational numbers and number fields, a fundamental step is a factorization of a polynomial over a finite field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since function maximization subject to equality constraints is most conveniently done using a Lagrangean expression of the problem, the score test can be equivalently understood as a test of the magnitude of the Lagrange multipliers associated with the constraints where, again, if the constraints are non-binding at the maximum likelihood, the vector of Lagrange multipliers should not differ from zero by more than sampling error. The equivalence of these two approaches was first shown by S. D. Silvey in 1959, which led to the name Lagrange multiplier test that has become more commonly used, particularly in econometrics, since Breusch and Pagan's much-cited 1980 paper.The main advantage of the score test over the Wald test and likelihood-ratio test is that the score test only requires the computation of the restricted estimator. This makes testing feasible when the unconstrained maximum likelihood estimate is a boundary point in the parameter space. Further, because the score test only requires the estimation of the likelihood function under the null hypothesis, it is less specific than the likelihood ratio test about the alternative hypothesis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a standard normal table, also called the unit normal table or Z table, is a mathematical table for the values of \u03a6, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution. Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal (known as a z-score) and then use the standard normal table to find probabilities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard logarithm. Historically, it was known as logarithmus decimalis or logarithmus decadis. It is indicated by log(x), log10 (x), or sometimes Log(x) with a capital L (however, this notation is ambiguous, since it can also mean the complex natural logarithmic multi-valued function).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Assuming there is a trunk, merges from branches can be considered as \"external\" to the tree \u2013 the changes in the branch are packaged up as a patch, which is applied to HEAD (of the trunk), creating a new revision without any explicit reference to the branch, and preserving the tree structure. Thus, while the actual relations between versions form a DAG, this can be considered a tree plus merges, and the trunk itself is a line. In distributed revision control, in the presence of multiple repositories these may be based on a single original version (a root of the tree), but there need not be an original root, and thus only a separate root (oldest revision) for each repository, for example, if two people starting working on a project separately. Similarly in the presence of multiple data sets (multiple projects) that exchange data or merge, there is not a single root, though for simplicity one may think of one project as primary and the other as secondary, merged into the first with or without its own revision history.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable X is often denoted by E(X), E, or EX, with E also often stylized as E or E . {\\displaystyle \\mathbb {E} .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Patent US3541543) referred to as the \"Binary Decoder\". This was the first time a Read Only Memory had been made using MOS transistors. By the late 1970s, MOS ROM devices had become the most common example of nonvolatile memory used to provide the storage of fixed programs in digital equipment such as calculators and microprocessor systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The exchange of messages may be carried out asynchronously, or may use a synchronous \"rendezvous\" style in which the sender blocks until the message is received. Asynchronous message passing may be reliable or unreliable (sometimes referred to as \"send and pray\"). Message-passing concurrency tends to be far easier to reason about than shared-memory concurrency, and is typically considered a more robust form of concurrent programming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference. Important special cases of the order statistics are the minimum and maximum value of a sample, and (with some qualifications discussed below) the sample median and other sample quantiles. When using probability theory to analyze order statistics of random samples from a continuous distribution, the cumulative distribution function is used to reduce the analysis to the case of order statistics of the uniform distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, the fast folding algorithm (Staelin, 1969) is an efficient algorithm for the detection of approximately-periodic events within time series data. It computes superpositions of the signal modulo various window sizes simultaneously. The FFA is best known for its use in the detection of pulsars, as popularised by SETI@home and Astropulse. It was also used by the Breakthrough Listen Initiative during their 2023 Investigation for Periodic Spectral Signals campaign.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In class-based object-oriented programming, abstract types are implemented as abstract classes (also known as abstract base classes), and concrete types as concrete classes. In generic programming, the analogous notion is a concept, which similarly specifies syntax and semantics, but does not require a subtype relationship: two unrelated types may satisfy the same concept. Often, abstract types will have one or more implementations provided separately, for example, in the form of concrete subtypes that can be instantiated. In object-oriented programming, an abstract class may include abstract methods or abstract properties that are shared by its subclasses. Other names for language features that are (or may be) used to implement abstract types include traits, mixins, flavors, roles, or type classes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Pointed maps are the homomorphisms of these algebraic structures. The class of all pointed sets together with the class of all based maps form a category. In this category the pointed singleton sets ( { a } , a ) {\\displaystyle (\\{a\\},a)} are initial objects and terminal objects, i.e. they are zero objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a scalar parameter, there are four principal types of alternative hypothesis: Point. Point alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is a fully defined distribution, with no unknown parameters; such hypotheses are usually of no practical interest but are fundamental to theoretical considerations of statistical inference and are the basis of the Neyman\u2013Pearson lemma. One-tailed directional. A one-tailed directional alternative hypothesis is concerned with the region of rejection for only one tail of the sampling distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the term \"error\" arises in two ways. Firstly, it arises in the context of decision making, where the probability of error may be considered as being the probability of making a wrong decision and which would have a different value for each type of error. Secondly, it arises in the context of statistical modelling (for example regression) where the model's predicted value may be in error regarding the observed outcome and where the term probability of error may refer to the probabilities of various amounts of error occurring.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The initial population is in this case randomly generated (or created with a greedy algorithm), and then enhanced through an iterative process. At each generation of the process, the whole population (or a part of it) is replaced by newly generated individuals (often the best ones). These techniques are called exploration-oriented methods, since their main ability resides in the diversification in the search space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In response, Kris McDaniel has argued the Weyl tile argument depends on accepting a \"size thesis\" which posits that the distance between two points is given by the number of tiles between the two points. However, as McDaniel points out, the size thesis is not accepted for continuous spaces. Thus, we might have reason not to accept the size thesis for discrete spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the result that the intersection of two subsemigroups of a semigroup T is a subsemigroup of T becomes valid even when the intersection is empty. When a semigroup is defined to have additional structure, the issue may not arise. For example, the definition of a monoid requires an identity element, which rules out the empty semigroup as a monoid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . a 1 b m , a 2 b 1 , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A property that is invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedness, which allows distinguishing a circle from two non-intersecting circles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, D'Agostino's K2 test, named for Ralph D'Agostino, is a goodness-of-fit measure of departure from normality, that is the test aims to gauge the compatibility of given data with the null hypothesis that the data is a realization of independent, identically distributed Gaussian random variables. The test is based on transformations of the sample kurtosis and skewness, and has power only against the alternatives that the distribution is skewed and/or kurtic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Berlekamp's root finding algorithm, also called the Berlekamp\u2013Rabin algorithm, is the probabilistic method of finding roots of polynomials over a field Z p {\\displaystyle \\mathbb {Z} _{p}} . The method was discovered by Elwyn Berlekamp in 1970 as an auxiliary to the algorithm for polynomial factorization over finite fields. The algorithm was later modified by Rabin for arbitrary finite fields in 1979. The method was also independently discovered before Berlekamp by other researchers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Page tables make it easier to allocate additional memory, as each new page can be allocated from anywhere in physical memory. On some systems a page table entry can also designate a page as read-only. Some operating systems set up a different address space for each process, which provides hard memory protection boundaries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. That is, a topological space X is a Moore space if the following conditions hold: Any two distinct points can be separated by neighbourhoods, and any closed set and any point in its complement can be separated by neighbourhoods. (X is a regular Hausdorff space.) There is a countable collection of open covers of X, such that for any closed set C and any point p in its complement there exists a cover in the collection such that every neighbourhood of p in the cover is disjoint from C.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of computability theory, a cost function is a computable function c: N \u00d7 N \u2192 Q \u2265 0 . {\\displaystyle c:\\mathbb {N} \\times \\mathbb {N} \\to \\mathbb {Q} ^{\\geq 0}.} For a computable approximation \u27e8 A s \u27e9 {\\displaystyle \\langle A_{s}\\rangle } of \u0394 2 0 {\\displaystyle \\Delta _{2}^{0}} set A, such a function measures the cost c(n,s) of changing the approximation to A(n) at stage s. The first cost function construction was due to Ku\u010dera and Terwijn. They built a computably enumerable set that is low for Martin-L\u00f6f-randomness but not computable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Recall that the elementary discussion on maxima or minima for real-valued functions implies that if f {\\displaystyle f} is continuous on  {\\displaystyle } and differentiable on ( a , b ) {\\displaystyle (a,b)} , then there is a point c {\\displaystyle c} in ( a , b ) {\\displaystyle (a,b)} such that f ( b ) \u2212 f ( a ) b \u2212 a = f \u2032 ( c ) . {\\displaystyle {f(b)-f(a) \\over b-a}=f^{\\prime }(c).} For vector-valued functions with V {\\displaystyle V} a finite-dimensional normed space, there is no analogue of the equality above, indeed it fails.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning. In each case, the designation \"linear\" is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When storing and manipulating sparse matrices on a computer, it is beneficial and often necessary to use specialized algorithms and data structures that take advantage of the sparse structure of the matrix. Specialized computers have been made for sparse matrices, as they are common in the machine learning field. Operations using standard dense-matrix structures and algorithms are slow and inefficient when applied to large sparse matrices as processing and memory are wasted on the zeros. Sparse data is by nature more easily compressed and thus requires significantly less storage. Some very large sparse matrices are infeasible to manipulate using standard dense-matrix algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But by the mid-1980s, the concepts had matured enough to be seen as commercially viable.Commercial RISC designs began to emerge in the mid-1980s. The first MIPS R2000 appeared in January 1986, followed shortly thereafter by Hewlett-Packard's PA-RISC in some of their computers. In the meantime, the Berkeley effort had become so well known that it eventually became the name for the entire concept.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The function does not return a value and has to be called as a stand-alone function, e.g., Function1 This function returns a result (the number 5), and the call can be part of an expression, e.g., x + Function2() This function converts a number between 0 and 6 into the initial letter of the corresponding day of the week, namely 0 to 'M', 1 to 'T', ..., 6 to 'S'. The result of calling it might be assigned to a variable, e.g., num_day = Function3(number). This function does not return a value but modifies the variable whose address is passed as the parameter; it would be called with \"Function4(variable_to_increment)\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Order is particularly important in the theories of composition techniques originating in the 20th century such as the twelve-tone technique and serialism. Analytical techniques such as set theory take care to distinguish between ordered and unordered collections. In traditional theory concepts like voicing and form include ordering; for example, many musical forms, such as rondo, are defined by the order of their sections.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An object of ( s \u2193 T ) {\\displaystyle (s\\downarrow T)} is called a morphism from s {\\displaystyle s} to T {\\displaystyle T} or a T {\\displaystyle T} -structured arrow with domain s {\\displaystyle s} . An object of ( S \u2193 t ) {\\displaystyle (S\\downarrow t)} is called a morphism from S {\\displaystyle S} to t {\\displaystyle t} or a S {\\displaystyle S} -costructured arrow with codomain t {\\displaystyle t} .Another special case occurs when both S {\\displaystyle S} and T {\\displaystyle T} are functors with domain 1 {\\displaystyle {\\textbf {1}}} . If S ( \u2217 ) = A {\\displaystyle S(*)=A} and T ( \u2217 ) = B {\\displaystyle T(*)=B} , then the comma category ( S \u2193 T ) {\\displaystyle (S\\downarrow T)} , written ( A \u2193 B ) {\\displaystyle (A\\downarrow B)} , is the discrete category whose objects are morphisms from A {\\displaystyle A} to B {\\displaystyle B} . An inserter category is a (non-full) subcategory of the comma category where A = B {\\displaystyle {\\mathcal {A}}={\\mathcal {B}}} and f = g {\\displaystyle f=g} are required. The comma category can also be seen as the inserter of S \u2218 \u03c0 1 {\\displaystyle S\\circ \\pi _{1}} and T \u2218 \u03c0 2 {\\displaystyle T\\circ \\pi _{2}} , where \u03c0 1 {\\displaystyle \\pi _{1}} and \u03c0 2 {\\displaystyle \\pi _{2}} are the two projection functors out of the product category A \u00d7 B {\\displaystyle {\\mathcal {A}}\\times {\\mathcal {B}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information science, a classical information channel (often called simply classical channel) is a communication channel that can be used to transmit classical information (as opposed to quantum channel which can transmit quantum information). An example would be a light travelling over fiber optics lines or electricity travelling over phone lines. Although classical channels cannot transmit quantum information by themselves, they can be useful in combination with quantum channels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, convex metric spaces are, intuitively, metric spaces with the property any \"segment\" joining two points in that space has other points in it besides the endpoints. Formally, consider a metric space (X, d) and let x and y be two points in X. A point z in X is said to be between x and y if all three points are distinct, and d ( x , z ) + d ( z , y ) = d ( x , y ) , {\\displaystyle d(x,z)+d(z,y)=d(x,y),\\,} that is, the triangle inequality becomes an equality. A convex metric space is a metric space (X, d) such that, for any two distinct points x and y in X, there exists a third point z in X lying between x and y. Metric convexity: does not imply convexity in the usual sense for subsets of Euclidean space (see the example of the rational numbers) nor does it imply path-connectedness (see the example of the rational numbers) nor does it imply geodesic convexity for Riemannian manifolds (consider, for example, the Euclidean plane with a closed disc removed).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a basic algebraic operation is any one of the common operations of arithmetic, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power). These operations may be performed on numbers, in which case they are often called arithmetic operations. They may also be performed, in a similar way, on variables, algebraic expressions, and more generally, on elements of algebraic structures, such as groups and fields.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most developed nations, all new developments are assessed for flood risks. The aim is to ensure flood risk is taken into account in all stages of the planning process to avoid inappropriate development in areas of high risk. When development is required in areas of high risk, structures should be built to flood-resistant standards and living or working areas should be raised well above the worst-case scenario flood levels. For existing structures in high-risk areas, funding should be allocated to i.e. raise the electrical wiring/sockets so any water that enters the home can not reach the electrics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here the indices \u03bb and \u03bc are integer partitions and K\u03bb\u03bc(q, t) is polynomial in the variables q and t. Sometimes one considers single-variable versions of these polynomials that arise by setting q = 0, i.e., by considering the polynomial K\u03bb\u03bc(t) = K\u03bb\u03bc(0, t). There are two slightly different versions of them, one called transformed Kostka polynomials.The one-variable specializations of the Kostka polynomials can be used to relate Hall-Littlewood polynomials P\u03bc to Schur polynomials s\u03bb: s \u03bb ( x 1 , \u2026 , x n ) = \u2211 \u03bc K \u03bb \u03bc ( t ) P \u03bc ( x 1 , \u2026 , x n ; t ) . {\\displaystyle s_{\\lambda }(x_{1},\\ldots ,x_{n})=\\sum _{\\mu }K_{\\lambda \\mu }(t)P_{\\mu }(x_{1},\\ldots ,x_{n};t).\\ } These polynomials were conjectured to have non-negative integer coefficients by Foulkes, and this was later proved in 1978 by Alain Lascoux and Marcel-Paul Sch\u00fctzenberger.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the column after determines exactly one case, this case is given as the subsequent one, otherwise there are question marks. The loop is contained in the sections from Start_D through \"Delete case D2\", where the problem of rebalancing is escalated \u0394 h = 1 {\\displaystyle \\Delta h=1} level higher in the tree in that the parent P becomes the new current node N. So it takes maximally h {\\displaystyle h} iterations to repair the tree (where h {\\displaystyle h} is the height of the tree). Because the probability of escalation decreases exponentially with each iteration the total rebalancing cost is constant on average, indeed amortized constant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to solve the equation ln \u2061 ( x ) = y {\\displaystyle \\ln(x)=y} the BKM algorithm takes advantage of a basic property of logarithms ln \u2061 ( a b ) = ln \u2061 ( a ) + ln \u2061 ( b ) {\\displaystyle \\ln(ab)=\\ln(a)+\\ln(b)} Using Pi notation, this identity generalizes to ln \u2061 ( \u220f k = 0 n a k ) = \u2211 k = 0 n ln \u2061 ( a k ) {\\displaystyle \\ln \\left(\\prod _{k=0}^{n}a_{k}\\right)=\\sum _{k=0}^{n}\\ln(a_{k})} Because any number can be represented by a product, this allows us to choose any set of values a k {\\displaystyle a_{k}} which multiply to give the value we started with. In computer systems, it's much faster to multiply and divide by multiples of 2, but because not every number is a multiple of 2, using a k = 1 + 2 m {\\displaystyle a_{k}=1+2^{m}} is a better option than a more simple choice of a k = 2 m {\\displaystyle a_{k}=2^{m}} . Since we want to start with large changes and get more accurate as k {\\displaystyle k} increases, we can more specifically use a k = 1 + 2 \u2212 k {\\displaystyle a_{k}=1+2^{-k}} , allowing the product to approach any value between 1 and ~4.768, depending on which subset of a k {\\displaystyle a_{k}} we use in the final product.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a vector. Specifically, the vectorization of a m \u00d7 n matrix A, denoted vec(A), is the mn \u00d7 1 column vector obtained by stacking the columns of the matrix A on top of one another: Here, a i , j {\\displaystyle a_{i,j}} represents the element in the i-th row and j-th column of A, and the superscript T {\\displaystyle {}^{\\mathrm {T} }} denotes the transpose. Vectorization expresses, through coordinates, the isomorphism R m \u00d7 n := R m \u2297 R n \u2245 R m n {\\displaystyle \\mathbf {R} ^{m\\times n}:=\\mathbf {R} ^{m}\\otimes \\mathbf {R} ^{n}\\cong \\mathbf {R} ^{mn}} between these (i.e., of matrices and vectors) as vector spaces. For example, for the 2\u00d72 matrix A =  {\\displaystyle A={\\begin{bmatrix}a&b\\\\c&d\\end{bmatrix}}} , the vectorization is vec \u2061 ( A ) =  {\\displaystyle \\operatorname {vec} (A)={\\begin{bmatrix}a\\\\c\\\\b\\\\d\\end{bmatrix}}} . The connection between the vectorization of A and the vectorization of its transpose is given by the commutation matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When that user places a call, the calling line ID would be that of a Los Angeles number, although they are actually located in New York. This allows a call return without having to incur long distance calling charges. With cellphones, the biggest issue appears to be in the passing of calling line ID information through the network. Cellphone companies must support interconnecting trunks to a significant number of wireline and PSTN access carriers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the electronics industry, embedded instrumentation refers to the integration of test and measurement instrumentation into semiconductor chips (or integrated circuit devices). Embedded instrumentation differs from embedded system, which are electronic systems or subsystems that usually comprise the control portion of a larger electronic system. Instrumentation embedded into chips (embedded instrumentation) is employed in a variety of electronic test applications, including validating and testing chips themselves, validating, testing and debugging the circuit boards where these chips are deployed, and troubleshooting systems once they have been installed in the field. A working group of the IEEE (Institute of Electrical and Electronics Engineers) that is developing a standard for accessing embedded instruments (the IEEE 1687 Internal JTAG standard) defines embedded instrumentation as follows: Any logic structure within a device whose purpose is Design for Test (DFT), Design-for-Debug (DFD), Design-for-Yield (DFY), Test... There exists the widespread use of embedded instrumentation (such as BIST (built-in self-test) Engines, Complex I/O Characterization and Calibration, Embedded Timing Instrumentation, etc.).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom information about an individual's HIV status is kept confidential within the National Health Service. This is based in law, in the NHS Constitution, and in key NHS rules and procedures. It is also outlined in every NHS employee's contract of employment and in professional standards set by regulatory bodies. The National AIDS Trust's Confidentiality in the NHS: Your Information, Your Rights outlines these rights.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most modern digital cable systems the signals are encrypted, so cases of people obtaining illegal service are less common. The subscriber requires a set-top box provided by the cable company to decrypt and receive the cable signal. Unlike the older analog set-top boxes, the digital set-top box will not function until the cable company activates it by sending it a unique activation key through the cable, which is sent only after the subscriber signs up. Each set-top box is individually addressable, so a given box can be deactivated by command from the company if the subscriber fails to pay their bill (this is sometimes colloquially referred to as a \"bullet\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here, \u039b {\\displaystyle \\Lambda } denotes the likelihood ratio, and the \u03c7 2 {\\displaystyle \\chi ^{2}} distribution has degrees of freedom equal to the difference in dimensionality of \u0398 {\\displaystyle \\Theta } and \u0398 0 {\\displaystyle \\Theta _{0}} , where \u0398 {\\displaystyle \\Theta } is the full parameter space and \u0398 0 {\\displaystyle \\Theta _{0}} is the subset of the parameter space associated with H 0 {\\displaystyle H_{0}} . This result means that for large samples and a great variety of hypotheses, a practitioner can compute the likelihood ratio \u039b {\\displaystyle \\Lambda } for the data and compare \u2212 2 log \u2061 ( \u039b ) {\\displaystyle -2\\log(\\Lambda )} to the \u03c7 2 {\\displaystyle \\chi ^{2}} value corresponding to a desired statistical significance as an approximate statistical test. The theorem no longer applies when the true value of the parameter is on the boundary of the parameter space: Wilks\u2019 theorem assumes that the \u2018true\u2019 but unknown values of the estimated parameters lie within the interior of the supported parameter space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical optimization, meta-optimization is the use of one optimization method to tune another optimization method. Meta-optimization is reported to have been used as early as in the late 1970s by Mercer and Sampson for finding optimal parameter settings of a genetic algorithm. Meta-optimization and related concepts are also known in the literature as meta-evolution, super-optimization, automated parameter calibration, hyper-heuristics, etc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\sum _{x=0}^{\\infty }{\\frac {\\mu ^{x}}{x! }}C_{n}(x;\\mu )C_{m}(x;\\mu )=\\mu ^{-n}e^{\\mu }n!\\delta _{nm},\\quad \\mu >0.} They form a Sheffer sequence related to the Poisson process, similar to how Hermite polynomials relate to the Brownian motion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most indicating instruments, the accuracy is guaranteed to a certain percentage of full-scale reading. The limits of these deviations from the specified values are known as limiting errors or guarantee errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples of such notations are: 3 + 4 {\\displaystyle 3+4}: refers to the process of adding as well as the outcome of the process. \u2211 n = 0 \u221e ( a n ) {\\displaystyle \\sum _{n=0}^{\\infty }(a_{n})}: refers to the process of summing an infinite sequence, and to the outcome of the process. f ( x ) = 3 x + 2 {\\displaystyle f(x)=3x+2}: refers to the process of mapping x to 3x+2 as well as the outcome of that process, the function f {\\displaystyle f} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By setting pi = \u03bbn/n, we see that this generalizes the usual Poisson limit theorem. When \u03bb n {\\displaystyle \\lambda _{n}} is large a better bound is possible: \u2211 k = 0 \u221e | Pr ( S n = k ) \u2212 \u03bb n k e \u2212 \u03bb n k ! | < 2 ( 1 \u2227 1 \u03bb n ) ( \u2211 i = 1 n p i 2 ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number theoretic significance. In particular, according to the prime number theorem, it is a very good approximation to the prime-counting function, which is defined as the number of prime numbers less than or equal to a given value x {\\displaystyle x} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern cryptography, null encryption (or selecting null cipher or NONE cipher) is choosing not to use encryption in a system where various encryption options are offered. When this option is used, the text is the same before and after encryption, which can be practical for testing/debugging, or authentication-only communication. In mathematics such a function is known as the identity function. Examples of this are the \"eNULL\" and \"aNULL\" cipher suite in OpenSSL, and the \"NULL Encryption Algorithm\" in IPSec.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", g , g + 1 , g + 2 , \u2026 . {\\displaystyle 1,?,?,\\dots ,?,g,g+1,g+2,\\dots .} What we know about the ?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Littlewood conjecture is an open problem (as of May 2021) in Diophantine approximation, proposed by John Edensor Littlewood around 1930. It states that for any two real numbers \u03b1 and \u03b2, lim inf n \u2192 \u221e n \u2016 n \u03b1 \u2016 \u2016 n \u03b2 \u2016 = 0 , {\\displaystyle \\liminf _{n\\to \\infty }\\ n\\,\\Vert n\\alpha \\Vert \\,\\Vert n\\beta \\Vert =0,} where \u2016 x \u2016 := min ( | x \u2212 \u230a x \u230b | , | x \u2212 \u2308 x \u2309 | ) {\\displaystyle \\Vert x\\Vert :=\\min(|x-\\lfloor x\\rfloor |,|x-\\lceil x\\rceil |)} is the distance to the nearest integer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plane geometry, the square root of 7 can be constructed via a sequence of dynamic rectangles, that is, as the largest diagonal of those rectangles illustrated here.The minimal enclosing rectangle of an equilateral triangle of edge length 2 has a diagonal of the square root of 7.Due to the Pythagorean theorem and Legendre's three-square theorem, 7 {\\displaystyle {\\sqrt {7}}} is the smallest square root of a natural number that cannot be the distance between any two points of a cubic integer lattice (or equivalently, the length of the space diagonal of a rectangular cuboid with integer side lengths). 15 {\\displaystyle {\\sqrt {15}}} is the next smallest such number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following Diophantine equations, w, x, y, and z are the unknowns and the other letters are given constants:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In photography, a negative is an image, usually on a strip or sheet of transparent plastic film, in which the lightest areas of the photographed subject appear darkest and the darkest areas appear lightest. This reversed order occurs because the extremely light-sensitive chemicals a camera film must use to capture an image quickly enough for ordinary picture-taking are darkened, rather than bleached, by exposure to light and subsequent photographic processing. In the case of color negatives, the colors are also reversed into their respective complementary colors. Typical color negatives have an overall dull orange tint due to an automatic color-masking feature that ultimately results in improved color reproduction.Negatives are normally used to make positive prints on photographic paper by projecting the negative onto the paper with a photographic enlarger or making a contact print.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, i.e., by means not of a theoretical sample space but of an actual experiment. More generally, empirical probability estimates probabilities from experience and observation.Given an event A in a sample space, the relative frequency of A is the ratio m n , {\\displaystyle {\\tfrac {m}{n}},} m being the number of outcomes in which the event A occurs, and n being the total number of outcomes of the experiment.In statistical terms, the empirical probability is an estimator or estimate of a probability. In simple cases, where the result of a trial only determines whether or not the specified event has occurred, modelling using a binomial distribution might be appropriate and then the empirical estimate is the maximum likelihood estimate. It is the Bayesian estimate for the same case if certain assumptions are made for the prior distribution of the probability. If a trial yields more information, the empirical probability can be improved on by adopting further assumptions in the form of a statistical model: if such a model is fitted, it can be used to derive an estimate of the probability of the specified event", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming practice, \"snippet\" refers narrowly to a portion of source code that is literally included by an editor program into a file, and is a form of copy and paste programming. This concrete inclusion is in contrast to abstraction methods, such as functions or macros, which are abstraction within the language. Snippets are thus primarily used when these abstractions are not available or not desired, such as in languages that lack abstraction, or for clarity and absence of overhead.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since the text cursor's next key (viz., the n key) retained directional positioning information (whether the up or down key was formerly pressed), the dot macro (the . key) could then be used to place the text cursor on the next brace, given a suitable coding style. Instead, inspecting the block boundaries using the % key can be used to enforce a coding standard.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here students are asked various questions prior to class, the instructor uses these responses to adapt his or her teaching to the students' prior knowledge and misconceptions. Finally, there is a more research-intensive approach that involves interviewing students for the purpose of generating the items that will make up a concept inventory or other forms of diagnostic instruments. Concept inventories require intensive validation efforts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following transcriptions, diacritics may be used to distinguish between apical  and laminal .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Conversely, the smaller the base, the fewer pandigital numbers without redundant digits there are. 2 is the only such pandigital number in base 2, while there are more of these in base 10. Sometimes, the term is used to refer only to pandigital numbers with no redundant digits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of integers. This generalized Euclidean algorithm can be put to many of the same uses as Euclid's original algorithm in the ring of integers: in any Euclidean domain, one can apply the Euclidean algorithm to compute the greatest common divisor of any two elements. In particular, the greatest common divisor of any two elements exists and can be written as a linear combination of them (B\u00e9zout's identity). Also every ideal in a Euclidean domain is principal, which implies a suitable generalization of the fundamental theorem of arithmetic: every Euclidean domain is a unique factorization domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a telecommunications service is a service provided by a telecommunications provider, or a specified set of user-information transfer capabilities provided to a group of users by a telecommunications system. The telecommunications service user is responsible for the information content of the message. The telecommunications service provider has the responsibility for the acceptance, transmission, and delivery of the message.For purposes of regulation by the Federal Communications Commission under the U.S. Communications Act of 1934 and Telecommunications Act of 1996, the definition of telecommunications service is \"the offering of telecommunications for a fee directly to the public, or to such classes of users as to be effectively available directly to the public, regardless of the facilities used.\" Telecommunications, in turn, is defined as \"the transmission, between or among points specified by the user, of information of the user\u2019s choosing, without change in the form or content of the information as sent and received.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reconfigurable computing and in supercomputing these terms refer to the data path width. The use of about one-bit wide processing elements like the configurable logic blocks (CLBs) in an FPGA is called fine-grained computing or fine-grained reconfigurability, whereas using wide data paths, such as, for instance, 32 bits wide resources, like microprocessor CPUs or data-stream-driven data path units (DPUs) like in a reconfigurable datapath array (rDPA) is called coarse-grained computing or coarse-grained reconfigurability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonology and historical linguistics, cluster reduction is the simplification of consonant clusters in certain environments or over time. Cluster reduction can happen in different languages, dialects of those languages, in world Englishes, and as a part of language acquisition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Normally, model building codes have a 3\u20135 year update cycle. That is, a new edition of the building code comes out every 3 to 5 years. However, due to the length of time that it takes for a jurisdiction to review and approve a new code, the currently enforced version of the local code is often not the most recent edition of the model building code on which the adopted code is based.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Gaussian moat problem asks whether it is possible to find an infinite sequence of distinct Gaussian prime numbers such that the difference between consecutive numbers in the sequence is bounded. More colorfully, if one imagines the Gaussian primes to be stepping stones in a sea of complex numbers, the question is whether one can walk from the origin to infinity with steps of bounded size, without getting wet. The problem was first posed in 1962 by Basil Gordon (although it has sometimes been erroneously attributed to Paul Erd\u0151s) and it remains unsolved.With the usual prime numbers, such a sequence is impossible: the prime number theorem implies that there are arbitrarily large gaps in the sequence of prime numbers, and there is also an elementary direct proof: for any n, the n \u2212 1 consecutive numbers n! + 2, n!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In simulations with electric fields the most important characteristics of a test particle is its electric charge and its mass. In this situation it is often referred to as a test charge. Similar to the case of classical gravitation, the electric field created by a point charge q is defined by E = k q r 2 r ^ {\\displaystyle {\\textbf {E}}=k{\\frac {q}{r^{2}}}{\\hat {r}}} ,where k is the Coulomb constant. Multiplying this field by a test charge q test {\\displaystyle q_{\\textrm {test}}} gives an electric force (Coulomb's law) exerted by the field on a test charge. Note that both the force and the electric field are vector quantities, so a positive test charge will experience a force in the direction of the electric field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the data exhibit a trend, the regression model is likely incorrect; for example, the true function may be a quadratic or higher order polynomial. If they are random, or have no trend, but \"fan out\" - they exhibit a phenomenon called heteroscedasticity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nightly builds also ensure that the build tools have not broken due to system updates, and are therefore often run whether any source code has changed or not. In contrast, continuous integration environments automatically rebuild the project whenever changes are checked in \u2013 often several times a day \u2013 and provide more immediate feedback; however, they do not necessarily include nightly builds. As a result, compiler and tool updates may break the ability to compile older projects easily without warning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s, the American National Bureau of Standards (NBS), which was later renamed to the National Institute of Standards and Technology (NIST), defined a set of convenient numbers when it was developing procedures for metrication in the United States. An NBS technical note describes that system of convenient metric values as the 1-2-5 series in reverse, with assigned preferences for those numbers which are multiples of 5, 2, and 1 (plus their powers of 10). Linear dimensions above 100 mm were excluded (because such measurements are defined by another set of rules). A table of this 5, 2, 1 series can be seen below in the section \"Schedule of convenient numbers between 10 and 100\".The NBS technical note also states that \"Basically, integers are more convenient than expressions which include decimal parts .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From the remaining N \u2212 n1 \u2212 n2 items choose n3 to label 3. Again, this can be done ( N \u2212 n 1 \u2212 n 2 n 3 ) {\\displaystyle {\\tbinom {N-n_{1}-n_{2}}{n_{3}}}} ways.Multiplying the number of choices at each step results in: ( N n 1 ) ( N \u2212 n 1 n 2 ) ( N \u2212 n 1 \u2212 n 2 n 3 ) \u22ef = N ! ( N \u2212 n 1 ) !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the area of additive number theory, the Erd\u0151s\u2013Fuchs theorem is a statement about the number of ways that numbers can be represented as a sum of elements of a given additive basis, stating that the average order of this number cannot be too close to being a linear function. The theorem is named after Paul Erd\u0151s and Wolfgang Heinrich Johannes Fuchs, who published it in 1956.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For some characters, like \u514c/\u5151 (U+514C/U+5151), either method can be used to display the different glyphs. In the following table, each row compares variants that have been assigned different code points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The question arises what precisely a \"class\" is or should be. For Dedekind and Frege, a class is a distinct entity in its own right, a 'unity' that can be identified with all those entities x that satisfy some propositional function F. (This symbolism appears in Russell, attributed there to Frege: \"The essence of a function is what is left when the x is taken away, i.e in the above instance, 2( )3 + ( ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, most forms of censorship are self-imposed rather than enforced by the government. The government does not routinely censor material, although state and local governments often restrict what is provided in libraries and public schools. In addition, distribution, receipt, and transmission (but not mere private possession) of obscene material may be prohibited by law. Furthermore, under FCC v. Pacifica Foundation, the FCC has the power to prohibit the transmission of indecent material over broadcast. Additionally, critics of campaign finance reform in the United States say this reform imposes widespread restrictions on political speech.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, Wolfe duality, named after Philip Wolfe, is type of dual problem in which the objective function and constraints are all differentiable functions. Using this concept a lower bound for a minimization problem can be found because of the weak duality principle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s Cook worked as a research assistant to Stephen Wolfram, assisting with work on Wolfram's book, A New Kind of Science. Among other things, he developed a proof showing that the Rule 110 cellular automaton is Turing-complete. Cook presented his proof at the Santa Fe Institute conference CA98 before the publishing of Wolfram's book\u2014an action that led Wolfram Research to accuse Cook of violating his NDA and resulted in the blocking of the publication of the proof in the conference proceedings. A New Kind of Science was released in 2002 with an outline of the proof. In 2004, Cook published his proof in Wolfram's journal Complex Systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The technique goes back as far as the 1960s having been used in IBM System/360 Model 91 and in CDC 6600.Modern high-end desktop and workstation processors such as the AMD Ryzen Threadripper series and the Intel Core i9 Extreme Edition lineup support quad-channel memory. Server processors from the AMD Epyc series and the Intel Xeon platforms give support to memory bandwidth starting from quad-channel module layout to up to octa-channel layout. In March 2010, AMD released Socket G34 and Magny-Cours Opteron 6100 series processors with support for quad-channel memory. In 2006, Intel released chipsets that support quad-channel memory for its LGA771 platform and later in 2011 for its LGA2011 platform. Microcomputer chipsets with even more channels were designed; for example, the chipset in the AlphaStation 600 (1995) supports eight-channel memory, but the backplane of the machine limited operation to four channels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum teleportation, a sender wishes to transmit an arbitrary quantum state of a particle to a possibly distant receiver. Quantum teleportation is able to achieve faithful transmission of quantum information by substituting classical communication and prior entanglement for a direct quantum channel. Using teleportation, an arbitrary unknown qubit can be faithfully transmitted via a pair of maximally-entangled qubits shared between sender and receiver, and a 2-bit classical message from the sender to the receiver. Quantum teleportation requires a noiseless quantum channel for sharing perfectly entangled particles, and therefore entanglement distillation satisfies this requirement by providing the noiseless quantum channel and maximally entangled qubits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example the majorities are all different, and this is what will usually happen when the number of voters is large. If ties are unlikely, then it does not matter much how they are resolved, so a random choice can be made. However this is not Tideman's procedure, which is considerably more complicated. See his paper for details.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the federal crime of witness tampering is defined by statute at 18 U.S.C. \u00a7 1512, which is entitled \"tampering with a witness, victim, or an informant.\" The statute is broad; the Justice Manual notes that it \"proscribes conduct intended to illegitimately affect the presentation of evidence in Federal proceedings or the communication of information to Federal law enforcement officers\" and applies to tampering with witnesses in \"proceedings before Congress, executive departments, and administrative agencies, and to civil and criminal judicial proceedings, including grand jury proceedings.\" Witness tampering is a crime even if a proceeding is not actually pending, and even if the testimony sought to be influenced, delayed, or prevented would not be admissible in evidence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first design of the Altair, the parts needed to make a complete machine would not fit on a single motherboard, and the machine consisted of four boards stacked on top of each other with stand-offs. Another problem facing Roberts was that the parts needed to make a truly useful computer were not available, or would not be designed in time for the January launch date. So during the construction of the second model, he decided to build most of the machine on removable cards, reducing the motherboard to nothing more than an interconnect between the cards, a backplane. The basic machine consisted of five cards, including the CPU on one and memory on another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the Ky Fan-k-norm is the sum of first k singular values, the trace norm is the sum of all singular values, and the Schatten norm is the pth root of the sum of the pth powers of the singular values. Note that each norm is defined only on a special class of operators, hence s-numbers are useful in classifying different operators. In the finite-dimensional case, a matrix can always be decomposed in the form U \u03a3 V \u2217 {\\displaystyle \\mathbf {U\\Sigma V^{*}} } , where U {\\displaystyle \\mathbf {U} } and V \u2217 {\\displaystyle \\mathbf {V^{*}} } are unitary matrices and \u03a3 {\\displaystyle \\mathbf {\\Sigma } } is a rectangular diagonal matrix with the singular values lying on the diagonal. This is the singular value decomposition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The full statement of Vinogradov's theorem gives asymptotic bounds on the number of representations of an odd integer as a sum of three primes. The notion of \"sufficiently large\" was ill-defined in Vinogradov's original work, but in 2002 it was shown that 101346 is sufficiently large. Additionally numbers up to 1020 had been checked via brute force methods, thus only a finite number of cases to check remained before the odd Goldbach conjecture would be proven or disproven. In 2013, Harald Helfgott proved Goldbach's weak conjecture for all cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other means make use of the antenna pattern, which supports angular determination and phase discrimination. Newer phones may also allow the tracking of the phone even when turned on but not active in a telephone call. This results from the roaming procedures that perform hand-over of the phone from one base station to another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point. An event at point A {\\displaystyle A} cannot cause a result at point B {\\displaystyle B} in a time less than T = D / c {\\displaystyle T=D/c} , where D {\\displaystyle D} is the distance between the points and c {\\displaystyle c} is the speed of light in vacuum. Bell test experiments show that quantum mechanics broadly violates the inequalities established in Bell's theorem. According to some interpretations of quantum mechanics, this result implies that some quantum effects must be non-local.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s the precalciner was pioneered in Japan, and has subsequently become the equipment of choice for new large installations worldwide. The precalciner is a development of the suspension preheater. The philosophy is this: the amount of fuel that can be burned in the kiln is directly related to the size of the kiln. If part of the fuel necessary to burn the rawmix is burned outside the kiln, the output of the system can be increased for a given kiln size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples of tasks in mistrustful cryptography are commitment schemes and secure computations, the latter including the further examples of coin flipping and oblivious transfer. Key distribution does not belong to the area of mistrustful cryptography. Mistrustful quantum cryptography studies the area of mistrustful cryptography using quantum systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The new proof relied almost exclusively on the behavior of cyclotomic polynomials over finite fields. The new upper bound on time complexity was O ~ ( log \u2061 ( n ) 10.5 ) {\\displaystyle {\\tilde {O}}(\\log(n)^{10.5})} , later reduced using additional results from sieve theory to O ~ ( log \u2061 ( n ) 7.5 ) {\\displaystyle {\\tilde {O}}(\\log(n)^{7.5})} . In 2005, Pomerance and Lenstra demonstrated a variant of AKS that runs in O ~ ( log \u2061 ( n ) 6 ) {\\displaystyle {\\tilde {O}}(\\log(n)^{6})} operations, leading to another updated version of the paper. Agrawal, Kayal and Saxena proposed a variant which would run in O ~ ( log \u2061 ( n ) 3 ) {\\displaystyle {\\tilde {O}}(\\log(n)^{3})} if Agrawal's conjecture were true; however, a heuristic argument by Pomerance and Lenstra suggested that it is probably false.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Natural deduction. Every (conditional) line has exactly one asserted proposition on the right. Sequent calculus.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Brunn\u2013Minkowski theorem (or Brunn\u2013Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn\u2013Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact nonconvex sets stated here is due to Lazar Lyusternik (1935).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another complication in applying LDA and Fisher's discriminant to real data occurs when the number of measurements of each sample (i.e., the dimensionality of each data vector) exceeds the number of samples in each class. In this case, the covariance estimates do not have full rank, and so cannot be inverted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a rank correlation is any of several statistics that measure an ordinal association\u2014the relationship between rankings of different ordinal variables or different rankings of the same variable, where a \"ranking\" is the assignment of the ordering labels \"first\", \"second\", \"third\", etc. to different observations of a particular variable. A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them. For example, two common nonparametric methods of significance that use rank correlation are the Mann\u2013Whitney U test and the Wilcoxon signed-rank test.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Hjelmslev's interpretation, there are no physical, psychological or other a priori principles that explain why languages are the way they are. Cross-linguistic similarities on the expression plane depend on a necessity to express meaning; conversely, cross-linguistic similarities on the content plane depend on the necessity to structure meaning potential according to the necessities of expression. \"The linguist must be equally interested in the similarity and in the difference between languages, two complementary sides of the same thing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The data is presented to the users in a common format. Many programs aimed to aid in the creation of such warehouses are designed to be extremely versatile to allow for them to be implemented in diverse research projects. One advantage of this approach is that data is available for analysis at a single site, using a uniform schema.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, palatalization is used as a morpheme or part of a morpheme. In some cases, a vowel caused a consonant to become palatalized, and then this vowel was lost by elision. Here, there appears to be a phonemic contrast when analysis of the deep structure shows it to be allophonic. In Romanian, consonants are palatalized before /i/.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reverse mathematics, one starts with a framework language and a base theory\u2014a core axiom system\u2014that is too weak to prove most of the theorems one might be interested in, but still powerful enough to develop the definitions necessary to state these theorems. For example, to study the theorem \u201cEvery bounded sequence of real numbers has a supremum\u201d it is necessary to use a base system that can speak of real numbers and sequences of real numbers. For each theorem that can be stated in the base system but is not provable in the base system, the goal is to determine the particular axiom system (stronger than the base system) that is necessary to prove that theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The plain voiceless and voiced aspirated series would thus be replaced by just voiceless and voiced, with aspiration being a non-distinctive quality of both. That example of the application of linguistic typology to linguistic reconstruction has become known as the glottalic theory. It has a large number of proponents but is not generally accepted.The reconstruction of proto-sounds logically precedes the reconstruction of grammatical morphemes (word-forming affixes and inflectional endings), patterns of declension and conjugation and so on. The full reconstruction of an unrecorded protolanguage is an open-ended task.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The problem of edge coloring has also been studied in the distributed model. Panconesi & Rizzi (2001) achieve a (2\u0394 \u2212 1)-coloring in O(\u0394 + log* n) time in this model. The lower bound for distributed vertex coloring due to Linial (1992) applies to the distributed edge coloring problem as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the RSA cryptosystem, Bob might tend to use a small value of d, rather than a large random number to improve the RSA decryption performance. However, Wiener\u2019s attack shows that choosing a small value for d will result in an insecure system in which an attacker can recover all secret information, i.e., break the RSA system. This break is based on Wiener\u2019s Theorem, which holds for small values of d. Wiener has proved that the attacker may efficiently find d when d < 1 3 N 1 4 {\\displaystyle d<{\\frac {1}{3}}N^{\\frac {1}{4}}} .Wiener's paper also presented some countermeasures against his attack that allow fast decryption. Two techniques are described as follows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Secure\" phones are defined as \"telephones that are approved by the U.S. Government for the transmission of classified or sensitive voice communications.\" In 2003, the FCC adopted rules to make digital wireless telephones compatible with hearing aids and cochlear implants.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Costas array can be regarded geometrically as a set of n points, each at the center of a square in an n\u00d7n square tiling such that each row or column contains only one point, and all of the n(n \u2212 1)/2 displacement vectors between each pair of dots are distinct. This results in an ideal \"thumbtack\" auto-ambiguity function, making the arrays useful in applications such as sonar and radar. Costas arrays can be regarded as two-dimensional cousins of the one-dimensional Golomb ruler construction, and, as well as being of mathematical interest, have similar applications in experimental design and phased array radar engineering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the \"SIR\" model, there are three states: Susceptible (S) -- has not yet been infected, and has no immunity Infected (I)-- currently \"sick\" and contagious to Susceptible neighbors Removed (R), where the removal from further participation in the process is assumed to be permanent, due to immunization or deathIt is to be distinguished from the \"SIS\" model, where sites recover without immunization, and are thus not \"removed\". The asynchronous simulation of the model on a lattice is carried out as follows: Pick a site. If it is I, then generate a random number x in (0,1). If x < c then let I go to R. Otherwise, pick one nearest neighbor randomly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "According to Avery, Calem, and Canner in Credit Report Accuracy and Access to Credit, \"the parties that bear the costs of correcting errors or providing more timely and complete information  may not receive much benefit from the improvement in accuracy. \"The formula to calculate consumer credit scores by a consumer reporting agency is proprietary and considered a trade secret of the agency in the United States.Some consumer reporting agencies in the United States provide two credit scores - an 'educational' score to the consumer and a customary FICO-like score to the lender or business. Liz Weston writes that some consumer advocates refer to these other  credit scores as \"FAKO scores\" (a play on acronym of FICO).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It shows whether what has been achieved is above or below expectation. Secondly, it gives the planners a chance to learn, that is, to gather new general insight, for instance, regarding the strength and weakness of certain weapons or techniques of action. Thirdly, this fact-finding should serve as a basis for correctly planning the next step. Finally, it serves as a basis for modifying the \"overall plan.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This idea was \"sharply\" criticized by Church.Thus Post in his 1936 paper was also discounting Kurt G\u00f6del's suggestion to Church in 1934\u20131935 that the thesis might be expressed as an axiom or set of axioms.Turing adds another definition, Rosser equates all three: Within just a short time, Turing's 1936\u20131937 paper \"On Computable Numbers, with an Application to the Entscheidungsproblem\" appeared. In it he stated another notion of \"effective computability\" with the introduction of his a-machines (now known as the Turing machine abstract computational model). And in a proof-sketch added as an \"Appendix\" to his 1936\u20131937 paper, Turing showed that the classes of functions defined by \u03bb-calculus and Turing machines coincided.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We would then like to choose a hypothesis that minimizes the expected risk: In most cases, we don't know the joint distribution of X n + 1 , y n + 1 {\\displaystyle X_{n+1},\\,y_{n+1}} outright. In these cases, a common strategy is to choose the hypothesis that minimizes the empirical risk: Under certain assumptions about the sequence of random variables X k , y k {\\displaystyle X_{k},\\,y_{k}} (for example, that they are generated by a finite Markov process), if the set of hypotheses being considered is small enough, the minimizer of the empirical risk will closely approximate the minimizer of the expected risk as n {\\displaystyle n} grows large. This approach is called empirical risk minimization, or ERM.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where x 1 , \u2026 , x m {\\displaystyle x_{1},\\dots ,x_{m}} are not known in advance, Kedlaya and Umans gave a data structure for evaluating polynomials over a finite field of size F q {\\displaystyle F_{q}} in time ( log \u2061 n ) O ( 1 ) ( log 2 \u2061 q ) 1 + o ( 1 ) {\\displaystyle (\\log n)^{O(1)}(\\log _{2}q)^{1+o(1)}} per evaluation after some initial preprocessing. This was shown by Larsen to be essentially optimal. The idea is to transform P ( x ) {\\displaystyle P(x)} of degree n {\\displaystyle n} into a multivariate polynomial f ( x 1 , x 2 , \u2026 , x m ) {\\displaystyle f(x_{1},x_{2},\\dots ,x_{m})} , such that P ( x ) = f ( x , x d , x d 2 , \u2026 , x d m ) {\\displaystyle P(x)=f(x,x^{d},x^{d^{2}},\\dots ,x^{d^{m}})} and the individual degrees of f {\\displaystyle f} is at most d {\\displaystyle d} . Since this is over mod q {\\displaystyle {\\bmod {q}}} , the largest value f {\\displaystyle f} can take (over Z {\\displaystyle \\mathbb {Z} } ) is M = d m ( q \u2212 1 ) d m {\\displaystyle M=d^{m}(q-1)^{dm}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, objects with more structure than sets. Let T be a finitely splitting rooted tree of height \u03c9, n a positive integer, and S T n {\\displaystyle \\mathbb {S} _{T}^{n}} the collection of all strongly embedded subtrees of T of height n. In one of its simple forms, Milliken's tree theorem states that if S T n = C 1 \u222a . . . \u222a C r {\\displaystyle \\mathbb {S} _{T}^{n}=C_{1}\\cup ...\\cup C_{r}} then for some strongly embedded infinite subtree R of T, S R n \u2282 C i {\\displaystyle \\mathbb {S} _{R}^{n}\\subset C_{i}} for some i \u2264 r. This immediately implies Ramsey's theorem; take the tree T to be a linear ordering on \u03c9 vertices. Define S n = \u22c3 T S T n {\\displaystyle \\mathbb {S} ^{n}=\\bigcup _{T}\\mathbb {S} _{T}^{n}} where T ranges over finitely splitting rooted trees of height \u03c9. Milliken's tree theorem says that not only is S n {\\displaystyle \\mathbb {S} ^{n}} partition regular for each n < \u03c9, but that the homogeneous subtree R guaranteed by the theorem is strongly embedded in T.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These categories are characterized by fundamental ontological concepts, including particularity and universality, abstractness and concreteness, or possibility and necessity. Of special interest is the concept of ontological dependence, which determines whether the entities of a category exist on the most fundamental level.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One striking one is the result announced by Dan Goldston, J\u00e1nos Pintz, and Cem Y\u0131ld\u0131r\u0131m, which shows (assuming this conjecture) that there are infinitely many pairs of primes which differ by at most 16. In November 2013, James Maynard showed that subject to the Elliott\u2013Halberstam conjecture, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 12. In August 2014, Polymath group showed that subject to the generalized Elliott\u2013Halberstam conjecture, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 6. Without assuming any form of the conjecture, the lowest proven bound is 246.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Linear-chain CRFs have many of the same applications as conceptually simpler hidden Markov models (HMMs), but relax certain assumptions about the input and output sequence distributions. An HMM can loosely be understood as a CRF with very specific feature functions that use constant probabilities to model state transitions and emissions. Conversely, a CRF can loosely be understood as a generalization of an HMM that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence. Notably, in contrast to HMMs, CRFs can contain any number of feature functions, the feature functions can inspect the entire input sequence X {\\displaystyle X} at any point during inference, and the range of the feature functions need not have a probabilistic interpretation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each rule is defined to match a specific context. A context involves two pivots ( p {\\displaystyle p} and q {\\displaystyle q} ) and five clauses ( \u03b1 {\\displaystyle \\alpha } , \u03b2 {\\displaystyle \\beta } , \u03b3 {\\displaystyle \\gamma } , \u03b4 {\\displaystyle \\delta } and \u03b7 {\\displaystyle \\eta } ). The structure of a context is shown in (1).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a \"generic\" type, using variables in place of actual types, and then instantiated with particular types as needed. : 340 Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For such a graph, with m {\\displaystyle m} edges and n {\\displaystyle n} vertices, the size of a minimum feedback arc set is always at least ( m 2 + m n ) / 2 n 2 {\\displaystyle (m^{2}+mn)/2n^{2}} . There are infinitely many Eulerian directed graphs for which this bound is tight. If a directed graph has n {\\displaystyle n} vertices, with at most three edges per vertex, then it has a feedback arc set of at most n / 3 {\\displaystyle n/3} edges, and some graphs require this many. If a directed graph has m {\\displaystyle m} edges, with at most four edges per vertex, then it has a feedback arc set of at most m / 3 {\\displaystyle m/3} edges, and some graphs require this many. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2016/2017 QS World University Rankings\u00ae Result tables, GIST was ranked number 2 in the world in the category of citations per faculty. In the Times Higher Education World University Rankings 2014\u20132015, GIST was ranked 96th in the world in the category of Engineering & Technology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The only output from the programs was the patterns of lights on the panel. Nevertheless, many were sold in this form. Development was already underway on additional cards, including a paper tape reader for storage, additional RAM cards, and an RS-232 interface to connect to a proper teletype terminal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When opening the airbrake disturbs the airfoil shape thereby slowing the mill. It was invented by German airplane engineer Kurt Bilau early in the twentieth century and became quite popular in Germany where it was fitted to over 140 mills. A similar system was invented by a millwright by the name of Van Riet of Goes where the leading edge and the airbrake together form a more complete airfoil.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle B_{k}^{(-k)}\\sim (k! )^{2}{\\sqrt {\\frac {1}{k\\pi (1-\\log 2)}}}\\left({\\frac {1}{\\log 2}}\\right)^{2k+1},\\quad {\\text{as }}k\\rightarrow \\infty .} For a positive integer n and a prime number p, the poly-Bernoulli numbers satisfy B n ( \u2212 p ) \u2261 2 n ( mod p ) , {\\displaystyle B_{n}^{(-p)}\\equiv 2^{n}{\\pmod {p}},} which can be seen as an analog of Fermat's little theorem. Further, the equation B x ( \u2212 n ) + B y ( \u2212 n ) = B z ( \u2212 n ) {\\displaystyle B_{x}^{(-n)}+B_{y}^{(-n)}=B_{z}^{(-n)}} has no solution for integers x, y, z, n > 2; an analog of Fermat's Last Theorem. Moreover, there is an analogue of Poly-Bernoulli numbers (like Bernoulli numbers and Euler numbers) which is known as Poly-Euler numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the equivalence of models of computability, a parallel is drawn between Turing machines that do not terminate for certain inputs and an undefined result for that input in the corresponding partial recursive function. The unbounded search operator is not definable by the rules of primitive recursion as those do not provide a mechanism for \"infinite loops\" (undefined values).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of descriptive complexity theory, NP corresponds precisely to the set of languages definable by existential second-order logic (Fagin's theorem). NP can be seen as a very simple type of interactive proof system, where the prover comes up with the proof certificate and the verifier is a deterministic polynomial-time machine that checks it. It is complete because the right proof string will make it accept if there is one, and it is sound because the verifier cannot accept if there is no acceptable proof string.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to get a classical style reciprocity law from the Hilbert reciprocity law \u03a0(a,b)p=1, one needs to know the values of (a,b)p for p dividing n. Explicit formulas for this are sometimes called explicit reciprocity laws.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "2. Inconsistency factors: features of the individual or the situation that can affect test scores but have nothing to do with the attribute being measured. These factors include: Temporary but general characteristics of the individual: health, fatigue, motivation, emotional strain Temporary and specific characteristics of individual: comprehension of the specific test task, specific tricks or techniques of dealing with the particular test materials, fluctuations of memory, attention or accuracy Aspects of the testing situation: freedom from distractions, clarity of instructions, interaction of personality, etc. Chance factors: luck in selection of answers by sheer guessing, momentary distractionsThe goal of estimating reliability is to determine how much of the variability in test scores is due to measurement errors and how much is due to variability in true scores (true value).A true score is the replicable feature of the concept being measured.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\delta \\left((x,y),(x',y')\\right)=\\min \\left\\{\\max\\{|x-x'|,|y-y'|\\},\\max \\left\\{{\\frac {y-x}{2}},{\\frac {y'-x'}{2}}\\right\\}\\right\\}.} Roughly speaking, the matching distance d match {\\displaystyle d_{\\text{match}}} between two size functions is the minimum, over all the matchings between the cornerpoints of the two size functions, of the maximum of the L \u221e {\\displaystyle L_{\\infty }} -distances between two matched cornerpoints. Since two size functions can have a different number of cornerpoints, these can be also matched to points of the diagonal \u0394 {\\displaystyle \\Delta } . Moreover, the definition of \u03b4 {\\displaystyle \\delta } implies that matching two points of the diagonal has no cost.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, a match report is a report that compares two distinct data dictionaries and creates a list of the data elements that have been identified as semantically equivalent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The theorem is further generalized by Carmichael's theorem. The theorem may be used to easily reduce large powers modulo n {\\displaystyle n} . For example, consider finding the ones place decimal digit of 7 222 {\\displaystyle 7^{222}} , i.e. 7 222 ( mod 10 ) {\\displaystyle 7^{222}{\\pmod {10}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some scenarios where the majority of files are shorter than half the block size, such as in a folder of small source code files or small bitmap images, tail packing can increase storage efficiency even more than twofold, compared to file systems without tail packing.This not only translates into conservation of disk space, but may also introduce performance increases, as due to higher locality of reference, less data has to be read, also translating into higher page cache efficiency. However, these advantages can be negated by the increased complexity of implementation.As of 2015, the most widely used read-write file systems with support for block suballocation are Btrfs and FreeBSD UFS2 (where it is called \"block level fragmentation\"). ReiserFS and Reiser4 also support tail packing. Several read-only file systems do not use blocks at all and are thus implicitly using space as efficiently as suballocating file systems; such file systems double as archive formats.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to decide which clusters should be combined (for agglomerative), or where a cluster should be split (for divisive), a measure of dissimilarity between sets of observations is required. In most methods of hierarchical clustering, this is achieved by use of an appropriate distance d, such as the Euclidean distance, between single observations of the data set, and a linkage criterion, which specifies the dissimilarity of sets as a function of the pairwise distances of observations in the sets. The choice of metric as well as linkage can have a major impact on the result of the clustering, where the lower level metric determines which objects are most similar, whereas the linkage criterion influences the shape of the clusters. For example, complete-linkage tends to produce more spherical clusters than single-linkage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this formulation, the statement is reviewed by Leinster.A related example is discussed by Leinster: the codensity monad of the inclusion of finite-dimensional vector spaces (over a fixed field k {\\displaystyle k} ) into all vector spaces is the double dualization monad given by sending a vector space V {\\displaystyle V} to its double dual Thus, in this example, the end formula mentioned above simplifies to considering (in the notation above) only one object d , {\\displaystyle d,} namely a one-dimensional vector space, as opposed to considering all objects in D . {\\displaystyle D.} Ad\u00e1mek show that, in a number of situations, the codensity monad of the inclusion of finitely presented objects (also known as compact objects) is a double dualization monad with respect to a sufficiently nice cogenerating object.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number of elements in G), then G contains an element of order p. That is, there is x in G such that p is the smallest positive integer with xp = e, where e is the identity element of G. It is named after Augustin-Louis Cauchy, who discovered it in 1845.The theorem is related to Lagrange's theorem, which states that the order of any subgroup of a finite group G divides the order of G. Cauchy's theorem implies that for any prime divisor p of the order of G, there is a subgroup of G whose order is p\u2014the cyclic group generated by the element in Cauchy's theorem. Cauchy's theorem is generalized by Sylow's first theorem, which implies that if pn is the maximal power of p dividing the order of G, then G has a subgroup of order pn (and using the fact that a p-group is solvable, one can show that G has subgroups of order pr for any r less than or equal to n).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more general mathematical settings, the Boltzmann distribution is also known as the Gibbs measure. In statistics and machine learning, it is called a log-linear model. In deep learning, the Boltzmann distribution is used in the sampling distribution of stochastic neural networks such as the Boltzmann machine, restricted Boltzmann machine, energy-based models and deep Boltzmann machine. In deep learning, the Boltzmann machine is considered to be one of the unsupervised learning models. In the design of Boltzmann machine in deep learning , as the number of nodes are increased the difficulty of implementing in real time applications becomes critical, so a different type of architecture named Restricted Boltzmann machine is introduced.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming languages, dynamic compilers are particularly good candidates for performing escape analysis. In traditional static compilation, method overriding can make escape analysis impossible, as any called method might be overridden by a version that allows a pointer to escape. Dynamic compilers can perform escape analysis using the available information on overloading, and re-do the analysis when relevant methods are overridden by dynamic code loading.The popularity of the Java programming language has made escape analysis a target of interest. Java's combination of heap-only object allocation, built-in threading, the Sun HotSpot dynamic compiler, and OpenJ9's just-in-time compiler (JIT) creates a candidate platform for escape analysis related optimizations (see Escape analysis in Java). Escape analysis is implemented in Java Standard Edition 6. Some JVMs support a stronger variant of escape analysis called partial escape analysis that makes scalar replacement of an allocated object possible even if the object escapes in some paths of a function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the noncentral beta distribution is a continuous probability distribution that is a noncentral generalization of the (central) beta distribution. The noncentral beta distribution (Type I) is the distribution of the ratio X = \u03c7 m 2 ( \u03bb ) \u03c7 m 2 ( \u03bb ) + \u03c7 n 2 , {\\displaystyle X={\\frac {\\chi _{m}^{2}(\\lambda )}{\\chi _{m}^{2}(\\lambda )+\\chi _{n}^{2}}},} where \u03c7 m 2 ( \u03bb ) {\\displaystyle \\chi _{m}^{2}(\\lambda )} is a noncentral chi-squared random variable with degrees of freedom m and noncentrality parameter \u03bb {\\displaystyle \\lambda } , and \u03c7 n 2 {\\displaystyle \\chi _{n}^{2}} is a central chi-squared random variable with degrees of freedom n, independent of \u03c7 m 2 ( \u03bb ) {\\displaystyle \\chi _{m}^{2}(\\lambda )} . In this case, X \u223c Beta ( m 2 , n 2 , \u03bb ) {\\displaystyle X\\sim {\\mbox{Beta}}\\left({\\frac {m}{2}},{\\frac {n}{2}},\\lambda \\right)} A Type II noncentral beta distribution is the distribution of the ratio Y = \u03c7 n 2 \u03c7 n 2 + \u03c7 m 2 ( \u03bb ) , {\\displaystyle Y={\\frac {\\chi _{n}^{2}}{\\chi _{n}^{2}+\\chi _{m}^{2}(\\lambda )}},} where the noncentral chi-squared variable is in the denominator only. If Y {\\displaystyle Y} follows the type II distribution, then X = 1 \u2212 Y {\\displaystyle X=1-Y} follows a type I distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with \"11\" and contains no other instances of \"11\" before the end. The Fibonacci code is closely related to the Zeckendorf representation, a positional numeral system that uses Zeckendorf's theorem and has the property that no number has a representation with consecutive 1s. The Fibonacci code word for a particular integer is exactly the integer's Zeckendorf representation with the order of its digits reversed and an additional \"1\" appended to the end.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five nonisomorphic semigroups having two elements: O2, the null semigroup of order two, LO2, the left zero semigroup of order two, RO2, the right zero semigroup of order two, ({0,1}, \u2227) (where \"\u2227\" is the logical connective \"and\"), or equivalently the set {0,1} under multiplication: the only semilattice with two elements and the only non-null semigroup with zero of order two, also a monoid, and ultimately the two-element Boolean algebra, (Z2, +2) (where Z2 = {0,1} and \"+2\" is \"addition modulo 2\"), or equivalently ({0,1}, \u2295) (where \"\u2295\" is the logical connective \"xor\"), or equivalently the set {\u22121,1} under multiplication: the only group of order two.The semigroups LO2 and RO2 are antiisomorphic. O2, ({0,1}, \u2227) and (Z2, +2) are commutative, and LO2 and RO2 are noncommutative. LO2, RO2 and ({0,1}, \u2227) are bands.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, results depend on choosing a good strategy for clustering the outcomes into classes. A Huffman tree was used for this in Google's word2vec models (introduced in 2013) to achieve scalability.A second kind of remedies is based on approximating the softmax (during training) with modified loss functions that avoid the calculation of the full normalization factor. These include methods that restrict the normalization sum to a sample of outcomes (e.g. Importance Sampling, Target Sampling).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory. It applies the concept of the Sieve of Eratosthenes to find upper or lower bounds on the number of primes within a given set of integers. Because it is a simple extension of Eratosthenes' idea, it is sometimes called the Legendre\u2013Eratosthenes sieve.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Even though reporting p-values of statistical tests is common practice in academic publications of many quantitative fields, misinterpretation and misuse of p-values is widespread and has been a major topic in mathematics and metascience. In 2016, the American Statistician Association (ASA) made a formal statement that \"p-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone\" and that \"a p-value, or statistical significance, does not measure the size of an effect or the importance of a result\" or \"evidence regarding a model or hypothesis.\" That said, a 2019 task force by ASA has issued a statement on statistical significance and replicability, concluding with: \"p-values and significance tests, when properly applied and interpreted, increase the rigor of the conclusions drawn from data.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical testing problems, one usually is not interested in the component vectors themselves, but rather in their squared lengths, or Sum of Squares. The degrees of freedom associated with a sum-of-squares is the degrees-of-freedom of the corresponding component vectors. The three-population example above is an example of one-way Analysis of Variance. The model, or treatment, sum-of-squares is the squared length of the second vector, SST = n ( X \u00af \u2212 M \u00af ) 2 + n ( Y \u00af \u2212 M \u00af ) 2 + n ( Z \u00af \u2212 M \u00af ) 2 {\\displaystyle {\\text{SST}}=n({\\bar {X}}-{\\bar {M}})^{2}+n({\\bar {Y}}-{\\bar {M}})^{2}+n({\\bar {Z}}-{\\bar {M}})^{2}} with 2 degrees of freedom.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical terms, quantum discord is defined in terms of the quantum mutual information. More specifically, quantum discord is the difference between two expressions which each, in the classical limit, represent the mutual information. These two expressions are: I ( A ; B ) = H ( A ) + H ( B ) \u2212 H ( A , B ) {\\displaystyle I(A;B)=H(A)+H(B)-H(A,B)} J ( A ; B ) = H ( A ) \u2212 H ( A | B ) {\\displaystyle J(A;B)=H(A)-H(A|B)} where, in the classical case, H(A) is the information entropy, H(A, B) the joint entropy and H(A|B) the conditional entropy, and the two expressions yield identical results. In the nonclassical case, the quantum physics analogy for the three terms are used \u2013 S(\u03c1A) the von Neumann entropy, S(\u03c1) the joint quantum entropy and S(\u03c1A|\u03c1B) a quantum generalization of conditional entropy (not to be confused with conditional quantum entropy), respectively, for probability density function \u03c1; I ( \u03c1 ) = S ( \u03c1 A ) + S ( \u03c1 B ) \u2212 S ( \u03c1 ) {\\displaystyle I(\\rho )=S(\\rho _{A})+S(\\rho _{B})-S(\\rho )} J A ( \u03c1 ) = S ( \u03c1 B ) \u2212 S ( \u03c1 B | \u03c1 A ) {\\displaystyle J_{A}(\\rho )=S(\\rho _{B})-S(\\rho _{B}|\\rho _{A})} The difference between the two expressions defines the basis-dependent quantum discord D A ( \u03c1 ) = I ( \u03c1 ) \u2212 J A ( \u03c1 ) , {\\displaystyle {\\mathcal {D}}_{A}(\\rho )=I(\\rho )-J_{A}(\\rho ),} which is asymmetrical in the sense that D A ( \u03c1 ) {\\displaystyle {\\mathcal {D}}_{A}(\\rho )} can differ from D B ( \u03c1 ) {\\displaystyle {\\mathcal {D}}_{B}(\\rho )} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of IT systems and data center management, a \"workload\" can be broadly defined as \"the total requests made by users and applications of a system.\" However, it is also possible to break down the entire workload of a given system into sets of self-contained units. Such a self-contained unit constitutes a \"workload\" in the narrow sense: an integrated stack consisting of application, middleware, database, and operating system devoted to a specific computing task. Typically, a workload is \"platform agnostic,\" meaning that it can run in physical, virtual or cloud computing environments. Finally, a collection of related workloads which allow end users to complete a specific set of business tasks can be defined as a \"business service.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We say that ( X , L ) {\\displaystyle (X,L)} is: K-semistable if \u03bc \u2061 ( X , L ) \u2265 0 {\\displaystyle \\operatorname {\\mu } ({\\mathcal {X}},{\\mathcal {L}})\\geq 0} for all test configurations ( X , L ) {\\displaystyle ({\\mathcal {X}},{\\mathcal {L}})} for ( X , L ) {\\displaystyle (X,L)} . K-stable if \u03bc \u2061 ( X , L ) \u2265 0 {\\displaystyle \\operatorname {\\mu } ({\\mathcal {X}},{\\mathcal {L}})\\geq 0} for all test configurations ( X , L ) {\\displaystyle ({\\mathcal {X}},{\\mathcal {L}})} for ( X , L ) {\\displaystyle (X,L)} , and additionally \u03bc \u2061 ( X , L ) > 0 {\\displaystyle \\operatorname {\\mu } ({\\mathcal {X}},{\\mathcal {L}})>0} whenever \u2016 ( X , L ) \u2016 > 0 {\\displaystyle \\|({\\mathcal {X}},{\\mathcal {L}})\\|>0} . K-polystable if ( X , L ) {\\displaystyle (X,L)} is K-semistable, and additionally whenever \u03bc \u2061 ( X , L ) = 0 {\\displaystyle \\operatorname {\\mu } ({\\mathcal {X}},{\\mathcal {L}})=0} , the test configuration ( X , L ) {\\displaystyle ({\\mathcal {X}},{\\mathcal {L}})} is a product configuration. K-unstable if it is not K-semistable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the broadest definition, document comparison can refer to any act of marking changes made between two versions of the same document and presenting those changes in a third document via a graphical user interface (GUI). There are several variants in the types of changes registered through the process of document comparison. Some programs limit comparison to solely text and table content in word processing documents, while others register changes made in spreadsheets and presentations, along with changes made in versions of PDF documents. Certain programs also exist that compare changes made to objects like JPEG, TIFF, BMP, PNG images embedded in documents, and plain text files.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "E.g. the Linux tool scanmem supports PIE this way. For the configured memory offset the game trainer determines the load address as well and adds it back during run-time. The same method can be used for dynamic libraries as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Its GPS receiver compares the PGK's flight pattern to the coordinates of where it should hit, and the fins adjust its path to match where the round will actually impact. A fail safe exists where if the shell does not impact within 150 m (490 ft) of the intended target, it will land but not explode; the PGK \"decides\" five seconds after launch whether it expects to impact close enough to detonate. This safety feature is expected to give soldiers more confidence when calling in artillery support close to their position.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a trivial semigroup (a semigroup with one element) is a semigroup for which the cardinality of the underlying set is one. The number of distinct nonisomorphic semigroups with one element is one. If S = { a } is a semigroup with one element, then the Cayley table of S is The only element in S is the zero element 0 of S and is also the identity element 1 of S. However not all semigroup theorists consider the unique element in a semigroup with one element as the zero element of the semigroup. They define zero elements only in semigroups having at least two elements.In spite of its extreme triviality, the semigroup with one element is important in many situations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The case (x, y, z) = (3, 6, n) and all its permutations were proven for n \u2265 3 by Bennett, Chen, Dahmen and Yazdani in 2014. The case (x, y, z) = (2n, 3, 4) and all its permutations were proven for n \u2265 2 by Bennett, Chen, Dahmen and Yazdani in 2014. The cases (5, 5, 7), (5, 5, 19), (7, 7, 5) and all their permutations were proven by Sander R. Dahmen and Samir Siksek in 2013.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Forr\u00f3 trios, where the only pitch instrument (apart from the voice) is the accordion (which plays together with two percussionists), the accordionist usually \"puxa\" (\"pulls\") the next song as soon as the previous has finished. Some album notations distinguish track listings through the use of symbols, such as a >, \u2192, or / to indicate songs that flow seamlessly. The alternative rock band Failure separates these musical transitions into individual tracks, which are simply given numerical distinctions such as Segue 1. This system began with their 1996 album Fantastic Planet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode: if a < b then set c to True else set c to False In guarded command language: if a < b \u2192 c := true \u25a1 a \u2265 b \u2192 c := false fi", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Freedman\u2013Diaconis rule can be used to select the width of the bins to be used in a histogram. It is named after David A. Freedman and Persi Diaconis. For a set of empirical measurements sampled from some probability distribution, the Freedman-Diaconis rule is designed roughly to minimize the integral of the squared difference between the histogram (i.e., relative frequency density) and the density of the theoretical probability distribution. The general equation for the rule is: Bin width = 2 IQR ( x ) n 3 {\\displaystyle {\\text{Bin width}}=2\\,{{\\text{IQR}}(x) \\over {\\sqrt{n}}}} where IQR \u2061 ( x ) {\\displaystyle \\operatorname {IQR} (x)} is the interquartile range of the data and n {\\displaystyle n} is the number of observations in the sample x . {\\displaystyle x.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern logic, the term \"proposition\" is often used for sentences of a formal language. In this usage, propositions are formal syntactic objects which can be studied independently of the meaning they would receive from a semantics. Propositions are also called sentences, statements, statement forms, formulas, and well-formed formulas, though these terms are usually not synonymous within a single text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network theory, link prediction is the problem of predicting the existence of a link between two entities in a network. Examples of link prediction include predicting friendship links among users in a social network, predicting co-authorship links in a citation network, and predicting interactions between genes and proteins in a biological network. Link prediction can also have a temporal aspect, where, given a snapshot of the set of links at time t {\\displaystyle t} , the goal is to predict the links at time t + 1 {\\displaystyle t+1} . Link prediction is widely applicable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are currently 46 relations in the UNL Specs. They jointly define the UNL syntax. Attributes represent information that cannot be conveyed by UWs and relations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2-dimensional nonsingular case ( k = rank \u2061 ( \u03a3 ) = 2 {\\displaystyle k=\\operatorname {rank} \\left(\\Sigma \\right)=2} ), the probability density function of a vector \u2032 {\\displaystyle {\\text{\u2032}}} is: where \u03c1 {\\displaystyle \\rho } is the correlation between X {\\displaystyle X} and Y {\\displaystyle Y} and where \u03c3 X > 0 {\\displaystyle \\sigma _{X}>0} and \u03c3 Y > 0 {\\displaystyle \\sigma _{Y}>0} . In this case, \u03bc = ( \u03bc X \u03bc Y ) , \u03a3 = ( \u03c3 X 2 \u03c1 \u03c3 X \u03c3 Y \u03c1 \u03c3 X \u03c3 Y \u03c3 Y 2 ) . {\\displaystyle {\\boldsymbol {\\mu }}={\\begin{pmatrix}\\mu _{X}\\\\\\mu _{Y}\\end{pmatrix}},\\quad {\\boldsymbol {\\Sigma }}={\\begin{pmatrix}\\sigma _{X}^{2}&\\rho \\sigma _{X}\\sigma _{Y}\\\\\\rho \\sigma _{X}\\sigma _{Y}&\\sigma _{Y}^{2}\\end{pmatrix}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Again, minimize the maximal load of all remaining links, but now without the bottlenecks of the 2nd network layer as well. Repeat this algorithm until the entire communication footprint is enclosed in the bottlenecks of the constructed layers.At each functional layer of the network protocol, after minimizing the maximal load of links, the bottlenecks of the layer are discovered in a bottleneck detection process. At each iteration of the detection loop, we minimize the sending of traffic over all links having maximal loading, and being suspected as bottlenecks. Links unable to maintain their traffic load at the maximum are eventually removed from the candidate path list. The bottleneck detection process stops when there are no more links to remove, because this best path is now known.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Choice or Select. U.S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although the study of multiplicative partitions has been ongoing since at least 1923, the name \"multiplicative partition\" appears to have been introduced by Hughes & Shallit (1983). The Latin name \"factorisatio numerorum\" had been used previously. MathWorld uses the term unordered factorization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The solution is to provide a small amount of very fast memory known as a CPU cache which holds recently accessed data. As long as the data that the CPU needs is in the cache, the performance is much higher than it is when the CPU has to get the data from the main memory. On the other side, however, it may still be limited to storing repetitive programs or data and still has a storage size limitation, and other potential problems associated with it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of dimension one, varieties are classified by only the topological genus, but, in dimension two, one needs to distinguish the arithmetic genus p a {\\displaystyle p_{a}} and the geometric genus p g {\\displaystyle p_{g}} because one cannot distinguish birationally only the topological genus. Then, irregularity is introduced for the classification of varieties. A summary of the results (in detail, for each kind of surface refers to each redirection), follows: Examples of algebraic surfaces include (\u03ba is the Kodaira dimension): \u03ba = \u2212\u221e: the projective plane, quadrics in P3, cubic surfaces, Veronese surface, del Pezzo surfaces, ruled surfaces \u03ba = 0: K3 surfaces, abelian surfaces, Enriques surfaces, hyperelliptic surfaces \u03ba = 1: elliptic surfaces \u03ba = 2: surfaces of general type.For more examples see the list of algebraic surfaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, the activity-driven model is a temporal network model in which each node has a randomly-assigned \"activity potential\", which governs how it links to other nodes over time. Each node j {\\displaystyle j} (out of N {\\displaystyle N} total) has its activity potential x i {\\displaystyle x_{i}} drawn from a given distribution F ( x ) {\\displaystyle F(x)} . A sequence of timesteps unfolds, and in each timestep each node j {\\displaystyle j} forms ties to m {\\displaystyle m} random other nodes at rate a i = \u03b7 x i {\\displaystyle a_{i}=\\eta x_{i}} (more precisely, it does so with probability a i \u0394 t {\\displaystyle a_{i}\\,\\Delta t} per timestep). All links are then deleted after each timestep.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since around 1970, D-module theory has been built up, mainly as a response to the ideas of Mikio Sato on algebraic analysis, and expanding on the work of Sato and Joseph Bernstein on the Bernstein\u2013Sato polynomial. Early major results were the Kashiwara constructibility theorem and Kashiwara index theorem of Masaki Kashiwara.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s, the rise of broadband networks and the dotcom boom presented the internet as mass media to a whole generation. By the late 1990s, VoIP and net phones and chat had emerged. For the first time, people used computers primarily as communications, not \"computing\" devices. This, however, had long been anticipated, predicted, and studied by experts in the field. Video collaboration is not usually studied. Online videoconferencing and webcams have been studied in small scale use for decades but since people simply do not have built-in facilities to create video together directly, they are properly a communication, not collaboration, concern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory, ludics is an analysis of the principles governing inference rules of mathematical logic. Key features of ludics include notion of compound connectives, using a technique known as focusing or focalisation (invented by the computer scientist Jean-Marc Andreoli), and its use of locations or loci over a base instead of propositions. More precisely, ludics tries to retrieve known logical connectives and proof behaviours by following the paradigm of interactive computation, similarly to what is done in game semantics to which it is closely related. By abstracting the notion of formulae and focusing on their concrete uses\u2014that is distinct occurrences\u2014it provides an abstract syntax for computer science, as loci can be seen as pointers on memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It may be noted that the conservation of entropy holds for a quantum system undergoing unitary time evolution and if entropy represents information in quantum theory, then it is believed then that information should somehow be conserved. For example, one can prove that pure states remain pure states and probabilistic combination of pure states (called as mixed states) remain mixed states under unitary evolution. However, it was never proved that if the probability amplitude disappears from one system, it will reappear in another system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most cases, the size of the model is simply the number of parameters. However, one complication arises with the use of sparse models, such as mixture-of-expert models. In sparse models, during every inference, only a fraction of the parameters are used. In comparison, most other kinds of neural networks, such as Transformer networks, always use all their parameters during every inference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, developers need to make systems that are intuitive to the user in order to have information security and system security.Another key step to end user security is informing the people and employees about the security threats and what they can do to avoid them or protect themselves and the organization. Underlining clearly the capabilities and risks makes users more aware and informed whilst they are using the products. Some situations that could put the user at risk are: Auto-logon as administrator options Auto-fill options, in which a computer or program \"remembers\" a user's personal information and HTTP \"cookies\" Opening junk emails of suspicious emails and/or opening/running attachments or computer files contained in these Email can be monitored by third parties, especially when using Wi-Fi connections Unsecure Wi-Fi or use of a public Wi-Fi network at a coffee shop or hotel Weak passwords (using a person's own name, own birthdate, name or birthdate of children, or easy-to-guess passwords such as \"1234\") Malicious programs such as virusesEven if the security measures in place are strong, the choices the user makes and his/her behaviour have a major impact on how secure their information really is.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, the backpressure routing algorithm is a method for directing traffic around a queueing network that achieves maximum network throughput, which is established using concepts of Lyapunov drift. Backpressure routing considers the situation where each job can visit multiple service nodes in the network. It is an extension of max-weight scheduling where each job visits only a single service node.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principal components analysis, \"Variables measured on different scales or on a common scale with widely differing ranges are often standardized.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "He did this by calculating Avogadro's number using three different methods, all involving liquid phase systems. First, he used a gamboge soap-like emulsion, second by doing experimental work on Brownian motion, and third by confirming Einstein's theory of particle rotation in the liquid phase.In 1937, chemist K.L.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This very much parallels the way in which mathematical proofs are carried out in practice by mathematicians. Predicate calculus proofs are generally much easier to discover with this approach, and are often shorter. Natural deduction systems are more suited to practical theorem-proving. Sequent calculus systems are more suited to theoretical analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "x c \u2208 { 0 , \u2026 , n } {\\displaystyle x_{c}\\in \\{0,\\ldots ,n\\}} for all c in C (- there are at most n bins overall, so at most n of each individual configuration). The configuration LP is an integer linear program, so in general it is NP-hard. Moreover, even the problem itself is generally very large: it has C variables and S constraints.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Wisdom of the crowd is the emergent opinion arising from multiple actors. It is not the union of all the knowledge of these actors, it does not necessarily include the contribution of all the actors, it does not refer to all the knowledge of these actors, and typically broadly includes opinions and guesswork. Wisdom of the crowd is a concept useful in the context of social sciences, rather than in the more formal multi-agent systems or Knowledge-based systems research.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 68, 168, 468, and 1468 are the patterns related to Braille pattern dots-56, since the two additional dots of kantenji patterns 056, 567, and 0567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, J ( \u03b8 ) {\\displaystyle {\\mathcal {J}}(\\theta )} is usually replaced by I ( \u03b8 ) = E  {\\displaystyle {\\mathcal {I}}(\\theta )=\\mathrm {E} } , the Fisher information, thus giving us the Fisher Scoring Algorithm: \u03b8 m + 1 = \u03b8 m + I \u2212 1 ( \u03b8 m ) V ( \u03b8 m ) {\\displaystyle \\theta _{m+1}=\\theta _{m}+{\\mathcal {I}}^{-1}(\\theta _{m})V(\\theta _{m})} ..Under some regularity conditions, if \u03b8 m {\\displaystyle \\theta _{m}} is a consistent estimator, then \u03b8 m + 1 {\\displaystyle \\theta _{m+1}} (the correction after a single step) is 'optimal' in the sense that its error distribution is asymptotically identical to that of the true max-likelihood estimate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, an 8-bit byte can have values ranging from 00000000 to 11111111 (0 to 255 decimal) in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value 30,227 would be expressed in hexadecimal as 761316.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Multiple sets of coded bits are generated, each representing the same set of information bits. The re-transmission typically uses a different set of coded bits than the previous transmission, with different redundancy versions generated by puncturing the encoder output. Thus, at every re-transmission the receiver gains extra information.Several variants of the two main methods exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, we assume that the N\u00d7M matrix is stored in row-major order with zero-based indices. This means that the (n,m) element, for n = 0,...,N\u22121 and m = 0,...,M\u22121, is stored at an address a = Mn + m (plus some offset in memory, which we ignore). In the transposed M\u00d7N matrix, the corresponding (m,n) element is stored at the address a' = Nm + n, again in row-major order. We define the transposition permutation to be the function a' = P(a) such that: N m + n = P ( M n + m ) {\\displaystyle Nm+n=P(Mn+m)\\,} for all ( n , m ) \u2208  \u00d7  .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the competitive chunking hypothesis, knowledge of a letter string develops along a hierarchy of \"chunks\", beginning with bigrams (two letters), leading to trigrams, four-grams, and so on. \"Chunk strength\" refers to the frequency of occurrence of any given chunk during the learning phase. The higher the chunk strength of an item, the more likely it is to be determined grammatical.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In single color mode, the entire 4\u00d74 block is painted with a single color. This mode can also be considered as a 1-color palette mode.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each realized variation of that object is an instance of its class. That is, it is a member of a given class that has specified values rather than variables. In a non-programming context, you could think of \"dog\" as a type and your particular dog as an instance of that class.In class-based programming, objects are created as instances of classes by subroutines called constructors, and destroyed by destructors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In row reduction (also known as Gaussian elimination), the linear system is represented as an augmented matrix:  . {\\displaystyle \\left{\\text{.}}} This matrix is then modified using elementary row operations until it reaches reduced row echelon form. There are three types of elementary row operations: Type 1: Swap the positions of two rows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For this description, the following functions and operators are used: Head (data, a): returns the first a bits of the 'data' string. Tail (data, a): returns the last a bits of the 'data' string. Encrypt (K, data): use the underlying block cipher in encrypt mode on the 'data' string using the key K. Decrypt (K, data): use the underlying block cipher in decrypt mode on the 'data' string using the key K. XOR: Bitwise Exclusive-OR.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As with complete linkage and average distance, the difficulty of calculating cluster distances causes the nearest-neighbor chain algorithm to take time and space O(n2) to compute the single-linkage clustering. However, the single-linkage clustering can be found more efficiently by an alternative algorithm that computes the minimum spanning tree of the input distances using Prim's algorithm, and then sorts the minimum spanning tree edges and uses this sorted list to guide the merger of pairs of clusters. Within Prim's algorithm, each successive minimum spanning tree edge can be found by a sequential search through an unsorted list of the smallest edges connecting the partially constructed tree to each additional vertex. This choice saves the time that the algorithm would otherwise spend adjusting the weights of vertices in its priority queue. Using Prim's algorithm in this way would take time O(n2) and space O(n), matching the best bounds that could be achieved with the nearest-neighbor chain algorithm for distances with constant-time calculations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a proof of impossibility is a proof that demonstrates that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general. Such a case is also known as a negative proof, proof of an impossibility theorem, or negative result. Proofs of impossibility often are the resolutions to decades or centuries of work attempting to find a solution, eventually proving that there is no solution. Proving that something is impossible is usually much harder than the opposite task, as it is often necessary to develop a proof that works in general, rather than to just show a particular example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Edwards curves are a family of elliptic curves studied by Harold Edwards in 2007. The concept of elliptic curves over finite fields is widely used in elliptic curve cryptography. Applications of Edwards curves to cryptography were developed by Daniel J. Bernstein and Tanja Lange: they pointed out several advantages of the Edwards form in comparison to the more well known Weierstrass form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances between different types of objects, such as the distance from a point to a line. In advanced mathematics, the concept of distance has been generalized to abstract metric spaces, and other distances than Euclidean have been studied. In some applications in statistics and optimization, the square of the Euclidean distance is used instead of the distance itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Gradient descent should not be confused with local search algorithms, although both are iterative methods for optimization. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Haskell Curry in 1944, with the method becoming increasingly well-studied and used in the following decades.A simple extension of gradient descent, stochastic gradient descent, serves as the most basic algorithm used for training most deep networks today.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The rows in the synopsis are ordered such that the coverage of all possible RB cases is easily comprehensible. The column rotation indicates whether a rotation contributes to the rebalancing. The column assignment shows an assignment of N before entering a subsequent iteration step.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All other groups, which are more complicated, are called \"nontrivial\". In graph theory, the trivial graph is a graph which has only 1 vertex and no edge. Database theory has a concept called functional dependency, written X \u2192 Y {\\displaystyle X\\to Y} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a weighted network, this triplet is expanded to a quadruplet e = ( u , v , d , w ) {\\displaystyle e=(u,v,d,w)} , where w {\\displaystyle w} is the weight on the link between u {\\displaystyle u} and v {\\displaystyle v} in the dimension d {\\displaystyle d} . Further, as is often useful in social network analysis, link weights may take on positive or negative values. Such signed networks can better reflect relations like amity and enmity in social networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In radio communication systems, information is transported across space using radio waves. At the sending end, the information to be sent, in the form of a time-varying electrical signal, is applied to a radio transmitter. The information, called the modulation signal, can be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing data from a computer. In the transmitter, an electronic oscillator generates an alternating current oscillating at a radio frequency, called the carrier wave because it creates the radio waves that \"carry\" the information through the air.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In planning, more precisely in classical planning, one is interested in knowing if one can attain a state from an initial state from a description of actions. The description of actions defines a graph of implicit states, which is of exponential size in the size of the description. In symbolic model checking, the model (the underlying graph) is described with the aid of a symbolic representation such as binary decision diagrams.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The royalty that is paid to the composer and publisher is determined by the method of assessment used by the PRO to gauge the use of the music, there being no external metrics as in mechanical royalties or the reporting system used in the UK. Very basically, a PRO aggregates the royalties that are due to all of the composers/songwriters \"who are its members\" and each composer and publisher is paid royalties based on the assessed frequency of the music's performance, post deductions of charges (which are many). The PROs are audited agencies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A formal system is used to derive one expression from one or more other expressions. Although a formal language can be identified with its formulas, a formal system cannot be likewise identified by its theorems. Two formal systems F S {\\displaystyle {\\mathcal {FS}}} and F S \u2032 {\\displaystyle {\\mathcal {FS'}}} may have all the same theorems and yet differ in some significant proof-theoretic way (a formula A may be a syntactic consequence of a formula B in one but not another for instance).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The index signal is asserted when the shaft is in its reference orientation, which causes the encoder interface to jam the reference angle into its position counter. Some incremental encoder applications lack reference position detectors and therefore must implement homing by other means. For example a computer, when using a mouse or trackball pointing device, typically will home the device by assuming a central, initial screen position upon booting, and jam the corresponding counts into the X and Y position counters. In the case of panel encoders used as hand-operated controls (e.g., audio volume control), the initial position typically is retrieved from flash or other non-volatile memory upon power-up and jammed into the position counter, and upon power-down the current position count is saved to non-volatile memory to serve as the initial position for the next power-up.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Channels just above the AM broadcast band were selected manually by the user. Some of the frequencies used are now part of the expanded AM radio band, and can be heard by anyone with an AM radio. There are reports of people still using these phones, and using them as makeshift AM radio stations that can be heard for a couple of city blocks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions. There are six convex and ten star regular 4-polytopes, giving a total of sixteen.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The \"no\"-answer version of this problem is stated as: \"given a finite set of integers, does every non-empty subset have a nonzero sum?\". The verifier-based definition of NP does not require an efficient verifier for the \"no\"-answers. The class of problems with such verifiers for the \"no\"-answers is called co-NP. In fact, it is an open question whether all problems in NP also have verifiers for the \"no\"-answers and thus are in co-NP. In some literature the verifier is called the \"certifier\", and the witness the \"certificate\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\u03bby. x, sometimes called the K combinator, is written as \u03bb \u03bb 2 with De Bruijn indices. The binder for the occurrence x is the second \u03bb in scope.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, a person will be declared dead even without any remains or doctor's declaration. This is under one of two circumstances. First, if a person was known to be in mortal peril when last seen, they can often be declared dead shortly after. Examples would be the passengers of the Titanic that were not rescued after the ship sank. Second, if a person has not been seen for a certain period of time and there has been no evidence that they are alive. The amount of time that has passed varies by jurisdiction, from as little as four years in the US state of Georgia to twenty years in Italy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In computer science the parity stripe or parity disk in a RAID provides error-correction. Parity bits are written at the rate of one parity bit per n bits, where n is the number of disks in the array. When a read error occurs, each bit in the error region is recalculated from its set of n bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The outputs of the replications are compared using a voting circuit. A machine with two replications of each element is termed dual modular redundant (DMR). The voting circuit can then only detect a mismatch and recovery relies on other methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-Euclidean geometry, squares are more generally polygons with 4 equal sides and equal angles. In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles. Unlike the square of plane geometry, the angles of such a square are larger than a right angle. Larger spherical squares have larger angles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the classic formalization of generative grammars first proposed by Noam Chomsky in the 1950s, a grammar G consists of the following components: A finite set N of nonterminal symbols, that is disjoint with the strings formed from G. A finite set \u03a3 {\\displaystyle \\Sigma } of terminal symbols that is disjoint from N. A finite set P of production rules, each rule of the form ( \u03a3 \u222a N ) \u2217 N ( \u03a3 \u222a N ) \u2217 \u2192 ( \u03a3 \u222a N ) \u2217 {\\displaystyle (\\Sigma \\cup N)^{*}N(\\Sigma \\cup N)^{*}\\rightarrow (\\Sigma \\cup N)^{*}} where \u2217 {\\displaystyle {*}} is the Kleene star operator and \u222a {\\displaystyle \\cup } denotes set union. That is, each production rule maps from one string of symbols to another, where the first string (the \"head\") contains an arbitrary number of symbols provided at least one of them is a nonterminal. In the case that the second string (the \"body\") consists solely of the empty string\u2014i.e., that it contains no symbols at all\u2014it may be denoted with a special notation (often \u039b {\\displaystyle \\Lambda } , e or \u03f5 {\\displaystyle \\epsilon } ) in order to avoid confusion.A distinguished symbol S \u2208 N {\\displaystyle S\\in N} that is the start symbol, also called the sentence symbol.A grammar is formally defined as the tuple ( N , \u03a3 , P , S ) {\\displaystyle (N,\\Sigma ,P,S)} . Such a formal grammar is often called a rewriting system or a phrase structure grammar in the literature.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in the field of commutative algebra, a connected ring is a commutative ring A that satisfies one of the following equivalent conditions: A possesses no non-trivial (that is, not equal to 1 or 0) idempotent elements; the spectrum of A with the Zariski topology is a connected space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle f_{i-1}(r_{1}\\dots r)=(1-r)f_{i}(r_{1},\\dots ,r_{i-1},0)+rf_{i}(r_{1},\\dots ,r_{i-1},1){\\text{ if }}{\\mathsf {S}}=\\mathrm {R} .} If either fails then reject. V \u2192 P: V picks a random r in F and sends it to P.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence U n ( P , Q ) {\\displaystyle U_{n}(P,Q)} for which P = 1, and Q = \u22122\u2014and are defined by a similar recurrence relation: in simple terms, the sequence starts with 0 and 1, then each following number is found by adding the number before it to twice the number before that. The first Jacobsthal numbers are: 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, \u2026 (sequence A001045 in the OEIS)A Jacobsthal prime is a Jacobsthal number that is also prime. The first Jacobsthal primes are: 3, 5, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243, \u2026 (sequence A049883 in the OEIS)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the statement \"there is an integer n such that if there is a sequence of rooted trees T1, T2, ..., Tn such that Tk has at most k+10 vertices, then some tree can be homeomorphically embedded in a later one\"is provable in Peano arithmetic, but the shortest proof has length at least A(1000), where A(0)=1 and A(n+1)=2A(n). The statement is a special case of Kruskal's theorem and has a short proof in second order arithmetic. If one takes Peano arithmetic together with the negation of the statement above, one obtains an inconsistent theory whose shortest known contradiction is equivalently long.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most of the more successful systems use lexical statistics (that is, they consider the identities of the words involved, as well as their part of speech). However such systems are vulnerable to overfitting and require some kind of smoothing to be effective.Parsing algorithms for natural language cannot rely on the grammar having 'nice' properties as with manually designed grammars for programming languages. As mentioned earlier some grammar formalisms are very difficult to parse computationally; in general, even if the desired structure is not context-free, some kind of context-free approximation to the grammar is used to perform a first pass.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After period one, the market value changes to 120k:80k:600k. We now rebalance to increase exposure on the outperforming asset and reduce exposure to the worst-performing asset. Asset A is the best performer, so its rebalanced to be left at 120k, B is the worst performer, to its rebalanced to 60k, and C is the remaining, 800k-120k-60k=620k. We are now back to the original fixed weights of 120:60:620 or ratio-wise 2:1:remaining.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, geology, and cartography, a surface map is a 2D perspective representation of a 3-dimensional surface. Surface maps usually represent real-world entities such as landforms or the surfaces of objects. They can, however, serve as an abstraction where the third, or even all of the dimensions correspond to non-spatial data. In this capacity they act more as graphs than maps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a schema migration (also database migration, database change management) refers to the management of version-controlled, incremental and reversible changes to relational database schemas. A schema migration is performed on a database whenever it is necessary to update or revert that database's schema to some newer or older version. Migrations are performed programmatically by using a schema migration tool. When invoked with a specified desired schema version, the tool automates the successive application or reversal of an appropriate sequence of schema changes until it is brought to the desired state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A simultaneous embedding in a grid of linear dimensions is also possible for any number of graphs that are all stars. Other pairs of graph types that always admit a simultaneous embedding, but that might need larger grid sizes, include a wheel graph and a cycle graph, a tree and a matching, or a pair of graphs both of which have maximum degree two. However, pairs of planar graphs and a matching, or of a Angelini, Geyer, Neuwirth and Kaufmann showed that a tree and a path exist, that have no simultaneous geometric embedding.Testing whether two graphs admit a simultaneous geometric embedding is NP-hard.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is generally done at two levels, at the sentence level, where scores are calculated by the metric for a set of translated sentences, and then correlated against human judgment for the same sentences. And at the corpus level, where scores over the sentences are aggregated for both human judgments and metric judgments, and these aggregate scores are then correlated. Figures for correlation at the sentence level are rarely reported, although Banerjee et al. (2005) do give correlation figures that show that, at least for their metric, sentence-level correlation is substantially worse than corpus level correlation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Making use of currying, n-ary type operators can be (re)written as a sequence of applications of unary type operators. Therefore, we can view the type operators as a simply typed lambda calculus, which has only one basic type, usually denoted \u2217 {\\displaystyle *} , and pronounced \"type\", which is the type of all types in the underlying language, which are now called proper types in order to distinguish them from the types of the type operators in their own calculus, which are called kinds. Type operators may bind type variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical terms, a vector optimization problem can be written as: C - \u2061 min x \u2208 S f ( x ) {\\displaystyle C\\operatorname {-} \\min _{x\\in S}f(x)} where f: X \u2192 Z {\\displaystyle f:X\\to Z} for a partially ordered vector space Z {\\displaystyle Z} . The partial ordering is induced by a cone C \u2286 Z {\\displaystyle C\\subseteq Z} . X {\\displaystyle X} is an arbitrary set and S \u2286 X {\\displaystyle S\\subseteq X} is called the feasible set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More generally, data depth, gives a center-outward ordering of data points, and thereby provides a mechanism for constructing rank statistics of various kinds of multidimensional data. For instance, functional data examples can be ordered using the method of band depth or a modified band depth. In contour data analysis, each observation is a feature-set (a subset of the domain), and therefore not a function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Both Alice and Bob announce these bits publicly and run a check to see whether more than a certain number of them agree. If this check passes, Alice and Bob proceed to use information reconciliation and privacy amplification techniques to create some number of shared secret keys. Otherwise, they cancel and start over.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When substantiating a civil fraud claim, the plaintiff is generally required to prove that the defendant falsely represented a material fact, that this representation was made with intent to deceive, that the plaintiff reasonably relied on the representation, and the representation resulted in damages to the plaintiff. Some legal experts have recommended strengthening existing intellectual property laws to address the growing problem of art forgeries proliferating in the mass market. They argue that the existing legal regime is ineffective in combating this growing trend.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As an example, a 4-byte value consists of 8 nibbles, wherein the upper 7 nibbles store the digits of a 7-digit decimal value, and the lowest nibble indicates the sign of the decimal integer value. Standard sign values are 1100 (hex C) for positive (+) and 1101 (D) for negative (\u2212). This convention comes from the zone field for EBCDIC characters and the signed overpunch representation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the coefficient of variation (COV), also known as Normalized Root-Mean-Square Deviation (NRMSD), Percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation \u03c3 {\\displaystyle \\sigma } to the mean \u03bc {\\displaystyle \\mu } (or its absolute value, | \u03bc | {\\displaystyle |\\mu |} ), and often expressed as a percentage (\"%RSD\"). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, and in neuroscience.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An important problem in computational logic is to determine fragments of well-known logics such as first-order logic that are as expressive as possible yet are decidable or more strongly have low computational complexity. The field of descriptive complexity theory aims at establishing a link between logics and computational complexity theory, by identifying logical fragments that exactly capture certain complexity classes. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All object-oriented programming (OOP) systems support encapsulation, but encapsulation is not unique to OOP. Implementations of abstract data types, modules, and libraries, among other systems, also offer encapsulation. The similarity has been explained by programming language theorists in terms of existential types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The generalized version was popularized by Hoffmeister & B\u00e4ck and M\u00fchlenbein et al. Finding the minimum of this function is a fairly difficult problem due to its large search space and its large number of local minima. On an n {\\displaystyle n} -dimensional domain it is defined by: f ( x ) = A n + \u2211 i = 1 n  {\\displaystyle f(\\mathbf {x} )=An+\\sum _{i=1}^{n}\\left} where A = 10 {\\displaystyle A=10} and x i \u2208  {\\displaystyle x_{i}\\in } . There are many extrema: The global minimum is at x = 0 {\\displaystyle \\mathbf {x} =\\mathbf {0} } where f ( x ) = 0 {\\displaystyle f(\\mathbf {x} )=0} . The maximum function value for x i \u2208  {\\displaystyle x_{i}\\in } is located around x i \u2208  {\\displaystyle x_{i}\\in } :Here are all the values at 0.5 interval listed for the 2D Rastrigin function with x i \u2208  {\\displaystyle x_{i}\\in }: The abundance of local minima underlines the necessity of a global optimization algorithm when needing to find the global minimum. Local optimization algorithms are likely to get stuck in a local minimum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 268, 1268, 2468, and 12468 are the patterns related to Braille pattern dots-156, since the two additional dots of kantenji patterns 0156, 1567, and 01567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although von Neumann's name is popularly attached to the conjecture, its first written appearance seems to be due to Mahlon Marsh Day in 1957. The Tits alternative is a fundamental theorem which, in particular, establishes the conjecture within the class of linear groups. The historically first potential counterexample is Thompson group F. While its amenability is a wide open problem, the general conjecture was shown to be false in 1980 by Alexander Ol'shanskii; he demonstrated that Tarski monster groups, constructed by him, which are easily seen not to have free subgroups of rank 2, are not amenable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The finer the granularity, the greater the potential for parallelism and hence speed-up, but the greater the overheads of synchronization and communication. Granularity disintegrators exist as well and are important to understand in order to determine the accurate level of granularity.In order to attain the best parallel performance, the best balance between load and communication overhead needs to be found. If the granularity is too fine, the performance can suffer from the increased communication overhead. On the other side, if the granularity is too coarse, the performance can suffer from load imbalance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Krohn\u2013Rhodes complexity is an important topic in the study of finite semigroups and automata. In Network theory complexity is the product of richness in the connections between components of a system, and defined by a very unequal distribution of certain measures (some elements being highly connected and some very few, see complex network). In software engineering, programming complexity is a measure of the interactions of the various elements of the software. This differs from the computational complexity described above in that it is a measure of the design of the software.Other fields introduce less precisely defined notions of complexity: A complex adaptive system has some or all of the following attributes:The number of parts (and types of parts) in the system and the number of relations between the parts is non-trivial \u2013 however, there is no general rule to separate \"trivial\" from \"non-trivial\"; The system has memory or includes feedback; The system can adapt itself according to its history or feedback; The relations between the system and its environment are non-trivial or non-linear; The system can be influenced by, or can adapt itself to, its environment; The system is highly sensitive to initial conditions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The associativity of this product follows from that of the group product. The product of group subsets therefore defines a natural monoid structure on the power set of G. A lot more can be said in the case where S and T are subgroups. The product of two subgroups S and T of a group G is itself a subgroup of G if and only if ST = TS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Scrum framework, which claims to be consistent with agile values and principles, the scrum master role is accountable for ensuring the scrum process is followed and for coaching the scrum team through that process. A common pitfall is for a scrum master to act as a contributor. While not prohibited by the Scrum framework, the scrum master needs to ensure they have the capacity to act in the role of scrum master first and not work on development tasks. A scrum master's role is to facilitate the process rather than create the product.Having the scrum master also multitasking may result in too many context switches to be productive. Additionally, as a scrum master is responsible for ensuring roadblocks are removed so that the team can make forward progress, the benefit gained by individual tasks moving forward may not outweigh roadblocks that are deferred due to lack of capacity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For algorithms operating on this representation, this requires an All-to-All communication step as well as O ( m ) {\\displaystyle {\\mathcal {O}}(m)} message buffer sizes, as each PE potentially has outgoing edges to every other PE.2D partitioning: Every processor gets a submatrix of the adjacency matrix. Assume the processors are aligned in a rectangle p = p r \u00d7 p c {\\displaystyle p=p_{r}\\times p_{c}} , where p r {\\displaystyle p_{r}} and p c {\\displaystyle p_{c}} are the amount of processing elements in each row and column, respectively. Then each processor gets a submatrix of the adjacency matrix of dimension ( n / p r ) \u00d7 ( n / p c ) {\\displaystyle (n/p_{r})\\times (n/p_{c})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of telephony, companies used manual telephone switchboards, and switchboard operators connected calls by inserting a pair of phone plugs into the appropriate jacks. They were gradually phased out and replaced by automated systems, first those allowing direct dialing within a local area, then for long-distance and international direct dialing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(Some authors write it as fg. )such that the following axiom holds: (associativity) if f: A \u2192 B, g: B \u2192 C and h: C \u2192 D then h \u2218 (g \u2218 f) = (h \u2218 g) \u2218 f. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 235678, 1235678, 2345678, and 12345678 are the patterns related to Braille pattern dots-123456, since the two additional dots of kantenji patterns 0123456, 1234567, and 01234567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution, and Xi, i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log(p) distribution, then \u2211 i = 1 N X i {\\displaystyle \\sum _{i=1}^{N}X_{i}} has a negative binomial distribution. In this way, the negative binomial distribution is seen to be a compound Poisson distribution. R. A. Fisher described the logarithmic distribution in a paper that used it to model relative species abundance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A near-bijection from the unit square to the unit interval can be obtained by interleaving the digits of the decimal representations of the Cartesian coordinates of points in the square. The ambiguities of decimal, exemplified by the two decimal representations of 1 = 0.999..., cause this to be an injection rather than a bijection, but this issue can be repaired by using the Schr\u00f6der\u2013Bernstein theorem. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, we want to find a small cut in a graph G = ( V , E ) {\\displaystyle G=(V,E)} that partitions the graph into nearly equal-size pieces. We usually call a cut b-balanced or a (b,1 \u2212 b)-separator (for b \u2264 1/2) if b \u03c0 ( V ) \u2264 \u03c0 ( U ) \u2264 ( 1 \u2212 b ) \u03c0 ( V ) {\\displaystyle b\\pi (V)\\leq \\pi (U)\\leq (1-b)\\pi (V)} where \u03c0 ( U ) {\\displaystyle \\pi (U)} is the sum of the node weights in U. This is also an NP-hard problem. An approximation algorithm has been designed for this problem, and the core idea is that G has a b-balanced cut of size S, then we find a b\u2032-balanced cut of size O ( S log \u2061 n b \u2212 b \u2032 ) {\\displaystyle O\\left(S\\log {\\frac {n}{b}}-b'\\right)} for any b' where b\u2032 < b and b\u2032 \u2264 1/3. Then we repeat the process then finally obtain the result that total weight of the edges in the cut is at most O ( S log \u2061 n b \u2212 b \u2032 ) {\\displaystyle O\\left({\\frac {S\\log n}{b-b'}}\\right)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The mixed product is an example of an operation of arity 3, also called ternary operation. Generally, the arity is taken to be finite. However, infinitary operations are sometimes considered, in which case the \"usual\" operations of finite arity are called finitary operations. A partial operation is defined similarly to an operation, but with a partial function in place of a function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some contexts a regularized version of the least squares solution may be preferable. Tikhonov regularization (or ridge regression) adds a constraint that \u2016 \u03b2 \u2016 2 2 {\\displaystyle \\|\\beta \\|_{2}^{2}} , the squared \u2113 2 {\\displaystyle \\ell _{2}} -norm of the parameter vector, is not greater than a given value to the least squares formulation, leading to a constrained minimization problem. This is equivalent to the unconstrained minimization problem where the objective function is the residual sum of squares plus a penalty term \u03b1 \u2016 \u03b2 \u2016 2 2 {\\displaystyle \\alpha \\|\\beta \\|_{2}^{2}} and \u03b1 {\\displaystyle \\alpha } is a tuning parameter (this is the Lagrangian form of the constrained minimization problem).In a Bayesian context, this is equivalent to placing a zero-mean normally distributed prior on the parameter vector.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of cryptography, encryption serves as a mechanism to ensure confidentiality. Since data may be visible on the Internet, sensitive information such as passwords and personal communication may be exposed to potential interceptors. The process of encrypting and decrypting messages involves keys. The two main types of keys in cryptographic systems are symmetric-key and public-key (also known as asymmetric-key).Many complex cryptographic algorithms often use simple modular arithmetic in their implementations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software testing, recovery testing is the activity of testing how well an application is able to recover from crashes, hardware failures and other similar problems. Recovery testing is the forced failure of the software in a variety of ways to verify that recovery is properly performed. Recovery testing should not be confused with reliability testing, which tries to discover the specific point at which failure occurs. Recovery testing is basically done in order to check how fast and better the application can recover against any type of crash or hardware failure etc. Recovery testing is simulating failure modes or actually causing failures in a controlled environment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Stewart in 1971, it was the first numerically stable method that could be systematically applied to solve such equations. The algorithm works by using the real Schur decompositions of A {\\displaystyle A} and B {\\displaystyle B} to transform A X \u2212 X B = C {\\displaystyle AX-XB=C} into a triangular system that can then be solved using forward or backward substitution. In 1979, G. Golub, C. Van Loan and S. Nash introduced an improved version of the algorithm, known as the Hessenberg\u2013Schur algorithm. It remains a standard approach for solving Sylvester equations when X {\\displaystyle X} is of small to moderate size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other words, it is similar to VIEWS in databases modelling. Like VIEW in Oracle or MySQL. For each page there is One abstract Table of data. But it is merged from other tables. Uses WebML-OQL (WebML-Object Query Language)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The middle compartment contains the attributes of the class. They are left-aligned and the first letter is lowercase. The bottom compartment contains the operations the class can execute. They are also left-aligned and the first letter is lowercase.In the design of a system, a number of classes are identified and grouped together in a class diagram that helps to determine the static relations between them. In detailed modeling, the classes of the conceptual design are often split into subclasses.In order to further describe the behavior of systems, these class diagrams can be complemented by a state diagram or UML state machine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because they are all part of a single mathematical system \u2014 often they represent different properties of an individual statistical unit. For example, while a given person has a specific age, height and weight, the representation of these features of an unspecified person from within a group would be a random vector. Normally each element of a random vector is a real number. Random vectors are often used as the underlying implementation of various types of aggregate random variables, e.g. a random matrix, random tree, random sequence, stochastic process, etc. More formally, a multivariate random variable is a column vector X = ( X 1 , \u2026 , X n ) T {\\displaystyle \\mathbf {X} =(X_{1},\\dots ,X_{n})^{\\mathsf {T}}} (or its transpose, which is a row vector) whose components are scalar-valued random variables on the same probability space as each other, ( \u03a9 , F , P ) {\\displaystyle (\\Omega ,{\\mathcal {F}},P)} , where \u03a9 {\\displaystyle \\Omega } is the sample space, F {\\displaystyle {\\mathcal {F}}} is the sigma-algebra (the collection of all events), and P {\\displaystyle P} is the probability measure (a function returning each event's probability).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, it is more efficient to use an extended variant of Euclid's algorithm to calculate the Jacobi symbol ( a n ) {\\displaystyle \\left({\\frac {a}{n}}\\right)} . If n {\\displaystyle n} is an odd prime, this is equal to the Legendre symbol, and decides whether a {\\displaystyle a} is a quadratic residue modulo n {\\displaystyle n} . On the other hand, since the equivalence of a n \u2212 1 2 {\\displaystyle a^{\\frac {n-1}{2}}} to the Jacobi symbol holds for all odd primes, but not necessarily for composite numbers, calculating both and comparing them can be used as a primality test, specifically the Solovay\u2013Strassen primality test. Composite numbers for which the congruence holds for a given a {\\displaystyle a} are called Euler\u2013Jacobi pseudoprimes to base a {\\displaystyle a} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the theory of infinite sets was first developed by Georg Cantor. Although this work has become a thoroughly standard fixture of classical set theory, it has been criticized in several areas by mathematicians and philosophers. Cantor's theorem implies that there are sets having cardinality greater than the infinite cardinality of the set of natural numbers. Cantor's argument for this theorem is presented with one small change.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At any point in a trip the camel may leave any amount of bananas that it is carrying at a camp post, or may collect any amount of bananas that was left at a camp post on a previous trip, as long as its banana load never exceeds 1 unit. The problem asks for the maximum units of bananas that can be transported to the market. In the travelers across the desert problem, the starting base has unlimited units of supplies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psychological coercion, the threatened injury regards the victim's relationships with other people. The most obvious example is blackmail, where the threat consists of the dissemination of damaging information. However, many other types are possible e.g. \"emotional blackmail\", which typically involves threats of rejection from or disapproval by a peer-group, or creating feelings of guilt/obligation via a display of anger or hurt by someone whom the victim loves or respects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the TCP/IP network model, the transport layer of the network (Layer 4) is responsible for the reliable transport of data. The TCP protocol is the principal means of ensuring reliable unicast (point-to-point) transport. TCP does this through an ACK mechanism. With the ACK mechanism, data packets are sequentially numbered, and the sender does not send a packet in a sequence until it receives an acknowledgement (ACK) from the receiver that the previous packet has been successfully received.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most common method is the Gram\u2013Schmidt process. Which creates a set of orthogonal basis vectors, which can then easily be normalized. This method begins by first selecting any standard basis \u03b2={v1, v2,...,vn}.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical hypothesis testing, the alternative hypothesis is one of the proposed proposition in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test (null hypothesis). It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc. However, the research hypothesis is sometimes consistent with the null hypothesis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "David Hilbert argued in favor of the study of the infinite, saying \"No one shall expel us from the Paradise that Cantor has created.\" Mathematicians began to search for axiom systems that could be used to formalize large parts of mathematics. In addition to removing ambiguity from previously naive terms such as function, it was hoped that this axiomatization would allow for consistency proofs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matrix theory, the Rule of Sarrus is a mnemonic device for computing the determinant of a 3 \u00d7 3 {\\displaystyle 3\\times 3} matrix named after the French mathematician Pierre Fr\u00e9d\u00e9ric Sarrus.Consider a 3 \u00d7 3 {\\displaystyle 3\\times 3} matrix M =  , {\\displaystyle M={\\begin{bmatrix}a_{11}&a_{12}&a_{13}\\\\a_{21}&a_{22}&a_{23}\\\\a_{31}&a_{32}&a_{33}\\end{bmatrix}},} then its determinant can be computed by the following scheme. Write out the first two columns of the matrix to the right of the third column, giving five columns in a row. Then add the products of the diagonals going from top to bottom (solid) and subtract the products of the diagonals going from bottom to top (dashed). This yields det ( M ) = det  = a 11 a 22 a 33 + a 12 a 23 a 31 + a 13 a 21 a 32 \u2212 a 31 a 22 a 13 \u2212 a 32 a 23 a 11 \u2212 a 33 a 21 a 12 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Jensen\u2013Shannon divergence is a method of measuring the similarity between two probability distributions. It is also known as information radius (IRad) or total divergence to the average. It is based on the Kullback\u2013Leibler divergence, with some notable (and useful) differences, including that it is symmetric and it always has a finite value. The square root of the Jensen\u2013Shannon divergence is a metric often referred to as Jensen\u2013Shannon distance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, the processing of an item Y by a stage A may depend on the results or effect of processing a previous item X by some later stage B of the pipeline. In that case, stage A cannot correctly process item Y until item X has cleared stage B. This situation occurs very often in instruction pipelines. For example, suppose that Y is an arithmetic instruction that reads the contents of a register that was supposed to have been modified by an earlier instruction X. Let A be the stage that fetches the instruction operands, and B be the stage that writes the result to the specified register. If stage A tries to process instruction Y before instruction X reaches stage B, the register may still contain the old value, and the effect of Y would be incorrect.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation of a population or sample and the standard error of a statistic (e.g., of the sample mean) are quite different, but related.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle s(G)=\\sum _{(u,v)\\in E}\\deg(u)\\cdot \\deg(v).} This is maximized when high-degree nodes are connected to other high-degree nodes. Now define S ( G ) = s ( G ) s max , {\\displaystyle S(G)={\\frac {s(G)}{s_{\\max }}},} where smax is the maximum value of s(H) for H in the set of all graphs with degree distribution identical to that of G. This gives a metric between 0 and 1, where a graph G with small S(G) is \"scale-rich\", and a graph G with S(G) close to 1 is \"scale-free\". This definition captures the notion of self-similarity implied in the name \"scale-free\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most command-line interfaces or text editors, the text cursor, also known as a caret, is an underscore, a solid rectangle, or a vertical line, which may be flashing or steady, indicating where text will be placed when entered (the insertion point). In text mode displays, it was not possible to show a vertical bar between characters to show where the new text would be inserted, so an underscore or block cursor was used instead. In situations where a block was used, the block was usually created by inverting the pixels of the character using the boolean math exclusive or function. On text editors and word processors of modern design on bitmapped displays, the vertical bar is typically used instead.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the precision matrix or concentration matrix is the matrix inverse of the covariance matrix or dispersion matrix, P = \u03a3 \u2212 1 {\\displaystyle P=\\Sigma ^{-1}} . For univariate distributions, the precision matrix degenerates into a scalar precision, defined as the reciprocal of the variance, p = 1 \u03c3 2 {\\displaystyle p={\\frac {1}{\\sigma ^{2}}}} .Other summary statistics of statistical dispersion also called precision (or imprecision) include the reciprocal of the standard deviation, p = 1 \u03c3 {\\displaystyle p={\\frac {1}{\\sigma }}} ; the standard deviation itself and the relative standard deviation; as well as the standard error and the confidence interval (or its half-width, the margin of error).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a public land mobile network (PLMN) is a combination of wireless communication services offered by a specific operator in a specific country. A PLMN typically consists of several cellular technologies like GSM/2G, UMTS/3G, LTE/4G, offered by a single operator within a given country, often referred to as a cellular network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model checking, a field of computer science, a region is a convex polytope in R d {\\displaystyle \\mathbb {R} ^{d}} for some dimension d {\\displaystyle d} , and more precisely a zone, satisfying some minimality property. The regions partition R d {\\displaystyle \\mathbb {R} ^{d}} . The set of zones depends on a set K {\\displaystyle K} of constraints of the form x \u2264 c {\\displaystyle x\\leq c} , x \u2265 c {\\displaystyle x\\geq c} , x 1 \u2264 x 2 + c {\\displaystyle x_{1}\\leq x_{2}+c} and x 1 \u2265 x 2 + c {\\displaystyle x_{1}\\geq x_{2}+c} , with x 1 {\\displaystyle x_{1}} and x 2 {\\displaystyle x_{2}} some variables, and c {\\displaystyle c} a constant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming, the command pattern is a behavioral design pattern in which an object is used to encapsulate all information needed to perform an action or trigger an event at a later time. This information includes the method name, the object that owns the method and values for the method parameters. Four terms always associated with the command pattern are command, receiver, invoker and client. A command object knows about receiver and invokes a method of the receiver.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Often the functions to be minimized are not f i {\\displaystyle f_{i}} but | f i \u2212 z i \u2217 | {\\displaystyle |f_{i}-z_{i}^{*}|} for some scalars z i \u2217 {\\displaystyle z_{i}^{*}} . Then f T c h b ( x , w ) = max i w i | f i ( x ) \u2212 z i \u2217 | . {\\displaystyle f_{Tchb}(x,w)=\\max _{i}w_{i}|f_{i}(x)-z_{i}^{*}|.} All three functions are named in honour of Pafnuty Chebyshev.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first normal form each field contains a single value. A field may not contain a set of values or a nested record. Subject contains a set of subject values, meaning it does not comply. To solve the problem, the subjects are extracted into a separate Subject table: In Subject, ISBN is a foreign key: It refers to the primary key in Book, and makes the relationship between these two tables explicit. Instead of one table in unnormalized form, there are now two tables conforming to the 1NF.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Due to the large game trees of complex games such as chess, algorithms that are designed to play this class of games will use partial game trees, which makes computation feasible on modern computers. Various methods exist to solve game trees. If a complete game tree can be generated, a deterministic algorithm, such as backward induction or retrograde analysis can be used. Randomized algorithms and minimax algorithms such as MCTS can be used in cases where a complete game tree is not feasible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Lord Denning, first of the High Court of Justice, later of the Court of Appeal, provided a famous example of this evolutionary process in his development of the concept of estoppel starting in the High Trees case: Central London Property Trust Ltd v. High Trees House Ltd  K.B. 130.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In science, a prediction is a rigorous, often quantitative, statement, forecasting what would be observed under specific conditions; for example, according to theories of gravity, if an apple fell from a tree it would be seen to move towards the center of the earth with a specified and constant acceleration. The scientific method is built on testing statements that are logical consequences of scientific theories. This is done through repeatable experiments or observational studies. A scientific theory whose predictions are contradicted by observations and evidence will be rejected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The resulting control-flow graph for the sequences of \"if\"s thus has many more nodes and almost twice as many edges, with these not adding any useful information. However, the simple branches in the if statements are individually conceptually easier than the complex branch of a switch statement. In terms of cyclomatic complexity, both of these options increase it by k\u22121 if given k cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These give a sense in which the functions x\u2022 and x\\ are pseudoinverses or adjoints of each other, and likewise for \u2022x and /x. This last definition is purely in terms of inequalities, noting that monotonicity can be axiomatized as x\u2022y \u2264 (x\u2228z)\u2022y and similarly for the other operations and their arguments. Moreover, any inequality x \u2264 y can be expressed equivalently as an equation, either x\u2227y = x or x\u2228y = y. This along with the equations axiomatizing lattices and monoids then yields a purely equational definition of residuated lattices, provided the requisite operations are adjoined to the signature (L, \u2264, \u2022, I) thereby expanding it to (L, \u2227, \u2228, \u2022, I, /, \\).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Ditkin set, introduced by (Ditkin 1939), is a closed subset of the circle such that a function f vanishing on the set can be approximated by functions \u03c6nf with \u03c6 vanishing in a neighborhood of the set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two likelihood functions are equivalent if one is a scalar multiple of the other. The likelihood principle is this: All information from the data that is relevant to inferences about the value of the model parameters is in the equivalence class to which the likelihood function belongs. The strong likelihood principle applies this same criterion to cases such as sequential experiments where the sample of data that is available results from applying a stopping rule to the observations earlier in the experiment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, it is argued that chunking, rather than moving straight to short division, gives a better introduction to division, in part because the focus is always holistic, focusing throughout on the whole calculation and its meaning, rather than just rules for generating successive digits. The more freeform nature of chunking also means that it requires more genuine understanding \u2013 rather than just the ability to follow a ritualised procedure \u2013 to be successful.An alternative way of performing chunking involves the use of the standard long division tableau \u2013 except that the partial quotients are stacked up on the top of each other above the long division sign, and that all numbers are spelled out in full. By allowing one to subtract more chunks than what one currently has, it is also possible to expand chunking into a fully bidirectional method as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In philosophy, a core ontology is a basic and minimal ontology consisting only of the minimal concepts required to understand the other concepts. It must be based on a core glossary in some human language so humans can comprehend the concepts and distinctions made. Each natural language tends to rely on its own conceptual metaphor structure, and so tends to have its own core ontology (according to W. V. Quine). It could be said also to represent the moral core of a human linguistic culture, and to self-correct so as to better represent core cultural ideas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The scale normalized Laplacian (in L 1 {\\displaystyle L_{1}} -norm) is frequently used as a blob detector and for automatic scale selection in computer vision applications; see Laplacian of Gaussian and scale space. The relation between this Laplacian of the Gaussian operator and the difference-of-Gaussians operator is explained in appendix A in Lindeberg (2015). The Mexican hat wavelet can also be approximated by derivatives of cardinal B-splines.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a domain model is a conceptual model of the domain that incorporates both behavior and data. In ontology engineering, a domain model is a formal representation of a knowledge domain with concepts, roles, datatypes, individuals, and rules, typically grounded in a description logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to reduce failures, a precise knowledge of bond strength quality measurement during product design and subsequent manufacture is of vital importance. The best place to start is with the failure mode. This is based on the assumption that there is a particular failure mode, or range of modes, that may occur within a product. It is therefore reasonable to assume that the bond test should replicate the mode, or modes of interest.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2003 version, the codes were as follows: PL1 CENTRALNY PL11 Lodzkie PL111 Lodzki PL112 Piotrkowsko-skierniewicki PL113 Miasto Lodz PL12 Mazowieckie PL121 Ciechanowsko-plocki PL122 Ostrolecko-siedlecki PL124 Radomski PL126 Warszawski PL127 Miasto Warszawa PL2 POLUDNIOWY PL21 Malopolskie PL211 Krakowsko-tarnowski PL212 Nowosadecki PL213 Miasto Krakow PL22 Slaskie PL224 Czestochowski PL225 Bielsko-bialski PL226 Centralny slaski PL227 Rybnicko-jastrzebski PL3 WSCHODNI PL31 Lubelskie PL311 Bialskopodlaski PL312 Chelmsko-zamojski PL313 Lubelski PL32 Podkarpackie PL321 Rzeszowsko-tarnobrzeski PL322 Krosniensko-przemyski PL33 Swietokrzyskie PL330 Swietokrzyski PL34 Podlaskie PL341 Bialostocko-suwalski PL342 Lomzynski PL4 POLNOCNO-ZACHODNI PL41 Wielkopolskie PL411 Pilski PL412 Poznanski PL413 Kaliski PL414 Koninski PL415 Miasto Poznan PL42 Zachodniopomorskie PL421 Szczecinski PL422 Koszalinski PL43 Lubuskie PL431 Gorzowski PL432 Zielonogorski PL5 POLUDNIOWO-ZACHODNI PL51 Dolnoslaskie PL511 Jeleniogorsko-walbrzyski PL512 Legnicki PL513 Wroclawski PL514 Miasto Wroclaw PL52 Opolskie PL520 Opolski PL6 POLNOCNY PL61 Kujawsk", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a filter on a set X {\\displaystyle X} is a family B {\\displaystyle {\\mathcal {B}}} of subsets such that: X \u2208 B {\\displaystyle X\\in {\\mathcal {B}}} and \u2205 \u2209 B {\\displaystyle \\emptyset \\notin {\\mathcal {B}}} if A \u2208 B {\\displaystyle A\\in {\\mathcal {B}}} and B \u2208 B {\\displaystyle B\\in {\\mathcal {B}}} , then A \u2229 B \u2208 B {\\displaystyle A\\cap B\\in {\\mathcal {B}}} If A , B \u2282 X , A \u2208 B {\\displaystyle A,B\\subset X,A\\in {\\mathcal {B}}} , and A \u2282 B {\\displaystyle A\\subset B} , then B \u2208 B {\\displaystyle B\\in {\\mathcal {B}}} A filter on a set may be thought of as representing a \"collection of large subsets\", one intuitive example being the neighborhood filter. Filters appear in order theory, model theory, and set theory, but can also be found in topology, from which they originate. The dual notion of a filter is an ideal. Filters were introduced by Henri Cartan in 1937 and as described in the article dedicated to filters in topology, they were subsequently used by Nicolas Bourbaki in their book Topologie G\u00e9n\u00e9rale as an alternative to the related notion of a net developed in 1922 by E. H. Moore and Herman L. Smith. Order filters are generalizations of filters from sets to arbitrary partially ordered sets. Specifically, a filter on a set is just a proper order filter in the special case where the partially ordered set consists of the power set ordered by set inclusion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alternatives for I include e and 1'. Alternative notations for the residuals are x \u2192 y for x\\y and y \u2190 x for y/x, suggested by the similarity between residuation and implication in logic, with the multiplication of the monoid understood as a form of conjunction that need not be commutative. When the monoid is commutative the two residuals coincide. When not commutative, the intuitive meaning of the monoid as conjunction and the residuals as implications can be understood as having a temporal quality: x\u2022y means x and then y, x \u2192 y means had x (in the past) then y (now), and y \u2190 x means if-ever x (in the future) then y (at that time), as illustrated by the natural language example at the end of the examples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, direct-sequence spread spectrum (DSSS) is a spread-spectrum modulation technique primarily used to reduce overall signal interference. The direct-sequence modulation makes the transmitted signal wider in bandwidth than the information bandwidth. After the despreading or removal of the direct-sequence modulation in the receiver, the information bandwidth is restored, while the unintentional and intentional interference is substantially reduced.Swiss inventor, Gustav Guanella proposed a \"means for and method of secret signals\". With DSSS, the message symbols are modulated by a sequence of complex values known as spreading sequence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, it is often important to find factors of an integer number N. Any number N has four obvious factors: \u00b11 and \u00b1N. These are called \"trivial factors\". Any other factor, if it exists, would be called \"nontrivial\". The homogeneous matrix equation A x = 0 {\\displaystyle A\\mathbf {x} =\\mathbf {0} } , where A {\\displaystyle A} is a fixed matrix, x {\\displaystyle \\mathbf {x} } is an unknown vector, and 0 {\\displaystyle \\mathbf {0} } is the zero vector, has an obvious solution x = 0 {\\displaystyle \\mathbf {x} =\\mathbf {0} } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics, configuration entropy is the portion of a system's entropy that is related to discrete representative positions of its constituent particles. For example, it may refer to the number of ways that atoms or molecules pack together in a mixture, alloy or glass, the number of conformations of a molecule, or the number of spin configurations in a magnet. The name might suggest that it relates to all possible configurations or particle positions of a system, excluding the entropy of their velocity or momentum, but that usage rarely occurs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Intel 80386 and later, protected mode retains the segmentation mechanism of 80286 protected mode, but a paging unit has been added as a second layer of address translation between the segmentation unit and the physical bus. Also, importantly, address offsets are 32-bit (instead of 16-bit), and the segment base in each segment descriptor is also 32-bit (instead of 24-bit). The general operation of the segmentation unit is otherwise unchanged. The paging unit may be enabled or disabled; if disabled, operation is the same as on the 80286.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In ASCII and Unicode, the character is encoded at U+0004 . It can be referred to as Ctrl+D, ^D in caret notation. Unicode provides the character U+2404 \u2404 SYMBOL FOR END OF TRANSMISSION for when EOT needs to be displayed graphically. In addition, U+2301 \u2301 ELECTRIC ARROW can also be used as a graphic representation of EOT; it is defined in Unicode as \"symbol for End of Transmission\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metalogic, 'syntax' has to do with formal languages or formal systems without regard to any interpretation of them, whereas, 'semantics' has to do with interpretations of formal languages. The term 'syntactic' has a slightly wider scope than 'proof-theoretic', since it may be applied to properties of formal languages without any deductive systems, as well as to formal systems. 'Semantic' is synonymous with 'model-theoretic'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a right group is an algebraic structure consisting of a set together with a binary operation that combines two elements into a third element while obeying the right group axioms. The right group axioms are similar to the group axioms, but while groups can have only one identity and any element can have only one inverse, right groups allow for multiple one-sided identity elements and multiple one-sided inverse elements. It can be proven (theorem 1.27 in ) that a right group is isomorphic to the direct product of a right zero semigroup and a group, while a right abelian group is the direct product of a right zero semigroup and an abelian group. Left group and left abelian group are defined in analogous way, by substituting right for left in the definitions. The rest of this article will be mostly concerned about right groups, but everything applies to left groups by doing the appropriate right/left substitutions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then instead of storing only a single node in each entry of prev we would store all nodes satisfying the relaxation condition. For example, if both r and source connect to target and both of them lie on different shortest paths through target (because the edge cost is the same in both cases), then we would add both r and source to prev. When the algorithm completes, prev data structure will actually describe a graph that is a subset of the original graph with some edges removed. Its key property will be that if the algorithm was run with some starting node, then every path from that node to any other node in the new graph will be the shortest path between those nodes in the original graph, and all paths of that length from the original graph will be present in the new graph. Then to actually find all these shortest paths between two given nodes we would use a path finding algorithm on the new graph, such as depth-first search.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence the inputs to the neural network are contributions, future needs and wealth, and the output the percentage split predicted. On each arc there is a statistical weight. Using back propagation the neural network learns the necessary pattern to recognize the prediction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, a {\\displaystyle a} and b , {\\displaystyle b,} which are the minimum and maximum values. The interval can either be closed (i.e.  {\\displaystyle } ) or open (i.e. ( a , b ) {\\displaystyle (a,b)} ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some researchers identify various steps in the process of problem solving. These steps include recognizing the problem, trying to understand its nature, identifying general criteria the solution should meet, deciding how these criteria should be prioritized, monitoring the progress, and evaluating the results.An important distinction concerns the type of problem that is faced. For well-structured problems, it is easy to determine which steps need to be taken to solve them, but executing these steps may still be difficult.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The other 2 GiB are used by the operating system. On later 32-bit editions of Microsoft Windows, it is possible to extend the user-mode virtual address space to 3 GiB while only 1 GiB is left for kernel-mode virtual address space by marking the programs as IMAGE_FILE_LARGE_ADDRESS_AWARE and enabling the /3GB switch in the boot.ini file.On Microsoft Windows 64-bit, in a process running an executable that was linked with /LARGEADDRESSAWARE:NO, the operating system artificially limits the user mode portion of the process's virtual address space to 2 GiB. This applies to both 32- and 64-bit executables. Processes running executables that were linked with the /LARGEADDRESSAWARE:YES option, which is the default for 64-bit Visual Studio 2010 and later, have access to more than 2 GiB of virtual address space: up to 4 GiB for 32-bit executables, up to 8 TiB for 64-bit executables in Windows through Windows 8, and up to 128 TiB for 64-bit executables in Windows 8.1 and later.Allocating memory via C's malloc establishes the page file as the backing store for any new virtual address space. However, a process can also explicitly map file bytes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is how Minsky solves the problem, but the G\u00f6del numbering he uses represents a great inconvenience to the model, and the result is nothing at all like our intuitive notion of a \"stored program computer\". Elgot and Robinson (1964) come to a similar conclusion with respect to a RASP that is \"finitely determined\". Indeed it can access an unbounded number of registers (e.g. to fetch instructions from them) but only if the RASP allows \"self modification\" of its program instructions, and has encoded its \"data\" in a G\u00f6del number (Fig. 2 p.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practical applications, the following considerations are commonly taken into account. One does not need to construct the convex hull of a polygon to find a suitable vertex. A common choice is the vertex of the polygon with the smallest X-coordinate. If there are several of them, the one with the smallest Y-coordinate is picked.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In neurophysiology, commutation is the process by which the brain's neural circuits exhibit non-commutativity. Physiologist Douglas B. Tweed and coworkers have considered whether certain neural circuits in the brain exhibit noncommutativity and state: In noncommutative algebra, order makes a difference to multiplication, so that a \u00d7 b \u2260 b \u00d7 a {\\displaystyle a\\times b\\neq b\\times a} . This feature is necessary for computing rotary motion, because order makes a difference to the combined effect of two rotations. It has therefore been proposed that there are non-commutative operators in the brain circuits that deal with rotations, including motor system circuits that steer the eyes, head and limbs, and sensory system circuits that handle spatial information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In applications that do not need to run older binary software, compressed RISCs are growing to dominate sales. Another approach to RISCs was the minimal instruction set computer (MISC), niladic, or zero-operand instruction set. This approach realized that most space in an instruction was used to identify the operands of the instruction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, Great Britain, and Germany, the concept of a national centralized server model of healthcare data has been poorly received. Issues of privacy and security in such a model have been of concern.In the European Union (EU), a new directly binding instrument, a regulation of the European Parliament and of the council, was passed in 2016 to go into effect in 2018 to protect the processing of personal data, including that for purposes of health care, the General Data Protection Regulation. Threats to health care information can be categorized under three headings: Human threats, such as employees or hackers Natural and environmental threats, such as earthquakes, hurricanes and fires. Technology failures, such as a system crashingThese threats can either be internal, external, intentional and unintentional.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real analysis, the symbol \u221e {\\displaystyle \\infty } , called \"infinity\", is used to denote an unbounded limit. The notation x \u2192 \u221e {\\displaystyle x\\rightarrow \\infty } means that x {\\displaystyle x} increases without bound, and x \u2192 \u2212 \u221e {\\displaystyle x\\to -\\infty } means that x {\\displaystyle x} decreases without bound. For example, if f ( t ) \u2265 0 {\\displaystyle f(t)\\geq 0} for every t {\\displaystyle t} , then \u222b a b f ( t ) d t = \u221e {\\displaystyle \\int _{a}^{b}f(t)\\,dt=\\infty } means that f ( t ) {\\displaystyle f(t)} does not bound a finite area from a {\\displaystyle a} to b . {\\displaystyle b.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of length, word count is typically anywhere from 1,000 to 4,000 for short stories; however, some have 15,000 words and are still classed as short stories. Stories of fewer than 1,000 words are sometimes referred to as \"short short stories\", or \"flash fiction\".Short stories have no set length. In terms of word count, there is no official demarcation between an anecdote, a short story, and a novel. Rather, the form's parameters are given by the rhetorical and practical context in which a given story is produced and considered so that what constitutes a short story may differ between genres, countries, eras, and commentators. Like the novel, the short story's predominant shape reflects the demands of the available markets for publication, and the evolution of the form seems closely tied to the evolution of the publishing industry and the submission guidelines of its constituent houses.As a point of reference for the genre writer, the Science Fiction and Fantasy Writers of America define short story length in the Nebula Awards for science fiction submission guidelines as having fewer than 7,500 words.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In settings with deadlines, it is possible that, if the job is completed by the deadline, there is a profit pj. Otherwise, there is no profit. The goal is to maximize the profit. Single-machine scheduling with deadlines is NP-hard; Sahni presents both exact exponential-time algorithms and a polynomial-time approximation algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Pr  > 2 3 , if f ( x , y ) = 0 {\\displaystyle \\Pr>{\\frac {2}{3}},{\\textrm {if}}\\,f(x,y)=0} Pr  > 2 3 , if f ( x , y ) = 1 {\\displaystyle \\Pr>{\\frac {2}{3}},{\\textrm {if}}\\,f(x,y)=1} A randomized protocol is a deterministic protocol that uses an extra random string in addition to its normal input. There are two models for this: a public string is a random string that is known by both parties beforehand, while a private string is generated by one party and must be communicated to the other party. A theorem presented below shows that any public string protocol can be simulated by a private string protocol that uses O(log n) additional bits compared to the original.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using the relation between \u03c8 2 m {\\displaystyle \\psi _{2m}} and \u03c8 2 m + 1 {\\displaystyle \\psi _{2m+1}} , along with the equation of the curve, the functions \u03c8 n 2 {\\displaystyle \\psi _{n}^{2}} , \u03c8 2 n y , \u03c8 2 n + 1 {\\displaystyle {\\frac {\\psi _{2n}}{y}},\\psi _{2n+1}} , \u03d5 n {\\displaystyle \\phi _{n}} are all in K  {\\displaystyle K} . Let p > 3 {\\displaystyle p>3} be prime and let E: y 2 = x 3 + A x + B {\\displaystyle E:y^{2}=x^{3}+Ax+B} be an elliptic curve over the finite field F p {\\displaystyle \\mathbb {F} _{p}} , i.e., A , B \u2208 F p {\\displaystyle A,B\\in \\mathbb {F} _{p}} . The \u2113 {\\displaystyle \\ell } -torsion group of E {\\displaystyle E} over F \u00af p {\\displaystyle {\\bar {\\mathbb {F} }}_{p}} is isomorphic to Z / \u2113 \u00d7 Z / \u2113 {\\displaystyle \\mathbb {Z} /\\ell \\times \\mathbb {Z} /\\ell } if \u2113 \u2260 p {\\displaystyle \\ell \\neq p} , and to Z / \u2113 {\\displaystyle \\mathbb {Z} /\\ell } or { 0 } {\\displaystyle \\{0\\}} if \u2113 = p {\\displaystyle \\ell =p} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of IBM mainframe computers in the S/360 line, a data set (IBM preferred) or dataset is a computer file having a record organization. Use of this term began with, e.g., DOS/360, OS/360, and is still used by their successors, including the current z/OS. Documentation for these systems historically preferred this term rather than file. A data set is typically stored on a direct access storage device (DASD) or magnetic tape, however unit record devices, such as punch card readers, card punches, line printers and page printers can provide input/output (I/O) for a data set (file).Data sets are not unstructured streams of bytes, but rather are organized in various logical record and block structures determined by the DSORG (data set organization), RECFM (record format), and other parameters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Tasks such as network access and file access are often heavily intertwined with the distinctive implementations of each platform. The java.net and java.io libraries implement an abstraction layer in native OS code, then provide a standard interface for the Java applications to perform those tasks. Finally, when some underlying platform does not support all of the features a Java application expects, the class libraries work to gracefully handle the absent components, either by emulation to provide a substitute, or at least by providing a consistent way to check for the presence of a specific feature.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "* file exists within a given directory, the web server may be configured to provide an automatically generated listing of the files within the directory instead. With the Apache web server, for example, this behavior is provided by the mod_autoindex module and controlled by the Options +Indexes directive in the web server configuration files. These automated directory listings are sometimes a security risk because they enumerate sensitive files which may not be intended for public access, in a process known as a directory indexing attack. Such a security misconfiguration may also assist in other attacks, such as a path or directory traversal attack.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As such, it is important for people and organizations to need know that the information and data they are storing, using, or sending over computer networks or storing on computer systems is secure. However, developers of software and hardware are faced with many challenges in developing a system that can be both user friendly, accessible 24/7 on almost any device and be truly secure. Security leaks happen, even to individuals and organizations that have security measures in place to protect their data and information (e.g., firewalls, encryption, strong passwords).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, a deaf individual may misinterpret or become confused about the meaning of written text that is based on a spoken language.Researchers Zhao, et al. (2000), developed a prototype called TEAM (translation from English to ASL by machine) that completed English to American Sign Language (ASL) translations. The program would first analyze the syntactic, grammatical, and morphological aspects of the English text. Following this step, the program accessed a sign synthesizer, which acted as a dictionary for ASL. This synthesizer housed the process one must follow to complete ASL signs, as well as the meanings of these signs. Once the entire text is analyzed and the signs necessary to complete the translation are located in the synthesizer, a computer generated human appeared and would use ASL to sign the English text to the user.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, however, optimization relies on using more elaborate algorithms, making use of \"special cases\" and special \"tricks\" and performing complex trade-offs. A \"fully optimized\" program might be more difficult to comprehend and hence may contain more faults than unoptimized versions. Beyond eliminating obvious antipatterns, some code level optimizations decrease maintainability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The CPU excels in serial processing and accurate mathematical computation. The overarching goal of the requirements management effort for a software project would thus be to make sure the work being automated gets assigned to the proper processor. For instance, \u201cDon\u2019t make the human remember where she is in the interface. Make the interface report the human\u2019s location in the system at all times.\u201d Or \u201cDon\u2019t make the human enter the same data in two screens. Make the system store the data and fill in the second screen as needed.\u201d The deliverable from the Feasibility stage is the budget and schedule for the project.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in the theory of generalized functions, the limit of a sequence of distributions is the distribution that sequence approaches. The distance, suitably quantified, to the limiting distribution can be made arbitrarily small by selecting a distribution sufficiently far along the sequence. This notion generalizes a limit of a sequence of functions; a limit as a distribution may exist when a limit of functions does not. The notion is a part of distributional calculus, a generalized form of calculus that is based on the notion of distributions, as opposed to classical calculus, which is based on the narrower concept of functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let us suppose we have a function s i z e ( f ) {\\displaystyle size(f)} that can measure the complexity of f {\\displaystyle f} . Let Oracle ( x ) {\\displaystyle {\\text{Oracle}}(x)} be an oracle that, whenever called, returns an example x {\\displaystyle x} and its correct label f ( x ) {\\displaystyle f(x)} . When no noise corrupts the data, we can define learning in the Valiant setting:Definition: We say that f {\\displaystyle f} is efficiently learnable using H {\\displaystyle {\\mathcal {H}}} in the Valiant setting if there exists a learning algorithm A {\\displaystyle {\\mathcal {A}}} that has access to Oracle ( x ) {\\displaystyle {\\text{Oracle}}(x)} and a polynomial p ( \u22c5 , \u22c5 , \u22c5 , \u22c5 ) {\\displaystyle p(\\cdot ,\\cdot ,\\cdot ,\\cdot )} such that for any 0 < \u03b5 \u2264 1 {\\displaystyle 0<\\varepsilon \\leq 1} and 0 < \u03b4 \u2264 1 {\\displaystyle 0<\\delta \\leq 1} it outputs, in a number of calls to the oracle bounded by p ( 1 \u03b5 , 1 \u03b4 , n , size ( f ) ) {\\displaystyle p\\left({\\frac {1}{\\varepsilon }},{\\frac {1}{\\delta }},n,{\\text{size}}(f)\\right)} , a function h \u2208 H {\\displaystyle h\\in {\\mathcal {H}}} that satisfies with probability at least 1 \u2212 \u03b4 {\\displaystyle 1-\\delta } the condition error ( h ) \u2264 \u03b5 {\\displaystyle {\\text{error}}(h)\\leq \\varepsilon } . In the following we will define learnability of f {\\displaystyle f} when data have suffered some modification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, flood openings are used to provide for the automatic equalization of hydrostatic pressure on either side of a wall. Building codes usually require the installation of flood openings in the walls of structures located in A-type flood zones recognized by the Federal Emergency Management Agency. Various agencies in the United States define necessary characteristics for flood openings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Though the most straightforward application is to finite sets (such as pigeons and boxes), it is also used with infinite sets that cannot be put into one-to-one correspondence. To do so requires the formal statement of the pigeonhole principle, which is \"there does not exist an injective function whose codomain is smaller than its domain\". Advanced mathematical proofs like Siegel's lemma build upon this more general concept.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum. )This conjecture is called \"weak\" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, then this would also be true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "label for var ( list ) block label for var ( list ) block continue block label foreach var ( list ) block label foreach var ( list ) block continue block In foreach, var is a scalar variable that defaults to $_ if omitted. For each element of list, var is aliased to the element, and the loop body is executed once. The keywords for and foreach are synonyms and are always interchangeable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above situation, one can prove that the value of any flow through a network is less than or equal to the capacity of any s-t cut, and that furthermore a flow with maximal value and a cut with minimal capacity exist. The main theorem links the maximum flow value with the minimum cut capacity of the network. Max-flow min-cut theorem. The maximum value of an s-t flow is equal to the minimum capacity over all s-t cuts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For the case of a system of particles, the space V consists of functions called wave functions or state vectors. In the case of transformation laws in quantum mechanics, the requisite automorphisms are unitary (or antiunitary) linear transformations of the Hilbert space V. Under Galilean relativity or special relativity, the mathematics of frames of reference is particularly simple, considerably restricting the set of physically meaningful observables. In quantum mechanics, measurement of observables exhibits some seemingly unintuitive properties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In overlapping domain decomposition methods, the subdomains overlap by more than the interface. Overlapping domain decomposition methods include the Schwarz alternating method and the additive Schwarz method. Many domain decomposition methods can be written and analyzed as a special case of the abstract additive Schwarz method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is therefore up to an opponent to prove that they don't exist. Such hypotheses can be used to expose the pretensions of dogmatism. Kant explicitly praises Hume on his critique of religion for being beyond the field of natural science.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If not, the function is evaluated, and another entry is added to the lookup table for reuse. Lazy evaluation is difficult to combine with imperative features such as exception handling and input/output, because the order of operations becomes indeterminate. The opposite of lazy evaluation is eager evaluation, sometimes known as strict evaluation. Eager evaluation is the evaluation strategy employed in most programming languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Leveraging the ANDF format, the DWARF standardized debugging format, and the OMI protocol for communicating with target board debug monitors, SCORE was able to provide a common building and debugging environment for real-time application developers. Support for Embedded C++ was added to SCORE in 2003, by which time it could integrate with a variety of target board scenarios on Intel x86 and Power PC processors. The C and Embedded C++ compilers for ANDF came from a licensing arrangement for the TenDRA Compiler (later DDC-I became the maintainer of those compilers). Subsequently, Ada 95 support for the older 1750A and TMS320C4x processors was added to SCORE.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Scaleform provides GFx for high performance Flash UI and high-quality video playback, and an Input Method Editor (IME) add-on for in-game Asian chat support. Other middleware is used for performance optimisation\u2014for example 'Simplygon' helps to optimise and generate level of detail meshes, and 'Umbra' adds occlusion culling optimisations to 3d graphics. Some middleware contains full source code, others just provide an API reference for a compiled binary library. Some middleware programs can be licensed either way, usually for a higher fee for full source code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, this conclusion is not a mathematical certainty; there exist undirected graphs (such as the graph formed by removing a single edge from a large complete graph) that are unlikely to arise as social networks but in which most vertices have higher degree than the average of their neighbors' degrees. The Friendship Paradox may be restated in graph theory terms as \"the average degree of a randomly selected node in a network is less than the average degree of neighbors of a randomly selected node\", but this leaves unspecified the exact mechanism of averaging (i.e., macro vs micro averaging). Let G = ( V , E ) {\\displaystyle G=(V,E)} be an undirected graph with | V | = N {\\displaystyle |V|=N} and | E | = M {\\displaystyle |E|=M} , having no isolated nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A natural example is strings with concatenation as the binary operation, and the empty string as the identity element. Restricting to non-empty strings gives an example of a semigroup that is not a monoid. Positive integers with addition form a commutative semigroup that is not a monoid, whereas the non-negative integers do form a monoid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s IBM researcher Harlan Mills oversaw the development of the COBOL Structuring Facility, which applied a structuring algorithm to COBOL code. Mills's transformation involved the following steps for each procedure. Identify the basic blocks in the procedure. Assign a unique label to each block's entry path, and label each block's exit paths with the labels of the entry paths they connect to.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fine-grained multithreading\u2014such as in a barrel processor\u2014issues instructions for different threads after every cycle, while coarse-grained multithreading only switches to issue instructions from another thread when the current executing thread causes some long latency events (like page fault etc.). Coarse-grain multithreading is more common for less context switch between threads. For example, Intel's Montecito processor uses coarse-grained multithreading, while Sun's UltraSPARC T1 uses fine-grained multithreading.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Ostrowski's theorem, due to Alexander Ostrowski (1916), states that every non-trivial absolute value on the rational numbers Q {\\displaystyle \\mathbb {Q} } is equivalent to either the usual real absolute value or a p-adic absolute value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the plus sign \"+\" almost invariably indicates an operation that satisfies the axioms assigned to addition in the type of algebraic structure that is known as a field. For boolean algebra, this means that the logical operation signified by \"+\" is not the same as the inclusive disjunction signified by \"\u2228\" but is actually equivalent to the logical inequality operator signified by \"\u2260\", or what amounts to the same thing, the exclusive disjunction signified by \"XOR\" or \"\u2295\". Naturally, these variations in usage have caused some failures to communicate between mathematicians and switching engineers over the years. At any rate, one has the following array of corresponding forms for the symbols associated with logical inequality: x + y x \u2262 y J x y x X O R y x \u2260 y {\\displaystyle {\\begin{aligned}x&+y&x&\\not \\equiv y&Jxy\\\\x&\\mathrm {~XOR~} y&x&\\neq y\\end{aligned}}} This explains why \"EQ\" is often called \"XNOR\" in the combinational logic of circuit engineers, since it is the negation of the XOR operation; \"NXOR\" is a less commonly used alternative. Another rationalization of the admittedly circuitous name \"XNOR\" is that one begins with the \"both false\" operator NOR and then adds the eXception \"or both true\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the decision version of problems, the problem of producing an integer flow satisfying all demands is NP-complete, even for only two commodities and unit capacities (making the problem strongly NP-complete in this case). If fractional flows are allowed, the problem can be solved in polynomial time through linear programming, or through (typically much faster) fully polynomial time approximation schemes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The notion of counting may be extended to them in the sense of establishing (the existence of) a bijection with some well-understood set. For instance, if a set can be brought into bijection with the set of all natural numbers, then it is called \"countably infinite.\" This kind of counting differs in a fundamental way from counting of finite sets, in that adding new elements to a set does not necessarily increase its size, because the possibility of a bijection with the original set is not excluded.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic and computer science, the calculus of constructions (CoC) is a type theory created by Thierry Coquand. It can serve as both a typed programming language and as constructive foundation for mathematics. For this second reason, the CoC and its variants have been the basis for Coq and other proof assistants. Some of its variants include the calculus of inductive constructions (which adds inductive types), the calculus of (co)inductive constructions (which adds coinduction), and the predicative calculus of inductive constructions (which removes some impredicativity).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics graph theory a process graph or P-graph is a directed bipartite graph used in workflow modeling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An attacker would then be able to run system commands using the application's privileges. Texas Instruments calculators (particularly the TI-85 and TI-82) were originally designed to use only interpreted programs written in dialects of TI-BASIC; however, after users discovered bugs that could be exploited to allow native Z-80 code to run on the calculator hardware, TI released programming data to support third-party development. (This did not carry on to the ARM-based TI-Nspire, for which jailbreaks using Ndless have been found but are still actively fought against by Texas Instruments.) Some versions of the iPhone allow an unauthorised user to access the phone while it is locked.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a \"cutoff\", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that \"new physics\" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an \"effective theory\" within its intended scale of use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The main categories for non-iid data can be summarized as follows: Covariate shift: local nodes may store examples that have different statistical distributions compared to other nodes. An example occurs in natural language processing datasets where people typically write the same digits/letters with different stroke widths or slants. Prior probability shift: local nodes may store labels that have different statistical distributions compared to other nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Non-redundant information is most often obtained through contacts in different clusters. When two separate clusters possess non-redundant information, there is said to be a structural hole between them. Thus, a network that bridges structural holes will provide network benefits that are in some degree additive, rather than overlapping.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real analysis, the following result is called Young's convolution inequality:Suppose f {\\displaystyle f} is in the Lebesgue space L p ( R d ) {\\displaystyle L^{p}(\\mathbb {R} ^{d})} and g {\\displaystyle g} is in L q ( R d ) {\\displaystyle L^{q}(\\mathbb {R} ^{d})} and with 1 \u2264 p , q , r \u2264 \u221e . {\\displaystyle 1\\leq p,q,r\\leq \\infty .} Then Here the star denotes convolution, L p {\\displaystyle L^{p}} is Lebesgue space, and denotes the usual L p {\\displaystyle L^{p}} norm. Equivalently, if p , q , r \u2265 1 {\\displaystyle p,q,r\\geq 1} and 1 p + 1 q + 1 r = 2 {\\textstyle {\\frac {1}{p}}+{\\frac {1}{q}}+{\\frac {1}{r}}=2} then", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Coxeter matroids are generalization of matroids depending on a choice of a Coxeter group W and a parabolic subgroup P. Ordinary matroids correspond to the case when P is a maximal parabolic subgroup of a symmetric group W. They were introduced by Gelfand and Serganova (1987, 1987b), who named them after H. S. M. Coxeter. Borovik, Gelfand & White (2003) give a detailed account of Coxeter matroids.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of telecommunications, a terminal is a device which ends a telecommunications link and is the point at which a signal enters or leaves a network. Examples of terminal equipment include telephones, fax machines, computer terminals, printers and workstations. An end instrument is a piece of equipment connected to the wires at the end of a telecommunications link. In telephony, this is usually a telephone connected to a local loop. End instruments that relate to data terminal equipment include printers, computers, barcode readers, automated teller machines (ATMs) and the console ports of routers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the rank, Pr\u00fcfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines the size of the largest free abelian group contained in A. If A is torsion-free then it embeds into a vector space over the rational numbers of dimension rank A. For finitely generated abelian groups, rank is a strong invariant and every such group is determined up to isomorphism by its rank and torsion subgroup. Torsion-free abelian groups of rank 1 have been completely classified. However, the theory of abelian groups of higher rank is more involved. The term rank has a different meaning in the context of elementary abelian groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Rather than adopting an updated set of primary colors, proponents of split-primary theory explain this lack of chroma by the purported presence of chemical impurities, small amounts of other colors, in the paints, or biases away from the ideal primary toward one or the other of the adjacent colors. Every red paint, for example, is said to be tainted with, or biased toward, either blue or yellow, every blue paint toward either red or green, and every yellow toward either green or orange. These biases are said to result in mixtures that contain sets of complementary colors, darkening the resulting color.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Languages such as Japanese and Chinese form possessive constructions with nouns using possessive particles, in the same way as described for pronouns above. An example from Japanese is neko no iro (\"the cat's color\"), where neko means \"cat\", no is the particle, and iro means \"color\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the (n2 \u2212 1) -dimensional adjoint representation, the generators are represented by (n2 \u2212 1) \u00d7 (n2 \u2212 1) matrices, whose elements are defined by the structure constants themselves: ( T a ) j k = \u2212 i f a j k . {\\displaystyle \\left(T_{a}\\right)_{jk}=-if_{ajk}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "8. Specifying relevant conditions to which the concept applies, as a procedure (computer programming, formal concept analysis). 9.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Output: prefix sum \u2a01 0 \u2264 j \u2264 i m j {\\displaystyle \\bigoplus _{0\\leq j\\leq i}m_{j}} of processor i {\\displaystyle i} . x := m i {\\displaystyle x:=m_{i}} \u03c3 := m i {\\displaystyle \\sigma :=m_{i}} for 0 \u2264 k \u2264 d \u2212 1 {\\displaystyle 0\\leq k\\leq d-1} do y := i XOR 2 k {\\displaystyle y:=i{\\text{ XOR }}2^{k}} Send \u03c3 {\\displaystyle \\sigma } to y {\\displaystyle y} Receive m {\\displaystyle m} from y {\\displaystyle y} \u03c3 := \u03c3 \u2295 m {\\displaystyle \\sigma :=\\sigma \\oplus m} if bit k {\\displaystyle k} in i {\\displaystyle i} is set then x := x \u2295 m {\\displaystyle x:=x\\oplus m} endfor The algorithm works as follows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics a group is a set together with a binary operation on the set called multiplication that obeys the group axioms. The axiom of choice is an axiom of ZFC set theory which in one form states that every set can be wellordered. In ZF set theory, i.e. ZFC without the axiom of choice, the following statements are equivalent: For every nonempty set X there exists a binary operation \u2022 such that (X, \u2022) is a group. The axiom of choice is true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The distance of products to each other indicate either how different they are. The dimensions must be labelled by the researcher. This requires subjective judgement and is often very challenging. See perceptual mapping.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a terminal adapter or TA acts as an interface between a terminal device, such as a computer or telephone, and a communications network (typically an integrated services digital network).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications it may be acceptable to retrieve a \"good guess\" of the nearest neighbor. In those cases, we can use an algorithm which doesn't guarantee to return the actual nearest neighbor in every case, in return for improved speed or memory savings. Often such an algorithm will find the nearest neighbor in a majority of cases, but this depends strongly on the dataset being queried. Algorithms that support the approximate nearest neighbor search include locality-sensitive hashing, best bin first and balanced box-decomposition tree based search.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Rosati involution, named after Carlo Rosati, is an involution of the rational endomorphism ring of an abelian variety induced by a polarization. Let A {\\displaystyle A} be an abelian variety, let A ^ = P i c 0 ( A ) {\\displaystyle {\\hat {A}}=\\mathrm {Pic} ^{0}(A)} be the dual abelian variety, and for a \u2208 A {\\displaystyle a\\in A} , let T a: A \u2192 A {\\displaystyle T_{a}:A\\to A} be the translation-by- a {\\displaystyle a} map, T a ( x ) = x + a {\\displaystyle T_{a}(x)=x+a} . Then each divisor D {\\displaystyle D} on A {\\displaystyle A} defines a map \u03d5 D: A \u2192 A ^ {\\displaystyle \\phi _{D}:A\\to {\\hat {A}}} via \u03d5 D ( a ) =  {\\displaystyle \\phi _{D}(a)=} . The map \u03d5 D {\\displaystyle \\phi _{D}} is a polarization if D {\\displaystyle D} is ample.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, software system safety optimizes system safety in the design, development, use, and maintenance of software systems and their integration with safety-critical hardware systems in an operational environment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges of the original graph that cross between the groups will produce edges in the partitioned graph. If the number of resulting edges is small compared to the original graph, then the partitioned graph may be better suited for analysis and problem-solving than the original. Finding a partition that simplifies graph analysis is a hard problem, but one that has applications to scientific computing, VLSI circuit design, and task scheduling in multiprocessor computers, among others.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As with Racter, the question is how much the programmer filtered the output of the program, keeping only the occasional interesting output. Also, mathematics being a very specialized domain, it is doubtful whether the techniques used can be abstracted to general cognition. Another mathematical program, called Geometry, was celebrated for making an insightful discovery of an original proof that an isosceles triangle has equal base angles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In simple terms, a convex function refers to a function whose graph is shaped like a cup \u222a {\\displaystyle \\cup } (or a straight line like a linear function), while a concave function's graph is shaped like a cap \u2229 {\\displaystyle \\cap } . Convex functions play an important role in many areas of mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In philately, an invert error occurs when part of a stamp is printed upside-down. Inverts are perhaps the most spectacular of postage stamp errors, not only because of their striking visual appearance, but because some are quite rare, and highly valued by stamp collectors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operators. The rank of an operator is called its precedence, and an operation with a higher precedence is performed before operations with lower precedence. Calculators generally perform operations with the same precedence from left to right, but some programming languages and calculators adopt different conventions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Which is succeeded by an account of the fellowship examination, in 1823 (G. and W. B. Whittaker, London, 1823)Question 1249 in the Gentleman's Diary; or Mathematical Repository for 1829 (so appearing in late 1828) takes up the theme, with solutions appearing in the issue for the following year. One of the solvers, T. S. Davies then generalized the result in Question 1265 that year, presenting his own solution the following year, drawing on a paper he had already contributed to the Philosophical Magazine in 1826. There are no cross-references in this material to that described above.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, the use of models is an alternative to more common code-based development techniques. A model always conforms to a unique metamodel. One of the currently most active branch of Model Driven Engineering is the approach named model-driven architecture proposed by OMG.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a harmonic divisor number, or Ore number (named after \u00d8ystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are: 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 (sequence A001599 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The null hypothesis may be true, whereas we reject H0. On the other hand, the alternative hypothesis H1 may be true, whereas we do not reject H0. Two types of error are distinguished: type I error and type II error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, interpolative decomposition (ID) factors a matrix as the product of two matrices, one of which contains selected columns from the original matrix, and the other of which has a subset of columns consisting of the identity matrix and all its values are no greater than 2 in absolute value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music information retrieval, techniques have been developed to determine the key of a piece of classical Western music (recorded in audio data format) automatically. These methods are often based on a compressed representation of the pitch content in a 12-dimensional pitch-class profile (chromagram) and a subsequent procedure that finds the best match between this representation and one of the prototype vectors of the 24 minor and major keys. For implementation, often the constant-Q transform is used, displaying the musical signal on a log frequency scale. Although a radical (over)simplification of the concept of tonality, such methods can predict the key of classical Western music well for most pieces. Other methods also take into consideration the sequentiality of music.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, for k L + M + 1 \u2264 n \u2264 k L + L + M {\\displaystyle kL+M+1\\leq n\\leq kL+L+M} , and equivalently M + 1 \u2264 n \u2212 k L \u2264 L + M {\\displaystyle M+1\\leq n-kL\\leq L+M} , we can write: y  = \u2211 m = 1 M h  \u22c5 x k  \u225c y k  . {\\displaystyle y=\\sum _{m=1}^{M}h\\cdot x_{k}\\ \\ \\triangleq \\ \\ y_{k}.} With the substitution j = n \u2212 k L {\\displaystyle j=n-kL} , the task is reduced to computing y k  {\\displaystyle y_{k}} for M + 1 \u2264 j \u2264 L + M {\\displaystyle M+1\\leq j\\leq L+M} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest. Since the forecast error is derived from the same scale of data, comparisons between the forecast errors of different series can only be made when the series are on the same scale.In simple cases, a forecast is compared with an outcome at a single time-point and a summary of forecast errors is constructed over a collection of such time-points. Here the forecast may be assessed using the difference or using a proportional error. By convention, the error is defined using the value of the outcome minus the value of the forecast.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical calculation, the days of the week are represented as weekday numbers. If Monday is the first day of the week, the days may be coded 1 to 7, for Monday through Sunday, as is practiced in ISO 8601. The day designated with 7 may also be counted as 0, by applying the arithmetic modulo 7, which calculates the remainder of a number after division by 7. Thus, the number 7 is treated as 0, the number 8 as 1, the number 9 as 2, the number 18 as 4, and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The court added: \"In any case, a computer . . . is apparatus not mathematics.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and directional statistics, a circular uniform distribution is a probability distribution on the unit circle whose density is uniform for all angles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the classic vector space model proposed by Salton, Wong and Yang the term-specific weights in the document vectors are products of local and global parameters. The model is known as term frequency-inverse document frequency model. The weight vector for document d is v d =  T {\\displaystyle \\mathbf {v} _{d}=^{T}} , where w t , d = t f t , d \u22c5 log \u2061 | D | | { d \u2032 \u2208 D | t \u2208 d \u2032 } | {\\displaystyle w_{t,d}=\\mathrm {tf} _{t,d}\\cdot \\log {\\frac {|D|}{|\\{d'\\in D\\,|\\,t\\in d'\\}|}}} and t f t , d {\\displaystyle \\mathrm {tf} _{t,d}} is term frequency of term t in document d (a local parameter) log \u2061 | D | | { d \u2032 \u2208 D | t \u2208 d \u2032 } | {\\displaystyle \\log {\\frac {|D|}{|\\{d'\\in D\\,|\\,t\\in d'\\}|}}} is inverse document frequency (a global parameter). | D | {\\displaystyle |D|} is the total number of documents in the document set; | { d \u2032 \u2208 D | t \u2208 d \u2032 } | {\\displaystyle |\\{d'\\in D\\,|\\,t\\in d'\\}|} is the number of documents containing the term t.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, errors-in-variables models or measurement error models are regression models that account for measurement errors in the independent variables. In contrast, standard regression models assume that those regressors have been measured exactly, or observed without error; as such, those models account only for errors in the dependent variables, or responses. In the case when some regressors have been measured with errors, estimation based on the standard assumption leads to inconsistent estimates, meaning that the parameter estimates do not tend to the true values even in very large samples. For simple linear regression the effect is an underestimate of the coefficient, known as the attenuation bias. In non-linear models the direction of the bias is likely to be more complicated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. Historically, it was once thought that certain theorems, like the prime number theorem, could only be proved by invoking \"higher\" mathematical theorems or techniques. However, as time progresses, many of these results have also been subsequently reproven using only elementary techniques.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is important to compare the class of Euclidean domains with the larger class of principal ideal domains (PIDs). An arbitrary PID has much the same \"structural properties\" of a Euclidean domain (or, indeed, even of the ring of integers), but when an explicit algorithm for Euclidean division is known, one may use the Euclidean algorithm and extended Euclidean algorithm to compute greatest common divisors and B\u00e9zout's identity. In particular, the existence of efficient algorithms for Euclidean division of integers and of polynomials in one variable over a field is of basic importance in computer algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, most landlord-tenant law is state-specific.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C++ programming language, is a part of the C++ Standard Library. It is a header file that provides templates and types that enable interoperation between stream buffers and string objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Pingelapese language, transitive verbs are used in one of four of their most common sentence structures. Transitive verbs according to this language have two main characteristics. These characteristics are action verbs and the sentence must contain a direct object. To elaborate, an action verb is a verb that has a physical action associated to its meaning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Metaclasses permit concepts to be construed as tokens of other concepts while retaining their ontological status as types. This enables types to be enumerated over, while preserving the ability to inherit from types. For example, metaclasses could allow a machine reasoner to infer from a human-friendly ontology how many elements are in the periodic table, or, given that number of protons is a property of chemical element and isotopes are a subclass of elements, how many protons exist in the isotope hydrogen-2. Metaclasses are sometime organized by levels, in a similar way to the simple Theory of types where classes that are not metaclasses are assigned the first level, classes of classes in the first level are in the second level, classes of classes in the second level on the next and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another common choice of equivalent martingale measure is the minimal martingale measure, which minimises the variance of the equivalent martingale. For certain situations, the resultant measure Q {\\displaystyle Q} will not be equivalent to P {\\displaystyle P} . In a finite probability model, for objective probabilities p i {\\displaystyle p_{i}} and risk-neutral probabilities q i {\\displaystyle q_{i}} then one must minimise the Kullback\u2013Leibler divergence D K L ( Q \u2016 P ) = \u2211 i = 1 N q i ln \u2061 ( q i p i ) {\\displaystyle D_{KL}(Q\\|P)=\\sum _{i=1}^{N}q_{i}\\ln \\left({\\frac {q_{i}}{p_{i}}}\\right)} subject to the requirement that the expected return is r {\\displaystyle r} , where r {\\displaystyle r} is the risk-free rate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples of words with these sounds in English are shin , chin , gin  and vision  (in the middle of the word). Like most other coronal consonants, palato-alveolar consonants can be articulated either with the tip or blade of the tongue, and are correspondingly called apical or laminal. Speakers of English use both variants, and it does not appear to significantly affect the sound of the consonants.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of cybersecurity, new threats are emerging that target these smart systems. The timeline of cyber-kinetic attacks attests incidents from as early as 1982. Such attacks on information systems that can have physical world impacts are a complete shift in paradigms within the cyber security community, though not unheard of.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In taxonomy the basis of any particular type of classification is the way in which objects in the domain resemble each other. A resemblance of a type that seems appropriate to the classification that we propose, we may call an affinity, and when we decide how to classify say, a specimen of rock or butterfly, we justify our decision according to the affinities that we observe. Other resemblances we dismiss as being out of context or at least non-cogent; for example, in deciding whether to classify a lizard as having closer affinities to a snake than to a table, biologists rely on affinities such as the scales, blood, physiology, vertebral anatomy, and reproductive system as being more relevant than the possession of four \"feet\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Grassmann had published his results in 1844, but Saint-Venant claimed that he had first developed these ideas in 1832. One of the first mathematicians to appreciate Grassmann's ideas during his lifetime was Hermann Hankel, whose 1867 Theorie der complexen Zahlensysteme. , he developed  some of Hermann Grassmann's algebras and W.R.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It employed the most powerful coding techniques available at the time, including channel encoding and shape encoding. From the mere four bits per symbol (9.6 kbit/s), the new standards used the functional equivalent of 6 to 10 bits per symbol, plus increasing baud rates from 2,400 to 3,429, to create 14.4, 28.8, and 33.6 kbit/s modems. This rate is near the theoretical Shannon limit of a phone line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C# programming language, pointers are supported by either marking blocks of code that include pointers with the unsafe keyword, or by using the System.Runtime.CompilerServices assembly provisions for pointer access. The syntax is essentially the same as in C++, and the address pointed can be either managed or unmanaged memory. However, pointers to managed memory (any pointer to a managed object) must be declared using the fixed keyword, which prevents the garbage collector from moving the pointed object as part of memory management while the pointer is in scope, thus keeping the pointer address valid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, the demarcation point is the point at which the public switched telephone network ends and connects with the customer's on-premises wiring. It is the dividing line which determines who is responsible for installation and maintenance of wiring and equipment\u2014customer/subscriber, or telephone company/provider. The demarcation point varies between countries and has changed over time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In category theory, morphism is a broadly similar idea: the mathematical objects involved need not be sets, and the relationships between them may be something other than maps, although the morphisms between the objects of a given category have to behave similarly to maps in that they have to admit an associative operation similar to function composition. A morphism in category theory is an abstraction of a homomorphism.The study of morphisms and of the structures (called \"objects\") over which they are defined is central to category theory. Much of the terminology of morphisms, as well as the intuition underlying them, comes from concrete categories, where the objects are simply sets with some additional structure, and morphisms are structure-preserving functions. In category theory, morphisms are sometimes also called arrows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Slepian's lemma (1962), named after David Slepian, is a Gaussian comparison inequality. It states that for Gaussian random variables X = ( X 1 , \u2026 , X n ) {\\displaystyle X=(X_{1},\\dots ,X_{n})} and Y = ( Y 1 , \u2026 , Y n ) {\\displaystyle Y=(Y_{1},\\dots ,Y_{n})} in R n {\\displaystyle \\mathbb {R} ^{n}} satisfying E \u2061  = E \u2061  = 0 {\\displaystyle \\operatorname {E} =\\operatorname {E} =0} , E \u2061  = E \u2061  , i = 1 , \u2026 , n , and E \u2061  \u2264 E \u2061  for i \u2260 j . {\\displaystyle \\operatorname {E} =\\operatorname {E} ,\\quad i=1,\\dots ,n,{\\text{ and }}\\operatorname {E} \\leq \\operatorname {E} {\\text{ for }}i\\neq j.} the following inequality holds for all real numbers u 1 , \u2026 , u n {\\displaystyle u_{1},\\ldots ,u_{n}}: Pr  \u2264 Pr  , {\\displaystyle \\Pr \\left\\leq \\Pr \\left,} or equivalently, Pr  \u2265 Pr  .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This method is easiest to use for IP assets with positive cash flows, for those whose cash flows can be estimated with some degree of reliability for future periods, and where a proxy for risk can be used to obtain discount rates. Cost approach: The cost approach is based on the economic principle of substitution. This principle states that an investor will pay no more for an asset than the cost to obtain, by purchasing or constructing, a substitute asset of equal utility.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In text data, any Unicode character not available in the encoding declared in the header can be represented using a nnn; numerical character reference. But the text within a CDATA section is strictly limited to the characters available in the encoding. Because of this, using a CDATA section programmatically to quote data that could potentially contain '&' or '<' characters can cause problems when the data happens to contain characters that cannot be represented in the encoding. Depending on the implementation of the encoder, these characters can get lost, can get converted to the characters of the nnn; character reference, or can cause the encoding to fail.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In molecular biology, the Btk-type zinc finger or Btk motif (BM) is a conserved zinc-binding motif containing conserved cysteines and a histidine that is present in certain eukaryotic signalling proteins. The motif is named after Bruton's tyrosine kinase (Btk), an enzyme which is essential for B cell maturation in humans and mice. Btk is a member of the Tec family of protein tyrosine kinases (PTK). These kinases contain a conserved Tec homology (TH) domain between the N-terminal pleckstrin homology (PH) domain and the Src homology 3 (SH3) domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the configuration random graph, the size distribution of connected components can be expressed via the convolution power of the excess degree distribution (Kryven (2017)): w ( n ) = { \u03bc 1 n \u2212 1 u 1 \u2217 n ( n \u2212 2 ) , n > 1 , u ( 0 ) n = 1. {\\displaystyle w(n)={\\begin{cases}{\\frac {\\mu _{1}}{n-1}}u_{1}^{*n}(n-2),&n>1,\\\\u(0)&n=1.\\end{cases}}} Here, w ( n ) {\\displaystyle w(n)} is the size distribution for connected components, u 1 ( k ) = k + 1 \u03bc 1 u ( k + 1 ) , {\\displaystyle u_{1}(k)={\\frac {k+1}{\\mu _{1}}}u(k+1),} is the excess degree distribution, and u ( k ) {\\displaystyle u(k)} denotes the degree distribution. As convolution algebras are special cases of Hopf algebras, the convolution power is a special case of the (ordinary) power in a Hopf algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The pointwise information is contained in the distortion tensor G ( x , f ) = { | J ( x , f ) | \u2212 2 / n D T f ( x ) D f ( x ) if J ( x , f ) \u2260 0 I if J ( x , f ) = 0. {\\displaystyle G(x,f)={\\begin{cases}|J(x,f)|^{-2/n}D^{T}f(x)Df(x)&{\\text{if }}J(x,f)\\not =0\\\\I&{\\text{if }}J(x,f)=0.\\end{cases}}} The outer distortion KO and inner distortion KI are defined via the Rayleigh quotients K O ( x ) = sup \u03be \u2260 0 \u27e8 G ( x ) \u03be , \u03be \u27e9 n / 2 | \u03be | n , K O ( x ) = sup \u03be \u2260 0 \u27e8 G \u2212 1 ( x ) \u03be , \u03be \u27e9 n / 2 | \u03be | n . {\\displaystyle K_{O}(x)=\\sup _{\\xi \\not =0}{\\frac {\\langle G(x)\\xi ,\\xi \\rangle ^{n/2}}{|\\xi |^{n}}},\\quad K_{O}(x)=\\sup _{\\xi \\not =0}{\\frac {\\langle G^{-1}(x)\\xi ,\\xi \\rangle ^{n/2}}{|\\xi |^{n}}}.} The outer distortion can also be characterized by means of an inequality similar to that given in the two-dimensional case. If \u03a9 is an open set in Rn, then a function \u0192 \u2208 W1,1loc(\u03a9,Rn) has finite distortion if its Jacobian is locally integrable and does not change sign, and there is a measurable function KO (the outer distortion) such that | D f ( x ) | n \u2264 K O ( x ) | J ( x , f ) | {\\displaystyle |Df(x)|^{n}\\leq K_{O}(x)|J(x,f)|} almost everywhere.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By construction, such functions respect equality in the sense that x = y \u2192 f ( x ) = f ( y ) {\\displaystyle x=y\\to f(x)=f(y)} , for any inputs from A {\\displaystyle A} . This is worth mentioning since also more broader concepts of \"operations\" exist in the literature, which may not respect this. And as noted, care must be taken with nomenclature \"function\", a word which sees use in most mathematical frameworks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of proving lower bounds, our knowledge is very limited. Since we study the computation of formal polynomials, we know that polynomials of very large degree require large circuits, for example, a polynomial of degree 2 2 n {\\displaystyle 2^{2^{n}}} require a circuit of size roughly 2 n . {\\displaystyle 2^{n}.} So, the main goal is to prove lower bound for polynomials of small degree, say, polynomial in n .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other Dutch digraphs are never treated as single letters. In Hungarian, the digraphs \u27e8cs\u27e9, \u27e8dz\u27e9, \u27e8gy\u27e9, \u27e8ly\u27e9, \u27e8ny\u27e9, \u27e8sz\u27e9, \u27e8ty\u27e9, \u27e8zs\u27e9, and the trigraph \u27e8dzs\u27e9, have their own places in the alphabet (where \u27e8cs\u27e9 follows \u27e8c\u27e9, \u27e8dz\u27e9 and \u27e8dzs\u27e9 follow \u27e8d\u27e9, etc.) In Spanish, the digraphs \u27e8ch\u27e9 and \u27e8ll\u27e9 were formerly treated as distinct letters, but are now split into their constituent letters. In Welsh, the alphabet includes the digraphs \u27e8ch\u27e9, \u27e8dd\u27e9, \u27e8ff\u27e9, \u27e8ll\u27e9, \u27e8ng\u27e9, \u27e8ph\u27e9, \u27e8rh\u27e9, \u27e8th\u27e9.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of reinforcement learning, a softmax function can be used to convert values into action probabilities. The function commonly used is: where the action value q t ( a ) {\\displaystyle q_{t}(a)} corresponds to the expected reward of following action a and \u03c4 {\\displaystyle \\tau } is called a temperature parameter (in allusion to statistical mechanics). For high temperatures ( \u03c4 \u2192 \u221e {\\displaystyle \\tau \\to \\infty } ), all actions have nearly the same probability and the lower the temperature, the more expected rewards affect the probability. For a low temperature ( \u03c4 \u2192 0 + {\\displaystyle \\tau \\to 0^{+}} ), the probability of the action with the highest expected reward tends to 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Simone et al. use the following order of preference for the rules (if applicable to the given context): B2 > B3 > { B2', B1 } > A1' > A2 (X > Y means that X is preferred over Y). Experiments have shown that ReduceAndReconstruct alone has a worse compression/time ratio than the algorithm RecyclePivots. However, while RecyclePivots can be applied only once to a proof, ReduceAndReconstruct may be applied multiple times to produce a better compression. An attempt to combine ReduceAndReconstruct and RecyclePivots algorithms has led to good results. == Notes ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In meteorology, an inversion is a deviation from the normal change of an atmospheric property with altitude. It almost always refers to an inversion of the air temperature lapse rate, in which case it is called a temperature inversion. Normally, air temperature decreases with an increase in altitude, but during an inversion warmer air is held above cooler air.An inversion traps air pollution, such as smog, close to the ground.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, palatalization is a distinctive feature that distinguishes two consonant phonemes. This feature occurs in Russian, Irish, and Scottish Gaelic, among others. Phonemic palatalization may be contrasted with either plain or velarized articulation. In many of the Slavic languages, and some of the Baltic and Finnic languages, palatalized consonants contrast with plain consonants, but in Irish they contrast with velarized consonants.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the coindexing stage, each noun phrase is given a unique index, called a \"referential index\". In the contraindexing stage, each non-anaphoric noun phrase (i.e. each noun phrase that is not a reflexive pronoun like \"herself\" or a reciprocal pronoun like \"each other\") is given a set of \"anaphoric indices\". This set consists of the referential indices of all elements that c-command it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory, an area of mathematical logic, resolution proof reduction via local context rewriting is a technique for resolution proof reduction via local context rewriting. This proof compression method was presented as an algorithm named ReduceAndReconstruct, that operates as a post-processing of resolution proofs. ReduceAndReconstruct is based on a set of local proof rewriting rules that transform a subproof into an equivalent or stronger one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some countries such as France, such schemes may be initiated by the central government: Sch\u00e9ma directeur d'am\u00e9nagement et de gestion des eaux", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics the let expression is described as the conjunction of expressions. In functional languages the let expression is also used to limit scope. In mathematics scope is described by quantifiers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Cutting-plane methods for general convex continuous optimization and variants are known under various names: Kelley's method, Kelley\u2013Cheney\u2013Goldstein method, and bundle methods. They are popularly used for non-differentiable convex minimization, where a convex objective function and its subgradient can be evaluated efficiently but usual gradient methods for differentiable optimization can not be used. This situation is most typical for the concave maximization of Lagrangian dual functions. Another common situation is the application of the Dantzig\u2013Wolfe decomposition to a structured optimization problem in which formulations with an exponential number of variables are obtained. Generating these variables on demand by means of delayed column generation is identical to performing a cutting plane on the respective dual problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, the action of a general reflection will be to switch the entries at positions j \u2212 kn and i + kn for each k, fixing all inputs at positions not congruent to i or j modulo n.In the geometric action of S ~ n {\\displaystyle {\\widetilde {S}}_{n}} , the generator s i {\\displaystyle s_{i}} acts on an alcove A by reflecting it across one of the bounding planes of the fundamental alcove A0. In the inverse action, it instead reflects A across one of its own bounding planes. From this perspective, a reduced word corresponds to an alcove walk on the tessellated space V.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL's use of SELECT) is a unary operation written as \u03c3 a \u03b8 b ( R ) {\\displaystyle \\sigma _{a\\theta b}(R)} or \u03c3 a \u03b8 v ( R ) {\\displaystyle \\sigma _{a\\theta v}(R)} where: a {\\displaystyle a} and b {\\displaystyle b} are attribute names, \u03b8 {\\displaystyle \\theta } is a binary operation in the set { < , \u2264 , = , \u2260 , \u2265 , > } , {\\displaystyle \\{<,\\leq ,=,\\neq ,\\geq ,>\\},} v {\\displaystyle v} is a value constant, R {\\displaystyle R} is a relation.The selection \u03c3 a \u03b8 b ( R ) {\\displaystyle \\sigma _{a\\theta b}(R)} selects all those tuples in R {\\displaystyle R} for which \u03b8 {\\displaystyle \\theta } holds between the a {\\displaystyle a} and the b {\\displaystyle b} attribute. The selection \u03c3 a \u03b8 v ( R ) {\\displaystyle \\sigma _{a\\theta v}(R)} selects all those tuples in R {\\displaystyle R} for which \u03b8 {\\displaystyle \\theta } holds between the a {\\displaystyle a} attribute and the value v . {\\displaystyle v.} Thus, the selection operator restricts to a subset of the entire database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In response to various compliance pressures, organizations can introduce unique identifiers for its entire user base to validate that each user belongs in each specific system or application in which he/she has login capabilities. To effectuate such a policy, various individuals familiar with the organization's entire user base and each system-specific user base must be responsible for validating that certain identities should be linked together and other identities should be disassociated from each other. Once the validation process is complete, a unique identifier can be assigned to that individual and his or her associated system-specific account login IDs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Birch's theorem, named for Bryan John Birch, is a statement about the representability of zero by odd degree forms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The result was presented at the conference 100 Years in Seattle: the mathematics of Klee and Gr\u00fcnbaum and appeared in Annals of Mathematics. Specifically, the paper presented a 43-dimensional polytope of 86 facets with a diameter of more than 43. The counterexample has no direct consequences for the analysis of the simplex method, as it does not rule out the possibility of a larger but still linear or polynomial number of steps. Various equivalent formulations of the problem had been given, such as the d-step conjecture, which states that the diameter of any 2d-facet polytope in d-dimensional Euclidean space is no more than d; Santos Leal's counterexample also disproves this conjecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the data stream model, the frequent elements problem is to output a set of elements that constitute more than some fixed fraction of the stream. A special case is the majority problem, which is to determine whether or not any value constitutes a majority of the stream. More formally, fix some positive constant c > 1, let the length of the stream be m, and let fi denote the frequency of value i in the stream. The frequent elements problem is to output the set { i | fi > m/c }.Some notable algorithms are: Boyer\u2013Moore majority vote algorithm Count-Min sketch Lossy counting Multi-stage Bloom filters Misra\u2013Gries heavy hitters algorithm Misra\u2013Gries summary", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For let the first terms, of the combination of which all others consist, be designated by signs; these signs will be a kind of alphabet. It will be convenient for the signs to be as natural as possible\u2014e.g., for one, a point; for numbers, points; for the relations of one entity with another, lines; for the variation of angles and of extremities in lines, kinds of relations. If these are correctly and ingeniously established, this universal writing will be as easy as it is common, and will be capable of being read without any dictionary; at the same time, a fundamental knowledge of all things will be obtained.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Keynesian beauty contest, participants are asked to choose a number that will be as close as possible to some fraction of the average of all participants' guesses. Suppose there are many players, each attempting to guess \u00bd of the average from the range 1-100. A level zero player will select a number non-strategically. That number might be selected at random, or may have special significance to the player (in which case it is indistinguishable from a random number by other players).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical physics, noncommutative quantum field theory (or quantum field theory on noncommutative spacetime) is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions are noncommutative. One commonly studied version of such theories has the \"canonical\" commutation relation:  = i \u03b8 \u03bc \u03bd {\\displaystyle =i\\theta ^{\\mu \\nu }\\,\\!} which means that (with any given set of axes), it is impossible to accurately measure the position of a particle with respect to more than one axis. In fact, this leads to an uncertainty relation for the coordinates analogous to the Heisenberg uncertainty principle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of \"samples\". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values.A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points. The original signal can be reconstructed from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a type of low-pass filter called a reconstruction filter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, the specified hardware and software environment can be set up as a testbed for the application under test. In this context, a testbed is also known as the test environment made of: Testing hardware equipment (test bench, optical table, custom testing rig, dummy equipment as simulates an actual product or its counterpart, external environment means, like showers, heaters, fans, vacuum chamber, anechoic chamber). Computing equipment (processing units, data centers, in-line FPGA, environment simulation equipment).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, bilateral synchronization (or bilateral control) is a synchronization control system between exchanges A and B in which the clock at telephone exchange A controls the data received at exchange B and the clock at exchange B controls the data received at exchange A. Bilateral synchronization is usually implemented by deriving the timing from the incoming bitstream. Source: from Federal Standard 1037C in support of MIL-STD-188", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From the perspective of copy elimination, this heuristic has the best results. On the other hand, aggressive coalescing could impact the colorability of the inference graph. Conservative Coalescing it mainly uses the same heuristic as aggressive coalescing but it merges moves if, and only if, it does not compromise the colorability of the interference graph. Iterated coalescing it removes one particular move at the time, while keeping the colorability of the graph. Optimistic coalescing it is based on aggressive coalescing, but if the inference graph colorability is compromised, then it gives up as few moves as possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In graphs that have negative cycles, the set of shortest simple paths from v to all other vertices do not necessarily form a tree. For simple connected graphs, shortest-path trees can be used to suggest a non-linear relationship between two network centrality measures, closeness and degree. By assuming that the branches of the shortest-path trees are statistically similar for any root node in one network, one may show that the size of the branches depend only on the number of branches connected to the root vertex, i.e. to the degree of the root node. From this one deduces that the inverse of closeness, a length scale associated with each vertex, varies approximately linearly with the logarithm of degree. The relationship is not exact but it captures a correlation between closeness and degree in large number of networks constructed from real data and this success suggests that shortest-path trees can be a useful approximation in network analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It iteratively does hill-climbing, each time with a random initial condition x 0 {\\displaystyle x_{0}} . The best x m {\\displaystyle x_{m}} is kept: if a new run of hill climbing produces a better x m {\\displaystyle x_{m}} than the stored state, it replaces the stored state. Random-restart hill climbing is a surprisingly effective algorithm in many cases. It turns out that it is often better to spend CPU time exploring the space, than carefully optimizing from an initial condition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. This quantity is studied in the context of spectral graph theory. More precisely, let G be a graph with n vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following discussion, let K(s) be the complexity of the string s. It is not hard to see that the minimal description of a string cannot be too much larger than the string itself \u2014 the program GenerateString2 above that outputs s is a fixed amount larger than s. Theorem: There is a constant c such that \u2200s. K(s) \u2264 |s| + c.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to find information on the Web, most users make use of search engines, which crawl the web, index it and show a list of results ordered by relevance. The use of search engines to access information through the web has become a key factor for online businesses, which depend on the flow of users visiting their pages. One of these companies is Foundem. Foundem provides a \"vertical search\" service to compare products available on online markets for the U.K.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Understanding how individual interactions within networks influence coevolution, and conversely how coevolution influences the overall structure of networks, requires an appreciation for how pair-wise interactions change due to their broader community contexts as well as how this community context shapes selective pressures. Accordingly, research is now focusing on how reciprocal selection influences and is embedded within the structure of multispecies interactive webs, not only on particular species in isolation.Coevolution in a community context can be addressed theoretically via mathematical modeling and simulation, by looking at ancient footprints of evolutionary history via ecological patterns that persist and are observable today, and by performing laboratory experiments with microorganisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plant morphology, a cataphyll (sometimes also called a cataphyllum or cataphyll leaf) is a reduced, small leaf. Many plants have both \"true leaves\" (euphylls), which perform most of the photosynthesis, and cataphylls, which are modified to perform other functions.Cataphylls include bracts, bracteoles and bud scales, as well as any small leaves that resemble scales, known as scale leaves. The functions of cataphylls, such as bud scales, may be short-lived, and they are often shed after their function is fulfilled.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In text processing, a proximity search looks for documents where two or more separately matching term occurrences are within a specified distance, where distance is the number of intermediate words or characters. In addition to proximity, some implementations may also impose a constraint on the word order, in that the order in the searched text must be identical to the order of the search query. Proximity searching goes beyond the simple matching of words by adding the constraint of proximity and is generally regarded as a form of advanced search. For example, a search could be used to find \"red brick house\", and match phrases such as \"red house of brick\" or \"house made of red brick\". By limiting the proximity, these phrases can be matched while avoiding documents where the words are scattered or spread across a page or in unrelated articles in an anthology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Standing or kneeling targets must be no more than 45 yards (41 m) from the firing line. Points are scored with 1 for a hit (resulting in the faceplate falling), and 0 for a miss (whether it strikes the surrounding faceplate, misses it, or \"splits\" on the edge of the kill but fails to down the target). The highest score of a competition forms the benchmark for all the other scores \u2013 they are calculated as a percentage of this score rather than the total number of targets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Due to its difficulty, it is fairly scarcely done. Lag The effect experienced when the game runs slower than its normal speed due to an excess of instructions for the CPU to calculate in the time of one frame. Thus, the CPU will spread the calculations over multiple frames.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In surveying, the repetition method is used to improve precision and accuracy of measurements of horizontal angles. The same angle is measured multiple times, with the survey instrument rotated so that systematic errors tend to cancel. The arithmetic mean of these observations gives true value of an angle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In such case three possibilities exists: Continue with both processors: This is based on the assumption that the fault is transient and may not appear again. Take out the active processor and continue with the other. Continue with active processor but remove other processor from service.When a processor is taken out, it is subjected to extensive testing to identify a marginal failure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the category FdHilb has all finite-dimensional Hilbert spaces for objects and the linear transformations between them as morphisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Station identification in that case usually consists of the station's name, frequency, and a slogan; unlicensed stations are not allowed to use formal call signs. International shortwave broadcasters usually do not use callsigns, instead giving the name of the service and the location of the home office, and occasionally the frequencies that the current broadcast is being transmitted on. There are a few exceptions, particularly in the United States, the time station WWV being a prime example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Which 3D point xest is the best estimate of x given y 1 \u2032 {\\displaystyle \\mathbf {y} '_{1}} and y 2 \u2032 {\\displaystyle \\mathbf {y} '_{2}} and the geometry of the cameras? The answer is often found by defining an error measure which depends on xest and then minimizing this error. In the following sections, some of the various methods for computing xest presented in the literature are briefly described. All triangulation methods produce xest = x in the case that y 1 = y 1 \u2032 {\\displaystyle \\mathbf {y} _{1}=\\mathbf {y} '_{1}} and y 2 = y 2 \u2032 {\\displaystyle \\mathbf {y} _{2}=\\mathbf {y} '_{2}} , that is, when the epipolar constraint is satisfied (except for singular points, see below). It is what happens when the constraint is not satisfied which differs between the methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "4. Computing term frequencies or tf-idf After pre-processing the text data, we can then proceed to generate features. For document clustering, one of the most common ways to generate features for a document is to calculate the term frequencies of all its tokens.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the four-spiral semigroup is a special semigroup generated by four idempotent elements. This special semigroup was first studied by Karl Byleen in a doctoral dissertation submitted to the University of Nebraska in 1977. It has several interesting properties: it is one of the most important examples of bi-simple but not completely-simple semigroups; it is also an important example of a fundamental regular semigroup; it is an indispensable building block of bisimple, idempotent-generated regular semigroups. A certain semigroup, called double four-spiral semigroup, generated by five idempotent elements has also been studied along with the four-spiral semigroup.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The complexities of creating such a secure system come from the fact that the behaviour of humans is not always rational or predictable. Even in a very-well secured computer system, a malicious individual can telephone a worker and pretend to be a private investigator working for the software company, and ask for the individual's password, a dishonest process called \"phishing\". As well, even with a well-secured system, if a worker decides to put the company's electronic files on a USB drive to take them home to work on them over the weekend (against many companies' policies), and then loses this USB drive, the company's data may be compromised.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as \"memory\", \"search\" and \"stimulus\".In contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result.As an effective method, an algorithm can be expressed within a finite amount of space and time, and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing \"output\" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the symbolic method in invariant theory is an algorithm developed by Arthur Cayley, Siegfried Heinrich Aronhold, Alfred Clebsch, and Paul Gordan in the 19th century for computing invariants of algebraic forms. It is based on treating the form as if it were a power of a degree one form, which corresponds to embedding a symmetric power of a vector space into the symmetric elements of a tensor product of copies of it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the TSVD setting, given the eigen-decomposition K = Q \u03a3 Q T {\\displaystyle K=Q\\Sigma Q^{T}} and using a prescribed threshold \u03bb n {\\displaystyle \\lambda n} , a regularized inverse can be formed for the kernel matrix by discarding all the eigenvalues that are smaller than this threshold. Thus, the filter function for TSVD can be defined as G \u03bb ( \u03c3 ) = { 1 / \u03c3 , if \u03c3 \u2265 \u03bb n 0 , otherwise . {\\displaystyle G_{\\lambda }(\\sigma )=\\left\\{{\\begin{array}{lcll}1/\\sigma &,&{\\text{if }}\\sigma \\geq \\lambda n\\\\0&,&{\\text{otherwise}}\\\\\\end{array}}\\right..} It can be shown that TSVD is equivalent to the (unsupervised) projection of the data using (kernel) Principal Component Analysis (PCA), and that it is also equivalent to minimizing the empirical risk on the projected data (without regularization). Note that the number of components kept for the projection is the only free parameter here. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reverse Polish notation, the operators follow their operands. For example, to add 3 and 4 together, the expression is 3 4 + rather than 3 + 4. The expression 3 \u2212 4 + 5 in conventional notation is 3 4 \u2212 5 + in reverse Polish notation: 4 is first subtracted from 3, then 5 is added to it. The concept of a stack, a last-in/first-out construct, is integral to the left-to-right evaluation of RPN.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Calkin\u2013Wilf tree is a tree in which the vertices correspond one-to-one to the positive rational numbers. The tree is rooted at the number 1, and any rational number expressed in simplest terms as the fraction a/b has as its two children the numbers a/a + b and a + b/b. Every positive rational number appears exactly once in the tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This possibly induces a reassignment of the other nodes P, C, S, D also. If something has been changed by the case, this is shown in the column group after. An arrow \u2192 in column next signifies that the rebalancing is complete with this step.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints\u2014primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here k {\\displaystyle k} is the ratio of magnification or dilation factor or scale factor or similitude ratio. Such a transformation can be called an enlargement if the scale factor exceeds 1. The above-mentioned fixed point S is called homothetic center or center of similarity or center of similitude.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the configuration model, the degree of each vertex is pre-defined, rather than having a probability distribution from which the given degree is chosen. As opposed to the Erd\u0151s\u2013R\u00e9nyi model, the degree sequence of the configuration model is not restricted to have a Poisson distribution, the model allows the user to give the network any desired degree distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications of elliptic curve cryptography and the elliptic curve method of factorization (ECM) it is necessary to consider the scalar multiplication P. One way to do this is to compute successively: P ,  P = P + P ,  P =  P + P , \u2026 ,  P =  P + P {\\displaystyle P,\\quad P=P+P,\\quad P=P+P,\\dots ,P=P+P} But it is faster to use double-and-add method, e.g. P = (P) + P. In general to compute P, write k = \u2211 i \u2264 l k i 2 i {\\displaystyle k=\\sum _{i\\leq l}k_{i}2^{i}} with ki in {0,1} and l =  {\\displaystyle l=} , kl = 1, then:  ( . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation; it is a simple corollary that the opposite is true of concave transformations.Jensen's inequality generalizes the statement that the secant line of a convex function lies above the graph of the function, which is Jensen's inequality for two points: the secant line consists of weighted means of the convex function (for t \u2208 ), t f ( x 1 ) + ( 1 \u2212 t ) f ( x 2 ) , {\\displaystyle tf(x_{1})+(1-t)f(x_{2}),} while the graph of the function is the convex function of the weighted means, f ( t x 1 + ( 1 \u2212 t ) x 2 ) . {\\displaystyle f(tx_{1}+(1-t)x_{2}).} Thus, Jensen's inequality is f ( t x 1 + ( 1 \u2212 t ) x 2 ) \u2264 t f ( x 1 ) + ( 1 \u2212 t ) f ( x 2 ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\|f\\|_{\\mathcal {D}}^{2}=\\sum _{n\\geq 0}(n+1)|a_{n}|^{2}.} Clearly, D {\\displaystyle {\\mathcal {D}}} contains all the polynomials and, more generally, all functions f {\\displaystyle f} , holomorphic on D {\\displaystyle \\mathbb {D} } such that f \u2032 {\\displaystyle f'} is bounded on D {\\displaystyle \\mathbb {D} } . The reproducing kernel of D {\\displaystyle {\\mathcal {D}}} at w \u2208 C \u2216 { 0 } {\\displaystyle w\\in \\mathbb {C} \\setminus \\{0\\}} is given by k w ( z ) = 1 z w \u00af log \u2061 ( 1 1 \u2212 z w \u00af ) ( z \u2208 C \u2216 { 0 } ) . {\\displaystyle k_{w}(z)={\\frac {1}{z{\\overline {w}}}}\\log \\left({\\frac {1}{1-z{\\overline {w}}}}\\right)\\;\\;\\;\\;\\;(z\\in \\mathbb {C} \\setminus \\{0\\}).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Dirichlet distribution is the conjugate prior of the multinomial in Bayesian statistics. Dirichlet-multinomial distribution. Beta-binomial distribution. Negative multinomial distribution Hardy\u2013Weinberg principle (it is a trinomial distribution with probabilities ( \u03b8 2 , 2 \u03b8 ( 1 \u2212 \u03b8 ) , ( 1 \u2212 \u03b8 ) 2 ) {\\displaystyle (\\theta ^{2},2\\theta (1-\\theta ),(1-\\theta )^{2})} )", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Considering there are no short term incentives to reward this front load effort required from companies engaging in collaboration, the motivation to do so is weak. To combat these high initial upfront costs, some organizations with complementary interests collaborate with each other to form \"clusters\". With a common goal driving the group, there is noticeably increased efficiency in providing services which is why there is a faster return on investments working like this. Unfortunately, the success of agencies with similar missions clustering together discourages more comprehensive collaborations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a three-parameter family of continuous probability distributions. It has a location parameter \u03bc {\\displaystyle \\mu } , scale parameter \u03b8 {\\displaystyle \\theta } and a shape parameter k {\\displaystyle k} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the chemical and process industries, a process has inherent safety if it has a low level of danger even if things go wrong. Inherent safety contrasts with other processes where a high degree of hazard is controlled by protective systems. As perfect safety cannot be achieved, common practice is to talk about inherently safer design. \u201cAn inherently safer design is one that avoids hazards instead of controlling them, particularly by reducing the amount of hazardous material and the number of hazardous operations in the plant.\u201d", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Definition Let L {\\displaystyle L} be a partial differential operator in the plane; define and be ordinary differential operators with respect to x {\\displaystyle x} or y {\\displaystyle y} ; a i , b i \u2208 Q ( x , y ) {\\displaystyle a_{i},b_{i}\\in \\mathbb {Q} (x,y)} for all i; m {\\displaystyle m} and n {\\displaystyle n} are natural numbers not less than 2. Assume the coefficients a i {\\displaystyle a_{i}} , i = 0 , \u2026 , m \u2212 1 {\\displaystyle i=0,\\ldots ,m-1} are such that L {\\displaystyle L} and l m {\\displaystyle {\\mathfrak {l}}_{m}} form a Janet basis. If m {\\displaystyle m} is the smallest integer with this property then L x m ( L ) \u2261 \u27e8 \u27e8 L , l m \u27e9 \u27e9 {\\displaystyle \\mathbb {L} _{x^{m}}(L)\\equiv {\\langle \\langle }L,{\\mathfrak {l}}_{m}{\\rangle \\rangle }} is called a Laplace divisor of L {\\displaystyle L} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A BIOS interrupt handler would then translate the program's request to match the hardware that was actually present. The SMM in the 386SL is a better way to do this. Some 8-bit home computers used the NMI line to permit a \"warm start\" if the system had locked up.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The loser of each game puts one unit into the pot. Play continues in like fashion through all the players until one of the players has beaten all the others in succession. The original problem, stated in a letter dated 10 April 1711, from Montmort to Nicholas Bernoulli is for n = 2 and is attributed to M. de Waldegrave. The problem, according to Montmort, is to find the expectation of each player and the probability that the pool will be won within a specified number of games.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early stages of product development, it is common to use development boards with dedicated and readily accessible debug interfaces for connecting the debug tools. SoCs employed in the mobile market rely on two debug technologies: stop-mode debugging via a scan chain and stop-mode debugging via memory-mapped debug registers. The following non-MIPI debug standards are well established in the embedded market: IEEE 1149.1 JTAG (5-pin) and ARM Serial Wire Debug (2-pin), both using single-ended pins. Thus, there was no need for the MIPI Debug Working Group to specify a stop-mode debug protocol or to specify a debug interface.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of fair item allocation, the following results are known. Unanimous approximate maximin-share fairness: When there are two groups, a positive multiplicative approximation to MMS-fairness can be guaranteed if-and-only-if the numbers of agents in the groups are (1,n-1) or (2,2) or (2,3). The positive results are attainable by polynomial-time algorithms. In all other cases, there are instances in which at least one agent with a positive MMS gets a zero value in all allocations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another useful application for GIS regards flood risk assessment. Using digital elevation models combined with peak discharge data can predict which areas of a floodplain will be submerged depending on the amount of rainfall. In a study of the Illinois River watershed, Rabie (2014) found that a decently accurate flood risk map could be generated using only DEMs and stream gauge data. Analysis based on these two parameters alone does not account for manmade developments including levees or drainage systems, and therefore should not be considered a comprehensive result.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the RV coefficient is a multivariate generalization of the squared Pearson correlation coefficient (because the RV coefficient takes values between 0 and 1). It measures the closeness of two set of points that may each be represented in a matrix. The major approaches within statistical multivariate data analysis can all be brought into a common framework in which the RV coefficient is maximised subject to relevant constraints. Specifically, these statistical methodologies include: principal component analysis canonical correlation analysis multivariate regression statistical classification (linear discrimination).One application of the RV coefficient is in functional neuroimaging where it can measure the similarity between two subjects' series of brain scans or between different scans of a same subject.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Primer-BLAST is widely used, and freely accessible from the National Center for Biotechnology Information (NCBI) website. On the other hand, FastPCR, a commercial application, allows simultaneous testing of a single primer or a set of primers designed for multiplex target sequences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6, ...).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, the Whitney covering lemma, or Whitney decomposition, asserts the existence of a certain type of partition of an open set in a Euclidean space. Originally it was employed in the proof of Hassler Whitney's extension theorem. The lemma was subsequently applied to prove generalizations of the Calder\u00f3n\u2013Zygmund decomposition. Roughly speaking, the lemma states that it is possible to decompose an open set by cubes each of whose diameters is proportional, within certain bounds, to its distance from the boundary of the open set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The more sophisticated record-oriented file systems have more in common with simple databases than with other file systems. CMS file system \u2013 The native file system of the Conversational Monitor System component of VM/370 Files-11 \u2013 early versions were record-oriented; support for \"streams\" was added later Michigan Terminal System (MTS) \u2013 provides \"line files\" where record lengths and line numbers are associated as metadata with each record in the file, lines can be added, replaced, updated with the same or different length records, and deleted anywhere in the file without the need to read and rewrite the entire file. OS4000 for GEC's OS4000 operating system, on the GEC 4000 series minicomputers A FAT12 and FAT16 (and FAT32) extension to support database-like file types random file, direct file, keyed file and sequential file in Digital Research FlexOS, IBM 4680 OS and Toshiba 4690 OS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).For instance, if X is used to denote the outcome of a coin toss (\"the experiment\"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names..", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of mobile telephony, the operators (carriers) charged for all air time consumed by the mobile phone user, which included both outbound and inbound telephone calls. As mobile phone adoption rates increased, competition between operators meant that some decided not to charge for incoming calls in some markets (also called \"calling party pays\"). The European market adopted a calling party pays model throughout the GSM environment and soon various other GSM markets also started to emulate this model. In Hong Kong, Singapore, Canada, and the United States, it is common for the party receiving the call to be charged per minute, although a few carriers are beginning to offer unlimited received phone calls.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and statistics, in the context of Markov processes, the Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, are a pair of systems of differential equations that describe the time evolution of the process's distribution. This article, as opposed to the article titled Kolmogorov equations, focuses on the scenario where we have a continuous-time Markov chain (so the state space \u03a9 {\\displaystyle \\Omega } is countable). In this case, we can treat the Kolmogorov equations as a way to describe the probability P ( x , s ; y , t ) {\\displaystyle P(x,s;y,t)} , where x , y \u2208 \u03a9 {\\displaystyle x,y\\in \\Omega } (the state space) and t > s , t , s \u2208 R \u2265 0 {\\displaystyle t>s,t,s\\in \\mathbb {R} _{\\geq 0}} are the final and initial times, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most of the approaches listed here, a well-understood block cipher (such as AES) is used as a primitive to take the place of an ideal random function. This has the advantage that incorporation of a secret key into the algorithm is easy. Where AES is mentioned in the following discussion, any other good block cipher would work as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following figure, the graph C is a covering graph of the graph H. The covering map f from C to H is indicated with the colours. For example, both blue vertices of C are mapped to the blue vertex of H. The map f is a surjection: each vertex of H has a preimage in C. Furthermore, f maps bijectively each neighbourhood of a vertex v in C onto the neighbourhood of the vertex f(v) in H. For example, let v be one of the purple vertices in C; it has two neighbours in C, a green vertex u and a blue vertex t. Similarly, let v\u2032 be the purple vertex in H; it has two neighbours in H, the green vertex u\u2032 and the blue vertex t\u2032. The mapping f restricted to {t, u, v} is a bijection onto {t\u2032, u\u2032, v\u2032}. This is illustrated in the following figure: Similarly, we can check that the neighbourhood of a blue vertex in C is mapped one-to-one onto the neighbourhood of the blue vertex in H:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A profinite identity is a pair u and v of profinite words. A semigroup S is said to satisfy the profinite identity u = v if, for each semigroup morphism \u03d5: A + \u2192 S {\\displaystyle \\phi :A^{+}\\to S} , the equality \u03d5 ^ ( u ) = \u03d5 ^ ( v ) {\\displaystyle {\\hat {\\phi }}(u)={\\hat {\\phi }}(v)} holds. A variety of finite semigroups is the class of finite semigroups satisfying a set of profinite identities P. A variety of finite monoids is defined like a variety of finite semigroups, with the difference that one should consider monoid morphisms \u03d5: A \u2217 \u2192 M {\\displaystyle \\phi :A^{*}\\to M} instead of semigroup morphisms \u03d5: A + \u2192 M {\\displaystyle \\phi :A^{+}\\to M} . A variety of finite ordered semigroups/monoids is also given by a similar definition, with the difference that one should consider morphisms of ordered semigroups/monoids.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most countries have legal requirements that mandate electromagnetic compatibility: electronic and electrical hardware must still work correctly when subjected to certain amounts of EMI, and should not emit EMI, which could interfere with other equipment (such as radios). Radio frequency signal quality has declined throughout the 21st century by roughly one decibel per year as the spectrum becomes increasingly crowded. This has inflicted a Red Queen's race on the mobile phone industry as companies have been forced to put up more cellular towers (at new frequencies) that then cause more interference thereby requiring more investment by the providers and frequent upgrades of mobile phones to match.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This pattern of alternation ensures the resulting sums are all positive integers. Changing the rule so that either the odd- or even-indexed summands are given negative signs (regardless of the parity of n) changes the signs of the resulting sums but not their absolute values. Miodrag Zivkovi\u0107 proved in 1999 that there are only a finite number of alternating factorials that are also prime numbers, since 3612703 divides af(3612702) and therefore divides af(n) for all n \u2265 3612702. As of 2006, the known primes and probable primes are af(n) for (sequence A001272 in the OEIS) n = 3, 4, 5, 6, 7, 8, 10, 15, 19, 41, 59, 61, 105, 160, 661, 2653, 3069, 3943, 4053, 4998, 8275, 9158, 11164Only the values up to n = 661 have been proved prime in 2006. af(661) is approximately 7.818097272875 \u00d7 101578.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, a natural exponential family (NEF) is a class of probability distributions that is a special case of an exponential family (EF).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In shape analysis, skeleton (or topological skeleton) of a shape is a thin version of that shape that is equidistant to its boundaries. The skeleton usually emphasizes geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. Together with the distance of its points to the shape boundary, the skeleton can also serve as a representation of the shape (they contain all the information necessary to reconstruct the shape). Skeletons have several different mathematical definitions in the technical literature, and there are many different algorithms for computing them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the coupon collector's problem describes \"collect all coupons and win\" contests. It asks the following question: If each box of a brand of cereals contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought to collect all n coupons? An alternative statement is: Given n coupons, how many coupons do you expect you need to draw with replacement before having drawn each coupon at least once? The mathematical analysis of the problem reveals that the expected number of trials needed grows as \u0398 ( n log \u2061 ( n ) ) {\\displaystyle \\Theta (n\\log(n))} . For example, when n = 50 it takes about 225 trials on average to collect all 50 coupons.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, every vector v in three-dimensional space can be written uniquely as v x e x + v y e y + v z e z , {\\displaystyle v_{x}\\,\\mathbf {e} _{x}+v_{y}\\,\\mathbf {e} _{y}+v_{z}\\,\\mathbf {e} _{z},} the scalars v x {\\displaystyle v_{x}} , v y {\\displaystyle v_{y}} , v z {\\displaystyle v_{z}} being the scalar components of the vector v. In the n-dimensional Euclidean space R n {\\displaystyle \\mathbb {R} ^{n}} , the standard basis consists of n distinct vectors { e i: 1 \u2264 i \u2264 n } , {\\displaystyle \\{\\mathbf {e} _{i}:1\\leq i\\leq n\\},} where ei denotes the vector with a 1 in the ith coordinate and 0's elsewhere. Standard bases can be defined for other vector spaces, whose definition involves coefficients, such as polynomials and matrices. In both cases, the standard basis consists of the elements of the space such that all coefficients but one are 0 and the non-zero one is 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a symbol is any of many different generalizations of the Legendre symbol. This article describes the relations between these various generalizations. The symbols below are arranged roughly in order of the date they were introduced, which is usually (but not always) in order of increasing generality. Legendre symbol ( a p ) {\\displaystyle \\left({\\frac {a}{p}}\\right)} defined for p a prime, a an integer, and takes values 0, 1, or \u22121.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, aggregate data are data combined from several measurements. When data is aggregated, groups of observations are replaced with summary statistics based on those observations.In a data warehouse, the use of aggregate data dramatically reduces the time to query large sets of data. Developers pre-summarise queries that are regularly used, such as Weekly Sales across several dimensions for example by item hierarchy or geographical hierarchy. In economics, aggregate data or data aggregates are high-level data that are composed from a multitude or combination of other more individual data, such as: in macroeconomics, data such as the overall price level or overall inflation rate; and in microeconomics, data of an entire sector of an economy composed of many firms, or of all households in a city or region.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to provide performance guarantees to traffic flows it is necessary to specify some minimal performance of the server (depending on reservations in the network, or scheduling policy, etc.). Service curves provide a means of expressing resource availability. Several kinds of service curves exists, like weakly strict, variable capacity node, etc. See for an overview.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As an example, a bag of 100 real-world dice is a random probability mass function (random pmf)\u2014to sample this random pmf you put your hand in the bag and draw out a die, that is, you draw a pmf. A bag of dice manufactured using a crude process 100 years ago will likely have probabilities that deviate wildly from the uniform pmf, whereas a bag of state-of-the-art dice used by Las Vegas casinos may have barely perceptible imperfections. We can model the randomness of pmfs with the Dirichlet distribution.The Dirichlet process is specified by a base distribution H {\\displaystyle H} and a positive real number \u03b1 {\\displaystyle \\alpha } called the concentration parameter (also known as scaling parameter).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Even if testing is automated and tests effectively measure the level of business risk, teams without a coordinated end-to-end quality process tend to have trouble satisfying the business expectations within today's compressed delivery cycles. Trying to remove risks at the end of each iteration has been shown to be significantly slower and more resource-intensive than building quality into the product through defect prevention strategies such as development testing.Organizations adopt Continuous Testing because they recognize that these problems are preventing them from delivering quality software at the desired speed. They recognize the growing importance of software as well as the rising cost of software failure, and they are no longer willing to make a tradeoff between time, scope, and quality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A positive integer that has no square divisors except 1 is called square-free. For a non-negative integer n, the nth square number is n2, with 02 = 0 being the zeroth one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, if S and T intersect only in the identity, then every element of ST has a unique expression as a product st with s in S and t in T. If S and T also commute, then ST is a group, and is called a Zappa\u2013Sz\u00e9p product. Even further, if S or T is normal in ST, then ST coincides with the semidirect product of S and T. Finally, if both S and T are normal in ST, then ST coincides with the direct product of S and T. If S and T are subgroups whose intersection is the trivial subgroup (identity element) and additionally ST = G, then S is called a complement of T and vice versa. By a (locally unambiguous) abuse of terminology, two subgroups that intersect only on the (otherwise obligatory) identity are sometimes called disjoint.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a balanced matrix is a 0-1 matrix (a matrix where every entry is either zero or one) that does not contain any square submatrix of odd order having all row sums and all column sums equal to 2. Balanced matrices are studied in linear programming. The importance of balanced matrices comes from the fact that the solution to a linear programming problem is integral if its matrix of coefficients is balanced and its right hand side or its objective vector is an all-one vector. In particular, if one searches for an integral solution to a linear program of this kind, it is not necessary to explicitly solve an integer linear program, but it suffices to find an optimal vertex solution of the linear program itself. As an example, the following matrix is a balanced matrix:  {\\displaystyle {\\begin{bmatrix}1&1&1&1\\\\1&1&0&0\\\\1&0&1&0\\\\1&0&0&1\\\\\\end{bmatrix}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was described as a \"stunning advance\" in the citation for Wiles's Abel Prize award in 2016. It also proved much of the Taniyama\u2013Shimura conjecture, subsequently known as the modularity theorem, and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques. The unsolved problem stimulated the development of algebraic number theory in the 19th and 20th centuries. It is among the most notable theorems in the history of mathematics and prior to its proof was in the Guinness Book of World Records as the \"most difficult mathematical problem\", in part because the theorem has the largest number of unsuccessful proofs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In qualification rounds, teams are ranked by their Ranking Score, or their average number of Ranking Points (RP) per match. To ensure high placement, it is not only important to win matches, but to complete the secondary objectives as well, to amass as many Ranking Points as possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A recursive ordinal notation must satisfy the following two additional properties: the subset of natural numbers is a recursive set the induced well-ordering on the subset of natural numbers is a recursive relationThere are many such schemes of ordinal notations, including schemes by Wilhelm Ackermann, Heinz Bachmann, Wilfried Buchholz, Georg Cantor, Solomon Feferman, Gerhard J\u00e4ger, Isles, Pfeiffer, Wolfram Pohlers, Kurt Sch\u00fctte, Gaisi Takeuti (called ordinal diagrams), Oswald Veblen. Stephen Cole Kleene has a system of notations, called Kleene's O, which includes ordinal notations but it is not as well behaved as the other systems described here. Usually one proceeds by defining several functions from ordinals to ordinals and representing each such function by a symbol.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A typical assessment includes identifying the extent of the project area, evaluating existing uses, documenting amenities and characteristics such as habitats, species, public access, development, and considering impact of future desired use. If the team decides the site is fit to implement soft engineering, a complex process is designed in order to achieve the predetermined goals of the development and complete with objectives. Standards and targets must then be created to measure project development and progress.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, if vertex v has d(v) edges touching it (representing a person who has d(v) friends), then the average number \u03bc of friends of a random person in the graph is \u03bc = \u2211 v \u2208 V d ( v ) | V | = 2 | E | | V | . {\\displaystyle \\mu ={\\frac {\\sum _{v\\in V}d(v)}{|V|}}={\\frac {2|E|}{|V|}}.} The average number of friends that a typical friend has can be modeled by choosing a random person (who has at least one friend), and then calculating how many friends their friends have on average.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, smoothness of a density function is a measure which determines how many times the density function can be differentiated, or equivalently the limiting behavior of distribution\u2019s characteristic function. Formally, we call the distribution of a random variable X ordinary smooth of order \u03b2 if its characteristic function satisfies d 0 | t | \u2212 \u03b2 \u2264 | \u03c6 X ( t ) | \u2264 d 1 | t | \u2212 \u03b2 as t \u2192 \u221e {\\displaystyle d_{0}|t|^{-\\beta }\\leq |\\varphi _{X}(t)|\\leq d_{1}|t|^{-\\beta }\\quad {\\text{as }}t\\to \\infty } for some positive constants d0, d1, \u03b2. The examples of such distributions are gamma, exponential, uniform, etc. The distribution is called supersmooth of order \u03b2 if its characteristic function satisfies d 0 | t | \u03b2 0 exp \u2061 ( \u2212 | t | \u03b2 / \u03b3 ) \u2264 | \u03c6 X ( t ) | \u2264 d 1 | t | \u03b2 1 exp \u2061 ( \u2212 | t | \u03b2 / \u03b3 ) as t \u2192 \u221e {\\displaystyle d_{0}|t|^{\\beta _{0}}\\exp {\\big (}-|t|^{\\beta }/\\gamma {\\big )}\\leq |\\varphi _{X}(t)|\\leq d_{1}|t|^{\\beta _{1}}\\exp {\\big (}-|t|^{\\beta }/\\gamma {\\big )}\\quad {\\text{as }}t\\to \\infty } for some positive constants d0, d1, \u03b2, \u03b3 and constants \u03b20, \u03b21. Such supersmooth distributions have derivatives of all orders. Examples: normal, Cauchy, mixture normal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multitasking operating systems, processes (running programs) need a way to create new processes, e.g. to run other programs. Fork and its variants are typically the only way of doing so in Unix-like systems. For a process to start the execution of a different program, it first forks to create a copy of itself. Then, the copy, called the \"child process\", calls the exec system call to overlay itself with the other program: it ceases execution of its former program in favor of the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert (1895) as a generalization of Cayley's formula for the distance in the Cayley\u2013Klein model of hyperbolic geometry, where the convex set is the n-dimensional open unit ball. Hilbert's metric has been applied to Perron\u2013Frobenius theory and to constructing Gromov hyperbolic spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements. The relation of two fields is expressed by the notion of a field extension. Galois theory, initiated by \u00c9variste Galois in the 1830s, is devoted to understanding the symmetries of field extensions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, due to growing computational power, which allows for training in large ensemble learning in a reasonable time frame, the number of ensemble learning applications has grown increasingly. Some of the applications of ensemble classifiers include:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates allow the primality of a number to be rapidly checked without having to run an expensive or unreliable primality test. \"Succinct\" usually means that the proof should be at most polynomially larger than the number of digits in the number itself (for example, if the number has b bits, the proof might contain roughly b2 bits). Primality certificates lead directly to proofs that problems such as primality testing and the complement of integer factorization lie in NP, the class of problems verifiable in polynomial time given a solution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using these preliminaries, it is possible to investigate the effect of sample size on the standard errors of the mean and median. The observed mean is 3.16, the observed raw median is 3 and the observed interpolated median is 3.174. The following table gives some comparison statistics. The expected value of the median falls slightly as sample size increases while, as would be expected, the standard errors of both the median and the mean are proportionate to the inverse square root of the sample size. The asymptotic approximation errs on the side of caution by overestimating the standard error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They describe precisely all recursively enumerable languages, which makes parsing impossible in general: it is an undecidable problem to decide whether a given string can be generated by a given W-grammar. Hence, their use must be seriously constrained when used for automatic parsing or translation. Restricted and modified variants of W-grammars were developed to address this, e.g. Extended Affix Grammars (EAGs), applied to describe the grammars of natural language such as English and Spanish); Q-systems, also applied to natural language processing; the CDL series of languages, applied as compiler construction languages for programming languages.After the 1970s, interest in the approach waned; occasionally, new studies are published.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In radiology and nuclear medicine applications, the practice of dictating and transcribing (or using speech recognition) is well entrenched and the output of these is typically unstructured or minimally structured prose, encoded as plain text and distributed by fax or HL7 version 2 messages or some equally primitive mechanism. The persistent form of these \"documents\" is not well-standardized, but many customers expect a VNA to be able to accept them in whatever local format is preferred. The same principles apply as for the storage of any non-DICOM content, including the use of HL7 version 2 messages or XDS to provide metadata in lieu of a structured \"header\", such as in the case of reports rendered as PDF, when they have not been encapsulated in DICOM or CDA objects. Now that HL7 has promised to relax its previously closed IP policy, including offering CDA free for use, it is possible that CDA will become the preferred form of encoding, but VNAs will still need to accept (and possibly transcode) reports in a plethora of form from the installed base. DICOM defines templates for the encoding of human-generated reports as DICOM Structured Report (SR) objects, and IHE specifies these in the Simple Image and Numeric Report (SINR) profile.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, predicative adjectives and copular complements receive a form of person agreement that is distinct from that used on ordinary predicative verbs. Although that is a form of conjugation in that it refers back to the person of the subject, it is not \"verbal\" because it always derives from pronouns that have become clitic to the nouns to which they refer. An example of nonverbal person agreement, along with contrasting verbal conjugation, can be found from Beja (person agreement affixes in bold): wun.tu.wi, \u201cyou (fem.) are big\u201d had\u00e1.b.wa, \u201cyou (masc.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is still used in some areas.The second Egyptian multiplication and division technique was known from the hieratic Moscow and Rhind Mathematical Papyri written in the seventeenth century B.C. by the scribe Ahmes.Although in ancient Egypt the concept of base 2 did not exist, the algorithm is essentially the same algorithm as long multiplication after the multiplier and multiplicand are converted to binary. The method as interpreted by conversion to binary is therefore still in wide use today as implemented by binary multiplier circuits in modern computer processors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Load balancing the servers that host the desktops. Managing desktop images. Redirecting multimedia processing to the client. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The UK national variant of ISO 646 was standardised as BS 4730 in 1985. This code was identical to ASCII except for two characters: x23 encoded \u00a3 instead of #, while x7E encoded \u203e (overline) instead of ~ (tilde). MS-DOS on the IBM PC originally used a proprietary 8-bit character set Code page 437 in which the \u00a3 symbol was encoded as x9C; adoption of the ISO/IEC 8859-1 (\"ISO Latin-1\") standard code xA3 only came later with Microsoft Windows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Cram\u00e9r's conjecture, formulated by the Swedish mathematician Harald Cram\u00e9r in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be. It states that p n + 1 \u2212 p n = O ( ( log \u2061 p n ) 2 ) , {\\displaystyle p_{n+1}-p_{n}=O((\\log p_{n})^{2}),\\ } where pn denotes the nth prime number, O is big O notation, and \"log\" is the natural logarithm. While this is the statement explicitly conjectured by Cram\u00e9r, his heuristic actually supports the stronger statement lim sup n \u2192 \u221e p n + 1 \u2212 p n ( log \u2061 p n ) 2 = 1 , {\\displaystyle \\limsup _{n\\rightarrow \\infty }{\\frac {p_{n+1}-p_{n}}{(\\log p_{n})^{2}}}=1,} and sometimes this formulation is called Cram\u00e9r's conjecture. However, this stronger version is not supported by more accurate heuristic models, which nevertheless support the first version of Cram\u00e9r's conjecture. Neither form has yet been proven or disproven.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an automatic semigroup is a finitely generated semigroup equipped with several regular languages over an alphabet representing a generating set. One of these languages determines \"canonical forms\" for the elements of the semigroup, the other languages determine if two canonical forms represent elements that differ by multiplication by a generator. Formally, let S {\\displaystyle S} be a semigroup and A {\\displaystyle A} be a finite set of generators. Then an automatic structure for S {\\displaystyle S} with respect to A {\\displaystyle A} consists of a regular language L {\\displaystyle L} over A {\\displaystyle A} such that every element of S {\\displaystyle S} has at least one representative in L {\\displaystyle L} and such that for each a \u2208 A \u222a { \u03b5 } {\\displaystyle a\\in A\\cup \\{\\varepsilon \\}} , the relation consisting of pairs ( u , v ) {\\displaystyle (u,v)} with u a = v {\\displaystyle ua=v} is regular, viewed as a subset of (A# \u00d7 A#)*. Here A# is A augmented with a padding symbol.The concept of an automatic semigroup was generalized from automatic groups by Campbell et al. (2001) Unlike automatic groups (see Epstein et al. 1992), a semigroup may have an automatic structure with respect to one generating set, but not with respect to another. However, if an automatic semigroup has an identity, then it has an automatic structure with respect to any generating set (Duncan et al. 1999).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example shown below, a group that initially contains members {A,B,C} is asked to add {D,E,F}, but member C fails during the protocol. Membership change requests are treated as a special kind of multicast and the sequence of events is the same. The example is thus nearly identical to the prior one, but now a series of new view events are delivered to the application. (Quorum size = 2, view1={A,B,C}) Member Leader Members Application Layer A A B C D E F A B C D E F | | | | | | | | | | | X-------->| | | | | | | | | | Request(\"add D,E,F\") | X--------->|->|->| | | | | | | Propose(1.1: \"add D,E,F\") | | | | * | | * | | | !!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode: algorithm Halton-Sequence is inputs: index i {\\displaystyle i} base b {\\displaystyle b} output: result r {\\displaystyle r} f \u2190 1 {\\displaystyle f\\leftarrow 1} r \u2190 0 {\\displaystyle r\\leftarrow 0} while i > 0 {\\displaystyle i>0} do f \u2190 f / b {\\displaystyle f\\leftarrow f/b} r \u2190 r + f \u2217 ( i mod \u2061 b ) {\\displaystyle r\\leftarrow r+f*(i\\operatorname {mod} b)} i \u2190 \u230a i / b \u230b {\\displaystyle i\\leftarrow \\lfloor i/b\\rfloor } return r {\\displaystyle r} An alternative implementation that produces subsequent numbers of a Halton sequence for base b is given in the following generator function (in Python). This algorithm uses only integer numbers internally, which makes it robust against round-off errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the called subroutine, the first code executed is usually termed the subroutine prologue, since it does the necessary housekeeping before the code for the statements of the routine is begun. For instruction set architectures in which the instruction used to call a subroutine puts the return address into a register, rather than pushing it onto the stack, the prologue will commonly save the return address by pushing the value onto the call stack, although if the called subroutine does not call any other routines it may leave the value in the register. Similarly, the current stack pointer and/or frame pointer values may be pushed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Variables often store simple data, like integers and literal strings, but some programming languages allow a variable to store values of other datatypes as well. Such languages may also enable functions to be parametric polymorphic. These functions operate like variables to represent data of multiple types. For example, a function named length may determine the length of a list. Such a length function may be parametric polymorphic by including a type variable in its type signature, since the number of elements in the list is independent of the elements' types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The following theorems will aim to find the remaining nine axioms of standard PC within the \"theorem-space\" of Frege's PC, showing that the theory of standard PC is contained within the theory of Frege's PC. (A theory, also called here, for figurative purposes, a \"theorem-space\", is a set of theorems that are a subset of a universal set of well-formed formulas. The theorems are linked to each other in a directed manner by inference rules, forming a sort of dendritic network. At the roots of the theorem-space are found the axioms, which \"generate\" the theorem-space much like a generating set generates a group.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fixed telephone network, a node may be a public or private telephone exchange, a remote concentrator or a computer providing some intelligent network service. In cellular communication, switching points and databases such as the base station controller, home location register, gateway GPRS Support Node (GGSN) and serving GPRS support node (SGSN) are examples of nodes. Cellular network base stations are not considered to be nodes in this context. In cable television systems (CATV), this term has assumed a broader context and is generally associated with a fiber optic node. This can be defined as those homes or businesses within a specific geographic area that are served from a common fiber optic receiver. A fiber optic node is generally described in terms of the number of \"homes passed\" that are served by that specific fiber node.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one academic model, mobile banking is defined as: Mobile Banking refers to provision and availment of banking- and financial services with the help of mobile telecommunication devices.The scope of offered services may include facilities to conduct bank and stock market transactions, to administer accounts and to access customised information.\" According to this model mobile banking can be said to consist of three inter-related concepts: Mobile accounting Mobile financial information servicesMost services in the categories designated accounting and brokerage are transaction-based. The non-transaction-based services of an informational nature are however essential for conducting transactions \u2013 for instance, balance inquiries might be needed before committing a money remittance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the course of studying the problem, Church and his student Stephen Kleene introduced the notion of \u03bb-definable functions, and they were able to prove that several large classes of functions frequently encountered in number theory were \u03bb-definable. The debate began when Church proposed to G\u00f6del that one should define the \"effectively computable\" functions as the \u03bb-definable functions. G\u00f6del, however, was not convinced and called the proposal \"thoroughly unsatisfactory\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, continuous operation is an operation in which certain components, such as nodes, facilities, circuits, or equipment, are in an operational state at all times. Continuous operation usually requires that there be fully redundant configuration, or at least a sufficient X out of Y degree of redundancy for compatible equipment, where X is the number of spare components and Y is the number of operational components. This article incorporates public domain material from Federal Standard 1037C. General Services Administration. (in support of MIL-STD-188).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Intersection, union, complementation, and containment of elements is expressed in U. Let V be the collection of n \u00d7 n matrices that have entries taken from U. Complementation of such a matrix is obtained by complementing each element. The intersection or union of two such matrices is obtained by applying the operation to entries of each pair of elements to obtain the corresponding matrix intersection or union. A matrix is contained in another if each entry of the first is contained in the corresponding entry of the second.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and are not applicable in the cases that are the exceptions to the rules. The traditional way of presenting a mathematical fallacy is to give an invalid step of deduction mixed in with valid steps, so that the meaning of fallacy is here slightly different from the logical fallacy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, this type of arrangement is needed for boat cruises that do not return to the departure city. In other cases, the traveller wishes to explore between two points and using alternative transport (e.g. buses, trains, ferries or flights on another ticket). For example, a traveller might fly from London to Bangkok, travel around Thailand by public transport and fly back home to London from Phuket. Another example would be a traveller flying from New York City to London, travelling around different countries in Europe by taking buses / trains or low-cost carrier flights, then returning from Vilnius.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Raju.) The third column contains ISO 15919 transliterations of the lines given in the second column. The digits encoded by the lines in second column are given in Arabic numerals in the fourth column.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, let G = (V, E) denote an undirected Graph with a set of vertices V and a set of edges E \u2286 V \u00d7 V. The set sizes are denoted by |V| = n and |E| = m. Additionally, if not noted otherwise, the metric space [0,1)d with the euclidean distance is considered, i.e. for any points x , y \u2208 [ 0 , 1 ) d {\\displaystyle x,y\\in [0,1)^{d}} the euclidean distance of x and y is defined as d ( x , y ) = | | x \u2212 y | | 2 = \u2211 i = 1 d ( x i \u2212 y i ) 2 {\\displaystyle d(x,y)=||x-y||_{2}={\\sqrt {\\sum _{i=1}^{d}(x_{i}-y_{i})^{2}}}} .A random geometric graph (RGG) is an undirected geometric graph with nodes randomly sampled from the uniform distribution of the underlying space [0,1)d. Two vertices p, q \u2208 V are connected if, and only if, their distance is less than a previously specified parameter r \u2208 (0,1), excluding any loops. Thus, the parameters r and n fully characterize a RGG.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in computational geometry, geometric nonrobustness is a problem wherein branching decisions in computational geometry algorithms are based on approximate numerical computations, leading to various forms of unreliability including ill-formed output and software failure through crashing or infinite loops. For instance, algorithms for problems like the construction of a convex hull rely on testing whether certain \"numerical predicates\" have values that are positive, negative, or zero. If an inexact floating-point computation causes a value that is near zero to have a different sign than its exact value, the resulting inconsistencies can propagate through the algorithm causing it to produce output that is far from the correct output, or even to crash. One method for avoiding this problem involves using integers rather than floating point numbers for all coordinates and other quantities represented by the algorithm, and determining the precision required for all calculations to avoid integer overflow conditions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(maximizing the weighted sum of covered elements). subject to \u2211 c ( S i ) \u22c5 x i \u2264 B {\\displaystyle \\sum {c(S_{i})\\cdot x_{i}}\\leq B} ; (the cost of the selected sets cannot exceed B {\\displaystyle B} ). \u2211 e j \u2208 S i x i \u2265 y j {\\displaystyle \\sum _{e_{j}\\in S_{i}}x_{i}\\geq y_{j}} ; (if y j > 0 {\\displaystyle y_{j}>0} then at least one set e j \u2208 S i {\\displaystyle e_{j}\\in S_{i}} is selected).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following C code, the value of zero is used to indicate a null pointer:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, two sequences of probability measures are said to be contiguous if asymptotically they share the same support. Thus the notion of contiguity extends the concept of absolute continuity to the sequences of measures. The concept was originally introduced by Le Cam (1960) as part of his foundational contribution to the development of asymptotic theory in mathematical statistics. He is best known for the general concepts of local asymptotic normality and contiguity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Clearly, summing the integers of a subset can be done in polynomial time, and the subset sum problem is therefore in NP. The above example can be generalized for any decision problem. Given any instance I of problem \u03a0 {\\displaystyle \\Pi } and witness W, if there exists a verifier V so that given the ordered pair (I, W) as input, V returns \"yes\" in polynomial time if the witness proves that the answer is \"yes\" or \"no\" in polynomial time otherwise, then \u03a0 {\\displaystyle \\Pi } is in NP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A minimum distance of 0.9 m should also be maintained between any two beds in a dormitory, bedroom, or cubicle. In case students are provided with a cubicle, then each student must be provided with a window and a floor area of 5.0 m2 at the least. A bedroom for a single student should be at least of the floor area of 6.0 m2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The minimum degree algorithm is derived from a method first proposed by Markowitz in 1959 for non-symmetric linear programming problems, which is loosely described as follows. At each step in Gaussian elimination row and column permutations are performed so as to minimize the number of off diagonal non-zeros in the pivot row and column. A symmetric version of Markowitz method was described by Tinney and Walker in 1967 and Rose later derived a graph theoretic version of the algorithm where the factorization is only simulated, and this was named the minimum degree algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) of a partially ordered set ( X , \u2264 ) {\\displaystyle (X,\\leq )} is a subset S \u2286 X {\\displaystyle S\\subseteq X} with the following property: if s is in S and if x in X is larger than s (that is, if s < x {\\displaystyle s", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Improvements in talkback and Presfax have made the BBC's usage of cue dots rare. The prevalence of digital television and the accompanying delays have made the use of cue dots to communicate with outside broadcast obsolete. Cue dots do have some other uses: presentation may be asked to \"flash your dots\" by an outside broadcast unit to confirm that their off-air check feed is correct, particularly when working regionally. The dots are also used during coverage of the Wimbledon tennis championships to warn other broadcasters that the BBC feed will be cutting to an interview intended for the UK audience only, so they should be ready to go to something else.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem. It involves finding solutions to the initial value problem for different initial conditions until one finds the solution that also satisfies the boundary conditions of the boundary value problem. In layman's terms, one \"shoots\" out trajectories in different directions from one boundary until one finds the trajectory that \"hits\" the other boundary condition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, there exist magmas that are commutative but not associative. A simple example of such a magma may be derived from the children's game of rock, paper, scissors. Such magmas give rise to non-associative algebras. A magma which is both commutative and associative is a commutative semigroup.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, new items also have the same problem. When new items are added to the system, they need to be rated by a substantial number of users before they could be recommended to users who have similar tastes to the ones who rated them. The new item problem does not affect content-based recommendations, because the recommendation of an item is based on its discrete set of descriptive qualities rather than its ratings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scientific visualization a tensor glyph is an object that can visualize all or most of the nine degrees of freedom, such as acceleration, twist, or shear \u2013 of a 3 \u00d7 3 {\\displaystyle 3\\times 3} matrix. It is used for tensor field visualization, where a data-matrix is available at every point in the grid. \"Glyphs, or icons, depict multiple data values by mapping them onto the shape, size, orientation, and surface appearance of a base geometric primitive.\" Tensor glyphs are a particular case of multivariate data glyphs. There are certain types of glyphs that are commonly used: Ellipsoid Cuboid Cylindrical SuperquadricsAccording to Thomas Schultz and Gordon Kindlmann, specific types of tensor fields \"play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in particular linear algebra, the matrix determinant lemma computes the determinant of the sum of an invertible matrix A and the dyadic product, u vT, of a column vector u and a row vector vT.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of criminal law, there are a variety of conditions that will tend to negate elements of a crime (particularly the intent element), known as defenses. The label may be apt in jurisdictions where the accused may be assigned some burden before a tribunal. However, in many jurisdictions, the entire burden to prove a crime is on the prosecution, which also must prove the absence of these defenses, where implicated. In other words, in many jurisdictions the absence of these so-called defenses is treated as an element of the crime. So-called defenses may provide partial or total refuge from punishment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The individual is significant not in and of themselves, but rather in terms of their status, their position in patterns of social relations, and the behaviours associated with their status. Therefore, the social structure is the network of statuses connected by associated roles. Functionalism also has an anthropological basis in the work of theorists such as Marcel Mauss, Bronis\u0142aw Malinowski and Radcliffe-Brown.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in topology, a topological group G {\\displaystyle G} is said to have no small subgroup if there exists a neighborhood U {\\displaystyle U} of the identity that contains no nontrivial subgroup of G . {\\displaystyle G.} An abbreviation '\"NSS\"' is sometimes used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matroid theory, the closure of X is the largest superset of X that has the same rank as X. The transitive closure of a set. The algebraic closure of a field. The integral closure of an integral domain in a field that contains it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above model, the marginal likelihood of the observations (i.e. the joint distribution of the observations, with the prior parameter marginalized out) is a Dirichlet-multinomial distribution: p ( X \u2223 \u03b1 ) = \u222b p p ( X \u2223 p ) p ( p \u2223 \u03b1 ) d p = \u0393 ( \u2211 k \u03b1 k ) \u0393 ( N + \u2211 k \u03b1 k ) \u220f k = 1 K \u0393 ( c k + \u03b1 k ) \u0393 ( \u03b1 k ) {\\displaystyle {\\begin{aligned}p(\\mathbb {X} \\mid {\\boldsymbol {\\alpha }})&=\\int _{\\mathbf {p} }p(\\mathbb {X} \\mid \\mathbf {p} )p(\\mathbf {p} \\mid {\\boldsymbol {\\alpha }}){\\textrm {d}}\\mathbf {p} \\\\&={\\frac {\\Gamma \\left(\\sum _{k}\\alpha _{k}\\right)}{\\Gamma \\left(N+\\sum _{k}\\alpha _{k}\\right)}}\\prod _{k=1}^{K}{\\frac {\\Gamma (c_{k}+\\alpha _{k})}{\\Gamma (\\alpha _{k})}}\\end{aligned}}} This distribution plays an important role in hierarchical Bayesian models, because when doing inference over such models using methods such as Gibbs sampling or variational Bayes, Dirichlet prior distributions are often marginalized out. See the article on this distribution for more details.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Analysis of POCS and related methods attempt to show that the algorithm converges (and if so, find the rate of convergence), and whether it converges to the projection of the original point. These questions are largely known for simple cases, but a topic of active research for the extensions. There are also variants of the algorithm, such as Dykstra's projection algorithm. See the references in the further reading section for an overview of the variants, extensions and applications of the POCS method; a good historical background can be found in section III of.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field called image processing, the focus of attention is formed by the operations that take (at least) one picture (and potentially several secondary parameters that are not images) and relate it to another picture. With these operations, we can define algorithms for improving the quality of images (e.g., contrast reinforcement), and procedures for extracting certain parts of an image (e.g., edge finding) or for stamping out pictorial patterns following a particular Gestalt criterion (e.g., blue screen technique). Compression algorithms for the efficient storing or transmitting of pictorial data also belong into this field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Arranging the numbers ( n 0 ) , ( n 1 ) , \u2026 , ( n n ) {\\displaystyle {\\tbinom {n}{0}},{\\tbinom {n}{1}},\\ldots ,{\\tbinom {n}{n}}} in successive rows for n = 0 , 1 , 2 , \u2026 {\\displaystyle n=0,1,2,\\ldots } gives a triangular array called Pascal's triangle, satisfying the recurrence relation ( n k ) = ( n \u2212 1 k \u2212 1 ) + ( n \u2212 1 k ) . {\\displaystyle {\\binom {n}{k}}={\\binom {n-1}{k-1}}+{\\binom {n-1}{k}}.} The binomial coefficients occur in many areas of mathematics, and especially in combinatorics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular arithmetic, the integers coprime (relatively prime) to n from the set { 0 , 1 , \u2026 , n \u2212 1 } {\\displaystyle \\{0,1,\\dots ,n-1\\}} of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n. Hence another name is the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. Here units refers to elements with a multiplicative inverse, which, in this ring, are exactly those coprime to n. This quotient group, usually denoted ( Z / n Z ) \u00d7 {\\displaystyle (\\mathbb {Z} /n\\mathbb {Z} )^{\\times }} , is fundamental in number theory. It is used in cryptography, integer factorization, and primality testing. It is an abelian, finite group whose order is given by Euler's totient function: | ( Z / n Z ) \u00d7 | = \u03c6 ( n ) . {\\displaystyle |(\\mathbb {Z} /n\\mathbb {Z} )^{\\times }|=\\varphi (n).} For prime n the group is cyclic, and in general the structure is easy to describe, but no simple general formula for finding generators is known.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of bioinformatics, clustering is used for a number of applications. One use is as a pattern recognition technique to analyze gene expression data from RNA-sequencing data or other technologies. In this case, genes with similar expression patterns are grouped into the same cluster, and different clusters display distinct, well-separated patterns of expression. Use of clustering can provide insight into gene function and regulation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This assertion, which uses set-builder notation, means that if the elements satisfying the property P ( x ) {\\displaystyle P(x)} are the same as the elements satisfying Q ( x ) , {\\displaystyle Q(x),} then the two uses of the set-builder notation define the same set. This property is often expressed as \"two sets that have the same elements are equal.\" It is one of the usual axioms of set theory, called axiom of extensionality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In much of probability, especially when conditional expectation is involved, one is concerned with sets that represent only part of all the possible information that can be observed. This partial information can be characterized with a smaller \u03c3-algebra which is a subset of the principal \u03c3-algebra; it consists of the collection of subsets relevant only to and determined only by the partial information. A simple example suffices to illustrate this idea. Imagine you and another person are betting on a game that involves flipping a coin repeatedly and observing whether it comes up Heads ( H {\\displaystyle H} ) or Tails ( T {\\displaystyle T} ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, single-linkage clustering is one of several methods of hierarchical clustering. It is based on grouping clusters in bottom-up fashion (agglomerative clustering), at each step combining two clusters that contain the closest pair of elements not yet belonging to the same cluster as each other. This method tends to produce long thin clusters in which nearby elements of the same cluster have small distances, but elements at opposite ends of a cluster may be much farther from each other than two elements of other clusters. For some classes of data, this may lead to difficulties in defining classes that could usefully subdivide the data. However, it is popular in astronomy for analyzing galaxy clusters, which may often involve long strings of matter; in this application, it is also known as the friends-of-friends algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Often, the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown. In the case of two variables, each solution may be interpreted as the Cartesian coordinates of a point of the Euclidean plane. The solutions of a linear equation form a line in the Euclidean plane, and, conversely, every line can be viewed as the set of all solutions of a linear equation in two variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, the WMB maintains program order only among writes. The SPARC V9 RMO model provides a MEMBAR instruction which can be customised to order previous reads and writes with respect to future read and write operations. There is no need for using read-modify-writes to achieve this order because the MEMBAR instruction can be used to order a write with respect to a succeeding read.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(Roughly speaking, Girard found pure systems in which one can express the sentence \"the types form a type\".) Furthermore, all known examples of pure type systems that are not strongly normalizing are not even (weakly) normalizing: they contain expressions that do not have normal forms, just like the untyped lambda calculus. It is a major open problem in the field whether this is always the case, i.e. whether a (weakly) normalizing PTS always has the strong normalization property. This is known as the Barendregt\u2013Geuvers\u2013Klop conjecture (named after Henk Barendregt, Herman Geuvers, and Jan Willem Klop).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Kolmogorov's Three-Series Theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite series of random variables in terms of the convergence of three different series involving properties of their probability distributions. Kolmogorov's three-series theorem, combined with Kronecker's lemma, can be used to give a relatively easy proof of the Strong Law of Large Numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A wide variety of mathematical theories to understand and analyze message-passing systems are available, including the actor model, and various process calculi. Message passing can be efficiently implemented via symmetric multiprocessing, with or without shared memory cache coherence.Shared memory and message passing concurrency have different performance characteristics. Typically (although not always), the per-process memory overhead and task switching overhead is lower in a message passing system, but the overhead of message passing is greater than for a procedure call. These differences are often overwhelmed by other performance factors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past. For instance, a machine may have two states, A and E. When it is in state A, there is a 40% chance of it moving to state E and a 60% chance of it remaining in state A. When it is in state E, there is a 70% chance of it moving to A and a 30% chance of it staying in E. The sequence of states of the machine is a Markov chain. If we denote the chain by X 0 , X 1 , X 2 , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since the minimum Hamming weight of ( 7 , 4 , 3 ) {\\displaystyle (7,4,3)} Hamming Code is 3, d H ( x 1 , x 2 ) \u2265 3 {\\displaystyle d_{H}(\\mathbf {x_{1}} ,\\mathbf {x_{2}} )\\geq 3} . Therefore, the input x {\\displaystyle \\mathbf {x} } can be recovered since d H ( x , y ) \u2264 1 {\\displaystyle d_{H}(\\mathbf {x} ,\\mathbf {y} )\\leq 1} . Similarly, the bits distribution with R X = 7 {\\displaystyle R_{X}=7} , R Y = 3 {\\displaystyle R_{Y}=3} can be achieved by reversing the roles of X {\\displaystyle X} and Y {\\displaystyle Y} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A different ontology arises if we need to attend to the electrodynamics in the device: Here signals propagate at finite speed and an object (like a resistor) that was previously viewed as a single component with an I/O behavior may now have to be thought of as an extended medium through which an electromagnetic wave flows. Ontologies can of course be written down in a wide variety of languages and notations (e.g., logic, LISP, etc.); the essential information is not the form of that language but the content, i.e., the set of concepts offered as a way of thinking about the world. Simply put, the important part is notions like connections and components, not the choice between writing them as predicates or LISP constructs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "S = \u2205 , T = \u2205 S \u2260 \u2205 , T \u2260 \u2205 , S \u2282 T S = \u2205 , T \u2260 \u2205 S \u2260 \u2205 , T \u2260 \u2205 , T \u2282 S S \u2260 \u2205 , T = \u2205 S \u2260 \u2205 , T \u2260 \u2205 , T = S S \u2260 \u2205 , T \u2260 \u2205 , S \u2229 T = \u2205 S \u2260 \u2205 , T \u2260 \u2205 , S \u2229 T \u2260 \u2205 , \u00ac ( S \u2286 T ) , \u00ac ( T \u2286 S ) , S \u2260 T {\\displaystyle {\\begin{array}{l|l}S=\\emptyset ,T=\\emptyset &S\\neq \\emptyset ,T\\neq \\emptyset ,S\\subset T\\\\\\hline S=\\emptyset ,T\\neq \\emptyset &S\\neq \\emptyset ,T\\neq \\emptyset ,T\\subset S\\\\\\hline S\\neq \\emptyset ,T=\\emptyset &S\\neq \\emptyset ,T\\neq \\emptyset ,T=S\\\\\\hline S\\neq \\emptyset ,T\\neq \\emptyset ,S\\cap T=\\emptyset &S\\neq \\emptyset ,T\\neq \\emptyset ,S\\cap T\\neq \\emptyset ,\\lnot (S\\subseteq T),\\lnot (T\\subseteq S),S\\neq T\\end{array}}} As can be noticed, standard partitions might change according to how much testing the engineer wants to perform. Sub-domain Propagation (SDP). This tactic is applied to expressions containing: Two or more mathematical operators for which there are already defined standard partitions, or Mathematical operators which are defined in terms of other mathematical operators.In any of these cases, the standard partitions of the operators appearing in the expression or in the definition of a complex one, are combined to produce a partition for the expression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, most cities have zoning codes that set the minimum size for a housing unit (often 400 square feet) as well as the number of non-related persons who can live together in one unit.In June 2016, New York City got its first microapartment building, Carmel Place, with 55 units that are as small as 250 square feet (23 m2) and ceilings from nine to ten feet (2.7 to 3.0 m). Common's Williamsburg in Brooklyn rents single rooms where tenants share a kitchen for $2,050 per month; The Guardian states that \"ingle room occupancy housing is obviously not a new concept, however, the genius of late capitalism is that it has made it desirable\" to high-income renters\".In 2017, California passed a law that encourages development of \"efficiency units\" of at least 150 sq ft by disallowing localities from limiting their numbers near public universities and public transportation. : 1 In San Francisco, Starcity is converting unused parking garages, commercial spaces and offices into single room residential units, where tenants (tech professionals are the typical renter) get a furnished bedroom and access to wifi, janitor services and common kitchens and lounges for $1,400 to $2,400 per month, an approach that has been called \"dorm living for grown ups\".Boston's first microapartment building opened in August 2016, on Commonwealth Avenue in Packard's Corner. As the largest microapartment building in the United States, the building is currently being leased by Boston University to house 341 students during the renovation of another university residence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In percolation theory one examines a finite or infinite graph and removes edges (or links) randomly. Thus the Erd\u0151s\u2013R\u00e9nyi process is in fact unweighted link percolation on the complete graph. (One refers to percolation in which nodes and/or links are removed with heterogeneous weights as weighted percolation). As percolation theory has much of its roots in physics, much of the research done was on the lattices in Euclidean spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that this implies that p {\\displaystyle p} is contained in \u03b2 {\\displaystyle \\beta } and \u03b3 {\\displaystyle \\gamma } (with opposite polarity) and q {\\displaystyle q} is contained in \u03b4 {\\displaystyle \\delta } and \u03b1 {\\displaystyle \\alpha } (also with opposite polarity). The table below shows the rewriting rules proposed by Simone et al.. The idea of the algorithm is to reduce proof size by opportunistically applying these rules. The first five rules were introduced in an earlier paper.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology. A splicing language is a language generated by iterated application of a splicing rule: the splicing languages form a proper subset of the regular languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of healthcare in the United States, a pre-existing condition is a medical condition that started before a person's health insurance went into effect. Before 2014, some insurance policies would not cover expenses due to pre-existing conditions. These exclusions by the insurance industry were meant to cope with adverse selection by potential customers. Such exclusions have been prohibited since January 1, 2014, by the Patient Protection and Affordable Care Act. According to the Kaiser Family Foundation, more than a quarter of adults below the age of 65 (approximately 52 million people) had pre-existing conditions in 2016.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fourth, the \"trialability\" of an innovation; that is, whether it can be tested without commitment for a period of time. An innovation that has an available trial period provides less uncertainty to the group member who will be trying it. Lastly, whether there are observable results with use of the innovation. The more positive and visible results, the higher the likelihood it gets adopted as a permanent idea for the group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, given a collection S of subsets of a set X, an exact hitting set X* is a subset of X such that each subset in S contains exactly one element in X*. One says that each subset in S is hit by exactly one element in X*. In computer science, the exact hitting set problem is a decision problem to find an exact hitting set or else determine none exists. The exact hitting set problem is an abstract exact cover problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The technique is also known as Wiener\u2013Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov. The theoretical basis for the method was developed by the French mathematician Georges Matheron based on the Master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the notion of cancellativity (or cancellability) is a generalization of the notion of invertibility. An element a in a magma (M, \u2217) has the left cancellation property (or is left-cancellative) if for all b and c in M, a \u2217 b = a \u2217 c always implies that b = c. An element a in a magma (M, \u2217) has the right cancellation property (or is right-cancellative) if for all b and c in M, b \u2217 a = c \u2217 a always implies that b = c. An element a in a magma (M, \u2217) has the two-sided cancellation property (or is cancellative) if it is both left- and right-cancellative. A magma (M, \u2217) has the left cancellation property (or is left-cancellative) if all a in the magma are left cancellative, and similar definitions apply for the right cancellative or two-sided cancellative properties. A left-invertible element is left-cancellative, and analogously for right and two-sided. If a\u207b\u00b9 is the inverse of a, then a \u2217 b = a \u2217 c implies a\u207b\u00b9 \u2217 a \u2217 b = a\u207b\u00b9 \u2217 a \u2217 c which implies b = c. For example, every quasigroup, and thus every group, is cancellative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, a sentence embedding refers to a numeric representation of a sentence in the form of a vector of real numbers which encodes meaningful semantic information.State of the art embeddings are based on the learned hidden layer representation of dedicated sentence transformer models. BERT pioneered an approach involving the use of a dedicated  token preprended to the beginning of each sentence inputted into the model; the final hidden state vector of this token encodes information about the sentence and can be fine-tuned for use in sentence classification tasks. In practice however, BERT's sentence embedding with the  token achieves poor performance, often worse than simply averaging non-contextual word embeddings. SBERT later achieved superior sentence embedding performance by fine tuning BERT's  token embeddings through the usage of a siamese neural network architecture on the SNLI dataset.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form x2 + bx + c = 0with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers. Common examples of quadratic integers are the square roots of rational integers, such as \u221a2, and the complex number i = \u221a\u22121, which generates the Gaussian integers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Adolescents and adults who know the rule are faster than those who do not. In the learning of a second language the correction of errors remains a controversial topic with many differing schools of thought. Throughout the last century much advancement has been made in research on the correction of students' errors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and group theory, the term multiplicative group refers to one of the following concepts: the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is (F \u2216 {0}, \u2022), where 0 refers to the zero element of F and the binary operation \u2022 is the field multiplication, the algebraic torus GL(1)..", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, reciprocity is a measure of the likelihood of vertices in a directed network to be mutually linked. Like the clustering coefficient, scale-free degree distribution, or community structure, reciprocity is a quantitative measure used to study complex networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Showing this with hundreds of pages of hand analysis, Appel and Haken concluded that no smallest counterexample exists because any must contain, yet do not contain, one of these 1,936 maps. This contradiction means there are no counterexamples at all and that the theorem is therefore true. Initially, their proof was not accepted by mathematicians at all because the computer-assisted proof was infeasible for a human to check by hand. However, the proof has since then gained wider acceptance, although doubts still remain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics parity can refer to the evenness or oddness of an integer, which, when written in its binary form, can be determined just by examining only its least significant bit. In information technology parity refers to the evenness or oddness, given any set of binary digits, of the number of those bits with value one. Because parity is determined by the state of every one of the bits, this property of parity\u2014being dependent upon all the bits and changing its value from even to odd parity if any one bit changes\u2014allows for its use in error detection and correction schemes. In telecommunications the parity referred to by some protocols is for error-detection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to achieve the highest level of privacy and protection when calculating and transmitting sensitive information, biometric tokenization leverages existing encryption algorithms, authentication protocols, as well as hardware trust zones. Combining some or all of these methods maximizes the level of protection needed to uphold the integrity of the process and security of data that could otherwise expose users to a breach of trust on a mass scale.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It must be sensitive to differences between MT systems and reliable in that MT systems that score similarly should be expected to perform similarly. Finally, the metric must be general, that is it should work with different text domains, in a wide range of scenarios and MT tasks. The aim of this subsection is to give an overview of the state of the art in automatic metrics for evaluating machine translation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "People interested in building a small home can encounter institutional \u201cdiscrimination\u201d when building codes require minimum size well above the size of a small home. Also, neighbors may be hostile because they fear negative impacts on their property values and have concerns about increased taxes.More broadly, these sentiments of \"othering\" homeless and unhoused persons have culminated into a broader movement of NIMBY-ism, or \"Not in My Backyard.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The use of this feature by programmers led to the Gate A20 compatibility issues in later CPU generations, where the linear address space was expanded past 20 bits. In 16-bit real mode, enabling applications to make use of multiple memory segments (in order to access more memory than available in any one 64K-segment) is quite complex, but was viewed as a necessary evil for all but the smallest tools (which could do with less memory). The root of the problem is that no appropriate address-arithmetic instructions suitable for flat addressing of the entire memory range are available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular arithmetic, the set of available numbers is restricted to a finite subset of the integers, and addition \"wraps around\" when reaching a certain value, called the modulus. For example, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory. The set of integers modulo 2 has just two elements; the addition operation it inherits is known in Boolean logic as the \"exclusive or\" function. A similar \"wrap around\" operation arises in geometry, where the sum of two angle measures is often taken to be their sum as real numbers modulo 2\u03c0. This amounts to an addition operation on the circle, which in turn generalizes to addition operations on many-dimensional tori.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other programming languages such as Pascal, indices may start at 1, so indexing in a block of memory can be changed to fit a start-at-1 addressing scheme by a simple linear transformation \u2013 in this scheme, the memory location of the ith element with base address b and element size s is b + (i \u2212 1)s.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical classification, the Fisher kernel, named after Ronald Fisher, is a function that measures the similarity of two objects on the basis of sets of measurements for each object and a statistical model. In a classification procedure, the class for a new object (whose real class is unknown) can be estimated by minimising, across classes, an average of the Fisher kernel distance from the new object to each known member of the given class. The Fisher kernel was introduced in 1998. It combines the advantages of generative statistical models (like the hidden Markov model) and those of discriminative methods (like support vector machines): generative models can process data of variable length (adding or removing data is well-supported) discriminative methods can have flexible criteria and yield better results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Furthermore, the warranty of habitability generally cannot be disclaimed.Contractual language can also limit the remedies available for breach of an implied warranty such as by capping recoverable damages or limiting the legal remedy to a replacement of a defective item. However, such a term can be found to be unconscionable. For example, if a defective product causes a personal injury, a contractual provision limiting recovery in such a case will be deemed prima facie unconscionable. UCC \u00a7 2-719(3)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model checking, a field of computer science, a difference bound matrix (DBM) is a data structure used to represent some convex polytopes called zones. This structure can be used to efficiently implement some geometrical operations over zones, such as testing emptyness, inclusion, equality, and computing the intersection and the sum of two zones. It is, for example, used in the Uppaal model checker; where it is also distributed as an independent library.More precisely, there is a notion of canonical DBM; there is a one-to-one relation between canonical DBMs and zones and from each DBM a canonical equivalent DBM can be efficiently computed. Thus, equality of zone can be tested by checking for equality of canonical DBMs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, events E1, E2, ..., En are said to be mutually exclusive if the occurrence of any one of them implies the non-occurrence of the remaining n \u2212 1 events. Therefore, two mutually exclusive events cannot both occur. Formally said, the intersection of each two of them is empty (the null event): A \u2229 B = \u2205.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , n + 1 , {\\displaystyle v_{k}=\\mathrm {constant} \\ \\forall \\ k=0,...,n+1,} and this corresponds to eigenvalue 0 {\\displaystyle 0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\u0939\u094b\u0928\u093e \u06c1\u0648\u0646\u0627 (hon\u0101) is the only verb in Hindi-Urdu to have the present indicative, imperfect indicative, presumptive mood and the present subjunctive conjugations, and all the other verbs in Hindi-Urdu lack them.The verb \u0939\u094b\u0928\u093e / \u06c1\u0648\u0646\u0627 (hon\u0101) can be translated as \"to be\", \"to exist\", \"to happen\" or \"to have\" depending on the context, and when used in the third person it could also be translated as \"there is/are\". Many verbs conjugations in Hindi-Urdu are derived from participles and hence are gendered and numbered, and they agree with either the object or the subject of the sentence depending on the grammatical case of the subject of the sentence. When the subject is in the ergative or the dative case (see\u02d0 dative construction & quirky subject) the verb agrees in gender and number with the object of the sentence and with the subject when the subject is in the nominative case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above no-tyranny scenario, suppose no floor federation, but (only) a room with some local governance. Suppose that the gym room is not used by all, but there is a \"community\" of regulars, there is a grouping of voters by its activity as speed-cyclists (illustrated as spiked hair), that have the gym room key for some activities on Sundays. They are acting collectively to preserve the gym room for a local cyclists group. In this situation the following facts hold: There is a subset of voters and some collective action, uniting them, making them a cohesive group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a speech signal, inputs are spectral coefficients over time. In order to learn critical acoustic-phonetic features (for example formant transitions, bursts, frication, etc.) without first requiring precise localization, the TDNN is trained time-shift-invariantly. Time-shift invariance is achieved through weight sharing across time during training: Time shifted copies of the TDNN are made over the input range (from left to right in Fig.1). Backpropagation is then performed from an overall classification target vector (see TDNN diagram, three phoneme class targets (/b/, /d/, /g/) are shown in the output layer), resulting in gradients that will generally vary for each of the time-shifted network copies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Haskell, there is no variable assignment; but operations similar to assignment (like assigning to a field of an array or a field of a mutable data structure) usually evaluate to the unit type, which is represented as (). This type has only one possible value, therefore containing no information. It is typically the type of an expression that is evaluated purely for its side effects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the matrix equation case in which A is a square matrix, eigenvalues \u03bb {\\displaystyle \\lambda } may be found by setting the determinant of the matrix equal to zero, i.e. finding where the matrix has no inverse. (Such a square matrix is said to be singular.) Finite matrices have only a finite number of eigenvalues/eigenvectors, whereas linear operators can have a countably infinite number of eigenvalues/eigenfunctions (in confined regions) or uncountably infinite (continuous) spectra of solutions, as in unbounded regions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alternatively, the elements of a free abelian group may be thought of as signed multisets containing finitely many elements of B {\\displaystyle B} , with the multiplicity of an element in the multiset equal to its coefficient in the formal sum. Another way to represent an element of a free abelian group is as a function from B {\\displaystyle B} to the integers with finitely many nonzero values; for this functional representation, the group operation is the pointwise addition of functions. Every set B {\\displaystyle B} has a free abelian group with B {\\displaystyle B} as its basis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Microsoft document \"Output Content Protection and Windows Vista\", it is claimed that: \"The security level achieved for typical video data is estimated to be approaching that of regular AES. This assertion is being tested by Intel putting its Cascaded Cipher out to the cryptography community to get their security assessment \u2014 that is, to see if they can break it.\" The security of the system requires that it is impossible to recover the currently active inner key from the output of the reduced round Serpent encrypted video stream. Furthermore, the security of this method is highly sensitive to the number of rounds used in Serpent, the mode of operation described in the patent application, and the number of times the inner key is reused.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such that a k \u2261 1 ( mod n ) {\\textstyle a^{k}\\ \\equiv \\ 1{\\pmod {n}}} .In other words, the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the integers modulo n. The order of a modulo n is sometimes written as ord n \u2061 ( a ) {\\displaystyle \\operatorname {ord} _{n}(a)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Dedekind psi function is the multiplicative function on the positive integers defined by \u03c8 ( n ) = n \u220f p | n ( 1 + 1 p ) , {\\displaystyle \\psi (n)=n\\prod _{p|n}\\left(1+{\\frac {1}{p}}\\right),} where the product is taken over all primes p {\\displaystyle p} dividing n . {\\displaystyle n.} (By convention, \u03c8 ( 1 ) {\\displaystyle \\psi (1)} , which is the empty product, has value 1.) The function was introduced by Richard Dedekind in connection with modular functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Feit\u2013Thompson conjecture is a conjecture in number theory, suggested by Walter Feit and John G. Thompson (1962). The conjecture states that there are no distinct prime numbers p and q such that p q \u2212 1 p \u2212 1 {\\displaystyle {\\frac {p^{q}-1}{p-1}}} divides q p \u2212 1 q \u2212 1 {\\displaystyle {\\frac {q^{p}-1}{q-1}}} .If the conjecture were true, it would greatly simplify the final chapter of the proof (Feit & Thompson 1963) of the Feit\u2013Thompson theorem that every finite group of odd order is solvable. A stronger conjecture that the two numbers are always coprime was disproved by Stephens (1971) with the counterexample p = 17 and q = 3313 with common factor 2pq + 1 = 112643. It is known that the conjecture is true for q = 3 (Le 2012). Informal probability arguments suggest that the \"expected\" number of counterexamples to the Feit\u2013Thompson conjecture is very close to 0, suggesting that the Feit\u2013Thompson conjecture is likely to be true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, in the United States, progress reports may be issued to track a student's performance in between report cards. They are typically issued at the midpoint of a grading period, (for example: 4\u00bd weeks into a nine-week grading period, or three weeks into a six-week grading period) and contain virtually the same information as the report card. These reports allow students and their parents to see if school performance is slipping and if intervention is required to bring up the grade.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These logarithms are equally spaced along a vertical line in the complex plane. A complex-valued function log: U \u2192 C {\\displaystyle \\log \\colon U\\to \\mathbb {C} } , defined on some subset U {\\displaystyle U} of the set C \u2217 {\\displaystyle \\mathbb {C} ^{*}} of nonzero complex numbers, satisfying e log \u2061 z = z {\\displaystyle e^{\\log z}=z} for all z {\\displaystyle z} in U {\\displaystyle U} . Such complex logarithm functions are analogous to the real logarithm function ln: R > 0 \u2192 R {\\displaystyle \\ln \\colon \\mathbb {R} _{>0}\\to \\mathbb {R} } , which is the inverse of the real exponential function and hence satisfies eln x = x for all positive real numbers x. Complex logarithm functions can be constructed by explicit formulas involving real-valued functions, by integration of 1 / z {\\displaystyle 1/z} , or by the process of analytic continuation.There is no continuous complex logarithm function defined on all of C \u2217 {\\displaystyle \\mathbb {C} ^{*}} . Ways of dealing with this include branches, the associated Riemann surface, and partial inverses of the complex exponential function. The principal value defines a particular complex logarithm function Log: C \u2217 \u2192 C {\\displaystyle \\operatorname {Log} \\colon \\mathbb {C} ^{*}\\to \\mathbb {C} } that is continuous except along the negative real axis; on the complex plane with the negative real numbers and 0 removed, it is the analytic continuation of the (real) natural logarithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 20th century, it was common for weather maps to be hand drawn. The symbols for cloud cover on these maps, like the modern symbols, were drawn inside the circle marking the position of the weather station making the measurements. Unlike the modern symbols, these ones consisted of straight lines only rather than filled in blocks which would have been less practical on a hand drawing. A reduced set of these symbols were used on teleprinters used for distributing weather information and warnings. These machines were 5-bit teleprinters using a modified version of the Baudot-Murray code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass-filtered signal at a sample rate below its Nyquist rate (twice the upper cutoff frequency), but is still able to reconstruct the signal. When one undersamples a bandpass signal, the samples are indistinguishable from the samples of a low-frequency alias of the high-frequency signal. Such sampling is also known as bandpass sampling, harmonic sampling, IF sampling, and direct IF-to-digital conversion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some situations, one can avoid using the transpose A \u22a4 {\\displaystyle A^{\\top }} , as proposed by Mikhail Lavrentyev. For example, if A {\\displaystyle A} is symmetric positive definite, i.e. A = A \u22a4 > 0 {\\displaystyle A=A^{\\top }>0} , so is its inverse A \u2212 1 {\\displaystyle A^{-1}} , which can thus be used to set up the weighted norm squared \u2016 x \u2016 P 2 = x \u22a4 A \u2212 1 x {\\displaystyle \\|x\\|_{P}^{2}=x^{\\top }A^{-1}x} in the generalized Tikhonov regularization, leading to minimizing \u2016 A x \u2212 b \u2016 A \u2212 1 2 + \u2016 x \u2212 x 0 \u2016 Q 2 {\\displaystyle \\|Ax-b\\|_{A^{-1}}^{2}+\\|x-x_{0}\\|_{Q}^{2}} or, equivalently up to a constant term, x \u22a4 ( A + Q ) x \u2212 2 x \u22a4 ( b + Q x 0 ) {\\displaystyle x^{\\top }(A+Q)x-2x^{\\top }(b+Qx_{0})} .This minimization problem has an optimal solution x \u2217 {\\displaystyle x^{*}} which can be written explicitly using the formula x \u2217 = ( A + Q ) \u2212 1 ( b + Q x 0 ) {\\displaystyle x^{*}=(A+Q)^{-1}(b+Qx_{0})} ,which is nothing but the solution of the generalized Tikhonov problem where A = A \u22a4 = P \u2212 1 . {\\displaystyle A=A^{\\top }=P^{-1}.} The Lavrentyev regularization, if applicable, is advantageous to the original Tikhonov regularization, since the Lavrentyev matrix A + Q {\\displaystyle A+Q} can be better conditioned, i.e., have a smaller condition number, compared to the Tikhonov matrix A \u22a4 A + \u0393 \u22a4 \u0393 . {\\displaystyle A^{\\top }A+\\Gamma ^{\\top }\\Gamma .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted to study of properties of the noncommutative rings, including the properties that apply also to commutative rings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the exploit, bidirectional characters are abused to visually reorder text in source code so that later execution occurs in a different order. Bidirectional characters can be inserted in areas of source code where string literals are allowed. This often applies to documentation, variables, or comments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Philippines, the Philippine Atmospheric, Geophysical and Astronomical Services Administration (PAGASA) branch of the Department of Science and Technology (DOST) issues general flood advisory (for non-telemetered river basins whenever there is a significant amount of rainfall recorded).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programming languages, the maximum size of the call stack is much less than the space available in the heap, and recursive algorithms tend to require more stack space than iterative algorithms. Consequently, these languages sometimes place a limit on the depth of recursion to avoid stack overflows; Python is one such language. Note the caveat below regarding the special case of tail recursion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Creating a measure or scale of the degree to which the concept applies (metrology). 18. Examining the distribution patterns or distributional frequency of (possibly different) uses of the concept (statistics).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some circumstances the natural key that uniquely identifies a tuple in a relation may be cumbersome to use for software development. For example, it may involve multiple columns or large text fields. In such cases, a surrogate key can be used instead as the primary key. In other situations there may be more than one candidate key for a relation, and no candidate key is obviously preferred.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The processors ran at 20 MHz in the integer units and 40 MHz for the FPUs, with the intention being to increase this to 50 MHz by the time it shipped. At about 12 Mflops peak per CU, the machine as a whole would deliver up to 1.5 Gflops, although due to the memory latencies this was typically closer to 250 Mflops. While this was fast for a CMOS machine processor of the time, it was hardly competitive for a supercomputer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s the chip design and fabrication process grew to the point where it was possible to build a commodity processor with every potential feature built into it. To improve performance, CPU designs started adding internal parallelism, becoming \"superscalar\". In any program there are instructions that work on unrelated data, so by adding more functional units these instructions can be run at the same time. A new portion of the CPU, the scheduler, looks for these independent instructions and feeds them into the units, taking their outputs and re-ordering them so externally it appears they ran in succession.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to use the above mentioned models efficiently, it is important to have a large amount of data. However, as users, we are stuck with limited data i.e. the original image. In order to compensate for these issues, we employ tricks such as random cropping. Random cropping refers to the act of randomly choosing certain sub images from the existing original image.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the shift operator. Formally, a Markov partition is used to provide a finite cover for the smooth system; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one covering set to another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\\displaystyle g(r)} in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle. If a given particle is taken to be at the origin O, and if \u03c1 = N / V {\\displaystyle \\rho =N/V} is the average number density of particles, then the local time-averaged density at a distance r {\\displaystyle r} from O is \u03c1 g ( r ) {\\displaystyle \\rho g(r)} . This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, issues may arise that complicate the process. In 1992, Christel and Kang identified problems that indicate the challenges for requirements elicitation: 'Problems of scope'. The boundary of the system is ill-defined or the customers/users specify unnecessary technical details that may confuse, rather than clarify, overall system objectives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a family F {\\displaystyle {\\mathcal {F}}} of sets is of finite character if for each A {\\displaystyle A} , A {\\displaystyle A} belongs to F {\\displaystyle {\\mathcal {F}}} if and only if every finite subset of A {\\displaystyle A} belongs to F {\\displaystyle {\\mathcal {F}}} . That is, For each A \u2208 F {\\displaystyle A\\in {\\mathcal {F}}} , every finite subset of A {\\displaystyle A} belongs to F {\\displaystyle {\\mathcal {F}}} . If every finite subset of a given set A {\\displaystyle A} belongs to F {\\displaystyle {\\mathcal {F}}} , then A {\\displaystyle A} belongs to F {\\displaystyle {\\mathcal {F}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In category theory, the empty semigroup is always admitted. It is the unique initial object of the category of semigroups. A semigroup with no elements is an inverse semigroup, since the necessary condition is vacuously satisfied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For constant k, this is in the same complexity class as the Lucas-Lehmer test. In practice however, the cost of doing many iterations and other differences leads to worse performance for Miller\u2013Rabin. The most efficient deterministic primality test for any n-digit number, the AKS primality test, requires \u00d5(n6) bit operations in its best known variant and is extremely slow even for relatively small values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and disciplines in which mathematics plays a major role, hand-waving refers to either absence of formal proof or methods that do not meet mathematical rigor. In practice, it often involves the use of unrepresentative examples, unjustified assumptions, key omissions and faulty logic, and while these may be useful in expository papers and seminar presentations, they ultimately fall short of the standard of proof needed to establish a result. The mathematical profession tends to be receptive to informed critiques from any listener, and a claimant to a new result is expected to be able to answer any such question with a logical argument, up to a full proof. Should a speaker apparently fail to give such an answer, anyone in the audience who can supply the needed demonstration may sometimes upstage the speaker.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and economics, a corner solution is a special solution to an agent's maximization problem in which the quantity of one of the arguments in the maximized function is zero. In non-technical terms, a corner solution is when the chooser is either unwilling or unable to make a trade-off between goods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational grammar, constituents that serve as the arguments to predicates are numbered in what is called the grammatical relations (GR) hierarchy. This numbering system corresponds loosely to the notions of subject, direct object and indirect object. The numbering scheme is subject \u2192 (1), direct object \u2192 (2) and indirect object \u2192 (3).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, many screens that almost comply with part F of the standard deviate in various minor ways, and most brands of compliant brackets are designed to handle these deviations with little or no trouble for the end user: Non-square patterns, such as 600 \u00d7 200 mm and 600 x 400 mm and 800 \u00d7 400 mm. These were apparently permitted by the version 1 (2002) standard. : vii\u2013viii The labeling for these may have been \"MIS-F, width, height\" e.g. \"MIS-F, 600, 200\" for 600 \u00d7 200 mm. A somewhat strange pattern of 280 \u00d7 150 mm. Various protrusions on the screen extending a few millimeters further back than the mounting surfaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(Fuzzy extractors convert biometric data into secret, uniformly random, and reliably reproducible random strings.) These techniques can also have other broader applications for other type of noisy inputs such as approximative data from human memory, images used as passwords, and keys from quantum channels. Fuzzy extractors also have applications in the proof of impossibility of the strong notions of privacy with regard to statistical databases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares, such that n = a2 + b2 for some integers a, b. An integer greater than one can be written as a sum of two squares if and only if its prime decomposition contains no factor pk, where prime p \u2261 3 ( mod 4 ) {\\displaystyle p\\equiv 3{\\pmod {4}}} and k is odd. In writing a number as a sum of two squares, it is allowed for one of the squares to be zero, or for both of them to be equal to each other, so all squares and all doubles of squares are included in the numbers that can be represented in this way. This theorem supplements Fermat's theorem on sums of two squares which says when a prime number can be written as a sum of two squares, in that it also covers the case for composite numbers. A number may have multiple representations as a sum of two squares, counted by the sum of squares function; for instance, every Pythagorean triple a 2 + b 2 = c 2 {\\displaystyle a^{2}+b^{2}=c^{2}} gives a second representation for c 2 {\\displaystyle c^{2}} beyond the trivial representation c 2 + 0 2 {\\displaystyle c^{2}+0^{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bg2 Kd4 2. Kd2 Ke5 3. Ke3 Kf5 4.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When an individual algorithm is profiled, as with complexity analysis, memory and cache considerations are often more significant than instruction counts or clock cycles; however, the profiler's findings can be considered in light of how the algorithm accesses data rather than the number of instructions it uses.Profiling may provide intuitive insight into an algorithm's behavior by revealing performance findings as a visual representation. Performance profiling has been applied, for example, during the development of algorithms for matching wildcards. Early algorithms for matching wildcards, such as Rich Salz' wildmat algorithm, typically relied on recursion, a technique criticized on grounds of performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a fair coin is defined as a probability space ( \u03a9 , F , P ) {\\displaystyle (\\Omega ,{\\mathcal {F}},P)} , which is in turn defined by the sample space, event space, and probability measure. Using H {\\displaystyle H} for heads and T {\\displaystyle T} for tails, the sample space of a coin is defined as: The event space for a coin includes all sets of outcomes from the sample space which can be assigned a probability, which is the full power set 2 \u03a9 {\\displaystyle 2^{\\Omega }} . Thus, the event space is defined as: { } {\\displaystyle \\{\\}} is the event where neither outcome happens (which is impossible and can therefore be assigned 0 probability), and { H , T } {\\displaystyle \\{H,T\\}} is the event where either outcome happens, (which is guaranteed and can be assigned 1 probability). Because the coin is fair, the possibility of any single outcome is 50-50.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, infinitives may be marked for grammatical categories like voice, aspect, and to some extent tense. This may be done by inflection, as with the Latin perfect and passive infinitives, or by periphrasis (with the use of auxiliary verbs), as with the Latin future infinitives or the English perfect and progressive infinitives. Latin has present, perfect and future infinitives, with active and passive forms of each. For details see Latin conjugation \u00a7 Infinitives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A complete version of the theorem with a self-contained proof was given by M.W. Liebeck, Cheryl Praeger and Jan Saxl. The theorem is now a standard part of textbooks on permutation groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is signified by the 'always false' proposition, called the \"falsum\", denoted \"\u22a5\". Since the consequence is false, at least one of the antecedents must be false. Thus for example, ' A1, A2 \u22a2 ' means that at least one of the antecedents A1 and A2 must be false.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metaphysics, ontology is the philosophical study of being. It investigates what types of entities exist, how they are grouped into categories, and how they are related to one another on the most fundamental level. Ontologists often try to determine what the categories or highest kinds are and how they form a system of categories that encompasses the classification of all entities. Commonly proposed categories include substances, properties, relations, states of affairs, and events.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consequently, a four-pole generator could output twice the voltage of a two-pole generator, a six-pole generator could output three times the voltage of a two-pole, and so forth. This allows output voltage to increase without also increasing the rotational rate. In a multipolar generator, the armature and field magnets are surrounded by a circular frame or \"ring yoke\" to which the field magnets are attached. This has the advantages of strength, simplicity, symmetrical appearance, and minimum magnetic leakage, since the pole pieces have the least possible surface and the path of the magnetic flux is shorter than in a two-pole design.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first base 10 pandigital prime is 10123457689; OEIS: A050288 lists more. For different reasons, redundant digits are also required for a pandigital number (in any base except unary) to also be a palindromic number in that base. The smallest pandigital palindromic number in base 10 is 1023456789876543201.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The concepts of the conceptual model can be mapped into physical design or implementation constructs using either manual or automated code generation approaches. The realization of conceptual models of many domains can be combined to a coherent platform. A conceptual model can be described using various notations, such as UML, ORM or OMT for object modelling, ITE, or IDEF1X for Entity Relationship Modelling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, epi-convergence is a type of convergence for real-valued and extended real-valued functions. Epi-convergence is important because it is the appropriate notion of convergence with which to approximate minimization problems in the field of mathematical optimization. The symmetric notion of hypo-convergence is appropriate for maximization problems. Mosco convergence is a generalization of epi-convergence to infinite dimensional spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In system software, a job queue (a.k.a. batch queue, input queue), is a data structure maintained by job scheduler software containing jobs to run.Users submit their programs that they want executed, \"jobs\", to the queue for batch processing. The scheduler software maintains the queue as the pool of jobs available for it to run. Multiple batch queues might be used by the scheduler to differentiate types of jobs depending on parameters such as: job priority estimated execution time resource requirementsThe use of a batch queue gives these benefits: sharing of computer resources among many users time-shifts job processing to when the computer is less busy avoids idling the compute resources without minute-by-minute human supervision allows around-the-clock high utilization of expensive computing resourcesAny process that comes to the CPU should wait in a queue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Currently, Simmons' algorithm is the only approximation algorithm for envy-free cake-cutting with connected pieces. Simmons' algorithm is one of the few fair division algorithms which have been implemented and put online.One nice thing about the algorithm is that the queries it asks the partners are very simple: they just have to decide, in each partition, which piece they prefer. This is in contrast to other algorithm, which ask numerical queries such as \"cut a piece with a value of 1/3\" etc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of security engineering, an oracle attack is an attack that exploits the availability of a weakness in a system that can be used as an \"oracle\" to give a simple go/no go indication to inform attackers how close they are to their goals. The attacker can then combine the oracle with a systematic search of the problem space to complete their attack.The padding oracle attack, and compression oracle attacks such as BREACH, are examples of oracle attacks, as was the practice of \"crib-dragging\" in the cryptanalysis of the Enigma machine. An oracle need not be 100% accurate: even a small statistical correlation with the correct go/no go result can frequently be enough for a systematic automated attack.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Associativity is not the same as commutativity, which addresses whether the order of two operands affects the result. For example, the order does not matter in the multiplication of real numbers, that is, a \u00d7 b = b \u00d7 a, so we say that the multiplication of real numbers is a commutative operation. However, operations such as function composition and matrix multiplication are associative, but not (generally) commutative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In part one of the book, d'Alembert provides a general introduction to the origin of knowledge, which led to the works found in the Encyclop\u00e9die. He asserts that the \"existence of our senses\" is \"indisputable,\" and that these senses are thus the principle of all knowledge. He links this idea to a chain of thinking and reflection that eventually leads to the need to communicate, which sets another chain of events in effect. One of his arguments for the origin of communication is that it was necessary for people to protect themselves from the evils of the world and to benefit from each other's knowledge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Variables are available as if they are registers and some C expressions are allowed. ARM Compiler used to have a similar facility.The two families of extensions represent different understandings of division of labor in processing inline assembly. The GCC form preserves the overall syntax of the language and compartmentizes what the compiler needs to know: what is needed and what is changed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized. Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A Q\u2013Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewness are similar or different in the two distributions. Q\u2013Q plots can be used to compare collections of data, or theoretical distributions. The use of Q\u2013Q plots to compare two samples of data can be viewed as a non-parametric approach to comparing their underlying distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of mathematical logic and computer science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator. A kind system is essentially a simply typed lambda calculus \"one level up\", endowed with a primitive type, denoted \u2217 {\\displaystyle *} and called \"type\", which is the kind of any data type which does not need any type parameters. A kind is sometimes confusingly described as the \"type of a (data) type\", but it is actually more of an arity specifier. Syntactically, it is natural to consider polymorphic types to be type constructors, thus non-polymorphic types to be nullary type constructors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such a network of co-authorship is not unusual in narrowly defined areas of science. When allegations of plagiarism in this section were examined, Wegman said that material in it had been \"basically copied and pasted\" by a student who was the \"most knowledgeable\" person about such analyses on his team, as she had taken a one-week course on network analysis with Kathleen Carley of Carnegie Mellon University. Carley described the paper based on this section as \"more of an opinion piece\", lacking the data needed to support its argument. The paper based on this social network analysis, published by Wegman and his former student Said, reached the conclusion that eminent scientists ought not work together, and that the findings of studies would be less biased when a \"principal author tends to co-author papers with younger colleagues who were his students\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an explicit reciprocity law is a formula for the Hilbert symbol of a local field. The name \"explicit reciprocity law\" refers to the fact that the Hilbert symbols of local fields appear in Hilbert's reciprocity law for the power residue symbol. The definitions of the Hilbert symbol are usually rather roundabout and can be hard to use directly in explicit examples, and the explicit reciprocity laws give more explicit expressions for the Hilbert symbol that are sometimes easier to use. There are also several explicit reciprocity laws for various generalizations of the Hilbert symbol to higher local fields, p-divisible groups, and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In text retrieval, full-text search refers to techniques for searching a single computer-stored document or a collection in a full-text database. Full-text search is distinguished from searches based on metadata or on parts of the original texts represented in databases (such as titles, abstracts, selected sections, or bibliographical references). In a full-text search, a search engine examines all of the words in every stored document as it tries to match search criteria (for example, text specified by a user).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They must be able to notate and reference any problems they find in detailed reports, meet deadlines with assignments and have the skill level to complete the game titles on their most difficult settings. Most of the time the position of game tester is a highly stressful and competitive position with little pay yet is highly sought after for it serves as a doorway into the industry. Game testers are observant individuals and can spot minor defects in the game build. A common misconception is that all game testers enjoy alpha or beta version of the game and report occasionally found bugs. In contrast, game testing is highly focused on finding bugs using established and often tedious methodologies before alpha version.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Exponential-Logarithmic (EL) distribution is a family of lifetime distributions with decreasing failure rate, defined on the interval [0, \u221e). This distribution is parameterized by two parameters p \u2208 ( 0 , 1 ) {\\displaystyle p\\in (0,1)} and \u03b2 > 0 {\\displaystyle \\beta >0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the airline industry a major problem is the scheduling of the flight crews. The airline scheduling problem can be considered as an application of extended maximum network flow. The input of this problem is a set of flights F which contains the information about where and when each flight departs and arrives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli numbers. The first few regular odd primes are: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, ... (sequence A007703 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "n 3 ! \u22ef . {\\displaystyle {N \\choose n_{1}}{N-n_{1} \\choose n_{2}}{N-n_{1}-n_{2} \\choose n_{3}}\\cdots ={\\frac {N!}{(N-n_{1})!n_{1}!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic means, i.e., without quantified variables. PFL employs a small number of algebraic devices called predicate functors (or predicate modifiers) that operate on terms to yield terms. PFL is mostly the invention of the logician and philosopher Willard Quine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory, the call-by-push-value (CBPV) paradigm, inspired by monads, allows writing semantics for lambda-calculus without writing two variants to deal with the difference between call-by-name and call-by-value. To do so, CBPV introduces a term language that distinguishes computations and values, according to the slogan a value is, a computation does; this term language has a single evaluation order. However, to evaluate a lambda-calculus term according to either the call-by-name (CBN) or call-by-value (CBV) reduction strategy, one can translate the term to CBPV using a call-by-name or call-by-value translation strategy, which give rise to different terms. Evaluating the result of the call-by-value translation corresponds to evaluating the original term with the call-by-value strategy; evaluating the result of the call-by-name translation corresponds instead to evaluating the original term with the call-by-name strategy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, an information-bearer channel is one of: A communication channel capable of transmitting all the information required for communication, such as user data, synchronizing sequences, and control signals. The information-bearer channel may operate at a higher data rate than that required for user data alone. A basic communications channel with the necessary bandwidth but without enhanced or value-added services.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel algorithms, the list ranking problem involves determining the position, or rank, of each item in a linked list. That is, the first item in the list should be assigned the number 1, the second item in the list should be assigned the number 2, etc. Although it is straightforward to solve this problem efficiently on a sequential computer, by traversing the list in order, it is more complicated to solve in parallel. As Anderson & Miller (1990) wrote, the problem was viewed as important in the parallel algorithms community both for its many applications and because solving it led to many important ideas that could be applied in parallel algorithms more generally.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be \"simpler\". It is often used to obtain results for ill-posed problems or to prevent overfitting.Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem. These terms could be priors, penalties, or constraints. Explicit regularization is commonly employed with ill-posed optimization problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Information obtained from the Atkin primes permits a further improvement which is asymptotically negligible but can be quite important in practice. The modification of Schoof's algorithm to use Elkies and Atkin primes is known as the Schoof\u2013Elkies\u2013Atkin (SEA) algorithm. The status of a particular prime \u2113 {\\displaystyle \\ell } depends on the elliptic curve E / F q {\\displaystyle E/\\mathbb {F} _{q}} , and can be determined using the modular polynomial \u03a8 \u2113 ( X , Y ) {\\displaystyle \\Psi _{\\ell }(X,Y)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formally, satisfiability is studied with respect to a fixed logic defining the syntax of allowed symbols, such as first-order logic, second-order logic or propositional logic. Rather than being syntactic, however, satisfiability is a semantic property because it relates to the meaning of the symbols, for example, the meaning of + {\\displaystyle +} in a formula such as x + 1 = x {\\displaystyle x+1=x} . Formally, we define an interpretation (or model) to be an assignment of values to the variables and an assignment of meaning to all other non-logical symbols, and a formula is said to be satisfiable if there is some interpretation which makes it true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These numbers are equal to or slightly smaller than (n \u2308lg n\u2309 \u2212 2\u2308lg n\u2309 + 1), which is between (n lg n \u2212 n + 1) and (n lg n + n + O(lg n)). Merge sort's best case takes about half as many iterations as its worst case.For large n and a randomly ordered input list, merge sort's expected (average) number of comparisons approaches \u03b1\u00b7n fewer than the worst case, where \u03b1 = \u2212 1 + \u2211 k = 0 \u221e 1 2 k + 1 \u2248 0.2645. {\\displaystyle \\alpha =-1+\\sum _{k=0}^{\\infty }{\\frac {1}{2^{k}+1}}\\approx 0.2645.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, we have the following bound on the probability that the empirical measure p ^ x n {\\displaystyle {\\hat {p}}_{x^{n}}} of the samples falls within the set A: q n ( p ^ x n \u2208 A ) \u2264 ( n + 1 ) | X | 2 \u2212 n D K L ( p \u2217 | | q ) {\\displaystyle q^{n}({\\hat {p}}_{x^{n}}\\in A)\\leq (n+1)^{|X|}2^{-nD_{\\mathrm {KL} }(p^{*}||q)}} ,where q n {\\displaystyle q^{n}} is the joint probability distribution on X n {\\displaystyle X^{n}} , and p \u2217 {\\displaystyle p^{*}} is the information projection of q onto A.In words, the probability of drawing an atypical distribution is bounded by a function of the KL divergence from the true distribution to the atypical one; in the case that we consider a set of possible atypical distributions, there is a dominant atypical distribution, given by the information projection. Furthermore, if A is the closure of its interior, lim n \u2192 \u221e 1 n log \u2061 q n ( p ^ x n \u2208 A ) = \u2212 D K L ( p \u2217 | | q ) . {\\displaystyle \\lim _{n\\to \\infty }{\\frac {1}{n}}\\log q^{n}({\\hat {p}}_{x^{n}}\\in A)=-D_{\\mathrm {KL} }(p^{*}||q).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The algorithm stops when it finds the minimum, determined when no progress is made after a direction reset (i.e. in the steepest descent direction), or when some tolerance criterion is reached. Within a linear approximation, the parameters \u03b1 {\\displaystyle \\displaystyle \\alpha } and \u03b2 {\\displaystyle \\displaystyle \\beta } are the same as in the linear conjugate gradient method but have been obtained with line searches. The conjugate gradient method can follow narrow (ill-conditioned) valleys, where the steepest descent method slows down and follows a criss-cross pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead, the Java platform provides a comprehensive set of its own standard class libraries containing many of the same reusable functions commonly found in modern operating systems. Most of the system library is also written in Java. For instance, the Swing library paints the user interface and handles the events itself, eliminating many subtle differences between how different platforms handle components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software, a spell checker (or spelling checker or spell check) is a software feature that checks for misspellings in a text. Spell-checking features are often embedded in software or services, such as a word processor, email client, electronic dictionary, or search engine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming, in languages such as C++, and Object Pascal, a virtual function or virtual method is an inheritable and overridable function or method for which dynamic dispatch is facilitated. This concept is an important part of the (runtime) polymorphism portion of object-oriented programming (OOP). In short, a virtual function defines a target function to be executed, but the target might not be known at compile time. Most programming languages, such as JavaScript, PHP and Python, treat all methods as virtual by default and do not provide a modifier to change this behavior. However, some languages provide modifiers to prevent methods from being overridden by derived classes (such as the final and private keywords in Java and PHP).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "String?? = String? ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical physics, an invariant differential operator is a kind of mathematical map from some objects to an object of similar type. These objects are typically functions on R n {\\displaystyle \\mathbb {R} ^{n}} , functions on a manifold, vector valued functions, vector fields, or, more generally, sections of a vector bundle. In an invariant differential operator D {\\displaystyle D} , the term differential operator indicates that the value D f {\\displaystyle Df} of the map depends only on f ( x ) {\\displaystyle f(x)} and the derivatives of f {\\displaystyle f} in x {\\displaystyle x} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Rosser's theorem states that the n {\\displaystyle n} th prime number is greater than n log \u2061 n {\\displaystyle n\\log n} , where log {\\displaystyle \\log } is the natural logarithm function. It was published by J. Barkley Rosser in 1939.Its full statement is: Let p n {\\displaystyle p_{n}} be the n {\\displaystyle n} th prime number. Then for n \u2265 1 {\\displaystyle n\\geq 1} p n > n log \u2061 n . {\\displaystyle p_{n}>n\\log n.} In 1999, Pierre Dusart proved a tighter lower bound: p n > n ( log \u2061 n + log \u2061 log \u2061 n \u2212 1 ) . {\\displaystyle p_{n}>n(\\log n+\\log \\log n-1).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, there are many integer factoring algorithms that heuristically have expected running time L n  = e ( 1 + o ( 1 ) ) ( log \u2061 n ) ( log \u2061 log \u2061 n ) {\\displaystyle L_{n}\\left=e^{(1+o(1)){\\sqrt {(\\log n)(\\log \\log n)}}}} in little-o and L-notation. Some examples of those algorithms are the elliptic curve method and the quadratic sieve. Another such algorithm is the class group relations method proposed by Schnorr, Seysen, and Lenstra, which they proved only assuming the unproved Generalized Riemann Hypothesis (GRH).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Masking depends on the spectral composition of both masker and masking signal, and on other variations with time. The basic block diagram of a perceptual coding system is shown in the figure. The input signal is decomposed into subsampled spectral components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A PC cannot currently contain 4 pebibytes of memory (due to the physical size of the memory chips), but AMD envisioned large servers, shared memory clusters, and other uses of physical address space that might approach this in the foreseeable future. Thus the 52-bit physical address provides ample room for expansion while not incurring the cost of implementing full 64-bit physical addresses. Similarly, the 48-bit virtual address space was designed to provide 65,536 (216) times the 32-bit limit of 4 GiB (4 \u00d7 10243 bytes), allowing room for later expansion and incurring no overhead of translating full 64-bit addresses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This means that the code is always executed first and then the expression or test condition is evaluated. This process is repeated as long as the expression evaluates to true. If the expression is false the loop terminates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor. It is common to make the additional stipulation that the ordinary least squares (OLS) method should be used: the accuracy of each predicted value is measured by its squared residual (vertical distance between the point of the data set and the fitted line), and the goal is to make the sum of these squared deviations as small as possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of integers, subtraction of one also plays a special role: for any integer a, the integer (a \u2212 1) is the largest integer less than a, also known as the predecessor of a.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Its cumulant generating function (logarithm of the characteristic function) is the inverse of the cumulant generating function of a Gaussian random variable. To indicate that a random variable X is inverse Gaussian-distributed with mean \u03bc and shape parameter \u03bb we write X \u223c IG \u2061 ( \u03bc , \u03bb ) {\\displaystyle X\\sim \\operatorname {IG} (\\mu ,\\lambda )\\,\\!} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a sequence transformation is an operator acting on a given space of sequences (a sequence space). Sequence transformations include linear mappings such as convolution with another sequence, and resummation of a sequence and, more generally, are commonly used for series acceleration, that is, for improving the rate of convergence of a slowly convergent sequence or series. Sequence transformations are also commonly used to compute the antilimit of a divergent series numerically, and are used in conjunction with extrapolation methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Faster image ingest: it will take no more than a few seconds to transfer a high-resolution RAW file from a memory card vs many minutes to scan film with a high-quality scanner. Flash: using flash in images can provide a different look such as the lighting of the image. Higher image quantity: which enables longer photography sessions without changing film rolls.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the ordered subset expectation maximization (OSEM) method is an iterative method that is used in computed tomography. In applications in medical imaging, the OSEM method is used for positron emission tomography, for single photon emission computed tomography, and for X-ray computed tomography. The OSEM method is related to the expectation maximization (EM) method of statistics. The OSEM method is also related to methods of filtered back projection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle x=({\\textbf {A}}^{\\mathrm {T} }{\\textbf {A}})^{-1}{\\textbf {A}}^{\\mathrm {T} }\\phi .} Here the matrix A can be based on any set of functions mutually independent (not necessarily orthogonal) when evaluated at the sample times; functions used for spectral analysis are typically sines and cosines evenly distributed over the frequency range of interest.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "1149.1-1990 after many years of initial use. In the same year, Intel released their first processor with JTAG (the 80486) which led to quicker industry adoption by all manufacturers. In 1994, a supplement that contains a description of the boundary scan description language (BSDL) was added.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Interpersonal relations may be regulated by law, custom, or mutual agreement, and form the basis of social groups and societies. They appear when people communicate or act with each other within specific social contexts, and they thrive on equitable and reciprocal compromises.Interdisciplinary analysis of relationships draws heavily upon the other social sciences, including, but not limited to: anthropology, linguistics, sociology, economics, political science, communication, mathematics, social work, communication, and cultural studies. This scientific analysis had evolved during the 1990s and has become \"relationship science\", through the researches of Ellen Berscheid and Elaine Hatfield. This interdisciplinary science attempts to provide evidence-based conclusions through the use of data analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, Cook's distance or Cook's D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook's distance can be used in several ways: to indicate influential data points that are particularly worth checking for validity; or to indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics normal convergence is a type of convergence for series of functions. Like absolute-convergence, it has the useful property that it is preserved when the order of summation is changed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "k ! F ( v \u2212 1 ) i ( 1 \u2212 F ( v ) ) k f ( v ) N \u2212 i \u2212 k {\\displaystyle \\Pr(\\operatorname {Median} =v)=\\sum _{i=0}^{n}\\sum _{k=0}^{n}{\\frac {N!}{i!(N-i-k)!k! }}F(v-1)^{i}(1-F(v))^{k}f(v)^{N-i-k}} Here, i is the number of points strictly less than the median and k the number strictly greater.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The biggest disadvantage is that it fails to take advantage of coefficient matrix to be a sparse matrix. The LU decomposition of a sparse matrix is usually not sparse, thus, for a large system of equations, LU decomposition may require a prohibitive amount of memory and number of arithmetical operations. In the preconditioned iterative methods, if the preconditioner matrix M is a good approximation of coefficient matrix A then the convergence is faster.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most practical cases deterministic algorithms or randomized algorithms are discussed, although theoretical computer science also considers nondeterministic algorithms and other advanced models of computation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The latter two cases end in -ar or -ur and -ur or -r. Irregular but not a weak noun.Most neuters are strong, and end in -s in the genitive singular with the exception of f\u00e9, genitive fj\u00e1r. Although strong neuters technically only belong to one category, it is a diverse group, so about a dozen paradigms are necessary to account for varieties and exceptions. The weak neuters are so few, that a list suffices, to be found on the page for weak nouns.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If F \u2264 B {\\displaystyle {\\mathcal {F}}\\leq {\\mathcal {B}}} is a sigma subalgebra of B {\\displaystyle {\\mathcal {B}}} , then the conditional expectation E  {\\displaystyle E} is the orthogonal projection of X {\\displaystyle X} onto the subspace of L 2 ( \u03a9 , P ) {\\displaystyle L^{2}(\\Omega ,P)} consisting of the F {\\displaystyle {\\mathcal {F}}} -measurable functions. If the random variable X {\\displaystyle X} in L 2 ( \u03a9 , P ) {\\displaystyle L^{2}(\\Omega ,P)} is independent of the sigma algebra F {\\displaystyle {\\mathcal {F}}} then conditional expectation E ( X | F ) = E ( X ) {\\displaystyle E(X|{\\mathcal {F}})=E(X)} , i.e., its projection onto the F {\\displaystyle {\\mathcal {F}}} -measurable functions is constant. Equivalently, the projection of its centering is zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1987 article \"A Framework for Information Systems Architecture\" Zachman noted that the term \"architecture\" was used loosely by information systems professionals, and meant different things to planners, designers, programmers, communication specialists, and others. In searching for an objective, independent basis upon which to develop a framework for information systems architecture, Zachman looked at the field of classical architecture, and a variety of complex engineering projects in industry. He saw a similar approach and concluded that architectures exist on many levels and involves at least three perspectives: raw material or data, function of processes, and location or networks.The Information Systems Architecture is designed to be a classification schema for organizing architecture models. It provides a synoptic view of the models needed for enterprise architecture. Information Systems Architecture does not define in detail what the models should contain, it does not enforce the modeling language used for each model, and it does not propose a method for creating these models.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, numerous studies have confirmed that by stacking several shallow structures into a single deep structure, the overall system could achieve better data representation, and, thus, more effectively deal with nonlinear and high complexity tasks. In 2018, a deep CMAC (DCMAC) framework was proposed and a backpropagation algorithm was derived to estimate the DCMAC parameters. Experimental results of an adaptive noise cancellation task showed that the proposed DCMAC can achieve better noise cancellation performance when compared with that from the conventional single-layer CMAC.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Grimm's conjecture (named after Carl Albert Grimm, 1 April 1926 \u2013 2 January 2018) states that to each element of a set of consecutive composite numbers one can assign a distinct prime that divides it. It was first published in American Mathematical Monthly, 76(1969) 1126-1128.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, structured analysis (SA) and structured design (SD) are methods for analyzing business requirements and developing specifications for converting practices into computer programs, hardware configurations, and related manual procedures. Structured analysis and design techniques are fundamental tools of systems analysis. They developed from classical systems analysis of the 1960s and 1970s.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a Tsallis distribution is a probability distribution derived from the maximization of the Tsallis entropy under appropriate constraints. There are several different families of Tsallis distributions, yet different sources may reference an individual family as \"the Tsallis distribution\". The q-Gaussian is a generalization of the Gaussian in the same way that Tsallis entropy is a generalization of standard Boltzmann\u2013Gibbs entropy or Shannon entropy. Similarly, if the domain of the variable is constrained to be positive in the maximum entropy procedure, the q-exponential distribution is derived.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each processor was about 2.5 times as fast as a 7600, so with all four running the machine as a whole would be about 10 times as fast, at about 100 MFLOPS. The government made it clear that all future computer purchases would require ASCII processing. To meet this requirement, the 8600 used a 64-bit word (eight eight-bit characters) instead of the earlier 60-bit word (ten six-bit characters) used in the 6600 and 7600.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a freeze is a point in time in the development process after which the rules for making changes to the source code or related resources become more strict, or the period during which those rules are applied. A freeze helps move the project forward towards a release or the end of an iteration by reducing the scale or frequency of changes, and may be used to help meet a roadmap. The exact rules depend on the type of freeze and the particular development process in use; for example, they may include only allowing changes which fix bugs, or allowing changes only after thorough review by other members of the development team.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A functional form, often linear, is hypothesized for the postulated causal relationship, and the parameters of the function are estimated from the data\u2014that is, are chosen so as to optimize is some way the fit of the function, thus parameterized, to the data. That is the estimation step. For the prediction step, explanatory variable values that are deemed relevant to future (or current but not yet observed) values of the dependent variable are input to the parameterized function to generate predictions for the dependent variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the integer square root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal to the square root of n, For example, isqrt \u2061 ( 27 ) = \u230a 27 \u230b = \u230a 5.19615242270663... \u230b = 5. {\\displaystyle \\operatorname {isqrt} (27)=\\lfloor {\\sqrt {27}}\\rfloor =\\lfloor 5.19615242270663...\\rfloor =5.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical physics and disordered systems, the Max Cut problem is equivalent to minimizing the Hamiltonian of a spin glass model, most simply the Ising model. For the Ising model on a graph G and only nearest-neighbor interactions, the Hamiltonian is H  = \u2212 \u2211 i j \u2208 E ( G ) J i j s i s j {\\displaystyle H=-\\sum _{ij\\in E(G)}J_{ij}s_{i}s_{j}} Here each vertex i of the graph is a spin site that can take a spin value s i = \u00b1 1. {\\displaystyle s_{i}=\\pm 1.} A spin configuration partitions V ( G ) {\\displaystyle V(G)} into two sets, those with spin up V + {\\displaystyle V^{+}} and those with spin down V \u2212 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, the term 'proof of concept' often characterizes several distinct processes with different objectives and participant roles: vendor business roles may utilize a proof of concept to establish whether a system satisfies some aspect of the purpose it was designed for. Once a vendor is satisfied, a prototype is developed which is then used to seek funding or to demonstrate to prospective customers.The US General Services Administration has a checklist for defining an Agile software proof of concept, which includes clear definitions of the problem, pre-POC input required, and output criteria (including success criteria).The key benefits of the proof of concept in software development are: The possibility to choose the best technology stack for the software (application or web platform) A higher probability of investors' interest in the future software product The ability to simplify and improve the ease of testing and validating ideas for the software's functionality Receiving valuable feedback of a target audience (users) even before building a full-scope system Onboarding first clients before an official software releaseA 'steel thread' is technical proof of concept that touches all of the technologies in a solution. By contrast, a 'proof of technology' aims to determine the solution to some technical problem (such as how two systems might integrate) or to demonstrate that a given configuration can achieve a certain throughput. No business users need be involved in a proof of technology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that B = {0, 1}. Paul Halmos's name for this algebra \"2\" has some following in the literature, and will be employed here.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For Aristotle and Euclid, relations were conceived as whole numbers (Michell, 1993). John Wallis later conceived of ratios of magnitudes as real numbers: When a comparison in terms of ratio is made, the resultant ratio often  leaves the genus of quantities compared, and passes into the numerical genus, whatever the genus of quantities compared may have been. That is, the ratio of magnitudes of any quantity, whether volume, mass, heat and so on, is a number. Following this, Newton then defined number, and the relationship between quantity and number, in the following terms: By number we understand not so much a multitude of unities, as the abstracted ratio of any quantity to another quantity of the same kind, which we take for unity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "User input allows for the users to manipulate a system, and device's output allows the system to indicate the effects of the users' manipulation. Overall, mobile UI design's goal is mainly for an understandable, user-friendly interface. Functionality is supported by mobile enterprise application platforms or integrated development environments (IDEs).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of very old works, the author's name may simply be lost over the course of history and time. In such cases the author is often referred to as Anonymus, the Latin form of \"anonymous\". In other cases, the creator's name is intentionally kept secret.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "was a fairly full featured (for the time) spreadsheet developed for the Amiga. Organize! was a flat file database package.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spatial analysis, the Huff model is a widely used tool for predicting the probability of a consumer visiting a site, as a function of the distance of the site, its attractiveness, and the relative attractiveness of alternatives. It was formulated by David Huff in 1963. It is used in marketing, economics, retail research and urban planning, and is implemented in several commercially available GIS systems. Its relative ease of use and applicability to a wide range of problems contribute to its enduring appeal.The formula is given as: P i j = A j \u03b1 D i j \u2212 \u03b2 \u2211 k = 1 n A k \u03b1 D i k \u2212 \u03b2 {\\displaystyle P_{ij}={\\frac {A_{j}^{\\alpha }D_{ij}^{-\\beta }}{\\sum _{k=1}^{n}A_{k}^{\\alpha }D_{ik}^{-\\beta }}}} where: A j {\\displaystyle A_{j}} is a measure of attractiveness of store j D i j {\\displaystyle D_{ij}} is the distance from the consumer's location, i, to store j. \u03b1 {\\displaystyle \\alpha } is an attractiveness parameter \u03b2 {\\displaystyle \\beta } is a distance decay parameter n {\\displaystyle n} is the total number of stores, including store j == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The binary search tree may be any balanced binary search tree data structure, such as a red\u2013black tree; all that is required is that insertions, deletions, and searches take logarithmic time. Similarly, the priority queue may be a binary heap or any other logarithmic-time priority queue; more sophisticated priority queues such as a Fibonacci heap are not necessary. Note that the space complexity of the priority queue depends on the data structure used to implement it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For distributing revocation information to clients, the timeliness of the discovery of revocation (and hence the window for an attacker to exploit a compromised certificate) trades off against resource usage in querying revocation statuses and privacy concerns. If revocation information is unavailable (either due to an accident or an attack), clients must decide whether to fail-hard and treat a certificate as if it is revoked (and so degrade availability) or to fail-soft and treat it as unrevoked (and allow attackers to sidestep revocation). Due to the cost of revocation checks and the availability impact from potentially-unreliable remote services, Web browsers limit the revocation checks they will perform, and will fail soft where they do. Certificate revocation lists are too bandwidth-costly for routine use, and the Online Certificate Status Protocol presents connection latency and privacy issues. Other schemes have been proposed but have not yet been successfully deployed to enable fail-hard checking.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some situations, \"maximal munch\" leads to undesirable or unintuitive outcomes. For instance, in the C programming language, the statement x=y/*z; (without any whitespace) will probably lead to a syntax error, since the /* character sequence initiates a (unintended) comment that is either unterminated or terminated by the end token */ of some later, unrelated actual comment (comments in C do not nest). What was actually meant in the statement was to assign to the variable x the result of dividing the value in y by the value obtained by dereferencing pointer z; this would be valid code. It can be stated by making use of whitespace, or using x=y/(*z);.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine if a production lot of material meets the governing specifications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This notational scheme is not strictly accurate, because the transaction counter is 21 bits, which is not an even multiple of 4 (the number of bits in a hex digit). Consequently, the transaction counter actually consumes one bit of the field that is the TRSM ID (in this example that means that the TRSM ID field can accommodate 2(5*4-1) devices, instead of 2(5*4), or about half a million). Also, it is common practice in the industry to use only 64-bits of the KSN (probably for reasons pertinent to legacy systems, and DES encryption), which would imply that the full KSN is padded to the left with four \u2018f\u2019 hex digits. The remaining 4 hex digits (16-bits) are available, nonetheless, to systems which can accommodate them. The 6-5-5 scheme mentioned above would permit about 16 million BDKs, 500,000 devices per BDK, and 1 million transactions per device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The relationships of objects or classes through inheritance give rise to a directed acyclic graph. An inherited class is called a subclass of its parent class or super class.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Application here is simply a short way of saying that the corresponding concatenation rule has been applied. The types of logics called predicate, quantificational, or n-order logic include variables, operators, predicate and function symbols, and quantifiers as symbols in their languages. The propositions in these logics are more complex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages, type erasure is the load-time process by which explicit type annotations are removed from a program, before it is executed at run-time. Operational semantics not requiring programs to be accompanied by types are named type-erasure semantics, in contrast with type-passing semantics. Type-erasure semantics is an abstraction principle, ensuring that the run-time execution of a program doesn't depend on type information. In the context of generic programming, the opposite of type erasure is named reification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semantics, words are categorized into semantic classes. Intersecting semantic classes share the same semantic features. Semantic features can include  and . These features may in some instances be realised morphologically, in which case they may also be called morphosemantic features.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scientific visualization, image-based flow visualization (or visualisation) is a computer modelling technique developed by Jarke van Wijk to visualize two dimensional flows of liquids such as water and air, like the wind movement of a tornado. Compared with integration techniques it has the advantage of producing a whole image at every step, as the technique relies upon graphical computing methods for frame-by-frame capture of the model of advective transport of a decaying dye. It is a method from the texture advection family.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many operators worldwide offer a femtocell service, mainly targeted at businesses but also offered to individual customers (often for a one-off fee) when they complain to the operator regarding a poor or non-existent signal at their location. Operators who have launched a femtocell service include SFR, AT&T, C Spire, Sprint Nextel, Verizon, Zain, Mobile TeleSystems, T-Mobile US, Orange, Vodafone, EE, O2, Three, and others. In 3GPP terminology, a Home NodeB (HNB) is a 3G femtocell.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, there can be many ways to test a single hypothesis from the same dataset. Although defensible, decisions in data analysis remain subjective, which can greatly affect research results. A way to counter this subjectivity is transparency. When data, analytic plans, and analytic decisions are made transparent and open access to the rest of the community, it facilitates criticism and gives the opportunity to explore alternative ways to analyse data.\u201cCrowdsourcing the analysis of the data reveals the extent to which research conclusions are contingent on the defensible yet subjective decision made by different analysts.\u201d\u2014Uhlmann et al., 2019", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo\u2013Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the raw polygon is hole-free, then an optimal partition can be found in time O ( n 4 ) {\\displaystyle O(n^{4})} , where n is the number of vertices of the polygon. In the special case of a \"histogram polygon\", the complexity improves to O ( n 3 ) {\\displaystyle O(n^{3})} . The algorithm uses dynamic programming and relies on the following fact: if the polygon is hole-free, then it has a minimum-length partition in which each maximal line-segment contains a vertex of the boundary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Local Leakage Rate Tests (Type B or Type C testing, or LLRTs) are performed much more frequently, both to identify the possible leakage in an accident and to locate and fix leakage paths. LLRTs are performed on containment isolation valves, hatches and other appurtenances penetrating the containment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Live media can be shared through any Internet website or application; thus, when people browse a specific website, they may find live media streams relevant to them.Live media can include coverage of various events such as concerts or live news coverage viewed using a web browser or apps such as Snapchat. James Harden and Trolli promoted an upcoming NBA All-Star Game through Snapchat. Many of LaBeouf, R\u00f6nkk\u00f6 & Turner's performance art were livestreamed, such as a stream of Shia LaBeouf in a theater viewing all his movies.However, live stream commerce nowadays allows sellers to sell products by a streamer to introduce and illustrate effects (just like sales in physical stores) to motivate buyers to buy the products and services. Merritt and Zhao mention that Chinese 'live stream-based retailing\u2019 has supported the economic growth of China and projected that about GBP 98 billion were generated from e-commerce live streaming in China. The McKinsey report also demonstrates that live stream commerce is expanding in China, the sales from live stream commerce were expected to achieve $423 billion by 2022, and the US live streaming industry was also expected to reach $25 billion by 2023.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by the fact that it decomposes into a string from that same language (on the left) and a suffix (on the right). For instance, 1 + 2 + 3 {\\displaystyle 1+2+3} can be recognized as a sum because it can be broken into 1 + 2 {\\displaystyle 1+2} , also a sum, and + 3 {\\displaystyle {}+3} , a suitable suffix. In terms of context-free grammar, a nonterminal is left-recursive if the leftmost symbol in one of its productions is itself (in the case of direct left recursion) or can be made itself by some sequence of substitutions (in the case of indirect left recursion).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, each time the user compiles their program, the user is essentially recompiling numerous header libraries as well. (These would be precompiled into shared objects or dynamic link libraries in non \"header\" libraries.) To reduce compilation times, some compilers allow header files to be compiled into a form that is faster for the compiler to process. This intermediate form is known as a precompiled header, and is commonly held in a file named with the extension .pch or similar, such as .gch under the GNU Compiler Collection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Notable examples of attacks on internet connected facilities include the 2010 Stuxnet attack on Iran's Natanz nuclear facilities and the December 2015 Ukraine power grid cyberattack. \u201cToday\u2019s threats are a result of hybrid and blended attacks utilizing Information Technology (IT), physical infrastructure, and Operational Technology (OT) as the enemy avenue of approach,\" notes former CISA Assistant Director for Infrastructure Security Brian Harrell. \"Highlighting this future threat landscape will ensure better situational awareness and a more rapid response.\u201d", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some other programming languages it may be possible to achieve the same thing with less boilerplate, when the language has built-in support for such common constructs. For example, the equivalent of the above Java code can be expressed in Scala using just one line of code:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Again, unranked preferences have no value. In positional voting, ranked ballots with tied options are normally considered as invalid. The counting process is straightforward.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the Economist provides a Big Mac Index that expresses the adjusted cost of a globally ubiquitous Big Mac as a percentage over or under the cost of a Big Mac in the U.S. in USD. Such indices can be used to help forecast currency values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where two objects are traveling in perpendicular directions, the relativistic relative velocity v \u2192 B | A {\\displaystyle {\\vec {v}}_{\\mathrm {B|A} }} is given by the formula: v \u2192 B | A = v \u2192 B \u03b3 A \u2212 v \u2192 A {\\displaystyle {\\vec {v}}_{\\mathrm {B|A} }={\\frac {{\\vec {v}}_{\\mathrm {B} }}{\\gamma _{\\mathrm {A} }}}-{\\vec {v}}_{\\mathrm {A} }} where \u03b3 A = 1 1 \u2212 ( v A c ) 2 {\\displaystyle \\gamma _{\\mathrm {A} }={\\frac {1}{\\sqrt {1-\\left({\\frac {v_{\\mathrm {A} }}{c}}\\right)^{2}}}}} The relative speed is given by the formula v B | A = c 4 \u2212 ( c 2 \u2212 v A 2 ) ( c 2 \u2212 v B 2 ) c {\\displaystyle v_{\\mathrm {B|A} }={\\frac {\\sqrt {c^{4}-\\left(c^{2}-v_{\\mathrm {A} }^{2}\\right)\\left(c^{2}-v_{\\mathrm {B} }^{2}\\right)}}{c}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of how well a PC system follows a programmer\u2019s intuition, it turns out that in properly synchronized systems, the outcomes of PC and SC are the same. Programmer\u2019s intuition is essentially how the programmer expects the instructions to execute, usually in what is referred to as \u201cprogram order.\u201d Program order in a multiprocessor system is the execution of instructions resulting in the same outcome as a sequential execution. The fact that PC and SC both follow this expectation is a direct consequence of the fact that corresponding loads and stores in PC systems are still ordered with respect to each other. For example, in lock synchronization, the only operation whose behavior is not fully defined by PC is the lock-acquire store, where subsequent loads are in the critical section and their order affects the outcome. This operation, however, is usually implemented with a store conditional or atomic instruction, so that if the operation fails it will be repeated later and all the younger loads will also be repeated. All loads occurring before this store are still ordered with respect to the loads occurring in the critical section, and as such all the older loads have to complete before loads in the critical section can run.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is also work on mapping some version of English (or another natural language) automatically to and from logic, as well as executing the logic directly. Examples are Attempto Controlled English, and Internet Business Logic, which do not seek to control the vocabulary or syntax. A feature of systems that support bidirectional English\u2013logic mapping and direct execution of the logic is that they can be made to explain their results, in English, at the business or scientific level.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The similarity between languages is their very structural principle; the difference between languages is the carrying out of that principle in concreto. Both the similarity and the difference between languages lie, then, in language and in languages themselves, in their internal structure; and no similarity or difference between languages rests on any factor outside language.\" \u2013 Louis Hjelmslev", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Societies are seen as coherent, bounded and fundamentally relational constructs that function like organisms, with their various (or social institutions) working together in an unconscious, quasi-automatic fashion toward achieving an overall social equilibrium. All social and cultural phenomena are therefore seen as functional in the sense of working together, and are effectively deemed to have \"lives\" of their own. They are primarily analyzed in terms of this function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software testing, conformance testing verifies that a product performs according to its specified standards. Compilers, for instance, are extensively tested to determine whether they meet the recognized standard for that language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1980s, with the advent of 32-bit microprocessors such as the Motorola 68000, several new competitors appeared, including Apollo Computer and Sun Microsystems, with workstations based on 68000 and Unix. Meanwhile, DARPA's VLSI Project created several spinoff graphics products, such as the Silicon Graphics 3130. Target markets were differentiated, with Sun and Apollo considered to be network workstations and SGI as graphics workstations. RISC CPUs increased in the mid-1980s, typical of workstation vendors.Workstations often feature SCSI or Fibre Channel disk storage systems, high-end 3D accelerators, single or multiple 64-bit processors, large amounts of RAM, and well-designed cooling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The precision of the measurement can exceed the least count of the instrument. used. The repetition method is used when high accuracy is required. For rough or approximate survey work, the ordinary method of measuring horizontal angles is used as it is less time consuming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There may be more than one generalized Bayes rule, since there may be multiple choices of \u03b4 ( x ) {\\displaystyle \\delta (x)\\,\\!} that achieve the same expected loss. At first, this may appear rather different from the Bayes rule approach of the previous section, not a generalization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multiprocessor computer systems, software lockout is the issue of performance degradation due to the idle wait times spent by the CPUs in kernel-level critical sections. Software lockout is the major cause of scalability degradation in a multiprocessor system, posing a limit on the maximum useful number of processors. To mitigate the phenomenon, the kernel must be designed to have its critical sections as short as possible, therefore decomposing each data structure in smaller substructures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This provides a concise and synthetic way for manipulating and studying systems of linear equations. Vector spaces are characterized by their dimension, which, roughly speaking, specifies the number of independent directions in the space. This means that, for two vector spaces over a given field and with the same dimension, the properties that depend only on the vector-space structure are exactly the same (technically the vector spaces are isomorphic).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The machine executed 3 instructions and then a NOP (no op) to slow it down, as nearly every component was identical to the 90/30). Later a 90/40 model was added, with improved performance from a faster clock rate (cycle time of 500ns vs 600ns), pre-fetching of the next instruction, and greater maximum main memory capacity (1M vs 512K).The Sperry UNIVAC System 80 series: The entire 90/xx series was eventually replaced in 1981 by the System 80, models 4 and 6. More powerful System 80's (models 8, 10 and 20) were introduced in 1984. These were Sperry-badged, IBM/360-like mainframes actually developed and engineered by Mitsubishi in Japan. The final System 80 was the model 7E, released in 1990 by Unisys.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In (Costantini & Zacher 2004) it is shown that every finite simple group is a complemented group. Note that in the classification of finite simple groups, K-group is more used to mean a group whose proper subgroups only have composition factors amongst the known finite simple groups. An example of a group that is not complemented (in either sense) is the cyclic group of order p2, where p is a prime number. This group only has one nontrivial subgroup H, the cyclic group of order p, so there can be no other subgroup L to be the complement of H.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, the singular cardinals hypothesis (SCH) arose from the question of whether the least cardinal number for which the generalized continuum hypothesis (GCH) might fail could be a singular cardinal. According to Mitchell (1992), the singular cardinals hypothesis is: If \u03ba is any singular strong limit cardinal, then 2\u03ba = \u03ba+.Here, \u03ba+ denotes the successor cardinal of \u03ba. Since SCH is a consequence of GCH, which is known to be consistent with ZFC, SCH is consistent with ZFC. The negation of SCH has also been shown to be consistent with ZFC, if one assumes the existence of a sufficiently large cardinal number. In fact, by results of Moti Gitik, ZFC + \u00acSCH is equiconsistent with ZFC + the existence of a measurable cardinal \u03ba of Mitchell order \u03ba++.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relation to the Japanese language and computers many adaptation issues arise, some unique to Japanese and others common to languages which have a very large number of characters. The number of characters needed in order to write in English is quite small, and thus it is possible to use only one byte (28=256 possible values) to encode each English character. However, the number of characters in Japanese is many more than 256 and thus cannot be encoded using a single byte - Japanese is thus encoded using two or more bytes, in a so-called \"double byte\" or \"multi-byte\" encoding. Problems that arise relate to transliteration and romanization, character encoding, and input of Japanese text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is an extension of Szemer\u00e9di's regularity lemma that partitions any given graph into bounded number parts such that edges between the parts behave almost randomly. Similarly, the hypergraph counting lemma is a generalization of the graph counting lemma that estimates number of copies of a fixed graph as a subgraph of a larger graph. There are several distinct formulations of the method, all of which imply the hypergraph removal lemma and a number of other powerful results, such as Szemer\u00e9di's theorem, as well as some of its multidimensional extensions. The following formulations are due to V. R\u00f6dl, B. Nagle, J. Skokan, M. Schacht, and Y. Kohayakawa, for alternative versions see Tao (2006), and Gowers (2007).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the home prime HP(n) of an integer n greater than 1 is the prime number obtained by repeatedly factoring the increasing concatenation of prime factors including repetitions. The mth intermediate stage in the process of determining HP(n) is designated HPn(m). For instance, HP(10) = 773, as 10 factors as 2\u00d75 yielding HP10(1) = 25, 25 factors as 5\u00d75 yielding HP10(2) = HP25(1) = 55, 55 = 5\u00d711 implies HP10(3) = HP25(2) = HP55(1) = 511, and 511 = 7\u00d773 gives HP10(4) = HP25(3) = HP55(2) = HP511(1) = 773, a prime number. Some sources use the alternative notation HPn for the homeprime, leaving out parentheses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Prohibiting courts from dismissing claims on the basis of the state secrets privilege until after they have reviewed all available evidence. Permitting the court to appoint an outside expert to scrutinize the evidence for national security content. Excluding illegal government action from the definition of \"state secrets,\" or otherwise allowing the court to address the legality (instead of just the secrecy) of government conduct. This would prevent the government from using the state secrets privilege to conceal its illegal conduct.On January 22, 2008, Senators Edward Kennedy, Patrick Leahy and Arlen Specter introduced S. 2533, the State Secrets Protection Act.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This widely generalizes the Abel\u2013Ruffini theorem, which asserts that a general polynomial of degree at least five cannot be solved by radicals. Galois theory has been used to solve classic problems including showing that two problems of antiquity cannot be solved as they were stated (doubling the cube and trisecting the angle), and characterizing the regular polygons that are constructible (this characterization was previously given by Gauss, but all known proofs that this characterization is complete require Galois theory).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are also some similar definitions for functions mapping \u03b1 {\\displaystyle \\alpha } to \u03b1 {\\displaystyle \\alpha }: A function mapping \u03b1 {\\displaystyle \\alpha } to \u03b1 {\\displaystyle \\alpha } is \u03b1 {\\displaystyle \\alpha } -recursively-enumerable, or \u03b1 {\\displaystyle \\alpha } -partial recursive, iff its graph is \u03a3 1 {\\displaystyle \\Sigma _{1}} -definable on ( L \u03b1 , \u2208 ) {\\displaystyle (L_{\\alpha },\\in )} . A function mapping \u03b1 {\\displaystyle \\alpha } to \u03b1 {\\displaystyle \\alpha } is \u03b1 {\\displaystyle \\alpha } -recursive iff its graph is \u0394 1 {\\displaystyle \\Delta _{1}} -definable on ( L \u03b1 , \u2208 ) {\\displaystyle (L_{\\alpha },\\in )} . Additionally, a function mapping \u03b1 {\\displaystyle \\alpha } to \u03b1 {\\displaystyle \\alpha } is \u03b1 {\\displaystyle \\alpha } -arithmetical iff there exists some n \u2208 \u03c9 {\\displaystyle n\\in \\omega } such that the function's graph is \u03a3 n {\\displaystyle \\Sigma _{n}} -definable on ( L \u03b1 , \u2208 ) {\\displaystyle (L_{\\alpha },\\in )} .Additional connections between recursion theory and \u03b1 recursion theory can be drawn, although explicit definitions may not have yet been written to formalize them: The functions \u0394 0 {\\displaystyle \\Delta _{0}} -definable in ( L \u03b1 , \u2208 ) {\\displaystyle (L_{\\alpha },\\in )} play a role similar to those of the primitive recursive functions.We say R is a reduction procedure if it is \u03b1 {\\displaystyle \\alpha } recursively enumerable and every member of R is of the form \u27e8 H , J , K \u27e9 {\\displaystyle \\langle H,J,K\\rangle } where H, J, K are all \u03b1-finite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, the Matthew effect is used to describe the preferential attachment of earlier nodes in a network, which explains that these nodes tend to attract more links early on. \"Because of preferential attachment, a node that acquires more connections than another one will increase its connectivity at a higher rate, and thus an initial difference in the connectivity between two nodes will increase further as the network grows, while the degree of individual nodes will grow proportional with the square root of time.\" The Matthew Effect therefore explains the growth of some nodes in vast networks such as the Internet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Confidentiality, Integrity and Availability (C, I, A) metrics were updated to have scores consisting of None, Low, or High, rather than the None, Partial, Complete of CVSSv2. This allows more flexibility in determining the impact of a vulnerability on CIA metrics. Access Complexity was renamed Attack Complexity (AC) to make clear that access privileges were moved to a separate metric. This metric now describes how repeatable exploit of this vulnerability may be; AC is High if the attacker requires perfect timing or other circumstances (other than user interaction, which is also a separate metric) which may not be easily duplicated on future attempts. Attack Vector (AV) saw the inclusion of a new metric value of Physical (P), to describe vulnerabilities that require physical access to the device or system to perform.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the clinical context, \"invisible light\" medical imaging is generally equated to radiology or \"clinical imaging\". \"Visible light\" medical imaging involves digital video or still pictures that can be seen without special equipment. Dermatology and wound care are two modalities that use visible light imagery.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regression analysis, the distinction between errors and residuals is subtle and important, and leads to the concept of studentized residuals. Given an unobservable function that relates the independent variable to the dependent variable \u2013 say, a line \u2013 the deviations of the dependent variable observations from this function are the unobservable errors. If one runs a regression on some data, then the deviations of the dependent variable observations from the fitted function are the residuals. If the linear model is applicable, a scatterplot of residuals plotted against the independent variable should be random about zero with no trend to the residuals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of SQL, data definition or data description language (DDL) is a syntax for creating and modifying database objects such as tables, indices, and users. DDL statements are similar to a computer programming language for defining data structures, especially database schemas. Common examples of DDL statements include CREATE, ALTER, and DROP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Graeffe's method or Dandelin\u2013Lobachesky\u2013Graeffe method is an algorithm for finding all of the roots of a polynomial. It was developed independently by Germinal Pierre Dandelin in 1826 and Lobachevsky in 1834. In 1837 Karl Heinrich Gr\u00e4ffe also discovered the principal idea of the method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Due to other concerns, this correspondence is inexact: for example, SP (Space) and 0 (zero) both have low bits 00000 (to ease collation for space and conversion to/from binary-coded decimal for 0), preventing 0 from lining up with ) (right parenthesis), its conventional value, and thus instead () corresponded to 89, instead of 90 as on typewriters. Further, while digits were placed in column 3, the characters ,-./ (conventionally unshifted) were placed in column 2, to ease collation, due to being used as separators, and the characters ;: (conventionally paired) were both placed in column 3. Other symbols also did not line up with their conventional digit pair, as detailed below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In peer-to-peer swarming systems, a swarm is self-sustaining if all the blocks of its files are available among peers (excluding seeds and publishers).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, the M/M/\u221e queue is a multi-server queueing model where every arrival experiences immediate service and does not wait. In Kendall's notation it describes a system where arrivals are governed by a Poisson process, there are infinitely many servers, so jobs do not need to wait for a server. Each job has an exponentially distributed service time. It is a limit of the M/M/c queue model where the number of servers c becomes very large. The model can be used to model bound lazy deletion performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to achieve linear time complexity, Re-Pair requires the following data structures A sequence representing the input string. Position i {\\displaystyle i} of the sequence contains the i-th symbol of the input string plus two references to other positions in the sequence. These references point to the next/previous positions, say k {\\displaystyle k} and m {\\displaystyle m} , such that the same substring begins at w  {\\displaystyle w} , w  {\\displaystyle w} and w  {\\displaystyle w} and all three occurrences are captured by the same reference (i.e. there is a variable in the grammar generating the string). A priority queue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following subsections, a selection of significant tests (by no means exhaustive) is listed, representative of the testing effort in each nuclear country.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One can define a sesquilinear form over any *-ring. Also, one can define *-versions of algebraic objects, such as ideal and subring, with the requirement to be *-invariant: x \u2208 I \u21d2 x* \u2208 I and so on. *-rings are unrelated to star semirings in the theory of computation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C family of languages, the following operators are unary: Increment: ++x, x++ Decrement: \u2212\u2212x, x\u2212\u2212 Address: &x Indirection: *x Positive: +x Negative: \u2212x Ones' complement: ~x Logical negation: !x Sizeof: sizeof x, sizeof(type-name) Cast: (type-name) cast-expression", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In several countries, a digital signature has a status somewhat like that of a traditional pen and paper signature, as in the 1999 EU digital signature directive and 2014 EU follow-on legislation. Generally, these provisions mean that anything digitally signed legally binds the signer of the document to the terms therein. For that reason, it is often thought best to use separate key pairs for encrypting and signing. Using the encryption key pair, a person can engage in an encrypted conversation (e.g., regarding a real estate transaction), but the encryption does not legally sign every message he or she sends.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result, students inherit all the attributes common to all persons. Additionally, students have unique attributes that other people do not have. Object-oriented languages model subset/superset relationships using inheritance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s, computer design was based on mounting electronic components (transistors, resistors, etc.) on circuit boards. Several boards formed a discrete logic element of the machine, known as a module. Overall machine cycle speed is strongly related to the signal path\u2014the length of the wiring\u2014requiring high-speed computers to make their modules as small as possible. This was at odds with the need to make the modules themselves more complex to increase functionality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s, backpropagation did not work well for deep FNNs and RNNs. Here the word \"deep\" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If a change to a property's use is made within a class, no permission for alterations is needed. If permission is granted, it may be unconditional, or under section 106 the local authority can attach conditions that the landowner must follow. Sections 171A to 196C contain the enforcement rules, which include allowing local authorities to charge people with offences for breach of planning rules, and to have a right of entry to property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular arithmetic, Barrett reduction is a reduction algorithm introduced in 1986 by P.D. Barrett.A naive way of computing c = a mod n {\\displaystyle c=a\\,{\\bmod {\\,}}n\\,} would be to use a fast division algorithm. Barrett reduction is an algorithm designed to optimize this operation assuming n {\\displaystyle n} is constant, and a < n 2 {\\displaystyle a", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alternatively, link signs may be figured as dimensions themselves, e.g. G = ( V , E , D ) {\\displaystyle G=(V,E,D)} where D = { \u2212 1 , 0 , 1 } {\\displaystyle D=\\{-1,0,1\\}} and E = { ( u , v , d ) ; u , v \u2208 V , d \u2208 D } {\\displaystyle E=\\{(u,v,d);u,v\\in V,d\\in D\\}} This approach has particular value when considering unweighted networks. This conception of dimensionality can be expanded should attributes in multiple dimensions need specification. In this instance, links are n-tuples e = ( u , v , d 1 \u2026 d n \u2212 2 ) {\\displaystyle e=(u,v,d_{1}\\dots d_{n-2})} . Such an expanded formulation, in which links may exist within multiple dimensions, is uncommon but has been used in the study of multidimensional time-varying networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1950s, it was found that there could be electrical coupling between the unencrypted side of a \"RED\" signal inside a secure communications facility, and either the conductor carrying the \"BLACK\" encrypted signal, or possibly the electrical ground(s) of the system. TEMPEST protective measures work against the situation when the frequency of the RED and BLACK signals are the same. The RED signal, at a low power level, may be intercepted directly, or there may be intermodulation between the RED and BLACK signals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a natural number is called k-almost prime if it has k prime factors. More formally, a number n is k-almost prime if and only if \u03a9(n) = k, where \u03a9(n) is the total number of primes in the prime factorization of n (can be also seen as the sum of all the primes' exponents): \u03a9 ( n ) := \u2211 a i if n = \u220f p i a i . {\\displaystyle \\Omega (n):=\\sum a_{i}\\qquad {\\mbox{if}}\\qquad n=\\prod p_{i}^{a_{i}}.} A natural number is thus prime if and only if it is 1-almost prime, and semiprime if and only if it is 2-almost prime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This gives rise to marked differences in the ways the modes are deployed and used in different parts of the world. Recently, there is a trend towards integrating the modes through intermodality and linking the modes ever more closely into production and distribution activities. At the same time; however, passenger and freight activity is becoming increasingly separated across most modes.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a function f is logarithmically convex or superconvex if log \u2218 f {\\displaystyle {\\log }\\circ f} , the composition of the logarithm with f, is itself a convex function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In neuroimaging, the most common variants are voxel-based morphometry, deformation-based morphometry and surface-based morphometry of the brain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regard to the future of information policy, it should be flexible and changing to different circumstances as the ability to access, store, and share information grows. Galvin suggests that information policy might include setting a boundary to the uncertainty in this field. As information policy becomes a larger and more important topic, it will also become a greater subject to governmental regulation in regards to the future of technology as well. It will also include the studies of these subjects: information science, communications, library science, and technology studies.The information policies will earn more advantages for national and organizational, such as getting the best from development of Web 2.0 nationally and in organization, influence people for paying attention to the socio aspect and socio-technical system, for securing preservation of digital content, bringing out information product, also respecting all users and making thinking time respectable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is approximately equal to log 2 \u2061 ( n ) \u2212 1 {\\displaystyle \\log _{2}(n)-1} iterations. When the target element is not in the array, binary search makes \u230a log 2 \u2061 ( n ) \u230b + 2 \u2212 2 \u230a log 2 \u2061 ( n ) \u230b + 1 / ( n + 1 ) {\\displaystyle \\lfloor \\log _{2}(n)\\rfloor +2-2^{\\lfloor \\log _{2}(n)\\rfloor +1}/(n+1)} iterations on average, assuming that the range between and outside elements is equally likely to be searched.In the best case, where the target value is the middle element of the array, its position is returned after one iteration.In terms of iterations, no search algorithm that works only by comparing elements can exhibit better average and worst-case performance than binary search.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra. For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition. This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the logical and (denoted \u2227 {\\displaystyle \\,\\land \\,} ) and the logical or (denoted \u2228 {\\displaystyle \\,\\lor \\,} ) distributes over the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Generalizations are in two directions. Firstly, to geometric questions about that morphism, for example the local Torelli theorem. Secondly, to other period mappings. A case that has been investigated deeply is for K3 surfaces (by Viktor S. Kulikov, Ilya Pyatetskii-Shapiro, Igor Shafarevich and Fedor Bogomolov) and hyperk\u00e4hler manifolds (by Misha Verbitsky, Eyal Markman and Daniel Huybrechts).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "395). On the other hand their RASP model P'0 equipped with an \"index register\" (indirect addressing) can compute all the \"partial recursive sequential functions\" (the mu recursive functions) (p.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Several languages like Tidore and Kuuk Thaayorre lack a general term meaning 'body'. On the basis of such data it has been argued that the highest level in the partonomy of body part terms would be the word for 'person'.Some other examples of proposed linguistic universals in semantics include the idea that all languages possess words with the meaning '(biological) mother' and 'you (second person singular pronoun)' as well as statistical tendencies of meanings of basic color terms in relation to the number of color terms used by a respective language. For example, if a languages possesses only two terms for describing color, their respective meanings will be 'black' and 'white' (or perhaps 'dark' and 'light').", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, return loss is a measure in relative terms of the power of the signal reflected by a discontinuity in a transmission line or optical fiber. This discontinuity can be caused by a mismatch between the termination or load connected to the line and the characteristic impedance of the line. It is usually expressed as a ratio in decibels (dB); R L ( d B ) = 10 log 10 \u2061 P i P r {\\displaystyle RL(\\mathrm {dB} )=10\\log _{10}{P_{\\mathrm {i} } \\over P_{\\mathrm {r} }}} where RL(dB) is the return loss in dB, Pi is the incident power and Pr is the reflected power.Return loss is related to both standing wave ratio (SWR) and reflection coefficient (\u0393).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"The Roman Rite of the Catholic Church also mentions use of blessed salt. The 1962 Rituale Romanum includes salt as component in three rites: Baptism: Before the candidates enter the church or baptistry, salt is blessed with an exorcism, and a pinch can be put in the mouth of the candidates. However, in modern practice this can be skipped. Reconsecration of an altar: In one rite for the reconsecration of an altar which has been disturbed, salt is exorcized, blessed, and mixed with ashes, water and wine, the resulting mixture being used to make the mortar with which the altar is resealed. Blessing holy water: Salt is added to water in silence after a prayer in which God is asked to bless the salt, recalling the blessed salt \"scattered over the water by the prophet Elisha\" and invoking the protective powers of salt and water, that they may \"drive away the power of evil\".An additional rite provides for the blessing of salt for animals.Blessed salt is also used in prayer services of Pentecostal churches, such as the Apostolic Church Fullness of God's Throne in Brasil.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a Boolean-valued model is a generalization of the ordinary Tarskian notion of structure from model theory. In a Boolean-valued model, the truth values of propositions are not limited to \"true\" and \"false\", but instead take values in some fixed complete Boolean algebra. Boolean-valued models were introduced by Dana Scott, Robert M. Solovay, and Petr Vop\u011bnka in the 1960s in order to help understand Paul Cohen's method of forcing. They are also related to Heyting algebra semantics in intuitionistic logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Much of the data stored and manipulated on computers, including text and images, can be represented as points in a high-dimensional space (see vector space model for the case of text). However, the essential algorithms for working with such data tend to become bogged down very quickly as dimension increases. It is therefore desirable to reduce the dimensionality of the data in a way that preserves its relevant structure. The Johnson\u2013Lindenstrauss lemma is a classic result in this vein. Also, the lemma is tight up to a constant factor, i.e. there exists a set of points of size m that needs dimension \u03a9 ( log \u2061 ( m ) \u03b5 2 ) {\\displaystyle \\Omega \\left({\\frac {\\log(m)}{\\varepsilon ^{2}}}\\right)} in order to preserve the distances between all pairs of points within a factor of ( 1 \u00b1 \u03b5 ) {\\displaystyle (1\\pm \\varepsilon )} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nephology is the science of clouds, which is undertaken in the cloud physics branch of meteorology. There are two methods of naming clouds in their respective layers of the homosphere, Latin and common name. Genus types in the troposphere, the atmospheric layer closest to Earth's surface, have Latin names because of the universal adoption of Luke Howard's nomenclature that was formally proposed in 1802.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A particularly important application of Dirichlet processes is as a prior probability distribution in infinite mixture models. The Dirichlet process was formally introduced by Thomas Ferguson in 1973. It has since been applied in data mining and machine learning, among others for natural language processing, computer vision and bioinformatics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, e.g., Rexx, no control expression is allowed and each alternative begins with a WHEN clause containing a boolean expression and a match occurs for the first case for which that expression evaluates to true.Each alternative begins with the particular value, or list of values (see below), that the control variable may match and which will cause the control to goto the corresponding sequence of statements. The value (or list/range of values) is usually separated from the corresponding statement sequence by a colon or by an implication arrow. In many languages, every case must also be preceded by a keyword such as case or when.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-synapsids, such as reptiles and crocodiles, teeth similar to canines may be termed \"caniniform\" (\"canine-shaped\") teeth.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, Cantor's paradox states that there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal number. In informal terms, the paradox is that the collection of all possible \"infinite sizes\" is not only infinite, but so infinitely large that its own infinite size cannot be any of the infinite sizes in the collection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of two nested square roots, the following theorem completely solves the problem of denesting.If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that if and only if a 2 \u2212 c {\\displaystyle a^{2}-c~} is the square of a rational number d. If the nested radical is real, x and y are the two numbers and a \u2212 d 2 , {\\displaystyle ~{\\frac {a-d}{2}}~,~} where d = a 2 \u2212 c {\\displaystyle ~d={\\sqrt {a^{2}-c}}~} is a rational number. In particular, if a and c are integers, then 2x and 2y are integers. This result includes denestings of the form as z may always be written z = \u00b1 z 2 , {\\displaystyle z=\\pm {\\sqrt {z^{2}}},} and at least one of the terms must be positive (because the left-hand side of the equation is positive).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is a polytope constructed via the bases of a matroid. Given a matroid M {\\displaystyle M} , the matroid polytope P M {\\displaystyle P_{M}} is the convex hull of the indicator vectors of the bases of M {\\displaystyle M} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The expression for vector { X } {\\displaystyle \\{\\ X\\}} may be written as { X } = { X \u2032 } + { \u0394 X } {\\displaystyle \\{\\ X\\}=\\{\\ X'\\}+\\{\\Delta \\ X\\}} The vector { X } {\\displaystyle \\{\\ X\\}} determination is related to minimization of the quadratic form \u03a0 {\\displaystyle \\ \\Pi } by incremental vector { \u0394 X } {\\displaystyle \\{\\Delta \\ X\\}} , i.e. \u2202 \u03a0 \u2202 \u0394 X k l = 0 {\\displaystyle {\\frac {\\partial \\Pi }{\\partial \\Delta X_{kl}}}=0} where l {\\displaystyle \\ l} - is the number of interior node of the area, k {\\displaystyle \\ k} - the number of co-ordinateAfter all transformations we may write the following two independent systems of linear algebraic equations  { \u0394 X 1 } = { B 1 } {\\displaystyle \\{\\Delta X_{1}\\}=\\{\\ B_{1}\\}}  { \u0394 X 2 } = { B 2 } {\\displaystyle \\{\\Delta X_{2}\\}=\\{\\ B_{2}\\}} where  {\\displaystyle } - symmetrical matrix in the banded form similar to global stiffness matrix of FEM assemblage, { \u0394 X 1 } {\\displaystyle \\{\\Delta \\ X_{1}\\}} and { \u0394 X 2 } {\\displaystyle \\{\\Delta \\ X_{2}\\}} - incremental vectors of co-ordinates of all nodes at axes 1, 2, { B 1 } {\\displaystyle \\{\\ B_{1}\\}} and { B 2 } {\\displaystyle \\{\\ B_{2}\\}} - the right part vectors that are combined by co-ordinates of all nodes in axes 1, 2.The solution of both systems, keeping all boundary nodes conservative, obtains new interior node positions corresponding to a non-distorted mesh with pseudo-regular elements. For example, Fig. 2 presents the rectangular area covered by a triangular mesh. The initial auto mesh possesses some degenerative triangles (left mesh).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Issai Schur showed in 1912 that for every nonconstant polynomial p(x) with integer coefficients, if S is the set of all nonzero values { p ( n ) \u2260 0: n \u2208 N } {\\displaystyle {\\begin{Bmatrix}p(n)\\neq 0:n\\in \\mathbb {N} \\end{Bmatrix}}} , then the set of primes that divide some member of S is infinite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(e.g. (a * b) * c = a * (b * c)). Many programming language manuals provide a table of operator precedence and associativity; see, for example, the table for C and C++.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practical implementations, especially with high dimensional data (large p), the naive covariance method is rarely used because it is not efficient due to high computational and memory costs of explicitly determining the covariance matrix. The covariance-free approach avoids the np2 operations of explicitly calculating and storing the covariance matrix XTX, instead utilizing one of matrix-free methods, for example, based on the function evaluating the product XT(X r) at the cost of 2np operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Again, a measure of distance between random variables may relate to the extent of dependence between them, rather than to their individual values. Statistical distance measures are not typically metrics, and they need not be symmetric. Some types of distance measures, which generalize squared distance, are referred to as (statistical) divergences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a Berger code is a unidirectional error detecting code, named after its inventor, J. M. Berger. Berger codes can detect all unidirectional errors. Unidirectional errors are errors that only flip ones into zeroes or only zeroes into ones, such as in asymmetric channels. The check bits of Berger codes are computed by counting all the zeroes in the information word, and expressing that number in natural binary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, many commercial recommender systems are based on large datasets. As a result, the user-item matrix used for collaborative filtering could be extremely large and sparse, which brings about challenges in the performance of the recommendation. One typical problem caused by the data sparsity is the cold start problem. As collaborative filtering methods recommend items based on users' past preferences, new users will need to rate a sufficient number of items to enable the system to capture their preferences accurately and thus provides reliable recommendations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The above property may then be stated as \u2200 ( a \u2208 A ) . \u2203 !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Minimum excluded values of subclasses of the ordinal numbers are used in combinatorial game theory to assign nim-values to impartial games. According to the Sprague\u2013Grundy theorem, the nim-value of a game position is the minimum excluded value of the class of values of the positions that can be reached in a single move from the given position.Minimum excluded values are also used in graph theory, in greedy coloring algorithms. These algorithms typically choose an ordering of the vertices of a graph and choose a numbering of the available vertex colors. They then consider the vertices in order, for each vertex choosing its color to be the minimum excluded value of the set of colors already assigned to its neighbors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Also, an explicit matrix for Qk\u2113 is rarely computed; instead, auxiliary values are computed and A is updated in an efficient and numerically stable way. However, for reference, we may write the matrix as Q k \u2113 =  . {\\displaystyle Q_{k\\ell }={\\begin{bmatrix}1&&&&&&\\\\&\\ddots &&&&0&\\\\&&c&\\cdots &s&&\\\\&&\\vdots &\\ddots &\\vdots &&\\\\&&-s&\\cdots &c&&\\\\&0&&&&\\ddots &\\\\&&&&&&1\\end{bmatrix}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the negative multinomial distribution is a generalization of the negative binomial distribution (NB(x0, p)) to more than two outcomes.As with the univariate negative binomial distribution, if the parameter x 0 {\\displaystyle x_{0}} is a positive integer, the negative multinomial distribution has an urn model interpretation. Suppose we have an experiment that generates m+1\u22652 possible outcomes, {X0,...,Xm}, each occurring with non-negative probabilities {p0,...,pm} respectively. If sampling proceeded until n observations were made, then {X0,...,Xm} would have been multinomially distributed. However, if the experiment is stopped once X0 reaches the predetermined value x0 (assuming x0 is a positive integer), then the distribution of the m-tuple {X1,...,Xm} is negative multinomial. These variables are not multinomially distributed because their sum X1+...+Xm is not fixed, being a draw from a negative binomial distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Choosing large public key: Replace e {\\displaystyle e} by e \u2032 {\\displaystyle e'} , where e \u2032 = e + k \u22c5 \u03bb ( N ) {\\displaystyle e'=e+k\\cdot \\lambda (N)} for some large of k {\\displaystyle k} . When e \u2032 {\\displaystyle e'} is large enough, i.e. e \u2032 > N 3 2 {\\displaystyle e'>N^{\\frac {3}{2}}} , then Wiener\u2019s attack can not be applied regardless of how small d {\\displaystyle d} is. Using the Chinese Remainder Theorem: Suppose one chooses d such that both d p = d mod ( p \u2212 1 ) {\\displaystyle d_{p}=d{\\bmod {(}}p-1)} and d q = d mod ( q \u2212 1 ) {\\displaystyle d_{q}=d{\\bmod {(}}q-1)} are small but d {\\displaystyle d} itself is not, then a fast decryption of C {\\displaystyle C} can be done as follows: 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications and computer networks, a channel access method or multiple access method allows more than two terminals connected to the same transmission medium to transmit over it and to share its capacity. Examples of shared physical media are wireless networks, bus networks, ring networks and point-to-point links operating in half-duplex mode. A channel access method is based on multiplexing, that allows several data streams or signals to share the same communication channel or transmission medium.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "He also describes the way that entities will be allowed in or out in the future. In describing this collective, Latour draws attention to the role of the spokesperson, who must be doubted but who must speak for otherwise mute things in order to ensure that the collective involves both \"humans and non-humans\". This is also an important aspect of Actor-network theory (ANT) that can be found in his main sociological works. The book includes a short summary at the end and a glossary of terms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, it is possible to model and measure geometrically the distance between a particular pitch and a particular key, both represented as points in the spiral array space. To preserve pitch spelling, because musically A# \u2260 Bb in their function and usage, the spiral array does not assume enharmonic equivalence, i.e. it does not fold into a torus. The spatial relationships between pitches, between chords, and between keys agree with those in other representations of tonal space.The model and its real-time algorithms have been implemented in the tonal visualization software MuSA.RT (Music on the Spiral Array . Real-Time) and a free app, MuSA_RT, both of which have been used in music education videos and in live performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 19th century, Sophie Germain developed several novel approaches to prove Fermat's Last Theorem for all exponents. First, she defined a set of auxiliary primes \u03b8 {\\displaystyle \\theta } constructed from the prime exponent p {\\displaystyle p} by the equation \u03b8 = 2 h p + 1 {\\displaystyle \\theta =2hp+1} , where h {\\displaystyle h} is any integer not divisible by three. She showed that, if no integers raised to the p t h {\\displaystyle p^{\\mathrm {th} }} power were adjacent modulo \u03b8 {\\displaystyle \\theta } (the non-consecutivity condition), then \u03b8 {\\displaystyle \\theta } must divide the product x y z {\\displaystyle xyz} . Her goal was to use mathematical induction to prove that, for any given p {\\displaystyle p} , infinitely many auxiliary primes \u03b8 {\\displaystyle \\theta } satisfied the non-consecutivity condition and thus divided x y z {\\displaystyle xyz} ; since the product x y z {\\displaystyle xyz} can have at most a finite number of prime factors, such a proof would have established Fermat's Last Theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of data compression, Shannon\u2013Fano coding, named after Claude Shannon and Robert Fano, is a name given to two different but related techniques for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). Shannon's method chooses a prefix code where a source symbol i {\\displaystyle i} is given the codeword length l i = \u2308 \u2212 log 2 \u2061 p i \u2309 {\\displaystyle l_{i}=\\lceil -\\log _{2}p_{i}\\rceil } . One common way of choosing the codewords uses the binary expansion of the cumulative probabilities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, an odd integer n is called an Euler\u2013Jacobi probable prime (or, more commonly, an Euler probable prime) to base a, if a and n are coprime, and a ( n \u2212 1 ) / 2 \u2261 ( a n ) ( mod n ) {\\displaystyle a^{(n-1)/2}\\equiv \\left({\\frac {a}{n}}\\right){\\pmod {n}}} where ( a n ) {\\displaystyle \\left({\\frac {a}{n}}\\right)} is the Jacobi symbol. If n is an odd composite integer that satisfies the above congruence, then n is called an Euler\u2013Jacobi pseudoprime (or, more commonly, an Euler pseudoprime) to base a.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predicate transformers semantics, expressions are restricted to terms of the logic (see above). However, this restriction seems too strong for most existing programming languages, where expressions may have side effects (call to a function having a side effect), may not terminate or abort (like division by zero). There are many proposals to extend weakest-preconditions or strongest-postconditions for imperative expression languages and in particular for monads. Among them, Hoare Type Theory combines Hoare logic for a Haskell-like language, separation logic and type theory. This system is currently implemented as a Coq library called Ynot. In this language, evaluation of expressions corresponds to computations of strongest-postconditions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory, relations between primitive notions are restricted by axioms. Some authors refer to the latter as \"defining\" primitive notions by one or more axioms, but this can be misleading.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a true scientific process, no consensus does exist and no consensus can exist as the process is conducted scientifically in the pursuit of knowledge. If any party involved in the process stands to personally lose or gain from the result, the process will be flawed and unscientific. In a true scientific process, a theory is formed after a scientist - amateur or professional - has observed a phenomenon and has asked \"why?\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For a binary channel the symbols (e.g. integers { 1 , \u2026 , 9 } {\\displaystyle \\{1,\\ldots ,9\\}} ) have to be mapped onto base 2. The binary erasure channel model however is not applicable because it erases only individual bits with some probability and not Sudoku symbols. If the symbols of the Sudoku are sent in packets the channel can be described as a packet erasure channel model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each processor also included a floating point unit from Weitek. For marketing purposes, each processor was called a \"computational unit\", and a card-cage populated with 16 was referred to as a \"processor\". This allowed favorable per-processor performance comparisons with other supercomputers of the era.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Phones (and often also phonemes) are commonly represented by using symbols of the International Phonetic Alphabet (IPA). For example, the English word spin consists of four phones, , ,  and  and so the word has the phonetic representation . The word pin has three phones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to determine the actual impacts of search customization on end users, researchers at Northeastern University determined in a study with logged in users vs. a control group that 11.7% of results show differences due to personalization. The research showed that this result varies widely by search query and result ranking position.In the following example, the Portent Team performed a search query for 'JavaScript' (shown on the right) and then performed a search for 'Programming Textbooks' and 'Books on HTML' prior to searching for 'JavaScript, which changed the search results by bringing in three book listings that were not part of the original set of results. The study showed that of the various factors being tested, the two with the most measurable impact were whether the user was logged in with a Google account and the IP address of searching users. This same study also investigated the impact of the 11.7% personalization by utilizing Amazon Mechanical Turk (AMT) (a crowdsourcing Internet Marketplace and a part of Amazon Web Services) vs. a control group to determine the difference between the two. The results showed that the top ranked URLs are less likely to change based on personalization, and that the most personalization is taking place at lower ranks of the resulting pages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set of n {\\displaystyle n} -tuples of real numbers ( X 1 , \u2026 X n ) {\\displaystyle (X_{1},\\dots X_{n})} for which F ( X 1 , \u2026 X n ) {\\displaystyle F(X_{1},\\dots X_{n})} is true is called a semialgebraic set, so the decision problem for the existential theory of the reals can equivalently be rephrased as testing whether a given semialgebraic set is nonempty.In determining the time complexity of algorithms for the decision problem for the existential theory of the reals, it is important to have a measure of the size of the input. The simplest measure of this type is the length of a sentence: that is, the number of symbols it contains. However, in order to achieve a more precise analysis of the behavior of algorithms for this problem, it is convenient to break down the input size into several variables, separating out the number of variables to be quantified, the number of polynomials within the sentence, and the degree of these polynomials.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Further, in On similar arcs, he commented on Ptolemy's Karpos (or Centiloquium); many scholars believe that ibn Yusuf was in fact the true author of that work. He also wrote a book on the astrolabe. He invented methods to solve tax problems that were later presented in Fibonacci's Liber Abaci. He was also quoted by mathematicians such as Thomas Bradwardine, Jordanus de Nemore and Luca Pacioli.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The cluster of nuclear profiles was calculated based on their similarity to each other using a k-means clustering method. To begin the process, three nuclear profiles were chosen at random as the \u2018centers\u2019 of the cluster. After the centers were chosen at random, every other nuclear profile is assigned to a cluster based on its distance from each center using a calculated distance value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self-dual condition, Modular law a \u2264 b implies a \u2228 (x \u2227 b) = (a \u2228 x) \u2227 bwhere x, a, b are arbitrary elements in the lattice, \u2264 is the partial order, and \u2228 and \u2227 (called join and meet respectively) are the operations of the lattice. This phrasing emphasizes an interpretation in terms of projection onto the sublattice , a fact known as the diamond isomorphism theorem. An alternative but equivalent condition stated as an equation (see below) emphasizes that modular lattices form a variety in the sense of universal algebra. Modular lattices arise naturally in algebra and in many other areas of mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication and information theory, the code rate (or information rate) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant). That is, if the code rate is k / n {\\displaystyle k/n} for every k bits of useful information, the coder generates a total of n bits of data, of which n \u2212 k {\\displaystyle n-k} are redundant. If R is the gross bit rate or data signalling rate (inclusive of redundant error coding), the net bit rate (the useful bit rate exclusive of error correction codes) is \u2264 R \u22c5 k / n {\\displaystyle \\leq R\\cdot k/n} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", p + q ) {\\displaystyle (\\alpha ^{p}\\smile \\beta ^{q})(\\sigma )=\\alpha ^{p}(\\sigma \\circ \\iota _{0,1,...p})\\cdot \\beta ^{q}(\\sigma \\circ \\iota _{p,p+1,...,p+q})} where \u03c3 is a singular (p + q) -simplex and \u03b9 S , S \u2282 { 0 , 1 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical terms, a MOLP can be written as: min x P x s.t. a \u2264 B x \u2264 b , \u2113 \u2264 x \u2264 u {\\displaystyle \\min _{x}Px\\quad {\\text{s.t. }}\\quad a\\leq Bx\\leq b,\\;\\ell \\leq x\\leq u} where B {\\displaystyle B} is an ( m \u00d7 n ) {\\displaystyle (m\\times n)} matrix, P {\\displaystyle P} is a ( q \u00d7 n ) {\\displaystyle (q\\times n)} matrix, a {\\displaystyle a} is an m {\\displaystyle m} -dimensional vector with components in R \u222a { \u2212 \u221e } {\\displaystyle \\mathbb {R} \\cup \\{-\\infty \\}} , b {\\displaystyle b} is an m {\\displaystyle m} -dimensional vector with components in R \u222a { + \u221e } {\\displaystyle \\mathbb {R} \\cup \\{+\\infty \\}} , \u2113 {\\displaystyle \\ell } is an n {\\displaystyle n} -dimensional vector with components in R \u222a { \u2212 \u221e } {\\displaystyle \\mathbb {R} \\cup \\{-\\infty \\}} , u {\\displaystyle u} is an n {\\displaystyle n} -dimensional vector with components in R \u222a { + \u221e } {\\displaystyle \\mathbb {R} \\cup \\{+\\infty \\}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the central limit theorem states that, under certain circumstances, the probability distribution of the scaled mean of a random sample converges to a normal distribution as the sample size increases to infinity. Under stronger assumptions, the Berry\u2013Esseen theorem, or Berry\u2013Esseen inequality, gives a more quantitative result, because it also specifies the rate at which this convergence takes place by giving a bound on the maximal error of approximation between the normal distribution and the true distribution of the scaled sample mean. The approximation is measured by the Kolmogorov\u2013Smirnov distance. In the case of independent samples, the convergence rate is n\u22121/2, where n is the sample size, and the constant is estimated in terms of the third absolute normalized moment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one of the early works, Chang and Roberts proposed a uniform algorithm in which a processor with the highest ID is selected as the leader. Each processor sends its ID in a clockwise direction. A process receiving a message and compares it with its own. If it is bigger, it passes it through, otherwise it will discard the message. They show that this algorithm uses at most O ( n 2 ) {\\displaystyle O(n^{2})} messages and O ( n log \u2061 n ) {\\displaystyle O(n\\log n)} in the average case.Hirschberg and Sinclair improved this algorithm with O ( n log \u2061 n ) {\\displaystyle O(n\\log n)} message complexity by introducing a 2 directional message passing scheme allowing the processors to send messages in both directions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the singular value decomposition (SVD) of A {\\displaystyle A} , A = W \u03a3 V \u2217 {\\displaystyle A=W\\Sigma V^{*}} , one haswhere U {\\displaystyle U} , V {\\displaystyle V} , and W {\\displaystyle W} are unitary matrices (called orthogonal matrices if the field is the reals R {\\displaystyle \\mathbb {R} } ). This confirms that P {\\displaystyle P} is positive-definite and U {\\displaystyle U} is unitary. Thus, the existence of the SVD is equivalent to the existence of polar decomposition. One can also decompose A {\\displaystyle A} in the formHere U {\\displaystyle U} is the same as before and P \u2032 {\\displaystyle P'} is given byThis is known as the left polar decomposition, whereas the previous decomposition is known as the right polar decomposition. Left polar decomposition is also known as reverse polar decomposition. The polar decomposition of a square invertible real matrix A {\\displaystyle A} is of the form where | A | = ( A A T ) 1 2 {\\displaystyle |A|=\\left(AA^{\\textsf {T}}\\right)^{\\frac {1}{2}}} is a positive-definite matrix and R = | A | \u2212 1 A {\\displaystyle R=|A|^{-1}A} is an orthogonal matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nevertheless, numerous early counter-mapping projects successfully utilised manual techniques, and many still use them. For instance, in recent years, the use of simple sketch mapping approaches has been revitalised, whereby maps are made on the ground, using natural materials. Similarly, the use of scale model constructions and felt boards, as means of representing cartographic claims of different groups, have become increasingly popular. Consequently, Wood et al. assert that counter-mappers can \"make gateau out of technological crumbs\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers. As an example, starting with the number 8991 in base 10: 9981 \u2013 1899 = 8082 8820 \u2013 0288 = 8532 8532 \u2013 2358 = 6174 7641 \u2013 1467 = 61746174, known as Kaprekar's constant, is a fixed point of this algorithm. Any four-digit number (in base 10) with at least two distinct digits will reach 6174 within seven iterations. The algorithm runs on any natural number in any given number base.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "x}}\\right)} uniformly in \u03b8 {\\displaystyle \\theta } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or \"hat\", as in v ^ {\\displaystyle {\\hat {\\mathbf {v} }}} (pronounced \"v-hat\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It also includes reciprocals of some numbers of more than six places, such as 323 (2 1 4 8 3 0 7 in sexagesimal), whose reciprocal has 17 sexagesimal digits. Noting the difficulty of both calculating these numbers and sorting them, Donald Knuth in 1972 hailed Inaqib\u0131t-Anu as \"the first man in history to solve a computational problem that takes longer than one second of time on a modern electronic computer!\" (Two tables are also known giving approximations of reciprocals of non-regular numbers, one of which gives reciprocals for all the numbers from 56 to 80.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the real number system, square numbers are non-negative. A non-negative integer is a square number when its square root is again an integer. For example, 9 = 3 , {\\displaystyle {\\sqrt {9}}=3,} so 9 is a square number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Hasse norm theorem states that if L/K is a cyclic extension of number fields, then if a nonzero element of K is a local norm everywhere, then it is a global norm. Here to be a global norm means to be an element k of K such that there is an element l of L with N L / K ( l ) = k {\\displaystyle \\mathbf {N} _{L/K}(l)=k} ; in other words k is a relative norm of some element of the extension field L. To be a local norm means that for some prime p of K and some prime P of L lying over K, then k is a norm from LP; here the \"prime\" p can be an archimedean valuation, and the theorem is a statement about completions in all valuations, archimedean and non-archimedean. The theorem is no longer true in general if the extension is abelian but not cyclic. Hasse gave the counterexample that 3 is a local norm everywhere for the extension Q ( \u2212 3 , 13 ) / Q {\\displaystyle {\\mathbf {Q} }({\\sqrt {-3}},{\\sqrt {13}})/{\\mathbf {Q} }} but is not a global norm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Agile development process, unit testing is done per user story and comes in the later half of the sprint after requirements gathering and development are complete. Typically, the developers or other members from the development team, such as consultants, will write step-by-step 'test scripts' for the developers to execute in the tool. Test scripts are generally written to prove the effective and technical operation of specific developed features in the tool, as opposed to full fledged business processes that would be interfaced by the end user, which is typically done during user acceptance testing. If the test-script can be fully executed from start to finish without incident, the unit test is considered to have \"passed\", otherwise errors are noted and the user story is moved back to development in an 'in-progress' state. User stories that successfully pass unit tests are moved on to the final steps of the sprint - Code review, peer review, and then lastly a 'show-back' session demonstrating the developed tool to stakeholders.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: 1 \u2212 2 is not a natural number, although both 1 and 2 are. Similarly, a subset is said to be closed under a collection of operations if it is closed under each of the operations individually.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quicksort, one of the critical operations is choosing the pivot: the element around which the list is partitioned. The simplest pivot selection algorithm is to take the first or the last element of the list as the pivot, causing poor behavior for the case of sorted or nearly sorted input. Niklaus Wirth's variant uses the middle element to prevent these occurrences, degenerating to O(n2) for contrived sequences. The median-of-3 pivot selection algorithm takes the median of the first, middle, and last elements of the list; however, even though this performs well on many real-world inputs, it is still possible to contrive a median-of-3 killer list that will cause dramatic slowdown of a quicksort based on this pivot selection technique.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the revised simplex method is a variant of George Dantzig's simplex method for linear programming. The revised simplex method is mathematically equivalent to the standard simplex method but differs in implementation. Instead of maintaining a tableau which explicitly represents the constraints adjusted to a set of basic variables, it maintains a representation of a basis of the matrix representing the constraints. The matrix-oriented approach allows for greater computational efficiency by enabling sparse matrix operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a binary repetition code, there exist two code words - all ones and all zeros - which have a length of n {\\displaystyle n} . Therefore, the minimum Hamming distance of the code equals its length n {\\displaystyle n} . This gives the repetition code an error correcting capacity of n \u2212 1 2 {\\displaystyle {\\tfrac {n-1}{2}}} (i.e. it will correct up to n \u2212 1 2 {\\displaystyle {\\tfrac {n-1}{2}}} errors in any code word). If the length of a binary repetition code is odd, then it's a perfect code. The binary repetition code of length n is equivalent to the (n,1)-Hamming code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The addition of an instruction pipeline changes this. In such machines the CPU will \"look ahead\" and begin fetching succeeding instructions while the current instruction is still being processed. In this assembly line fashion any one instruction still requires as long to complete, but as soon as it finishes executing, the next instruction is right behind it, with most of the steps required for its execution already completed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Communications Decency Act of 1996, section 230 states that \"No provider or user of an interactive computer service shall be treated as the publisher or speaker of any information provided by another information content provider\". Section 230 protects the media from liabilities or being sued of third-party content, such as illegal activity from a user. However, this approach reduces a company's incentive to remove harmful content or misinformation. This loophole has allowed social media companies to maximize profits through pushing radical content without legal risks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since this happens O(p) times, the total time complexity is O(p3). A more efficient multiplication algorithm is the Sch\u00f6nhage\u2013Strassen algorithm, which is based on the Fast Fourier transform. It only requires O(p log p log log p) time to square a p-bit number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metal typesetting some fonts have default increased or decreased leading. To achieve this, a smaller font face is cast on the body of a larger font or vice versa. Such fonts are usually called \"bastard\" fonts or types. In the notation they are usually written with the face and the body size separated by a slash, like 10/12 that is a 10-point font face on a 12-point body, or 12/10, a 12-point font face on a 10-point body.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Plans that include nationwide long distance and/or nationwide roaming at no additional charge over \"local\" outgoing calls are popular. Mobile networks in Europe, Asia (except Hong Kong, Macau (Macao) and Singapore), Australia, and Argentina only charge their subscribers for outgoing calls. Incoming calls are free to the mobile subscriber with the exception of receiving a call while the subscriber is roaming as described below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The current cellular location of the phone (i.e., which BTS it is at) is entered into the VLR record and will be used during a process called paging when the GSM network wishes to locate the mobile phone. Every SIM card contains a secret key, called the Ki, which is used to provide authentication and encryption services. This is useful to prevent theft of service, and also to prevent \"over the air\" snooping of a user's activity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Intuitively, when two programs of equal size are mated intimately, the complexity is not additive, but multiplicative, because the connections between the program halves multiply out of control. Another lesson from the Z80 days, which was corrected on the 80386 compiler, was to write as much of the code as possible into Pascal itself, even the support library. Having the 80386 support code all written in Pascal has made it so modular and portable that most of it was moved out of the operating system specific area and into the \"common code\" library section, a section reserved for code that never changes for each machine and operating system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern linguistic theory, tense is understood as a category that expresses (grammaticalizes) time reference; namely one which, using grammatical means, places a state or action in time. Nonetheless, in many descriptions of languages, particularly in traditional European grammar, the term \"tense\" is applied to verb forms or constructions that express not merely position in time, but also additional properties of the state or action \u2013 particularly aspectual or modal properties. The category of aspect expresses how a state or action relates to time \u2013 whether it is seen as a complete event, an ongoing or repeated situation, etc. Many languages make a distinction between perfective aspect (denoting complete events) and imperfective aspect (denoting ongoing or repeated situations); some also have other aspects, such as a perfect aspect, denoting a state following a prior event. Some of the traditional \"tenses\" express time reference together with aspectual information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": " primes including 2 are the only primes that exist. If either pn# + 1 or pn# \u2212 1 is a primorial prime, it means that there are larger primes than the nth prime (if neither is a prime, that also proves the infinitude of primes, but less directly; each of these two numbers has a remainder of either p \u2212 1 or 1 when divided by any of the first n primes, and hence all its prime factors are larger than pn).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of quantum computing, the quantum walk search is a quantum algorithm for finding a marked node in a graph.The concept of a quantum walk is inspired by classical random walks, in which a walker moves randomly through a graph or lattice. In a classical random walk, the position of the walker can be described using a probability distribution over the different nodes of the graph. In a quantum walk, on the other hand, the walker is represented by a quantum state, which can be in a superposition of several locations simultaneously.Search algorithms based on quantum walks have the potential to find applications in various fields, including optimization, machine learning, cryptography, and network analysis. The efficiency and probability of success of a quantum walk search depend heavily on the structure of the search space. In general, quantum walk search algorithms offer an asymptotic quadratic speedup similar to that of Grover's algorithm.One of the first works on the application of quantum walk to search problems was proposed by Neil Shenvi, Julia Kempe, and K. Birgitta Whaley.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of private persons, calls and conversations may be recorded by any active participant. There is no requirement to make other parties aware of the recording, but the use of recordings, depending on their content, may be subject to various laws, such as data protection (privacy) legislation, libel laws, laws governing trade and national secrets, and any agreements, such as non-disclosure agreements.Recording of calls by a company or an employer is subject to data protection legislation and, as a general rule, requires informing the participants prior to recording.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Unicode Standard v. 5.1 (4 April 2008), 152 medieval and classical glyphs were given specific locations outside of the Private Use Area. Specifically, they are located in the charts \"Combining Diacritical Marks Supplement\" (26 characters), \"Latin Extended Additional\" (10 characters), \"Supplemental Punctuation\" (15 characters), \"Ancient Symbols\" (12 characters) and especially \"Latin Extended-D\" (89 characters). These consist in both precomposed characters and modifiers for other characters, called combining diacritical marks (such as writing in LaTeX or using overstrike in MS Word). Characters are \"the smallest components of written language that have semantic value\" but glyphs are \"the shapes that characters can have when they are rendered or displayed\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In personal computers, the IGP (integrated graphics processors) are mostly manufactured by Intel and AMD and are integrated onto their CPUs. They are commonly known as: Intel HD and Iris Graphics - also called HD series and Iris series AMD Accelerated Processing Unit (APU) - also formerly known as: fusion", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical hypothesis testing, there are various notions of so-called type III errors (or errors of the third kind), and sometimes type IV errors or higher, by analogy with the type I and type II errors of Jerzy Neyman and Egon Pearson. Fundamentally, type III errors occur when researchers provide the right answer to the wrong question, i.e. when the correct hypothesis is rejected but for the wrong reason. Since the paired notions of type I errors (or \"false positives\") and type II errors (or \"false negatives\") that were introduced by Neyman and Pearson are now widely used, their choice of terminology (\"errors of the first kind\" and \"errors of the second kind\"), has led others to suppose that certain sorts of mistakes that they have identified might be an \"error of the third kind\", \"fourth kind\", etc.None of these proposed categories have been widely accepted. The following is a brief account of some of these proposals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, reversing the digits of a number n sometimes produces another number m that is divisible by n. This happens trivially when n is a palindromic number; the nontrivial reverse divisors are 1089, 2178, 10989, 21978, 109989, 219978, 1099989, 2199978, ... (sequence A008919 in the OEIS).For instance, 1089 \u00d7 9 = 9801, the reversal of 1089, and 2178 \u00d7 4 = 8712, the reversal of 2178. The multiples produced by reversing these numbers, such as 9801 or 8712, are sometimes called palintiples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, an optimality criterion provides a measure of the fit of the data to a given hypothesis, to aid in model selection. A model is designated as the \"best\" of the candidate models if it gives the best value of an objective function measuring the degree of satisfaction of the criterion used to evaluate the alternative hypotheses. The term has been used to identify the different criteria that are used to evaluate a phylogenetic tree. For example, in order to determine the best topology between two phylogenetic trees using the maximum likelihood optimality criterion, one would calculate the maximum likelihood score of each tree and choose the one that had the better score.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of communications research and informetrics, the concept of self-organizing systems appears in mid-1990s research related to scientific communications. Scientometrics and bibliometrics are areas of research in which discrete data are available, as are several other areas of social communications research such as sociolinguistics. Social complexity is also a concept used in semiotics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In specifying disk drive capacities, manufacturers have always used conventional decimal SI prefixes representing powers of 10. Storage in a rotating disk drive is organized in platters and tracks whose sizes and counts are determined by mechanical engineering constraints so that the capacity of a disk drive has hardly ever been a simple multiple of a power of 2. For example, the first commercially sold disk drive, the IBM 350 (1956), had 50 physical disk platters containing a total of 50000 sectors of 100 characters each, for a total quoted capacity of 5 million characters.Moreover, since the 1960s, many disk drives used IBM's disk format, where each track was divided into blocks of user-specified size; and the block sizes were recorded on the disk, subtracting from the usable capacity. For example, the|IBM 3336]] disk pack was quoted to have a 200-megabyte capacity, achieved only with a single 13030-byte block in each of its 808 x 19 tracks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let the interest r follow a Markov process with probability transition function Q ( r , d \u03bc r ) {\\displaystyle Q(r,d\\mu _{r})} where d \u03bc r {\\displaystyle d\\mu _{r}} denotes the probability measure governing the distribution of interest rate next period if current interest rate is r {\\displaystyle r} . In this model the consumer decides their current period consumption after the current period interest rate is announced. Rather than simply choosing a single sequence { c t } {\\displaystyle \\{{\\color {OliveGreen}c_{t}}\\}} , the consumer now must choose a sequence { c t } {\\displaystyle \\{{\\color {OliveGreen}c_{t}}\\}} for each possible realization of a { r t } {\\displaystyle \\{r_{t}\\}} in such a way that their lifetime expected utility is maximized: max { c t } t = 0 \u221e E ( \u2211 t = 0 \u221e \u03b2 t u ( c t ) ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to define A {\\displaystyle A} , we define an objective function describing classification accuracy in the transformed space and try to determine A \u2217 {\\displaystyle A^{*}} such that this objective function is maximized. A \u2217 = argmax A f ( A ) {\\displaystyle A^{*}={\\mbox{argmax}}_{A}f(A)}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is acyclic. A polytree is an example of an oriented graph. The term polytree was coined in 1987 by Rebane and Pearl.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In medicine, a sequence is a series of ordered consequences due to a single cause.It differs from a syndrome in that seriality is more predictable: if A causes B, and B causes C, and C causes D, then D would not be seen if C is not seen. However, in less formal contexts, the term \"syndrome\" is sometimes used instead of sequence. Examples include: oligohydramnios sequence (also known as Potter sequence) Pierre Robin sequence Poland sequence == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is a general advantage of the axiomatic approach in mathematics. The axiomatic approach to Kolmogorov complexity was further developed in the book (Burgin 2005) and applied to software metrics (Burgin and Debnath, 2003; Debnath and Burgin, 2003). In information theory, information fluctuation complexity is the fluctuation of information about information entropy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is very similar to the z-score but with the difference that t-statistic is used when the sample size is small or the population standard deviation is unknown. For example, the t-statistic is used in estimating the population mean from a sampling distribution of sample means if the population standard deviation is unknown. It is also used along with p-value when running hypothesis tests where the p-value tells us what the odds are of the results to have happened.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a submodular set function (also known as a submodular function) is a set function that, informally, describes the relationship between a set of inputs and an output, where adding more of one input has a decreasing additional benefit (diminishing returns). The natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory (as functions modeling user preferences) and electrical networks. Recently, submodular functions have also found immense utility in several real world problems in machine learning and artificial intelligence, including automatic summarization, multi-document summarization, feature selection, active learning, sensor placement, image collection summarization and many other domains.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the event of accumulation in the long-term, the capacity at which the bottlenecked machine is running could be so slow that the accumulated resources that are in the queue need to be stored. The cost of storing resources is significant as it takes resources to transport the materials back and forth as well as requiring space, another potential cost.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Programming languages may, however, share the syntax with markup languages if a computational semantics is defined. XSLT, for example, is a Turing complete language entirely using XML syntax. Moreover, LaTeX, which is mostly used for structuring documents, also contains a Turing complete subset.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, the term system integrity has the following meanings: That condition of a system wherein its mandated operational and technical parameters are within the prescribed limits. The quality of an AIS when it performs its intended function in an unimpaired manner, free from deliberate or inadvertent unauthorized manipulation of the system. The state that exists when there is complete assurance that under all conditions an IT system is based on the logical correctness and reliability of the operating system, the logical completeness of the hardware and software that implement the protection mechanisms, and data integrity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Corners are detected through the simplest implementation which literally extracts a ring of 16 pixels and compares the intensity values with an appropriate threshold. For candidate p, each location on the circle x \u2208 {1, 2, 3, ..., 16} can be denoted by p\u2192x. The state of each pixel, Sp\u2192x must be in one of the following three states: d, Ip\u2192x \u2264 Ip - t (darker) s, Ip - t \u2264 Ip\u2192x \u2264 Ip + t (similar) b, Ip\u2192x\u2265 Ip + t (brighter)Then choosing an x (same for all p) partitions P (the set of all pixels of all training images) into 3 different subsets, Pd, Ps, Pb where: Pd = {p \u2208 P: Sp\u2192x = d } Ps = {p \u2208 P: Sp\u2192x = s } Pb = {p \u2208 P: Sp\u2192x = b }Secondly, a decision tree algorithm, the ID3 algorithm is applied to the 16 locations in order to achieve the maximum information gain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, it has become a popular subject of discourse among test-takers on various social media networks. Many of them poke fun at passages or questions in the PSAT that they find strange or amusing. The level of discussion is so significant that in 2013, the hashtag #PSAT reached trending status on Twitter near its administration date. This is despite the fact that since 2012, test participants have been required to copy and sign a statement agreeing to the test regulations, which include not discussing the test. Previously, that statement had to be written in cursive, a requirement that had drawn ire from both students and teachers, as many students found writing the statement in cursive to be difficult. However, in 2015, the requirement to write the statement in cursive was removed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case that X and Y are both finite-dimensional (i.e. linearly isomorphic to Rm and Rn for some natural numbers m and n) then writing out equation (L) in matrix form shows that \u03bb is the usual Lagrange multiplier vector; in the case n = 1, \u03bb is the usual Lagrange multiplier, a real number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the below table, Columns I, II, III, IV, and V show the code; the Let. and Fig. columns show the letters and numbers for the Continental and UK versions; and the sort keys present the table in the order: alphabetical, Gray and UK Baudot developed his first multiplexed telegraph in 1872 and patented it in 1874. In 1876, he changed from a six-bit code to a five-bit code, as suggested by Carl Friedrich Gauss and Wilhelm Weber in 1834, with equal on and off intervals, which allowed for transmission of the Roman alphabet, and included punctuation and control signals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So, given an integral domain R, it is often very useful to know that R has a Euclidean function: in particular, this implies that R is a PID. However, if there is no \"obvious\" Euclidean function, then determining whether R is a PID is generally a much easier problem than determining whether it is a Euclidean domain. Euclidean domains appear in the following chain of class inclusions: rngs \u2283 rings \u2283 commutative rings \u2283 integral domains \u2283 integrally closed domains \u2283 GCD domains \u2283 unique factorization domains \u2283 principal ideal domains \u2283 Euclidean domains \u2283 fields \u2283 algebraically closed fields", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For tossing two coins, the sample space is { H H , H T , T H , T T } {\\displaystyle \\{HH,HT,TH,TT\\}} , where the outcome is H H {\\displaystyle HH} if both coins are heads, H T {\\displaystyle HT} if the first coin is heads and the second is tails, T H {\\displaystyle TH} if the first coin is tails and the second is heads, and T T {\\displaystyle TT} if both coins are tails. The event that at least one of the coins is heads is given by E = { H H , H T , T H } {\\displaystyle E=\\{HH,HT,TH\\}} . For tossing a single six-sided die one time, where the result of interest is the number of pips facing up, the sample space is { 1 , 2 , 3 , 4 , 5 , 6 } {\\displaystyle \\{1,2,3,4,5,6\\}} .A well-defined, non-empty sample space S {\\displaystyle S} is one of three components in a probabilistic model (a probability space).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, support vector machines find a hyperplane that separates the feature space into two classes with the maximum margin. If the problem is not originally linearly separable, the kernel trick can be used to turn it into a linearly separable one, by increasing the number of dimensions. Thus a general hypersurface in a small dimension space is turned into a hyperplane in a space with much larger dimensions. Neural networks try to learn the decision boundary which minimizes the empirical error, while support vector machines try to learn the decision boundary which maximizes the empirical margin between the decision boundary and data points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle K/p.} The ring K  / ( p ) {\\displaystyle K/(p)} is a field if and only if p is an irreducible polynomial. In fact, if p is irreducible, every nonzero polynomial q of lower degree is coprime with p, and B\u00e9zout's identity allows computing r and s such that sp + qr = 1; so, r is the multiplicative inverse of q modulo p. Conversely, if p is reducible, then there exist polynomials a, b of degrees lower than deg(p) such that ab = p ; so a, b are nonzero zero divisors modulo p, and cannot be invertible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is due, in part, because two ISPs may be connected through multiple connections. In choosing the single router-level path, it is common practice for each ISP to employ hot-potato routing: sending traffic along the path that minimizes the distance through the ISP's own network\u2014even if that path lengthens the total distance to the destination. For example, consider two ISPs, A and B. Each has a presence in New York, connected by a fast link with latency 5 ms\u2014and each has a presence in London connected by a 5 ms link.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Hebrew letter aleph ( \u2135 {\\displaystyle \\,\\aleph \\,} ).The cardinality of the natural numbers is \u2135 0 {\\displaystyle \\,\\aleph _{0}\\,} (read aleph-nought or aleph-zero; the term aleph-null is also sometimes used), the next larger cardinality of a well-ordered set is aleph-one \u2135 1 , {\\displaystyle \\,\\aleph _{1}\\;,} then \u2135 2 {\\displaystyle \\,\\aleph _{2}\\,} and so on. Continuing in this manner, it is possible to define a cardinal number \u2135 \u03b1 {\\displaystyle \\,\\aleph _{\\alpha }\\,} for every ordinal number \u03b1 , {\\displaystyle \\,\\alpha \\;,} as described below. The concept and notation are due to Georg Cantor, who defined the notion of cardinality and realized that infinite sets can have different cardinalities. The aleph numbers differ from the infinity ( \u221e {\\displaystyle \\,\\infty \\,} ) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that \"diverges to infinity\" or \"increases without bound\"), or as an extreme point of the extended real number line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the most common form of pre-emption right is the right of existing shareholders to acquire new shares issued by a company in a rights issue, usually a public offering. In this context, the pre-emptive right is also called subscription right or subscription privilege. It is the right but not the obligation of existing shareholders to buy the new shares before they are offered to the public. In that way, existing shareholders can maintain their proportional ownership of the company and thus prevent stock dilution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, only two of these symbols were used for letters, making it largely binary. The third symbol only appeared in control characters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Java programming language, the constant interface pattern describes the use of an interface solely to define constants, and having classes implement that interface in order to achieve convenient syntactic access to those constants. However, since constants are very often merely an implementation detail, and the interfaces implemented by a class are part of its exported API, this practice amounts to putting implementations details into the API, which was considered inappropriate by, e.g., Java designer Joshua Bloch. In general, collecting system constants into classes independent of behaviour might create a poor object-oriented design because it is often a sign of low cohesion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similar lists exist for several other types of products. They vary and often deviate significantly from any geometric series in order to accommodate traditional sizes when feasible. Adjacent package sizes in these lists differ typically by factors 2\u20443 or 3\u20444, in some cases even 1\u20442, 4\u20445, or some other ratio of two small integers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 257, 1257, 2457, and 12457 are the patterns related to Braille pattern dots-134, since the two additional dots of kantenji patterns 0134, 1347, and 01347 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Myanmar North Korea \u2013 The US Bureau of Diplomatic Security advises visitors that they have \"no right to privacy in North Korea and should assume your communications are monitored\" which excludes the possibility of satellite phone technology. Russia \u2013 in 2012, new regulations governing the use of satellite phones inside Russia or its territories were developed with the stated aim of fighting terrorism by enabling the Russian government to intercept calls. These regulations allow non-Russian visitors to register their SIM cards for use within Russian territory for up to six months.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, this is not the case in a strong algorithm. In the past few years a number of research articles have addressed the development of strong multi-time-step algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, the use of object-oriented programming often results in a greater number of \"smaller\" calls, which can be accommodated by increasing the windows from eight to sixteen for instance. This was the approach used in the SPARC, which has included more register windows with newer generations of the architecture. The end result is fewer slow register window spill and fill operations because the register windows overflow less often.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are times when rumors are created with malicious intent, but shared by unknowing users. With the large audiences that can be reached and the experts on various subjects on social media, some believe social media could also be the key to correcting misinformation.Agent-based models and other computational models have been used by researchers to explain how false beliefs spread through networks. Epistemic network analysis is one example of a computational method for evaluating connections in data shared in a social media network or similar network. In The Misinformation Age: How False Beliefs Spread, a trade book by philosopher Cailin O'Connor and physicist James Owen Weatherall, the authors used a combination of case studies and agent-based models to show how false beliefs spread on social media and scientific networks. This book analyses the social nature of scientific research; the nature of information flow between scientists, propagandists, and politicians; and the spread of false beliefs among the general population.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some examples: All Greeks are human and all humans are mortal; therefore, all Greeks are mortal. : Valid argument; if the premises are true the conclusion must be true. Some Greeks are logicians and some logicians are tiresome; therefore, some Greeks are tiresome.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the observations are correlated, the expression S = \u2211 k \u2211 j r k W k j r j {\\textstyle S=\\sum _{k}\\sum _{j}r_{k}W_{kj}r_{j}\\,} applies. In this case the weight matrix should ideally be equal to the inverse of the variance-covariance matrix of the observations). The normal equations are then: This method is used in iteratively reweighted least squares.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The rules above are to be obeyed for large-scale maps. If the map being drawn is a small-scale map (less than 1:500 000 according to Imhof), rules may be relaxed in order to obtain a more suggestive representation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically statistics and information geometry, a Bregman divergence or Bregman distance is a measure of difference between two points, defined in terms of a strictly convex function; they form an important class of divergences. When the points are interpreted as probability distributions \u2013 notably as either values of the parameter of a parametric model or as a data set of observed values \u2013 the resulting distance is a statistical distance. The most basic Bregman divergence is the squared Euclidean distance. Bregman divergences are similar to metrics, but satisfy neither the triangle inequality (ever) nor symmetry (in general).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure of the deviation of the position of a particle with respect to a reference position over time. It is the most common measure of the spatial extent of random motion, and can be thought of as measuring the portion of the system \"explored\" by the random walker. In the realm of biophysics and environmental engineering, the Mean Squared Displacement is measured over time to determine if a particle is spreading slowly due to diffusion, or if an advective force is also contributing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The modulo operation is the operation that produces such a remainder when given a dividend and divisor. Alternatively, a remainder is also what is left after subtracting one number from another, although this is more precisely called the difference. This usage can be found in some elementary textbooks; colloquially it is replaced by the expression \"the rest\" as in \"Give me two dollars back and keep the rest.\" However, the term \"remainder\" is still used in this sense when a function is approximated by a series expansion, where the error expression (\"the rest\") is referred to as the remainder term.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matrix form, Oja's rule can be written d w ( t ) d t = w ( t ) Q \u2212 d i a g  w ( t ) {\\displaystyle \\,{\\frac {{\\text{d}}w(t)}{{\\text{d}}t}}~=~w(t)Q-\\mathrm {diag} w(t)} ,and the Gram-Schmidt algorithm is \u0394 w ( t ) = \u2212 l o w e r  w ( t ) {\\displaystyle \\,\\Delta w(t)~=~-\\mathrm {lower} w(t)} ,where w(t) is any matrix, in this case representing synaptic weights, Q = \u03b7 x xT is the autocorrelation matrix, simply the outer product of inputs, diag is the function that diagonalizes a matrix, and lower is the function that sets all matrix elements on or above the diagonal equal to 0. We can combine these equations to get our original rule in matrix form, \u0394 w ( t ) = \u03b7 ( t ) ( y ( t ) x ( t ) T \u2212 L T  w ( t ) ) {\\displaystyle \\,\\Delta w(t)~=~\\eta (t)\\left(\\mathbf {y} (t)\\mathbf {x} (t)^{\\mathrm {T} }-\\mathrm {LT} w(t)\\right)} ,where the function LT sets all matrix elements above the diagonal equal to 0, and note that our output y(t) = w(t) x(t) is a linear neuron.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The let expression is a conjunction within an existential quantifier. ( \u2203 x E \u2227 F ) \u27fa let \u2061 x: E in \u2061 F {\\displaystyle (\\exists xE\\land F)\\iff \\operatorname {let} x:E\\operatorname {in} F} where E and F are of type Boolean. The let expression allows the substitution to be applied to another expression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set or into |X| singleton sets. Otherwise, if G is transitive and G does preserve a nontrivial partition, G is called imprimitive. While primitive permutation groups are transitive, not all transitive permutation groups are primitive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence cost is the metric used in the standard modeling paradigm applied to economic processes. Costs (pl.) are often further described based on their timing or their applicability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In salt bath nitriding the nitrogen donating medium is a nitrogen-containing salt such as cyanide salt. The salts used also donate carbon to the workpiece surface making salt bath a nitrocarburizing process. The temperature used is typical of all nitrocarburizing processes: 550 to 570 \u00b0C. The advantages of salt nitriding is that it achieves higher diffusion in the same period of time compared to any other method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is also true for several other infinite sets, such as any n-dimensional Euclidean space R n {\\displaystyle \\mathbb {R} ^{n}} (see space filling curve). That is, The smallest infinite cardinal number is \u2135 0 {\\displaystyle \\aleph _{0}} (aleph-null). The second smallest is \u2135 1 {\\displaystyle \\aleph _{1}} (aleph-one). The continuum hypothesis, which asserts that there are no sets whose cardinality is strictly between \u2135 0 {\\displaystyle \\aleph _{0}} and c {\\displaystyle {\\mathfrak {c}}} , means that c = \u2135 1 {\\displaystyle {\\mathfrak {c}}=\\aleph _{1}} . The truth or falsity of this hypothesis is undecidable and cannot be proven within the widely used Zermelo\u2013Fraenkel set theory with axiom of choice (ZFC).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 28, 128, 248, and 1248 are the patterns related to Braille pattern dots-16, since the two additional dots of kantenji patterns 016, 167, and 0167 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to understand the performance paradox, it is helpful to first have a basic understanding of performance appraisals. Performance appraisals, also known as performance evaluations, are assessments that many organizations use to measure individuals' productivity, ability and talent in their respective job positions. The goal of these appraisals is not only to measure each person's performance, but also to align all of the employee's values, goals and motivations and become a better performing organization as a whole. While the implementation of performance evaluations has been characterized as beneficial and even essential for organizational success, many of these performance evaluations have also become more ineffective over time due to both the excessive number of evaluation measures and employee reactivity to these evaluations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a singular trace is a trace on a space of linear operators of a separable Hilbert space that vanishes on operators of finite rank. Singular traces are a feature of infinite-dimensional Hilbert spaces such as the space of square-summable sequences and spaces of square-integrable functions. Linear operators on a finite-dimensional Hilbert space have only the zero functional as a singular trace since all operators have finite rank. For example, matrix algebras have no non-trivial singular traces and the matrix trace is the unique trace up to scaling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum computing, the Brassard-H\u00f8yer-Tapp algorithm or BHT algorithm is a quantum algorithm that solves the collision problem. In this problem, one is given n and an r-to-1 function f: { 1 , \u2026 , n } \u2192 { 1 , \u2026 , n } {\\displaystyle f:\\,\\{1,\\ldots ,n\\}\\rightarrow \\{1,\\ldots ,n\\}} and needs to find two inputs that f maps to the same output. The BHT algorithm only makes O ( n 1 / 3 ) {\\displaystyle O(n^{1/3})} queries to f, which matches the lower bound of \u03a9 ( n 1 / 3 ) {\\displaystyle \\Omega (n^{1/3})} in the black box model.The algorithm was discovered by Gilles Brassard, Peter H\u00f8yer, and Alain Tapp in 1997. It uses Grover's algorithm, which was discovered the year before.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this case, the space requirements are no longer guaranteed to be constant since it requires storing all previous data points, but the solution may take less time to compute with the addition of a new data point, as compared to batch learning techniques. A common strategy to overcome the above issues is to learn using mini-batches, which process a small batch of b \u2265 1 {\\displaystyle b\\geq 1} data points at a time, this can be considered as pseudo-online learning for b {\\displaystyle b} much smaller than the total number of training points. Mini-batch techniques are used with repeated passing over the training data to obtain optimized out-of-core versions of machine learning algorithms, for example, stochastic gradient descent. When combined with backpropagation, this is currently the de facto training method for training artificial neural networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A typically diverse area is in the representation of sounds not present in most varieties of Romani. For example, the centralised vowel phonemes of several varieties of Vlax and Xaladitka, when they are indicated separately from the non-centralised vowels, can be represented using \u0259, \u044a or \u0103. Another particularly variant area is the representation of palatalised consonants, which are absent from a number of dialects. Some variant graphemes for /t\u02b2/ include tj, ty, \u0107, \u010dj and t\u1fbf. Finally, the representation of the second rhotic, which in several dialects has been merged with /r/, tends to vary between \u0159, rr, and rh, and sometimes even gh, with the first two being the most frequently found variants.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nondeterministic communication complexity, Alice and Bob have access to an oracle. After receiving the oracle's word, the parties communicate to deduce f ( x , y ) {\\displaystyle f(x,y)} . The nondeterministic communication complexity is then the maximum over all pairs ( x , y ) {\\displaystyle (x,y)} over the sum of number of bits exchanged and the coding length of the oracle word. Viewed differently, this amounts to covering all 1-entries of the 0/1-matrix by combinatorial 1-rectangles (i.e., non-contiguous, non-convex submatrices, whose entries are all one (see Kushilevitz and Nisan or Dietzfelbinger et al.)). The nondeterministic communication complexity is the binary logarithm of the rectangle covering number of the matrix: the minimum number of combinatorial 1-rectangles required to cover all 1-entries of the matrix, without covering any 0-entries. Nondeterministic communication complexity occurs as a means to obtaining lower bounds for deterministic communication complexity (see Dietzfelbinger et al.), but also in the theory of nonnegative matrices, where it gives a lower bound on the nonnegative rank of a nonnegative matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In addition, by usually regressing on only a subset of all the principal components, PCR can result in dimension reduction through substantially lowering the effective number of parameters characterizing the underlying model. This can be particularly useful in settings with high-dimensional covariates. Also, through appropriate selection of the principal components to be used for regression, PCR can lead to efficient prediction of the outcome based on the assumed model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Spijker's lemma is a result in the theory of rational mappings of the Riemann sphere. It states that the image of a circle under a complex rational map with numerator and denominator having degree at most n has length at most 2n\u03c0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems that support privileged mode, only privileged applications (usually the OS kernel) may modify the Interrupt flag. In an x86 system this only applies to protected mode code (Real mode code may always modify the Interrupt flag). CLI and STI are privileged instructions, which cause a general protection fault if an unprivileged application attempts to execute them. The POPF instruction will not modify the Interrupt flag if the application is unprivileged.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar multiplication) are also continuous functions. Such a topology is called a vector topology and every topological vector space has a uniform topological structure, allowing a notion of uniform convergence and completeness.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the U.S. the Bureau of Labor Statistics makes available extensive statistics on workplace accidents and injuries. For example:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonology and linguistics, a phoneme () is a unit of phone that can distinguish one word from another in a particular language. For example, in most dialects of English, with the notable exception of the West Midlands and the north-west of England, the sound patterns (sin) and (sing) are two separate words that are distinguished by the substitution of one phoneme, /n/, for another phoneme, /\u014b/. Two words like this that differ in meaning through the contrast of a single phoneme form a minimal pair. If, in another language, any two sequences differing only by pronunciation of the final sounds  or  are perceived as being the same in meaning, then these two sounds are interpreted as phonetic variants of a single phoneme in that language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the uncoordinated checkpointing, each process checkpoints its own state independently. It must be stressed that simply forcing processes to checkpoint their state at fixed time intervals is not sufficient to ensure global consistency. The need for establishing a consistent state (i.e., no missing messages or duplicated messages) may force other processes to roll back to their checkpoints, which in turn may cause other processes to roll back to even earlier checkpoints, which in the most extreme case may mean that the only consistent state found is the initial state (the so-called domino effect).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In structured programming, the ordered sequencing of successive commands is considered one of the basic control structures, which is used as a building block for programs alongside iteration, recursion and choice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the hypergraph regularity method is a powerful tool in extremal graph theory that refers to the combined application of the hypergraph regularity lemma and the associated counting lemma. It is a generalization of the graph regularity method, which refers to the use of Szemer\u00e9di's regularity and counting lemmas. Very informally, the hypergraph regularity lemma decomposes any given k {\\displaystyle k} -uniform hypergraph into a random-like object with bounded parts (with an appropriate boundedness and randomness notions) that is usually easier to work with. On the other hand, the hypergraph counting lemma estimates the number of hypergraphs of a given isomorphism class in some collections of the random-like parts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More generally, optimization includes finding the best available element of some function given a defined domain and may use a variety of different computational optimization techniques.Economics is closely enough linked to optimization by agents in an economy that an influential definition relatedly describes economics qua science as the \"study of human behavior as a relationship between ends and scarce means\" with alternative uses. Optimization problems run through modern economics, many with explicit economic or technical constraints. In microeconomics, the utility maximization problem and its dual problem, the expenditure minimization problem for a given level of utility, are economic optimization problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If defined as blue-dominated colors between blue and red, violet colors in Munsell's system would be classified as having the 7.5PB and 10.0PB hue, which is confirmed in visual experiments The truly purple color, defined as being within the range of the red-dominated colors between red and blue, is sometimes confusingly labeled as red-violet color, or more correctly artist's purple. It is the pigment color that would be on a pigment color color wheel between pigment violet and pigment (process) magenta. In the Munsell color system, this color at its maximum chroma of 12 is called Red-Purple, or more specifically Munsell 5RP. Artists' pigments and colored pencils labeled as purple are typically colored the red-violet color. On an RYB color wheel, the so-called red-violet color is the color between red and violet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In synchronous systems, the participants simultaneously receive and send information in \"real time\", and a message is usually followed by a response in a short time span. This type of communication is used for communication that requires an immediate response when the other participant is promptly available or for more informal communication in a direct setting. It can be used in an enterprise to answer questions quickly, discuss ideas, convey important developments that need attention or any other important message.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such a position leads to a form of skepticism about knowledge since the great majority of regular beliefs do not live up to these requirements. It would imply that people know very little and that most who claim to know a certain fact are mistaken. However, a more common view among epistemologists is that knowledge does not require infallibility and that many knowledge claims in everyday life are true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the JIS X 0201 specification (1969), katakana are encoded in A0\u2013DF (hexadecimal) block \u2013 how they are displayed is not specified, and there is no separate encoding of full-width and half-width kana. In JIS X 0208, katakana, hiragana, and kanji are all encoded (and displayed as full-width characters; there are no half-width characters), though the ordering of the kana is different \u2013 see JIS X 0208#Hiragana and katakana. In Shift JIS, which combines JIS X 0201 and JIS X 0208, these encodings (both of which can encode Latin characters and katakana) are stored separately, with JIS X 0201 all being displayed as half-width (thus the JIS X 0201 katakana are displayed as half-width kana), while JIS X 0208 are all displayed as full-width (thus the JIS X 0208 Latin characters are all displayed as full-width Latin characters). Thus in Shift JIS, Latin characters and katakana have two encodings with two separate display forms, both half-width and full-width. In Unicode, katakana and hiragana are primarily used as normal, full-width characters (the Katakana and Hiragana blocks are displayed as full-width characters); a separate block, the Halfwidth and Fullwidth Forms block is used to store variant characters, including half-width kana and full-width Latin characters. Thus, the katakana in JIS X 0201 and the corresponding part of derived encodings (the JIS X 0201 part of Shift JIS) are displayed as half-width, while in Unicode half-width forms are specified separately.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem. This issue is particularly prominent in applied areas such as numerical analysis and statistics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the artificial lateral line, neuromast's function is carried out by using transducers. These tiny structures employ various systems such as hot-wire anemometry, optoelectronics or piezoelectric cantilevers to detect mechanical changes in water. Neuromasts are primarily classified into two types based on their location. The superficial neuromast located on the skin is used for velocity sensing to locate certain moving targets, whereas Canal Neuromasts located below the epidermis enclosed in the canal utilize pressure gradient between the inlet and outlet for object detection and avoidance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Various calculi that attempt to capture the theoretical properties of object-oriented programming may be derived from system F<:. The concept of subtyping is related to the linguistic notions of hyponymy and holonymy. It is also related to the concept of bounded quantification in mathematical logic (see Order-sorted logic). Subtyping should not be confused with the notion of (class or object) inheritance from object-oriented languages; subtyping is a relation between types (interfaces in object-oriented parlance) whereas inheritance is a relation between implementations stemming from a language feature that allows new objects to be created from existing ones. In a number of object-oriented languages, subtyping is called interface inheritance, with inheritance referred to as implementation inheritance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social systems theory (cf. Niklas Luhmann), markets are also conceptualized as inner environments of the economy. As horizon of all potential investment decisions the market represents the environment of the actually realized investment decisions. However, such inner environments can also be observed in further function systems of society like in political, scientific, religious or mass media systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This might improve the performance but increases the total latency (maximum number of registers from input to output path) of the circuit. Many times logic circuit changes are handled by user's EDA tools based on timing constraint directives prepared by a designer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a p-constrained group is a finite group resembling the centralizer of an element of prime order p in a group of Lie type over a finite field of characteristic p. They were introduced by Gorenstein and Walter (1964, p.169) in order to extend some of Thompson's results about odd groups to groups with dihedral Sylow 2-subgroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a dicut is a partition of the vertices of a directed graph into two subsets, so that each edge that has an endpoint in both subsets is directed from the first subset to the second. Each strongly connected component of the graph must be entirely contained in one of the two subsets, so a strongly connected graph has no nontrivial dicuts.The second of the two subsets in a dicut, a subset of vertices with no edges that exit the subset, is called a closure. The closure problem is the algorithmic problem of finding a dicut, in an edge-weighted directed graph, whose total weight is as large as possible. It can be solved in polynomial time.In planar graphs, dicuts and cycles are dual concepts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While Bell's theorem established nonlocality to be a feature of any hidden variable theory that recovers the predictions of quantum mechanics, the KS theorem established contextuality to be an inevitable feature of such theories. The theorem proves that there is a contradiction between two basic assumptions of the hidden-variable theories intended to reproduce the results of quantum mechanics: that all hidden variables corresponding to quantum-mechanical observables have definite values at any given time, and that the values of those variables are intrinsic and independent of the device used to measure them. The contradiction is caused by the fact that quantum-mechanical observables need not be commutative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Bhattacharyya distance measures the similarity of two probability distributions. It is closely related to the Bhattacharyya coefficient, which is a measure of the amount of overlap between two statistical samples or populations. It is not a metric, despite named a \"distance\", since it does not obey the triangle inequality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a monoidal category (or tensor category) is a category C {\\displaystyle \\mathbf {C} } equipped with a bifunctor \u2297: C \u00d7 C \u2192 C {\\displaystyle \\otimes :\\mathbf {C} \\times \\mathbf {C} \\to \\mathbf {C} } that is associative up to a natural isomorphism, and an object I that is both a left and right identity for \u2297, again up to a natural isomorphism. The associated natural isomorphisms are subject to certain coherence conditions, which ensure that all the relevant diagrams commute. The ordinary tensor product makes vector spaces, abelian groups, R-modules, or R-algebras into monoidal categories.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One example of a linear regression using this method is the least squares method\u2014which evaluates appropriateness of linear regression model to model bivariate dataset, but whose limitation is related to known distribution of the data. The term mean squared error is sometimes used to refer to the unbiased estimate of error variance: the residual sum of squares divided by the number of degrees of freedom. This definition for a known, computed quantity differs from the above definition for the computed MSE of a predictor, in that a different denominator is used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network security, evasion is bypassing an information security defense in order to deliver an exploit, attack, or other form of malware to a target network or system, without detection. Evasions are typically used to counter network-based intrusion detection and prevention systems (IPS, IDS) but can also be used to by-pass firewalls and defeat malware analysis. A further target of evasions can be to crash a network security defense, rendering it in-effective to subsequent targeted attacks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Further control over data and code came in 2002 when object-oriented programming, user-defined functions and user-defined data types were included. Nevertheless, much important legacy COBOL software uses unstructured code, which has become practically unmaintainable. It can be too risky and costly to modify even a simple section of code, since it may be used from unknown places in unknown ways.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Neural networks with Stochastic Depth were made possible given the Residual Network architectures. This training procedure randomly drops a subset of layers and lets the signal propagate through the identity skip connection. Also known as \"DropPath\", this is an effective regularization method for training large and deep models, such as the Vision Transformer (ViT).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a positive polynomial (respectively non-negative polynomial) on a particular set is a polynomial whose values are positive (respectively non-negative) on that set. Precisely, Let p be a polynomial in n variables with real coefficients and let S be a subset of the n-dimensional Euclidean space \u211dn. We say that: p is positive on S if p(x) > 0 for every x in S. p is non-negative on S if p(x) \u2265 0 for every x in S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the budgeted maximum coverage version, not only does every element e j {\\displaystyle e_{j}} have a weight w ( e j ) {\\displaystyle w(e_{j})} , but also every set S i {\\displaystyle S_{i}} has a cost c ( S i ) {\\displaystyle c(S_{i})} . Instead of k {\\displaystyle k} that limits the number of sets in the cover a budget B {\\displaystyle B} is given. This budget B {\\displaystyle B} limits the total cost of the cover that can be chosen. maximize \u2211 e \u2208 E w ( e j ) \u22c5 y j {\\displaystyle \\sum _{e\\in E}w(e_{j})\\cdot y_{j}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Columns might represent things like company name, company street address, whether the company is publicly held, its VAT number, etc. In a table that represents the association of employees with departments, each row would associate one employee with one department. The implicit structure of a row, and the meaning of the data values in a row, requires that the row be understood as providing a succession of data values, one in each column of the table.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, an acoustic coupler is an interface device for coupling electrical signals by acoustical means\u2014usually into and out of a telephone. The link is achieved through converting electric signals from the phone line to sound and reconvert sound to electric signals needed for the end terminal, such as a teletypewriter, and back, rather than through direct electrical connection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Proto-Indo-European language (PIE), the nasal infix *\u27e8n(\u00e9)\u27e9 is one of several means to form the athematic present tense. It is inserted immediately before the last consonant of the zero-grade root. The infix appeared as *\u27e8n\u00e9\u27e9 in the forms where a full-grade stem would be expected, and as *\u27e8n\u27e9 in forms where zero-grade would be expected. For example, the PIE root *weik- \"to win\" would yield a nasal-infixed present stem *wi\u27e8n\u00e9\u27e9k- ~ *wi\u27e8n\u27e9k-.These presents are called nasal infix presents or simply nasal presents and are typically active transitive verbs, often with durative aspect.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, Q(2,9) has the elements and relations a > b > c < d > e > f < g > h > i . {\\displaystyle a>b>c e>f h>i.} In this notation, a fence is a partially ordered set of the form Q(1,n).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UK and the US, the refractive index is generally specified concerning the yellow He-d Fraunhofer line, commonly abbreviated as nd. Lens materials are classified by their refractive index, as follows: Normal index: 1.48 \u2264 nd < 1.54 Mid-index: 1.54 \u2264 nd < 1.60 High-index: 1.60 \u2264 nd < 1.74 Very high index: 1.76 \u2264 ndThis is a general classification. Indexes of nd values that are \u2265 1.60 can be, often for marketing purposes, referred to as high-index. Likewise, Trivex and other borderline normal/mid-index materials may be referred to as mid-index.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical finite group theory, a quadratic pair for the odd prime p, introduced by Thompson (1971), is a finite group G together with a quadratic module, a faithful representation M on a vector space over the finite field with p elements such that G is generated by elements with minimal polynomial (x \u2212 1)2. Thompson classified the quadratic pairs for p \u2265 5. Chermak (2004) classified the quadratic pairs for p = 3. With a few exceptions, especially for p = 3, groups with a quadratic pair for the prime p tend to be more or less groups of Lie type in characteristic p.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let I {\\displaystyle I} be an ideal of R {\\displaystyle R} . The tight closure of I {\\displaystyle I} , denoted by I \u2217 {\\displaystyle I^{*}} , is another ideal of R {\\displaystyle R} containing I {\\displaystyle I} . The ideal I \u2217 {\\displaystyle I^{*}} is defined as follows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Overall the studies identify 26 articles, only 12 of them could be reproduced and 11 of them could be outperformed by much older and simpler properly tuned baselines. The articles also highlights a number of potential problems in today's research scholarship and call for improved scientific practices in that area. Similar issues have been spotted also in sequence-aware recommender systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psycholinguistics, parsing involves not just the assignment of words to categories (formation of ontological insights), but the evaluation of the meaning of a sentence according to the rules of syntax drawn by inferences made from each word in the sentence (known as connotation). This normally occurs as words are being heard or read. Consequently, psycholinguistic models of parsing are of necessity incremental, meaning that they build up an interpretation as the sentence is being processed, which is normally expressed in terms of a partial syntactic structure. Creation of initially wrong structures occurs when interpreting garden-path sentences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the set of positive integers is not in fact larger than the set of perfect squares: both sets are infinite and countable and can therefore be put in one-to-one correspondence. Nevertheless if one goes through the natural numbers, the squares become increasingly scarce. The notion of natural density makes this intuition precise for many, but not all, subsets of the naturals (see Schnirelmann density, which is similar to natural density but defined for all subsets of N {\\displaystyle \\mathbb {N} } ). If an integer is randomly selected from the interval , then the probability that it belongs to A is the ratio of the number of elements of A in  to the total number of elements in . If this probability tends to some limit as n tends to infinity, then this limit is referred to as the asymptotic density of A. This notion can be understood as a kind of probability of choosing a number from the set A. Indeed, the asymptotic density (as well as some other types of densities) is studied in probabilistic number theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Falling\", similarly, would be stored as \"fall\" and suffixed with the \"ing\" inflection.Though proponents of the decompositional model recognize that a morpheme-by-morpheme analysis may require significantly more computation, they argue that the unpacking of morphological information is necessary for other processes (such as syntactic structure) which may occur parallel to lexical searches. As a whole, research into systems of human lexical recognition is limited due to little experimental evidence that fully discriminates between the three main models.In any case, lexical recognition likely contributes significantly to speech segmentation through the contextual clues it provides, given that it is a heavily probabilistic system\u2014based on the statistical likelihood of certain words or constituents occurring together. For example, one can imagine a situation where a person might say \"I bought my dog at a ____ shop\" and the missing word's vowel is pronounced as in \"net\", \"sweat\", or \"pet\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s memory was relatively expensive, and CPU designers produced instruction sets that densely encoded instructions and data in order to better utilize this resource. For instance, the add A to B to produce C instruction would be provided in many different forms that would gather A and B from different places; main memory, indexes, or registers. Providing these different instructions allowed the programmer to select the instruction that took up the least possible room in memory, reducing the program's needs and leaving more room for data. Actually making these instructions work required circuitry in the CPU, which was a significant limitation in early designs and required designers to select just those instructions that were really needed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, strong subadditivity of quantum entropy (SSA) is the relation among the von Neumann entropies of various quantum subsystems of a larger quantum system consisting of three subsystems (or of one quantum system with three degrees of freedom). It is a basic theorem in modern quantum information theory. It was conjectured by D. W. Robinson and D. Ruelle in 1966 and O. E. Lanford III and D. W. Robinson in 1968 and proved in 1973 by E.H.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s, Kodak developed DX Encoding (from Digital indeX), or DX coding, a feature that was eventually adapted by all camera and film manufacturers. DX encoding provides information on both the film cassette and on the film regarding the type of film, number of exposures, speed (ISO/ASA rating) of the film. It consists of three types of identification. First is a barcode near the film opening of the cassette, identifying the manufacturer, film type and processing method (see image below left).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set, though that is an ambiguous term that many authors reserve for partially ordered sets or totally ordered sets. The term pre-ordered set is unambiguous, and is always synonymous with a mathematical hierarchy. The term hierarchy is used to stress a hierarchical relation among the elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result, implementing an electromechanical keyboard that produced an ASCII encoding but had conventional typewriter key mappings would require significant complexity due to key-specific shift mechanisms for digits and symbol keys. This could be avoided by changing the key mappings to correspond to the ASCII table, which was notably done in the Teletype Model 33 (1963). Later keyboards continued to use this mapping, which was formalized in the American Standards Association X4.14-1971 standard and the European Computer Manufacturers' Association ECMA-23 standard, where it is referred to as logical bit pairing, and contrasted with typewriter pairing. In everyday usage these were referred to as bit-paired and typewriter-paired keyboards.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics the assumed mean is a method for calculating the arithmetic mean and standard deviation of a data set. It simplifies calculating accurate values by hand. Its interest today is chiefly historical but it can be used to quickly estimate these statistics. There are other rapid calculation methods which are more suited for computers which also ensure more accurate results than the obvious methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Remove randomly a fraction 1 \u2212 p \u2032 {\\displaystyle 1-p'} of nodes and leave only a fraction p \u2032 {\\displaystyle p'} from the network. There exists a critical percolation threshold p c \u2032 = 1 \u27e8 k \u27e9 {\\displaystyle p'_{c}={\\tfrac {1}{\\langle k\\rangle }}} below which the network becomes fragmented while above p c \u2032 {\\displaystyle p'_{c}} a giant connected component of order n exists. The relative size of the giant component, P\u221e, is given by P \u221e = p \u2032  . {\\displaystyle P_{\\infty }=p'.\\,}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The receiver is designed so that either codeword of the pair decodes to the same data bits. Most line codes use either a paired disparity code or a constant-weight code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some aspects can be traced as far back as F. L. Hitchcock in 1928, but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, further advocated by L. De Lathauwer et al. in their Multilinear SVD work that employs the power method, or advocated by Vasilescu and Terzopoulos that developed M-mode SVD a parallel algorithm that employs the matrix SVD. The term higher order singular value decomposition (HOSVD) was coined be DeLathauwer, but the algorithm referred to commonly in the literature as the HOSVD and attributed to either Tucker or DeLathauwer was developed by Vasilescu and Terzopoulos. Robust and L1-norm-based variants of HOSVD have also been proposed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a heteroclinic network is an invariant set in the phase space of a dynamical system. It can be thought of loosely as the union of more than one heteroclinic cycle. Heteroclinic networks arise naturally in a number of different types of applications, including fluid dynamics and populations dynamics. The dynamics of trajectories near to heteroclinic networks is intermittent: trajectories spend a long time performing one type of behaviour (often, close to equilibrium), before switching rapidly to another type of behaviour. This type of intermittent switching behaviour has led to several different groups of researchers using them as a way to model and understand various type of neural dynamics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory \u2013 specifically in the theory of stochastic processes, a stationary sequence is a random sequence whose joint probability distribution is invariant over time. If a random sequence X j is stationary then the following holds: F X n , X n + 1 , \u2026 , X n + N \u2212 1 ( x n , x n + 1 , \u2026 , x n + N \u2212 1 ) = F X n + k , X n + k + 1 , \u2026 , X n + k + N \u2212 1 ( x n , x n + 1 , \u2026 , x n + N \u2212 1 ) , {\\displaystyle {\\begin{aligned}&{}\\quad F_{X_{n},X_{n+1},\\dots ,X_{n+N-1}}(x_{n},x_{n+1},\\dots ,x_{n+N-1})\\\\&=F_{X_{n+k},X_{n+k+1},\\dots ,X_{n+k+N-1}}(x_{n},x_{n+1},\\dots ,x_{n+N-1}),\\end{aligned}}} where F is the joint cumulative distribution function of the random variables in the subscript. If a sequence is stationary then it is wide-sense stationary. If a sequence is stationary then it has a constant mean (which may not be finite): E ( X  ) = \u03bc for all n . {\\displaystyle E(X)=\\mu \\quad {\\text{for all }}n.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The simplest paired disparity code is alternate mark inversion signal. Other paired disparity codes include 8b/10b, 8B12B, the modified AMI codes, coded mark inversion, and 4B3T. The digits may be represented by disparate physical quantities, such as two different frequencies, phases, voltage levels, magnetic polarities, or electrical polarities, each one of the pair representing a 0 or a 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and econometrics, extremum estimators are a wide class of estimators for parametric models that are calculated through maximization (or minimization) of a certain objective function, which depends on the data. The general theory of extremum estimators was developed by Amemiya (1985).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, in the theory relating to sampling from finite populations, the sampling probability (also known as inclusion probability) of an element or member of the population, is its probability of becoming part of the sample during the drawing of a single sample. For example, in simple random sampling the probability of a particular unit i {\\displaystyle i} to be selected into the sample is p i = ( N \u2212 1 n \u2212 1 ) ( N n ) = n N {\\displaystyle p_{i}={\\frac {\\binom {N-1}{n-1}}{\\binom {N}{n}}}={\\frac {n}{N}}} where n {\\displaystyle n} is the sample size and N {\\displaystyle N} is the population size.Each element of the population may have a different probability of being included in the sample. The inclusion probability is also termed the \"first-order inclusion probability\" to distinguish it from the \"second-order inclusion probability\", i.e. the probability of including a pair of elements. Generally, the first-order inclusion probability of the ith element of the population is denoted by the symbol \u03c0i and the second-order inclusion probability that a pair consisting of the ith and jth element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by \u03c0ij.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1990s, IBM engineer Frank Canova realised that chip-and-wireless technology was becoming small enough to use in handheld devices. The first commercially available device that could be properly referred to as a \"smartphone\" began as a prototype called \"Angler\" developed by Canova in 1992 while at IBM and demonstrated in November of that year at the COMDEX computer industry trade show. A refined version was marketed to consumers in 1994 by BellSouth under the name Simon Personal Communicator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the latter case, he becomes privately informed after the contract has been signed. In most adverse selection models, it is assumed that the agent's private information is \"soft\" (i.e., the information cannot be certified). Yet, there are also some adverse selection models with \"hard\" information (i.e., the agent may have evidence to prove that claims he makes about his type are true).Adverse selection models can be further categorized into models with private values and models with interdependent or common values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The C programming language reifies the low-level detail of memory addresses.Many programming language designs encapsulate the details of memory allocation in the compiler and the run-time system. In the design of the C programming language, the memory address is reified and is available for direct manipulation by other language constructs. For example, the following code may be used when implementing a memory-mapped device driver.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, a hypothetical current 50 km wide, 500 m (0.5 km) deep, and moving at 2 m/s would be transporting 50 Sv of water. The sverdrup is distinct from the SI sievert unit or the non-SI svedberg unit. All three use the same symbol. They are not related.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "it soon became clear that some better tools than the Backus notation might be advantageous . I developed a scheme  which enables the design of a language to carry much more information in the syntax than is normally carried. Quite peculiar to W-grammars was their strict treatment of attributes as strings, defined by a context-free grammar, on which concatenation is the only possible operation; complex data structures and operations can be defined by pattern matching.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language type theory, row polymorphism is a kind of polymorphism that allows one to write programs that are polymorphic on row types such as record types and polymorphic variants. A row-polymorphic type system and proof of type inference was introduced by Mitchell Wand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the expected utility theory of von Neumann and Morgenstern, four axioms together imply that individuals act in situations of risk as if they maximize the expected value of a utility function. One of the axioms is an independence axiom analogous to the IIA axiom: If L \u227a M {\\displaystyle \\,L\\prec M} , then for any N {\\displaystyle \\,N} and p \u2208 ( 0 , 1 ] {\\displaystyle \\,p\\in (0,1]} , p L + ( 1 \u2212 p ) N \u227a p M + ( 1 \u2212 p ) N , {\\displaystyle \\,pL+(1-p)N\\prec pM+(1-p)N,} where p is a probability, pL+(1-p)N means a gamble with probability p of yielding L and probability (1-p) of yielding N, and L \u227a M {\\displaystyle \\,L\\prec M} means that M is preferred over L. This axiom says that if one outcome (or lottery ticket) L is considered to be not as good as another (M), then having a chance with probability p of receiving L rather than N is considered to be not as good as having a chance with probability p of receiving M rather than N.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The latter two symbols were introduced by the Bourbaki group (specifically Andr\u00e9 Weil) in 1939, inspired by the letter \u00d8 in the Danish and Norwegian alphabets (and not related in any way to the Greek letter \u03a6).Empty sets are used in set operations. For example: A = { 2 , 3 , 5 , 7 , 11 } {\\displaystyle A=\\{2,3,5,7,11\\}} B = { 4 , 6 , 8 , 9 } {\\displaystyle B=\\{4,6,8,9\\}} A \u2229 B = ? {\\displaystyle A\\cap B=?} There are no common elements in the solution; so it should be denoted as: A \u2229 B = \u2205 {\\displaystyle A\\cap B=\\varnothing } or A \u2229 B = { } {\\displaystyle A\\cap B=\\{\\}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical set theory, a Cohen algebra, named after Paul Cohen, is a type of Boolean algebra used in the theory of forcing. A Cohen algebra is a Boolean algebra whose completion is isomorphic to the completion of a free Boolean algebra (Koppelberg 1993).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The case (x, y, z) = (3, 3, n) and all its permutations have been proven for 3 \u2264 n \u2264 109 and various modulo congruences when n is prime. The case (x, y, z) = (3, 4, 5) and all its permutations were proven by Siksek and Stoll in 2011. The case (x, y, z) = (3, 5, 5) and all its permutations were proven by Bjorn Poonen in 1998.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These include, lexical definitions, or the common dictionary definitions of words already in a language; demonstrative definitions, which define something by pointing to an example of it (\"This,\" , \"is an Asian elephant. \"); and precising definitions, which reduce the vagueness of a word, typically in some special sense (\"'Large', among female Asian elephants, is any individual weighing over 5,500 pounds. \").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the SARG04 scheme, Alice wishes to send a private key to Bob. She begins with two strings of bits, a {\\displaystyle a} and b {\\displaystyle b} , each n {\\displaystyle n} bits long. She then encodes these two strings as a string of n {\\displaystyle n} qubits, | \u03c8 \u27e9 = \u2a02 i = 1 n | \u03c8 a i b i \u27e9 . {\\displaystyle |\\psi \\rangle =\\bigotimes _{i=1}^{n}|\\psi _{a_{i}b_{i}}\\rangle .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Young\u2013Fibonacci graph is the graph of this lattice, and has a vertex for each digit sequence. As the graph of a modular lattice, it is a modular graph. The Young\u2013Fibonacci graph and the Young\u2013Fibonacci lattice were both initially studied in two papers by Fomin (1988) and Stanley (1988). They are named after the closely related Young's lattice and after the Fibonacci number of their elements at any given rank.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The cutoff frequency can be calculated from that value. Pre-emphasis is commonly used in telecommunications, digital audio recording, record cutting, in FM broadcasting transmissions, and in displaying the spectrograms of speech signals. One example of this is the RIAA equalization curve on 33 rpm and 45 rpm vinyl records.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This means that the concept of general Diophantine set, apparently belonging to number theory, can be taken rather in logical or recursion-theoretic terms. This is far from obvious, however, and represented the culmination of some decades of work. Matiyasevich's completion of the MRDP theorem settled Hilbert's tenth problem. Hilbert's tenth problem was to find a general algorithm which can decide whether a given Diophantine equation has a solution among the integers. While Hilbert's tenth problem is not a formal mathematical statement as such, the nearly universal acceptance of the (philosophical) identification of a decision algorithm with a total computable predicate allows us to use the MRDP theorem to conclude that the tenth problem is unsolvable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The best and most informative systems use Activity based costing (ABC) that track costs by each marketing activity, rather than traditional cost accounting by salaries, facilities, equipment, and materials. ABC methods have the best fidelity as they show contribution efficiency (Brand Experience/$ spent) of each activity, and they may be summed in desired combinations (or campaigns). Understanding competitors costs and brand experience can lead to benchmarking, a comparison to what is considered the best in class. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At this point, organizations tend to recognize the need to extend their test automation efforts. Even after more automation is added to the existing test process, managers still lack adequate insight into the level of risk associated with an application at any given point in time. Understanding these risks is critical for making the rapid go/no go decisions involved in Continuous Delivery processes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The \"text\" vs. \"binary\" distinction can sometimes refer to the semantic content of a file (e.g. a written document vs. a digital image). However, it often refers specifically to whether the individual bytes of a file are interpretable as text (see character encoding) or cannot so be interpreted. When this last meaning is intended, the more specific terms binary format and text(ual) format are sometimes used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some real-time applications one needs to find eigenvectors for matrices with a speed of millions of matrices per second. In such applications, typically the statistics of matrices is known in advance and one can take as an approximate eigenvalue the average eigenvalue for some large matrix sample. Better, one may calculate the mean ratio of the eigenvalues to the trace or the norm of the matrix and estimate the average eigenvalue as the trace or norm multiplied by the average value of that ratio. Clearly such a method can be used only with discretion and only when high precision is not critical. This approach of estimating an average eigenvalue can be combined with other methods to avoid excessively large error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each bundle is a class whose members are collections, i.e. classes; thus each is a class of classes\" (Russell 1919:14). Step 3: Define the null class: Notice that a certain class of classes is special because its classes contain no elements, i.e. no elements satisfy the predicates whose assertion defined this particular class/collection. The resulting entity may be called \"the null class\" or \"the empty class\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This means the relabel operation could potentially be performed 2| V | \u2212 1 times for all nodes V \\ {s, t} (i.e. | V | \u2212 2). This results in a bound of O(V 2) for the relabel operation. Each saturating push on an admissible arc (u, v) removes the arc from Gf .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming, a cipher suite is referred to in both plural and non-plural forms. Each one has different definitions: CipherSuite cipher_suites a list of the cryptographic options supported by the client. An example of how cipher_suites is usually used during the handshake process: CipherSuite cipher_suite the cipher suite selected by the server from the client's cipher_suites. An example of how cipher_suite is usually used during the handshake process:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psychological testing, Sawilowsky is a co-author of two self-determination assessment batteries; an instrument designed to assess locus of control, self-esteem, and self-concept among at-risk adolescents; an instrument \"which measures future orientation, knowledge of the realities of child rearing, personal intentions, and sexual self-efficacy;\" and a college well-being instrument. Sawilowsky was the initial proponent in favor of psychometric theory (reliability refers to the test) over datametric theory (reliability refers to the data), a controversy with implications for test theory, role of tests in expert testimony, test validity, etc. The debate was discussed in Educational and Psychological Measurement and elsewhere. Although the issue has not been resolved, the current non-aligned opinion \"lean toward the Sawilowsky position.\" In classical test theory, he developed the Sawilowsky I test, a statistical test used to help demonstrate evidence of construct validity in the multitrait-multimethod matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, overseeing key performance indicators can prove expensive or difficult for organizations. Some indicators such as staff morale may be impossible to quantify. As such, dubious KPIs can be adopted that can be used as a rough guide rather than a precise benchmark.Key performance indicators can also lead to perverse incentives and unintended consequences as a result of employees working to the specific measurements at the expense of the actual quality or value of their work.Sometimes, collecting statistics can become a substitute for a better understanding of the problems, so the use of dubious KPIs can result in progress in aims and measured effectiveness becoming different. For example, during the Vietnam War, US soldiers were shown to be effective in kill ratios and high body counts, but this was misleading when used to measure aims as it did not show the lack of progress towards the US goal of increasing South Vietnamese government control of its territory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of first-order logic, the symbols in a signature are also known as the non-logical symbols, because together with the logical symbols they form the underlying alphabet over which two formal languages are inductively defined: The set of terms over the signature and the set of (well-formed) formulas over the signature. In a structure, an interpretation ties the function and relation symbols to mathematical objects that justify their names: The interpretation of an n {\\displaystyle n} -ary function symbol f {\\displaystyle f} in a structure A {\\displaystyle \\mathbf {A} } with domain A {\\displaystyle A} is a function f A: A n \u2192 A , {\\displaystyle f^{\\mathbf {A} }:A^{n}\\to A,} and the interpretation of an n {\\displaystyle n} -ary relation symbol is a relation R A \u2286 A n . {\\displaystyle R^{\\mathbf {A} }\\subseteq A^{n}.} Here A n = A \u00d7 A \u00d7 \u22ef \u00d7 A {\\displaystyle A^{n}=A\\times A\\times \\cdots \\times A} denotes the n {\\displaystyle n} -fold cartesian product of the domain A {\\displaystyle A} with itself, and so f {\\displaystyle f} is in fact an n {\\displaystyle n} -ary function, and R {\\displaystyle R} an n {\\displaystyle n} -ary relation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, particularly in hypothesis testing, the Hotelling's T-squared distribution (T2), proposed by Harold Hotelling, is a multivariate probability distribution that is tightly related to the F-distribution and is most notable for arising as the distribution of a set of sample statistics that are natural generalizations of the statistics underlying the Student's t-distribution. The Hotelling's t-squared statistic (t2) is a generalization of Student's t-statistic that is used in multivariate hypothesis testing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In rhetoric, emotive or emotional conjugation (also known as Russell's conjugation) is a rhetorical technique used to create an intrinsic bias towards or against a piece of information. Bias is created by using the emotional connotation of a word to prime a response from the audience by creating a loaded statement. Used seriously, such loaded language can lend false support to an argument through emotional connotation and implication, rather than through fact. While emotional conjugation is considered effective by researchers, it ultimately employs a logical fallacy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Because of this analogy, the metric is known in computer science as the earth mover's distance. The name \"Wasserstein distance\" was coined by R. L. Dobrushin in 1970, after learning of it in the work of Leonid Vaser\u0161te\u012dn on Markov processes describing large systems of automata (Russian, 1969). However the metric was first defined by Leonid Kantorovich in The Mathematical Method of Production Planning and Organization (Russian original 1939) in the context of optimal transport planning of goods and materials. Some scholars thus encourage use of the terms \"Kantorovich metric\" and \"Kantorovich distance\". Most English-language publications use the German spelling \"Wasserstein\" (attributed to the name \"Vaser\u0161te\u012dn\" (Russian: \u0412\u0430\u0441\u0435\u0440\u0448\u0442\u0435\u0439\u043d) being of German origin).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physical simulations, sweep and prune is a broad phase algorithm used during collision detection to limit the number of pairs of solids that need to be checked for collision, i.e. intersection. This is achieved by sorting the starts (lower bound) and ends (upper bound) of the bounding volume of each solid along a number of arbitrary axes. As the solids move, their starts and ends may overlap. When the bounding volumes of two solids overlap in all axes they are flagged to be tested by more precise and time-consuming algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C standard library, the character reading functions such as getchar return a value equal to the symbolic value (macro) EOF to indicate that an end-of-file condition has occurred. The actual value of EOF is implementation-dependent and must be negative (but is commonly \u22121, such as in glibc). Block-reading functions return the number of bytes read, and if this is fewer than asked for, then the end of file was reached or an error occurred (checking of errno or dedicated function, such as ferror is required to determine which).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the design of experiments, hypotheses are applied to experimental units in a treatment group. In comparative experiments, members of a control group receive a standard treatment, a placebo, or no treatment at all. There may be more than one treatment group, more than one control group, or both.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mid-September 2013, a media report revealed that Nokia tested the Android operating system on both its Lumia and Asha hardware. On 11 December 2013, a report showed that development of the Asha-like device, codenamed \"Normandy\", was continuing, despite the finalisation of Nokia's acquisition by Microsoft. In February 2014, in Barcelona, Spain, the Nokia X family was unveiled at Mobile World Congress. These devices, which were aimed towards emerging markets, run a modified version of Android known as Nokia X Software Platform, which was aligned towards Microsoft services and did not use Google Play Store. In a company memo released in July 2014, it was announced that, as part of cutbacks, Microsoft would end the Asha, Series 40, and X range entirely, in favor of solely producing and encouraging the use of Windows Phone products.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical modeling, a guess value is more commonly called a starting value or initial value. These are necessary for most optimization problems which use search algorithms, because those algorithms are mainly deterministic and iterative, and they need to start somewhere. One common type of application is nonlinear regression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the result of the test corresponds with reality, then a correct decision has been made. However, if the result of the test does not correspond with reality, then an error has occurred. There are two situations in which the decision is wrong.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C and C++ programming languages, an inline function is one qualified with the keyword inline; this serves two purposes: It serves as a compiler directive that suggests (but does not require) that the compiler substitute the body of the function inline by performing inline expansion, i.e. by inserting the function code at the address of each function call, thereby saving the overhead of a function call. In this respect it is analogous to the register storage class specifier, which similarly provides an optimization hint. The second purpose of inline is to change linkage behavior; the details of this are complicated. This is necessary due to the C/C++ separate compilation + linkage model, specifically because the definition (body) of the function must be duplicated in all translation units where it is used, to allow inlining during compiling, which, if the function has external linkage, causes a collision during linking (it violates uniqueness of external symbols). C and C++ (and dialects such as GNU C and Visual C++) resolve this in different ways.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, it is useful to have an ultimate age associated with a mortality table. Once the ultimate age is reached, the mortality rate is assumed to be 1.000. This age may be the point at which life insurance benefits are paid to a survivor or annuity payments cease. Four methods can be used to end mortality tables: The Forced Method: Select an ultimate age and set the mortality rate at that age equal to 1.000 without any changes to other mortality rates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When a person creates a key-pair, they keep one key private and the other, known as the public-key, is uploaded to a server where it can be accessed by anyone to send the user a private, encrypted, message. Secure Sockets Layer (SSL) uses Diffie\u2013Hellman key exchange if the client does not have a public-private key pair and a published certificate in the public key infrastructure, and Public Key Cryptography if the user does have both the keys and the credential. Key distribution is an important issue in wireless sensor network (WSN) design.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another exercise is completing the square in a quadratic polynomial. An artificially produced word problem is a genre of exercise intended to keep mathematics relevant. Stephen Leacock described this type: The student of arithmetic who has mastered the first four rules of his art and successfully striven with sums and fractions finds himself confronted by an unbroken expanse of questions known as problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is important that the radix is finite, from which follows that the number of digits is quite low. Otherwise, the length of a numeral would not necessarily be logarithmic in its size. (In certain non-standard positional numeral systems, including bijective numeration, the definition of the base or the allowed digits deviates from the above.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Further, if a subtype can be defined for the reals, to separate positive and negative reals, two functions can be written for the reals, one to return a real when the parameter is positive, and another to return a complex value when the parameter is negative. In object-oriented programming, when a series of functions with the same name can accept different parameter profiles or parameters of different types, each of the functions is said to be overloaded. Here is an example of function overloading in C++, demonstrating the implementation of two functions with the same name (Area) but different parameters: As another example, a function might construct an object that will accept directions, and trace its path to these points on screen.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In strong sampling, we assume observation is randomly sampled from the true hypothesis: P ( x | h ) = { 1 | h | , if x \u2208 h 0 , otherwise {\\displaystyle P(x|h)={\\begin{cases}{\\frac {1}{|h|}}&{\\text{, if }}x\\in h\\\\0&{\\text{, otherwise}}\\end{cases}}} In weak sampling, we assume observations randomly sampled and then classified: P ( x | h ) = { 1 , if x \u2208 h 0 , otherwise {\\displaystyle P(x|h)={\\begin{cases}1&{\\text{, if }}x\\in h\\\\0&{\\text{, otherwise}}\\end{cases}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the US, there is a move to require both traditional operators and Over-the-top messaging providers to support texting to 911. In Asia, SMS is used for tsunami warnings and in Europe, SMS is used to inform individuals of imminent disasters. Since the location of a handset is known, systems can alert everyone in an area that the events have made impossible to pass through e.g. an avalanche.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "J ( x ) \u22a2 K {\\displaystyle \\Lambda x\\in C.J(x)\\vdash K} . An implementation of the LF logical framework is provided by the Twelf system at Carnegie Mellon University. Twelf includes a logic programming engine meta-theoretic reasoning about logic programs (termination, coverage, etc.) an inductive meta-logical theorem prover", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Iterative gradient descent that is typically used in adaptive filters has also gained popularity in offline batch-mode support vector based machine learning because of its computational efficiency for large data set processing. Both time series and batch data processing performance is reported to be able to easily handle over 100,000 training examples using as little as 10kB RAM. Data sizes this large are challenging to the original formulations of support vector machines and other kernel methods, which for example relied on constrained optimisation using linear or quadratic programming techniques. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, the classical capacity of a quantum channel is the maximum rate at which classical data can be sent over it error-free in the limit of many uses of the channel. Holevo, Schumacher, and Westmoreland proved the following least upper bound on the classical capacity of any quantum channel N {\\displaystyle {\\mathcal {N}}}: \u03c7 ( N ) = max \u03c1 X A I ( X ; B ) N ( \u03c1 ) {\\displaystyle \\chi ({\\mathcal {N}})=\\max _{\\rho ^{XA}}I(X;B)_{{\\mathcal {N}}(\\rho )}} where \u03c1 X A {\\displaystyle \\rho ^{XA}} is a classical-quantum state of the following form: \u03c1 X A = \u2211 x p X ( x ) | x \u27e9 \u27e8 x | X \u2297 \u03c1 x A , {\\displaystyle \\rho ^{XA}=\\sum _{x}p_{X}(x)\\vert x\\rangle \\langle x\\vert ^{X}\\otimes \\rho _{x}^{A},} p X ( x ) {\\displaystyle p_{X}(x)} is a probability distribution, and each \u03c1 x A {\\displaystyle \\rho _{x}^{A}} is a density operator that can be input to the channel N {\\displaystyle {\\mathcal {N}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a polynomial decomposition expresses a polynomial f as the functional composition g \u2218 h {\\displaystyle g\\circ h} of polynomials g and h, where g and h have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time. Polynomials which are decomposable in this way are composite polynomials; those which are not are indecomposable polynomials or sometimes prime polynomials (not to be confused with irreducible polynomials, which cannot be factored into products of polynomials). The degree of a composite polynomial is always a composite number, the product of the degrees of the composed polynomials. The rest of this article discusses only univariate polynomials; algorithms also exist for multivariate polynomials of arbitrary degree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the public exponent is small and the plaintext m {\\displaystyle m} is very short, then the RSA function may be easy to invert, which makes certain attacks possible. Padding schemes ensure that messages have full lengths, but additionally choosing the public exponent e = 2 16 + 1 {\\displaystyle e=2^{16}+1} is recommended. When this value is used, signature verification requires 17 multiplications, as opposed to about 25 when a random e {\\displaystyle e} of similar size is used. Unlike low private exponent (see Wiener's attack), attacks that apply when a small e {\\displaystyle e} is used are far from a total break, which would recover the secret key d. The most powerful attacks on low public exponent RSA are based on the following theorem, which is due to Don Coppersmith.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the area of algebra known as group theory, a more than fifty-year effort was made to answer a conjecture of (Burnside 1911): are all groups of odd order solvable? Progress was made by showing that CA-groups, groups in which the centralizer of a non-identity element is abelian, of odd order are solvable (Suzuki 1957). Further progress was made showing that CN-groups, groups in which the centralizer of a non-identity element is nilpotent, of odd order are solvable (Feit, Thompson & Hall 1960). The complete solution was given in (Feit & Thompson 1963), but further work on CN-groups was done in (Suzuki 1961), giving more detailed information about the structure of these groups. For instance, a non-solvable CN-group G is such that its largest solvable normal subgroup O\u221e(G) is a 2-group, and the quotient is a group of even order.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, such as the air conditioner example, the distribution of survival times may be approximated well by a function such as the exponential distribution. Several distributions are commonly used in survival analysis, including the exponential, Weibull, gamma, normal, log-normal, and log-logistic. These distributions are defined by parameters. The normal (Gaussian) distribution, for example, is defined by the two parameters mean and standard deviation. Survival functions that are defined by parameters are said to be parametric. In the four survival function graphs shown above, the shape of the survival function is defined by a particular probability distribution: survival function 1 is defined by an exponential distribution, 2 is defined by a Weibull distribution, 3 is defined by a log-logistic distribution, and 4 is defined by another Weibull distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more precisely in algebra, an \u00e9tale group scheme is a certain kind of group scheme.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the absence of any external or internal stimuli, cells may move randomly without any directional preference. In this case, the reorientation operator may be defined through a transition probability where Z = \u2211 s O \u03b4 n ( s ) , n ( s O ) {\\displaystyle Z=\\sum _{\\mathbf {s} ^{\\mathcal {O}}}\\delta _{n\\left(\\mathbf {s} \\right),n\\left(\\mathbf {s} ^{\\mathcal {O}}\\right)}} . Such transition probability allows any post-reorientation configuration s O {\\displaystyle \\mathbf {s} ^{\\mathcal {O}}} with the same number of particles as the pre-reorientation configuration s {\\displaystyle \\mathbf {s} } , to be picked uniformly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a varimax rotation is used to simplify the expression of a particular sub-space in terms of just a few major items each. The actual coordinate system is unchanged, it is the orthogonal basis that is being rotated to align with those coordinates. The sub-space found with principal component analysis or factor analysis is expressed as a dense basis with many non-zero weights which makes it hard to interpret. Varimax is so called because it maximizes the sum of the variances of the squared loadings (squared correlations between variables and factors).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately by conditioning it relative to their age, rather than simply assuming that the individual is typical of the population as a whole. One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesian statistics, being considered by one authority as; \"to the theory of probability what Pythagoras's theorem is to geometry.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance.From the perspective of Bayesian inference, MLE is generally equivalent to maximum a posteriori (MAP) estimation with uniform prior distributions (or a normal prior distribution with a standard deviation of infinity). In frequentist inference, MLE is a special case of an extremum estimator, with the objective function being the likelihood.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An application of this principle is the notion of sub-distributivity as explained in the article on interval arithmetic. In category theory, if ( S , \u03bc , \u03bd ) {\\displaystyle (S,\\mu ,\\nu )} and ( S \u2032 , \u03bc \u2032 , \u03bd \u2032 ) {\\displaystyle \\left(S^{\\prime },\\mu ^{\\prime },\\nu ^{\\prime }\\right)} are monads on a category C , {\\displaystyle C,} a distributive law S .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was formulated for the purpose of illustrating the logical groups and scopes of functions needed in the design of the suite of internetworking protocols of TCP/IP, as needed for the operation of the Internet. In general, direct or strict comparisons of the OSI and TCP/IP models should be avoided, because the layering in TCP/IP is not a principal design criterion and in general, considered to be \"harmful\" (RFC 3439). In particular, TCP/IP does not dictate a strict hierarchical sequence of encapsulation requirements, as is attributed to OSI protocols.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A fuze is a device that detonates a munition's explosive material under specified conditions. In addition, a fuze will have safety and arming mechanisms that protect users from premature or accidental detonation. For example, an artillery fuze's battery is activated by the high acceleration of cannon launch, and the fuze must be spinning rapidly before it will function. \"Complete bore safety\" can be achieved with mechanical shutters that isolate the detonator from the main charge until the shell is fired.A fuze may contain only the electronic or mechanical elements necessary to signal or actuate the detonator, but some fuzes contain a small amount of primary explosive to initiate the detonation. Fuzes for large explosive charges may include an explosive booster.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public key cryptography, padding is the process of preparing a message for encryption or signing using a specification or scheme such as PKCS#1 v2.2, OAEP, PSS, PSSR, IEEE P1363 EMSA2 and EMSA5. A modern form of padding for asymmetric primitives is OAEP applied to the RSA algorithm, when it is used to encrypt a limited number of bytes. The operation is referred to as \"padding\" because originally, random material was simply appended to the message to make it long enough for the primitive. This form of padding is not secure and is therefore no longer applied. A modern padding scheme aims to ensure that the attacker cannot manipulate the plaintext to exploit the mathematical structure of the primitive and will usually be accompanied by a proof, often in the random oracle model, that breaking the padding scheme is as hard as solving the hard problem underlying the primitive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-threaded programs some threads can be executing inside infinite loops without causing the entire program to be stuck in an infinite loop. If the main thread exits all threads of the process are forcefully stopped thus all execution ends and the process/program terminates. The threads inside the infinite loops can perform \"housekeeping\" tasks or they can be in a blocked state waiting for input (from socket/queue) and resume execution every time input is received.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of mobile communications, a \"generation\" generally refers to a change in the fundamental nature of the service, non-backwards-compatible transmission technology, higher peak bit rates, new frequency bands, wider channel frequency bandwidth in Hertz, and higher capacity for many simultaneous data transfers (higher system spectral efficiency in bit/second/Hertz/site). New mobile generations have appeared about every ten years since the first move from 1981 analog (1G) to digital (2G) transmission in 1992. This was followed, in 2001, by 3G multi-media support, spread spectrum transmission and a minimum peak bit rate of 200 kbit/s, in 2011/2012 to be followed by \"real\" 4G, which refers to all-IP packet-switched networks giving mobile ultra-broadband (gigabit speed) access.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "history (two of which resulted in the recall of the governor) and 38 recall elections for state legislators (55% of which succeeded). Nineteen states and the District of Columbia have a recall function for state officials. Additional states have recall functions for local jurisdictions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metaphysics, object-oriented ontology (OOO) is a 21st-century Heidegger-influenced school of thought that rejects the privileging of human existence over the existence of nonhuman objects. This is in contrast to what it calls the \"anthropocentrism\" of Kant's philosophy by proposing a metaphorical Copernican Revolution, which would displace the human from the center of the universe like Copernicus displaced the Earth from being the center of the universe. Object-oriented ontology maintains that objects exist independently (as Kantian noumena) of human perception and are not ontologically exhausted by their relations with humans or other objects. For object-oriented ontologists, all relations, including those between nonhumans, distort their related objects in the same basic manner as human consciousness and exist on an equal footing with one another.Object-oriented ontology is often viewed as a subset of speculative realism, a contemporary school of thought that criticizes the post-Kantian reduction of philosophical enquiry to a correlation between thought and being (correlationism), such that the reality of anything outside of this correlation is unknowable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The structure of graphs exchanged by GXL streams is given by a schema represented as a Unified Modeling Language (UML) class diagram.Since GXL is a general graph exchange format, it can also be used to interchange any graph-based data, including models between computer-aided software engineering (CASE) tools, data between graph transformation systems, or graph visualization tools. GXL includes support for hypergraphs and hierarchical graphs, and can be extended to support other types of graphs. GXL originated in the merger of GRAph eXchange format (GraX: University of Koblenz, DE) for exchanging typed, attributed, ordered, directed graphs (TGraphs), Tuple Attribute Language (TA: University of Waterloo, CA), and the graph format of the PROGRES graph rewriting system (University Bw M\u00fcnchen, DE). Furthermore, GXL includes ideas from exchange formats from reverse engineering, including Relation Partition Algebra (RPA: Philips Research Eindhoven, NL) and Rigi Standard Format (RSF: University of Victoria, CA). The development of GXL was also influenced by various formats used in graph drawing (e.g. daVinci, Graph Modelling Language (GML), Graphlet, GraphXML) and current discussions on exchange formats for graph transformation systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Use of POCSAG on the 26 MHz and 27 MHz band has been logged by several listeners in Europe, specifically frequencies 26.350 MHz, 26.500 MHz, 26.705 MHz, 26.725 MHz, 26.755 MHz, 27.005 MHz, 27.007 MHz, 27.255 MHz (see note below regarding legal use of 27.255 MHz for paging in the United States). It appears that US-specification paging systems operating on 27.255 MHz have been sold in Italy and other European countries. The former monopoly operator SIP (which later became TIM) used the following frequencies for their pager service, called Teledrin: 161.175 MHz (for tone/voice only and numeric pagers, probably for the alphanumeric pagers); 466.075 MHz (for tone/voice only, numeric and alphanumeric pagers, using the narrow frequencies of the TACS phone system)In France, POCSAG is operated by E*Message over the AlphaPage network on the 466 MHz frequency: 466.025 MHz 466.050 MHz 466.075 MHz 466.175 MHz 466.20625 MHz 466.23125 MHz", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to suppress the ICI and thereby reduce SNR degradation, the residual CFO must be sufficiently small. For example, when using the 64QAM constellation, it is better to keep the residual CFO below 0. 01/s to ensure that DSNR < 0 . 3 dB for moderate SNR. On the other hand, when QPSK is used, the residual CFO can be up to 0.03 fs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a latter presentation this nominal set of views was presented as an Extended RASDS Semantic Information Model Derivation. Hereby RASDS stands for Reference Architecture for Space Data Systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a diophantine m-tuple is a set of m positive integers { a 1 , a 2 , a 3 , a 4 , \u2026 , a m } {\\displaystyle \\{a_{1},a_{2},a_{3},a_{4},\\ldots ,a_{m}\\}} such that a i a j + 1 {\\displaystyle a_{i}a_{j}+1} is a perfect square for any 1 \u2264 i < j \u2264 m . {\\displaystyle 1\\leq i", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, economics, and finance, an index is a statistical measure of change in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and employment. Economic indices track economic health from different perspectives. Examples include the consumer price index, which measures changes in retail prices paid by consumers, and the cost-of-living index (COLI), which measures the relative cost of living over time.Influential global financial indices such as the Global Dow, and the NASDAQ Composite track the performance of selected large and powerful companies in order to evaluate and predict economic trends.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In section VIII, James finally moves beyond what he considers mere preliminaries. Here James first identifies areas of belief where he holds that to believe without evidence would be unjustified: \"Wherever the option between losing truth and gaining it is not momentous, we can throw the chance of gaining truth away, and at any rate save ourselves from any chance of believing falsehood, by not making up our minds at all till objective evidence has come. In scientific questions, this is almost always the case ... The questions here are always trivial options, the hypotheses are hardly living (at any rate not living for us spectators), the choice between believing truth or falsehood is seldom forced.\" James concludes this section by asking us to agree \"that wherever there is no forced option, the dispassionately judicial intellect with no pet hypothesis, saving us, as it does from dupery at any rate, ought to be our ideal.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following transcriptions, diacritics may be used to distinguish between apical  and laminal . The commonality of  cross-linguistically is 6% in a phonological analysis of 2155 languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This idea was well known at the time; e.g. Donald Knuth visited the ALGOL 68 design committee while developing his own version of it, attribute grammars.By augmenting the syntax description with attributes, constraints like the above can be checked, ruling many invalid programs out at compile time. As Van Wijngaarden wrote in his preface: My main objections were certain to me unnecessary restrictions and the definition of the syntax and semantics. Actually the syntax viewed in MR 75 produces a large number of programs, whereas I should prefer to have the subset of meaningful programs as large as possible, which requires a stricter syntax.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When a program is stopped to let another run, the program with the highest priority in the run queue is then allowed to execute. Processes are also removed from the run queue when they ask to sleep, are waiting on a resource to become available, or have been terminated. In the Linux operating system (prior to kernel 2.6.23), each CPU in the system is given a run queue, which maintains both an active and expired array of processes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the odd greedy expansion problem asks whether a greedy algorithm for finding Egyptian fractions with odd denominators always succeeds. As of 2021, it remains unsolved.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same order. This common order must be a prime number, and the elementary abelian groups in which the common order is p are a particular kind of p-group. A group for which p = 2 (that is, an elementary abelian 2-group) is sometimes called a Boolean group.Every elementary abelian p-group is a vector space over the prime field with p elements, and conversely every such vector space is an elementary abelian group. By the classification of finitely generated abelian groups, or by the fact that every vector space has a basis, every finite elementary abelian group must be of the form (Z/pZ)n for n a non-negative integer (sometimes called the group's rank).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, there are several relationships among probability distributions. These relations can be categorized in the following groups: One distribution is a special case of another with a broader parameter space Transforms (function of a random variable); Combinations (function of several variables); Approximation (limit) relationships; Compound relationships (useful for Bayesian inference); Duality; Conjugate priors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Robbins' problem of optimal stopping, named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information.Let X1, ... , Xn be independent, identically distributed random variables, uniform on . We observe the Xk's sequentially and must stop on exactly one of them. No recall of preceding observations is permitted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is an XML-based markup language for technical documentation that bears some resemblance to Texinfo, in broad outlines. It is also possible to convert Docbook files to Texinfo, using the docbook2X program. XML (Generated via makeinfo --xml.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Zolotarev's lemma states that the Legendre symbol ( a p ) {\\displaystyle \\left({\\frac {a}{p}}\\right)} for an integer a modulo an odd prime number p, where p does not divide a, can be computed as the sign of a permutation: ( a p ) = \u03b5 ( \u03c0 a ) {\\displaystyle \\left({\\frac {a}{p}}\\right)=\\varepsilon (\\pi _{a})} where \u03b5 denotes the signature of a permutation and \u03c0a is the permutation of the nonzero residue classes mod p induced by multiplication by a. For example, take a = 2 and p = 7. The nonzero squares mod 7 are 1, 2, and 4, so (2|7) = 1 and (6|7) = \u22121. Multiplication by 2 on the nonzero numbers mod 7 has the cycle decomposition (1,2,4)(3,6,5), so the sign of this permutation is 1, which is (2|7). Multiplication by 6 on the nonzero numbers mod 7 has cycle decomposition (1,6)(2,5)(3,4), whose sign is \u22121, which is (6|7).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of artificial intelligence (AI), AI alignment research aims to steer AI systems towards humans' intended goals, preferences, or ethical principles. An AI system is considered aligned if it advances the intended objectives. A misaligned AI system pursues some objectives, but not the intended ones.It can be challenging for AI designers to align an AI system because it can be difficult for them to specify the full range of desired and undesired behaviors. To avoid this difficulty, they typically use simpler proxy goals, such as gaining human approval.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, the IA-64 (Itanium) architecture used variable-sized windows, with 32 global registers and 96 for the windows. In the Infineon C166 architecture, most registers are simply locations in internal RAM which have the additional property of being accessible as registers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an endomorphism is a morphism from a mathematical object to itself. An endomorphism that is also an isomorphism is an automorphism. For example, an endomorphism of a vector space V is a linear map f: V \u2192 V, and an endomorphism of a group G is a group homomorphism f: G \u2192 G. In general, we can talk about endomorphisms in any category. In the category of sets, endomorphisms are functions from a set S to itself. In any category, the composition of any two endomorphisms of X is again an endomorphism of X. It follows that the set of all endomorphisms of X forms a monoid, the full transformation monoid, and denoted End(X) (or EndC(X) to emphasize the category C).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some species have several ArgR paralogs. In a neighbour-joining tree, some of these paralogous sequences show long branches and differ significantly from the well-conserved C-terminal region. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, an algorithm ( ) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first 10 superior highly composite numbers and their factorization are listed. For a superior highly composite number n there exists a positive real number \u03b5 such that for all natural numbers k smaller than n we have and for all natural numbers k larger than n we have where d(n), the divisor function, denotes the number of divisors of n. The term was coined by Ramanujan (1915).For example, the number with the most divisors per square root of the number itself is 12; this can be demonstrated using some highly composites near 12. 120 is another superior highly composite number because it has the highest ratio of divisors to itself raised to the .4 power. The first 15 superior highly composite numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 (sequence A002201 in the OEIS) are also the first 15 colossally abundant numbers, which meet a similar condition based on the sum-of-divisors function rather than the number of divisors. Neither set, however, is a subset of the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, two transactions may, in the course of their processing, attempt to access the same portion of a database at the same time, in a way that prevents them from proceeding. For example, transaction A may access portion X of the database, and transaction B may access portion Y of the database. If at that point, transaction A then tries to access portion Y of the database while transaction B tries to access portion X, a deadlock occurs, and neither transaction can move forward. Transaction-processing systems are designed to detect these deadlocks when they occur.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Open software. Promotion of reflexive and interpretive uses of the metrics, to prevent their misuse in quantitative assessments.This definition has been implemented in research programs, like ROSI (Reference implementation for open scientometric indicators). In 2017, the European Commission Expert Group on Altmetrics expanded the open metrics program of Ulrich Herb under a new concept, the Next-generation metrics. These metrics should be managed by \"open, transparent and linked data infrastructure\". The expert group underline that not everything should be measured and not all metrics are relevants: \"Measure what matters: the next generation of metrics should begin with those qualities and impacts that European societies most value and need indices for, rather than those which are most easily collected and measure\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, 2E6 is the name of a family of Steinberg or twisted Chevalley groups. It is a quasi-split form of E6, depending on a quadratic extension of fields K\u2282L. Unfortunately the notation for the group is not standardized, as some authors write it as 2E6(K) (thinking of 2E6 as an algebraic group taking values in K) and some as 2E6(L) (thinking of the group as a subgroup of E6(L) fixed by an outer involution). Over finite fields these groups form one of the 18 infinite families of finite simple groups, and were introduced independently by Tits (1958) and Steinberg (1959).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multivariate statistics, exploratory factor analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify the underlying relationships between measured variables. It is commonly used by researchers when developing a scale (a scale is a collection of questions used to measure a particular research topic) and serves to identify a set of latent constructs underlying a battery of measured variables. It should be used when the researcher has no a priori hypothesis about factors or patterns of measured variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, probability theory and information theory, pointwise mutual information (PMI), or point mutual information, is a measure of association. It compares the probability of two events occurring together to what this probability would be if the events were independent.PMI (especially in its positive pointwise mutual information variant) has been described as \"one of the most important concepts in NLP\", where it \"draws on the intuition that the best way to weigh the association between two words is to ask how much more the two words co-occur in  corpus than we would have a priori expected them to appear by chance. \"The concept was introduced in 1961 by Robert Fano under the name of \"mutual information\", but today that term is instead used for a related measure of dependence between random variables: The mutual information (MI) of two discrete random variables refers to the average PMI of all possible events.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Dirichlet characters can be seen as a special case of this definition. Multiplicative characters are linearly independent, i.e. if \u03c7 1 , \u03c7 2 , \u2026 , \u03c7 n {\\displaystyle \\chi _{1},\\chi _{2},\\ldots ,\\chi _{n}} are different characters on a group G then from a 1 \u03c7 1 + a 2 \u03c7 2 + \u22ef + a n \u03c7 n = 0 {\\displaystyle a_{1}\\chi _{1}+a_{2}\\chi _{2}+\\cdots +a_{n}\\chi _{n}=0} it follows that a 1 = a 2 = \u22ef = a n = 0. {\\displaystyle a_{1}=a_{2}=\\cdots =a_{n}=0.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, linguistics, and neighboring fields, Linguistic Linked Open Data (LLOD) describes a method and an interdisciplinary community concerned with creating, sharing, and (re-)using language resources in accordance with Linked Data principles. The Linguistic Linked Open Data Cloud was conceived and is being maintained by the Open Linguistics Working Group (OWLG) of the Open Knowledge Foundation, but has been a point of focal activity for several W3C community groups, research projects, and infrastructure efforts since then.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Every clean ring is an exchange ring. A matrix ring over a clean ring is itself clean. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context to structural analysis, a structure refers to a body or system of connected parts used to support a load. Important examples related to Civil Engineering include buildings, bridges, and towers; and in other branches of engineering, ship and aircraft frames, tanks, pressure vessels, mechanical systems, and electrical supporting structures are important. To design a structure, an engineer must account for its safety, aesthetics, and serviceability, while considering economic and environmental constraints. Other branches of engineering work on a wide variety of non-building structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory and set theory, the minimum overlap problem is a problem proposed by Hungarian mathematician Paul Erd\u0151s in 1955.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other systems (e.g., IP/RTP systems), the coded data is carried in packets that are framed by the system transport protocol, and identification of the boundaries of NAL units within the packets can be established without use of start code prefix patterns. In such systems, the inclusion of start code prefixes in the data would be a waste of data carrying capacity, so instead the NAL units can be carried in data packets without start code prefixes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a delta-matroid or \u0394-matroid is a family of sets obeying an exchange axiom generalizing an axiom of matroids. A non-empty family of sets is a delta-matroid if, for every two sets E {\\displaystyle E} and F {\\displaystyle F} in the family, and for every element e {\\displaystyle e} in their symmetric difference E \u25b3 F {\\displaystyle E\\triangle F} , there exists an f \u2208 E \u25b3 F {\\displaystyle f\\in E\\triangle F} such that E \u25b3 { e , f } {\\displaystyle E\\triangle \\{e,f\\}} is in the family. For the basis sets of a matroid, the corresponding exchange axiom requires in addition that e \u2208 E {\\displaystyle e\\in E} and f \u2208 F {\\displaystyle f\\in F} , ensuring that E {\\displaystyle E} and F {\\displaystyle F} have the same cardinality. For a delta-matroid, either of the two elements may belong to either of the two sets, and it is also allowed for the two elements to be equal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, ... (sequence A005150 in the OEIS).To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. For example: 1 is read off as \"one 1\" or 11. 11 is read off as \"two 1s\" or 21. 21 is read off as \"one 2, one 1\" or 1211.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, a tree is a partially ordered set (T, <) such that for each t \u2208 T, the set {s \u2208 T: s < t} is well-ordered by the relation <. Frequently trees are assumed to have only one root (i.e. minimal element), as the typical questions investigated in this field are easily reduced to questions about single-rooted trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some computing environments, user workstations and computing nodes do not host installations of the full range of software that users might want to access. Systems may be \"imaged\" with a minimal or typical cross-section of the most commonly used software. Also, in some environments, users might require specialized or occasional access to older versions of software (for instance, developers may need to perform bug fixes and regression testing, or some users may need access to archived data using outdated tools). Commonly, organizations will provide repositories or \"depots\" of such software, ready for installation as required.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 \u00d7 5 is an integer factorization of 15, and (x \u2013 2)(x + 2) is a polynomial factorization of x2 \u2013 4. Factorization is not usually considered meaningful within number systems possessing division, such as the real or complex numbers, since any x {\\displaystyle x} can be trivially written as ( x y ) \u00d7 ( 1 / y ) {\\displaystyle (xy)\\times (1/y)} whenever y {\\displaystyle y} is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After the news a net is carried out with signal reports exchanged, both with UK listeners and others further afield. This band is unique in the United Kingdom insofar as UK 5 MHz operators may also communicate under controlled operating conditions with UK Military stations or UK Military Cadet Youth Organizations with links to the MoD using these frequencies. They use MoD allocated call signs, which differ significantly from those issued by Ofcom to the Amateur Radio Service in the UK.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. This systematic error can be approximately modeled based on our past data about the measuring instrument and the process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted r {\\displaystyle r} ) occurs. For example, we can define rolling a 6 on a dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ( r = 3 {\\displaystyle r=3} ). In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution. An alternative formulation is to model the number of total trials (instead of the number of failures).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are also power associative. Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the latency across the network makes possible the kind of race condition described. In this case, heading off race conditions by imposing a form of control over access to the shared resource\u2014say, appointing one server to control who holds what privileges\u2014would mean turning the distributed network into a centralized one (at least for that one part of the network operation). Race conditions can also exist when a computer program is written with non-blocking sockets, in which case the performance of the program can be dependent on the speed of the network link.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Higher-order moments and cumulants are obtained by higher derivatives. This technique is often useful when T is a complicated function of the data, whose moments are difficult to calculate by integration. Another way to see this that does not rely on the theory of cumulants is to begin from the fact that the distribution of an exponential family must be normalized, and differentiate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For nine to twenty taxa, it will generally be preferable to use branch-and-bound, which is also guaranteed to return the best tree. For greater numbers of taxa, a heuristic search must be performed. Because the most-parsimonious tree is always the shortest possible tree, this means that\u2014in comparison to a hypothetical \"true\" tree that actually describes the unknown evolutionary history of the organisms under study\u2014the \"best\" tree according to the maximum-parsimony criterion will often underestimate the actual evolutionary change that could have occurred.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, a word of n bytes can contain up to (2n)\u22121 decimal digits, which is always an odd number of digits. A decimal number with d digits requires 1/2(d+1) bytes of storage space. For example, a 4-byte (32-bit) word can hold seven decimal digits plus a sign and can represent values ranging from \u00b19,999,999.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At the same time, he was sent to Hamburg and Geneva to doing some cooperation research in the field of high energy physics. In the 1980s, he began teaching, but at the same time, he still did his research in many physics fields. Later, he joined in the AMS study (Alfa spectrometer).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This result is a major application of the large sieve method, which developed rapidly in the early 1960s, from its beginnings in work of Yuri Linnik two decades earlier. Besides Bombieri, Klaus Roth was working in this area. In the late 1960s and early 1970s, many of the key ingredients and estimates were simplified by Patrick X. Gallagher.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other words, the It\u00f4 integral, as a function from the space L a d 2 (  \u00d7 \u03a9 ) {\\displaystyle L_{\\mathrm {ad} }^{2}(\\times \\Omega )} of square-integrable adapted processes to the space L 2 ( \u03a9 ) {\\displaystyle L^{2}(\\Omega )} of square-integrable random variables, is an isometry of normed vector spaces with respect to the norms induced by the inner products ( X , Y ) L a d 2 (  \u00d7 \u03a9 ) := E \u2061 ( \u222b 0 T X t Y t d t ) {\\displaystyle {\\begin{aligned}(X,Y)_{L_{\\mathrm {ad} }^{2}(\\times \\Omega )}&:=\\operatorname {E} \\left(\\int _{0}^{T}X_{t}\\,Y_{t}\\,\\mathrm {d} t\\right)\\end{aligned}}} and ( A , B ) L 2 ( \u03a9 ) := E \u2061 ( A B ) . {\\displaystyle (A,B)_{L^{2}(\\Omega )}:=\\operatorname {E} (AB).} As a consequence, the It\u00f4 integral respects these inner products as well, i.e. we can write E \u2061  = E \u2061  {\\displaystyle \\operatorname {E} \\left=\\operatorname {E} \\left} for X , Y \u2208 L a d 2 (  \u00d7 \u03a9 ) {\\displaystyle X,Y\\in L_{\\mathrm {ad} }^{2}(\\times \\Omega )} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is harder to think of words with K as the third letter, such as lake, or acknowledge, although objectively these are three times more common. This leads people to the incorrect conclusion that K is more common at the start of words. In another experiment, subjects heard the names of many celebrities, roughly equal numbers of whom were male and female.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Synthetic instruments are implemented on generic hardware, i.e., generic meaning that the underlying hardware is not explicitly designed to perform the particular measurement. This is probably the most salient characteristic of a synthetic instrument. Measurement specificity is encapsulated totally in software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically algebraic topology, a pair ( X , A ) {\\displaystyle (X,A)} is shorthand for an inclusion of topological spaces i: A \u21aa X {\\displaystyle i\\colon A\\hookrightarrow X} . Sometimes i {\\displaystyle i} is assumed to be a cofibration. A morphism from ( X , A ) {\\displaystyle (X,A)} to ( X \u2032 , A \u2032 ) {\\displaystyle (X',A')} is given by two maps f: X \u2192 X \u2032 {\\displaystyle f\\colon X\\rightarrow X'} and g: A \u2192 A \u2032 {\\displaystyle g\\colon A\\rightarrow A'} such that i \u2032 \u2218 g = f \u2218 i {\\displaystyle i'\\circ g=f\\circ i} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 2000s, speech recognition was still dominated by traditional approaches such as Hidden Markov Models combined with feedforward artificial neural networks. Today, however, many aspects of speech recognition have been taken over by a deep learning method called Long short-term memory (LSTM), a recurrent neural network published by Sepp Hochreiter & J\u00fcrgen Schmidhuber in 1997. LSTM RNNs avoid the vanishing gradient problem and can learn \"Very Deep Learning\" tasks that require memories of events that happened thousands of discrete time steps ago, which is important for speech.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix, say P, represents a permutation of m elements and, when used to multiply another matrix, say A, results in permuting the rows (when pre-multiplying, to form PA) or columns (when post-multiplying, to form AP) of the matrix A.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to define the data structure difference bound matrix, it is first required to give a data structure to encode atomic constraints. Furthermore, we introduce an algebra for atomic constraints. This algebra is similar to the tropical semiring, with two modifications: An arbitrary ordered monoid may be used instead of \u211d. In order to distinguish between \" < m {\\displaystyle", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, an exception to this is from using the IntPtr structure, which is a memory managed equivalent to int*, and does not require the unsafe keyword nor the CompilerServices assembly. This type is often returned when using methods from the System.Runtime.InteropServices, for example: The .NET framework includes many classes and methods in the System and System.Runtime.InteropServices namespaces (such as the Marshal class) which convert .NET types (for example, System.String) to and from many unmanaged types and pointers (for example, LPWSTR or void*) to allow communication with unmanaged code. Most such methods have the same security permission requirements as unmanaged code, since they can affect arbitrary places in memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On such a machine, an all-to-all algorithm requires at least \u2308 log 2 \u2061 n \u2309 {\\displaystyle \\lceil \\log _{2}n\\rceil } communication rounds. Further a minimum of \u2308 m ( n \u2212 1 ) \u2309 {\\displaystyle \\left\\lceil m(n-1)\\right\\rceil } units of data is transferred. Optimum for both these measures can not be achieved simultaneously.Depending on the network topology (fully connected, hypercube, ring), different all-to-all algorithms are required.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Retrieval is done by separating the instrument from the balloon after a sufficient amount of exposure, and a parachute opens to somewhat slow the descent of the instrument. Although the experiment is designed to meet the structural requirements of the Columbia Scientific Balloon Facility, it is inevitable that some damage will be incurred to replaceable parts of the instrument. The main priority is data retrieval; all other systems are considered secondary at this point.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, textual entailment (TE), also known as natural language inference (NLI), is a directional relation between text fragments. The relation holds whenever the truth of one text fragment follows from another text.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, search engines covering specific regions may provide locally-specific extensions of microdata. For example, Yandex, a major search engine in Russia, supports microformats such as hCard (company contact information), hRecipe (food recipe), hReview (market reviews) and hProduct (product data) and provides its own format for definition of the terms and encyclopedic articles. This extension was made in order to solve transliteration problems between the Cyrillic and Latin alphabets. After the implementation of additional parameters from Schema's vocabulary, indexation of information in Russian-language web-pages became more successful.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, the arrival theorem (also referred to as the random observer property, ROP or job observer property) states that \"upon arrival at a station, a job observes the system as if in steady state at an arbitrary instant for the system without that job. \"The arrival theorem always holds in open product-form networks with unbounded queues at each node, but it also holds in more general networks. A necessary and sufficient condition for the arrival theorem to be satisfied in product-form networks is given in terms of Palm probabilities in Boucherie & Dijk, 1997.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Exploiting the behavior of a buffer overflow is a well-known security exploit. On many systems, the memory layout of a program, or the system as a whole, is well defined. By sending in data designed to cause a buffer overflow, it is possible to write into areas known to hold executable code and replace it with malicious code, or to selectively overwrite data pertaining to the program's state, therefore causing behavior that was not intended by the original programmer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "k ! ( n \u2212 k ) ! .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the other uses of radio spectrum growing in the 1990s, the FCC made available some bands of spectrum as unlicensed channels. This included spectrum for cordless phones and Wi-Fi. As a result, some of these channels have been used for news gathering by websites and more informal news outlets. One major disadvantage of unlicensed use is that there is no frequency coordination, which can result in interference or blocking of signals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, sequential estimation refers to estimation methods in sequential analysis where the sample size is not fixed in advance. Instead, data is evaluated as it is collected, and further sampling is stopped in accordance with a predefined stopping rule as soon as significant results are observed. The generic version is called the optimal Bayesian estimator, which is the theoretical underpinning for every sequential estimator (but cannot be instantiated directly). It includes a Markov process for the state propagation and measurement process for each state, which yields some typical statistical independence relations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The so-called kommunalka became the most common type of accommodation for the residents of large cities. In each communal apartment one room belonged to one family, while bathroom, toilet and kitchen were shared. Such a scheme was widespread until the mid-1950s, and in some cities there are more communal apartments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics and applied mathematics, analytical regularization is a technique used to convert boundary value problems which can be written as Fredholm integral equations of the first kind involving singular operators into equivalent Fredholm integral equations of the second kind. The latter may be easier to solve analytically and can be studied with discretization schemes like the finite element method or the finite difference method because they are pointwise convergent. In computational electromagnetics, it is known as the method of analytical regularization. It was first used in mathematics during the development of operator theory before acquiring a name.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, statistics and elsewhere, sums of squares occur in a number of contexts:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a primefree sequence is a sequence of integers that does not contain any prime numbers. More specifically, it usually means a sequence defined by the same recurrence relation as the Fibonacci numbers, but with different initial conditions causing all members of the sequence to be composite numbers that do not all have a common divisor. To put it algebraically, a sequence of this type is defined by an appropriate choice of two composite numbers a1 and a2, such that the greatest common divisor g c d ( a 1 , a 2 ) {\\displaystyle \\mathrm {gcd} (a_{1},a_{2})} is equal to 1, and such that for n > 2 {\\displaystyle n>2} there are no primes in the sequence of numbers calculated from the formula a n = a n \u2212 1 + a n \u2212 2 {\\displaystyle a_{n}=a_{n-1}+a_{n-2}} .The first primefree sequence of this type was published by Ronald Graham in 1964.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early years of Windows Mobile devices were able to be managed and synced from a remote computer using ActiveSync; a data synchronization technology and protocol developed by Microsoft, originally released in 1996. This allowed servers running Microsoft Exchange Server, or other third party variants, to act as a personal information manager and share information such as email, calendar appointments, contacts or internet favorites. With the release of Windows Vista, ActiveSync was replaced with Windows Mobile Device Center. Device Center is included with Vista and Windows 7 and provides many front end enhancements, allowing a home user to sync PIM information with Microsoft Outlook 2003 and later, photos from Windows Photo Gallery, videos or music from Windows Media Player and favorites with Internet Explorer; without the need for a server back end. Devices at this time also included a base driver compatible with Mobile Device Center so a user can connect to a computer without a need for any configuration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a paired difference test is a type of location test that is used when comparing two sets of paired measurements to assess whether their population means differ. A paired difference test uses additional information about the sample that is not present in an ordinary unpaired testing situation, either to increase the statistical power, or to reduce the effects of confounders. Specific methods for carrying out paired difference tests are, for normally distributed difference t-test (where the population standard deviation of difference is not known) and the paired Z-test (where the population standard deviation of the difference is known), and for differences that may not be normally distributed the Wilcoxon signed-rank test as well as the paired permutation test.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the erasure channel model a symbol gets either transmitted correctly with probability 1 \u2212 p e {\\displaystyle 1-p_{e}} or is erased with probability p e {\\displaystyle p_{e}} (see Figure \\ref{fig:Sudoku3x3channel}). The channel introduces no errors, i.e. no channel input is changed to another symbol. The example in Figure \\ref{fig:Sudoku3x3BSC} shows the transmission of a 3 \u00d7 3 {\\displaystyle 3\\times 3} Sudoku code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Write operations invalidate other copies, but often don't wait for their acknowledgements. Read operations typically don't check every redundant copy prior to answering, potentially missing the preceding write operation. The large amount of metadata signal traffic would require specialized hardware and short distances to be handled with acceptable performance (i.e., act like a non-clustered storage device or database).Whenever strong data consistency is expected, look for these indicators: the use of InfiniBand, Fibrechannel or similar low-latency networks to avoid performance degradation with increasing cluster size and number of redundant copies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the matrix ( 1 \u2212 1 1 1 ) {\\displaystyle {\\begin{pmatrix}1&-1\\\\1&1\\end{pmatrix}}} is sometimes called the quincunx matrix. It is a 2\u00d72 Hadamard matrix, and its rows form the basis of a diagonal square lattice consisting of the integer points whose coordinates both have the same parity; this lattice is a two-dimensional analogue of the three-dimensional body-centered cubic lattice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But, in balanced ternary, we can't omit the rightmost trailing infinite \u22121s after the radix point in order to gain a representations of integer or terminating fraction. Donald Knuth has pointed out that truncation and rounding are the same operation in balanced ternary\u2014they produce exactly the same result (a property shared with other balanced numeral systems). The number 1/2 is not exceptional; it has two equally valid representations, and two equally valid truncations: 0.1 (round to 0, and truncate to 0) and 1.\ud835\uddb3 (round to 1, and truncate to 1).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UMTS cellular communication system, received signal code power (RSCP) denotes the power measured by a receiver on a particular physical communication channel. It is used as an indication of signal strength, as a handover criterion, in downlink power control, and to calculate path loss. In CDMA systems, a physical channel corresponds to a particular spreading code, hence the name (Received signal code power). RSCP is also called Receiver Side Call Power.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With an odd radix, double rounding is also equivalent to directly rounding to the final precision, unlike with an even radix. The basic operations\u2014addition, subtraction, multiplication, and division\u2014are done as in regular ternary. Multiplication by two can be done by adding a number to itself, or subtracting itself after a-trit-left-shifting. An arithmetic shift left of a balanced ternary number is the equivalent of multiplication by a (positive, integral) power of 3; and an arithmetic shift right of a balanced ternary number is the equivalent of division by a (positive, integral) power of 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In strategic planning, resource allocation is a plan for using available resources, for example human resources, especially in the near term, to achieve goals for the future. It is the process of allocating scarce resources among the various projects or business units.There are a number of approaches to solving resource allocation problems e.g. resources can be allocated using a manual approach, an algorithmic approach (see below), or a combination of both.There may be contingency mechanisms such as a priority ranking of items excluded from the plan, showing which items to fund if more resources should become available and a priority ranking of some items included in the plan, showing which items should be sacrificed if total funding must be reduced.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to match certain signatures, an IDS is required to keep state related to the connections it is monitoring. For example, an IDS must maintain \"TCP control blocks\" (TCBs), chunks of memory which track information such as sequence numbers, window sizes, and connection states (ESTABLISHED, RELATED, CLOSED, etc.), for each TCP connection monitored by the IDS. Once all of the IDS's random-access memory (RAM) is consumed, it is forced to utilize virtual memory on the hard disk which is much slower than RAM, leading to performance problems and dropped packets similar to the effects of CPU exhaustion.If the IDS doesn't garbage collect TCBs correctly and efficiently, an attacker can exhaust the IDS's memory by starting a large number of TCP connections very quickly. Similar attacks can be made by fragmenting a large number of packets into a larger number of smaller packets, or send a large number of out-of-order TCP segments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the middle-square method is a method of generating pseudorandom numbers. In practice it is a highly flawed method for many practical purposes, since its period is usually very short and it has some severe weaknesses; repeated enough times, the middle-square method will either begin repeatedly generating the same number or cycle to a previous number in the sequence and loop indefinitely.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, Fisher's noncentral hypergeometric distribution is a generalization of the hypergeometric distribution where sampling probabilities are modified by weight factors. It can also be defined as the conditional distribution of two or more binomially distributed variables dependent upon their fixed sum. The distribution may be illustrated by the following urn model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead, they bear a legend statement \"Authorized by Drawer\". This type of instrument is usually used by credit card companies, utility companies, or telemarketers. Remotely created checks are vulnerable to fraud.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, privacy concerns have been addressed by the US Congress via the passage of regulatory controls such as the Health Insurance Portability and Accountability Act (HIPAA). The HIPAA requires individuals to give their \"informed consent\" regarding information they provide and its intended present and future uses. According to an article in Biotech Business Week, \"'n practice, HIPAA may not offer any greater protection than the longstanding regulations in the research arena,' says the AAHC. More importantly, the rule's goal of protection through informed consent is approach a level of incomprehensibility to average individuals.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In response to a series of earthquakes near Comrie in Scotland in 1839, a committee was formed in the United Kingdom in order to produce better detection devices for earthquakes. The outcome of this was an inverted pendulum seismometer constructed by James David Forbes, first presented in a report by David Milne-Home in 1842, which recorded the measurements of seismic activity through the use of a pencil placed on paper above the pendulum. The designs provided did not prove effective, according to Milne's reports. It was Milne who coined the word seismometer in 1841, to describe this instrument.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Merchant codes and product codes are used at the point of sale (required by law by certain merchants by certain states in the U.S.) to restrict sales if they do not qualify. Because of the extra checking and documenting that goes on, later, the statement can be used to substantiate these purchases for tax deductions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At the same time, the availability of published material online opens more doors for plagiarism, unauthorized use, or re-use of the material. Some publishers are trying to address these concerns. For example, in 2011, HarperCollins limited the number of times that one of its e-books could be lent in a public library. Other publishers, such as Penguin, are attempting to incorporate e-book elements into their regular paper publications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In simplest terms it is a measure of the probability of finding a particle at a distance of r {\\displaystyle r} away from a given reference particle, relative to that for an ideal gas. The general algorithm involves determining how many particles are within a distance of r {\\displaystyle r} and r + d r {\\displaystyle r+dr} away from a particle. This general theme is depicted to the right, where the red particle is our reference particle, and blue particles are those whose centers are within the circular shell, dotted in orange.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Carath\u00e9odory kernel theorem is a result in complex analysis and geometric function theory established by the Greek mathematician Constantin Carath\u00e9odory in 1912. The uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can be formulated purely geometrically in terms of the limiting behaviour of the images of the functions. The kernel theorem has wide application in the theory of univalent functions and in particular provides the geometric basis for the Loewner differential equation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, given two jointly distributed random variables X {\\displaystyle X} and Y {\\displaystyle Y} , the conditional probability distribution of Y {\\displaystyle Y} given X {\\displaystyle X} is the probability distribution of Y {\\displaystyle Y} when X {\\displaystyle X} is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value x {\\displaystyle x} of X {\\displaystyle X} as a parameter. When both X {\\displaystyle X} and Y {\\displaystyle Y} are categorical variables, a conditional probability table is typically used to represent the conditional probability. The conditional distribution contrasts with the marginal distribution of a random variable, which is its distribution without reference to the value of the other variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, we want to find a channel code, which is able to partition the space of input X {\\displaystyle X} into several cosets, where each coset has a unique syndrome associated with it. With a given coset and y {\\displaystyle \\mathbf {y} } , there is only one x {\\displaystyle \\mathbf {x} } that is possible to be the input given the correlation between two sources. In this example, we can use the ( 7 , 4 , 3 ) {\\displaystyle (7,4,3)} binary Hamming Code C {\\displaystyle \\mathbf {C} } , with parity check matrix H {\\displaystyle \\mathbf {H} } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, negafibonacci coding is a universal code which encodes nonzero integers into binary code words. It is similar to Fibonacci coding, except that it allows both positive and negative integers to be represented. All codes end with \"11\" and have no \"11\" before the end.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Pierpont prime is a prime number of the form for some nonnegative integers u and v. That is, they are the prime numbers p for which p \u2212 1 is 3-smooth. They are named after the mathematician James Pierpont, who used them to characterize the regular polygons that can be constructed using conic sections. The same characterization applies to polygons that can be constructed using ruler, compass, and angle trisector, or using paper folding. Except for 2 and the Fermat primes, every Pierpont prime must be 1 modulo 6. The first few Pierpont primes are: It has been conjectured that there are infinitely many Pierpont primes, but this remains unproven.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example 3 4 -, first the 3 is put onto the stack, then the 4; the 4 is now on top and the 3 below it. The subtraction operator removes the top two items from the stack, performs 3 - 4, and puts the result of -1 onto the stack. The common terminology is that added items are pushed on the stack and removed items are popped. The advantage of reverse Polish notation is that it removes the need for order of operations and parentheses that are required by infix notation and can be evaluated linearly, left-to-right. For example, the infix expression (3 \u00d7 4) + (5 \u00d7 6) becomes 3 4 \u00d7 5 6 \u00d7 + in reverse Polish notation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The axiom of choice is also rejected in most intuitionistic set theories, though in some versions it is accepted. In intuitionism, the term \"explicit construction\" is not cleanly defined, and that has led to criticisms. Attempts have been made to use the concepts of Turing machine or computable function to fill this gap, leading to the claim that only questions regarding the behavior of finite algorithms are meaningful and should be investigated in mathematics. This has led to the study of the computable numbers, first introduced by Alan Turing. Not surprisingly, then, this approach to mathematics is sometimes associated with theoretical computer science.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the concept of a residuated mapping arises in the theory of partially ordered sets. It refines the concept of a monotone function. If A, B are posets, a function f: A \u2192 B is defined to be monotone if it is order-preserving: that is, if x \u2264 y implies f(x) \u2264 f(y). This is equivalent to the condition that the preimage under f of every down-set of B is a down-set of A. We define a principal down-set to be one of the form \u2193{b} = { b' \u2208 B: b' \u2264 b }.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation model, such as a linear regression. A small RSS indicates a tight fit of the model to the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real world application, one often observe only a few entries corrupted at least by a small amount of noise. For example, in the Netflix problem, the ratings are uncertain. Cand\u00e8s and Plan showed that it is possible to fill in the many missing entries of large low-rank matrices from just a few noisy samples by nuclear norm minimization. The noisy model assumes that we observe Y i j = M i j + Z i j , ( i , j ) \u2208 \u03a9 , {\\displaystyle Y_{ij}=M_{ij}+Z_{ij},(i,j)\\in \\Omega ,} where Z i j: ( i , j ) \u2208 \u03a9 {\\displaystyle {Z_{ij}:(i,j)\\in \\Omega }} is a noise term.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of energy\u2014or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level. It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite. In computer science this implies that non-finite models such as Turing machines are not realizable as finite devices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here, the original observations are effectively mapped into a higher dimensional non-linear space. Linear classification in this non-linear space is then equivalent to non-linear classification in the original space. The most commonly used example of this is the kernel Fisher discriminant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A surface is a two-dimensional space; this means that a moving point on a surface may move in two directions (it has two degrees of freedom). In other words, around almost every point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth resembles (ideally) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it (except at the poles and along the 180th meridian). The concept of surface is widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, one sets y 2 = x 3 + A x + B {\\displaystyle y^{2}=x^{3}+Ax+B} , and then \u03c8 2 m + 1 \u2208 Z  {\\displaystyle \\psi _{2m+1}\\in \\mathbb {Z} } and \u03c8 2 m \u2208 2 y Z  {\\displaystyle \\psi _{2m}\\in 2y\\mathbb {Z} } . The division polynomials form a generic elliptic divisibility sequence over the ring Q  / ( y 2 \u2212 x 3 \u2212 A x \u2212 B ) {\\displaystyle \\mathbb {Q} /(y^{2}-x^{3}-Ax-B)} . If an elliptic curve E {\\displaystyle E} is given in the Weierstrass form y 2 = x 3 + A x + B {\\displaystyle y^{2}=x^{3}+Ax+B} over some field K {\\displaystyle K} , i.e. A , B \u2208 K {\\displaystyle A,B\\in K} , one can use these values of A , B {\\displaystyle A,B} and consider the division polynomials in the coordinate ring of E {\\displaystyle E} . The roots of \u03c8 2 n + 1 {\\displaystyle \\psi _{2n+1}} are the x {\\displaystyle x} -coordinates of the points of E  \u2216 { O } {\\displaystyle E\\setminus \\{O\\}} , where E  {\\displaystyle E} is the ( 2 n + 1 ) th {\\displaystyle (2n+1)^{\\text{th}}} torsion subgroup of E {\\displaystyle E} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Conceptual errors are a developer's misunderstanding of what the software must do. The resulting software may perform according to the developer's understanding, but not what is really needed. Other types:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the continuing struggle to create the fastest and most advanced 3D accelerator, ATI came up with the RAGE 128. The chip was announced in two flavors, the RAGE 128 GL and the RAGE 128 VR. Aside from the VR chip's lower price, the main difference was that the former was a full 128-bit design, while the VR, still a 128-bit processor internally, used a 64-bit external memory interface. Magnum - A workstation board for OEMs with 32 MB SDRAM.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the deques of this structure, elements are kept in sorted order according to their working set size. Formally, element x {\\displaystyle x} lies after y {\\displaystyle y} in deque Q i {\\displaystyle Q_{i}} if and only if w ( x ) < w ( y ) {\\displaystyle w(x)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a morphic word or substitutive word is an infinite sequence of symbols which is constructed from a particular class of endomorphism of a free monoid. Every automatic sequence is morphic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and signal processing, the orthogonality principle is a necessary and sufficient condition for the optimality of a Bayesian estimator. Loosely stated, the orthogonality principle says that the error vector of the optimal estimator (in a mean square error sense) is orthogonal to any possible estimator. The orthogonality principle is most commonly stated for linear estimators, but more general formulations are possible. Since the principle is a necessary and sufficient condition for optimality, it can be used to find the minimum mean square error estimator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Turkish terms for the constructive and inflectional endings, three roots are involved: ek \"supplement, affix\" (notably Turkish has no prefixes) yap- \"make\" \u00e7ek- \"pull, draw\"For the last two verbal roots, the constructive suffix -im can be added to form nouns for instances of the actions denoted by the roots: yap\u0131m \"construction\"; \u00e7ekim \" pull or draw\" (or a \"take\" in cinema).Either of these nouns can be compounded with the noun ek, resulting in an indefinite compound (belirtisiz tamlama), the sign of which is the inflectional suffix -i attached to ek: yap\u0131m eki \"structure-suffix\"; \u00e7ekim eki \"inflection-suffix\".The inflectional suffix -ler comes before the -i to form the plural, so yap\u0131m ekleri, \u00e7ekim ekleri. Many words in Turkish\u2014 particularly many grammatical terms\u2014 are neologisms invented to replace earlier words borrowed from Arabic or Persian, which have largely been successful at permanently superseding the previously used foreign terms. (See the main article on Turkish language.) In some cases, the foreign term continues to be in use alongside the neologism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multiprocessing, omega networks may be used as connectors between the CPUs and their shared memory, in order to decrease the probability that the CPU-to-memory connection becomes a bottleneck. This class of networks has been built into the Illinois Cedar Multiprocessor, into the IBM RP3, and into the NYU Ultracomputer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, for p =1, the latent variables of all entities i = 1 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, computer programming, philosophy and linguistics fuzzy concepts can be analyzed and defined more accurately or comprehensively, by describing or modelling the concepts using the terms of fuzzy logic or other substructural logics. More generally, clarification techniques can be used such as: 1. Contextualizing the concept by defining the setting or situation in which the concept is used, or how it is used appropriately (context). 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for self-interaction feedback. Regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations. However, it is now well understood and has proven to yield useful, accurate predictions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It also depends on f {\\displaystyle f} , \u03b1 0 {\\displaystyle \\alpha _{0}} , \u03c4 {\\displaystyle \\tau } and c {\\displaystyle c} of course, although these dependencies can be left implicit if they are assumed to be fixed with respect to the optimization problem. The detailed steps are thus, see Armijo (1966), Bertsekas (2016): Choose an initial starting point x 0 {\\displaystyle \\mathbf {x} _{0}} and set the iteration counter n = 0 {\\displaystyle n=0} . Until some stopping condition is satisfied, choose a descent direction p n {\\displaystyle \\mathbf {p} _{n}} , increment n {\\displaystyle n} , and update the position to x n + 1 = x n + \u03b1 ( x n , p n ) p n {\\displaystyle \\mathbf {x} _{n+1}=\\mathbf {x} _{n}+\\alpha (\\mathbf {x} _{n},\\mathbf {p} _{n})\\,\\mathbf {p} _{n}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, certain digraphs and trigraphs are counted as distinct letters in themselves, and assigned to a specific place in the alphabet, separate from that of the sequence of characters that composes them, for purposes of orthography and collation. For example: In the Gaj\u2019s Latin alphabet used to write Serbo-Croatian, the digraphs \u27e8d\u017e\u27e9, \u27e8lj\u27e9 and \u27e8nj\u27e9, which correspond to the single Cyrillic letters \u27e8\u045f\u27e9, \u27e8\u0459\u27e9, \u27e8\u045a\u27e9, are treated as distinct letters. In the Czech and Slovak alphabet, \u27e8ch\u27e9 is treated as a distinct letter, coming after \u27e8h\u27e9 in the alphabet. Also, in the Slovak alphabet the relatively rare digraphs \u27e8dz\u27e9 and \u27e8d\u017e\u27e9 are treated as distinct letters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such experiments allow researchers to quantify the role of historical contingency and repeatability in network evolution, enabling predictions about the architecture and dynamics of large networks of interacting species. The inclusion of ecological interactions in digital systems enables new research avenues: investigations using self-replicating computer programs complement laboratory efforts by broadening the breadth of viable experiments focused on the emergence and diversification of coevolving interactions in complex communities. This cross-disciplinary research program provides fertile grounds for new collaborations between computer scientists and evolutionary biologists.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Sierpi\u0144ski number is an odd natural number k such that k \u00d7 2 n + 1 {\\displaystyle k\\times 2^{n}+1} is composite for all natural numbers n. In 1960, Wac\u0142aw Sierpi\u0144ski proved that there are infinitely many odd integers k which have this property. In other words, when k is a Sierpi\u0144ski number, all members of the following set are composite: { k \u22c5 2 n + 1: n \u2208 N } . {\\displaystyle \\left\\{\\,k\\cdot 2^{n}+1:n\\in \\mathbb {N} \\,\\right\\}.} If the form is instead k \u00d7 2 n \u2212 1 {\\displaystyle k\\times 2^{n}-1} , then k is a Riesel number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This idea can be applied to any commutative monoid. On the other hand, the set of integers Z requires a more sophisticated argument for its hierarchical structure, since we can always solve the equation n + m = n \u2032 {\\displaystyle n+m=n'} by writing m = ( n \u2032 \u2212 n ) {\\displaystyle m=(n'-n)} .A mathematical hierarchy (a pre-ordered set) should not be confused with the more general concept of a hierarchy in the social realm, particularly when one is constructing computational models that are used to describe real-world social, economic or political systems. These hierarchies, or complex networks, are much too rich to be described in the category Set of sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle {\\begin{pmatrix}0&0&2&0\\\\0&2&-1&1\\\\2&-1&2&-1\\\\0&1&-1&2\\end{pmatrix}};\\quad {\\begin{pmatrix}0&0&2&0&0\\\\0&1&-1&2&0\\\\2&-1&-1&0&2\\\\0&0&2&0&0\\\\0&2&0&0&0\\end{pmatrix}};\\quad {\\begin{pmatrix}0&0&0&2\\\\0&2&0&0\\\\2&-2&2&0\\\\0&2&0&0\\end{pmatrix}};\\quad {\\begin{pmatrix}0&2&0&0\\\\0&0&0&2\\\\2&0&0&0\\\\0&0&2&0\\end{pmatrix}}.} The set of HSASMs is a superset of the ASMs. The extreme points of the convex hull of the set of r-spin HSASMs are themselves integer multiples of the usual ASMs. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, f k {\\displaystyle f_{k}} denotes the value of the function f: { 0 , 1 } n \u2192 { 0 , 1 } {\\displaystyle f:\\{0,1\\}^{n}\\rightarrow \\{0,1\\}} when applied to an input vector of weight k {\\displaystyle k} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an aperiodic semigroup is a semigroup S such that every element is aperiodic, that is, for each x in S there exists a positive integer n such that xn = xn+1. An aperiodic monoid is an aperiodic semigroup which is a monoid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , m a x d \u2212 1 , + \u221e } {\\displaystyle k_{max}=\\{max_{0},+\\infty ,max_{1},+\\infty ,...,max_{d-1},+\\infty \\}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases the observations may be weighted\u2014for example, they may not be equally reliable. In this case, one can minimize the weighted sum of squares: where wi > 0 is the weight of the ith observation, and W is the diagonal matrix of such weights. The weights should, ideally, be equal to the reciprocal of the variance of the measurement. (This implies that the observations are uncorrelated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We use the potential function \u03a6 = \u03a3 \ud835\udcc1(u) (i.e. \u03a6 is the sum of the labels of all active nodes). It is obvious that \u03a6 is 0 initially and stays nonnegative throughout the execution of the algorithm. Both relabels and saturating pushes can increase \u03a6. However, the value of \u03a6 must be equal to 0 at termination since there cannot be any remaining active nodes at the end of the algorithm's execution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In such theories, the speech act of assertion is often analyzed as a proposal to add an additional proposition to the common ground. Similarly, presuppositions are taken to be licensed when they are already established in the common ground. While such approaches are typically construed as pragmatic, the framework of dynamic semantics treats the semantic denotations of sentences as functions which update the common ground. In many theories, the common ground is one of several elements of the conversational scoreboard.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Brent's method is due to Richard Brent and builds on an earlier algorithm by Theodorus Dekker. Consequently, the method is also known as the Brent\u2013Dekker method. Modern improvements on Brent's method include Chandrupatla's method, which is simpler and faster for functions that are flat around their roots; Ridders' method, which performs exponential interpolations instead of quadratic providing a simpler closed formula for the iterations; and the ITP method which is a hybrid between regula-falsi and bisection that achieves optimal worst-case and asymptotic guarantees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function. The hyperbolic secant function is equivalent to the reciprocal hyperbolic cosine, and thus this distribution is also called the inverse-cosh distribution. Generalisation of the distribution gives rise to the Meixner distribution, also known as the Natural Exponential Family - Generalised Hyperbolic Secant or NEF-GHS distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If we restrict loops to be of a predictably finite size (like the FOR loop in BASIC), we can express all of the primitive recursive functions (Meyer and Ritchie, 1967). An example of such a machine is provided by the toy programming language PL-{GOTO} of Brainerd and Landweber (1974).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Furthermore, the objective should be to obtain an experts' carefully considered judgment based on a systematic consideration of all relevant evidence. For this reason one should take care to adopt strategies designed to help the expert being interviewed to avoid overlooking relevant evidence. Additionally, vocabulary used should face intense scrutiny; qualitative uncertainty words such as \"likely\" and \"unlikely\" are not sufficient and can lead to confusion. Such words can mean very different things to different people, or to the same people in different situations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some parts of the world, including the United Kingdom, 2G remains widely used for older feature phones and for internet of things (IoT) devices such as smart meters, eCall systems and vehicle trackers to avoid the high patent licensing cost of newer technologies. Terminating 2G services could leave vulnerable people who rely on 2G infrastructure unable to communicate even with emergency contacts, causing harm and possibly deaths.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization and other branches of mathematics, and in search algorithms (a topic in computer science), a candidate solution is a member of the set of possible solutions in the feasible region of a given problem. A candidate solution does not have to be a likely or reasonable solution to the problem\u2014it is simply in the set that satisfies all constraints; that is, it is in the set of feasible solutions. Algorithms for solving various types of optimization problems often narrow the set of candidate solutions down to a subset of the feasible solutions, whose points remain as candidate solutions while the other feasible solutions are henceforth excluded as candidates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most GSM/UMTS phones support all four bands, while most CDMA2000/1xRTT phones (mostly North America and voice transmission only) do not, and so are considered only dual-band devices. A few phones support both of the domestic frequencies but only one foreign one for limited roaming, making them tri-band phones.The term penta-band describes a device that supports a fifth frequency band, commonly the 1700/2100 MHz band in much of the world. The Advanced Wireless Services (AWS) 1700 MHz band is also seeing increased usage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "2D spatial directions are numerically equivalent to points on the unit circle and spatial directions in 3D are equivalent to a point on the unit sphere. The normalized vector \u00fb of a non-zero vector u is the unit vector in the direction of u, i.e., u ^ = u \u2016 u \u2016 {\\displaystyle \\mathbf {\\hat {u}} ={\\frac {\\mathbf {u} }{\\|\\mathbf {u} \\|}}} where \u2016u\u2016 is the norm (or length) of u. The term normalized vector is sometimes used as a synonym for unit vector. Unit vectors are often chosen to form the basis of a vector space, and every vector in the space may be written as a linear combination of unit vectors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In standard matrix notation, each element of Rn is typically written as a column vector and sometimes as a row vector: The coordinate space Rn may then be interpreted as the space of all n \u00d7 1 column vectors, or all 1 \u00d7 n row vectors with the ordinary matrix operations of addition and scalar multiplication. Linear transformations from Rn to Rm may then be written as m \u00d7 n matrices which act on the elements of Rn via left multiplication (when the elements of Rn are column vectors) and on elements of Rm via right multiplication (when they are row vectors). The formula for left multiplication, a special case of matrix multiplication, is: Any linear transformation is a continuous function (see below). Also, a matrix defines an open map from Rn to Rm if and only if the rank of the matrix equals to m.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number. For example: 7 = 71, 9 = 32 and 64 = 26 are prime powers, while 6 = 2 \u00d7 3, 12 = 22 \u00d7 3 and 36 = 62 = 22 \u00d7 32 are not. The sequence of prime powers begins: 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, \u2026 (sequence A246655 in the OEIS). The prime powers are those positive integers that are divisible by exactly one prime number; in particular, the number 1 is not a prime power. Prime powers are also called primary numbers, as in the primary decomposition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, profiling (\"program profiling\", \"software profiling\") is a form of dynamic program analysis that measures, for example, the space (memory) or time complexity of a program, the usage of particular instructions, or frequency and duration of function calls. The most common use of profiling information is to aid program optimization. Profiling is achieved by instrumenting either the program source code or its binary executable form using a tool called a profiler (or code profiler). A number of different techniques may be used by profilers, such as event-based, statistical, instrumented, and simulation methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In robust statistics, the convex hull provides one of the key components of a bagplot, a method for visualizing the spread of two-dimensional sample points. The contours of Tukey depth form a nested family of convex sets, with the convex hull outermost, and the bagplot also displays another polygon from this nested family, the contour of 50% depth.In statistical decision theory, the risk set of a randomized decision rule is the convex hull of the risk points of its underlying deterministic decision rules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Beta Langfi pointed out that \"it is not only to study parts and processes in isolation, but also to study the interaction of various parts. The organism should be considered as a whole or system. Environmental protection requires systematic thinking. Landscape planning is required for overall planning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Typically, people try to systematically \"retrace their steps\" to determine all of the possible places where the item might be located. Based on the role that context plays in determining recall, it is not at all surprising that individuals often quite easily discover the lost item upon returning to the correct context. This concept is heavily related to the encoding specificity principle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The selection of central office names was conducted in a careful manner to avoid misunderstanding of the verbal requests.For automatic telephone service, impulse senders (dials) were installed on customer telephones, so that subscribers did not need operators to initiate a call, but simply dial the directory number themselves. This required a digit or letter identification of central offices, so that the central office for the recipient could be dialed before the line number. Telephone dials were typically supplemented with letters next to the numerals on the dial, as seen in the right-hand photo, so that a name could be dialed by its first letter, or by multiple letters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "using Bayes' theorem). Having made explicit the expected loss for each given x {\\displaystyle x\\,\\!} separately, we can define a decision rule \u03b4 {\\displaystyle \\delta \\,\\!}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of digital privacy, communication privacy is the notion that individuals should have the freedom, or right, to communicate information digitally with the expectation that their communications are secure\u2014meaning that messages and communications will only be accessible to the sender's original intended recipient.However, communications can be intercepted or delivered to other recipients without the sender's knowledge, in a multitude of ways. Communications can be intercepted directly through various hacking methods, such as the man-in-the-middle attack (MITM). Communications can also be delivered to recipients unbeknown to the sender due to false assumptions made regarding the platform or medium that was used to send information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the design of algorithms, partition refinement is a technique for representing a partition of a set as a data structure that allows the partition to be refined by splitting its sets into a larger number of smaller sets. In that sense it is dual to the union-find data structure, which also maintains a partition into disjoint sets but in which the operations merge pairs of sets. In some applications of partition refinement, such as lexicographic breadth-first search, the data structure maintains as well an ordering on the sets in the partition. Partition refinement forms a key component of several efficient algorithms on graphs and finite automata, including DFA minimization, the Coffman\u2013Graham algorithm for parallel scheduling, and lexicographic breadth-first search of graphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In functional programming languages, and many others, it provides a way of automatically managing how arguments are passed to functions and exceptions. In theoretical computer science, it provides a way to study functions with multiple arguments in simpler theoretical models which provide only one argument. The most general setting for the strict notion of currying and uncurrying is in the closed monoidal categories, which underpins a vast generalization of the Curry\u2013Howard correspondence of proofs and programs to a correspondence with many other structures, including quantum mechanics, cobordisms and string theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The S-box used is derived from the multiplicative inverse over GF(28), known to have good non-linearity properties. To avoid attacks based on simple algebraic properties, the S-box is constructed by combining the inverse function with an invertible affine transformation. The S-box is also chosen to avoid any fixed points (and so is a derangement), i.e., S ( a i , j ) \u2260 a i , j {\\displaystyle S(a_{i,j})\\neq a_{i,j}} , and also any opposite fixed points, i.e., S ( a i , j ) \u2295 a i , j \u2260 FF 16 {\\displaystyle S(a_{i,j})\\oplus a_{i,j}\\neq {\\text{FF}}_{16}} . While performing the decryption, the InvSubBytes step (the inverse of SubBytes) is used, which requires first taking the inverse of the affine transformation and then finding the multiplicative inverse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there is an edge between every interacting pair of qubits. In particular, they are a convenient way of representing certain types of entangled states. Graph states are useful in quantum error-correcting codes, entanglement measurement and purification and for characterization of computational resources in measurement based quantum computing models. A graph state is a particular case of a 2-uniform hypergraph state, a generalization where the edges have N cardinality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The challenge problems do not require the formalisation of large programming languages, but they do require sophistication in reasoning about: Binding Most programming languages have some form of binding, ranging in complexity from the simple binders of simply typed lambda calculus to complex, potentially infinite binders needed in the treatment of record patterns. Induction Properties such as subject reduction and strong normalisation often require complex induction arguments. Reuse Furthering collaboration being a key aim of the challenge, the solutions are expected to contain reusable components that would allow researchers to share language features and designs without requiring them to start from scratch every time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a monolithic application describes a software application that is designed as a single service. Multiple services can be desirable in certain scenarios as it can facilitate maintenance by allowing repair or replacement of parts of the application without requiring wholesale replacement. Modularity is achieved to various extents by different modular programming approaches.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Welch bounds are a family of inequalities pertinent to the problem of evenly spreading a set of unit vectors in a vector space. The bounds are important tools in the design and analysis of certain methods in telecommunication engineering, particularly in coding theory. The bounds were originally published in a 1974 paper by L. R. Welch.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Wiener\u2013Wintner theorem, named after Norbert Wiener and Aurel Wintner, is a strengthening of the ergodic theorem, proved by Wiener and Wintner (1941).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system (usually formulated within model theory) that describes a set of sentences that is closed under logical implication. A formal proof is a complete rendition of a mathematical proof within a formal system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each work item consists of a series of instructions, to be executed sequentially, but in the course of its execution, a work item may also spawn new work items that can feasibly be executed in parallel with its other work. These new items are initially put on the queue of the processor executing the work item. When a processor runs out of work, it looks at the queues of the other processors and \"steals\" their work items.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\|T\\|_{1}\\geq \\|T\\|_{p}\\geq \\|T\\|_{p'}\\geq \\|T\\|_{\\infty }.} Duality: Let H 1 , H 2 {\\displaystyle H_{1},H_{2}} be finite-dimensional Hilbert spaces, p \u2208  {\\displaystyle p\\in } and q {\\displaystyle q} such that 1 p + 1 q = 1 {\\displaystyle {\\frac {1}{p}}+{\\frac {1}{q}}=1} , then \u2016 S \u2016 p = sup { | \u27e8 S , T \u27e9 | \u2223 \u2016 T \u2016 q = 1 } , {\\displaystyle \\|S\\|_{p}=\\sup \\lbrace |\\langle S,T\\rangle |\\mid \\|T\\|_{q}=1\\rbrace ,} where \u27e8 S , T \u27e9 = t r ( S \u2217 T ) {\\displaystyle \\langle S,T\\rangle =\\mathrm {tr} (S^{*}T)} denotes the Hilbert\u2013Schmidt inner product. Let ( e k ) k , ( f k \u2032 ) k \u2032 {\\displaystyle (e_{k})_{k},(f_{k'})_{k'}} be two orthonormal basis of the Hilbert spaces H 1 , H 2 {\\displaystyle H_{1},H_{2}} , then for p = 1 {\\displaystyle p=1} \u2016 T \u2016 1 \u2264 \u2211 k , k \u2032 | T k , k \u2032 | {\\displaystyle \\|T\\|_{1}\\leq \\sum _{k,k'}\\left|T_{k,k'}\\right|} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the generalized canonical correlation analysis (gCCA), is a way of making sense of cross-correlation matrices between the sets of random variables when there are more than two sets. While a conventional CCA generalizes principal component analysis (PCA) to two sets of random variables, a gCCA generalizes PCA to more than two sets of random variables. The canonical variables represent those common factors that can be found by a large PCA of all of the transformed random variables after each set underwent its own PCA.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, it can be used about primes in an arithmetic progression of the form a n + b {\\displaystyle an+b} , where a and b are coprime which according to Dirichlet's theorem on arithmetic progressions contains infinitely many primes, along with infinitely many composites. For integer k \u2265 3, an AP-k (also called PAP-k) is any sequence of k primes in arithmetic progression. An AP-k can be written as k primes of the form a\u00b7n + b, for fixed integers a (called the common difference) and b, and k consecutive integer values of n. An AP-k is usually expressed with n = 0 to k \u2212 1. This can always be achieved by defining b to be the first prime in the arithmetic progression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, an M/D/c queue represents the queue length in a system having c servers, where arrivals are determined by a Poisson process and job service times are fixed (deterministic). The model name is written in Kendall's notation. Agner Krarup Erlang first published on this model in 1909, starting the subject of queueing theory. The model is an extension of the M/D/1 queue which has only a single server.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, ingredient-flavor networks are networks describing the sharing of flavor compounds of culinary ingredients. In the bipartite form, an ingredient-flavor network consist of two different types of nodes: the ingredients used in the recipes and the flavor compounds that contributes to the flavor of each ingredients. The links connecting different types of nodes are undirected, represent certain compound occur in each ingredients. The ingredient-flavor network can also be projected in the ingredient or compound space where nodes are ingredients or compounds, links represents the sharing of the same compounds to different ingredients or the coexistence in the same ingredient of different compounds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are a finite number of possible configurations in the section between two walls so the automaton must eventually start repeating inside each section, though the period may be very long if the section is wide enough. These walls will form with probability 1 for completely random initial conditions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to assign a digital representation to an entity, the attributing party must trust that the claim of an attribute (such as name, location, role as an employee, or age) is correct and associated with the person or thing presenting the attribute. Conversely, the individual claiming an attribute may only grant selective access to its information (e.g., proving identity in a bar or PayPal authentication for payment at a website). In this way, digital identity is better understood as a particular viewpoint within a mutually-agreed relationship than as an objective property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A typical pole stage plantation tree is 7\u201330 cm in diameter at breast height (dbh). Such trees are sometimes not suitable for timber, but are used as pulp for paper and particleboard, and as chips for oriented strand board. As the trees grow and become dense and crowded again, the thinning process is repeated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces. Bl\u00e1thy had suggested the use of closed cores, Zipernowsky had suggested the use of parallel shunt connections, and D\u00e9ri had performed the experiments; In early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores.Transformers today are designed on the principles discovered by the three engineers. They also popularized the word 'transformer' to describe a device for altering the EMF of an electric current although the term had already been in use by 1882. In 1886, the ZBD engineers designed, and the Ganz factory supplied electrical equipment for, the world's first power station that used AC generators to power a parallel connected common electrical network, the steam-powered Rome-Cerchi power plant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For an example, given set y {\\displaystyle y} , let Q ( n ) {\\displaystyle Q(n)} denote the existential statement that a certain function space set exist, \u2203 h . h \u2243 y { 0 , 1 , \u2026 , n \u2212 1 } {\\displaystyle \\exists h.h\\simeq y^{\\{0,1,\\dots ,n-1\\}}} . Here the existential quantifier is not merely one over natural numbers or bounded by any other set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, specifically regression analysis, a binary regression estimates a relationship between one or more explanatory variables and a single output binary variable. Generally the probability of the two alternatives is modeled, instead of simply outputting a single value, as in linear regression. Binary regression is usually analyzed as a special case of binomial regression, with a single outcome ( n = 1 {\\displaystyle n=1} ), and one of the two alternatives considered as \"success\" and coded as 1: the value is the count of successes in 1 trial, either 0 or 1. The most common binary regression models are the logit model (logistic regression) and the probit model (probit regression).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The multinational control of the export of cryptography on the Western side of the cold war divide was done via the mechanisms of CoCom. By the 1960s, however, financial organizations were beginning to require strong commercial encryption on the rapidly growing field of wired money transfer. The U.S. Government's introduction of the Data Encryption Standard in 1975 meant that commercial uses of high quality encryption would become common, and serious problems of export control began to arise. Generally these were dealt with through case-by-case export license request proceedings brought by computer manufacturers, such as IBM, and by their large corporate customers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This approach is good solely for instructive purposes. The Euler\u2013Lagrange equation will now be used to find the extremal function f ( x ) {\\displaystyle f(x)} that minimizes the functional A  . {\\displaystyle A.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When clock speeds of CPUs began to move into the 3\u20135 GHz range, CPU power dissipation and other problems became more important. The ability of industry to produce ever-faster single CPU systems (linked to Moore's Law about the periodic doubling of transistor counts) began to be threatened. In the early 21st century, many flavors of parallel computing began to proliferate, including multi-core architectures at the low-end and massively parallel processing at the high end.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The simple logistic function varies by less than 0.01 from the cumulative normal ogive across the range, given an arbitrary scale factor. In the BTL model, the probability that object j is judged to have more of an attribute than object i is: Pr { X j i = 1 } = e \u03b4 j \u2212 \u03b4 i 1 + e \u03b4 j \u2212 \u03b4 i = \u03c3 ( \u03b4 j \u2212 \u03b4 i ) , {\\displaystyle \\Pr\\{X_{ji}=1\\}={\\frac {e^{{\\delta _{j}}-{\\delta _{i}}}}{1+e^{{\\delta _{j}}-{\\delta _{i}}}}}=\\sigma (\\delta _{j}-\\delta _{i}),} where \u03b4 i {\\displaystyle \\delta _{i}} is the scale location of object i {\\displaystyle i} ; \u03c3 {\\displaystyle \\sigma } is the logistic function (the inverse of the logit). For example, the scale location might represent the perceived quality of a product, or the perceived weight of an object.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They were introduced in the course of Stanley's enumeration of the reduced decompositions of permutations, and in particular his proof that the permutation w0 = n(n \u2212 1)...21 (written here in one-line notation) has exactly ( n 2 ) ! 1 n \u2212 1 \u22c5 3 n \u2212 2 \u22c5 5 n \u2212 3 \u22ef ( 2 n \u2212 3 ) 1 {\\displaystyle {\\frac {{\\binom {n}{2}}! }{1^{n-1}\\cdot 3^{n-2}\\cdot 5^{n-3}\\cdots (2n-3)^{1}}}} reduced decompositions. (Here ( n 2 ) {\\displaystyle {\\binom {n}{2}}} denotes the binomial coefficient n(n \u2212 1)/2 and ! denotes the factorial.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Subscribers are often provided with several set-top boxes as part of their subscription, and can give or sell unneeded activated boxes to neighboring nonsubscribers who can use them in their own residences, though a provider using IP location using the cable modem within a set-top box featuring advanced two-way features can avert this situation. This system is dependent on the security of the encryption system chosen by the cable company in question. Old cable equipment used an analog signal that was scrambled by tuning the signal so the picture was unsteady, just as Macrovision does at an attempt to copy a video.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to gain access to the software, the Scientologists must first sign a contract. Section 7 of this contract states that the members must agree to \"use the specific Internet Filter Program that CSI has provided to you which allows you freedom to view other sites on Dianetics, Scientology or its principals without threat of accessing sites deemed to be using the Marks or Works in an unauthorized fashion or deemed to be improper or discreditable to the Scientology religion. \"The program works by preventing the user from accessing sites with certain keywords which Scientology has identified as being objectionable material for viewing by their members. This use of keywords functions as a way to prevent members from learning of guarded Scientology doctrine, such as Xenu, OT III, and other material relating to Space opera in Scientology scripture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But then, by the same argument as before, 2 divides b2, so b must be even. However, if a and b are both even, they have 2 as a common factor. This contradicts our previous statement that a and b have no common factor, so we must conclude that 2 {\\displaystyle {\\sqrt {2}}} is an irrational number.To paraphrase: if one could write 2 {\\displaystyle {\\sqrt {2}}} as a fraction, this fraction could never be written in lowest terms, since 2 could always be factored from numerator and denominator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Part of the overhead is transmitted, then part of the payload, then the next part of the overhead, then the next part of the payload, until the entire frame has been transmitted. In the case of an STS-1, the frame is 810 octets in size, while the STM-1/STS-3c frame is 2,430 octets in size. For STS-1, the frame is transmitted as three octets of overhead, followed by 87 octets of payload.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Legendre's equation is the Diophantine equation The equation is named for Adrien-Marie Legendre who proved in 1785 that it is solvable in integers x, y, z, not all zero, if and only if \u2212bc, \u2212ca and \u2212ab are quadratic residues modulo a, b and c, respectively, where a, b, c are nonzero, square-free, pairwise relatively prime integers, not all positive or all negative .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1819, Charles Babbage showed the same congruence modulo p2, which holds for p \u2265 3 {\\displaystyle p\\geq 3} . An equivalent formulation is the congruence ( a p b p ) \u2261 ( a b ) ( mod p 3 ) {\\displaystyle {ap \\choose bp}\\equiv {a \\choose b}{\\pmod {p^{3}}}} for p \u2265 5 {\\displaystyle p\\geq 5} , which is due to Wilhelm Ljunggren (and, in the special case b = 1 {\\displaystyle b=1} , to J. W. L. Glaisher) and is inspired by Lucas' theorem. No known composite numbers satisfy Wolstenholme's theorem and it is conjectured that there are none (see below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A read from one such memory can happen before the write to this memory completes. Therefore, the data read can be stale. Thus, a processor under PC can execute a younger load when an older store needs to be stalled.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following section it is shown that for 455 spheres the sausage packing is non-optimal, and that there instead exists a special cluster packing that occupies a smaller volume. The volume of a convex hull of a sausage packing with n {\\displaystyle n} spheres of radius r {\\displaystyle r} is calculable with elementary geometry. The middle part of the hull is a cylinder with length h = 2 r \u22c5 ( n \u2212 1 ) {\\displaystyle h=2r\\cdot (n-1)} while the caps at the end are half-spheres with radius r {\\displaystyle r} . The total volume V W {\\displaystyle V_{W}} is therefore given by.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One of the most notably cyber attacks that had a physical impact, causing significant degradation of a target system, were the Stuxnet and Aurora worms. The Stuxnet worm was first revealed in 2010 and specially targeted weaknesses in Programmable Logic Controllers (PLCs), devices in the SCADA category of systems. Though it was never positivity attributed, it is widely believed that the malicious software was developed jointly by the United States and Israel to disrupt the Iranian nuclear enrichment facility at Natanz.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Euler's theorem (also known as the Fermat\u2013Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers, and \u03c6 ( n ) {\\displaystyle \\varphi (n)} is Euler's totient function, then a raised to the power \u03c6 ( n ) {\\displaystyle \\varphi (n)} is congruent to 1 modulo n; that is a \u03c6 ( n ) \u2261 1 ( mod n ) . {\\displaystyle a^{\\varphi (n)}\\equiv 1{\\pmod {n}}.} In 1736, Leonhard Euler published a proof of Fermat's little theorem (stated by Fermat without proof), which is the restriction of Euler's theorem to the case where n is a prime number. Subsequently, Euler presented other proofs of the theorem, culminating with his paper of 1763, in which he proved a generalization to the case where n is not prime.The converse of Euler's theorem is also true: if the above congruence is true, then a {\\displaystyle a} and n {\\displaystyle n} must be coprime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of recorded music, a hidden track (sometimes called a ghost track, secret track or unlisted track) is a song or a piece of audio that has been placed on a CD, audio cassette, LP record, or other recorded medium, in such a way as to avoid detection by the casual listener. In some cases, the piece of music may simply have been left off the track listing, while in other cases, more elaborate methods are used. In rare cases, a 'hidden track' is actually the result of an error that occurred during the mastering stage production of the recorded media. However, since the rise of digital and streaming services such as iTunes and Spotify in the late 2000s and early 2010s, the inclusion of hidden tracks has declined on studio albums.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is the starting point for understanding the structure of semigroups. It serves as a counterexample in illuminating many situations. For example, the semigroup with one element is the only semigroup in which 0 = 1, that is, the zero element and the identity element are equal. Further, if S is a semigroup with one element, the semigroup obtained by adjoining an identity element to S is isomorphic to the semigroup obtained by adjoining a zero element to S. The semigroup with one element is also a group. In the language of category theory, any semigroup with one element is a terminal object in the category of semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "2 S ( n + 1 , j + 1 ) S ( k + 1 , j + 1 ) , {\\displaystyle B_{n}^{(-k)}=\\sum _{j=0}^{\\min(n,k)}(j! )^{2}S(n+1,j+1)S(k+1,j+1),} where S ( n , k ) {\\displaystyle S(n,k)} is the number of ways to partition a size n {\\displaystyle n} set into k {\\displaystyle k} non-empty subsets (the Stirling number of the second kind). A combinatorial interpretation is that the poly-Bernoulli numbers of negative index enumerate the set of n {\\displaystyle n} by k {\\displaystyle k} (0,1)-matrices uniquely reconstructible from their row and column sums.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down. For example, consider the problem of minimizing the function x 2 + y 4 {\\displaystyle x^{2}+y^{4}} with respect to the variables x {\\displaystyle x} and y , {\\displaystyle y,} subject to 1 \u2264 x \u2264 10 {\\displaystyle 1\\leq x\\leq 10} and 5 \u2264 y \u2264 12. {\\displaystyle 5\\leq y\\leq 12.\\,} Here the feasible set is the set of pairs (x, y) in which the value of x is at least 1 and at most 10 and the value of y is at least 5 and at most 12.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and variance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to implement general-purpose coroutines, a second call stack must be obtained, which is a feature not directly supported by the C language. A reliable (albeit platform-specific) way to achieve this is to use a small amount of inline assembly to explicitly manipulate the stack pointer during initial creation of the coroutine. This is the approach recommended by Tom Duff in a discussion on its relative merits vs. the method used by Protothreads. On platforms which provide the POSIX sigaltstack system call, a second call stack can be obtained by calling a springboard function from within a signal handler to achieve the same goal in portable C, at the cost of some extra complexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", a n ( R ) {\\displaystyle \\Pi _{a_{1},...,a_{n}}(R)} , where R {\\displaystyle R} is a relation and a 1 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At a higher logical level, the MCH also sees two channels, each with four ranks. In contrast, banks, while similar from a logical perspective to ranks, are implemented quite differently in physical hardware. Banks are sub-units inside a single memory chip, while ranks are sub-units composed of a subset of the chips on a module. Similar to chip select, banks are selected by bank select bits, which are part of the memory interface.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, the term bit-count integrity (BCI) has the following meanings: In message communications, the preservation of the exact number of bits that are in the original message. In connection-oriented services, preservation of the number of bits per unit time.Note: Bit-count integrity is not the same as bit integrity, which requires that the delivered bits correspond exactly with the original bits. Source: from Federal Standard 1037C and from MIL-STD-188", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sequential code it is possible to control the flow of the program using if-then-else statements and various forms of loops. Such flow control structures have only recently been added to GPUs. Conditional writes could be performed using a properly crafted series of arithmetic/bit operations, but looping and conditional branching were not possible. Recent GPUs allow branching, but usually with a performance penalty. Branching should generally be avoided in inner loops, whether in CPU or GPU code, and various methods, such as static branch resolution, pre-computation, predication, loop splitting, and Z-cull can be used to achieve branching when hardware support does not exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Social hierarchies within the 17th century were highly regarded, as architecture was able to epitomize the servants and the upper class. More privacy is offered to the occupant as Pratt further claims, \"the ordinary servants may never publicly appear in passing to and fro for their occasions there.\" This social divide between rich and poor favored the physical integration of the corridor into housing by the 19th century. Sociologist Witold Rybczynski wrote, \"the subdivision of the house into day and night uses, and into formal and informal areas, had begun.\" Rooms were changed from public to private as single entryways forced notions of entering a room with a specific purpose.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since classical algorithms for NP-complete problems require exponentially many steps, and Grover's algorithm provides at most a quadratic speedup over the classical solution for unstructured search, this suggests that Grover's algorithm by itself will not provide polynomial-time solutions for NP-complete problems (as the square root of an exponential function is an exponential, not polynomial, function).Unlike other quantum algorithms, which may provide exponential speedup over their classical counterparts, Grover's algorithm provides only a quadratic speedup. However, even quadratic speedup is considerable when N {\\displaystyle N} is large, and Grover's algorithm can be applied to speed up broad classes of algorithms. Grover's algorithm could brute-force a 128-bit symmetric cryptographic key in roughly 264 iterations, or a 256-bit key in roughly 2128 iterations. It may not be the case that Grover's algorithm poses a significantly increased risk to encryption over existing classical algorithms, however.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle {\\boldsymbol {S}}=J~{\\boldsymbol {F}}^{-1}\\cdot {\\boldsymbol {\\sigma }}\\cdot {\\boldsymbol {F}}^{-T}~.} In index notation with respect to an orthonormal basis, S I L = J F I k \u2212 1 F L m \u2212 1 \u03c3 k m = J \u2202 X I \u2202 x k \u2202 X L \u2202 x m \u03c3 k m {\\displaystyle S_{IL}=J~F_{Ik}^{-1}~F_{Lm}^{-1}~\\sigma _{km}=J~{\\cfrac {\\partial X_{I}}{\\partial x_{k}}}~{\\cfrac {\\partial X_{L}}{\\partial x_{m}}}~\\sigma _{km}\\!\\,\\!} This tensor, a one-point tensor, is symmetric. If the material rotates without a change in stress state (rigid rotation), the components of the second Piola\u2013Kirchhoff stress tensor remain constant, irrespective of material orientation. The second Piola\u2013Kirchhoff stress tensor is energy conjugate to the Green\u2013Lagrange finite strain tensor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "259) but offers no firm resolution. He asserts: \"In general a RPT operation could not be an instruction in the finite-state part of the machine ... this might exhaust any particular amount of storage allowed in the finite part of the computer . RPT operations require infinite registers of their own.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example on the right, the rows restricted to the first three columns contain the 8 possible ordered triples consisting of 0's and 1's, each appearing once. The same holds for any other choice of three columns. Thus this is an orthogonal array of strength 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson\u2013gamma distributions which have positive mass at zero, but are otherwise continuous. Tweedie distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models.The Tweedie distributions were named by Bent J\u00f8rgensen after Maurice Tweedie, a statistician and medical physicist at the University of Liverpool, UK, who presented the first thorough study of these distributions in 1984.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 23678, 123678, 234678, and 1234678 are the patterns related to Braille pattern dots-12356, since the two additional dots of kantenji patterns 012356, 123567, and 0123567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectrum. The spectral radius is often denoted by \u03c1(\u00b7).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This control structure can be known as a post-test loop. This means the do-while loop is an exit-condition loop. However a while loop will test the condition before the code within the block is executed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semantics, pragmatics, and philosophy of language, the common ground of a conversation is the set of propositions that the interlocutors have agreed to treat as true. For a proposition to be in the common ground, it must be common knowledge in the conversational context. The set of possible worlds compatible with the common ground is often called the context set.The concept is fundamental to many theories of discourse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following diagram, only one instance (or \"execution\") of the basic Paxos protocol, with an initial Leader (a Proposer), is shown. Note that a Multi-Paxos consists of several instances of the basic Paxos protocol. Client Proposer Acceptor Learner | | | | | | | --- First Request --- X-------->| | | | | | Request | X--------->|->|->| | | Prepare(N) | |<---------X--X--X | | Promise(N,I,{Va,Vb,Vc}) | X--------->|->|->| | | Accept! (N,I,V) | |<---------X--X--X------>|->| Accepted(N,I,V) |<---------------------------------X--X Response | | | | | | | where V = last of (Va, Vb, Vc).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a compression oracle attack the use of adaptive data compression on a mixture of chosen plaintext and unknown plaintext can result in content-sensitive changes in the length of the compressed text that can be detected even though the content of the compressed text itself is then encrypted. This can be used in protocol attacks to detect when the injected known plaintext is even partially similar to the unknown content of a secret part of the message, greatly reducing the complexity of a search for a match for the secret text. The CRIME and BREACH attacks are examples of protocol attacks using this phenomenon.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of psychometrics, the Standards for Educational and Psychological Testing place standards about validity and reliability, along with errors of measurement and issues related to the accommodation of individuals with disabilities. The third and final major topic covers standards related to testing applications, credentialing, plus testing in program evaluation and public policy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The largest known prime number, 282,589,933 \u2212 1, is a Mersenne prime. Since 1997, all newly found Mersenne primes have been discovered by the Great Internet Mersenne Prime Search, a distributed computing project. In December 2020, a major milestone in the project was passed after all exponents below 100 million were checked at least once.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most deployments of Paxos, each participating process acts in three roles; Proposer, Acceptor and Learner. This reduces the message complexity significantly, without sacrificing correctness: In Paxos, clients send commands to a leader. During normal operation, the leader receives a client's command, assigns it a new command number i {\\displaystyle i} , and then begins the i {\\displaystyle i} th instance of the consensus algorithm by sending messages to a set of acceptor processes. By merging roles, the protocol \"collapses\" into an efficient client-master-replica style deployment, typical of the database community. The benefit of the Paxos protocols (including implementations with merged roles) is the guarantee of its safety properties. A typical implementation's message flow is covered in the section Multi-Paxos.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in algebraic topology, an induced homomorphism is a homomorphism derived in a canonical way from another map. For example, a continuous map from a topological space X to a topological space Y induces a group homomorphism from the fundamental group of X to the fundamental group of Y. More generally, in category theory, any functor by definition provides an induced morphism in the target category for each morphism in the source category. For example, fundamental groups, higher homotopy groups, singular homology, and De Rham cohomology are algebraic structures that are functorial, meaning that their definition provides a functor from (e.g.) the category of topological spaces to (e.g.) the category of groups or rings. This means that each space is associated with an algebraic structure, while each continuous map between spaces is associated with a structure-preserving map between structures, called an induced homomorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. Then the LARS algorithm provides a means of producing an estimate of which variables to include, as well as their coefficients. Instead of giving a vector result, the LARS solution consists of a curve denoting the solution for each value of the L1 norm of the parameter vector. The algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one's correlations with the residual.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the infinity symbol is used more often to represent a potential infinity, rather than an actually infinite quantity as included in the cardinal numbers and the ordinal numbers (which use other notations, such as \u2135 0 {\\displaystyle \\,\\aleph _{0}\\,} and \u03c9, for infinite values). For instance, in mathematical expressions with summations and limits such as the infinity sign is conventionally interpreted as meaning that the variable grows arbitrarily large towards infinity, rather than actually taking an infinite value, although other interpretations are possible.The infinity symbol may also be used to represent a point at infinity, especially when there is only one such point under consideration. This usage includes, in particular, the infinite point of a projective line, and the point added to a topological space to form its one-point compactification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of mathematics known as graph theory, a tree is said to be starlike if it has exactly one vertex of degree greater than 2. This high-degree vertex is the root and a starlike tree is obtained by attaching at least three linear graphs to this central vertex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Computer frameworks may have a few audit trails each gave to a specific sort of action. Related to proper apparatuses and systems, audit trails can help with distinguishing security infringement, execution issues and application issues. Routine log audits and investigation are valuable for distinguishing security episodes, approach infringement, fake movement, and operational issues soon after they have happened, and for giving information valuable to settling such issues.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Capturing two opposing tokens by occupying the single square separating them, also known as interception. Declaring an \"attack\" on an opposing token, and then determining the outcome of the attack, either in a deterministic way by the game rules (e.g. Stratego, Illuminati), or by using a randomising method (e.g. Illuminati: New World Order). Surrounding a token or region with one's own tokens in some manner (e.g. go), also known as enclosure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Programming languages commonly associated with buffer overflows include C and C++, which provide no built-in protection against accessing or overwriting data in any part of memory and do not automatically check that data written to an array (the built-in buffer type) is within the boundaries of that array. Bounds checking can prevent buffer overflows, but requires additional code and processing time. Modern operating systems use a variety of techniques to combat malicious buffer overflows, notably by randomizing the layout of memory, or deliberately leaving space between buffers and looking for actions that write into those areas (\"canaries\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For each integer n {\\displaystyle n} the smallest fusible number that is greater than n {\\displaystyle n} has the form n + 1 / 2 k {\\displaystyle n+1/2^{k}} . The existence of k {\\displaystyle k} for each n {\\displaystyle n} cannot be proven in Peano arithmetic, and k {\\displaystyle k} grows so rapidly as a function of n {\\displaystyle n} that for n = 3 {\\displaystyle n=3} it is (in Knuth's up-arrow notation for large numbers) already larger than 2 \u2191 9 16 {\\displaystyle 2\\uparrow ^{9}16} .The usual proof of Urysohn's lemma utilizes the dyadic fractions for constructing the separating function from the lemma. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The upper bound on the fraction of agents that can be guaranteed 1 of their best c items (a property weaker than 1-out-of-c MMS) is ( 1 \u2212 1 / 2 c ) {\\displaystyle (1-1/2^{c})} . For c = 2 {\\displaystyle c=2} , the lower bound for 1-out-of-best-c allocation can be improved from 1/2 to 3/5; it is an open question whether the upper bound of 3/4 can always be attained. It is NP-hard to decide if a given instance admits an allocation that gives each agent a positive utility.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, the term data element is an atomic unit of data that has precise meaning or precise semantics. A data element has: An identification such as a data element name A clear data element definition One or more representation terms Optional enumerated values Code (metadata) A list of synonyms to data elements in other metadata registries Synonym ringData elements usage can be discovered by inspection of software applications or application data files through a process of manual or automated Application Discovery and Understanding. Once data elements are discovered they can be registered in a metadata registry. In telecommunication, the term data element has the following components: A named unit of data that, in some contexts, is considered indivisible and in other contexts may consist of data items.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ": 87 As Quine points out: 'The basis combination in which general and singular terms find their contrasting roles is that of predication. ': 87 Predication combines general terms with singular terms, in a sentence that is true or false just as the general term ('F') is true or false of the object to which the singular term ('a') refers. Predication is thus logically represented as 'Fa'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the application of integrated circuits, process control monitoring (PCM) is the procedure followed to obtain detailed information about the process used. PCM is associated with designing and fabricating special structures that can monitor technology specific parameters such as Vth in CMOS and Vbe in bipolars. These structures are placed across the wafer at specific locations along with the chip produced so that a closer look into the process variation is possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Besicovitch inequality is a geometric inequality relating volume of a set and distances between certain subsets of its boundary. The inequality was first formulated by Abram Besicovitch.Consider the n-dimensional cube  n {\\displaystyle ^{n}} with a Riemannian metric g {\\displaystyle g} . Let denote the distance between opposite faces of the cube.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s and early 1990s, when the 8088 and 80286 were still in common use, the term x86 usually represented any 8086-compatible CPU. Today, however, x86 usually implies a binary compatibility also with the 32-bit instruction set of the 80386. This is due to the fact that this instruction set has become something of a lowest common denominator for many modern operating systems and probably also because the term became common after the introduction of the 80386 in 1985. A few years after the introduction of the 8086 and 8088, Intel added some complexity to its naming scheme and terminology as the \"iAPX\" of the ambitious but ill-fated Intel iAPX 432 processor was tried on the more successful 8086 family of chips, applied as a kind of system-level prefix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix A {\\displaystyle A} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 36, 136, 346, and 1346 are the patterns related to Braille pattern dots-25, since the two additional dots of kantenji patterns 025, 257, and 0257 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory. Intuitively, schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer \u00e9tale topology. Alternatively one can think of schemes as being locally isomorphic to affine schemes in the Zariski topology, while algebraic spaces are locally isomorphic to affine schemes in the \u00e9tale topology. The resulting category of algebraic spaces extends the category of schemes and allows one to carry out several natural constructions that are used in the construction of moduli spaces but are not always possible in the smaller category of schemes, such as taking the quotient of a free action by a finite group (cf. the Keel\u2013Mori theorem).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In philosophy, counterexamples are usually used to argue that a certain philosophical position is wrong by showing that it does not apply in certain cases. Alternatively, the first philosopher can modify their claim so that the counterexample no longer applies; this is analogous to when a mathematician modifies a conjecture because of a counterexample. For example, in Plato's Gorgias, Callicles, trying to define what it means to say that some people are \"better\" than others, claims that those who are stronger are better. But Socrates replies that, because of their strength of numbers, the class of common rabble is stronger than the propertied class of nobles, even though the masses are prima facie of worse character.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics Chow\u2013Liu tree is an efficient method for constructing a second-order product approximation of a joint probability distribution, first described in a paper by Chow & Liu (1968). The goals of such a decomposition, as with such Bayesian networks in general, may be either data compression or inference.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is useful if the user wants to do a prior art search (e.g. finding an existing approach to complete a specific task, finding a document that discloses a system that exhibits a procedural behavior collaboratively conducted by several components and links between these components). Web search engines which support proximity search via an explicit proximity operator in their query language include Walhello, Exalead, Yandex, Yahoo!, Altavista, and Bing: When using the Walhello search-engine, the proximity can be defined by the number of characters between the keywords. The search engine Exalead allows the user to specify the required proximity, as the maximum number of words between keywords.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1930s, J. H. C. Whitehead claimed a proof but then retracted it. In the process, he discovered some examples of simply-connected (indeed contractible, i.e. homotopically equivalent to a point) non-compact 3-manifolds not homeomorphic to R 3 {\\displaystyle \\mathbb {R} ^{3}} , the prototype of which is now called the Whitehead manifold. In the 1950s and 1960s, other mathematicians attempted proofs of the conjecture only to discover that they contained flaws. Influential mathematicians such as Georges de Rham, R. H. Bing, Wolfgang Haken, Edwin E. Moise, and Christos Papakyriakopoulos attempted to prove the conjecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for the minimization problem to have a well-defined solution, we have to place constraints on the set H {\\displaystyle {\\mathcal {H}}} of hypotheses being considered. If H {\\displaystyle {\\mathcal {H}}} is a normed space (as is the case for SVM), a particularly effective technique is to consider only those hypotheses f {\\displaystyle f} for which \u2016 f \u2016 H < k {\\displaystyle \\lVert f\\rVert _{\\mathcal {H}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All these results are employed in probability and statistics with a particular importance in the theory of point processes and queueing theory as well as the related fields stochastic geometry, continuum percolation theory, and spatial statistics.Another result by the name of Campbell's theorem is specifically for the Poisson point process and gives a method for calculating moments as well as the Laplace functional of a Poisson point process. The name of both theorems stems from the work by Norman R. Campbell on thermionic noise, also known as shot noise, in vacuum tubes, which was partly inspired by the work of Ernest Rutherford and Hans Geiger on alpha particle detection, where the Poisson point process arose as a solution to a family of differential equations by Harry Bateman. In Campbell's work, he presents the moments and generating functions of the random sum of a Poisson process on the real line, but remarks that the main mathematical argument was due to G. H. Hardy, which has inspired the result to be sometimes called the Campbell\u2013Hardy theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the explained sum of squares (ESS), alternatively known as the model sum of squares or sum of squares due to regression (SSR \u2013 not to be confused with the residual sum of squares (RSS) or sum of squares of errors), is a quantity used in describing how well a model, often a regression model, represents the data being modelled. In particular, the explained sum of squares measures how much variation there is in the modelled values and this is compared to the total sum of squares (TSS), which measures how much variation there is in the observed data, and to the residual sum of squares, which measures the variation in the error between the observed data and modelled values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To prevent critical races and inconsistency, only one processor (CPU) at a given time is allowed to access a particular data structure (a memory portion), while other CPUs trying to access at the same time are locked-out, waiting in idle status.Three cases can be distinguished when this idle wait is either necessary, convenient, or not convenient. The idle wait is necessary when the access is to a ready list for a low level scheduling operation. The idle wait is not necessary but convenient in the case of a critical section for synchronization/IPC operations, which require less time than a context switch (executing another process to avoid idle wait).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "G\u00f6del's incompleteness theorems were other examples that uncovered fundamental limitations in the provability of formal systems.In computational complexity theory, techniques like relativization (the addition of an oracle) allow for \"weak\" proofs of impossibility, in that proofs techniques that are not affected by relativization cannot resolve the P versus NP problem. Another technique is the proof of completeness for a complexity class, which provides evidence for the difficulty of problems by showing them to be just as hard to solve as any other problem in the class. In particular, a complete problem is intractable if one of the problems in its class is.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 278, 1278, 2478, and 12478 are the patterns related to Braille pattern dots-136, since the two additional dots of kantenji patterns 0136, 1367, and 01367 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of transportation, bilevel optimization commonly appears in the toll-setting problem. Consider a network of highways that is operated by the government. The government wants to maximize its revenues by choosing the optimal toll setting for the highways. However, the government can maximize its revenues only by taking the highway users' problem into account.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let G denote the subcollection of F consisting of all balls from the cN disjoint families A1,...,AcN. The less precise following statement is clearly true: every point x \u2208 RN belongs to at most cN different balls from the subcollection G, and G remains a cover for E (every point y \u2208 E belongs to at least one ball from the subcollection G). This property gives actually an equivalent form for the theorem (except for the value of the constant). There exists a constant bN depending only on the dimension N with the following property: Given any Besicovitch cover F of a bounded set E, there is a subcollection G of F such that G is a cover of the set E and every point x \u2208 E belongs to at most bN different balls from the subcover G.In other words, the function SG equal to the sum of the indicator functions of the balls in G is larger than 1E and bounded on RN by the constant bN, 1 E \u2264 S G := \u2211 B \u2208 G 1 B \u2264 b N . {\\displaystyle \\mathbf {1} _{E}\\leq S_{\\mathbf {G} }:=\\sum _{B\\in \\mathbf {G} }\\mathbf {1} _{B}\\leq b_{N}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Proposer Acceptor Learner | | | | | | | X--------->|->|->| | | Prepare(1) |<---------X--X--X | | Promise(1,{null,null,null}) x--------->|->| | | | Accept! (1,V1) | | X--X--------->|->| Accepted(1,V1) ! | | | | | | !!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical mechanics, probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model. It is used to study random combinatorial structures, electrical networks, etc. It is also referred to as the RC model or sometimes the FK representation after its founders Cees Fortuin and Piet Kasteleyn.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Conclusions that assume limiting operations do 'commute' are called formal. The analyst tries to delineate conditions under which such conclusions are valid; in other words mathematical rigour is established by the specification of some set of sufficient conditions for the formal analysis to hold. This approach justifies, for example, the notion of uniform convergence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By comparison, the Sun Microsystems SPARC architecture provides simultaneous visibility into four sets of eight registers each. Three sets of eight registers each are \"windowed\". Eight registers (i0 through i7) form the input registers to the current procedure level.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated). Polycyclic groups are finitely presented, which makes them interesting from a computational point of view.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a transverse redundancy check (TRC) or vertical redundancy check is a redundancy check for synchronized parallel bits applied once per bit time, across the bit streams. This requires additional parallel channels for the check bit or bits. The term usually applies to a single parity bit, although it could also be used to refer to a larger Hamming code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This brings one to idea of using approximate factorization LU of A as the iteration matrix M. A version of incomplete lower-upper decomposition method was proposed by Stone in 1968. This method is designed for equation system arising from discretisation of partial differential equations and was firstly used for a pentadiagonal system of equations obtained while solving an elliptic partial differential equation in a two-dimensional space by a finite difference method. The LU approximate decomposition was looked in the same pentadiagonal form as the original matrix (three diagonals for L and three diagonals for U) as the best match of the seven possible equations for the five unknowns for each row of the matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A chain of responsibility can be used to allow native code to better inter-operate with the JVM. On Windows platforms, Structured Exception Handling (SEH) may be employed to wrap native code in SEH try/catch blocks so as to capture machine (CPU/FPU) generated software interrupts (such as NULL pointer access violations and divide-by-zero operations), and to handle these situations before the interrupt is propagated back up into the JVM (i.e. Java side code), in all likelihood resulting in an unhandled exception.The encoding used for the NewStringUTF, GetStringUTFLength, GetStringUTFChars, ReleaseStringUTFChars and GetStringUTFRegion functions is \"modified UTF-8\", which is not valid UTF-8 for all inputs, but a different encoding really. The null character (U+0000) and codepoints not on the Basic Multilingual Plane (greater than or equal to U+10000, i.e. those represented as surrogate pairs in UTF-16) are encoded differently in modified UTF-8. Many programs actually use these functions incorrectly and treat the UTF-8 strings returned or passed into the functions as standard UTF-8 strings instead of modified UTF-8 strings. Programs should use the NewString, GetStringLength, GetStringChars, ReleaseStringChars, GetStringRegion, GetStringCritical and ReleaseStringCritical functions, which use UTF-16LE encoding on little-endian architectures and UTF-16BE on big-endian architectures, and then use a UTF-16 to UTF-8 conversion routine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Diophantine approximations and transcendental number theory are very close areas that share many theorems and methods. Diophantine approximations also have important applications in the study of Diophantine equations. The 2022 Fields Medal was awarded to James Maynard for his work on Diophantine approximation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is, however, the Information Commissioner's Office (ICO), an independent public body set up to promote access to official information and protect personal information. They do this by promoting good practice, ruling on eligible complaints, giving information to individuals and organisations, and taking action when the law is broken. The relevant UK laws include: Data Protection Act 1998; Freedom of Information Act 2000; Environmental Information Regulations 2004; Privacy and Electronic Communications Regulations 2003. The ICO has also provided a \"Personal Information Toolkit\" online which explains in more detail the various ways of protecting privacy online.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For every representation ( \u03c1 , V ) {\\displaystyle (\\rho ,V)} of a group G {\\displaystyle G} we define V G := { v \u2208 V: \u03c1 ( s ) v = v \u2200 s \u2208 G } . {\\displaystyle V^{G}:=\\{v\\in V:\\rho (s)v=v\\,\\,\\,\\,\\forall \\,s\\in G\\}.} In general, \u03c1 ( s ): V \u2192 V {\\displaystyle \\rho (s):V\\to V} is not G {\\displaystyle G} -linear.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, asynchronous communication is transmission of data, generally without the use of an external clock signal, where data can be transmitted intermittently rather than in a steady stream. Any timing required to recover data from the communication symbols is encoded within the symbols. The most significant aspect of asynchronous communications is that data is not transmitted at regular intervals, thus making possible variable bit rate, and that the transmitter and receiver clock generators do not have to be exactly synchronized all the time. In asynchronous transmission, data is sent one byte at a time and each byte is preceded by start and stop bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first of their famous series of papers on graph minors, Neil Robertson and Paul Seymour (1983) define a path-decomposition of a graph G to be a sequence of subsets Xi of vertices of G, with two properties: For each edge of G, there exists an i such that both endpoints of the edge belong to subset Xi, and For every three indices i \u2264 j \u2264 k, X i \u2229 X k \u2286 X j . {\\displaystyle X_{i}\\cap X_{k}\\subseteq X_{j}.} The second of these two properties is equivalent to requiring that the subsets containing any particular vertex form a contiguous subsequence of the whole sequence. In the language of the later papers in Robertson and Seymour's graph minor series, a path-decomposition is a tree decomposition (X,T) in which the underlying tree T of the decomposition is a path graph. The width of a path-decomposition is defined in the same way as for tree-decompositions, as maxi |Xi| \u2212 1, and the pathwidth of G is the minimum width of any path-decomposition of G. The subtraction of one from the size of Xi in this definition makes little difference in most applications of pathwidth, but is used to make the pathwidth of a path graph be equal to one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, one may wish to compute the location of a corner with subpixel accuracy. To achieve an approximate solution, the F\u00f6rstner algorithm solves for the point closest to all the tangent lines of the corner in a given window and is a least-square solution. The algorithm relies on the fact that for an ideal corner, tangent lines cross at a single point. The equation of a tangent line T x \u2032 ( x ) {\\displaystyle T_{\\mathbf {x} '}(\\mathbf {x} )} at pixel x \u2032 {\\displaystyle \\mathbf {x} '} is given by: T x \u2032 ( x ) = \u2207 I ( x \u2032 ) \u22a4 ( x \u2212 x \u2032 ) = 0 {\\displaystyle T_{\\mathbf {x'} }(\\mathbf {x} )=\\nabla I(\\mathbf {x'} )^{\\top }(\\mathbf {x} -\\mathbf {x'} )=0} where \u2207 I ( x \u2032 ) =  \u22a4 {\\displaystyle \\nabla I(\\mathbf {x'} )={\\begin{bmatrix}I_{\\mathbf {x} }&I_{\\mathbf {y} }\\end{bmatrix}}^{\\top }} is the gradient vector of the image I {\\displaystyle I} at x \u2032 {\\displaystyle \\mathbf {x'} } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, a sufficiently aggressive optimizing compiler could destroy the effectiveness of Kahan summation: for example, if the compiler simplified expressions according to the associativity rules of real arithmetic, it might \"simplify\" the second step in the sequence t = sum + y; c = (t - sum) - y;to c = ((sum + y) - sum) - y;and then to c = 0;thus eliminating the error compensation. In practice, many compilers do not use associativity rules (which are only approximate in floating-point arithmetic) in simplifications, unless explicitly directed to do so by compiler options enabling \"unsafe\" optimizations, although the Intel C++ Compiler is one example that allows associativity-based transformations by default. The original K&R C version of the C programming language allowed the compiler to re-order floating-point expressions according to real-arithmetic associativity rules, but the subsequent ANSI C standard prohibited re-ordering in order to make C better suited for numerical applications (and more similar to Fortran, which also prohibits re-ordering), although in practice compiler options can re-enable re-ordering, as mentioned above. A portable way to inhibit such optimizations locally is to break one of the lines in the original formulation into two statements, and make two of the intermediate products volatile: function KahanSum(input) var sum = 0.0 var c = 0.0 for i = 1 to input.length do var y = input - c volatile var t = sum + y volatile var z = t - sum c = z - y sum = t next i return sum", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Those object types in turn reference the primitive object types defined in the GML standard. Some other markup languages for geography use schema constructs, but GML builds on the existing XML schema model instead of creating a new schema language. Application schemas are normally designed using ISO 19103 (Geographic information \u2013 Conceptual schema language) conformant UML, and then the GML Application created by following the rules given in Annex E of ISO 19136.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To assure that no single particle could trigger the counters he spread them out in a horizontal plane. In this configuration, the frequency of coincidences was greater than that calculated on the basis of the individual rates and the resolving time of the coincidence circuit. Rossi concluded that:... once in a while the recording equipment is struck by very extensive showers of particles, which cause coincidences between counters, even placed at large distances from one another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In single-linkage or nearest-neighbor clustering, the oldest form of agglomerative hierarchical clustering, the dissimilarity between clusters is measured as the minimum distance between any two points from the two clusters. With this dissimilarity, d ( A \u222a B , C ) = min ( d ( A , C ) , d ( B , C ) ) , {\\displaystyle d(A\\cup B,C)=\\min(d(A,C),d(B,C)),} meeting as an equality rather than an inequality the requirement of reducibility. (Single-linkage also obeys a Lance\u2013Williams formula, but with a negative coefficient from which it is more difficult to prove reducibility.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One can use this isomorphism to construct a lot of non-commutative endomorphism rings. For example: End \u2061 ( Z \u00d7 Z ) \u2245 M 2 ( Z ) {\\displaystyle \\operatorname {End} (\\mathbb {Z} \\times \\mathbb {Z} )\\cong M_{2}(\\mathbb {Z} )} , since End \u2061 ( Z ) \u2245 Z {\\displaystyle \\operatorname {End} (\\mathbb {Z} )\\cong \\mathbb {Z} } . Also, when R = K {\\displaystyle R=K} is a field, there is a canonical isomorphism End \u2061 ( K ) \u2245 K {\\displaystyle \\operatorname {End} (K)\\cong K} , so End \u2061 ( K n ) \u2245 M n ( K ) {\\displaystyle \\operatorname {End} (K^{n})\\cong M_{n}(K)} , that is, the endomorphism ring of a K {\\displaystyle K} -vector space is identified with the ring of n-by-n matrices with entries in K {\\displaystyle K} . More generally, the endomorphism algebra of the free module M = R n {\\displaystyle M=R^{n}} is naturally n {\\displaystyle n} -by- n {\\displaystyle n} matrices with entries in the ring R {\\displaystyle R} .As a particular example of the last point, for any ring R with unity, End(RR) = R, where the elements of R act on R by left multiplication. In general, endomorphism rings can be defined for the objects of any preadditive category.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, the term clusters denotes small, polyatomic particles. As a rule of thumb, any particle made of between 3\u00d7100 and 3\u00d7107 atoms is considered a cluster. The term can also refer to the organization of protons and neutrons within an atomic nucleus, e.g. the alpha particle (also known as \"\u03b1-cluster\"), consisting of two protons and two neutrons (as in a helium nucleus).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D: A \u2192 A that satisfies Leibniz's law: D ( a b ) = a D ( b ) + D ( a ) b . {\\displaystyle D(ab)=aD(b)+D(a)b.} More generally, if M is an A-bimodule, a K-linear map D: A \u2192 M that satisfies the Leibniz law is also called a derivation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Equivalently, a divisor a of b is a unitary divisor if and only if every prime factor of a has the same multiplicity in a as it has in b. The sum-of-unitary-divisors function is denoted by the lowercase Greek letter sigma thus: \u03c3*(n). The sum of the k-th powers of the unitary divisors is denoted by \u03c3*k(n): \u03c3 k \u2217 ( n ) = \u2211 d \u2223 n gcd ( d , n / d ) = 1 d k . {\\displaystyle \\sigma _{k}^{*}(n)=\\sum _{d\\,\\mid \\,n \\atop \\gcd(d,\\,n/d)=1}\\!\\!d^{k}.} If the proper unitary divisors of a given number add up to that number, then that number is called a unitary perfect number. The concept of a unitary divisor originates from R. Vaidyanathaswamy (1931)  who used the term block divisor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was initially optimized for the Pentium 4 processor and managed to immediately boost the performance of a supercomputer based on that CPU from 1.5 TFLOPS to 2 TFLOPS. As of 2005, the library was available at no cost for noncommercial use. A later open source version was released under the terms of the BSD license.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "But if there is both a right identity and a left identity, then they must be equal, resulting in a single two-sided identity. To see this, note that if l is a left identity and r is a right identity, then l = l \u2217 r = r. In particular, there can never be more than one two-sided identity: if there were two, say e and f, then e \u2217 f would have to be equal to both e and f. It is also quite possible for (S, \u2217) to have no identity element, such as the case of even integers under the multiplication operation. Another common example is the cross product of vectors, where the absence of an identity element is related to the fact that the direction of any nonzero cross product is always orthogonal to any element multiplied. That is, it is not possible to obtain a non-zero vector in the same direction as the original. Yet another example of structure without identity element involves the additive semigroup of positive natural numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Once all the multiples of each discovered prime have been marked as composites, the remaining unmarked numbers are primes. The earliest known reference to the sieve (Ancient Greek: \u03ba\u03cc\u03c3\u03ba\u03b9\u03bd\u03bf\u03bd \u1f18\u03c1\u03b1\u03c4\u03bf\u03c3\u03b8\u03ad\u03bd\u03bf\u03c5\u03c2, k\u00f3skinon Eratosth\u00e9nous) is in Nicomachus of Gerasa's Introduction to Arithmetic, an early 2nd cent. CE book which attributes it to Eratosthenes of Cyrene, a 3rd cent. BCE Greek mathematician, though describing the sieving by odd numbers instead of by primes.One of a number of prime number sieves, it is one of the most efficient ways to find all of the smaller primes. It may be used to find primes in arithmetic progressions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "+ error term {\\displaystyle y_{t}=a+w_{0}x_{t}+w_{1}x_{t-1}+w_{2}x_{t-2}+...+{\\text{error term}}} or the form y t = a + w 0 x t + w 1 x t \u2212 1 + w 2 x t \u2212 2 + . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For type sum, the identity object is the void type, which stores no information and it is impossible to address an inhabitant. The concept of monoidal category does not presume that values of such aggregate types can be taken apart; on the contrary, it provides a framework that unifies classical and quantum information theory.In category theory, monoidal categories can be used to define the concept of a monoid object and an associated action on the objects of the category. They are also used in the definition of an enriched category.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases these functions are not defined on the whole of \u211d3. For example, the trilinears of X365 which is the 365th entry in the Encyclopedia of Triangle Centers, are a1/2: b1/2: c1/2 so a, b, c cannot be negative. Furthermore, in order to represent the sides of a triangle they must satisfy the triangle inequality. So, in practice, every function's domain is restricted to the region of \u211d3 where a \u2264 b + c, b \u2264 c + a, and c \u2264 a + b. This region T is the domain of all triangles, and it is the default domain for all triangle-based functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In GIS, the RMSD is one measure used to assess the accuracy of spatial analysis and remote sensing. In hydrogeology, RMSD and NRMSD are used to evaluate the calibration of a groundwater model. In imaging science, the RMSD is part of the peak signal-to-noise ratio, a measure used to assess how well a method to reconstruct an image performs relative to the original image.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In planning and problem solving, or more formally one-person games, the search space is seen as a directed graph with states as nodes, and transitions as edges. States can have properties, and such a property P is hereditary if for each state S that has P, each state that can be reached from S also has P. The subset of all states that have P plus the subset of all states that have ~P form a partition of the set of states called a hereditary partition. This notion can trivially be extended to more discriminating partitions by instead of properties, considering aspects of states and their domains. If states have an aspect A, with di \u2282 D a partition of the domain D of A, then the subsets of states for which A \u2208 di form a hereditary partition of the total set of states iff \u2200i, from any state where A \u2208 di only other states where A \u2208 di can be reached.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational algebra, if R \u2286 X \u00d7 Y {\\displaystyle R\\subseteq X\\times Y} and S \u2286 Y \u00d7 Z {\\displaystyle S\\subseteq Y\\times Z} are relations, then the composite relation S R \u2286 X \u00d7 Z {\\displaystyle SR\\subseteq X\\times Z} is defined so that x S R z {\\displaystyle x\\,SR\\,z} if and only if there is a y \u2208 Y {\\displaystyle y\\in Y} such that x R y {\\displaystyle x\\,R\\,y} and y S z {\\displaystyle y\\,S\\,z} . This definition is a generalisation of the definition of functional composition. The defining properties of an equivalence relation R {\\displaystyle R} on a set X {\\displaystyle X} can then be reformulated as follows: id \u2286 R {\\displaystyle \\operatorname {id} \\subseteq R} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additional methods for improving the algorithm's efficiency were developed in the 20th century. The Euclidean algorithm has many theoretical and practical applications. It is used for reducing fractions to their simplest form and for performing division in modular arithmetic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephony, a message-waiting indicator (MWI) is a Telcordia Technologies (formerly Bellcore) term for an FSK-based telephone calling feature that illuminates an LED on selected telephones to notify a telephone user of waiting voicemail messages on most North American public telephone networks and PBXs. As described in Telcordia Generic Requirements document GR-283-CORE, a Message_Waiting_Indicator (MWI) is a mechanism that informs the subscriber about the status of recorded messages. The subscriber may subscribe to a notification feature that makes use of the status of this MWI.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the keyboard and display modules strapped to the operator's forearms, text could be entered by bringing the wrists together and typing. The same technology was used by IBM researchers to create the half-keyboard \"belt computer. Also in 1994, Mik Lamming and Mike Flynn at Xerox EuroPARC demonstrated the Forget-Me-Not, a wearable device that would record interactions with people and devices and store this information in a database for later query.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear-fractional program in which the denominator is the constant function 1. Formally, a linear-fractional program is defined as the problem of maximizing (or minimizing) a ratio of affine functions over a polyhedron, maximize c T x + \u03b1 d T x + \u03b2 subject to A x \u2264 b , {\\displaystyle {\\begin{aligned}{\\text{maximize}}\\quad &{\\frac {\\mathbf {c} ^{T}\\mathbf {x} +\\alpha }{\\mathbf {d} ^{T}\\mathbf {x} +\\beta }}\\\\{\\text{subject to}}\\quad &A\\mathbf {x} \\leq \\mathbf {b} ,\\end{aligned}}} where x \u2208 R n {\\displaystyle \\mathbf {x} \\in \\mathbb {R} ^{n}} represents the vector of variables to be determined, c , d \u2208 R n {\\displaystyle \\mathbf {c} ,\\mathbf {d} \\in \\mathbb {R} ^{n}} and b \u2208 R m {\\displaystyle \\mathbf {b} \\in \\mathbb {R} ^{m}} are vectors of (known) coefficients, A \u2208 R m \u00d7 n {\\displaystyle A\\in \\mathbb {R} ^{m\\times n}} is a (known) matrix of coefficients and \u03b1 , \u03b2 \u2208 R {\\displaystyle \\alpha ,\\beta \\in \\mathbb {R} } are constants. The constraints have to restrict the feasible region to { x | d T x + \u03b2 > 0 } {\\displaystyle \\{\\mathbf {x} |\\mathbf {d} ^{T}\\mathbf {x} +\\beta >0\\}} , i.e. the region on which the denominator is positive. Alternatively, the denominator of the objective function has to be strictly negative in the entire feasible region.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The utility function has the linear form: u ( x 1 , x 2 ) = x 1 + x 2 . {\\displaystyle u(x_{1},x_{2})=x_{1}+x_{2}.} The utility function is only weakly convex, and indeed the demand is not unique: when p 1 = p 2 {\\displaystyle p_{1}=p_{2}} , the consumer may divide his income in arbitrary ratios between product types 1 and 2 and get the same utility.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x60CB. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Unified Modeling Language (UML), an Element is an abstract class with no superclass. It is used as the superclass or base class, as known by object oriented programmers, for all the metaclasses in the UML infrastructure library. All other elements in the UML inherit, directly or indirectly from Element. An Element has a derived composition association to itself to support the general capability for elements to own other elements. As such, it has no additional attributes as part of its specification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, n, is sparsely totient if for all m > n, \u03c6 ( m ) > \u03c6 ( n ) {\\displaystyle \\varphi (m)>\\varphi (n)} where \u03c6 {\\displaystyle \\varphi } is Euler's totient function. The first few sparsely totient numbers are: 2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690, 840, 870, 1050, 1260, 1320, 1470, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990, 4620, 4830, 5460, 5610, 5670, 6090, 6930, 7140, 7350, 8190, 9240, 9660, 9870, ... (sequence A036913 in the OEIS). The concept was introduced by David Masser and Peter Man-Kit Shiu in 1986. As they showed, every primorial is sparsely totient.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, the phenomenon under study may have important spatial or temporal structure that must be considered during analysis, such as time series or image-based data. In 2005, Tibshirani and colleagues introduced the fused lasso to extend the use of lasso to this type of data. The fused lasso objective function is min \u03b2 { 1 N \u2211 i = 1 N ( y i \u2212 x i t \u03b2 ) 2 } subject to \u2211 j = 1 p | \u03b2 j | \u2264 t 1 and \u2211 j = 2 p | \u03b2 j \u2212 \u03b2 j \u2212 1 | \u2264 t 2 . {\\displaystyle {\\begin{aligned}&\\min _{\\beta }\\left\\{{\\frac {1}{N}}\\sum _{i=1}^{N}\\left(y_{i}-x_{i}^{t}\\beta \\right)^{2}\\right\\}\\\\&{\\text{ subject to }}\\sum _{j=1}^{p}|\\beta _{j}|\\leq t_{1}{\\text{ and }}\\sum _{j=2}^{p}|\\beta _{j}-\\beta _{j-1}|\\leq t_{2}.\\end{aligned}}} The first constraint is the lasso constraint, while the second directly penalizes large changes with respect to the temporal or spatial structure, which forces the coefficients to vary smoothly to reflect the system's underlying logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All these principles limit the set of possible correlations in non-trivial ways. Moreover, they are all device-independent: this means that they can be falsified under the assumption that we can decide if two or more events are space-like separated. The drawback of the device-independent approach is that, even when taken together, all the afore-mentioned physical principles do not suffice to single out the set of quantum correlations. In other words: all such reconstructions are partial.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By quadratic reciprocity and the restriction of the vertices to primes congruent to 1 mod 4, this is a symmetric relation, so it defines an undirected graph, which turns out to be isomorphic to the Rado graph.Another construction of the Rado graph shows that it is an infinite circulant graph, with the integers as its vertices and with an edge between each two integers whose distance (the absolute value of their difference) belongs to a particular set S {\\displaystyle S} . To construct the Rado graph in this way, S {\\displaystyle S} may be chosen randomly, or by choosing the indicator function of S {\\displaystyle S} to be the concatenation of all finite binary sequences.The Rado graph can also be constructed as the block intersection graph of an infinite block design in which the number of points and the size of each block are countably infinite. It can also be constructed as the Fra\u00efss\u00e9 limit of the class of finite graphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "z \u2208 I \u2217 {\\displaystyle z\\in I^{*}} if and only if there exists a c \u2208 R {\\displaystyle c\\in R} , where c {\\displaystyle c} is not contained in any minimal prime ideal of R {\\displaystyle R} , such that c z p e \u2208 I  {\\displaystyle cz^{p^{e}}\\in I^{}} for all e \u226b 0 {\\displaystyle e\\gg 0} . If R {\\displaystyle R} is reduced, then one can instead consider all e > 0 {\\displaystyle e>0} .Here I  {\\displaystyle I^{}} is used to denote the ideal of R {\\displaystyle R} generated by the p e {\\displaystyle p^{e}} 'th powers of elements of I {\\displaystyle I} , called the e {\\displaystyle e} th Frobenius power of I {\\displaystyle I} . An ideal is called tightly closed if I = I \u2217 {\\displaystyle I=I^{*}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically group theory, finite groups of prime power order p n {\\displaystyle p^{n}} , for a fixed prime number p {\\displaystyle p} and varying integer exponents n \u2265 0 {\\displaystyle n\\geq 0} , are briefly called finite p-groups. The p-group generation algorithm by M. F. Newman and E. A. O'Brien is a recursive process for constructing the descendant tree of an assigned finite p-group which is taken as the root of the tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This signal would feed into the sound-card audio-input of the PC, and Banpaia would decode the ESN/MDN pair from this signal and display it on the screen. The hacker could then copy that data into the Oki 900 phone and reboot it, after which the phone network could not distinguish the Oki from the original phone whose signal had been received. This gave the cloner, through the Oki phone, the ability to use the mobile-phone service of the legitimate subscriber whose phone was cloned \u2013 just as if that phone had been physically stolen, except that the subscriber retained his or her phone, unaware that the phone had been cloned\u2014at least until that subscriber received his or her next bill.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For every input position, the parser generates a state set. Each state is a tuple (X \u2192 \u03b1 \u2022 \u03b2, i), consisting of the production currently being matched (X \u2192 \u03b1 \u03b2) the current position in that production (visually represented by the dot \u2022) the position i in the input at which the matching of this production began: the origin position(Earley's original algorithm included a look-ahead in the state; later research showed this to have little practical effect on the parsing efficiency, and it has subsequently been dropped from most implementations.) A state is finished when its current position is the last position of the right side of the production, that is, when there is no symbol to the right of the dot \u2022 in the visual representation of the state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operations research, the makespan of a project is the length of time that elapses from the start of work to the end. This type of multi-mode resource constrained project scheduling problem (MRCPSP) seeks to create the shortest logical project schedule, by efficiently using project resources, adding the lowest number of additional resources as possible to achieve the minimum makespan. The term commonly appears in the context of scheduling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle (A-\\mu I)^{-1}.} The closer the approximation \u03bc {\\displaystyle \\mu } to the eigenvalue is chosen, the faster the algorithm converges; however, incorrect choice of \u03bc {\\displaystyle \\mu } can lead to slow convergence or to the convergence to an eigenvector other than the one desired. In practice, the method is used when a good approximation for the eigenvalue is known, and hence one needs only few (quite often just one) iterations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the data transformation stage, a series of rules or functions are applied to the extracted data in order to prepare it for loading into the end target. An important function of transformation is data cleansing, which aims to pass only \"proper\" data to the target. The challenge when different systems interact is in the relevant systems' interfacing and communicating.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(See, for example, the Fermi\u2013Pasta\u2013Ulam\u2013Tsingou experiment of 1953.) Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible. Systems that are ergodic are said to have the property of ergodicity; a broad range of systems in geometry, physics, and probability are ergodic. Ergodic systems are studied in ergodic theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s, a tiny CPU that executed FORTH was fabricated into a DRAM chip to improve PUSH and POP. FORTH is a stack-oriented programming language and this improved its efficiency. The transputer also had large on chip memory given that it was made in the early 1980s making it essentially a processor-in-memory. Notable PIM projects include the Berkeley IRAM project (IRAM) at the University of California, Berkeley project and the University of Notre Dame PIM effort.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, Rd2xBd6. Concise reversible algebraic notation is similar to reversible algebraic notation, but omits the file or rank if it is not needed to disambiguate the move. For example, Rd2xB6.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular construction, modules are a bundle of redundant project components that are produced en masse prior to installation.Building components are often arranged into modules in the industrialization of construction. In industrial design, modularity refers to an engineering technique that builds larger systems by combining smaller subsystems. In manufacturing, modularity typically refers to modular design, either as the use of exchangeable parts or options in the fabrication of an object or the design and manufacture of modular components. In organizational design, Richard L. Daft and Arie Y. Lewin (1993) identified a paradigm called \"modular organization\" that had as its ground the need for flexible learning organizations in constant change and the need to solve their problems through coordinated self-organizing processes. This modular organization is characterized by decentralized decision-making, flatter hierarchies, self-organization of units.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Microsoft family of operating systems, Windows Vista and later versions have support for both MSI and MSI-X. Support was added in the Longhorn development cycle around 2004. MSI is not supported in earlier versions like Windows XP or Windows Server 2003.Solaris Express 6/05 released in 2005 added support for MSI an MSI-X as part of their new device driver interface (DDI) interrupt framework.FreeBSD 6.3 and 7.0 released in 2008 added support for MSI and MSI-X.OpenBSD 5.0 released in 2011 added support for MSI. 6.0 added support for MSI-X.Linux gained support for MSI and MSI-X around 2003.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Portuguese and Spanish also have unique forms for 1st, 2nd and 3rd person reflexive when they follow the preposition com/con ('with'). That holds true for both singular and plural pronouns for Portuguese, but only for singular in Spanish.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, Annotea is an RDF standard sponsored by the W3C to enhance document-based collaboration via shared document metadata based on tags, bookmarks, and other annotations. In this case document metadata includes: Keywords Comments Notes Explanations Errors CorrectionsIn general, Annotea associates text strings to a web document or selected parts of a web document without actually needing to modify the original document. Users that access any web documents can also load the metadata associated with it from a selected annotation server (or groups of servers) and see a peer group's comments on the document. Similarly shared metadata tags can be attached to web documents to help in future retrieval.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Tikhonov (Tychonoff) fixed-point theorem: Let V be a locally convex topological vector space. For any nonempty compact convex set X in V, any continuous function f: X \u2192 X has a fixed point. Browder fixed-point theorem: Let K be a nonempty closed bounded convex set in a uniformly convex Banach space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-PAE modes of 32-bit x86 processors, the usable RAM may be limited to less than 4 GB. Limits on memory and address space vary by platform and operating system. Limits on physical memory for 32-bit platforms also depend on the presence and use of Physical Address Extension (PAE), which allows 32-bit systems to use more than 4 GB of physical memory. PAE and 64-bit systems may be able to address up to the full address space of the x86 processor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with a unary operation (the successor function with n = 0). The sequence continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3). After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity. For the operations beyond exponentiation, the nth member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration (n = 4), pentation (n = 5), hexation (n = 6), etc.) and can be written as using n \u2212 2 arrows in Knuth's up-arrow notation. Each hyperoperation may be understood recursively in terms of the previous one by: a  b = a  ( a  ( a  ( \u22ef  ( a  ( a  a ) ) \u22ef ) ) ) \u23df b copies of a , n \u2265 2 {\\displaystyle ab=\\underbrace {a(a(a(\\cdots (a(aa))\\cdots )))} _{\\displaystyle b{\\mbox{ copies of }}a},\\quad n\\geq 2} It may also be defined according to the recursion rule part of the definition, as in Knuth's up-arrow version of the Ackermann function: a  b = a  ( a  ( b \u2212 1 ) ) , n \u2265 1 {\\displaystyle ab=a\\left(a\\left(b-1\\right)\\right),\\quad n\\geq 1} This can be used to easily show numbers much larger than those which scientific notation can, such as Skewes's number and googolplexplex (e.g. 50  50 {\\displaystyle 5050} is much larger than Skewes's number and googolplexplex), but there are some numbers which even they cannot easily show, such as Graham's number and TREE(3).This recursion rule is common to many variants of hyperoperations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network theory, link analysis is a data-analysis technique used to evaluate relationships (Tap link) between nodes. Relationships may be identified among various types of nodes (100k), including organizations, people and transactions. Link analysis has been used for investigation of criminal activity (fraud , counterterrorism, and intelligence), computer security analysis, search engine optimization, market research, medical research, and art.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Opteron CPU directly supports up to an 8-way configuration, which can be found in mid-level servers. Enterprise-level servers use additional (and expensive) routing chips to support more than 8 CPUs per box. In a variety of computing benchmarks, the Opteron architecture has demonstrated better multi-processor scaling than the Intel Xeon which didn't have a point to point system until QPI and integrated memory controllers with the Nehalem design.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Equipped with the \u03bb-calculus and \"general\" recursion, Kleene with help of Church and J. Barkley Rosser produced proofs (1933, 1935) to show that the two calculi are equivalent. Church subsequently modified his methods to include use of Herbrand\u2013G\u00f6del recursion and then proved (1936) that the Entscheidungsproblem is unsolvable: there is no algorithm that can determine whether a well formed formula has a beta normal form.Many years later in a letter to Davis (c. 1965), G\u00f6del said that \"he was, at the time of these  lectures, not at all convinced that his concept of recursion comprised all possible recursions\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another popular strategy for avoiding linguistic controversy is dependency grammar parsing. Most modern parsers are at least partly statistical; that is, they rely on a corpus of training data which has already been annotated (parsed by hand).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some machines that support parity or ECC allow checking to be enabled or disabled in the BIOS, permitting cheaper non-parity RAM to be used. If parity RAM is used the chipset will usually use it to implement error correction, rather than halting the machine on a single-bit parity error. However, as discussed in the article on ECC memory, errors, while not everyday events, are not negligibly infrequent. Even in the absence of manufacturing defects, naturally occurring radiation causes random errors; tests on Google's many servers found that memory errors were not rare events, and that the incidence of memory errors and the range of error rates across different DIMMs were much higher than previously reported.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin. In theoretical studies, the assumption that a coin is fair is often made by referring to an ideal coin. John Edmund Kerrich performed experiments in coin flipping and found that a coin made from a wooden disk about the size of a crown and coated on one side with lead landed heads (wooden side up) 679 times out of 1000.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In neural networking or heuristic algorithms (computer terms generally used to describe 'learning' computers or 'AI simulations'), a black box is used to describe the constantly changing section of the program environment which cannot easily be tested by the programmers. This is also called a white box in the context that the program code can be seen, but the code is so complex that it is functionally equivalent to a black box. In physics, a black box is a system whose internal structure is unknown, or need not be considered for a particular purpose. In cryptography to capture the notion of knowledge obtained by an algorithm through the execution of a cryptographic protocol such as a zero-knowledge proof protocol. If the output of an algorithm when interacting with the protocol matches that of a simulator given some inputs, it only needs to know the inputs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S1 and S2 such that the sum of the numbers in S1 equals the sum of the numbers in S2. Although the partition problem is NP-complete, there is a pseudo-polynomial time dynamic programming solution, and there are heuristics that solve the problem in many instances, either optimally or approximately. For this reason, it has been called \"the easiest hard problem\".There is an optimization version of the partition problem, which is to partition the multiset S into two subsets S1, S2 such that the difference between the sum of elements in S1 and the sum of elements in S2 is minimized. The optimization version is NP-hard, but can be solved efficiently in practice.The partition problem is a special case of two related problems: In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A branch may have one incoming control flow and two or more outgoing control flows. When the condition is fulfilled, a branch activates exactly only one of the outgoing control flows and deactivates the others. The counterpart of a branch is a merge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The service will then prompt the user to enter the dialed number of the party to be called. The disadvantage of this method of roaming is that the user will not be able to dial numbers directly from the handset. The advantage is that it works in almost all locations around the world since USSD is ubiquitous and free.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first half of the 20th century, telecommunication services developed progressively from completely manual setup of calls by operators called by subscribers, to automatic systems that could connect subscribers of the same local exchange through the use of telephone dials installed in each telephone. In the 1940s, the Bell System in the United States and Canada developed methods and technologies, called direct distance dialing and first implemented in 1951, that enabled telephone subscriber to dial long-distance telephone calls themselves without calling an operator. In the United Kingdom, a similar technology called subscriber trunk dialling (STD) was ready by 1958, when Queen Elizabeth II, who was in Bristol, publicised STD by dialling Edinburgh, the farthest distance a call could be directly dialled in the UK, on 5 December 1958. The STD system was completed in 1979.The technology was extended when, from 8 March 1963, subscribers in London were able to directly dial Paris using international direct dialling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem. A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. The method penalizes violations of inequality constraints using a Lagrange multiplier, which imposes a cost on violations. These added costs are used instead of the strict inequality constraints in the optimization. In practice, this relaxed problem can often be solved more easily than the original problem. The problem of maximizing the Lagrangian function of the dual variables (the Lagrangian multipliers) is the Lagrangian dual problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle E=E=\\alpha +\\beta x_{i}+E=\\alpha +\\beta x_{i}.} The line of best fit for the bivariate dataset takes the form y = \u03b1 + \u03b2x and is called the regression line. \u03b1 and \u03b2 correspond to the intercept and slope, respectively.In an experiment, the variable manipulated by an experimenter is something that is proven to work, called an independent variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Samuelson\u2013Berkowitz algorithm efficiently computes the characteristic polynomial of an n \u00d7 n {\\displaystyle n\\times n} matrix whose entries may be elements of any unital commutative ring. Unlike the Faddeev\u2013LeVerrier algorithm, it performs no divisions, so may be applied to a wider range of algebraic structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the absence of parentheses, the parallel operator is defined as taking precedence over addition or subtraction, similar to multiplication.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the prime signature of a number is the multiset of (nonzero) exponents of its prime factorization. The prime signature of a number having prime factorization p 1 m 1 p 2 m 2 \u2026 p n m n {\\displaystyle p_{1}^{m_{1}}p_{2}^{m_{2}}\\dots p_{n}^{m_{n}}} is the multiset { m 1 , m 2 , \u2026 , m n } {\\displaystyle \\left\\{m_{1},m_{2},\\dots ,m_{n}\\right\\}} . For example, all prime numbers have a prime signature of {1}, the squares of primes have a prime signature of {2}, the products of 2 distinct primes have a prime signature of {1, 1} and the products of a square of a prime and a different prime (e.g. 12, 18, 20, ...) have a prime signature of {2, 1}.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, individuals in a population can be assigned to compartments with labels \u2013 for example, S, I, or R, (Susceptible, Infectious, or Recovered) and they progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for instance, SIR means each individual is originally susceptible then changes to infectious and finally gets recovered and remained recovered (immune) forever. On the other hand, public health may apply some interventions such as vaccination or contact tracing to reduce the spread of an epidemic disease.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well. The other component is the pure-error sum of squares. The pure-error sum of squares is the sum of squared deviations of each value of the dependent variable from the average value over all observations sharing its independent variable value(s). These are errors that could never be avoided by any predictive equation that assigned a predicted value for the dependent variable as a function of the value(s) of the independent variable(s). The remainder of the residual sum of squares is attributed to lack of fit of the model since it would be mathematically possible to eliminate these errors entirely.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multitasking computer operating systems, a daemon ( or ) is a computer program that runs as a background process, rather than being under the direct control of an interactive user. Traditionally, the process names of a daemon end with the letter d, for clarification that the process is in fact a daemon, and for differentiation between a daemon and a normal computer program. For example, syslogd is a daemon that implements system logging facility, and sshd is a daemon that serves incoming SSH connections. In a Unix environment, the parent process of a daemon is often, but not always, the init process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The distinction arises because it is conventional to talk not about estimating fixed effects but rather about predicting random effects, but the two terms are otherwise equivalent. (This is a bit strange since the random effects have already been \"realized\"; they already exist. The use of the term \"prediction\" may be because in the field of animal breeding in which Henderson worked, the random effects were usually genetic merit, which could be used to predict the quality of offspring (Robinson page 28)).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Complementary configuration occurs when multiple information sources supply different information about the same features. This strategy is used for fusing information at raw data level within decision-making algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Effectiveness in using a system for controlling a continuous industrial process would generally be measured in very different terms to, say, effectiveness in using a text editor. Thus, it can be difficult, if not impossible, to answer the question \"is system A more usable than system B\", because the measures of effectiveness and efficiency may be very different. However, it can be argued that given a sufficiently high-level definition of subjective assessments of usability, comparisons can be made between systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical linear algebra, the Bartels\u2013Stewart algorithm is used to numerically solve the Sylvester matrix equation A X \u2212 X B = C {\\displaystyle AX-XB=C} . Developed by R.H. Bartels and G.W.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is specific verbal morphology\u2014a particular form of the verb indicates passive voice.The problem arises with non-European languages. Many constructions in these languages share at least one property with the canonical European passive, but not all. While it seems justified to call these constructions passive when comparing them to European languages' passive constructions, as a whole the passives of the world's languages do not share a single common feature.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In muscle physiology, physiological cross-sectional area (PCSA) is the area of the cross section of a muscle perpendicular to its fibers, generally at its largest point. It is typically used to describe the contraction properties of pennate muscles. It is not the same as the anatomical cross-sectional area (ACSA), which is the area of the crossection of a muscle perpendicular to its longitudinal axis. In a non-pennate muscle the fibers are parallel to the longitudinal axis, and therefore PCSA and ACSA coincide.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, 8b/10b is a line code that maps 8-bit words to 10-bit symbols to achieve DC balance and bounded disparity, and at the same time provide enough state changes to allow reasonable clock recovery. This means that the difference between the counts of ones and zeros in a string of at least 20 bits is no more than two, and that there are not more than five ones or zeros in a row. This helps to reduce the demand for the lower bandwidth limit of the channel necessary to transfer the signal.An 8b/10b code can be implemented in various ways with focus on different performance parameters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are infinite in number. They constitute the comparatively rare instances where the strict converse of Fermat's Little Theorem does not hold. This fact precludes the use of that theorem as an absolute test of primality.The Carmichael numbers form the subset K1 of the Kn\u00f6del numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this case, rather than simply counting through elements of the population and selecting every kth unit, we allocate each element a space along a number line according to its selection probability. We then generate a random start from a uniform distribution between 0 and 1, and move along the number line in steps of 1. Example: We have a population of 5 units (A to E).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relational databases, the information schema (information_schema) is an ANSI-standard set of read-only views that provide information about all of the tables, views, columns, and procedures in a database. It can be used as a source of the information that some databases make available through non-standard commands, such as: the SHOW command of MySQL the DESCRIBE command of Oracle's SQL*Plus the \\d command in psql (PostgreSQL's default command-line program). => SELECT count(table_name) FROM information_schema.tables; count ------- 99 (1 row) => SELECT column_name, data_type, column_default, is_nullable FROM information_schema.columns WHERE table_name='alpha'; column_name | data_type | column_default | is_nullable -------------+-----------+----------------+------------- foo | integer | | YES bar | character | | YES (2 rows) => SELECT * FROM information_schema.information_schema_catalog_name; catalog_name -------------- johnd (1 row)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software, semantic technology encodes meanings separately from data and content files, and separately from application code. This enables machines as well as people to understand, share and reason with them at execution time. With semantic technologies, adding, changing and implementing new relationships or interconnecting programs in a different way can be just as simple as changing the external model that these programs share. With traditional information technology, on the other hand, meanings and relationships must be predefined and \"hard wired\" into data formats and the application program code at design time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the European Union the classifications for vehicle types are defined by: Commission Directive 2001/116/EC of 20 December 2001, adapting to technical progress Council Directive 70/156/EEC on the approximation of the laws of the Member States relating to the type-approval of motor vehicles and their trailers Directive 2002/24/EC of the European Parliament and of the Council of 18 March 2002 relating to the type-approval of two or three wheeled motor vehicles and repealing Council Directive 92/61/EECEuropean Community, is based on the Community's WVTA (whole vehicle type-approval) system. Under this system, manufacturers can obtain certification for a vehicle type in one Member State if it meets the EC technical requirements and then market it EU-wide with no need for further tests. Total technical harmonization already has been achieved in three vehicle categories (passenger cars, motorcycles, and tractors) and soon will extend to other vehicle categories (coaches and utility vehicles). It is essential that European car manufacturers be ensured access to as large a market as possible. While the Community type-approval system allows manufacturers to benefit fully from internal market opportunities, worldwide technical harmonization in the context of the United Nations Economic Commission for Europe (UNECE) offers a market beyond European borders.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom \u2061 ( f ) {\\displaystyle \\operatorname {dom} (f)} or dom \u2061 f {\\displaystyle \\operatorname {dom} f} , where f is the function. In layman's terms, the domain of a function can generally be thought of as \"what x can be\".More precisely, given a function f: X \u2192 Y {\\displaystyle f\\colon X\\to Y} , the domain of f is X. In modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that X and Y are both subsets of R {\\displaystyle \\mathbb {R} } , the function f can be graphed in the Cartesian coordinate system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups. The list below gives all finite simple groups, together with their order, the size of the Schur multiplier, the size of the outer automorphism group, usually some small representations, and lists of all duplicates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 567, 1567, 4567, and 14567 are the patterns related to Braille pattern dots-345, since the two additional dots of kantenji patterns 0345, 3457, and 03457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As blacks integrate to white communities they are perpetuating a system in which blacks are inferior to whites. Blacks would continue to function in an environment of being second class citizens, he believes, never reaching equity to white citizens. Carmichael therefore uses the concept of black nationalism to promote an equality that would begin to dismantle institutional racism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: Uniform spanning tree, a spanning tree of a given graph in which each different tree is equally likely to be selected Random minimal spanning tree, spanning trees of a graph formed by choosing random edge weights and using the minimum spanning tree for those weights Random binary tree, binary trees with a given number of nodes, formed by inserting the nodes in a random order or by selecting all possible trees uniformly at random Random recursive tree, increasingly labelled trees, which can be generated using a simple stochastic growth rule. Treap or randomized binary search tree, a data structure that uses random choices to simulate a random binary tree for non-random update sequences Rapidly exploring random tree, a fractal space-filling pattern used as a data structure for searching high-dimensional spaces Brownian tree, a fractal tree structure created by diffusion-limited aggregation processes Random forest, a machine-learning classifier based on choosing random subsets of variables for each tree and using the most frequent tree output as the overall classification Branching process, a model of a population in which each individual has a random number of children", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an operation is a function which takes zero or more input values (also called \"operands\" or \"arguments\") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, we state two equivalent forms of the theorem, and show their equivalence. Later, we prove the theorem. This is done in the following steps: Reducing the theorem to sentences (formulas with no free variables) in prenex form, i.e. with all quantifiers (\u2200 and \u2203) at the beginning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, let X {\\displaystyle X} be a topological space, G , H {\\displaystyle G,H} topological groups and a group homomorphism \u03d5: H \u2192 G {\\displaystyle \\phi \\colon H\\to G} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1972, Jurjen Battjes, commissioned by the Dutch Technical Advisory Committee for Flood Defences, summarised the available research and provided a solid theoretical foundation. This work led to an improved version of Hunt's Formula, which explicitly included parameters for the angle of incidence of the waves, the effect of a berm, and the slope's roughness. However, the available experimental data on roughness and the berm were insufficient to establish a definitive formula.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The inequality is a limiting case of Sobolev imbedding and can be stated as the following theorem: Let \u03a9 {\\displaystyle \\Omega } be a bounded domain in R n {\\displaystyle \\mathbb {R} ^{n}} satisfying the cone condition. Let m p = n {\\displaystyle mp=n} and p > 1 {\\displaystyle p>1} . Set A ( t ) = exp \u2061 ( t n / ( n \u2212 m ) ) \u2212 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One of the biggest problems with this form of scientific fraud is that \"university investigations into research misconduct are often inadequate, opaque and poorly conducted. They challenge the idea that institutions can police themselves on research integrity. \"Sometimes intentional fabrication can be difficult to distinguish from unintentional academic incompetence or malpractice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result of being relatively close to the femtocell, the mobile phone (user equipment) expends significantly less power for communication with it, thus increasing battery life. They may also get better voice quality (via HD voice) depending on a number of factors such as operator/network support, customer contract/price plan, phone and operating system support. Some carriers may also offer more attractive tariffs, for example discounted calls from home.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Shortly after Neo visits the Oracle, Morpheus is captured by agents who plan to hack into his mind. Because Morpheus, as a hovercraft captain, possesses access codes to the Zion mainframe computer, the surviving members of the ship's crew are about to unplug Morpheus from the Matrix, without reconnecting his mind and body, a process that will kill him. Neo and Trinity, however, reenter the Matrix to make a daring and successful rescue of Morpheus. Neo saves Trinity from a helicopter crash, confirming Morpheus' belief that Neo is indeed the One. Neo is eventually killed by Agent Smith shortly after the rescue, but revived as the One and returned to the Nebuchadnezzar before the Machines' Sentinels can destroy the ship.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, topology (from the Greek words \u03c4\u03cc\u03c0\u03bf\u03c2, 'place, location', and \u03bb\u03cc\u03b3\u03bf\u03c2, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In puzzle games, scores are usually gained by solving the puzzles quickly. Higher scores can be gained by performing combos of puzzle solving. There is often a time bonus which can add extra points. The level number is often a multiplier on the points, so higher scores are possible on harder levels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, superdense coding (also referred to as dense coding) is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assumption of sender and receiver pre-sharing an entangled resource. In its simplest form, the protocol involves two parties, often referred to as Alice and Bob in this context, which share a pair of maximally entangled qubits, and allows Alice to transmit two bits (i.e., one of 00, 01, 10 or 11) to Bob by sending only one qubit. This protocol was first proposed by Charles H. Bennett and Stephen Wiesner in 1970 (though not published by them until 1992) and experimentally actualized in 1996 by Klaus Mattle, Harald Weinfurter, Paul G. Kwiat and Anton Zeilinger using entangled photon pairs. Superdense coding can be thought of as the opposite of quantum teleportation, in which one transfers one qubit from Alice to Bob by communicating two classical bits, as long as Alice and Bob have a pre-shared Bell pair.The transmission of two bits via a single qubit is made possible by the fact that Alice can choose among four quantum gate operations to perform on her share of the entangled state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Manchester Ship Canal at Latchford, Stockton Heath and Lower Walton in Warrington, and also slightly further west at Moore. Near the eastern end of the canal in Salford, the Barton Road Swing Bridge is adjacent to the Barton Swing Aqueduct \u2013 a 234-foot, 800-ton trough holding some 800 tons of water (retained by gates at either end) swings so that it is at right angles to the Bridgewater Canal to allow ships to pass up the Ship Canal. Myton Swing Bridge - road bridge in Kingston upon Hull Oulton Broad swing bridge \u2013 rail Reedham Swing Bridge (52.55887\u00b0N 1.57237\u00b0E\ufeff / 52.55887; 1.57237) \u2013 rail Ross Bridge, Penzance Sandwich Toll Bridge (rebuilt 1892) Selby swing bridge \u2013 rail Somerleyton swing bridge Trowse Bridge at Norwich.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle X.} Remark.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The goal is for the referee to find an algorithm such that if the statement is true, there is a way for Alice to win with probability greater than 3/4, and if the statement is false, there is a way for Bob to win with probability greater than 3/4. This probability is equal to 1-\u03b5.In the language of complexity theory, a promise problem L = ( L yes , L no ) {\\displaystyle L=(L_{\\text{yes}},L_{\\text{no}})} has a classical refereed game (classical RG) if there exists a referee described by polynomial time randomized computation, such that 1. for each x \u2208 L yes {\\displaystyle x\\in L_{\\text{yes}}} , there is a strategy for Alice to win with probability \u2265 3/4, and2. for each x \u2208 L no {\\displaystyle x\\in L_{\\text{no}}} , there is a strategy for Bob to win with probability \u2265 3/4.It is known that RG = EXP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It should not be confused with the dot product (projection product). If two vectors have the same direction or have the exact opposite direction from each other (that is, they are not linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "P(if A, then B) is normally interpreted not as an ordinary probability\u2014not, specifically, as P(A\u2032 \u2228 B)\u2014but as the conditional probability of B given A, P(B | A) = P(A \u2227 B) / P(A). This raises a question: what about a probability like P(if A, then B, and if C, then D)? For this, there is no standard answer. What would be needed, for consistency, is a treatment of if-then as a binary operation, \u2192, such that for conditional events A \u2192 B and C \u2192 D, P(A \u2192 B) = P(B | A), P(C \u2192 D) = P(D | C), and P((A \u2192 B) \u2227 (C \u2192 D)) is well-defined and reasonable. This treatment is what conditional event algebras try to provide.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real social networks individuals exhibit a tendency to re-connect with past contacts (ex. family, friends, co-workers, etc.) rather than strangers. In 1970, Mark Granovetter examined this behaviour in the social networks of a group of workers and identified tie strength, a characteristic of social ties describing the frequency of contact between two individuals. From this comes the idea of strong and weak ties, where an individual's strong ties are those she has come into frequent contact with. Link-centric preferential attachment aims to explain the mechanism behind strong and weak ties as a stochastic reinforcement process for old ties in agent-based modeling where nodes have long-term memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 378, 1378, 3478, and 13478 are the patterns related to Braille pattern dots-236, since the two additional dots of kantenji patterns 0236, 2367, and 02367 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimal transport, a branch of mathematics, polar factorization of vector fields is a basic result due to Brenier (1987), with antecedents of Knott-Smith (1984) and Rachev (1985), that generalizes many existing results among which are the polar decomposition of real matrices, and the rearrangement of real-valued functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is trained by repeatedly exposing it to examples of the problem and learning the significance (weights) of the input nodes. : 196 The neural network used by Split_up is said to generalise well if the output of the network is correct (or nearly correct) for examples not seen during training, which classifies it as an intelligent system. : 274", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, most prepaid phones now offer roaming using one of the following methods: The prepaid mobile phone user dials a \"trigger\" number from the foreign location using a USSD message which is not charged for while roaming. Upon receipt of the USSD, the customer's operator will then return the call. When the service calls back, the user is being charged for the cost of the service from the credit available in the home network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In part because the Shannon capacity is difficult to compute, researchers have looked for other graph invariants that are easy to compute and that provide bounds on the Shannon capacity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, XY is the notation representing the set of all functions from Y to X. As \"2\" can be defined as {0,1} (see, for example, von Neumann ordinals), 2S (i.e., {0,1}S) is the set of all functions from S to {0,1}. As shown above, 2S and the power set of S, P(S), are considered identical set-theoretically. This equivalence can be applied to the example above, in which S = {x, y, z}, to get the isomorphism with the binary representations of numbers from 0 to 2n \u2212 1, with n being the number of elements in the set S or |S| = n. First, the enumerated set { (x, 1), (y, 2), (z, 3) } is defined in which the number in each ordered pair represents the position of the paired element of S in a sequence of binary digits such as {x, y} = 011(2); x of S is located at the first from the right of this sequence and y is at the second from the right, and 1 in the sequence means the element of S corresponding to the position of it in the sequence exists in the subset of S for the sequence while 0 means it does not. For the whole power set of S, we get: Such a injective mapping from P(S) to integers is arbitrary, so this representation of all the subsets of S is not unique, but the sort order of the enumerated set does not change its cardinality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1976, refinanced by the Canada Development Corporation, it returned to operation as AES Data, and went on to successfully market its brand of word processors worldwide until its demise in the mid-1980s. Its first office product, the AES-90, combined for the first time a CRT-screen, a floppy-disk and a microprocessor, that is, the very same winning combination that would be used by IBM for its PC seven years later. The AES-90 software was able to handle French and English typing from the start, displaying and printing the texts side-by-side, a Canadian government requirement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, expose ( v ) {\\displaystyle {\\text{expose}}(v)} extracts the left child l {\\displaystyle l} , key k {\\displaystyle k} , and right child r {\\displaystyle r} of node v {\\displaystyle v} into a tuple ( l , k , r ) {\\displaystyle (l,k,r)} . Node ( l , k , r ) {\\displaystyle {\\text{Node}}(l,k,r)} creates a node with left child l {\\displaystyle l} , key k {\\displaystyle k} and right child r {\\displaystyle r} . \" s 1 | | s 2 {\\displaystyle s_{1}||s_{2}} \" means that two statements s 1 {\\displaystyle s_{1}} and s 2 {\\displaystyle s_{2}} can run in parallel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory language here, speak of a function class when f \u2282 A \u00d7 C {\\displaystyle f\\subset A\\times C} and provenly \u2200 ( a \u2208 A ) . \u2203 ! ( c \u2208 C ) . \u27e8 a , c \u27e9 \u2208 f {\\displaystyle \\forall (a\\in A).\\,\\exists !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Nevertheless, the machine was air cooled, and would have been the fastest such machine on the market. The machine ran an early version of the Mach kernel for multi-processor support. The compilers were designed to keep the processors as full as possible by reducing the number of branch delay slots, and did a particularly good job of it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the (complement of the) Boolean satisfiability problem. For first-order logic, resolution can be used as the basis for a semi-algorithm for the unsatisfiability problem of first-order logic, providing a more practical method than one following from G\u00f6del's completeness theorem. The resolution rule can be traced back to Davis and Putnam (1960); however, their algorithm required trying all ground instances of the given formula. This source of combinatorial explosion was eliminated in 1965 by John Alan Robinson's syntactical unification algorithm, which allowed one to instantiate the formula during the proof \"on demand\" just as far as needed to keep refutation completeness.The clause produced by a resolution rule is sometimes called a resolvent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, pairwise summation, also called cascade summation, is a technique to sum a sequence of finite-precision floating-point numbers that substantially reduces the accumulated round-off error compared to naively accumulating the sum in sequence. Although there are other techniques such as Kahan summation that typically have even smaller round-off errors, pairwise summation is nearly as good (differing only by a logarithmic factor) while having much lower computational cost\u2014it can be implemented so as to have nearly the same cost (and exactly the same number of arithmetic operations) as naive summation. In particular, pairwise summation of a sequence of n numbers xn works by recursively breaking the sequence into two halves, summing each half, and adding the two sums: a divide and conquer algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real analysis, a branch of mathematics, a modulus of convergence is a function that tells how quickly a convergent sequence converges. These moduli are often employed in the study of computable analysis and constructive mathematics. If a sequence of real numbers x i {\\displaystyle x_{i}} converges to a real number x {\\displaystyle x} , then by definition, for every real \u03b5 > 0 {\\displaystyle \\varepsilon >0} there is a natural number N {\\displaystyle N} such that if i > N {\\displaystyle i>N} then | x \u2212 x i | < \u03b5 {\\displaystyle \\left|x-x_{i}\\right|<\\varepsilon } . A modulus of convergence is essentially a function that, given \u03b5 {\\displaystyle \\varepsilon } , returns a corresponding value of N {\\displaystyle N} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Example: Slow memory diagram depicts a slow consistency example. The first process writes 1 to the memory location X and then it writes 1 to the memory location Y. The second process reads 1 from Y and it then reads 0 from X even though X was written before Y. Hutto, Phillip W., and Mustaque Ahamad (1990) illustrate that by appropriate programming, slow memory (consistency) can be expressive and efficient. They mention that slow memory has two valuable properties; locality and supporting reduction from atomic memory. They propose two algorithms to present the expressiveness of slow memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid\u2013Euler theorem asserts a one-to-one correspondence between even perfect numbers and Mersenne primes. Many of the largest known primes are Mersenne primes because Mersenne numbers are easier to check for primality. As of 2023, 51 Mersenne primes are known.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1970s, a noted nuclear scientist Isadore Perlman undertook the analysis of numerous Cypriot ceramics sent to him by the Swedish archaeologist, Einar Gherstad, when he pioneered high-precision methods of neutron activation analysis at the Lawrence Berkeley Laboratory in the US. Neutron activation analysis helps to determine the origin of ancient pottery and other artifacts through the analysis of the clay from which they were made. He was helped in the project by another noted scientist Frank Asaro.Second millennium BC pottery from Cyprus was one of the first archaeological projects that Perlman and Asaro undertook. The project of the origin of the then assumed Second Millennium Palestinian Bichrome Ware was undertaken as part of the PhD thesis of Michal Artzy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field. Suppose that we observe a random variable Y i {\\displaystyle Y_{i}} , where i \u2208 S {\\displaystyle i\\in S} . Hidden Markov random fields assume that the probabilistic nature of Y i {\\displaystyle Y_{i}} is determined by the unobservable Markov random field X i {\\displaystyle X_{i}} , i \u2208 S {\\displaystyle i\\in S} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. For example, 1200 = 2 4 \u22c5 3 1 \u22c5 5 2 = ( 2 \u22c5 2 \u22c5 2 \u22c5 2 ) \u22c5 3 \u22c5 ( 5 \u22c5 5 ) = 5 \u22c5 2 \u22c5 5 \u22c5 2 \u22c5 3 \u22c5 2 \u22c5 2 = \u2026 {\\displaystyle 1200=2^{4}\\cdot 3^{1}\\cdot 5^{2}=(2\\cdot 2\\cdot 2\\cdot 2)\\cdot 3\\cdot (5\\cdot 5)=5\\cdot 2\\cdot 5\\cdot 2\\cdot 3\\cdot 2\\cdot 2=\\ldots } The theorem says two things about this example: first, that 1200 can be represented as a product of primes, and second, that no matter how this is done, there will always be exactly four 2s, one 3, two 5s, and no other primes in the product. The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (for example, 12 = 2 \u22c5 6 = 3 \u22c5 4 {\\displaystyle 12=2\\cdot 6=3\\cdot 4} ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to further eliminate irrelevant links and search results, DeepPeep uses the HIerarchical Form Identification (HIFI) framework that classifies links and search results based on the website's structure and content. Unlike other forms of classification which solely relies on the web form labels for organization, HIFI utilizes both the structure and content of the web form for classification. Utilizing these two classifiers, HIFI organizes the web forms in a hierarchical fashion which ranks the a web form's relevance to the target keyword.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in abstract algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is commutative and the identity element is the only element with finite order. While finitely generated abelian groups are completely classified, not much is known about infinitely generated abelian groups, even in the torsion-free countable case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Lexical recognition is of particular value in the field of computer speech recognition, since the ability to build and search a network of semantically connected ideas would greatly increase the effectiveness of speech-recognition software. Statistical models can be used to segment and align recorded speech to words or phones. Applications include automatic lip-synch timing for cartoon animation, follow-the-bouncing-ball video sub-titling, and linguistic research. Automatic segmentation and alignment software is commercially available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of complex networks, attack tolerance is the network's robustness meaning the ability to maintain the overall connectivity and diameter of the network as nodes are removed. Several graph metrics have been proposed to predicate network robustness. Algebraic connectivity is a graph metric that shows the best graph robustness among them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, a vector typically arises as the outcome of a measurement or series of measurements, and is represented as a list (or tuple) of numbers such as ( v 1 , v 2 , v 3 ) . {\\displaystyle (v_{1},v_{2},v_{3}).} The numbers in the list depend on the choice of coordinate system. For instance, if the vector represents position with respect to an observer (position vector), then the coordinate system may be obtained from a system of rigid rods, or reference axes, along which the components v1, v2, and v3 are measured.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We illustrate using the simple case of a one-dimensional parameter, but an analogous derivation holds more generally. In the one-dimensional case, we have p ( x ) = g ( \u03b7 ) h ( x ) e \u03b7 T ( x ) . {\\displaystyle p(x)=g(\\eta )h(x)e^{\\eta T(x)}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Every variable Xi in the sequence is associated with a Bernoulli trial or experiment. They all have the same Bernoulli distribution. Much of what can be said about the Bernoulli process can also be generalized to more than two outcomes (such as the process for a six-sided die); this generalization is known as the Bernoulli scheme. The problem of determining the process, given only a limited sample of Bernoulli trials, may be called the problem of checking whether a coin is fair.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication and data storage, Manchester code (also known as phase encoding, or PE) is a line code in which the encoding of each data bit is either low then high, or high then low, for equal time. It is a self-clocking signal with no DC component. Consequently, electrical connections using a Manchester code are easily galvanically isolated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Others have attacked the problem from the database end, by defining an object-oriented data model for the database, and defining a database programming language that allows full programming capabilities as well as traditional query facilities. Object databases suffered because of a lack of standardization: although standards were defined by ODMG, they were never implemented well enough to ensure interoperability between products. Nevertheless, object databases have been used successfully in many applications: usually specialized applications such as engineering databases or molecular biology databases rather than mainstream commercial data processing. However, object database ideas were picked up by the relational vendors and influenced extensions made to these products and indeed to the SQL language. An alternative to translating between objects and relational databases is to use an object\u2013relational mapping (ORM) library.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other related phrasings include cumulative knowledge, collective knowledge or pooled knowledge. Distributed knowledge is the union of all the knowledge of individuals in a community of agents. Distributed knowledge differs from the concept of Wisdom of the crowd, in that the latter is concerned with opinions, not knowledge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice (a commutative semigroup of idempotents). Munn semigroups are named for the Scottish mathematician Walter Douglas Munn (1929\u20132008).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In petroleum and natural gas extraction, a Christmas tree, or \"tree\", is an assembly of valves, casing spools, and fittings used to regulate the flow of pipes in an oil well, gas well, water injection well, water disposal well, gas injection well, condensate well, and other types of well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A tone reproduction curve is applied to the electronic image prior to printing, so that the reflectance of the print closely approximates a proportionality to the luminance intent implied by the electronic image. It is easier to demonstrate the need for a TRC using halftoned printing methods such as inkjet, or xerographic technologies. However, the need also applies to continuous-tone methods such as photographic paper printing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x7613. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programming languages, const is a type qualifier (a keyword applied to a data type) that indicates that the data is read-only. While this can be used to declare constants, const in the C family of languages differs from similar constructs in other languages in being part of the type, and thus has complicated behavior when combined with pointers, references, composite data types, and type-checking. In other languages, the data is not in a single memory location, but copied at compile time on each use. Languages which use it include C, C++, D, JavaScript, Julia, and Rust.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In text databases, a document collection defined by a document by term D matrix (of size m\u00d7n, where m is the number of documents and n is the number of terms), the number of clusters can roughly be estimated by the formula m n t {\\displaystyle {\\tfrac {mn}{t}}} where t is the number of non-zero entries in D. Note that in D each row and each column must contain at least one non-zero element.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations: Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that \"addition and multiplication of real numbers are associative operations\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3). In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. As of 2018, the proof is widely accepted in the mathematics community, but it has not yet been published in a peer-reviewed journal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That a given psychological attribute is a continuous quantity is a logically coherent and empirically testable hypothesis. Appearing in the next issue of the same journal were important papers by Dana Scott (1964), who proposed a hierarchy of cancellation conditions for the indirect testing of the solvability and Archimedean axioms, and David Krantz (1964) who connected the Luce & Tukey work to that of H\u00f6lder (1901). Work soon focused on extending the theory of conjoint measurement to involve more than just two attributes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics a p-group G {\\displaystyle G} is called power closed if for every section H {\\displaystyle H} of G {\\displaystyle G} the product of p k {\\displaystyle p^{k}} powers is again a p k {\\displaystyle p^{k}} th power. Regular p-groups are an example of power closed groups. On the other hand, powerful p-groups, for which the product of p k {\\displaystyle p^{k}} powers is again a p k {\\displaystyle p^{k}} th power are not power closed, as this property does not hold for all sections of powerful p-groups. The power closed 2-groups of exponent at least eight are described in (Mann 2005, Th. 16).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. This process can be repeated, and for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan\u2013H\u00f6lder theorem. The complete classification of finite simple groups, completed in 2004, is a major milestone in the history of mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two nonsingular quadratic forms over F2 are isomorphic if and only if they have the same dimension and the same Arf invariant. This fact was essentially known to Leonard Dickson (1901), even for any finite field of characteristic 2, and Arf proved it for an arbitrary perfect field. The Arf invariant is particularly applied in geometric topology, where it is primarily used to define an invariant of (4k + 2)-dimensional manifolds (singly even-dimensional manifolds: surfaces (2-manifolds), 6-manifolds, 10-manifolds, etc.) with certain additional structure called a framing, and thus the Arf\u2013Kervaire invariant and the Arf invariant of a knot. The Arf invariant is analogous to the signature of a manifold, which is defined for 4k-dimensional manifolds (doubly even-dimensional); this 4-fold periodicity corresponds to the 4-fold periodicity of L-theory. The Arf invariant can also be defined more generally for certain 2k-dimensional manifolds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A tighter bound, was conjectured by Hirschman and Everett, proven in 1975 by W. Beckner and in the same year interpreted as a generalized quantum mechanical uncertainty principle by Bia\u0142ynicki-Birula and Mycielski. The equality holds in the case of Gaussian distributions. Note, however, that the above entropic uncertainty function is distinctly different from the quantum Von Neumann entropy represented in phase space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mid to late 2009 a tool named Detect and Eliminate Computer Acquired Forensics (DECAF) was announced by an uninvolved group of programmers. The tool would reportedly protect computers against COFEE and render the tool ineffective. It alleged that it would provide real-time monitoring of COFEE signatures on USB devices and in running applications and that when a COFEE signature is detected, DECAF would perform numerous user-defined processes. These included COFEE log clearing, ejecting USB devices, and contamination or spoofing of MAC addresses. On December 18, 2009, the DECAF creators announced that the tool was a hoax and part of \"a stunt to raise awareness for security and the need for better forensic tools\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern multitasking environment, an application process usually has in its address space (or spaces) chunks of memory of following types: Machine code, including: program's own code (historically known as code segment or text segment); shared libraries. Data, including: initialized data (data segment); uninitialized (but allocated) variables; run-time stack; heap; shared memory and memory mapped files.Some parts of address space may be not mapped at all. Some systems have a \"split\" memory architecture where machine code, constants, and data are in different locations, and may have different address sizes. For example, PIC18 microcontrollers have a 21-bit program counter to address machine code and constants in Flash memory, and 12-bit address registers to address data in SRAM.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of two thieves  and t colours, a fair split would require at most t cuts. If, however, only t \u2212 1 cuts are available, Hungarian mathematician G\u00e1bor Simonyi shows that the two thieves can achieve an almost fair division in the following sense. If the necklace is arranged so that no t-split is possible, then for any two subsets D1 and D2 of { 1, 2, ..., t }, not both empty, such that D 1 \u2229 D 2 = \u2205 {\\displaystyle D_{1}\\cap D_{2}=\\varnothing } , a (t \u2212 1)-split exists such that: If colour i \u2208 D 1 {\\displaystyle i\\in D_{1}} , then partition 1 has more beads of colour i than partition 2; If colour i \u2208 D 2 {\\displaystyle i\\in D_{2}} , then partition 2 has more beads of colour i than partition 1; If colour i is in neither partition, both partitions have equally many beads of colour i.This means that if the thieves have preferences in the form of two \"preference\" sets D1 and D2, not both empty, there exists a (t \u2212 1)-split so that thief 1 gets more beads of types in his preference set D1 than thief 2; thief 2 gets more beads of types in her preference set D2 than thief 1; and the rest are equal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predicate logic, what is described in layman's terms as \"something\" can more specifically be regarded as existential quantification, that is, the predication of a property or relation to at least one member of the domain. It is a type of quantifier, a logical constant which is interpreted as \"there exists,\" \"there is at least one,\" or \"for some.\" It expresses that a propositional function can be satisfied by at least one member of a domain of discourse. In other terms, it is the predication of a property or relation to at least one member of the domain. It asserts that a predicate within the scope of an existential quantifier is true of at least one value of a predicate variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 358, 1358, 3458, and 13458 are the patterns related to Braille pattern dots-246, since the two additional dots of kantenji patterns 0246, 2467, and 02467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These scenarios will cause issues in the program running by providing false data. To prevent this, one method is that the entire data-structure can be kept under critical section so that only one operation is handled at a time. Another method is locking the node in use under critical section, so that other operations do not use the same node. Using critical section, thus, ensures that the code provides expected outputs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space E n {\\displaystyle \\mathbb {E} ^{n}} ; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations). The group depends only on the dimension n of the space, and is commonly denoted E(n) or ISO(n). The Euclidean group E(n) comprises all translations, rotations, and reflections of E n {\\displaystyle \\mathbb {E} ^{n}} ; and arbitrary finite combinations of them. The Euclidean group can be seen as the symmetry group of the space itself, and contains the group of symmetries of any figure (subset) of that space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alessandro Volta began investigating pneumatic chemistry in 1776 and argued that there were different types of inflammable air based on experiments on marsh gases. Pneumatic chemists credited with discovering chemical elements include Joseph Priestley, Henry Cavendish, Joseph Black, Daniel Rutherford, and Carl Scheele. Other individuals who investigated gases during this period include Robert Boyle, Stephen Hales, William Brownrigg, Antoine Lavoisier, Joseph Louis Gay-Lussac, and John Dalton.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The language they defined was known as CycL. After CycL, a number of ontology languages have been developed. Most are declarative languages, and are either frame languages, or are based on first-order logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following identities, \u03b4 {\\displaystyle \\delta } is a derivation of a differential ring R . {\\displaystyle R. }: 76 If r \u2208 R {\\displaystyle r\\in R} and c {\\displaystyle c} is a constant in R {\\displaystyle R} (that is, \u03b4 c = 0 {\\displaystyle \\delta c=0} ), then If r \u2208 R {\\displaystyle r\\in R} and u {\\displaystyle u} is a unit in R , {\\displaystyle R,} then If n {\\displaystyle n} is a nonnegative integer and r \u2208 R {\\displaystyle r\\in R} then If u 1 , \u2026 , u n {\\displaystyle u_{1},\\ldots ,u_{n}} are units in R , {\\displaystyle R,} and n 1 , \u2026 , n n {\\displaystyle n_{1},\\ldots ,n_{n}} are integers, one has the logarithmic derivative identity:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Monoidal categories can be seen as a generalization of these and other examples. Every (small) monoidal category may also be viewed as a \"categorification\" of an underlying monoid, namely the monoid whose elements are the isomorphism classes of the category's objects and whose binary operation is given by the category's tensor product. A rather different application, of which monoidal categories can be considered an abstraction, is that of a system of data types closed under a type constructor that takes two types and builds an aggregate type; the types are the objects and \u2297 {\\displaystyle \\otimes } is the aggregate constructor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A probability function, P {\\displaystyle P} , which assigns each event in the event space a probability, which is a number between 0 and 1.In order to provide a sensible model of probability, these elements must satisfy a number of axioms, detailed in this article. In the example of the throw of a standard die, we would take the sample space to be { 1 , 2 , 3 , 4 , 5 , 6 } {\\displaystyle \\{1,2,3,4,5,6\\}} . For the event space, we could simply use the set of all subsets of the sample space, which would then contain simple events such as { 5 } {\\displaystyle \\{5\\}} (\"the die lands on 5\"), as well as complex events such as { 2 , 4 , 6 } {\\displaystyle \\{2,4,6\\}} (\"the die lands on an even number\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Java virtual machine, internal type signatures are used to identify methods and classes at the level of the virtual machine code. Example: The method String String.substring(int, int) is represented in bytecode as Ljava/lang/String.substring(II)Ljava/lang/String;. The signature of the main method looks like this: And in the disassembled bytecode, it takes the form of Lsome/package/Main/main:([Ljava/lang/String;)V The method signature for the main() method contains three modifiers: public indicates that the main() method can be called by any object. static indicates that the main() method is a class method. void indicates that the main() method has no return value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Algorithms are needed for efficient computation of the statistics (e.g., mean and variance) of the modal parameters from the posterior distribution. Unlike non-Bayesian methods, the algorithms are often implicit and iterative. E.g., optimization algorithms may be involved in the determination of most probable value, which may not converge for poor quality data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example graph shown, the algorithm is initially called with R = \u00d8, P = {1,2,3,4,5,6}, and X = \u00d8. The pivot u should be chosen as one of the degree-three vertices, to minimize the number of recursive calls; for instance, suppose that u is chosen to be vertex 2. Then there are three remaining vertices in P \\ N(u): vertices 2, 4, and 6. The iteration of the inner loop of the algorithm for v = 2 makes a recursive call to the algorithm with R = {2}, P = {1,3,5}, and X = \u00d8. Within this recursive call, one of 1 or 5 will be chosen as a pivot, and there will be two second-level recursive calls, one for vertex 3 and the other for whichever vertex was not chosen as pivot. These two calls will eventually report the two cliques {1,2,5} and {2,3}.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mobile-telephone technology, the UniPro protocol stack follows the architecture of the classical OSI Reference Model. In UniPro, the OSI Physical Layer is split into two sublayers: Layer 1 (the actual physical layer) and Layer 1.5 (the PHY Adapter layer) which abstracts from differences between alternative Layer 1 technologies. The actual physical layer is a separate specification as the various PHY options are reused in other MIPI Alliance specifications. The UniPro specification itself covers Layers 1.5, 2, 3, 4 and the DME (Device Management Entity).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although much attention is focused on WCDMA, the concept is applicable to all standards, including GSM, CDMA2000, TD-SCDMA, WiMAX and LTE solutions. The use of femtocells allows network coverage in places where the signal to the main network cells might be too weak. Furthermore, femtocells lower contention on the main network cells, by forming a connection from the end user, through an internet connection, to the operator's private network infrastructure elsewhere.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent. It is particularly useful in machine learning for minimizing the cost or loss function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the class of L-matrices are those matrices whose off-diagonal entries are less than or equal to zero and whose diagonal entries are positive; that is, an L-matrix L satisfies L = ( \u2113 i j ) ; \u2113 i i > 0 ; \u2113 i j \u2264 0 , i \u2260 j . {\\displaystyle L=(\\ell _{ij});\\quad \\ell _{ii}>0;\\quad \\ell _{ij}\\leq 0,\\quad i\\neq j.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the affine hull or affine span of a set S in Euclidean space Rn is the smallest affine set containing S, or equivalently, the intersection of all affine sets containing S. Here, an affine set may be defined as the translation of a vector subspace. The affine hull aff(S) of S is the set of all affine combinations of elements of S, that is, aff \u2061 ( S ) = { \u2211 i = 1 k \u03b1 i x i | k > 0 , x i \u2208 S , \u03b1 i \u2208 R , \u2211 i = 1 k \u03b1 i = 1 } . {\\displaystyle \\operatorname {aff} (S)=\\left\\{\\sum _{i=1}^{k}\\alpha _{i}x_{i}\\,{\\Bigg |}\\,k>0,\\,x_{i}\\in S,\\,\\alpha _{i}\\in \\mathbb {R} ,\\,\\sum _{i=1}^{k}\\alpha _{i}=1\\right\\}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs. Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most practical contexts, a programming language involves a computer; consequently, programming languages are usually defined and studied this way. Programming languages differ from natural languages in that natural languages are only used for interaction between people, while programming languages also allow humans to communicate instructions to machines. The domain of the language is also worth consideration. Markup languages like XML, HTML, or troff, which define structured data, are not usually considered programming languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recreational number theory, a primeval number is a natural number n for which the number of prime numbers which can be obtained by permuting some or all of its digits (in base 10) is larger than the number of primes obtainable in the same way for any smaller natural number. Primeval numbers were first described by Mike Keith. The first few primeval numbers are 1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, 1379, 10079, 10123, 10136, 10139, 10237, 10279, 10367, 10379, 12379, 13679, ... (sequence A072857 in the OEIS)The number of primes that can be obtained from the primeval numbers is 0, 1, 3, 4, 5, 7, 11, 14, 19, 21, 26, 29, 31, 33, 35, 41, 53, 55, 60, 64, 89, 96, 106, ... (sequence A076497 in the OEIS)The largest number of primes that can be obtained from a primeval number with n digits is 1, 4, 11, 31, 106, 402, 1953, 10542, 64905, 362451, 2970505, ... (sequence A076730 in the OEIS)The smallest n-digit number to achieve this number of primes is 2, 37, 137, 1379, 13679, 123479, 1234679, 12345679, 102345679", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In standard logic, propositions are considered to be either true or false. In contradistinction, subjective logic assumes that humans cannot determine with absolute certainty whether a proposition about the real world is absolutely true or false. In subjective logic the posteriori probability estimates of binary events can be represented by beta distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The design freedom of the time was very important because designers were very constrained by the cost of electronics, and only starting to explore how a computer could best be organized. Some of the basic features introduced during this period included index registers (on the Ferranti Mark 1), a return address saving instruction (UNIVAC I), immediate operands (IBM 704), and detecting invalid operations (IBM 650). By the end of the 1950s, commercial builders had developed factory-constructed, truck-deliverable computers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Limit theory helps in operational usage. For instance, in KBE derivation of a populated design (geometrical objects, etc., similar concerns apply in shape theory), equivalence assumptions allow convergence where potentially large, and perhaps even computationally indeterminate, solution sets are handled deftly. Yet, in a chain of computation, downstream events may very well find some types of results from earlier resolutions of ramification as problematic for their own algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the measure \u03c1 is reducible with \u03bc the associated reducer, then if f is square integrable for \u03bc, and if g is square integrable for \u03c1 and is orthogonal with P0 = 1 one has equivalence: f ( x ) = \u222b I g ( t ) \u2212 g ( x ) t \u2212 x \u03c1 ( t ) d t \u21d4 g ( x ) = ( x \u2212 c 1 ) f ( x ) \u2212 T \u03bc ( f ( x ) ) = \u03c6 ( x ) \u03bc ( x ) \u03c1 ( x ) f ( x ) \u2212 T \u03c1 ( \u03bc ( x ) \u03c1 ( x ) f ( x ) ) {\\displaystyle f(x)=\\int _{I}{\\frac {g(t)-g(x)}{t-x}}\\rho (t)dt\\Leftrightarrow g(x)=(x-c_{1})f(x)-T_{\\mu }(f(x))={\\frac {\\varphi (x)\\mu (x)}{\\rho (x)}}f(x)-T_{\\rho }\\left({\\frac {\\mu (x)}{\\rho (x)}}f(x)\\right)} c1 indicates the moment of order 1 of \u03c1 and T\u03c1 the operator g ( x ) \u21a6 \u222b I g ( t ) \u2212 g ( x ) t \u2212 x \u03c1 ( t ) d t . {\\displaystyle g(x)\\mapsto \\int _{I}{\\frac {g(t)-g(x)}{t-x}}\\rho (t)\\,dt.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure A = (A, \u2228, \u2227, 0, 1, \u00ac) such that: (A, \u2228, \u2227, 0, 1) is a bounded distributive lattice, and \u00ac is a De Morgan involution: \u00ac(x \u2227 y) = \u00acx \u2228 \u00acy and \u00ac\u00acx = x. (i.e. an involution that additionally satisfies De Morgan's laws)In a De Morgan algebra, the laws \u00acx \u2228 x = 1 (law of the excluded middle), and \u00acx \u2227 x = 0 (law of noncontradiction)do not always hold. In the presence of the De Morgan laws, either law implies the other, and an algebra which satisfies them becomes a Boolean algebra. Remark: It follows that \u00ac(x \u2228 y) = \u00acx \u2227 \u00acy, \u00ac1 = 0 and \u00ac0 = 1 (e.g. \u00ac1 = \u00ac1 \u2228 0 = \u00ac1 \u2228 \u00ac\u00ac0 = \u00ac(1 \u2227 \u00ac0) = \u00ac\u00ac0 = 0).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This says that the least significant n bits of k plus the remaining bits of k are equivalent to k modulo 2n\u22121. This equivalence can be used repeatedly until at most n bits remain. In this way, the remainder after dividing k by the Mersenne number 2n\u22121 is computed without using division.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In radio or wireless telephony, Private Line is a term trademarked by Motorola to describe an implementation of a Continuous Tone-Coded Squelch System (CTCSS), a method of using low-frequency subaudible tones to share a single radio channel among multiple users. Each user group would use a different low frequency tone. Motorola's trade name, especially the abbreviation PL, has become a genericized trademark for the method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics the discrete least squares meshless (DLSM) method is a meshless method based on the least squares concept. The method is based on the minimization of a least squares functional, defined as the weighted summation of the squared residual of the governing differential equation and its boundary conditions at nodal points used to discretize the domain and its boundaries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following figure, the minimization problem on the left side of the equation is illustrated. One seeks to vary x such that the vertical distance between the convex and concave curves at x is as small as possible. The position of the vertical line in the figure is the (approximate) optimum. The next figure illustrates the maximization problem on the right hand side of the above equation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By varying the weighting parameter b, one can trace out the entire contract curve: If b = 1 the problem is the same as the previous problem, and it identifies an efficient point at one edge of the lens formed by the indifference curves of the initial endowment; if b = 0 all the weight is on person 2's utility instead of person 1's, and so the optimization identifies the efficient point on the other edge of the lens. As b varies smoothly between these two extremes, all the in-between points on the contract curve are traced out. Note that the above optimizations are not ones that the two people would actually engage in, either explicitly or implicitly. Instead, these optimizations are simply a way for the economist to identify points on the contract curve.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1980s, 1G was introduced as voice-only communication via \"brick phones\". Later in 1991, the development of 2G introduced Short Message Service (SMS) and Multimedia Messaging Service (MMS) capabilities, allowing picture messages to be sent and received between phones. In 1998, 3G was introduced to provide faster data-transmission speeds to support video calling and internet access. 4G was released in 2008 to support more demanding services such as gaming services, HD mobile TV, video conferencing, and 3D TV. 5G technology was initially released in 2019, but is still only available in certain areas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Wilson prime is a prime number p {\\displaystyle p} such that p 2 {\\displaystyle p^{2}} divides ( p \u2212 1 ) ! + 1 {\\displaystyle (p-1)!+1} , where \" ! {\\displaystyle !} \" denotes the factorial function; compare this with Wilson's theorem, which states that every prime p {\\displaystyle p} divides ( p \u2212 1 ) !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then either the inner or outer circle participants \u2013 or the front or back line of desks \u2013 moves to the next space. Following a brief settling-in period, the host starts the second round of meetings. In Round Robin speed networking, a participant would meet an average of 10 contacts during an hour-long event.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Inverses are commonly used in groups\u2014where every element is invertible, and rings\u2014where invertible elements are also called units. They are also commonly used for operations that are not defined for all possible operands, such as inverse matrices and inverse functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Planes are further subdivided into Unicode blocks, which, unlike planes, do not have a fixed size. The 327 blocks defined in Unicode 15.0 cover 26% of the possible code point space, and range in size from a minimum of 16 code points (sixteen blocks) to a maximum of 65,536 code points (Supplementary Private Use Area-A and -B, which constitute the entirety of planes 15 and 16). For future usage, ranges of characters have been tentatively mapped out for most known current and ancient writing systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With an attentive and planned assessment, a homeowner can spot many problems that cause energy losses and make decisions about possible energy efficiency upgrades. During a home energy audit it is important to have a checklist of areas that were inspected as well as problems identified. Once the audit is completed, a plan for suggested actions needs to be developed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1990, he asked \"Is There a Double Smoothly Undulating Integer? \", and he computed \"All Known Replicating Fibonacci Digits Less than One Billion\". With his colleague John R. Hendricks, he was the first to compute the smallest perfect (nasik) magic tesseract. The \"Pickover sequence\" dealing with e and pi was named after him, as was the \"Cliff random number generator\" and the Pickover attractor, sometimes also referred to as the Clifford Attractor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and in particular in information theory, total correlation (Watanabe 1960) is one of several generalizations of the mutual information. It is also known as the multivariate constraint (Garner 1962) or multiinformation (Studen\u00fd & Vejnarov\u00e1 1999). It quantifies the redundancy or dependency among a set of n random variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most proofs of soundness are trivial. For example, in an axiomatic system, proof of soundness amounts to verifying the validity of the axioms and that the rules of inference preserve validity (or the weaker property, truth). If the system allows Hilbert-style deduction, it requires only verifying the validity of the axioms and one rule of inference, namely modus ponens. (and sometimes substitution) Soundness properties come in two main varieties: weak and strong soundness, of which the former is a restricted form of the latter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical hypothesis testing, a result has statistical significance when a result at least as \"extreme\" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by \u03b1 {\\displaystyle \\alpha } , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value of a result, p {\\displaystyle p} , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when p \u2264 \u03b1 {\\displaystyle p\\leq \\alpha } . The significance level for a study is chosen before data collection, and is typically set to 5% or much lower\u2014depending on the field of study.In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here \"simple\" indicates that the underlying type theory is the theory of simple types, also called the simple theory of types. Leon Chwistek and Frank P. Ramsey proposed this as a simplification of the complicated and clumsy ramified theory of types specified in the Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Simple types is sometimes also meant to exclude polymorphic and dependent types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As many of these computers will give reduced privileges to ordinary users, it is possible that much of this has been done by network administrators. To some extent, this may be offset by better connectivity to home machines and increasing performance of home computers, especially those with GPUs, which have also benefited other volunteer computing projects such as Folding@Home. The spread of mobile computing devices provides another large resource for volunteer computing. For example, in 2012, Piotr Luszczek (a former doctoral student of Jack Dongarra) presented results showing that an iPad 2 matched the historical performance of a Cray-2 (the fastest computer in the world in 1985) on an embedded LINPACK benchmark.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A fuzzbox (or \"fuzz box\u201d) alters an audio signal until it is nearly a square wave and adds complex overtones by way of a frequency multiplier.A fuzz bass sound can be created by turning up the volume of a tube amp or transistor amp to the point that preamplifier tube (or transistor preamp) clipping\" occurs. In practice, when a bass amp is \"cranked\" to its maximum volume, the fuzz tone will also include some power amplifier clipping. While some musicians seek out the additional \"grit\" provided by power amp clipping, audio engineers and bass technicians recommend avoiding power amp clipping, as it can blow speakers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In contrast, the basis signals used to construct the signal subspace are identified empirically, and may for example be chirps, or particular characteristic shapes of transients after particular triggering events, rather than pure sinusoids. The Wiener filter grades smoothly between linear components that are dominated by signal, and linear components that are dominated by noise. The noise components are filtered out, but not quite completely; the signal components are retained, but not quite completely; and there is a transition zone which is partly accepted. In contrast, the signal subspace approach represents a sharp cut-off: an orthogonal component either lies within the signal subspace, in which case it is 100% accepted, or orthogonal to it, in which case it is 100% rejected. This reduction in dimensionality, abstracting the signal into a much shorter vector, can be a particularly desired feature of the method.In the simplest case signal subspace methods assume white noise, but extensions of the approach to colored noise removal and the evaluation of the subspace-based speech enhancement for robust speech recognition have also been reported.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These handicap ratings where a player receives points can be denoted with an \"R\" in front, where the \"R\" indicates the player is receiving points. It is also possible to have a handicap system where the player owes point due to being higher-skilled, in which case the same two-number system is also used. These owed handicaps are denoted with an \"O\" in front that is short for \"owed\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It has been proved useful in recognizing targets (i.e. battle tanks) in infrared images of real scenes after training with synthetic images, since real images of those targets are scarce. Due to the limitation of the training set, how realistic the synthetic images are matters a lot when it comes to recognize the real scenes test set. The overall CNN networks structure contains 7 convolution layers, 3 max pooling layers and a Softmax layer as output.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The geometric mean of two numbers, a {\\displaystyle a} and b {\\displaystyle b} , is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a {\\displaystyle a} and b {\\displaystyle b} . Similarly, the geometric mean of three numbers, a {\\displaystyle a} , b {\\displaystyle b} , and c {\\displaystyle c} , is the length of one edge of a cube whose volume is the same as that of a cuboid with sides whose lengths are equal to the three given numbers. The geometric mean is one of the three classical Pythagorean means, together with the arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between (see Inequality of arithmetic and geometric means.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, graphs are useful in geometry and certain parts of topology such as knot theory. Algebraic graph theory has close links with group theory. Algebraic graph theory has been applied to many areas including dynamic systems and complexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This could be simply presented in small cards or stories \u2013 the developers estimate the time needed for the implementation of each card. Thus the work organization changes into self-pulling system \u2013 each morning during a stand-up meeting, each member of the team reviews what has been done yesterday, what is to be done today and tomorrow, and prompts for any inputs needed from colleagues or the customer. This requires transparency of the process, which is also beneficial for team communication. The myth underlying this principle is haste makes waste. However, lean implementation has shown that it is a good practice to deliver fast in order to see and analyze the output as early as possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is usually referred to as simply a semigroup. It is perhaps most easily understood as the syntactic monoid describing the Dyck language of balanced pairs of parentheses. Thus, it finds common applications in combinatorics, such as describing binary trees and associative algebras.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "During the second quarter of 2004, it launched new low-power Geode NX processors based on the K7 Thoroughbred architecture with speeds of fanless processors 667 MHz and 1 GHz, and 1.4 GHz processor with fan, of TDP 25 W. This technology is used in a variety of embedded systems (Casino slot machines and customer kiosks for instance), several UMPC designs in Asia markets, as well as the OLPC XO-1 computer, an inexpensive laptop computer intended to be distributed to children in developing countries around the world. The Geode LX processor was announced in 2005 and is said will continue to be available through 2015.AMD has also introduced 64-bit processors into its embedded product line starting with the AMD Opteron processor. Leveraging the high throughput enabled through HyperTransport and the Direct Connect Architecture these server-class processors have been targeted at high-end telecom and storage applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph G is a set of cycles which are subgraphs of G and contain all vertices of G. If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. This is sometimes known as exact vertex cycle cover. In this case the set of the cycles constitutes a spanning subgraph of G. A disjoint cycle cover of an undirected graph (if it exists) can be found in polynomial time by transforming the problem into a problem of finding a perfect matching in a larger graph.If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In China, the Telecommunications Regulations of the People's Republic of China (promulgated on 25 September 2000), stipulated the Ministry of Industry and Information Technology (MIIT) as the government department regulating all telecommunications related activities, including electronic commerce. On the same day, the Administrative Measures on Internet Information Services were released, the first administrative regulations to address profit-generating activities conducted through the Internet, and lay the foundation for future regulations governing e-commerce in China. On 28 August 2004, the eleventh session of the tenth NPC Standing Committee adopted an Electronic Signature Law, which regulates data message, electronic signature authentication and legal liability issues. It is considered the first law in China's e-commerce legislation. It was a milestone in the course of improving China's electronic commerce legislation, and also marks the entering of China's rapid development stage for electronic commerce legislation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, in contrast to many Monte Carlo primality tests (randomized algorithms that can return a false positive), the primality testing algorithm based on Proth's theorem is a Las Vegas algorithm, always returning the correct answer but with a running time that varies randomly. Note that if a is chosen to be a quadratic nonresidue as described above, the runtime is constant, safe for the time spent on finding such a quadratic nonresidue. Finding such a value is very fast compared to the actual test.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In certain physics applications such as in the computation of bands in a periodic volume, it is often a case that the elements of a matrix will be very complicated functions of frequency and wavenumber, and the matrix will be non-singular (I.e., it has the inverse matrix.) for most combinations of frequency and wavenumber, but will also be singular (I.e., it does not have the inverse matrix.) for certain specific combinations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the late 1990s and early 2000s, the market shifted for buyers, but since 2003 and 2004, it has been a strong seller's market, with net-back as the best estimation for prices.. Research from Global Energy Monitor in 2019 warned that up to US$1.3 trillion in new LNG export and import infrastructure currently under development is at significant risk of becoming stranded, as global gas risks becoming oversupplied, particularly if the United States and Canada play a larger role.The current surge in unconventional oil and gas in the U.S. has resulted in lower gas prices in the U.S. This has led to discussions in Asia' oil linked gas markets to import gas based on Henry Hub index.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The concept of notational associativity described here is related to, but different from, the mathematical associativity. An operation that is mathematically associative, by definition requires no notational associativity. (For example, addition has the associative property, therefore it does not have to be either left associative or right associative.) An operation that is not mathematically associative, however, must be notationally left-, right-, or non-associative. (For example, subtraction does not have the associative property, therefore it must have notational associativity.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a rotation map is a function that represents an undirected edge-labeled graph, where each vertex enumerates its outgoing neighbors. Rotation maps were first introduced by Reingold, Vadhan and Wigderson (\u201cEntropy waves, the zig-zag graph product, and new constant-degree expanders\u201d, 2002) in order to conveniently define the zig-zag product and prove its properties. Given a vertex v {\\displaystyle v} and an edge label i {\\displaystyle i} , the rotation map returns the i {\\displaystyle i} 'th neighbor of v {\\displaystyle v} and the edge label that would lead back to v {\\displaystyle v} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2678, 12678, 24678, and 124678 are the patterns related to Braille pattern dots-1356, since the two additional dots of kantenji patterns 01356, 13567, and 013567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The names of architectural styles (as well as their adaptations) varied between countries. Many homes combined the elements of several different styles and are not easily distinguishable as one particular style or another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Those that remain are often used only in niche markets or as parts of other systems; of the designs from these traditional vendors, only SPARC and POWER have any significant remaining market.The ARM architecture is illustrative of the adaptations made by RISC vendors to respond to changing competitive circumstances, being first introduced to deliver higher performance in desktop computers such as the Acorn Archimedes, but also being introduced in embedded applications such as laser printer raster image processing. ARM, in partnership with Apple, developed a low-power design and then specialized in that market, which at the time was a niche. With the rise in mobile computing, especially after the introduction of the iPhone, ARM became the most widely used high-end CPU design in the market.Competition between RISC and conventional CISC approaches was also the subject of theoretical analysis in the early 1980s, leading, for example, to the iron law of processor performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So we take a sample of the k {\\displaystyle k} , get a sampling weight W(k) for all sampled k {\\displaystyle k} , and then sum up W ( k ) \u22c5 Y ( k ) {\\displaystyle W(k)\\cdot Y(k)} for all sampled k {\\displaystyle k} . One property usually common to the weights W ( k ) {\\displaystyle W(k)} described here is that if we sum them over all sampled k {\\displaystyle k} , then this sum is an estimate of the total number of units k {\\displaystyle k} in the population (for example, the total employment, or the total number of items). Because we have a sample, this estimate of the total number of units in the population will differ from the true population total.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the client-to-gateway implementation, one or more servers are protected behind an Accepting SDP Host such that the Accepting SDP Host acts as a gateway between the clients and the protected servers. This implementation can be used inside an enterprise network to mitigate common lateral movement attacks such as server scanning, OS and application vulnerability exploits, password cracking, man-in-the-middle, Pass-the-Hash (PtH), and others. Alternatively, it can be implemented on the Internet to isolate protected servers from unauthorized users and mitigate attacks such as denial of service, OS and application vulnerability exploits, password cracking, man-in-the-middle, and others.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the field of group theory, a group is said to be strictly simple if it has no proper nontrivial ascendant subgroups. That is, G {\\displaystyle G} is a strictly simple group if the only ascendant subgroups of G {\\displaystyle G} are { e } {\\displaystyle \\{e\\}} (the trivial subgroup), and G {\\displaystyle G} itself (the whole group). In the finite case, a group is strictly simple if and only if it is simple. However, in the infinite case, strictly simple is a stronger property than simple.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If we assume that a function f: R n \u2192 R {\\displaystyle f\\colon {\\textbf {R}}^{n}\\to {\\textbf {R}}} is differentiable (or even analytic) in each variable separately, it is not true that f {\\displaystyle f} will necessarily be continuous. A counterexample in two dimensions is given by f ( x , y ) = x y x 2 + y 2 . {\\displaystyle f(x,y)={\\frac {xy}{x^{2}+y^{2}}}.} If in addition we define f ( 0 , 0 ) = 0 {\\displaystyle f(0,0)=0} , this function has well-defined partial derivatives in x {\\displaystyle x} and y {\\displaystyle y} at the origin, but it is not continuous at origin. (Indeed, the limits along the lines x = y {\\displaystyle x=y} and x = \u2212 y {\\displaystyle x=-y} are not equal, so there is no way to extend the definition of f {\\displaystyle f} to include the origin and have the function be continuous there.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order candidate for P after the current one c. valid (P, c): check whether candidate c is a solution for P. output (P, c): use the solution c of P as appropriate to the application.The next procedure must also tell when there are no more candidates for the instance P, after the current one c. A convenient way to do that is to return a \"null candidate\", some conventional data value \u039b that is distinct from any real candidate. Likewise the first procedure should return \u039b if there are no candidates at all for the instance P. The brute-force method is then expressed by the algorithm c \u2190 first(P) while c \u2260 \u039b do if valid(P,c) then output(P, c) c \u2190 next(P, c) end while For example, when looking for the divisors of an integer n, the instance data P is the number n. The call first(n) should return the integer 1 if n \u2265 1, or \u039b otherwise; the call next(n,c) should return c + 1 if c < n, and \u039b otherwise; and valid(n,c) should return true if and only if c is a divisor of n. (In fact, if we choose \u039b to be n + 1, the tests n \u2265 1 and c < n are unnecessary. )The brute-force search algorithm above will call output for every candidate that is a solution to the given instance P. The algorithm is easily modified to stop after finding the first solution, or a specified number of solutions; or after testing a specified number of candidates, or after spending a given amount of CPU time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result, the variance for the estimator in GAN is usually much larger than that in Wasserstein GAN. See also Figure 3 of.The problem with D J S {\\displaystyle D_{JS}} is much more severe in actual machine learning situations. Consider training a GAN to generate ImageNet, a collection of photos of size 256-by-256.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real mode or V86 mode, the size of a segment can range from 1 byte up to 65,536 bytes (using 16-bit offsets). The 16-bit segment selector in the segment register is interpreted as the most significant 16 bits of a linear 20-bit address, called a segment address, of which the remaining four least significant bits are all zeros. The segment address is always added to a 16-bit offset in the instruction to yield a linear address, which is the same as physical address in this mode. For instance, the segmented address 06EFh:1234h (here the suffix \"h\" means hexadecimal) has a segment selector of 06EFh, representing a segment address of 06EF0h, to which the offset is added, yielding the linear address 06EF0h + 1234h = 08124h.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spite of its known drawbacks, one of the most widely used methods for community detection is modularity maximization. Modularity is a benefit function that measures the quality of a particular division of a network into communities. The modularity maximization method detects communities by searching over possible divisions of a network for one or more that have particularly high modularity. Since exhaustive search over all possible divisions is usually intractable, practical algorithms are based on approximate optimization methods such as greedy algorithms, simulated annealing, or spectral optimization, with different approaches offering different balances between speed and accuracy. A popular modularity maximization approach is the Louvain method, which iteratively optimizes local communities until global modularity can no longer be improved given perturbations to the current community state. An algorithm that utilizes the RenEEL scheme, which is an example of the Extremal Ensemble Learning (EEL) paradigm, is currently the best modularity maximizing algorithm.The usefulness of modularity optimization is questionable, as it has been shown that modularity optimization often fails to detect clusters smaller than some scale, depending on the size of the network (resolution limit); on the other hand the landscape of modularity values is characterized by a huge degeneracy of partitions with high modularity, close to the absolute maximum, which may be very different from each other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If N \u2212 1 and M \u2212 1 are coprime, on the other hand, the only two fixed points are the upper-left and lower-right corners of the matrix. The number of cycles of any length k>1 is given by (Cate & Twigg, 1977): 1 k \u2211 d | k \u03bc ( k / d ) gcd ( N d \u2212 1 , M N \u2212 1 ) , {\\displaystyle {\\frac {1}{k}}\\sum _{d|k}\\mu (k/d)\\gcd(N^{d}-1,MN-1),} where \u03bc is the M\u00f6bius function and the sum is over the divisors d of k. Furthermore, the cycle containing a=1 (i.e. the second element of the first row of the matrix) is always a cycle of maximum length L, and the lengths k of all other cycles must be divisors of L (Cate & Twigg, 1977). For a given cycle C, every element x \u2208 C {\\displaystyle x\\in C} has the same greatest common divisor d = gcd ( x , M N \u2212 1 ) {\\displaystyle d=\\gcd(x,MN-1)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network routing, VCG mechanisms are a family of payment schemes based on the added value concept. The basic idea of a VCG mechanism in network routing is to pay the owner of each link or node (depending on the network model) that is part of the solution, its declared cost plus its added value. In many routing problems, this mechanism is not only strategyproof, but also the minimum among all strategyproof mechanisms. In the case of network flows, unicast or multicast, a minimum cost flow (MCF) in graph G is calculated based on the declared costs dk of each of the links and payment is calculated as follows: Each link (or node) e k {\\displaystyle \\scriptstyle e_{k}} in the MCF is paid p k = d k + M C F ( G \u2212 e k ) \u2212 M C F ( G ) {\\displaystyle p_{k}=d_{k}+MCF(G-e_{k})-MCF(G)} ,where MCF(G) indicates the cost of the minimum cost flow in graph G and G \u2212 ek indicates graph G without the link ek.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, Linus's law is the assertion that \"given enough eyeballs, all bugs are shallow\". The law was formulated by Eric S. Raymond in his essay and book The Cathedral and the Bazaar (1999), and was named in honor of Linus Torvalds.A more formal statement is: \"Given a large enough beta-tester and co-developer base, almost every problem will be characterized quickly and the fix obvious to someone.\" Presenting the code to multiple developers with the purpose of reaching consensus about its acceptance is a simple form of software reviewing. Researchers and practitioners have repeatedly shown the effectiveness of reviewing processes in finding bugs and security issues.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Cantor set is an example of an uncountable set of Lebesgue measure 0 which is not of strong measure zero.Borel's conjecture states that every strong measure zero set is countable. It is now known that this statement is independent of ZFC (the Zermelo\u2013Fraenkel axioms of set theory, which is the standard axiom system assumed in mathematics). This means that Borel's conjecture can neither be proven nor disproven in ZFC (assuming ZFC is consistent).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern computer systems, files are typically accessed using names (filenames). In some operating systems, the name is associated with the file itself. In others, the file is anonymous, and is pointed to by links that have names. In the latter case, a user can identify the name of the link with the file itself, but this is a false analogue, especially where there exists more than one link to the same file.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the bijective base-26 system one may use the Latin alphabet letters \"A\" to \"Z\" to represent the 26 digit values one to twenty-six. (A=1, B=2, C=3, ..., Z=26) With this choice of notation, the number sequence (starting from 1) begins A, B, C, ..., X, Y, Z, AA, AB, AC, ..., AX, AY, AZ, BA, BB, BC, ... Each digit position represents a power of twenty-six, so for example, the numeral ABC represents the value 1 \u00d7 262 + 2 \u00d7 261 + 3 \u00d7 260 = 731 in base 10. Many spreadsheets including Microsoft Excel use this system to assign labels to the columns of a spreadsheet, starting A, B, C, ..., Z, AA, AB, ..., AZ, BA, ..., ZZ, AAA, etc. For instance, in Excel 2013, there can be up to 16384 columns (214 in binary code), labeled from A to XFD. A variant of this system is used to name variable stars. It can be applied to any problem where a systematic naming using letters is desired, while using the shortest possible strings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In qualitative research, there are many ways of analyzing data gathered in the field. One of the two most common methods of data analysis are thematic analysis and narrative analysis. As mentioned before, the type of analysis a researcher decides to use depends on the research question asked, the researcher's field, and the researcher's personal method of choice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They include standard JTAG (IEEE 1149.1), cJTAG (IEEE 1149.7) and 4-bit parallel trace interfaces (mainly used for system traces), supplemented by the ARM-specific Serial Wire Debug (SWD) standard. MIPI10/20/34 debug connectors became the standard for ARM-based embedded designs. Many embedded designs in the mobile space use high-speed parallel trace ports (up to 600 megabits per second per pin).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2578, 12578, 24578, and 124578 are the patterns related to Braille pattern dots-1346, since the two additional dots of kantenji patterns 01346, 13467, and 013467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Various broadcast relay stations can help to extend a station's area by retransmitting them on the same or another channel. What is usually called a repeater in amateur radio is called a broadcast translator (different channel) or booster (same channel) in American broadcasting, or the much broader category or rebroadcasters in Canadian broadcasting (which includes more than just the low-power broadcasting used in the U.S.) Boosters are used only within the broadcast range of the parent station, and serve the same function locally as regional and national single-frequency networks do in Europe. Distributed transmission has also undergone tests in the U.S., but to preserve stations' market share in their home media markets, these will be limited to the broadcast area of a single large station. Satellite radio, which is designed for use without a dish, also uses ground repeaters in large cities due to the many obstructions their high-rise buildings cause to the many current and potential customers that are concentrated there.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, an interacting particle system (IPS) is a stochastic process ( X ( t ) ) t \u2208 R + {\\displaystyle (X(t))_{t\\in \\mathbb {R} ^{+}}} on some configuration space \u03a9 = S G {\\displaystyle \\Omega =S^{G}} given by a site space, a countably-infinite-order graph G {\\displaystyle G} and a local state space, a compact metric space S {\\displaystyle S} . More precisely IPS are continuous-time Markov jump processes describing the collective behavior of stochastically interacting components. IPS are the continuous-time analogue of stochastic cellular automata. Among the main examples are the voter model, the contact process, the asymmetric simple exclusion process (ASEP), the Glauber dynamics and in particular the stochastic Ising model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, attempts have been made to explain stretched exponential behaviour as a linear superposition of simple exponential decays. This requires a nontrivial distribution of relaxation times, \u03c1(u), which is implicitly defined by Alternatively, a distribution is used. \u03c1 can be computed from the series expansion: For rational values of \u03b2, \u03c1(u) can be calculated in terms of elementary functions. But the expression is in general too complex to be useful except for the case \u03b2 = 1/2 where Figure 2 shows the same results plotted in both a linear and a log representation. The curves converge to a Dirac delta function peaked at u = 1 as \u03b2 approaches 1, corresponding to the simple exponential function. The moments of the original function can be expressed as The first logarithmic moment of the distribution of simple-exponential relaxation times is where Eu is the Euler constant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The graph density of simple graphs is defined to be the ratio of the number of edges |E| with respect to the maximum possible edges. For undirected simple graphs, the graph density is: D = | E | ( | V | 2 ) = 2 | E | | V | ( | V | \u2212 1 ) {\\displaystyle D={\\frac {|E|}{\\binom {|V|}{2}}}={\\frac {2|E|}{|V|(|V|-1)}}} For directed, simple graphs, the maximum possible edges is twice that of undirected graphs (as there are two directions to an edge) so the density is: D = | E | 2 ( | V | 2 ) = | E | | V | ( | V | \u2212 1 ) {\\displaystyle D={\\frac {|E|}{2{\\binom {|V|}{2}}}}={\\frac {|E|}{|V|(|V|-1)}}} where E is the number of edges and V is the number of vertices in the graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Selberg sieve is a technique for estimating the size of \"sifted sets\" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Atle Selberg in the 1940s.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Non-interpolated string literals are sometimes referred to as \"raw strings\", but this is distinct from \"raw string\" in the sense of escaping. For example, in Python, a string prefixed with r or R has no escaping or interpolation, a normal string (no prefix) has escaping but no interpolation, and a string prefixed with f or F has escaping and interpolation. For example, the following Perl code: produces the output: Nancy said Hello World to the crowd of people.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, a disclaimer must be conspicuous in the contract, such as in a different kind of print or font that makes it stand out. On the other hand, express warranty, or any affirmation of fact or promise to the buyer or description of the good, oral or written, can be negated or limited only if such disclaimers are reasonable. UCC \u00a7 2-316(1) Some jurisdictions, however, limit the ability of sellers or manufacturers to disclaim the implied warranty of merchantability or fitness, such as Massachusetts. (Massachusetts General Laws, Chapter 106: Section 2-316A).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Meiser (1993) designed a fast algorithm to determine the face of an arrangement of hyperplanes containing an input point. Another question about an arrangement in real space is to decide how many regions are simplices (the n-dimensional generalization of triangles and tetrahedra).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first problem to address is to determine whether a given prime is Elkies or Atkin. In order to do so, we make use of modular polynomials, which come from the study of modular forms and an interpretation of elliptic curves over the complex numbers as lattices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "]_{f}} which are composed by parallel computations. The ordinary denotation of \u03b1 {\\displaystyle \\alpha } is simply whatever denotation it would have in a non-alternative-based system. The focus denotation of a constituent is typically the set of all ordinary denotations one could get by substituting a focused constituent for another expression of the same type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This means that when something changes, previously unexchanged information needs to be exchanged, or two programs need to interoperate in a new way, the humans must get involved. Off-line, the parties must define and communicate between them the knowledge needed to make the change, and then recode the data structures and program logic to accommodate it, and then apply these changes to the database and the application. Then, and only then, can they implement the changes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programming languages an operator may be ad hoc polymorphic, that is, have definitions for more than one kind of data, (such as in Java where the + operator is used both for the addition of numbers and for the concatenation of strings). Such an operator is said to be overloaded. In languages that support operator overloading by the programmer (such as C++) but have a limited set of operators, operator overloading is often used to define customized uses for operators. In the example IF ORDER_DATE > \"12/31/2011\" AND ORDER_DATE < \"01/01/2013\" THEN CONTINUE ELSE STOP, the operators are: > (greater than), AND and < (less than).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "for every two objects A and B a set Mor(A,B) of things called morphisms from A to B. If f is in Mor(A,B), we write f: A \u2192 B. for every three objects A, B and C a binary operation Mor(A,B) \u00d7 Mor(B,C) \u2192 Mor(A,C) called composition of morphisms. The composition of f: A \u2192 B and g: B \u2192 C is written as g \u2218 f or gf.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a simple attack, a firewall could have a simple rule added to deny all incoming traffic from the attackers, based on protocols, ports, or the originating IP addresses. More complex attacks will however be hard to block with simple rules: for example, if there is an ongoing attack on port 80 (web service), it is not possible to drop all incoming traffic on this port because doing so will prevent the server from serving legitimate traffic. Additionally, firewalls may be too deep in the network hierarchy, with routers being adversely affected before the traffic gets to the firewall. Also, many security tools still do not support IPv6 or may not be configured properly, so the firewalls often might get bypassed during the attacks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to support user interaction with application directories, several files have special status.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Where a member becomes aware that irregularities have occurred in relation to a client's tax affairs he should advise the client of the consequences, and the manner of disclosure. If necessary, appropriate specialist advice should be taken. Where a client refuses to follow the advice of a member in relation to issues involving disclosure, the member should consider whether he should continue to act.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the spiral optimization (SPO) algorithm is a metaheuristic inspired by spiral phenomena in nature. The first SPO algorithm was proposed for two-dimensional unconstrained optimization based on two-dimensional spiral models. This was extended to n-dimensional problems by generalizing the two-dimensional spiral model to an n-dimensional spiral model. There are effective settings for the SPO algorithm: the periodic descent direction setting and the convergence setting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the environment of convergent network, specific services with certain network technologies will receive different regulatory treatments. The 1996 Act created distinct regulatory categories for services that are provided by different network technologies. Besides the existing regulation framework for regulating telecommunications services and cable services in another title, the 1996 Act defines a category of services, \u201cinformation services,\u201d that distinguished from \u201ctelecommunications services\u201d and was not subject to either telephone or cable regulation. \u201cInformation services\u201d are consisted of the offering of a capability for generating, acquiring, storing, transforming, processing, retrieving, utilizing, or making available information via telecommunications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, over time, the weak verbs have become the normal form of verbs in all Germanic languages, with most strong verbs being reassigned to the weak class. For example, in Old English the verb to lock (l\u016bcan) was strong (present tense ic l\u016bce 'I lock', past tense ic l\u0113ac 'I locked'), but has now become weak. This transition is ongoing. For example, the English verb to cleave currently exists in both a conservative strong form (past tense I clove) and an innovative weak form (past tense I cleaved).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can happen if datasets are regional and/or demographically partitioned. For example, datasets containing images of animals vary significantly from country to country. Concept drift (same label, different features): local nodes may share the same labels but some of them correspond to different features at different local nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Green\u2013Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms. The proof is an extension of Szemer\u00e9di's theorem. The problem can be traced back to investigations of Lagrange and Waring from around 1770.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the development of social networks, there has appeared a new economic phenomenon: doing business via social networks. For example, there are many users of WeChat called wei-businessmen (Wechat businessman, a new form of e-commerce in Wechat) who sell products on WeChat. Doing business via social networks is not that easy. The identities of users in social networks are not the same as that in the real world.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and machine learning, the bias\u2013variance tradeoff is the property of a model that the variance of the parameter estimated across samples can be reduced by increasing the bias in the estimated parameters. The bias\u2013variance dilemma or bias\u2013variance problem is the conflict in trying to simultaneously minimize these two sources of error that prevent supervised learning algorithms from generalizing beyond their training set: The bias error is an error from erroneous assumptions in the learning algorithm. High bias can cause an algorithm to miss the relevant relations between features and target outputs (underfitting). The variance is an error from sensitivity to small fluctuations in the training set. High variance may result from an algorithm modeling the random noise in the training data (overfitting).The bias\u2013variance decomposition is a way of analyzing a learning algorithm's expected generalization error with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the irreducible error, resulting from noise in the problem itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values. It is a measure of the skewness of a random variable's distribution\u2014that is, the distribution's tendency to \"lean\" to one side or the other of the mean. Its calculation does not require any knowledge of the form of the underlying distribution\u2014hence the name nonparametric. It has some desirable properties: it is zero for any symmetric distribution; it is unaffected by a scale shift; and it reveals either left- or right-skewness equally well. In some statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "LDA can be generalized to multiple discriminant analysis, where c becomes a categorical variable with N possible states, instead of only two. Analogously, if the class-conditional densities p ( x \u2192 \u2223 c = i ) {\\displaystyle p({\\vec {x}}\\mid c=i)} are normal with shared covariances, the sufficient statistic for P ( c \u2223 x \u2192 ) {\\displaystyle P(c\\mid {\\vec {x}})} are the values of N projections, which are the subspace spanned by the N means, affine projected by the inverse covariance matrix. These projections can be found by solving a generalized eigenvalue problem, where the numerator is the covariance matrix formed by treating the means as the samples, and the denominator is the shared covariance matrix. See \u201cMulticlass LDA\u201d above for details.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following scenario a web browser is developed using defense in depth - the browser developers receive security training the codebase is checked automatically using security analysis tools the browser is regularly audited by an internal security team ... is occasionally audited by an external security team ... is executed inside a sandbox", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Abundancy\" may also be expressed as \u03c3 \u2212 1 ( n ) {\\displaystyle \\sigma _{-1}(n)} where \u03c3 k {\\displaystyle \\sigma _{k}} denotes a divisor function with \u03c3 k ( n ) {\\displaystyle \\sigma _{k}(n)} equal to the sum of the k-th powers of the divisors of n. The numbers 1 through 5 are all solitary. The smallest \"friendly number\" is 6, forming for example, the \"friendly\" pair 6 and 28 with \"abundancy\" \u03c3(6) / 6 = (1+2+3+6) / 6 = 2, the same as \u03c3(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination\u2014for example, X = Y {\\displaystyle X=Y} leaves open what the value of X is\u2014while its opposite is a self-contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in mathematics an inconsistent system\u2014such as X = 2 , X = 3 {\\displaystyle X=2,X=3} , which has no solution. Logical ambiguity and self-contradiction is analogous to visual ambiguity and impossible objects, such as the Necker cube and impossible cube, or many of the drawings of M. C. Escher.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pharmacokinetics, a compartment is a defined volume of body fluids, typically of the human body, but also those of other animals with multiple organ systems. The meaning in this area of study is different from the concept of anatomic compartments, which are bounded by fasciae, the sheath of fibrous tissue that enclose mammalian organs. Instead, the concept focuses on broad types of fluidic systems. This analysis is used in attempts to mathematically describe distribution of small molecules throughout organisms with multiple compartments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, any gender markers have been so eroded over time (possibly through deflexion) that they are no longer recognizable. Many German nouns, for example, do not indicate their gender through either meaning or form. In such cases a noun's gender must simply be memorized, and gender can be regarded as an integral part of each noun when considered as an entry in the speaker's lexicon. (This is reflected in dictionaries, which typically indicate the gender of noun headwords where applicable.) Second-language learners are often encouraged to memorize a modifier, usually a definite article, in conjunction with each noun\u2014for example, a learner of French may learn the word for \"chair\" as la chaise (meaning \"the chair\"); this carries the information that the noun is chaise, and that it is feminine (because la is the feminine singular form of the definite article).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other constituents (such as oblique, genitive, and object of comparative) are called nonterms (N). The predicate is marked (P). According to Geoffrey K. Pullum (1977), the GR hierarchy directly corresponds to the accessibility hierarchy: A schematic representation of a clause in this formalism might look like:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first series of experiments, experts in the use of the various techniques were tasked with both the creation of the index and its use against the sample queries. Each system had its own concept about how a query should be structured, which would today be known as a query language. Much of the criticism of the first experiments focused on whether the experiments were truly testing the systems, or the user's ability to translate the query into the query language.This led to the second series of experiments, Cranfield 2, that considered the question of converting the query into the language. To do this, instead of considering the generation of the query as a black box, each step was broken down.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In politics, emergent democracy represents the rise of political structures and behaviors without central planning and by the action of many individual participants, especially when mediated by the Internet. It has been likened to the democratic system of ancient Greece in the sense that people could publicly participate as much or as little as they please, although a form of representation exists which is based on personal trust networks instead of party affiliations. More recently, American writer and researcher Clay Shirky has referred to this as \"the power of organizing without organizations.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let the set of neighbors of node u {\\displaystyle u} be denoted nbr \u2061 ( u ) {\\displaystyle \\operatorname {nbr} (u)} . The average degree is then \u03bc = 1 N \u2211 u \u2208 V | nbr \u2061 ( u ) | = 2 M N \u2265 1 {\\displaystyle \\mu ={\\frac {1}{N}}\\sum _{u\\in V}|\\operatorname {nbr} (u)|={\\frac {2M}{N}}\\geq 1} . Let the number of \"friends of friends\" of node u {\\displaystyle u} be denoted FF \u2061 ( u ) = \u2211 v \u2208 nbr \u2061 ( u ) | nbr \u2061 ( v ) | {\\displaystyle \\operatorname {FF} (u)=\\sum _{v\\in \\operatorname {nbr} (u)}|\\operatorname {nbr} (v)|} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most European countries the official accident statistics contain no information on rolling cars, only Great Britain can deliver official statistical data. Regarding other sources, only a few accident databases on rollover accidents exist. Although only less than 10% of all vehicle accidents with severe injuries involve rollovers, approximately 25% of all seriously injured occupants were involved in accidents where their car rolled. These numbers are currently increasing, as rollover frequency of several new vehicle types like mini vans, SUV or MPV is a lot higher than for most conventional cars.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. These groups were first studied by Reinhold Baer, who showed that a finite abelian group is capable if and only if it is a product of cyclic groups of orders n1,...,nk where ni divides ni+1 and nk\u20131=nk.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 2017, 2.3 million out of Kickstarter's 7.9 million users had donated toward more than one project.Traditionally, journalists are not involved in advertising and marketing. Crowdfunding means that journalists are attracting funders while trying to remain independent, which may pose a conflict. Therefore, being directly involved with financial aspects can call journalistic integrity and journalistic objectivity into question.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the \"cocktail party problem\" of listening in on one person's speech in a noisy room.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory, particularly the proof theory of constructive mathematics based on the Curry\u2013Howard correspondence, one often identifies a mathematical proposition with its set of proofs (if any). A given proposition may have many proofs, of course; according to the principle of proof irrelevance, normally only the truth of the proposition matters, not which proof was used. However, the Curry\u2013Howard correspondence can turn proofs into algorithms, and differences between algorithms are often important. So proof theorists may prefer to identify a proposition with a setoid of proofs, considering proofs equivalent if they can be converted into one another through beta conversion or the like.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regards to the typology of neolithic adzes, initially two types were distinguished, When width exceeds thickness they were named flat adzes (Flachhacke), when thickness exceeds width shoe-last adzes (Schuhleistenkeile), or high adzes. Within the latter group a distinction is sometimes made between intermediate Flomborn adzes and the higher Hinkelstein adzes (Buttler 1938; Bakels 1987; Merkel 1999). Later, subdivisions were made on the basis of metric characteristics into two groups (Schietzel 1965), six groups (Modderman 1970, 184) and finally two groups again (Dohrn-Ihmig 1983). All typologies were based on the width-height ratio, while Modderman added the absolute dimension. The wide variation, from small to large and from flat to high adzes, certainly reflects a functional differentiation, but the various types do not appear to be of chronological significance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These schemata are needed to link the pure category to sensed phenomenal appearances because the categories are, as Kant says, heterogeneous with sense intuition. Categories and sensed phenomena, however, do share one characteristic: time. Succession is the form of sense impressions and also of the Category of causality. Therefore, time can be said to be the schema of Categories or pure concepts of the understanding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, at 16 byte intervals. Since all segments are 64 KB long, this explains how overlap can occur between segments and why any location in the linear memory address space can be accessed with many segment:offset pairs. The actual location of the beginning of a segment in the linear address space can be calculated with segment\u00d716.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is computable in polynomial time as the determinant of a maximal principal submatrix of the Laplacian matrix of G, an early result in algebraic graph theory known as Kirchhoff\u2019s Matrix\u2013Tree theorem. Likewise, the dimension of the bicycle space at T G ( \u2212 1 , \u2212 1 ) {\\displaystyle T_{G}(-1,-1)} can be computed in polynomial time by Gaussian elimination. For planar graphs, the partition function of the Ising model, i.e., the Tutte polynomial at the hyperbola H 2 {\\displaystyle H_{2}} , can be expressed as a Pfaffian and computed efficiently via the FKT algorithm. This idea was developed by Fisher, Kasteleyn, and Temperley to compute the number of dimer covers of a planar lattice model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Full named-entity recognition is often broken down, conceptually and possibly also in implementations, as two distinct problems: detection of names, and classification of the names by the type of entity they refer to (e.g. person, organization, or location). The first phase is typically simplified to a segmentation problem: names are defined to be contiguous spans of tokens, with no nesting, so that \"Bank of America\" is a single name, disregarding the fact that inside this name, the substring \"America\" is itself a name. This segmentation problem is formally similar to chunking.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1920s, Louis Mordell posed a conjecture that implied that Fermat's equation has at most a finite number of nontrivial primitive integer solutions, if the exponent n is greater than two. This conjecture was proved in 1983 by Gerd Faltings, and is now known as Faltings's theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the event of a worst-case emergency, called a \"design basis accident\" in NRC regulations, the containment is designed to seal off and contain a meltdown. Redundant systems are installed to prevent a meltdown, but as a matter of policy, one is assumed to occur and thus the requirement for a containment building. For design purposes, the reactor vessel's piping is assumed to be breached, causing a \"LOCA\" (Loss Of Coolant Accident) where the water in the reactor vessel is released to the atmosphere inside the containment and flashes into steam.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the zero-truncated Poisson (ZTP) distribution is a certain discrete probability distribution whose support is the set of positive integers. This distribution is also known as the conditional Poisson distribution or the positive Poisson distribution. It is the conditional probability distribution of a Poisson-distributed random variable, given that the value of the random variable is not zero. Thus it is impossible for a ZTP random variable to be zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\chi '=\\sum _{i=1}^{n}k_{i}s_{i}^{2}.} where k i {\\displaystyle k_{i}} is a real positive number, typically k i = 1 \u03bd i + 1 {\\displaystyle k_{i}={\\frac {1}{\\nu _{i}+1}}} . In general, the probability distribution of \u03c7' cannot be expressed analytically.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to overcome the volume size limit of FAT16, while at the same time allowing DOS real-mode code to handle the format, Microsoft designed a new version of the file system, FAT32, which supported an increased number of possible clusters, but could reuse most of the existing code, so that the conventional memory footprint was increased by less than 5 KB under DOS. Cluster values are represented by 32-bit numbers, of which 28 bits are used to hold the cluster number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a common attack on asymmetric RSA relies on the fact that the encryption steps rely on the value of the key bits. Every bit is processed with a square operation and then a multiplication operation if and only if the bit is equal to 1. An attacker with a clear trace can deduce the key simply by observing where the multiplication operations are performed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice we have much fewer processors than the matrix elements. We can replace the matrix elements with submatrices, so that every processor processes more values. The scalar multiplication and addition become sequential matrix multiplication and addition. The width and height of the submatrices will be N = n / p {\\displaystyle N=n/{\\sqrt {p}}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In prehistoric time, quarter square multiplication involved floor function; that some sources attribute to Babylonian mathematics (2000\u20131600 BC). Antoine Voisin published a table of quarter squares from 1 to 1000 in 1817 as an aid in multiplication. A larger table of quarter squares from 1 to 100000 was published by Samuel Laundy in 1856, and a table from 1 to 200000 by Joseph Blater in 1888.Quarter square multipliers were used in analog computers to form an analog signal that was the product of two analog input signals. In this application, the sum and difference of two input voltages are formed using operational amplifiers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It would be superseded by Peripheral Component Interconnect (PCI), starting at speeds of 133 MB/s (32-bit at 33 MHz in the standard configuration) Thus for a short time, a market opening occurred where video card manufacturers and motherboard chipset makers created their own proprietary implementations of local buses to provide graphics cards direct access to the processor and system memory. This avoided the limitations of the ISA bus while being less costly than a \"licensed IBM MCA machine\". It is important to note that at the time the cost to migrate to an MCA architecture machine from an ISA machine was substantial.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of a graph-based computational procedure, SMILES is a string obtained by printing the symbol nodes encountered in a depth-first tree traversal of a chemical graph. The chemical graph is first trimmed to remove hydrogen atoms and cycles are broken to turn it into a spanning tree. Where cycles have been broken, numeric suffix labels are included to indicate the connected nodes. Parentheses are used to indicate points of branching on the tree. The resultant SMILES form depends on the choices: of the bonds chosen to break cycles, of the starting atom used for the depth-first traversal, and of the order in which branches are listed when encountered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the execute stage, the instruction operations are carried out. Instructions are delayed in this step until all of their operands are available, eliminating RAW hazards. Program correctness is maintained through effective address calculation to prevent hazards through memory. If one or more of the operands is not yet available then: wait for operand to become available on the CDB. When all operands are available, then: if the instruction is a load or store Compute the effective address when the base register is available, and place it in the load/store buffer If the instruction is a load then: execute as soon as the memory unit is available Else, if the instruction is a store then: wait for the value to be stored before sending it to the memory unit Else, the instruction is an arithmetic logic unit (ALU) operation then: execute the instruction at the corresponding functional unit", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the PINN framework, initial and boundary conditions are not analytically satisfied, thus they need to be included in the loss function of the network to be simultaneously learned with the differential equation (DE) unknown functions. Having competing objectives during the network's training can lead to unbalanced gradients while using gradient-based techniques, which causes PINNs to often struggle to accurately learn the underlying DE solution. This drawback is overcome by using functional interpolation techniques such as the Theory of Functional Connections (TFC)'s constrained expression, in the Deep-TFC framework, which reduces the solution search space of constrained problems to the subspace of neural network that analytically satisfies the constraints. A further improvement of PINN and functional interpolation approach is given by the Extreme Theory of Functional Connections (X-TFC) framework, where a single-layer Neural Network and the extreme learning machine training algorithm are employed. X-TFC allows to improve the accuracy and performance of regular PINNs, and its robustness and reliability are proved for stiff problems, optimal control, aerospace, and rarefied gas dynamics applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A more efficient version of the algorithm shortcuts these steps, instead replacing the larger of the two numbers by its remainder when divided by the smaller of the two (with this version, the algorithm stops when reaching a zero remainder). With this improvement, the algorithm never requires more steps than five times the number of digits (base 10) of the smaller integer. This was proven by Gabriel Lam\u00e9 in 1844 (Lam\u00e9's Theorem), and marks the beginning of computational complexity theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context modeling complexity the next-symbol predictions, of one or more statistical models, are combined or competing to yield a prediction that is based on events recorded in the past. The algorithmic information content derived from each symbol prediction can be used to compute algorithmic information profiles with a time proportional to the length of the sequence. The process has been applied to DNA sequence analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These coverings are called \"caps\". Depending on the method used for the shadow volume, the front end may be covered by the object itself, and the rear end may sometimes be omitted (see depth pass below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs. The concept of graph edit distance was first formalized mathematically by Alberto Sanfeliu and King-Sun Fu in 1983. A major application of graph edit distance is in inexact graph matching, such as error-tolerant pattern recognition in machine learning.The graph edit distance between two graphs is related to the string edit distance between strings. With the interpretation of strings as connected, directed acyclic graphs of maximum degree one, classical definitions of edit distance such as Levenshtein distance,Hamming distance and Jaro\u2013Winkler distance may be interpreted as graph edit distances between suitably constrained graphs. Likewise, graph edit distance is also a generalization of tree edit distance between rooted trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a {\\displaystyle a} and b {\\displaystyle b} with a > b > 0 {\\displaystyle a>b>0} , where the Greek letter phi ( \u03c6 {\\displaystyle \\varphi } or \u03d5 {\\displaystyle \\phi } ) denotes the golden ratio. The constant \u03c6 {\\displaystyle \\varphi } satisfies the quadratic equation \u03c6 2 = \u03c6 + 1 {\\displaystyle \\varphi ^{2}=\\varphi +1} and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names.Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In computability theory, a general recursive function is a partial function from the integers to the integers; no algorithm can exist for deciding whether an arbitrary such function is in fact total. When arrow notation is used for functions, a partial function f {\\displaystyle f} from X {\\displaystyle X} to Y {\\displaystyle Y} is sometimes written as f: X \u21c0 Y , {\\displaystyle f:X\\rightharpoonup Y,} f: X \u219b Y , {\\displaystyle f:X\\nrightarrow Y,} or f: X \u21aa Y . {\\displaystyle f:X\\hookrightarrow Y.} However, there is no general convention, and the latter notation is more commonly used for inclusion maps or embeddings.Specifically, for a partial function f: X \u21c0 Y , {\\displaystyle f:X\\rightharpoonup Y,} and any x \u2208 X , {\\displaystyle x\\in X,} one has either: f ( x ) = y \u2208 Y {\\displaystyle f(x)=y\\in Y} (it is a single element in Y), or f ( x ) {\\displaystyle f(x)} is undefined.For example, if f {\\displaystyle f} is the square root function restricted to the integers f: Z \u2192 N , {\\displaystyle f:\\mathbb {Z} \\to \\mathbb {N} ,} defined by: f ( n ) = m {\\displaystyle f(n)=m} if, and only if, m 2 = n , {\\displaystyle m^{2}=n,} m \u2208 N , n \u2208 Z , {\\displaystyle m\\in \\mathbb {N} ,n\\in \\mathbb {Z} ,} then f ( n ) {\\displaystyle f(n)} is only defined if n {\\displaystyle n} is a perfect square (that is, 0 , 1 , 4 , 9 , 16 , \u2026 {\\displaystyle 0,1,4,9,16,\\ldots } ). So f ( 25 ) = 5 {\\displaystyle f(25)=5} but f ( 26 ) {\\displaystyle f(26)} is undefined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the ASCII version of the format, the vertices and faces are each described one to a line with the numbers separated by white space. In the binary version, the data is simply packed closely together at the endianness specified in the header and with the data types given in the property records. For the common property list... representation for polygons, the first number for that element is the number of vertices that the polygon has and the remaining numbers are the indices of those vertices in the preceding vertex list.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phylogenetics, the metric is often used to compute a distance between two trees. The treedist program in the PHYLIP suite offers this function, as does the RAxML_standard package, the DendroPy Python library (under the name \"symmetric difference metric\"), and R packages TreeDist (`RobinsonFoulds()` function) and phangorn (`treedist()` function). For comparing groups of trees, the fastest implementations include HashRF and MrsRF. The Robinson\u2013Foulds metric has also been used in quantitative comparative linguistics to compute distances between trees that represent how languages are related to each other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s and 1990s, a variety of SVR4 versions of Unix were available commercially for the x86 PC platform. However, the market for commercial Unix on PCs declined after Linux and BSD became widely available. In late 1994, Eric S. Raymond discontinued his PC-clone UNIX Software Buyer's Guide on USENET, stating, \"The reason I am dropping this is that I run Linux now, and I no longer find the SVr4 market interesting or significant. \"In 1998, a confidential memo at Microsoft stated, \"Linux is on track to eventually own the x86 UNIX market\", and further predicted, \"I believe that Linux \u2013 moreso than NT \u2013 will be the biggest threat to SCO in the near future. \"An InfoWorld article from 2001 characterized SCO UnixWare as having a \"bleak outlook\" due to being \"trounced\" in the market by Linux and Solaris, and IDC predicted that SCO would \"continue to see a shrinking share of the market\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Babai and Szemer\u00e9di prove that every element of a finite group G has an SLP of length O(log2|G|) in every generating set. An efficient solution to the constructive membership problem is crucial to many group-theoretic algorithms. It can be stated in terms of SLPs as follows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly for the generator in Wasserstein GAN. For Wasserstein GAN, D W G A N {\\displaystyle D_{WGAN}} has gradient 1 almost everywhere, while for GAN, ln \u2061 ( 1 \u2212 D ) {\\displaystyle \\ln(1-D)} has flat gradient in the middle, and steep gradient elsewhere.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error. For example, suppose that the final result of a long, multi-step calculation can be safely rounded off to N decimal places. That is to say, the roundoff error introduced by this final roundoff makes a negligible contribution to the overall uncertainty. However, it is quite likely that it is not safe to round off the intermediate steps in the calculation to the same number of digits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition, multiplication, and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics. The question was solved in 1980 by Alex Wilkie, who showed that such unprovable identities do exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In response to some of these variants, and to other feedback, the paper \"PRIMES is in P\" was updated with a new formulation of the AKS algorithm and of its proof of correctness. (This version was eventually published in Annals of Mathematics.) While the basic idea remained the same, r was chosen in a new manner, and the proof of correctness was more coherently organized.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern positional numbers systems, such as the decimal system, the digits and their positions in the representation of an integer, for example, 45, are a shorthand notation for a polynomial in the radix or base, in this case, 4 \u00d7 101 + 5 \u00d7 100. As another example, in radix 5, a string of digits such as 132 denotes the (decimal) number 1 \u00d7 52 + 3 \u00d7 51 + 2 \u00d7 50 = 42. This representation is unique. Let b be a positive integer greater than 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, his f20 cores had 31 5-bit instructions, which fit four to a 20-bit word. RISC chips now dominate the market for 32-bit embedded systems. Smaller RISC chips are even growing common in the cost-sensitive 8-bit embedded-system market.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In summary, backtracking line search (and its modifications) is a method which is easy to implement, is applicable for very general functions, has very good theoretical guarantee (for both convergence to critical points and avoidance of saddle points) and works well in practice. Several other methods which have good theoretical guarantee, such as diminishing learning rates or standard GD with learning rate <1/L \u2013 both require the gradient of the objective function to be Lipschitz continuous, turn out to be a special case of Backtracking line search or satisfy Armijo's condition. Even though a priori one needs the cost function to be continuously differentiable to apply this method, in practice one can apply this method successfully also for functions which are continuously differentiable on a dense open subset such as f ( t ) = | t | {\\displaystyle f(t)=|t|} or f ( t ) = R e L u ( t ) = max { t , 0 } {\\displaystyle f(t)=ReLu(t)=\\max\\{t,0\\}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s and 1970s, Gallagher proved several results in large sieve methods in analytic number theory and simplified key ingredients used in the proof of the Bombieri\u2013Vinogradov theorem. He also applied the large sieve to study the asymptotics of Galois groups of monic integral polynomials of bounded height, improving on results by van der Waerden.In 1971, he invented the larger sieve.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social, pathological and biological networks. For a survey on recent trends in computational methods and applications see Buluc et al. (2013). Two common examples of graph partitioning are minimum cut and maximum cut problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the advent of high-speed computers, the minimization problem can be solved iteratively with adequate speed, and the communalities are calculated in the process, rather than being needed beforehand. The MinRes algorithm is particularly suited to this problem, but is hardly the only iterative means of finding a solution. If the solution factors are allowed to be correlated (as in 'oblimin' rotation, for example), then the corresponding mathematical model uses skew coordinates rather than orthogonal coordinates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, computer science and logic, convergence is the idea that different sequences of transformations come to a conclusion in a finite amount of time (the transformations are terminating), and that the conclusion reached is independent of the path taken to get to it (they are confluent). More formally, a preordered set of term rewriting transformations are said to be convergent if they are confluent and terminating.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\left(\\mathbf {P} ^{T}\\mathbf {A} \\mathbf {P} \\right)\\left(\\mathbf {P} ^{T}\\mathbf {x} \\right)=\\mathbf {P} ^{T}\\mathbf {b} .} The problem of finding the best ordering is an NP-complete problem and is thus intractable, so heuristic methods are used instead.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spectral graph theory, an eigenvalue of a graph is defined as an eigenvalue of the graph's adjacency matrix A {\\displaystyle A} , or (increasingly) of the graph's Laplacian matrix due to its discrete Laplace operator, which is either D \u2212 A {\\displaystyle D-A} (sometimes called the combinatorial Laplacian) or I \u2212 D \u2212 1 / 2 A D \u2212 1 / 2 {\\displaystyle I-D^{-1/2}AD^{-1/2}} (sometimes called the normalized Laplacian), where D {\\displaystyle D} is a diagonal matrix with D i i {\\displaystyle D_{ii}} equal to the degree of vertex v i {\\displaystyle v_{i}} , and in D \u2212 1 / 2 {\\displaystyle D^{-1/2}} , the i {\\displaystyle i} th diagonal entry is 1 / deg \u2061 ( v i ) {\\textstyle 1/{\\sqrt {\\deg(v_{i})}}} . The k {\\displaystyle k} th principal eigenvector of a graph is defined as either the eigenvector corresponding to the k {\\displaystyle k} th largest or k {\\displaystyle k} th smallest eigenvalue of the Laplacian. The first principal eigenvector of the graph is also referred to merely as the principal eigenvector. The principal eigenvector is used to measure the centrality of its vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the digital realm, there can be any number of conventional primary colors making up an image; a channel in this case is extended to be the grayscale image based on any such conventional primary color. By extension, a channel is any grayscale image of the same dimension as and associated with the original image. Channel is a conventional term used to refer to a certain component of an image. In reality, any image format can use any algorithm internally to store images.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The case where the classical communication is replaced by quantum communication was considered in. This is known as the Fully Quantum Slepian-Wolf Theorem, since everything is sent down the quantum channel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some important languages used in OGC-compliant systems are described in the following. XML stands for eXtensible Markup language and is widely used for displaying and interpreting data from computers. Thus the development of a web-based GI system requires several useful XML encodings that can effectively describe two-dimensional graphics such as maps SVG and, at the same time, store and transfer simple features GML.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model. The resulting fitted model can be used to summarize the data, to predict unobserved values from the same system, and to understand the mechanisms that may underlie the system. Mathematically, linear least squares is the problem of approximately solving an overdetermined system of linear equations A x = b, where b is not an element of the column space of the matrix A. The approximate solution is realized as an exact solution to A x = b', where b' is the projection of b onto the column space of A. The best approximation is then that which minimizes the sum of squared differences between the data values and their corresponding modeled values. The approach is called linear least squares since the assumed function is linear in the parameters to be estimated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In preparation to the attack, weaknesses in the key schedule of KTANTAN that allows the 3-subset MITM attack was identified. Since only two key-bits are used each round, the diffusion of the key per round is small - the safety lies in the number of rounds. Due to this structure of the key-schedule, it was possible to find a large number of consecutive rounds, which never utilized certain key-bits. More precisely, the authors of the attack found that: Round 1 to 111 never uses the key-bits: k 32 , k 39 , k 44 , k 61 , k 66 , k 75 {\\displaystyle k_{32},k_{39},k_{44},k_{61},k_{66},k_{75}} Round 131 to 254 never uses the key-bits: k 3 , k 20 , k 41 , k 47 , k 63 , k 74 {\\displaystyle k_{3},k_{20},k_{41},k_{47},k_{63},k_{74}} This characteristics of the key-schedule is used for staging the 3-subset MITM attack, as we now are able to split the cipher into two blocks with independent key-bits. The parameters for the attack are thus: A 0 {\\displaystyle A_{0}} = the keybits used by both blocks (which means the rest 68 bits not mentioned above) A 1 {\\displaystyle A_{1}} = the keybits used only by the first block (defined by round 1-111) A 2 {\\displaystyle A_{2}} = the keybits used only by the second block (defined by round 131-254)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the mediant of two fractions, generally made up of four positive integers a c {\\displaystyle {\\frac {a}{c}}\\quad } and b d {\\displaystyle \\quad {\\frac {b}{d}}\\quad } is defined as a + b c + d . {\\displaystyle \\quad {\\frac {a+b}{c+d}}.} That is to say, the numerator and denominator of the mediant are the sums of the numerators and denominators of the given fractions, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The area of a square is equal to the product of two of its sides (follows from 3).Next, each top square is related to a triangle congruent with another triangle related in turn to one of two rectangles making up the lower square. The proof is as follows: Let ACB be a right-angled triangle with right angle CAB.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language. These rules only address the location and manipulation of the strings of the language. It does not describe anything else about a language, such as its semantics (i.e. what the strings mean). (See also formal grammar).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in category theory, a morphism is a structure-preserving map from one mathematical structure to another one of the same type. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory, group homomorphisms; in analysis and topology, continuous functions, and so on.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some OWL flavors like OWL1-DL, entities can be either classes or instances, but cannot be both. This limitations forbids metaclasses and metamodeling. This is not the case in the OWL1 full flavor, but this allows the model to be computationally undecidable. In OWL2, metaclasses can implemented with punning, that is a way to treat classes as if they were individuals. Other approaches have also been proposed and used to check the properties of ontologies at a meta level.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The eigenvectors corresponding to the smaller eigenvalues will tend to be very sensitive to the exact choice of training data, and it is often necessary to use regularisation as described in the next section. If classification is required, instead of dimension reduction, there are a number of alternative techniques available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix. The LU decomposition was introduced by the Polish astronomer Tadeusz Banachiewicz in 1938. To quote: \"It appears that Gauss and Doolittle applied the method  only to symmetric equations. More recent authors, for example, Aitken, Banachiewicz, Dwyer, and Crout \u2026 have emphasized the use of the method, or variations of it, in connection with non-symmetric problems \u2026 Banachiewicz \u2026 saw the point \u2026 that the basic problem is really one of matrix factorization, or \u201cdecomposition\u201d as he called it.\" It's also referred to as LR decomposition (factors into left and right triangular matrices).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization, a descent direction is a vector p \u2208 R n {\\displaystyle \\mathbf {p} \\in \\mathbb {R} ^{n}} that points towards a local minimum x \u2217 {\\displaystyle \\mathbf {x} ^{*}} of an objective function f: R n \u2192 R {\\displaystyle f:\\mathbb {R} ^{n}\\to \\mathbb {R} } . Computing x \u2217 {\\displaystyle \\mathbf {x} ^{*}} by an iterative method, such as line search defines a descent direction p k \u2208 R n {\\displaystyle \\mathbf {p} _{k}\\in \\mathbb {R} ^{n}} at the k {\\displaystyle k} th iterate to be any p k {\\displaystyle \\mathbf {p} _{k}} such that \u27e8 p k , \u2207 f ( x k ) \u27e9 < 0 {\\displaystyle \\langle \\mathbf {p} _{k},\\nabla f(\\mathbf {x} _{k})\\rangle <0} , where \u27e8 , \u27e9 {\\displaystyle \\langle ,\\rangle } denotes the inner product. The motivation for such an approach is that small steps along p k {\\displaystyle \\mathbf {p} _{k}} guarantee that f {\\displaystyle \\displaystyle f} is reduced, by Taylor's theorem. Using this definition, the negative of a non-zero gradient is always a descent direction, as \u27e8 \u2212 \u2207 f ( x k ) , \u2207 f ( x k ) \u27e9 = \u2212 \u27e8 \u2207 f ( x k ) , \u2207 f ( x k ) \u27e9 < 0 {\\displaystyle \\langle -\\nabla f(\\mathbf {x} _{k}),\\nabla f(\\mathbf {x} _{k})\\rangle =-\\langle \\nabla f(\\mathbf {x} _{k}),\\nabla f(\\mathbf {x} _{k})\\rangle <0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an interval contractor (or contractor for short) associated to a set X {\\displaystyle X} is an operator C {\\displaystyle C} which associates to a hyperrectangle  {\\displaystyle } in R n {\\displaystyle {\\mathbf {R}}^{n}} another box C (  ) {\\displaystyle C()} of R n {\\displaystyle {\\mathbf {R}}^{n}} such that the two following properties are always satisfied: C (  ) \u2282  {\\displaystyle C()\\subset } (contractance property) C (  ) \u2229 X =  \u2229 X {\\displaystyle C()\\cap X=\\cap X} (completeness property)A contractor associated to a constraint (such as an equation or an inequality) is a contractor associated to the set X {\\displaystyle X} of all x {\\displaystyle x} which satisfy the constraint. Contractors make it possible to improve the efficiency of branch-and-bound algorithms classically used in interval analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In textbooks, channel length modulation in active mode usually is described using the Shichman\u2013Hodges model, accurate only for old technology: where I D {\\displaystyle I_{\\text{D}}} = drain current, K n \u2032 {\\displaystyle K'_{n}} = technology parameter sometimes called the transconductance coefficient, W, L = MOSFET width and length, V GS {\\displaystyle V_{\\text{GS}}} = gate-to-source voltage, V th {\\displaystyle V_{\\text{th}}} =threshold voltage, V DS {\\displaystyle V_{\\text{DS}}} = drain-to-source voltage, V DS,sat = V GS \u2212 V th {\\displaystyle V_{\\text{DS,sat}}=V_{\\text{GS}}-V_{\\text{th}}} , and \u03bb = channel-length modulation parameter. In the classic Shichman\u2013Hodges model, V th {\\displaystyle V_{\\text{th}}} is a device constant, which reflects the reality of transistors with long channels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a strictly convex space is a normed vector space (X, || ||) for which the closed unit ball is a strictly convex set. Put another way, a strictly convex space is one for which, given any two distinct points x and y on the unit sphere \u2202B (i.e. the boundary of the unit ball B of X), the segment joining x and y meets \u2202B only at x and y. Strict convexity is somewhere between an inner product space (all inner product spaces being strictly convex) and a general normed space in terms of structure. It also guarantees the uniqueness of a best approximation to an element in X (strictly convex) out of a convex subspace Y, provided that such an approximation exists. If the normed space X is complete and satisfies the slightly stronger property of being uniformly convex (which implies strict convexity), then it is also reflexive by Milman-Pettis theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For high-dimensional data, many of the existing methods fail due to the curse of dimensionality, which renders particular distance functions problematic in high-dimensional spaces. This led to new clustering algorithms for high-dimensional data that focus on subspace clustering (where only some attributes are used, and cluster models include the relevant attributes for the cluster) and correlation clustering that also looks for arbitrary rotated (\"correlated\") subspace clusters that can be modeled by giving a correlation of their attributes. Examples for such clustering algorithms are CLIQUE and SUBCLU.Ideas from density-based clustering methods (in particular the DBSCAN/OPTICS family of algorithms) have been adapted to subspace clustering (HiSC, hierarchical subspace clustering and DiSH) and correlation clustering (HiCO, hierarchical correlation clustering, 4C using \"correlation connectivity\" and ERiC exploring hierarchical density-based correlation clusters).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most post-Soviet states DD.MM.YYYY format is used with dots as separators and with leading zeros. Some, such as Lithuania, have adopted the ISO 8601 YYYY-MM-DD format; previously a mixed standard with ISO 8601 order but dots as separators was in use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since this relaxation in US export restrictions, and because most personal computers connected to the Internet include US-sourced web browsers such as Firefox or Internet Explorer, almost every Internet user worldwide has potential access to quality cryptography via their browsers (e.g., via Transport Layer Security). The Mozilla Thunderbird and Microsoft Outlook E-mail client programs similarly can transmit and receive emails via TLS, and can send and receive email encrypted with S/MIME. Many Internet users do not realize that their basic application software contains such extensive cryptosystems. These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally do not find it practical to do much to control distribution or use of cryptography of this quality, so even when such laws are in force, actual enforcement is often effectively impossible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A suitable generalization of the first definition is: Let D {\\displaystyle D} be a subset of R n . {\\displaystyle \\mathbb {R} ^{n}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is the smallest finite non-abelian group. A common example from physics is the rotation group SO(3) in three dimensions (for example, rotating something 90 degrees along one axis and then 90 degrees along a different axis is not the same as doing them in reverse order). Both discrete groups and continuous groups may be non-abelian. Most of the interesting Lie groups are non-abelian, and these play an important role in gauge theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Finally, this generates two clearly different proposals: \"cheap printer \u2013 expensive ink\" or \"expensive printer \u2013 cheap ink\". Ultimately, the consumer decision depends on their reference interest rate or their time preference. From an economics viewpoint, there is a clear trade-off between cost per copy and cost of the printer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to its being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, seismology, physics, economics, image processing, and telecommunications.The process is named after French mathematician Sim\u00e9on Denis Poisson despite Poisson's never having studied the process. Its name derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Visual Basic (classic) language, subprograms are termed functions or subs (or methods when associated with a class). Visual Basic 6 uses various terms called types to define what is being passed as a parameter. By default, an unspecified variable is registered as a variant type and can be passed as ByRef (default) or ByVal. Also, when a function or sub is declared, it is given a public, private, or friend designation, which determines whether it can be accessed outside the module or project that it was declared in.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, each wireless network controls how their MDCs will be used. As such, when wireless customers call a MDC, they're call is routed to the end user that their carrier selects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Evaluating the cross-products: | e x e y e z \u2212 x A 0 0 0 R 0 0 | + | e x e y e z L \u2212 x A 0 0 0 R B 0 | = \u2212 x A R 0 e z + ( L \u2212 x A ) R B e z = 0 . {\\displaystyle \\left|{\\begin{matrix}\\mathbf {e} _{x}&\\mathbf {e} _{y}&\\mathbf {e} _{z}\\\\-x_{A}&0&0\\\\0&R_{0}&0\\end{matrix}}\\right|+\\left|{\\begin{matrix}\\mathbf {e} _{x}&\\mathbf {e} _{y}&\\mathbf {e} _{z}\\\\L-x_{A}&0&0\\\\0&R_{B}&0\\end{matrix}}\\right|=-x_{A}R_{0}\\,\\mathbf {e} _{z}+(L-x_{A})R_{B}\\,\\mathbf {e} _{z}=0\\,.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "ASK query Used to provide a simple True/False result for a query on a SPARQL endpoint. DESCRIBE query Used to extract an RDF graph from the SPARQL endpoint, the content of which is left to the endpoint to decide, based on what the maintainer deems as useful information.Each of these query forms takes a WHERE block to restrict the query, although, in the case of the DESCRIBE query, the WHERE is optional. SPARQL 1.1 specifies a language for updating the database with several new query forms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, Continuous Tone-Coded Squelch System or CTCSS is one type of in-band signaling that is used to reduce the annoyance of listening to other users on a shared two-way radio communication channel. It is sometimes referred to as tone squelch or PL for Private Line, a trademark of Motorola. It does this by adding a low frequency audio tone to the voice. Where more than one group of users is on the same radio frequency (called co-channel users), CTCSS circuitry mutes those users who are using a different CTCSS tone or no CTCSS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 23567, 123567, 234567, and 1234567 are the patterns related to Braille pattern dots-12345, since the two additional dots of kantenji patterns 012345, 123457, and 0123457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Having established the necessary notions, the theorem is stated as follows. Chomsky\u2013Sch\u00fctzenberger theorem. If L {\\displaystyle L} is a context-free language admitting an unambiguous context-free grammar, and a k := | L \u2229 \u03a3 k | {\\displaystyle a_{k}:=|L\\ \\cap \\Sigma ^{k}|} is the number of words of length k {\\displaystyle k} in L {\\displaystyle L} , then G ( x ) = \u2211 k = 0 \u221e a k x k {\\displaystyle G(x)=\\sum _{k=0}^{\\infty }a_{k}x^{k}} is a power series over N {\\displaystyle \\mathbb {N} } that is algebraic over Q ( x ) {\\displaystyle \\mathbb {Q} (x)} .Proofs of this theorem are given by Kuich & Salomaa (1985), and by Panholzer (2005).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Given 2 1 \u00d7 0.100 2 \u2212 2 0 \u00d7 0.111 2 {\\displaystyle 2^{1}\\times 0.100_{2}-2^{0}\\times 0.111_{2}} we have to line up the binary points. This means we must add an extra digit to the first operand\u2014a guard digit. This gives us 2 1 \u00d7 0.1000 2 \u2212 2 1 \u00d7 0.0111 2 {\\displaystyle 2^{1}\\times 0.1000_{2}-2^{1}\\times 0.0111_{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples of phonemic or distinctive features are: ,  (binary features) and  (a unary feature; also a place feature). Surface representations can be expressed as the result of rules acting on the features of the underlying representation. These rules are formulated in terms of transformations on features.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is also possible to find a simultaneous embedding with fixed edges for any pair of a planar graph and a tree. It is an open question whether the existence of a simultaneous embedding with fixed edges for two given graphs can be tested in polynomial time. However, for three or more graphs, the problem is NP-complete. When simultaneous embeddings with fixed edges do exist, they can be found in polynomial time for pairs of outerplanar graphs, and for Biconnected graphs, i.e. pairs of graphs whose intersection is biconnected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of Arithmetica. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The analyst must learn the set of joint conditional opinions \u03c9 Z | X Y {\\displaystyle \\omega _{Z|XY}} in order to apply the deduction operator and derive the marginal opinion \u03c9 Z \u2016 X Y {\\displaystyle \\omega _{Z\\|XY}} on the variable Z {\\displaystyle Z} . The conditional opinions express a conditional relationship between the parent variables and the child variable. The deduced opinion is computed as \u03c9 Z \u2016 X Y = \u03c9 Z | X Y \u229a \u03c9 X Y {\\displaystyle \\omega _{Z\\|XY}=\\omega _{Z|XY}\\circledcirc \\omega _{XY}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In survey methodology, probability-proportional-to-size (pps) sampling is a sampling process where each element of the population (of size N) has some (independent) chance p i {\\displaystyle p_{i}} to be selected to the sample when performing one draw. This p i {\\displaystyle p_{i}} is proportional to some known quantity x i {\\displaystyle x_{i}} so that p i = x i \u2211 i = 1 N x i {\\displaystyle p_{i}={\\frac {x_{i}}{\\sum _{i=1}^{N}x_{i}}}} . : 97 One of the cases this occurs in, as developed by Hanson and Hurwitz in 1943, is when we have several clusters of units, each with a different (known upfront) number of units, then each cluster can be selected with a probability that is proportional to the number of units inside it. : 250 So, for example, if we have 3 clusters with 10, 20 and 30 units each, then the chance of selecting the first cluster will be 1/6, the second would be 1/3, and the third cluster will be 1/2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Expectancy is defined as the individual's subjectively held probability that a given action will lead to a given outcome. It can range from zero to one, with one representing 100% confidence in the outcome. For example, a person may entertain a given level of belief that they can make a foul shot in basketball or that an additional hour of study will improve their grade on an examination.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For each input command, a state-graph (or statetable or extended finite state automaton) is defined that provides a plan (or procedure for making a plan) for accomplishing the commanded task. The input command selects (or causes to be generated) an appropriate state-table, the execution of which generates a series of output commands to units at the next lower echelon. The library of state-tables contains a set of statesensitive procedural rules that identify all the task branching conditions and specify the corresponding state transition and output command parameters.The result of step 3 is that each organizational unit has for each input command a state-table of ordered production rules, each suitable for execution by an extended finite state automaton (FSA).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function values are maximized. In contrast to global maxima, which refers to the largest outputs of a function, arg max refers to the inputs, or arguments, at which the function outputs are as large as possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to explain the verifier-based definition of NP, consider the subset sum problem: Assume that we are given some integers, {\u22127, \u22123, \u22122, 5, 8}, and we wish to know whether some of these integers sum up to zero. Here the answer is \"yes\", since the integers {\u22123, \u22122, 5} corresponds to the sum (\u22123) + (\u22122) + 5 = 0. To answer whether some of the integers add to zero we can create an algorithm that obtains all the possible subsets. As the number of integers that we feed into the algorithm becomes larger, both the number of subsets and the computation time grows exponentially.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, let M be a G-module.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable. This sort of function usually comes in linear regression, where the coefficients are called regression coefficients. However, they also occur in various types of linear classifiers (e.g. logistic regression, perceptrons, support vector machines, and linear discriminant analysis), as well as in various other models, such as principal component analysis and factor analysis. In many of these models, the coefficients are referred to as \"weights\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociolinguistics, a register is a variety of language used for a particular purpose or particular communicative situation. For example, when speaking officially or in a public setting, an English speaker may be more likely to follow prescriptive norms for formal usage than in a casual setting, for example, by pronouncing words ending in -ing with a velar nasal instead of an alveolar nasal (e.g., walking rather than walkin'), choosing words that are considered more \"formal\" (such as father vs. dad or child vs. kid), and refraining from using words considered nonstandard, such as ain't and y'all. As with other types of language variation, there tends to be a spectrum of registers rather than a discrete set of obviously distinct varieties\u2014numerous registers can be identified, with no clear boundaries between them. Discourse categorization is a complex problem, and even according to the general definition of register given above (language variation defined by use rather than user), there are cases where other kinds of language variation, such as regional or age dialect, overlap.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "According to Paul A. Sabatier, the model has \"outlived its usefulness\" and should be replaced. The model's issues have led to a paradoxical situation in which current research and updated versions of the model continue to rely on the framework created by Anderson. But the very concept of the stages model has been discredited, which attacks the cycle's status as a heuristic.Due to these problems, alternative and newer versions of the model have aimed to create a more comprehensive view of the policy cycle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "748 If random vector X is elliptically distributed, then so is DX for any matrix D with full row rank. Thus any linear combination of the components of X is elliptical (though not necessarily with the same elliptical distribution), and any subset of X is elliptical. : p. 748", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included. Dilworth (1940) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts.The axioms defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom, antimatroids are defined instead by an anti-exchange axiom, from which their name derives. Antimatroids can be viewed as a special case of greedoids and of semimodular lattices, and as a generalization of partial orders and of distributive lattices. Antimatroids are equivalent, by complementation, to convex geometries, a combinatorial abstraction of convex sets in geometry. Antimatroids have been applied to model precedence constraints in scheduling problems, potential event sequences in simulations, task planning in artificial intelligence, and the states of knowledge of human learners.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Angles CBD and FBA are both right angles; therefore angle ABD equals angle FBC, since both are the sum of a right angle and angle ABC. Since AB is equal to FB, BD is equal to BC and angle ABD equals angle FBC, triangle ABD must be congruent to triangle FBC. Since A-K-L is a straight line, parallel to BD, then rectangle BDLK has twice the area of triangle ABD because they share the base BD and have the same altitude BK, i.e., a line normal to their common base, connecting the parallel lines BD and AL. (lemma 2) Since C is collinear with A and G, and this line is parallel to FB, then square BAGF must be twice in area to triangle FBC.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius r {\\displaystyle r} . This number is approximated by the area of the circle, so the real problem is to accurately bound the error term describing how the number of points differs from the area. The first progress on a solution was made by Carl Friedrich Gauss, hence its name.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below. For example, a square basic polygon results in the well-known polyominoes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spite of its apparently paradoxical nature, the phenomenon is real, and can be explained as a consequence of the general mathematical properties of social networks. The mathematics behind this are directly related to the arithmetic-geometric mean inequality and the Cauchy\u2013Schwarz inequality.Formally, Feld assumes that a social network is represented by an undirected graph G = (V, E), where the set V of vertices corresponds to the people in the social network, and the set E of edges corresponds to the friendship relation between pairs of people. That is, he assumes that friendship is a symmetric relation: if x is a friend of y, then y is a friend of x. The friendship between x and y is therefore modeled by the edge {x, y}, and the number of friends an individual has corresponds to a vertex's degree. The average number of friends of a person in the social network is therefore given by the average of the degrees of the vertices in the graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is one example where some upper bound helps in proving lower bounds; the construction of a circuit given by Baur and Strassen implies a lower bound for more general polynomials. The lack of ability to prove lower bounds brings us to consider simpler models of computation. Some examples are: monotone circuits (in which all the field elements are nonnegative real numbers), constant depth circuits, and multilinear circuits (in which every gate computes a multilinear polynomial). These restricted models have been studied extensively and some understanding and results were obtained.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, the no low-energy trivial state (NLTS) conjecture is a precursor to a quantum PCP theorem (qPCP) and posits the existence of families of Hamiltonians with all low-energy states of non-trivial complexity. An NLTS proof would be a consequence of one aspect of qPCP problems \u2013 the inability to certify an approximation of local Hamiltonians via NP completeness. In other words, an NLTS proof would be one consequence of the QMA complexity of qPCP problems. On a high level, if proved, NLTS would be one property of the non-Newtonian complexity of quantum computation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of Metrics that the QA & UX Manager work with, this task mainly is about collecting and analyze data an about game and gamer activity in relation to a particular game. In terms of the communication characterized parts of the work the QA & UX Manager do, this is often done in relation with meetings with the development team and where the QA & UX Manager pass on his or her knowledge and data to the development team. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to qualify for protection, a work must be an expression with a degree of originality, and it must be in a fixed medium, such as written down on paper or recorded digitally. The idea itself is not protected. That is, a copy of someone else's original idea is not infringing unless it copies that person's unique, tangible expression of the idea. Some of these limitations, especially regarding what qualifies as original, are embodied only in case law (judicial precedent), rather than in statutes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula c q ( n ) = \u2211 1 \u2264 a \u2264 q ( a , q ) = 1 e 2 \u03c0 i a q n , {\\displaystyle c_{q}(n)=\\sum _{1\\leq a\\leq q \\atop (a,q)=1}e^{2\\pi i{\\tfrac {a}{q}}n},} where (a, q) = 1 means that a only takes on values coprime to q. Srinivasa Ramanujan mentioned the sums in a 1918 paper. In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently large odd number is the sum of three primes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the example above, the algorithm was guided by the conditional expectation of a random variable F {\\displaystyle F} . In some cases, instead of an exact conditional expectation, an upper bound (or sometimes a lower bound) on some conditional expectation is used instead. This is called a pessimistic estimator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model theory, definable sets are important objects of study. For instance, in N {\\displaystyle \\mathbb {N} } the formula \u2200 u \u2200 v ( \u2203 w ( x \u00d7 w = u \u00d7 v ) \u2192 ( \u2203 w ( x \u00d7 w = u ) \u2228 \u2203 w ( x \u00d7 w = v ) ) ) \u2227 x \u2260 0 \u2227 x \u2260 1 {\\displaystyle \\forall u\\forall v(\\exists w(x\\times w=u\\times v)\\rightarrow (\\exists w(x\\times w=u)\\lor \\exists w(x\\times w=v)))\\land x\\neq 0\\land x\\neq 1} defines the subset of prime numbers, while the formula \u2203 y ( 2 \u00d7 y = x ) {\\displaystyle \\exists y(2\\times y=x)} defines the subset of even numbers. In a similar way, formulas with n free variables define subsets of M n {\\displaystyle {\\mathcal {M}}^{n}} . For example, in a field, the formula y = x \u00d7 x {\\displaystyle y=x\\times x} defines the curve of all ( x , y ) {\\displaystyle (x,y)} such that y = x 2 {\\displaystyle y=x^{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The U.S. Securities and Exchange Commission issued a statement in 1984 with the goal of reminding companies that securities fraud also applies to \"statements that can reasonably be expected to reach investors and the trading markets\".Several companies have been accused in court of using knowingly false announcements to gain market advantage. In 1969, the United States Justice Department accused IBM of doing this in the case United States v. IBM.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This generalized definition implies that the above-mentioned geometric entities are a special kind of vectors, as they are elements of a special kind of vector space called Euclidean space. This particular article is about vectors strictly defined as arrows in Euclidean space. When it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or Euclidean vectors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, the current non-integer solution is no longer feasible to the relaxation. This process is repeated until an optimal integer solution is found.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Its worst-case roundoff errors grow asymptotically as at most O(\u03b5 log n), where \u03b5 is the machine precision (assuming a fixed condition number, as discussed below). In comparison, the naive technique of accumulating the sum in sequence (adding each xi one at a time for i = 1, ..., n) has roundoff errors that grow at worst as O(\u03b5n). Kahan summation has a worst-case error of roughly O(\u03b5), independent of n, but requires several times more arithmetic operations. If the roundoff errors are random, and in particular have random signs, then they form a random walk and the error growth is reduced to an average of O ( \u03b5 log \u2061 n ) {\\displaystyle O(\\varepsilon {\\sqrt {\\log n}})} for pairwise summation.A very similar recursive structure of summation is found in many fast Fourier transform (FFT) algorithms, and is responsible for the same slow roundoff accumulation of those FFTs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s, the revolution of the personal computer and the popularity of computer bulletin board systems (BBSes) (accessed via modem) created an influx of tech-savvy users. These BBSes became popular for computer hackers and others interested in the technology, and served as a medium for previously scattered independent phone phreaks to share their discoveries and experiments. This not only led to unprecedented collaboration between phone phreaks, but also spread the notion of phreaking to others who took it upon themselves to study, experiment with, or exploit the telephone system. This was also at a time when the telephone company was a popular subject of discussion in the US, as the monopoly of AT&T Corporation was forced into divestiture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained code in data storage systems. Some signals are more prone to error than others as the physics of the communication channel or storage medium constrains the repertoire of signals that can be used reliably.Common line encodings are unipolar, polar, bipolar, and Manchester code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are differing views as to exactly what phonemes are and how a given language should be analyzed in phonemic (or phonematic) terms. However, a phoneme is generally regarded as an abstraction of a set (or equivalence class) of speech sounds (phones) that are perceived as equivalent to each other in a given language. For example, the English k sounds in the words kill and skill are not identical (as described below), but they are distributional variants of a single phoneme /k/.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function f ( x ) {\\displaystyle \\displaystyle f(x)} f ( x ) = \u2016 A x \u2212 b \u2016 2 , {\\displaystyle \\displaystyle f(x)=\\|Ax-b\\|^{2},} the minimum of f {\\displaystyle f} is obtained when the gradient is 0: \u2207 x f = 2 A T ( A x \u2212 b ) = 0 {\\displaystyle \\nabla _{x}f=2A^{T}(Ax-b)=0} .Whereas linear conjugate gradient seeks a solution to the linear equation A T A x = A T b {\\displaystyle \\displaystyle A^{T}Ax=A^{T}b} , the nonlinear conjugate gradient method is generally used to find the local minimum of a nonlinear function using its gradient \u2207 x f {\\displaystyle \\nabla _{x}f} alone. It works when the function is approximately quadratic near the minimum, which is the case when the function is twice differentiable at the minimum and the second derivative is non-singular there. Given a function f ( x ) {\\displaystyle \\displaystyle f(x)} of N {\\displaystyle N} variables to minimize, its gradient \u2207 x f {\\displaystyle \\nabla _{x}f} indicates the direction of maximum increase.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Gauss's inequality (or the Gauss inequality) gives an upper bound on the probability that a unimodal random variable lies more than any given distance from its mode. Let X be a unimodal random variable with mode m, and let \u03c4 2 be the expected value of (X \u2212 m)2. (\u03c4 2 can also be expressed as (\u03bc \u2212 m)2 + \u03c3 2, where \u03bc and \u03c3 are the mean and standard deviation of X.) Then for any positive value of k, Pr ( | X \u2212 m | > k ) \u2264 { ( 2 \u03c4 3 k ) 2 if k \u2265 2 \u03c4 3 1 \u2212 k \u03c4 3 if 0 \u2264 k \u2264 2 \u03c4 3 . {\\displaystyle \\Pr(|X-m|>k)\\leq {\\begin{cases}\\left({\\frac {2\\tau }{3k}}\\right)^{2}&{\\text{if }}k\\geq {\\frac {2\\tau }{\\sqrt {3}}}\\\\1-{\\frac {k}{\\tau {\\sqrt {3}}}}&{\\text{if }}0\\leq k\\leq {\\frac {2\\tau }{\\sqrt {3}}}.\\end{cases}}} The theorem was first proved by Carl Friedrich Gauss in 1823.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sometimes the stress of the 0 is made different from a letter o in some way, although many fonts do not do this.High-quality typesetting generally prefers text figures in body text: they integrate better with lowercase letters and small capitals, unlike runs of lining figures. Lining figures are called for in all-capitals settings (hence the alternative name titling figures), and may work better in tables and spreadsheets. Although many conventional typefaces have both types of numerals in full, early digital fonts only had one or the other (with the exception of those used by professional printers).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For \u03bd = 1 {\\displaystyle \\nu =1} the Student's t distribution t \u03bd {\\displaystyle t_{\\nu }} becomes the standard Cauchy distribution, whereas for \u03bd \u2192 \u221e {\\displaystyle \\nu \\rightarrow \\infty } it becomes the standard normal distribution N ( 0 , 1 ) {\\displaystyle N(0,1)} . The Student's t-distribution plays a role in a number of widely used statistical analyses, including Student's t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. In the form of the location-scale t-distribution l s t ( \u03bc , \u03c4 2 , \u03bd ) {\\displaystyle lst(\\mu ,\\tau ^{2},\\nu )} it generalizes the normal distribution and also arises in the Bayesian analysis of data from a normal family as a compound distribution when marginalizing over the variance parameter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An incomplete Cholesky factorization is given by a sparse lower triangular matrix K that is in some sense close to L. The corresponding preconditioner is KK*. One popular way to find such a matrix K is to use the algorithm for finding the exact Cholesky decomposition in which K has the same sparsity pattern as A (any entry of K is set to zero if the corresponding entry in A is also zero). This gives an incomplete Cholesky factorization which is as sparse as the matrix A.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s, specialized computers were released where two computers that each had their own memory controller could be networked at such a low level that the software run could use the memory, or CPU of either computer as if they were one unit. With AMD's release of the Opteron, and Intel's corresponding CPU, systems that share more than one memory controller in a single system have become common in applications that require the power of more than one common desktop. For these systems schemes like non-uniform memory architecture are used.Channels are the highest-level structure at the local memory controller level. Modern computers can have two, three or even more channels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language. Equivalently, a formal language is recursive if there exists a Turing machine that, when given a finite sequence of symbols as input, always halts and accepts it if it belongs to the language and halts and rejects it otherwise. In Theoretical computer science, such always-halting Turing machines are called total Turing machines or algorithms (Sipser 1997).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to understand the public's opinion on youth marketing, one must be able to understand the experiences that each generation has been exposed to while growing up. Generation Y is very similar to the baby boomer generation especially at different points in life. So it is essential to see what experiences each generation has experienced while growing up. But different formative experiences affect each person of Generation Y. For example, the events that made the biggest impression on members of Generation Y who graduated from school in 2000 were Columbine, the war in Kosovo, and Princess Diana's death.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The written test is usually done at a computerized learning center and results are available immediately. The oral and practical exams include questions about common rigging practices. The practical test consists of inspecting and repacking 20 reserves, along with hand sewing and a simple machine-sewn patch on a canopy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Russian Federation, a state secret (\u0413\u043e\u0441\u0443\u0434\u0430\u0440\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0442\u0430\u0439\u043d\u0430) is information protected by the state on its military, foreign policy, economic, intelligence, counterintelligence, operational and investigative and other activities, dissemination of which could harm state security.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909.It is sometimes called the Jeffreys distance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found. They can include constrained problems and multimodal problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This scheme, a type of virtual memory, allows in-memory data not currently in use to be moved to secondary storage and back in a way which is transparent to applications, to increase overall memory capacity. On some systems, a request for virtual storage may allocate a block of virtual addresses for which no page frames have been assigned, and the system will only assign and initialize page frames when page faults occur. On some systems a guard page may be used, either for error detection or to automatically grow data structures. On some systems, the page fault mechanism is also used for executable space protection such as W^X.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "295). Skolem's paradox is that every countable axiomatisation of set theory in first-order logic, if it is consistent, has a model that is countable. This appears contradictory because it is possible to prove, from those same axioms, a sentence that intuitively says (or that precisely says in the standard model of the theory) that there exist sets that are not countable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, bitstreams are not used directly to encode bytestreams; a communication channel may use a signalling method that does not directly translate to bits (for instance, by transmitting signals of multiple frequencies) and typically also encodes other information such as framing and error correction together with its data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, neural networks have generated a great deal of interest by outperforming traditional methods on longstanding problems across many fields. Machine learning, and by extension neural networks, have been used in many facets of MRI \u2014 for instance, speeding up image reconstruction, or improving reconstruction quality when working with a lack of data. Neural networks have also been used in motion artifact correction thanks to their ability to learn visual information from data, as well as infer underlying, latent representations in data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the director of the Cybersecurity and Infrastructure Security Agency (CISA), Jen Easterly, described the exploit as \"one of the most serious I've seen in my entire career, if not the most serious\", explaining that hundreds of millions of devices were affected and advising vendors to prioritize software updates. Civilian agencies contracted by the United States government had until 24 December 2021 to patch vulnerabilities. On 4 January, the Federal Trade Commission (FTC) stated its intent to pursue companies that fail to take reasonable steps to update used Log4j software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "decoding, determining the probability of a given label sequence Y {\\displaystyle Y} given X {\\displaystyle X} . inference, determining the most likely label sequence Y {\\displaystyle Y} given X {\\displaystyle X} .The conditional dependency of each Y i {\\displaystyle Y_{i}} on X {\\displaystyle X} is defined through a fixed set of feature functions of the form f ( i , Y i \u2212 1 , Y i , X ) {\\displaystyle f(i,Y_{i-1},Y_{i},X)} , which can be thought of as measurements on the input sequence that partially determine the likelihood of each possible value for Y i {\\displaystyle Y_{i}} . The model assigns each feature a numerical weight and combines them to determine the probability of a certain value for Y i {\\displaystyle Y_{i}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, as the general population has become more e-mail savvy, the lines have blurred somewhat between face-to-face and e-mail communication. E-mail is now thought of as a verbal tool, with its capacity to enable immediate feedback, leverage natural language, and embed emotion via acronyms and emoticons. However, there is a downside of e-mail: volume overload. Emails often have large unnecessary quantities of information which is non-job essential and/or spam.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, this factorization is unique up to the order of the factors. Although integer factorization is a sort of inverse to multiplication, it is much more difficult algorithmically, a fact which is exploited in the RSA cryptosystem to implement public-key cryptography. Polynomial factorization has also been studied for centuries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the theory of Latin squares is an active research area with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Problems posed here appeared in, for instance, the Loops (Prague) conferences and the Milehigh (Denver) conferences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the distributed memory model, the usual approach is to partition the vertex set V {\\displaystyle V} of the graph into p {\\displaystyle p} sets V 0 , \u2026 , V p \u2212 1 {\\displaystyle V_{0},\\dots ,V_{p-1}} . Here, p {\\displaystyle p} is the amount of available processing elements (PE). The vertex set partitions are then distributed to the PEs with matching index, additionally to the corresponding edges. Every PE has its own subgraph representation, where edges with an endpoint in another partition require special attention.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most EQA schemes, laboratories receive scores for their results. The most popular score is the Z-score, also called standard deviation index (SDI). The score is given per analyte and per test item.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(I3) If A {\\displaystyle A} and B {\\displaystyle B} are two independent sets (i.e., each set is independent) and A {\\displaystyle A} has more elements than B {\\displaystyle B} , then there exists x \u2208 A \u2216 B {\\displaystyle x\\in A\\backslash B} such that B \u222a { x } {\\displaystyle B\\cup \\{x\\}} is in I {\\displaystyle {\\mathcal {I}}} . This is sometimes called the augmentation property or the independent set exchange property.The first two properties define a combinatorial structure known as an independence system (or abstract simplicial complex). Actually, assuming (I2), property (I1) is equivalent to the fact that at least one subset of E {\\displaystyle E} is independent, i.e., I \u2260 \u2205 {\\displaystyle {\\mathcal {I}}\\neq \\emptyset } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The emergence of affordable consumer telephony devices with advanced features such as last number redial and preprogrammed numbers paralleled phone industry deregulation and the Breakup of the Bell System in the early 1980s. While Speed dial technology had been invented nearly a decade earlier by Bell Labs, it did not become a consumer product until deregulation. Previously, connecting non-AT&T handsets was generally prohibited and most phones were leased devices (similar to residential broadband routers).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The main cabinet of the minicomputer was the 6000 CPU, housing the computer's main Z80A microprocessor and nine expansion slots (none populated by default); the 6000 CPU-1, with a second Z80A processor seven expansion slots and a floppy disk drive; and the 6000 CPU-2, which has two such disk drives and a third Z80A processor. Each cabinet houses 64 KB of RAM with parity. Optional was a video board, additional disk controllers, a mass-storage controller board for hard disks and tape drives (the latter making use of the board's integrated parallel interface), a dual-channel RS-232 serial interface board, and a serial communication interface board with support for asynchronous, synchronous, and bit-oriented communications protocols.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to avoid this problem, additional framing bits are added to either end of every byte, typically one bit on either side known as the \"start and stop bits\". This guarantees at least one 1-to-0 transition for every byte, more than enough to keep the clocks locked. However, these bits also expand every 8 bits of data (one byte) to 10 bits, an overhead of 20%.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical computer science, analysis of Boolean functions is the study of real-valued functions on { 0 , 1 } n {\\displaystyle \\{0,1\\}^{n}} or { \u2212 1 , 1 } n {\\displaystyle \\{-1,1\\}^{n}} (such functions are sometimes known as pseudo-Boolean functions) from a spectral perspective. The functions studied are often, but not always, Boolean-valued, making them Boolean functions. The area has found many applications in combinatorics, social choice theory, random graphs, and theoretical computer science, especially in hardness of approximation, property testing, and PAC learning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some system distributions, sudo has largely supplanted the default use of a distinct superuser login for administrative tasks, most notably in some Linux distributions as well as Apple's macOS. This allows for more secure logging of admin commands and prevents some exploits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In case of any failure, the destination switches onto the alternative path/route. This architecture is simple for implementation and results fast restoration. Its major drawback is the wastage of bandwidth, since no traffic travels through the redundant path.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In politics, rankings focus on the comparison of economic, social, environmental and governance performance of countries. In relation to credit standing, the ranking of a security refers to where that particular security would stand in a wind up of the issuing company, i.e., its seniority in the company's capital structure. For instance, capital notes are subordinated securities; they would rank behind senior debt in a wind up. In other words, the holders of senior debt would be paid out before subordinated debt holders received any funds.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to accurately measure longitude, the precise time of a sextant sighting (down to the second, if possible) must be recorded. Each second of error is equivalent to 15 seconds of longitude error, which at the equator is a position error of .25 of a nautical mile, about the accuracy limit of manual celestial navigation. The spring-driven marine chronometer is a precision timepiece used aboard ship to provide accurate time for celestial observations. A chronometer differs from a spring-driven watch principally in that it contains a variable lever device to maintain even pressure on the mainspring, and a special balance designed to compensate for temperature variations.A spring-driven chronometer is set approximately to Greenwich mean time (GMT) and is not reset until the instrument is overhauled and cleaned, usually at three-year intervals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Furthermore, they may develop undesirable emergent goals that may be hard to detect before the system is in deployment, where it faces new situations and data distributions.Today, these problems affect existing commercial systems such as language models, robots, autonomous vehicles, and social media recommendation engines. Some AI researchers argue that more capable future systems will be more severely affected since these problems partially result from the systems being highly capable.Many leading AI scientists such as Geoffrey Hinton and Stuart Russell argue that AI is approaching superhuman capabilities and could endanger human civilization if misaligned.AI alignment is a subfield of AI safety, the study of how to build safe AI systems. Other subfields of AI safety include robustness, monitoring, and capability control. Research challenges in alignment include instilling complex values in AI, developing honest AI, scalable oversight, auditing and interpreting AI models, and preventing emergent AI behaviors like power-seeking. Alignment research has connections to interpretability research, (adversarial) robustness, anomaly detection, calibrated uncertainty, formal verification, preference learning, safety-critical engineering, game theory, algorithmic fairness, and the social sciences, among others.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The meaning of a sentence is conveyed if the truth conditions for the sentence are understood. Additionally, there are many sentences that are understood although their truth condition is uncertain. One popular argument for this view is that some sentences are necessarily true \u2014 that is, they are true whatever happens to obtain. All such sentences have the same truth conditions, but arguably do not thereby have the same meaning. Likewise, the sets {x: x is alive} and {x: x is alive and x is not a rock} are identical \u2014 they have precisely the same members \u2014 but presumably the sentences \"Nixon is alive\" and \"Nixon is alive and is not a rock\" have different meanings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Rage 128 used an 8 kB buffer to store texels that were used by the 3D engine. In order to improve performance even more, ATI engineers also incorporated an 8 KB pixel cache used to write pixels back to the frame buffer. 8 million transistors, 0.25 micrometer fabrication 3D Feature Set Hardware support for vertex arrays, fog and fog table support Alpha blending, vertex and Z-based fog, video textures, texture lighting Single clock bilinear and trilinear texture filtering and texture compositing Perspective-correct mip-mapped texturing with chroma-key support Vertex and Z-based reflections, shadows, spotlights, 1.00 biasing Hidden surface removal using 16, 24, or 32-bit Z-buffering Gouraud and specular shaded polygons Line and edge anti-aliasing, bump mapping, 8-bit stencil buffer 250 MHz RAMDAC, AGP 2\u00d7", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An example is Google's PageRank algorithm. The principal eigenvector of a modified adjacency matrix of the World Wide Web graph gives the page ranks as its components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel computing, the Geometric Arithmetic Parallel Processor (GAPP), invented by Polish mathematician W\u0142odzimierz Holszty\u0144ski in 1981, was patented by Martin Marietta and is now owned by Silicon Optix, Inc. The GAPP's network topology is a mesh-connected array of single-bit SIMD processing elements (PEs), where each PE can communicate with its neighbor to the north, east, south, and west. Each cell has its own memory. The space of addresses is the same for all cells. The data travels from the cell memories to the cell registers, and in the opposite direction, in parallel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Lazard's universal ring is a ring introduced by Michel Lazard in Lazard (1955) over which the universal commutative one-dimensional formal group law is defined. There is a universal commutative one-dimensional formal group law over a universal commutative ring defined as follows. We let F ( x , y ) {\\displaystyle F(x,y)} be x + y + \u2211 i , j c i , j x i y j {\\displaystyle x+y+\\sum _{i,j}c_{i,j}x^{i}y^{j}} for indeterminates c i , j {\\displaystyle c_{i,j}} , and we define the universal ring R to be the commutative ring generated by the elements c i , j {\\displaystyle c_{i,j}} , with the relations that are forced by the associativity and commutativity laws for formal group laws.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general of any finite dimension. Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.) Momentum space is the set of all momentum vectors p a physical system can have; the momentum vector of a particle corresponds to its motion, with units of \u22121.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The triples result in the graph shown in the given figure. One of the advantages of using Uniform Resource Identifiers (URIs) is that they can be dereferenced using the HTTP protocol. According to the so-called Linked Open Data principles, such a dereferenced URI should result in a document that offers further data about the given URI.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For an input x {\\displaystyle \\mathbf {x} } from source X {\\displaystyle X} , only the syndrome given by s = H x {\\displaystyle \\mathbf {s} =\\mathbf {H} \\mathbf {x} } is transmitted, which is 3 bits. With received y {\\displaystyle \\mathbf {y} } and s {\\displaystyle \\mathbf {s} } , suppose there are two inputs x 1 {\\displaystyle \\mathbf {x_{1}} } and x 2 {\\displaystyle \\mathbf {x_{2}} } with same syndrome s {\\displaystyle \\mathbf {s} } . That means H x 1 = H x 2 {\\displaystyle \\mathbf {H} \\mathbf {x_{1}} =\\mathbf {H} \\mathbf {x_{2}} } , which is H ( x 1 \u2212 x 2 ) = 0 {\\displaystyle \\mathbf {H} (\\mathbf {x_{1}} -\\mathbf {x_{2}} )=0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and n-ary form. Function symbols are used, together with constants and variables, to form terms. The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra). Theories with a non-empty set of equations are known as equational theories. The satisfiability problem for free theories is solved by syntactic unification; algorithms for the latter are used by interpreters for various computer languages, such as Prolog. Syntactic unification is also used in algorithms for the satisfiability problem for certain other equational theories, see Unification (computer science).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ")^{2}}}=\\prod \\limits _{k=1}^{n}{\\frac {n+k}{k}}{\\text{ for all }}n\\geq 0.} They are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle. The first few central binomial coefficients starting at n = 0 are: 1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ...; (sequence A000984 in the OEIS)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is called the Wooley integer semigroup and members of this semigroup are called Wooley integers. Similarly, the set of integers in W is itself a multiplicative semigroup. It is called the wild integer semigroup and members of this semigroup are called wild numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural languages, an indicative conditional is a conditional sentence such as \"If Leona is at home, she isn't in Paris\", whose grammatical form restricts it to discussing what could be true. Indicatives are typically defined in opposition to counterfactual conditionals, which have extra grammatical marking which allows them to discuss eventualities which are no longer possible. Indicatives are a major topic of research in philosophy of language, philosophical logic, and linguistics. Open questions include which logical operation indicatives denote, how such denotations could be composed from their grammatical form, and the implications of those denotations for areas including metaphysics, psychology of reasoning, and philosophy of mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a weighted median of a sample is the 50% weighted percentile. It was first proposed by F. Y. Edgeworth in 1888. Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform statistical weights related to, e.g., varying precision measurements in the sample.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\mathbf {\\lambda } _{j}=-\\mathbf {J} ^{-1}\\left.} After each iteration, the unconstrained particle positions are updated using x ^ i ( t + \u0394 t ) \u2190 x ^ i ( t + \u0394 t ) + \u2211 k = 1 n \u03bb k \u2202 \u03c3 k \u2202 x i ( \u0394 t ) 2 m i \u2212 1 . {\\displaystyle {\\hat {\\mathbf {x} }}_{i}(t+\\Delta t)\\leftarrow {\\hat {\\mathbf {x} }}_{i}(t+\\Delta t)+\\sum _{k=1}^{n}\\lambda _{k}{\\frac {\\partial \\sigma _{k}}{\\partial \\mathbf {x} _{i}}}\\left(\\Delta t\\right)^{2}m_{i}^{-1}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Mcgee and Prusak (1993) noted that core competencies are not what an organization owns, but rather what it knows.Bartlett (1999) indicates that empowerment is not possible in an autocratic organization, that networks cannot be sustained in fixed hierarchical structure, and that learning is not possible in an environment constrained by rigid policies and procedures. Davenport (1997) used an information ecology approach, in which he explored the use and abuse of information in the context of infighting, resource hoarding, and political battles as well as appropriate management in such a context. Simard (2000) states that knowledge is inextricably linked to organizational mandates. Some providers strive for objectivity, others selectively disseminate information and knowledge, while still others use information to further their agenda. Users must understand that information is not innocent, and that all information is not created equal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A fractional weighted version of the conjecture, posed by Jack Edmonds and Rick Giles, was refuted by Alexander Schrijver.The Lucchesi\u2013Younger theorem states that the minimum size of a dijoin, in any given directed graph, equals the maximum number of disjoint dicuts that can be found in the graph. The minimum weight dijoin in a weighted graph can be found in polynomial time, and is a special case of the submodular flow problem.In planar graphs, dijoins and feedback arc sets are dual concepts. The dual graph of a directed graph, embedded in the plane, is a graph with a vertex for each face of the given graph, and a dual edge between two dual vertices when the corresponding two faces are separated by an edge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where V = W {\\displaystyle V=W} , a linear map is called a linear endomorphism. Sometimes the term linear operator refers to this case, but the term \"linear operator\" can have different meanings for different conventions: for example, it can be used to emphasize that V {\\displaystyle V} and W {\\displaystyle W} are real vector spaces (not necessarily with V = W {\\displaystyle V=W} ), or it can be used to emphasize that V {\\displaystyle V} is a function space, which is a common convention in functional analysis. Sometimes the term linear function has the same meaning as linear map, while in analysis it does not. A linear map from V to W always maps the origin of V to the origin of W. Moreover, it maps linear subspaces in V onto linear subspaces in W (possibly of a lower dimension); for example, it maps a plane through the origin in V to either a plane through the origin in W, a line through the origin in W, or just the origin in W. Linear maps can often be represented as matrices, and simple examples include rotation and reflection linear transformations. In the language of category theory, linear maps are the morphisms of vector spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The primary achievement of ludics is the discovery of a relationship between two natural, but distinct notions of type, or proposition. The first view, which might be termed the proof-theoretic or Gentzen-style interpretation of propositions, says that the meaning of a proposition arises from its introduction and elimination rules. Focalization refines this viewpoint by distinguishing between positive propositions, whose meaning arises from their introduction rules, and negative propositions, whose meaning arises from their elimination rules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In solvent extraction, a distribution ratio is often quoted as a measure of how well-extracted a species is. The distribution ratio (Kd) is equal to the concentration of a solute in the organic phase divided by its concentration in the aqueous phase. Depending on the system, the distribution ratio can be a function of temperature, the concentration of chemical species in the system, and a large number of other parameters. Note that D is related to the \u0394G of the extraction process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In standard gematria (mispar hechrechi), each letter is given a numerical value between 1 and 400, as shown in the following table. In mispar gadol, the five final letters are given their own values, ranging from 500 to 900. It is possible that this well-known cipher was used to conceal other more hidden ciphers in Jewish texts. For instance, a scribe may discuss a sum using the 'standard gematria' cipher, but may intend the sum to be checked with a different secret cipher. A mathematical formula for finding a letter's corresponding number in mispar gadol is: f ( x ) = 10 \u230a x \u2212 1 9 \u230b \u00d7 ( ( x \u2212 1 mod 9 ) + 1 ) , {\\displaystyle f(x)=10^{\\left\\lfloor {\\frac {x-1}{9}}\\right\\rfloor }\\times ((x-1\\mod 9)+1),} where x is the position of the letter in the language letters index (regular order of letters), and the floor and modulo functions are used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, test design is the activity of deriving and specifying test cases from test conditions to test software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, a page fault may indicate a software bug, which can be prevented by using memory protection as one of key benefits of an MMU: an operating system can use it to protect against errant programs by disallowing access to memory that a particular program should not have access to. Typically, an operating system assigns each program its own virtual address space.An paged MMU also mitigates the problem of external fragmentation of memory. After blocks of memory have been allocated and freed, the free memory may become fragmented (discontinuous) so that the largest contiguous block of free memory may be much smaller than the total amount.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of equality constraints, this theorem is proved with the calculus of variations and Lagrange multipliers. The constraints can be written as \u222b \u2212 \u221e \u221e f j ( x ) p ( x ) d x = a j {\\displaystyle \\int _{-\\infty }^{\\infty }f_{j}(x)p(x)dx=a_{j}} We consider the functional J ( p ) = \u222b \u2212 \u221e \u221e p ( x ) ln \u2061 p ( x ) d x \u2212 \u03b7 0 ( \u222b \u2212 \u221e \u221e p ( x ) d x \u2212 1 ) \u2212 \u2211 j = 1 n \u03bb j ( \u222b \u2212 \u221e \u221e f j ( x ) p ( x ) d x \u2212 a j ) {\\displaystyle J(p)=\\int _{-\\infty }^{\\infty }p(x)\\ln {p(x)}dx-\\eta _{0}\\left(\\int _{-\\infty }^{\\infty }p(x)dx-1\\right)-\\sum _{j=1}^{n}\\lambda _{j}\\left(\\int _{-\\infty }^{\\infty }f_{j}(x)p(x)dx-a_{j}\\right)} where \u03b7 0 {\\displaystyle \\eta _{0}} and \u03bb j , j \u2265 1 {\\displaystyle \\lambda _{j},j\\geq 1} are the Lagrange multipliers. The zeroth constraint ensures the second axiom of probability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Optimizing the FSSE results in a compromise between fairness (especially avoiding scheduling starvation) and achieving high spectral efficiency. If the cost of each user is known, in terms of consumed resources per transferred information bit, the FSSE measure may be redefined to reflect proportional fairness. In a proportional fair system, this \"proportionally fair shared spectrum efficiency\" (or \"fairly shared radio resource cost\") is maximized. This policy is less fair since \"expensive\" users are given lower throughput than others, but still scheduling starvation is avoided.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All the preferences cast by voters are awarded the points associated with their rank position. Then, all the points for each option are tallied and the one with the most points is the winner. Where a few winners (W) are instead required following the count, the W highest-ranked options are selected. Positional voting is not only a means of identifying a single winner but also a method for converting sets of individual preferences (ranked ballots) into one collective and fully rank-ordered set. It is possible and legitimate for options to be tied in this resultant set; even in first place.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The circuit will not function when the path delay exceeds the clock cycle delay so modifying the circuit to remove the timing failure (and eliminate the critical path) is an important part of the logic design engineer's task. Critical path also defines the maximum delay in all the multiple register-to-register paths, and it must not be greater than the clock cycle time. After meeting the timing closure, one way to improve the circuit performance is to insert a register in between the combinational path of the critical path.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of calculus of variations in mathematics, the method of Lagrange multipliers on Banach spaces can be used to solve certain infinite-dimensional constrained optimization problems. The method is a generalization of the classical method of Lagrange multipliers as used to find extrema of a function of finitely many variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, Latent Dirichlet Allocation (LDA) is a Bayesian network (and, therefore, a generative statistical model) that explains a set of observations through unobserved groups, and each group explains why some parts of the data are similar. The LDA is an example of a Bayesian topic model. In this, observations (e.g., words) are collected into documents, and each word's presence is attributable to one of the document's topics. Each document will contain a small number of topics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On mechanical Dutch typewriters, there is a key that produces 'ij' (in a single letterspace, located directly to the right of the L). However, this is not the case on modern computer keyboards. In many word puzzles, such as Lingo, ij fills one square, but in others, such as Scrabble, ij fills two squares.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The examples within the position paper are just \"examples\" of current carrier practices for illustration purposes, but do not reflect any official Oftel regulation. The main networks often agree to unlock handsets for a charge, either at the end of a contract or, for prepaid handsets, after several months. Some Blackberry handsets supplied by Vodafone (e.g., Storm) are examples of a UK carrier not offering unlocking codes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A set of acronyms are commonly used: PMDr (premotor dorsal, rostral), PMDc, PMVr, PMVc. Some researchers use a different terminology. Field 7 or F7 denotes PMDr; F2 = PMDc; F5=PMVr; F4=PMVc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set of values of \u03b7 for which the function f X ( x ; \u03b7 ) {\\displaystyle f_{X}(x;\\eta )} is integrable is called the natural parameter space. It can be shown that the natural parameter space is always convex. A(\u03b7) is called the log-partition function because it is the logarithm of a normalization factor, without which f X ( x ; \u03b8 ) {\\displaystyle f_{X}(x;\\theta )} would not be a probability distribution: A ( \u03b7 ) = log \u2061 ( \u222b X h ( x ) exp \u2061 ( \u03b7 ( \u03b8 ) \u22c5 T ( x ) ) d x ) {\\displaystyle A(\\eta )=\\log \\left(\\int _{X}h(x)\\,\\exp(\\eta (\\theta )\\cdot T(x))\\,\\mathrm {d} x\\right)} The function A is important in its own right, because the mean, variance and other moments of the sufficient statistic T(x) can be derived simply by differentiating A(\u03b7). For example, because log(x) is one of the components of the sufficient statistic of the gamma distribution, E \u2061  {\\displaystyle \\operatorname {\\mathcal {E}} } can be easily determined for this distribution using A(\u03b7). Technically, this is true because K ( u \u2223 \u03b7 ) = A ( \u03b7 + u ) \u2212 A ( \u03b7 ) , {\\displaystyle K\\left(u\\mid \\eta \\right)=A(\\eta +u)-A(\\eta )\\,,} is the cumulant generating function of the sufficient statistic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted. For example, the numerical data 3.4, 5.1, 2.6, 7.3 are observed, the ranks of these data items would be 2, 3, 1 and 4 respectively. For example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, real trees (also called R {\\displaystyle \\mathbb {R} } -trees) are a class of metric spaces generalising simplicial trees. They arise naturally in many mathematical contexts, in particular geometric group theory and probability theory. They are also the simplest examples of Gromov hyperbolic spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, storefronts and aggregates have intervened to stop review bombs and delete the negative reviews. In February 2019, Rotten Tomatoes announced that it would no longer accept user reviews for a film until after its official release.In 2017, Valve added review histograms to Steam user review scores to show how these change over time; according to Valve's Alden Kroll, this can help a potential purchaser of a game recognize a short term review bomb that is not indicative of the game itself, compared to a game that has a long tail of bad reviews. Kroll said they did not want to silence the ability of users to leave reviews but recognized they needed to highlight phenomena like review bombs to aid customers. In March 2019, Valve stated that it would employ a new system to detect spikes of negative \"off-topic\" reviews on games: if it is determined that they were the result of a review bomb campaign, the time period will be flagged, and all reviews made during that period (whether negative or positive) will be excluded from the user rating displayed for a game.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Bareiss algorithm, named after Erwin Bareiss, is an algorithm to calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic; any divisions that are performed are guaranteed to be exact (there is no remainder). The method can also be used to compute the determinant of matrices with (approximated) real entries, avoiding the introduction of any round-off errors beyond those already present in the input.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 35678, 135678, 345678, and 1345678 are the patterns related to Braille pattern dots-23456, since the two additional dots of kantenji patterns 023456, 234567, and 0234567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This JNI interface pointer can be stored, but remains valid only in the current thread. Other threads must first call AttachCurrentThread() to attach themselves to the VM and obtain a JNI interface pointer. Once attached, a native thread works like a regular Java thread running within a native method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Foster's theorem, named after Gordon Foster, is used to draw conclusions about the positive recurrence of Markov chains with countable state spaces. It uses the fact that positive recurrent Markov chains exhibit a notion of \"Lyapunov stability\" in terms of returning to any state while starting from it within a finite time interval.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In networking, packets are the key foundation for scheduling. There are many different types of packet travelling around network core every day, and they are treated totally different. For example, voice and video packets have higher priority than normal packets. In order to manage and distribute packet effectively, network devices also use input queue to determine which packet will be transmitted first.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the counter-counter mode, the Cascaded Cipher uses full-strength AES-128 in counter mode to generate a secure key stream and supplies this key-stream to a reduced round Serpent also operating in counter mode to encrypt each plaintext block. To increase performance, each inner key stream block is reused several times to encrypt multiple blocks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In theory some measures of guarantee that an obtained solution solves the original problem with reasonable accuracy. Typically in applications only the first stage optimal solution x \u2217 {\\displaystyle x^{*}} has a practical value since almost always a \"true\" realization of the random data will be different from the set of constructed (generated) scenarios. Suppose \u03be {\\displaystyle \\xi } contains d {\\displaystyle d} independent random components, each of which has three possible realizations (for example, future realizations of each random parameters are classified as low, medium and high), then the total number of scenarios is K = 3 d {\\displaystyle K=3^{d}} . Such exponential growth of the number of scenarios makes model development using expert opinion very difficult even for reasonable size d {\\displaystyle d} . The situation becomes even worse if some random components of \u03be {\\displaystyle \\xi } have continuous distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Through her attempts to solve Fermat's Last Theorem, Germain developed a result now known as Germain's Theorem which states that if p is an odd prime and 2p + 1 is also prime, then p must divide x, y, or z. Otherwise, x n + y n \u2260 z n {\\textstyle x^{n}+y^{n}\\neq z^{n}} . This case where p does not divide x, y, or z is called the first case. Sophie Germain\u2019s work was the most progress achieved on Fermat\u2019s last theorem at that time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Next, set the first vector v1=u1. Then, we set u2=v2-proju1v2. This process is repeated to for k vectors, with the final vector being uk= vk-\u03a3(j=1)(k-1)projukvk.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Even if they are not words, morphemes can prime for complete words that include them. An example of this would be that the morpheme 'psych' can prime for the word 'psychology'. In support with further detail, when an individual processes a word sometimes that word can be affected when the prior word is linked semantically.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode, the general algorithm for building decision trees is: Check for the above base cases. For each attribute a, find the normalized information gain ratio from splitting on a. Let a_best be the attribute with the highest normalized information gain. Create a decision node that splits on a_best. Recurse on the sublists obtained by splitting on a_best, and add those nodes as children of node.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The edges forming the silhouette are extruded away from the light to construct the faces of the shadow volume. This volume must extend over the range of the entire visible scene; often the dimensions of the shadow volume are extended to infinity to accomplish this (see optimization below.) To form a closed volume, the front and back end of this extrusion must be covered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, given the neighbors N i {\\displaystyle N_{i}} of X i , X i {\\displaystyle X_{i},X_{i}} is independent of all other X j {\\displaystyle X_{j}} (Markov property). The main difference with a hidden Markov model is that neighborhood is not defined in 1 dimension but within a network, i.e. X i {\\displaystyle X_{i}} is allowed to have more than the two neighbors that it would have in a Markov chain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially order theory, a prefix ordered set generalizes the intuitive concept of a tree by introducing the possibility of continuous progress and continuous branching. Natural prefix orders often occur when considering dynamical systems as a set of functions from time (a totally-ordered set) to some phase space. In this case, the elements of the set are usually referred to as executions of the system. The name prefix order stems from the prefix order on words, which is a special kind of substring relation and, because of its discrete character, a tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A transition takes place to the next state as a result of a binary input 1 or 0 and the encoder's present output state. The encoding procedure is as follows. In general, the encoder outputs + level for a binary 1 input and a \u2212 level for a binary 0 input.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, a biased random walk on a graph is a time path process in which an evolving variable jumps from its current state to one of various potential new states; unlike in a pure random walk, the probabilities of the potential new states are unequal. Biased random walks on a graph provide an approach for the structural analysis of undirected graphs in order to extract their symmetries when the network is too complex or when it is not large enough to be analyzed by statistical methods. The concept of biased random walks on a graph has attracted the attention of many researchers and data companies over the past decade especially in the transportation and social networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In marketing, discriminant analysis was once often used to determine the factors which distinguish different types of customers and/or products on the basis of surveys or other forms of collected data. Logistic regression or other methods are now more commonly used. The use of discriminant analysis in marketing can be described by the following steps: Formulate the problem and gather data\u2014Identify the salient attributes consumers use to evaluate products in this category\u2014Use quantitative marketing research techniques (such as surveys) to collect data from a sample of potential customers concerning their ratings of all the product attributes. The data collection stage is usually done by marketing research professionals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Oxford Advanced Learner's Dictionary, the word alphabet is defined as \"a set of letters or symbols in a fixed order used for writing a language\". The YES \"alphabet\" is a list of Chinese character strokes in the order of \"\u31d0 \u31d5 \u31c5 \u31ce \u31e1 \u31cb \u31ca \u31cd \u31c8 \u31c6 \u31c7 \u31cc \u98de \u31c0 \u31d1 \u31d7 \u31de \u31c9 \u3123 \u31d9 \u31c4 \u31df \u31da \u31d3 \u31dc \u31db \u31e2 \u31d4 \u31cf \u31c2\". This stroke alphabet is built on the basis of Unicode CJK Strokes and the Standard of Chinese Character Bending Strokes of the GB13000.1 Character Set. There are totally 30 strokes, sorted by the standard basic strokes order of \u201cheng (\u6a6b, \u6a2a, \u4e00), ti (\u63d0, \u31c0), shu (\u8c4e, \u7ad6, \u4e28), pie (\u6487, \u4e3f), dian (\u9ede, \u70b9, \u4e36), na (\u637a, \u31cf)\u201d and the bending points order of \u201czhe (\u6298), wan (\u5f4e, \u5f2f) and gou (\u9264, \u94a9)\u201d.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this context, \"numeric\" means that the computer treats sequences of bits as binary numbers (base two numbers) and executes arithmetic operations like add, subtract, multiply, or divide. \"Logical\" refers to the Boolean logical operations of disjunction, conjunction, and negation between two sequences of bits, in which each bit in one sequence is simply compared to its counterpart in the other sequence. Programmers therefore have the option of working in and applying the rules of either numeric algebra or Boolean algebra as needed. A core differentiating feature between these families of operations is the existence of the carry operation in the first but not the second.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Phonetically palatalized consonants may vary in their exact realization. Some languages add semivowels before or after the palatalized consonant (onglides or offglides). In such cases, the vowel (especially a non-front vowel) following a palatalized consonant typically has a palatal onglide.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing a w-shingling is a set of unique shingles (therefore n-grams) each of which is composed of contiguous subsequences of tokens within a document, which can then be used to ascertain the similarity between documents. The symbol w denotes the quantity of tokens in each shingle selected, or solved for. The document, \"a rose is a rose is a rose\" can therefore be maximally tokenized as follows: (a,rose,is,a,rose,is,a,rose)The set of all contiguous sequences of 4 tokens (Thus 4=n, thus 4-grams) is { (a,rose,is,a), (rose,is,a,rose), (is,a,rose,is), (a,rose,is,a), (rose,is,a,rose) } Which can then be reduced, or maximally shingled in this particular instance to { (a,rose,is,a), (rose,is,a,rose), (is,a,rose,is) }.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, octic reciprocity is a reciprocity law relating the residues of 8th powers modulo primes, analogous to the law of quadratic reciprocity, cubic reciprocity, and quartic reciprocity. There is a rational reciprocity law for 8th powers, due to Williams. Define the symbol ( x p ) k {\\displaystyle \\left({\\frac {x}{p}}\\right)_{k}} to be +1 if x is a k-th power modulo the prime p and -1 otherwise. Let p and q be distinct primes congruent to 1 modulo 8, such that ( p q ) 4 = ( q p ) 4 = + 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements. In more technical terms, assuming the axiom of countable choice, a set is countable if its cardinality (the number of elements of the set) is not greater than that of the natural numbers. A countable set that is not finite is said to be countably infinite. The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not countable; for example the set of the real numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For each cell C {\\displaystyle C} , we let W ( C ) {\\displaystyle W(C)} be the sum of all W ( k ) {\\displaystyle W(k)} , where the sum is taken over all sampled k {\\displaystyle k} in the cell C {\\displaystyle C} . For each cell C {\\displaystyle C} , we let T ( C ) {\\displaystyle T(C)} be the auxiliary value for cell C {\\displaystyle C} , which is commonly called the \"benchmark target\" for cell C {\\displaystyle C} . Next, we compute a benchmark factor F ( C ) = T ( C ) / W ( C ) {\\displaystyle F(C)=T(C)/W(C)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One of the most widely used transmission system technologies in the Internet and the Public switched telephone network (PSTN) is synchronous optical networking (SONET). Also, transmission system is the medium through which data is transmitted from one point to another. Examples of common transmission systems people use everyday are: the internet, mobile networks, cordless cables, etc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a set B of vectors in a vector space V is called a basis (PL: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called basis vectors. Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B. In other words, a basis is a linearly independent spanning set. A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space. This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, family-wise error rate (FWER) is the probability of making one or more false discoveries, or type I errors when performing multiple hypotheses tests.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These two conditions are sufficient to ensure that all faces are alike and all vertices are alike. Note, however, that this definition does not work for abstract polytopes. A regular polytope can be represented by a Schl\u00e4fli symbol of the form {a, b, c, ..., y, z}, with regular facets as {a, b, c, ..., y}, and regular vertex figures as {b, c, ..., y, z}.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, loop variants are often taken to be non-negative integers, or even required to be so, but the requirement that every loop have an integer variant removes the expressive power of unbounded iteration from a programming language. Unless such a (formally verified) language allows a transfinite proof of termination for some other equally powerful construct such as a recursive function call, it is no longer capable of full \u03bc-recursion, but only primitive recursion. Ackermann's function is the canonical example of a recursive function that cannot be computed in a loop with an integer variant. In terms of their computational complexity, however, functions that are not primitive recursive lie far beyond the realm of what is usually considered tractable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is the number of successes in a series of n {\\displaystyle n} independent Bernoulli trials, where each trial has probability of success p {\\displaystyle p} . In binomial regression, the probability of a success is related to explanatory variables: the corresponding concept in ordinary regression is to relate the mean value of the unobserved response to explanatory variables. Binomial regression is closely related to binary regression: a binary regression can be considered a binomial regression with n = 1 {\\displaystyle n=1} , or a regression on ungrouped binary data, while a binomial regression can be considered a regression on grouped binary data (see comparison). Binomial regression models are essentially the same as binary choice models, one type of discrete choice model: the primary difference is in the theoretical motivation (see comparison). In machine learning, binomial regression is considered a special case of probabilistic classification, and thus a generalization of binary classification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Linnaeus made the same distinction between plantains and bananas when first naming two \"species\" of Musa. Members of the \"plantain subgroup\" of banana cultivars, most important as food in West Africa and Latin America, correspond to the Chiquita description, having long pointed fruit. They are described by Ploetz et al. as \"true\" plantains, distinct from other cooking bananas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years the long-standing use of term \"disorder\" to discuss entropy has met with some criticism. Critics of the terminology state that entropy is not a measure of 'disorder' or 'chaos', but rather a measure of energy's diffusion or dispersal to more microstates. Shannon's use of the term 'entropy' in information theory refers to the most compressed, or least dispersed, amount of code needed to encompass the content of a signal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The induced action of G {\\displaystyle G} on the symplectic manifold ( T \u2217 N , d \u03c4 ) {\\displaystyle (T^{*}N,\\mathrm {d} \\tau )} , given by g \u22c5 \u03b7 := ( T \u03c0 ( \u03b7 ) g \u2212 1 ) \u2217 \u03b7 {\\displaystyle g\\cdot \\eta :=(T_{\\pi (\\eta )}g^{-1})^{*}\\eta } for g \u2208 G , \u03b7 \u2208 T \u2217 N {\\displaystyle g\\in G,\\eta \\in T^{*}N} is Hamiltonian with momentum map \u2212 \u03b9 \u03c1 ( \u03be ) \u03c4 {\\displaystyle -\\iota _{\\rho (\\xi )}\\tau } for all \u03be \u2208 g {\\displaystyle \\xi \\in {\\mathfrak {g}}} . Here \u03b9 \u03c1 ( \u03be ) \u03c4 {\\displaystyle \\iota _{\\rho (\\xi )}\\tau } denotes the contraction of the vector field \u03c1 ( \u03be ) {\\displaystyle \\rho (\\xi )} , the infinitesimal action of \u03be {\\displaystyle \\xi } , with the 1-form \u03c4 {\\displaystyle \\tau } . The facts mentioned below may be used to generate more examples of momentum maps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as the \"cross your heart\" method because lines resembling a heart outline can be drawn to remember which things to multiply together. Given an equation like a b = c d , {\\displaystyle {\\frac {a}{b}}={\\frac {c}{d}},} where b and d are not zero, one can cross-multiply to get a d = b c or a = b c d . {\\displaystyle ad=bc\\quad {\\text{or}}\\quad a={\\frac {bc}{d}}.} In Euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , n 2 {\\displaystyle 1,2,...,n^{2}} , the magic square is said to be 'normal'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The size of a graph is | E | {\\displaystyle |E|} , its number of edges. The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some scenarios, an argument by example may be valid if it leads from a singular premise to an existential conclusion (i.e. proving that a claim is true for at least one case, instead of for all cases). For example: Socrates is wise. Therefore, someone is wise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Successful runs might also write a result on magnetic tape or generate some data cards to be used in a later computation. The turnaround time for a single job often spanned entire days.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semiotics, the commutation test is used to analyze a signifying system. The test identifies signifiers as well as their signifieds, value and significance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory a serial relation is a homogeneous relation expressing the connection of an element of a sequence to the following element. The successor function used by Peano to define natural numbers is the prototype for a serial relation. Bertrand Russell used serial relations in The Principles of Mathematics (1903) as he explored the foundations of order theory and its applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The algorithm takes time bounded by a polynomial in n {\\displaystyle n} , the dimension of K {\\displaystyle K} and 1 / \u03b5 {\\displaystyle 1/\\varepsilon } . The algorithm combines two ideas: By using a Markov chain Monte Carlo (MCMC) method, it is possible to generate points that are nearly uniformly randomly distributed within a given convex body. The basic scheme of the algorithm is a nearly uniform sampling from within K {\\displaystyle K} by placing a grid consisting of n {\\displaystyle n} -dimensional cubes and doing a random walk over these cubes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, this set of nodes is optimal for interpolation over C M n  {\\displaystyle C_{M}^{n}} the set of n times differentiable functions whose n-th derivatives are bounded in absolute values by a constant M as shown by N. S. Hoang. Using a computer, one can approximate the values of the minimal Lebesgue constants, here for the canonical interval: There are uncountable infinitely many sets of nodes in  that minimize, for fixed n > 1, the Lebesgue constant. Though if we assume that we always take \u22121 and 1 as nodes for interpolation (which is called a canonical node configuration), then such a set is unique and zero-symmetric.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "900 MHz (902\u2013928 MHz, allocated in 1993) 1.9 GHz (1920\u20131930 MHz, developed in 1993 and allocated in October 2005, especially with DECT 6.0) 2.4 GHz (2400\u20132500 MHz, allocated in 1998) 5.8 GHz (5725\u20135875 MHz, allocated in 2003 due to crowding on the 2.4 GHz band)Over-crowding of earlier frequency allocations led users to discontinue using telephone equipment that operated on those frequencies, leaving those bands relatively clear. Radio hobbyists monitor usage of the older equipment with telephone activity in the US AM broadcast band, some 27 MHz frequencies and most older 43-50 MHz frequencies. 1.7 MHz cordless phones were the earliest models available at retailers, and are generally identifiable by their large metal telescoping antennas.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the multiset {a, a, a, b, b, b}, a and b both have multiplicity 3.These objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, the order in which elements are listed does not matter in discriminating multisets, so {a, a, b} and {a, b, a} denote the same multiset. To distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used: the multiset {a, a, b} can be denoted by .The cardinality of a multiset is the sum of the multiplicities of all its elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, idempotent analysis is the study of idempotent semirings, such as the tropical semiring. The lack of an additive inverse in the semiring is compensated somewhat by the idempotent rule A \u2295 A = A {\\displaystyle A\\oplus A=A} . == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, the conditional entropy is generalized to the conditional quantum entropy. The latter can take negative values, unlike its classical counterpart.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "About the year 1900 I found this out\".Sheila Ostrander and Lynn Schroeder, authors of the paranormal, visited Czechoslovakia in 1968, where they happened upon a cardboard pyramid manufactured commercially by Drbal. They met Drbal, and dedicated a chapter of their popular 1970 book Psychic Discoveries Behind the Iron Curtain to pyramid power. This book introduced both the concept of pyramid power and the story about Antoine Bovis to the English-speaking world.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the Federal Communications Commission requires all interconnected VoIP service providers to comply with requirements comparable to those for traditional telecommunications service providers. VoIP operators in the US are required to support local number portability; make service accessible to people with disabilities; pay regulatory fees, universal service contributions, and other mandated payments; and enable law enforcement authorities to conduct surveillance pursuant to the Communications Assistance for Law Enforcement Act (CALEA). Operators of Interconnected VoIP (fully connected to the PSTN) are mandated to provide Enhanced 911 service without special request, provide for customer location updates, clearly disclose any limitations on their E-911 functionality to their consumers, obtain affirmative acknowledgements of these disclosures from all consumers, and may not allow their customers to opt-out of 911 service. VoIP operators also receive the benefit of certain US telecommunications regulations, including an entitlement to interconnection and exchange of traffic with incumbent local exchange carriers via wholesale carriers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telephone systems where calls from distant automated exchanges arrive for manual subscribers or non-dialable points, there often would be a ringdown operator (reachable from the distant operator console by dialling NPA+181) who would manually ring the desired subscriber on a party line or toll station. On some systems, this function was carried out by the inward operator (NPA+121). In both cases, this is a telephone operator at the destination who provides assistance solely to other operators on inbound toll calls; the ringdown operator nominally cannot be dialed directly by the subscriber.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison sort algorithms. These numbers give the worst-case number of comparisons used by both binary insertion sort and merge sort. However, there are other algorithms that use fewer comparisons.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern field of computational intelligence, the social learning theory is adopted to develop a new computer optimization algorithm, the social learning algorithm. Emulating the observational learning and reinforcement behaviors, a virtual society deployed in the algorithm seeks the strongest behavioral patterns with the best outcome. This corresponds to searching for the best solution in solving optimization problems. Compared with other bio-inspired global optimization algorithms that mimic natural evolution or animal behaviors, the social learning algorithm has its prominent advantages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the feature works properly, it is nearly transparent to the user, appearing as a single long text message. Previously, due to incompatibilities between providers and lack of support in some phone models, there was not widespread use of this feature.In the late 2000s to early 2010s, this feature was adopted more widely. Not only do many handsets support this feature, but support for the feature also exists amongst SMS gateway providers. The way concatenation works in GSM and UMTS networks is specified in SMS Point to Point specification, 3GPP TS 23.040.On networks which do not support Concatenated SMS (neither the standard scheme nor the simplified one), the message is delivered as individual SMS text messages rather than one concatenated message.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle 1,1,2,4,10,32,122,544,2770,15872,101042.} (sequence A001250 in the OEIS).The number of antichains in a fence is a Fibonacci number; the distributive lattice with this many elements, generated from a fence via Birkhoff's representation theorem, has as its graph the Fibonacci cube.A partially ordered set is series-parallel if and only if it does not have four elements forming a fence.Several authors have also investigated the number of order-preserving maps from fences to themselves, or to fences of other sizes.An up-down poset Q(a,b) is a generalization of a zigzag poset in which there are a downward orientations for every upward one and b total elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, zero dynamics is known as the concept of evaluating the effect of zero on systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Both of these tie in to notions of size. Importantly, injection existence between any two sets provides a preorder. A power class does not inject into its underlying set and the latter does not map onto the former.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following code sample, two optimizations can be applied. Although the calculation x = y + z and x * x is loop-invariant, precautions must be taken before moving the code outside the loop. It is possible that the loop condition is false (for example, if n holds a negative value), and in such case, the loop body should not be executed at all. One way of guaranteeing correct behaviour is using a conditional branch outside of the loop.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a BCMP network is a class of queueing network for which a product-form equilibrium distribution exists. It is named after the authors of the paper where the network was first described: Baskett, Chandy, Muntz, and Palacios. The theorem is a significant extension to a Jackson network allowing virtually arbitrary customer routing and service time distributions, subject to particular service disciplines.The paper is well known, and the theorem was described in 1990 as \"one of the seminal achievements in queueing theory in the last 20 years\" by J. Michael Harrison and Ruth J. Williams.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle T\\geqslant |S|-\\varepsilon N\\geqslant (1-R)N-\\varepsilon N=(1-R-\\varepsilon )N.} Finally, we have \u0394 ( C \u2217 ( m 1 ) , C \u2217 ( m 2 ) ) \u2a7e H q \u2212 1 ( 1 2 \u2212 \u03b5 ) \u22c5 2 k \u22c5 T \u2a7e H q \u2212 1 ( 1 2 \u2212 \u03b5 ) \u22c5 2 k \u22c5 ( 1 \u2212 R \u2212 \u03b5 ) \u22c5 N . {\\displaystyle \\Delta (C^{*}(m_{1}),C^{*}(m_{2}))\\geqslant H_{q}^{-1}\\left({\\tfrac {1}{2}}-\\varepsilon \\right)\\cdot 2k\\cdot T\\geqslant H_{q}^{-1}\\left({\\tfrac {1}{2}}-\\varepsilon \\right)\\cdot 2k\\cdot (1-R-\\varepsilon )\\cdot N.} This is true for any arbitrary m 1 \u2260 m 2 {\\displaystyle m_{1}\\neq m_{2}} . So C \u2217 {\\displaystyle C^{*}} has the relative distance at least ( 1 \u2212 R \u2212 \u03b5 ) H q \u2212 1 ( 1 2 \u2212 \u03b5 ) , {\\displaystyle (1-R-\\varepsilon )H_{q}^{-1}\\left({\\tfrac {1}{2}}-\\varepsilon \\right),} which completes the proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, n {\\displaystyle n} denotes the number of people in the initial circle, and k {\\displaystyle k} denotes the count for each step, that is, k \u2212 1 {\\displaystyle k-1} people are skipped and the k {\\displaystyle k} -th is executed. The people in the circle are numbered from 1 {\\displaystyle 1} to n {\\displaystyle n} , the starting position being 1 {\\displaystyle 1} and the counting being inclusive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However it is not the smallest such graph: it is known that there is a universal graph for n-vertex trees, with only n vertices and O(n log n) edges, and that this is optimal. A construction based on the planar separator theorem can be used to show that n-vertex planar graphs have universal graphs with O(n3/2) edges, and that bounded-degree planar graphs have universal graphs with O(n log n) edges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Inversion of control has been widely used by application development frameworks since the rise of GUI environments and continues to be used both in GUI environments and in web server application frameworks. Inversion of control makes the framework extensible by the methods defined by the application programmer.Event-driven programming is often implemented using IoC so that the custom code need only be concerned with the handling of events, while the event loop and dispatch of events/messages is handled by the framework or the runtime environment. In web server application frameworks, dispatch is usually called routing, and handlers may be called endpoints. The phrase \"inversion of control\" has separately also come to be used in the community of Java programmers to refer specifically to the patterns of injecting objects' dependencies that occur with \"IoC containers\" in Java frameworks such as the Spring framework. In this different sense, \"inversion of control\" refers to granting the framework control over the implementations of dependencies that are used by application objects rather than to the original meaning of granting the framework control flow (control over the time of execution of application code e.g. callbacks).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To illustrate this, consider the following statements: P {\\displaystyle P}: Sam ate an orange for lunch Q {\\displaystyle Q}: Sam ate a fruit for lunchThen, to say, \"Sam ate an orange for lunch\" implies \"Sam ate a fruit for lunch\" ( P \u2192 Q {\\displaystyle P\\to Q} ). Logically, if Sam did not eat a fruit for lunch, then Sam also cannot have eaten an orange for lunch (by contraposition). However, merely saying that Sam did not eat an orange for lunch provides no information on whether or not Sam ate a fruit (of any kind) for lunch.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of spoken languages, a phone is an unanalyzed sound of a language. A phone is a speech segment that possesses distinct physical or perceptual properties and serves as the basic unit of phonetic speech analysis. Phones are generally either vowels or consonants. A phonetic transcription (based on phones) is enclosed within square brackets (), rather than the slashes (/ /) of a phonemic transcription, (based on phonemes).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, the importance of the raters (experts) might not be the same as each other. In this case, the Weighted Kendall's W should be used. Suppose that object i {\\displaystyle i} is given the rank r i j {\\displaystyle r_{ij}} by judge number j {\\displaystyle j} , where there are in total n {\\displaystyle n} objects and m {\\displaystyle m} judges. Also, the weight of judge j {\\displaystyle j} is shown by \u03d1 j {\\displaystyle \\vartheta _{j}} (in real-world situation, the importance of each rater can be different).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An outstanding rationale for email authentication is the ability to automate email filtering at receiving servers. That way, spoofed messages can be rejected before they arrive to a user's Inbox. While protocols strive to devise ways to reliably block distrusted mail, security indicators can tag unauthenticated messages that still reach the Inbox. A 2018 study shows that security indicators can lower the click-through ratio by more than ten points, 48.9% to 37.2% of the users who open spoofed messages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In second-order intuitionistic logic, the second-order polymorphic lambda calculus (F2) was discovered by Girard (1972) and independently by Reynolds (1974). Girard proved the Representation Theorem: that in second-order intuitionistic predicate logic (P2), functions from the natural numbers to the natural numbers that can be proved total, form a projection from P2 into F2. Reynolds proved the Abstraction Theorem: that every term in F2 satisfies a logical relation, which can be embedded into the logical relations P2. Reynolds proved that a Girard projection followed by a Reynolds embedding form the identity, i.e., the Girard-Reynolds Isomorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates trellis decoding using a time-invariant trellis. Time invariant trellis decoding allows convolutional codes to be maximum-likelihood soft-decision decoded with reasonable complexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\textstyle \\bigcup _{n\\in \\mathbb {N} }A_{n}\\in N.} Briefly, a sigma-ideal must contain the empty set and contain subsets and countable unions of its elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The algorithms then adjust the weights, instead of adjusting the values associated with the individual state-action pairs. Methods based on ideas from nonparametric statistics (which can be seen to construct their own features) have been explored. Value iteration can also be used as a starting point, giving rise to the Q-learning algorithm and its many variants. Including Deep Q-learning methods when a neural network is used to represent Q, with various applications in stochastic search problems.The problem with using action-values is that they may need highly precise estimates of the competing action values that can be hard to obtain when the returns are noisy, though this problem is mitigated to some extent by temporal difference methods. Using the so-called compatible function approximation method compromises generality and efficiency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can be visualized as a checkerboard pattern in a matrix. Therefore, each processing unit can only have outgoing edges to PEs in the same row and column. This bounds the amount of communication partners for each PE to p r + p c \u2212 1 {\\displaystyle p_{r}+p_{c}-1} out of p = p r \u00d7 p c {\\displaystyle p=p_{r}\\times p_{c}} possible ones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most Unix and Unix-like operating systems, the ps program (short for \"process status\") displays the currently-running processes. A related Unix utility named top provides a real-time view of the running processes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples include 1ESS switch. A machine with three replications of each element is termed triple modular redundant (TMR). The voting circuit can determine which replication is in error when a two-to-one vote is observed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above procedure, the algorithm checks whether the middle element ( m {\\displaystyle m} ) is equal to the target ( T {\\displaystyle T} ) in every iteration. Some implementations leave out this check during each iteration. The algorithm would perform this check only when one element is left (when L = R {\\displaystyle L=R} ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Beaumont created a list of over 150 personally significant books and collected replicas from bookstores. The books were treated, burned, displayed, and arranged in over thirty feet of floor to ceiling shelving. Through the metaphor of fire and the social horror of book burning, the project grieves the irretrievable loss of species (DNA) contained in the rainforest, as irretrievable as the loss of the ancient body of knowledge contained at the Library of Alexandria\u2014both sources of encyclopedic information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The information asymmetry problem occurs in a scenario where one of the two people has more or less information than the other. In the context of public administration, bureaucrats have an information advantage over the government and ministers as the former work at the ground level and have more knowledge about the dynamic and changing situation. Due to this government may frame policies that are not based on complete information and therefore problems in the implementation of public policies may occur.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a directed line segment, or graphically as an arrow connecting an initial point A with a terminal point B, and denoted by A B \u2192 {\\displaystyle {\\overrightarrow {AB}}} . A vector is what is needed to \"carry\" the point A to the point B; the Latin word vector means \"carrier\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These are implemented in part because of the difficulty in ensuring that different terminals transmit at exactly the times required. Handsets that are moving will need to constantly adjust their timings to ensure their transmission is received at precisely the right time, because as they move further from the base station, their signal will take longer to arrive. This also means that the major TDMA systems have hard limits on cell sizes in terms of range, though in practice the power levels required to receive and transmit over distances greater than the supported range would be mostly impractical anyway.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to provide access to relevant data to users ChemXSeer provides new features that are not available in traditional search engines or digital libraries. Chemical Entity Search: A tool capable of identifying Chemical formulae and chemical names, and extracting and disambiguating them from general terms within documents. Those disambiguated terms are used for performing searches.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is determined to a great degree by the stage of the call setup procedure at which a call is counted as connected. In modern communications systems, such as cellular (mobile) networks, the call setup procedure maybe very complex and the point at which a call is considered successfully connected may be defined in a number of ways, thus influencing the way the call setup success rate is calculated. If a call is connected successfully but the dialled number is busy, the call is counted as successful.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Though multiple systems have been postulated, few have reported results. One system, \u201cSMILE,\u201d which attempted to automatically extract classifications from case texts, resulted in an f-measure (which is a calculation of both recall rate and precision) of under 0.3 (compared to perfect f-measure of 1.0). This is probably much lower than an acceptable rate for general usage.Despite the limited results, many theorists predict that the evolution of such systems will eventually replace manual classification systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In India, an idea was mooted in 2003 to create a National Do Not Call Registry, and finally got implemented in 2014. Since then the government is taking various measures to curb the menace that includes termination of the violators telecom resources. As of now there is no regulation for telecallers to classify an abandoned call or allowed percentage as yet, but it will come sooner or later.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following compilation, M is the length of the longest pattern, m their total length, n the length of the searchable text, o the number of occurrences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mycology, the terms teleomorph, anamorph, and holomorph apply to portions of the life cycles of fungi in the phyla Ascomycota and Basidiomycota: Teleomorph: the sexual reproductive stage (morph), typically a fruiting body. Anamorph: an asexual reproductive stage (morph), often mold-like. When a single fungus produces multiple morphologically distinct anamorphs, these are called synanamorphs. Holomorph: the whole fungus, including anamorphs and teleomorph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to recommend the most appropriate users to provide answers in a social network, we need to find approaches to detect users' authority in a social network. In the field of information retrieval, there has been a trend of research investigating ways to detect users' authority effectively and accurately in a social network. Cha et al. investigate possible metrics for determining authority users on popular social network Twitter. They propose the following three simple network-based metrics and discuss their usefulness in determining a user's influence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Given iterates x 1 , x 2 , . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With virtual memory, a contiguous range of virtual addresses can be mapped to several non-contiguous blocks of physical memory; this non-contiguous allocation is one of the benefits of paging.However, paged mapping causes another problem, internal fragmentation. This occurs when a program requests a block of memory that does not cleanly map into a page, for instance, if a program requests a 1 KB buffer to perform file work. In this case, the request results in an entire page being set aside even though only 1 KB of the page will ever be used; if pages are larger than 1 KB, the remainder of the page is wasted. If many small allocations of this sort are made, memory can be used up even though much of it remains empty.In some early microprocessor designs, memory management was performed by a separate integrated circuit such as the VLSI Technology VI475 (1986), the Motorola 68851 (1984) used with the Motorola 68020 CPU in the Macintosh II, or the Z8010 and Z8015 (1985) used with the Zilog Z8000 family of processors. Later microprocessors (such as the Motorola 68030 and the Zilog Z280) placed the MMU together with the CPU on the same integrated circuit, as did the Intel 80286 and later x86 microprocessors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, characterize continuous-time Markov processes. In particular, they describe how the probability that a continuous-time Markov process is in a certain state changes over time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These are normally used with vowels, but may occur with consonants. For example, in the Athabaskan language Hupa, voiceless velar fricatives distinguish three degrees of labialization, transcribed either /x/, /x\u0339/, /x\u02b7/ or /x/, /x\u031c\u02b7/, /x\u02b7/. The extensions to the IPA has two additional symbols for degrees of rounding: Spread  and open-rounded  (as in English).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At the software level, portability of measurement description is the key attribute that distinguishes a synthetic instrument from the more commonly found instrumentation software\u2014software that is limited to hardware scripting and data flow processing. Not all measurement related software systems inherently provide for the abstract, portable synthesis of measurements. Even if they do have such provisions, they may not typically be applied that way by users, especially if the system encourages non-abstracted access to hardware.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, there has been a surge in large data sets available on human movements. These data sets are usually obtained from cell phone or GPS data, with varying degrees of accuracy. For example, cell phone data is usually recorded whenever a call or a text message has been made or received by the user, and contains the location of the tower that the phone has connected to as well as the time stamp. In urban areas, user and the telecommunication tower might be only a few hundred meters away from each other, while in rural areas this distance might well be in region of a few kilometers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For polynomials, the standard basis thus consists of the monomials and is commonly called monomial basis. For matrices M m \u00d7 n {\\displaystyle {\\mathcal {M}}_{m\\times n}} , the standard basis consists of the m\u00d7n-matrices with exactly one non-zero entry, which is 1. For example, the standard basis for 2\u00d72 matrices is formed by the 4 matrices e 11 = ( 1 0 0 0 ) , e 12 = ( 0 1 0 0 ) , e 21 = ( 0 0 1 0 ) , e 22 = ( 0 0 0 1 ) . {\\displaystyle \\mathbf {e} _{11}={\\begin{pmatrix}1&0\\\\0&0\\end{pmatrix}},\\quad \\mathbf {e} _{12}={\\begin{pmatrix}0&1\\\\0&0\\end{pmatrix}},\\quad \\mathbf {e} _{21}={\\begin{pmatrix}0&0\\\\1&0\\end{pmatrix}},\\quad \\mathbf {e} _{22}={\\begin{pmatrix}0&0\\\\0&1\\end{pmatrix}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1964, IBM introduced its System/360 series which used microcode to allow a single expansive instruction set architecture (ISA) to run across a wide variety of machines by implementing more or less instructions in hardware depending on the need. This allowed the ISA to be expansive, and this became the paragon of computer design in the 1960s and 70s, the so-called orthogonal design. This style of memory access with wide variety of modes led to instruction sets with hundreds of different instructions, a style known today as CISC (Complex Instruction Set Computing).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UK \"abandoned\" calls must not be called back within 72 hours unless there is a dedicated agent available. GDPR (General Data Protection Regulation) also requires that the purpose of any call be related to the reason for collecting data in the first place.In the United States, if someone answers but no agent is available within 2 seconds of the person's greeting, Federal Communications Commission (FCC) regulations consider the call \"abandoned\" and require the dialer to play a recorded message. The FCC requires that predictive dialers abandon less than 3% of answered calls.In 1991 the Telephone Consumer Protection Act prohibited the use of an \u201cautomatic telephone dialing system\u201d to contact \u201cany telephone number assigned to a mobile telephone service\u201d without \u201cexpress prior consent\u201d from the party being called.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular representation theory, while Maschke's theorem does not hold when the characteristic divides the group order, the group algebra may be decomposed as the direct sum of a maximal collection of two-sided ideals known as blocks. When the field F has characteristic 0, or characteristic coprime to the group order, there is still such a decomposition of the group algebra F as a sum of blocks (one for each isomorphism type of simple module), but the situation is relatively transparent when F is sufficiently large: each block is a full matrix algebra over F, the endomorphism ring of the vector space underlying the associated simple module. To obtain the blocks, the identity element of the group G is decomposed as a sum of primitive idempotents in Z(R), the center of the group algebra over the maximal order R of F. The block corresponding to the primitive idempotent e is the two-sided ideal e R. For each indecomposable R-module, there is only one such primitive idempotent that does not annihilate it, and the module is said to belong to (or to be in) the corresponding block (in which case, all its composition factors also belong to that block). In particular, each simple module belongs to a unique block. Each ordinary irreducible character may also be assigned to a unique block according to its decomposition as a sum of irreducible Brauer characters. The block containing the trivial module is known as the principal block.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, to the stem of bog (to move) is added -a giving as its subjunctive in the first person boga m\u00e9: First conjugation: Second conjugation: E.g. \"go mbeanna\u00ed Dia th\u00fa\" \u2013 May God bless you. There is also some irregularity in certain verbs in the subjunctive. The verb b\u00ed (to be) is the most irregular verb in Irish (as in most Indo-European languages): The Irish phrase for \"thank you\" \u2013 go raibh maith agat \u2013 uses the subjunctive of \"b\u00ed\" and literally means \"may there be good at-you\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Technology companies have risen to meet the demand to help manage these complex systems. Cloud-based SCM technologies are at the forefront of next-generation supply chains due to their impact on optimization of time, resources, and inventory visibility. Cloud technologies facilitate work being processed offline from a mobile app which solves the common issue of inventory residing in areas with no online coverage or connectivity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Wall\u2013Sun\u2013Sun prime or Fibonacci\u2013Wieferich prime is a certain kind of prime number which is conjectured to exist, although none are known.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C++ programming language, static_cast is an operator that performs an explicit type conversion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hartman, Newman & Ziv (1991) and de Fraysseix, Ossona de Mendez & Pach (1991) proved that every bipartite planar graph can be represented as an intersection graph of horizontal and vertical line segments; for this result see also Czyzowicz, Kranakis & Urrutia (1998). De Castro et al. (2002) proved that every triangle-free planar graph can be represented as an intersection graph of line segments having only three directions; this result implies Gr\u00f6tzsch's theorem (Gr\u00f6tzsch 1959) that triangle-free planar graphs can be colored with three colors. de Fraysseix & Ossona de Mendez (2005) proved that if a planar graph G can be 4-colored in such a way that no separating cycle uses all four colors, then G has a representation as an intersection graph of segments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some early Soviet computer designers implemented systems based on ternary logic; that is, a bit could have three states: +1, 0, or -1, corresponding to positive, zero, or negative voltage. An early project for the U.S. Air Force, BINAC attempted to make a lightweight, simple computer by using binary arithmetic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other approaches are loosely based on the idea of distributional semantics applied to sentences. Skip-Thought trains an encoder-decoder structure for the task of neighboring sentences predictions. Though this has been shown to achieve worse performance than approaches such as InferSent or SBERT.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In protected mode, there are four privilege levels or rings, numbered from 0 to 3, with ring 0 being the most privileged and 3 being the least. The use of rings allows for system software to restrict tasks from accessing data, call gates or executing privileged instructions. In most environments, the operating system and some device drivers run in ring 0 and applications run in ring 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a continuously differentiable function F, a coordinate descent algorithm can be sketched as: The step size can be chosen in various ways, e.g., by solving for the exact minimizer of f(xi) = F(x) (i.e., F with all variables but xi fixed), or by traditional line search criteria.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In several scientific fields, \"complexity\" has a precise meaning: In computational complexity theory, the amounts of resources required for the execution of algorithms is studied. The most popular types of computational complexity are the time complexity of a problem equal to the number of steps that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm, and the space complexity of a problem equal to the volume of the memory used by the algorithm (e.g., cells of the tape) that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm. This allows classification of computational problems by complexity class (such as P, NP, etc.). An axiomatic approach to computational complexity was developed by Manuel Blum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some processor architectures, like that of the Intel 4004 4-bit processor, memory was divided into (256 byte) pages and special precautions had to be taken when the control flow crossed page boundaries, as some machine instructions exhibited different behaviour if located in the last few instructions of a page, so that only few instructions were recommended to jump between pages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite set of real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers a1, a2, ..., an, the geometric mean is defined as ( \u220f i = 1 n a i ) 1 n = a 1 a 2 \u22ef a n n {\\displaystyle \\left(\\prod _{i=1}^{n}a_{i}\\right)^{\\frac {1}{n}}={\\sqrt{a_{1}a_{2}\\cdots a_{n}}}} or, equivalently, as the arithmetic mean in logscale: exp \u2061 ( 1 n \u2211 i = 1 n ln \u2061 a i ) {\\displaystyle \\exp {\\left({{\\frac {1}{n}}\\sum \\limits _{i=1}^{n}\\ln a_{i}}\\right)}} Most commonly the numbers are restricted to being non-negative, to avoid complications related to negative numbers not having real roots, and frequently they are restricted to being positive, to enable the use of logarithms. For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, 2 \u22c5 8 = 4 {\\displaystyle {\\sqrt {2\\cdot 8}}=4} . As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2, that is, 4 \u22c5 1 \u22c5 1 / 32 3 = 1 / 2 {\\displaystyle {\\sqrt{4\\cdot 1\\cdot 1/32}}=1/2} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some points of clarification: first, the definitions above involve quantification over properties and hence higher-order logic. Second, in (1), expressions of the form ( \u2200 X ( X x \u2194 X y ) ) {\\displaystyle (\\forall X(Xx\\leftrightarrow Xy))} capture the concept of sharing all properties, or being indiscernible with respect to a set of properties. Thus, (1) can be understood more intuitively as the claim that all objects that are indiscernible with respect to a base set of properties are indiscernible with respect to a supervenient set of properties, or, as it is also sometimes said, that B-twins are A-twins.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formally, it is the sequence ( z i ) , i = 0 , 1 , 2 , \u2026 {\\displaystyle (z_{i}),i=0,1,2,\\ldots } given by z i := { x i / 2 if i is even, y ( i \u2212 1 ) / 2 if i is odd. {\\displaystyle z_{i}:={\\begin{cases}x_{i/2}&{\\text{ if }}i{\\text{ is even,}}\\\\y_{(i-1)/2}&{\\text{ if }}i{\\text{ is odd. }}\\end{cases}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Codes defined via a Hamming space necessarily have the same length for every codeword, so they are called block codes when it is necessary to distinguish them from variable-length codes that are defined by unique factorization on a monoid. The Hamming distance endows a Hamming space with a metric, which is essential in defining basic notions of coding theory such as error detecting and error correcting codes.Hamming spaces over non-field alphabets have also been considered, especially over finite rings (most notably over Z4) giving rise to modules instead of vector spaces and ring-linear codes (identified with submodules) instead of linear codes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All arbitrary (i.e. zero-symmetric or zero-asymmetric) optimal sets of nodes in  when n = 2 have been determined by F. Schurer, and in an alternative fashion by H.-J. Rack and R. Vajda (2014). If we assume that we take \u22121 and 1 as nodes for interpolation, then as shown by H.-J.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, this multiplication principle is often taken to be the definition of the product of cardinal numbers. We have | S 1 | \u22c5 | S 2 | \u22ef | S n | = | S 1 \u00d7 S 2 \u00d7 \u22ef \u00d7 S n | {\\displaystyle |S_{1}|\\cdot |S_{2}|\\cdots |S_{n}|=|S_{1}\\times S_{2}\\times \\cdots \\times S_{n}|} where \u00d7 {\\displaystyle \\times } is the Cartesian product operator. These sets need not be finite, nor is it necessary to have only finitely many factors in the product; see cardinal number. An extension of the rule of product considers there are n different types of objects, say sweets, to be associated with k objects, say people. How many different ways can the people receive their sweets? Each person may receive any of the n sweets available, and there are k people, so there are n \u22ef \u22c5 n \u23de k = n k {\\displaystyle \\overbrace {n\\cdots \\cdot n} ^{k}=n^{k}} ways to do this.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this vector. The GMRES method was developed by Yousef Saad and Martin H. Schultz in 1986.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Due to the nature of virtualization, the mapping of logical to physical requires some processing power and lookup tables. Therefore, every implementation will add some small amount of latency. In addition to response time concerns, throughput has to be considered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The polytope described by the linear program upper bounding the sum of edges taken per vertex is integral in the case of bipartite graphs, that is, it exactly describes the matching polytope, while for general graphs it is non-integral. Hence, for bipartite graphs, it suffices to solve the corresponding linear program to obtain a valid matching. For general graphs, however, there are two other characterizations of the matching polytope one of which makes use of the blossom inequality for odd subsets of vertices and hence allows to relax the integer program to a linear program while still obtaining valid matchings. These characterizations are of further interest in Edmonds' famous blossom algorithm used for finding such matchings in general graphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially homological algebra and other applications of abelian category theory, the short five lemma is a special case of the five lemma. It states that for the following commutative diagram (in any abelian category, or in the category of groups), if the rows are short exact sequences, and if g and h are isomorphisms, then f is an isomorphism as well. It follows immediately from the five lemma. The essence of the lemma can be summarized as follows: if you have a homomorphism f from an object B to an object B\u2032, and this homomorphism induces an isomorphism from a subobject A of B to a subobject A\u2032 of B\u2032 and also an isomorphism from the factor object B/A to B\u2032/A\u2032, then f itself is an isomorphism. Note however that the existence of f (such that the diagram commutes) has to be assumed from the start; two objects B and B\u2032 that simply have isomorphic sub- and factor objects need not themselves be isomorphic (for example, in the category of abelian groups, B could be the cyclic group of order four and B\u2032 the Klein four-group).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a shared-secret pepper, a single compromised password (via password reuse or other attack) along with a user's salt can lead to an attack to discover the pepper, rendering it ineffective. If an attacker knows a plaintext password and a user's salt, as well as the algorithm used to hash the password, then discovering the pepper can be a matter of brute forcing the values of the pepper. This is why NIST recommends the secret value be at least 112 bits, so that discovering it by exhaustive search is intractable. The pepper must be generated anew for every application it is deployed in, otherwise a breach of one application would result in lowered security of another application.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode, the algorithm works as follows:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of linear programming and related problems in mathematical optimization, convex polytopes are often described by a system of linear inequalities that their points must obey. When a polytope is integral, linear programming can be used to solve integer programming problems for the given system of inequalities, a problem that can otherwise be more difficult. Some polyhedra arising from combinatorial optimization problems are automatically integral.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Regularisation is particularly important feature for non-linear models and also often used in linear adaptive filters to reduce statistical uncertainties. However because nonlinear filters typically have a much higher potential structural complexity (or higher dimensional feature space) compared to the subspace actually required, regularisation of some kind must deal with the under-determined model. Though some specific forms of parameter regularisation such as prescribed by Vapink's SRM & SVM address the dimensionality problem statistically to some extent, there remain further statistical and practical issues for truly adaptive non-linear filters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Pal et al. designed features to measure a user's authority on a certain topic. For example, retweet impact refers to how many times a certain user has been retweeted on a certain topic. The impact is dampened by a factor measuring how many times the user had been retweeted by a unique author to avoid the cases when a user has fans who retweet regardless of the content. They first used a clustering approach to find the target cluster which has the highest average score across all features, and used a ranking algorithm to find the most authoritative users within the cluster. With these authority detection methods, social Q&A could be more effective in providing accurate answers to askers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most mathematics, the operations of addition and multiplication are associative. The associative law for addition, for example, states that ( a + b ) + c = a + ( b + c ) {\\displaystyle (a+b)+c=a+(b+c)} . This means that once the associative law is stated, the parentheses are unnecessary and are usually omitted. More generally, any sum, of any number of terms, can be written without parentheses and any product, of any number of factors, can be written without parentheses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to construct a shadow volume, project a ray from the light source through each vertex in the shadow casting object to some point (generally at infinity). These projections will together form a volume; any point inside that volume is in shadow, everything outside is lit by the light. For a polygonal model, the volume is usually formed by classifying each face in the model as either facing toward the light source or facing away from the light source. The set of all edges that connect a toward-face to an away-face form the silhouette with respect to the light source.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Written as a formula: r e l e v a n t _ r e t r i e v e d _ i n s t a n c e s a l l _ r e l e v a n t _ i n s t a n c e s {\\displaystyle {\\frac {relevant\\_retrieved\\_instances}{all\\_{\\mathbf {relevant}}\\_instances}}} . Both precision and recall are therefore based on relevance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of group theory, a sequence G 0 \u2192 f 1 G 1 \u2192 f 2 G 2 \u2192 f 3 \u22ef \u2192 f n G n {\\displaystyle G_{0}\\;{\\xrightarrow {f_{1}}}\\;G_{1}\\;{\\xrightarrow {f_{2}}}\\;G_{2}\\;{\\xrightarrow {f_{3}}}\\;\\cdots \\;{\\xrightarrow {f_{n}}}\\;G_{n}} of groups and group homomorphisms is called exact, if the image (or range) of each homomorphism is equal to the kernel of the next: i m ( f k ) = k e r ( f k + 1 ) {\\displaystyle \\mathrm {im} (f_{k})=\\mathrm {ker} (f_{k+1})} The sequence of groups and homomorphisms may be either finite or infinite. A similar definition can be made for certain other algebraic structures. For example, one could have an exact sequence of vector spaces and linear maps, or of modules and module homomorphisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Sinclair ZX80 and ZX81 characters sets used x0C (ASCII: form feed). The ZX Spectrum and the BBC Micro used x60 (ASCII: `, grave).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "First compute M p \u2261 C d p mod p {\\displaystyle M_{p}\\equiv C^{d_{p}}{\\bmod {p}}} and M q \u2261 C d q mod q {\\displaystyle M_{q}\\equiv C^{d_{q}}{\\bmod {q}}} . 2. Use the Chinese Remainder Theorem to compute the unique value of M \u2208 Z N {\\displaystyle M\\in \\mathbb {Z_{N}} } which satisfies M \u2261 M p mod p {\\displaystyle M\\equiv M_{p}{\\bmod {p}}} and M \u2261 M q mod q {\\displaystyle M\\equiv M_{q}{\\bmod {q}}} . The result of M {\\displaystyle M} satisfies M \u2261 C d mod N {\\displaystyle M\\equiv C^{d}{\\bmod {N}}} as needed. The point is that Wiener\u2019s attack does not apply here because the value of d mod \u03bb ( N ) {\\displaystyle d{\\bmod {\\lambda }}(N)} can be large.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to generate a single constraint from a pair of constraints applied to the same (pair of) variable, we formalize the notion of intersection of constraints and of order over constraints. Similarly, in order to define a new constraints from existing constraints, a notion of sum of constraint must also be defined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points. The theorem can be generalized in various ways: to higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and to objects that are not triangles at all but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps, and cartoons abound.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years a number of neural and deep-learning techniques have been proposed, some of which generalize traditional Matrix factorization algorithms via a non-linear neural architecture. While deep learning has been applied to many different scenarios: context-aware, sequence-aware, social tagging etc. its real effectiveness when used in a simple Collaborative filtering scenario has been put into question. Systematic analysis of publications applying deep learning or neural methods to the top-k recommendation problem, published in top conferences (SIGIR, KDD, WWW, RecSys, IJCAI), has shown that on average less than 40% of articles are reproducible, with as little as 14% in some conferences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Newer Digital Spread Spectrum (DSS) variants spread their signal over a range of frequencies, providing more resistance to signal fade. This technology enabled the digital information to spread in pieces among several frequencies between the receiver and the base, thereby making it almost impossible to eavesdrop on the cordless conversation. The FCC only allows DSS model phones to transmit at the full power of 1 watt, which allows increased range over older analog and digital models.Virtually all new cordless phones sold in the US use DECT 6.0 on the 1.9 GHz band, though legacy phones can remain in use on the older 900 MHz, 2.4 GHz and 5.8 GHz bands.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern landscape design olive trees are frequently used as ornamental features for their distinctively gnarled trunks and \"evergreen\" silvery gray foliage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is x 2 + y 4 . {\\displaystyle x^{2}+y^{4}.} In many problems, the feasible set reflects a constraint that one or more variables must be non-negative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1710s, Leibniz described Grandi's series in his correspondence with several other mathematicians. The letter with the most lasting impact was his first reply to Wolff, which he published in the Acta Eruditorum. In this letter, Leibniz attacked the problem from several angles. In general, Leibniz believed that the algorithms of calculus were a form of \"blind reasoning\" that ultimately had to be founded upon geometrical interpretations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, an average might be another statistic such as the median, or mode. For example, the average personal income is often given as the median\u2014the number below which are 50% of personal incomes and above which are 50% of personal incomes\u2014because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word \"average\" when discussing measures of central tendency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Szpiro's conjecture relates to the conductor and the discriminant of an elliptic curve. In a slightly modified form, it is equivalent to the well-known abc conjecture. It is named for Lucien Szpiro, who formulated it in the 1980s. Szpiro's conjecture and its equivalent forms have been described as \"the most important unsolved problem in Diophantine analysis\" by Dorian Goldfeld, in part to its large number of consequences in number theory including Roth's theorem, the Mordell conjecture, the Fermat\u2013Catalan conjecture, and Brocard's problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The general problem remains unsolved, apart from the best-known lower bound \u03a9 ( ( log \u2061 n ) / n 2 ) {\\displaystyle \\Omega ((\\log n)/n^{2})} (achievable; hence, Heilbronn's conjecture is not correct for general n {\\displaystyle n} ) and upper bound exp \u2061 ( c log \u2061 n ) / n 8 / 7 {\\displaystyle \\exp(c{\\sqrt {\\log n}})/n^{8/7}} (proven by Komlos, Pintsz and Szemeredi in 1982 and 1981, respectively). Using the incompressibility method, the average case was studied. It was proven that if the area is too small (or large) it can be compressed below the Kolmogorov complexity of a uniformly-random arrangement (high Kolmogorov complexity). This proves that for the overwhelming majority of the arrangements (and the expectation), the area of the smallest triangle formed by three of n {\\displaystyle n} points thrown uniformly at random in the unit square is \u0398 ( 1 / n 3 ) {\\displaystyle \\Theta (1/n^{3})} . In this case, the incompressibility method proves the lower and upper bounds of the property involved.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then given a query in natural language, the embedding for the query can be generated. A top k similarity search algorithm is then used between the query embedding and the document chunk embeddings to retrieve the most relevant document chunks as context information for question answering tasks. This approach is also known formally as retrieval augmented generationThough not as predominant as BERTScore, sentence embeddings are commonly used for sentence similarity evaluation which sees common use for the task of optimizing a Large language model's generation parameters is often performed via comparing candidate sentences against reference sentences. By using the cosine-similarity of the sentence embeddings of candidate and reference sentences as the evaluation function, a grid-search algorithm can be utilized to automate hyperparameter optimization. Sentence embedding is used by the deep learning software libraries PyTorch and TensorFlow.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory. For first-order theories, interpretations are commonly called structures. Given a structure or interpretation, a sentence will have a fixed truth value. A theory is satisfiable when it is possible to present an interpretation in which all of its sentences are true. The study of algorithms to automatically discover interpretations of theories that render all sentences as being true is known as the satisfiability modulo theories problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Burr\u2013Erd\u0151s conjecture was a problem concerning the Ramsey number of sparse graphs. The conjecture is named after Stefan Burr and Paul Erd\u0151s, and is one of many conjectures named after Erd\u0151s; it states that the Ramsey number of graphs in any sparse family of graphs should grow linearly in the number of vertices of the graph. The conjecture was proven by Choongbum Lee. Thus it is now a theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the ratio 1: 1: 2, adding up to 180\u00b0 or \u03c0 radians. Hence, the angles respectively measure 45\u00b0 (\u03c0/4), 45\u00b0 (\u03c0/4), and 90\u00b0 (\u03c0/2). The sides in this triangle are in the ratio 1: 1: \u221a2, which follows immediately from the Pythagorean theorem. Of all right triangles, the 45\u00b0 - 45\u00b0 - 90\u00b0 degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, namely \u221a2/2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization theory, the duality principle states that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. In general given two dual pairs separated locally convex spaces ( X , X \u2217 ) {\\displaystyle \\left(X,X^{*}\\right)} and ( Y , Y \u2217 ) . {\\displaystyle \\left(Y,Y^{*}\\right).} Then given the function f: X \u2192  , {\\displaystyle f:X\\to ,} we can define the primal problem as finding x {\\displaystyle x} such that inf x \u2208 X f ( x ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In military terminology, vulnerability is a subset of survivability, the others being susceptibility and recoverability. Vulnerability is defined in various ways depending on the nation and service arm concerned, but in general it refers to the near-instantaneous effects of a weapon attack. In aviation it is defined as the inability of an aircraft to withstand the damage caused by the man-made hostile environment. In some definitions, recoverability (damage control, firefighting, restoration of capability) is included in vulnerability. Some military services develop their own concept of vulnerability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pure Prolog, normal DCG rules with no extra arguments on the functors, such as the previous example, can only express context-free grammars; there is only one argument on the left side of the production. However, context-sensitive grammars can also be expressed with DCGs, by providing extra arguments, such as in the following example: This set of DCG rules describes the grammar which generates the language that consists of strings of the form a n b n c n {\\displaystyle a^{n}b^{n}c^{n}} . This set of DCG rules describes the grammar which generates the language that consists of strings of the form a n b n c n {\\displaystyle a^{n}b^{n}c^{n}} , by structurally representing n", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, k-medians clustering is a cluster analysis algorithm. It is a variation of k-means clustering where instead of calculating the mean for each cluster to determine its centroid, one instead calculates the median. This has the effect of minimizing error over all clusters with respect to the 1-norm distance metric, as opposed to the squared 2-norm distance metric (which k-means does.) This relates directly to the k-median problem with respect to the 1-norm, which is the problem of finding k centers such that the clusters formed by them are the most compact.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scientific visualization the asymptotic decider is an algorithm developed by Nielson and Hamann in 1991 that creates isosurfaces from a given scalar field. It was proposed as an improvement to the marching cubes algorithm, which can produce some \"bad\" topology, but can also be considered an algorithm in its own right.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Definition. The constraint equations (6) define an n {\\displaystyle \\displaystyle n} -dimensional manifold M {\\displaystyle \\displaystyle M} within the configuration space of the Newtonian dynamical system (3). This manifold M {\\displaystyle \\displaystyle M} is called the configuration space of the constrained system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In remote areas, an additional stage of clustering is used, in order to reduce travel requirements.Although cluster sampling and stratified sampling bear some superficial similarities, they are substantially different. In stratified sampling, a random sample is drawn from all the strata, where in cluster sampling only the selected clusters are studied, either in single- or multi-stage. Advantages Cost and speed that the survey can be done in Convenience of finding the survey sample Normally more accurate than cluster sampling for the same size sampleDisadvantages Not as accurate as Simple Random Sample if the sample is the same size More testing is difficult to do", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to bound the competitive ratio for tango trees, we must find a lower bound on the performance of the optimal offline tree that we use as a benchmark. Once we find an upper bound on the performance of the tango tree, we can divide them to bound the competitive ratio.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additivity and sigma-additivity are particularly important properties of measures. They are abstractions of how intuitive properties of size (length, area, volume) of a set sum when considering multiple objects. Additivity is a weaker condition than \u03c3-additivity; that is, \u03c3-additivity implies additivity. The term modular set function is equivalent to additive set function; see modularity below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the absolute value or modulus of a real number x {\\displaystyle x} , denoted | x | {\\displaystyle |x|} , is the non-negative value of x {\\displaystyle x} without regard to its sign. Namely, | x | = x {\\displaystyle |x|=x} if x {\\displaystyle x} is a positive number, and | x | = \u2212 x {\\displaystyle |x|=-x} if x {\\displaystyle x} is negative (in which case negating x {\\displaystyle x} makes \u2212 x {\\displaystyle -x} positive), and | 0 | = 0 {\\displaystyle |0|=0} . For example, the absolute value of 3 is 3, and the absolute value of \u22123 is also 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Narrowing reduces those worlds by eliminating combinations of different worlds from the same world set. Narrowing rules also detect situations where some combinations of worlds are shown to be impossible. No back tracking is required in the use of narrowing. By packaging the possible values in a value set all combinations of values may be considered at the same time. Evaluation proceeds as for a functional language, combining combinations of values in value sets, with narrowing rules eliminating impossible values from the sets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two companies have emerged that specialize in building multi-core processor devices using the MIPS architecture. Raza Microelectronics, Inc. bought the product line from failing SandCraft and later produced devices that contained eight cores for the telecommunication and networking markets. Cavium, originally a security processor vendor also produced devices with eight CPU cores, and later up to 32 cores, for the same markets. Both of these firms designed their cores in-house, only licensing the architecture instead of buying cores from MIPS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, B\u00e9zout's identity (also called B\u00e9zout's lemma), named after \u00c9tienne B\u00e9zout, is the following theorem: Here the greatest common divisor of 0 and 0 is taken to be 0. The integers x and y are called B\u00e9zout coefficients for (a, b); they are not unique. A pair of B\u00e9zout coefficients can be computed by the extended Euclidean algorithm, and this pair is, in the case of integers one of the two pairs such that | x | \u2264 | b / d | {\\displaystyle |x|\\leq |b/d|} and | y | \u2264 | a / d | ; {\\displaystyle |y|\\leq |a/d|;} equality occurs only if one of a and b is a multiple of the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications there may be different reasons why a handover might be conducted: when the phone is moving away from the area covered by one cell and entering the area covered by another cell the call is transferred to the second cell in order to avoid call termination when the phone gets outside the range of the first cell; when the capacity for connecting new calls of a given cell is used up and an existing or new call from a phone, which is located in an area overlapped by another cell, is transferred to that cell in order to free-up some capacity in the first cell for other users, who can only be connected to that cell; in non-CDMA networks when the channel used by the phone becomes interfered by another phone using the same channel in a different cell, the call is transferred to a different channel in the same cell or to a different channel in another cell in order to avoid the interference; again in non-CDMA networks when the user behaviour changes, e.g. when a fast-travelling user, connected to a large, umbrella-type of cell, stops then the call may be transferred to a smaller macro cell or even to a micro cell in order to free capacity on the umbrella cell for other fast-traveling users and to reduce the potential interference to other cells or users (this works in reverse too, when a user is detected to be moving faster than a certain threshold, the call can be transferred to a larger umbrella-type of cell in order to minimize the frequency of the handovers due to this movement); in CDMA networks a handover (see further down) may be induced in order to reduce the interference to a smaller neighboring cell due to the \"near\u2013far\" effect even when the phone still has an excellent connection to its current cell.The most basic form of handover is when a phone call in progress is redirected from its current cell (called source) to a new cell (called target). In terrestrial networks the source and the target cells may be served from two different cell sites or from one and the same cell site (in the latter case the two cells are usually referred to as two sectors on that cell site). Such a handover, in which the source and the target are different cells (even if they are on the same cell site) is called inter-cell handover. The purpose of inter-cell handover is to maintain the call as the subscriber is moving out of the area covered by the source cell and entering the area of the target cell.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pure Prolog, NAF literals of the form n o t p {\\displaystyle \\mathrm {not} ~p} can occur in the body of clauses and can be used to derive other NAF literals. For example, given only the four clauses p \u2190 q \u2227 n o t r {\\displaystyle p\\leftarrow q\\land \\mathrm {not} ~r} q \u2190 s {\\displaystyle q\\leftarrow s} q \u2190 t {\\displaystyle q\\leftarrow t} t \u2190 {\\displaystyle t\\leftarrow } NAF derives n o t s {\\displaystyle \\mathrm {not} ~s} , n o t r {\\displaystyle \\mathrm {not} ~r} and p {\\displaystyle ~p} as well as t {\\displaystyle ~t} and q {\\displaystyle ~q} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A function is most often denoted by letters such as f, g and h, and the value of a function f at an element x of its domain is denoted by f(x); the numerical value resulting from the function evaluation at a particular input value is denoted by replacing x with this value; for example, the value of f at x = 4 is denoted by f(4). When the function is not named and is represented by an expression E, the value of the function at, say, x = 4 may be denoted by E|x=4. For example, the value at 4 of the function that maps x to ( x + 1 ) 2 {\\displaystyle (x+1)^{2}} may be denoted by ( x + 1 ) 2 | x = 4 {\\displaystyle \\left.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, long-term evolution (LTE) is a standard for wireless broadband communication for mobile devices and data terminals, based on the GSM/EDGE and UMTS/HSPA standards. It improves on those standards' capacity and speed by using a different radio interface and core network improvements. LTE is the upgrade path for carriers with both GSM/UMTS networks and CDMA2000 networks. Because LTE frequencies and bands differ from country to country, only multi-band phones can use LTE in all countries where it is supported.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, DBA functions are often automated using restructuring tools that are tightly coupled to an active data dictionary. Software frameworks aimed at rapid application development sometimes include high-level data dictionary facilities, which can substantially reduce the amount of programming required to build menus, forms, reports, and other components of a database application, including the database itself. For example, PHPLens includes a PHP class library to automate the creation of tables, indexes, and foreign key constraints portably for multiple databases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real network problems, people are interested in determining the likelihood of occurring double links (with opposite directions) between vertex pairs. This problem is fundamental for several reasons. First, in the networks that transport information or material (such as email networks, World Wide Web (WWW), World Trade Web, or Wikipedia ), mutual links facilitate the transportation process. Second, when analyzing directed networks, people often treat them as undirected ones for simplicity; therefore, the information obtained from reciprocity studies helps to estimate the error introduced when a directed network is treated as undirected (for example, when measuring the clustering coefficient). Finally, detecting nontrivial patterns of reciprocity can reveal possible mechanisms and organizing principles that shape the observed network's topology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical morphology, the closing of a set (binary image) A by a structuring element B is the erosion of the dilation of that set, A \u2219 B = ( A \u2295 B ) \u2296 B , {\\displaystyle A\\bullet B=(A\\oplus B)\\ominus B,\\,} where \u2295 {\\displaystyle \\oplus } and \u2296 {\\displaystyle \\ominus } denote the dilation and erosion, respectively. In image processing, closing is, together with opening, the basic workhorse of morphological noise removal. Opening removes small objects, while closing removes small holes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and research design, an index is a composite statistic \u2013 a measure of changes in a representative group of individual data points, or in other words, a compound measure that aggregates multiple indicators. Indexes \u2013 also known as composite indicators \u2013 summarize and rank specific observations.Much data in the field of social sciences and sustainability are represented in various indices such as Gender Gap Index, Human Development Index or the Dow Jones Industrial Average. The \u2018Report by the Commission on the Measurement of Economic Performance and Social Progress\u2019, written by Joseph Stiglitz, Amartya Sen, and Jean-Paul Fitoussi in 2009 suggests that these measures have experienced a dramatic growth in recent years due to three concurring factors: improvements in the level of literacy (including statistical) increased complexity of modern societies and economies, and widespread availability of information technology.According to Earl Babbie, items in indexes are usually weighted equally, unless there are some reasons against it (for example, if two items reflect essentially the same aspect of a variable, they could have a weight of 0.5 each).According to the same author, constructing the items involves four steps. First, items should be selected based on their content validity, unidimensionality, the degree of specificity in which a dimension is to be measured, and their amount of variance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, regression validation is the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained from regression analysis, are acceptable as descriptions of the data. The validation process can involve analyzing the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates substantially when applied to data that were not used in model estimation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the equations below, the lowercase variables represent vectors. Matrices W q {\\displaystyle W_{q}} and U q {\\displaystyle U_{q}} contain, respectively, the weights of the input and recurrent connections, where the subscript q {\\displaystyle _{q}} can either be the input gate i {\\displaystyle i} , output gate o {\\displaystyle o} , the forget gate f {\\displaystyle f} or the memory cell c {\\displaystyle c} , depending on the activation being calculated. In this section, we are thus using a \"vector notation\". So, for example, c t \u2208 R h {\\displaystyle c_{t}\\in \\mathbb {R} ^{h}} is not just one unit of one LSTM cell, but contains h {\\displaystyle h} LSTM cell's units.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If there is a dependence of each state on an overall entity (e.g. a map or simply an overall state variable), one typically uses SLAM (simultaneous localization and mapping) techniques, which include the sequential estimator as a special case (when the overall state variable has just one state). It will estimate the state sequence and the overall entity. There are also none-causal variants, that have all measurements at the same time, batches of measurements or revert the state evolution to go backwards again.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For each node on the phylogeny, the nodal support is the percentage of pseudoreplicates containing that node.The statistical rigor of the bootstrap test has been empirically evaluated using viral populations with known evolutionary histories, finding that 70% bootstrap support corresponds to a 95% probability that the clade exists. However, this was tested under ideal conditions (e.g. no change in evolutionary rates, symmetric phylogenies). In practice, values above 70% are generally supported and left to the researcher or reader to evaluate confidence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a summability kernel is a family or sequence of periodic integrable functions satisfying a certain set of properties, listed below. Certain kernels, such as the Fej\u00e9r kernel, are particularly useful in Fourier analysis. Summability kernels are related to approximation of the identity; definitions of an approximation of identity vary, but sometimes the definition of an approximation of the identity is taken to be the same as for a summability kernel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sociolinguistics, a variety, also called an isolect or lect, is a specific form of a language or language cluster. This may include languages, dialects, registers, styles, or other forms of language, as well as a standard variety. The use of the word \"variety\" to refer to the different forms avoids the use of the term language, which many people associate only with the standard language, and the term dialect, which is often associated with non-standard varieties thought of as less prestigious or \"correct\" than the standard. Linguists speak of both standard and non-standard (vernacular) varieties. \"Lect\" avoids the problem in ambiguous cases of deciding whether two varieties are distinct languages or dialects of a single language. Variation at the level of the lexicon, such as slang and argot, is often considered in relation to particular styles or levels of formality (also called registers), but such uses are sometimes discussed as varieties as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to add first order protection against phase-flips within a single degree of freedom, a higher dimension manifold is required. The 4-component cat code uses the even-parity submanifold of the superposition of 4 coherent states to encode information. The odd-parity submanifold is also 2-dimensional and serves as an error space since a single photon loss switches the parity of the state. Hence, monitoring the parity is sufficient to detect errors caused by single photon loss.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A slide is a specially mounted individual transparency intended for projection onto a screen using a slide projector. This allows the photograph to be viewed by a large audience at once. The most common form is the 35 mm slide, with the image framed in a 2\u00d72 inch cardboard or plastic mount. Some specialized labs produce photographic slides from digital camera images in formats such as JPEG, from computer-generated presentation graphics, and from a wide variety of physical source material such as fingerprints, microscopic sections, paper documents, astronomical images, etc. Reversal film is sometimes used as motion picture film, mostly in the 16 mm, Super 8 and 8 mm \"cine\" formats, to yield a positive image on the camera original. This avoids the expense of using negative film, which requires additional film and processing to create a positive film print for projection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The three-dimensional angular momentum for a point particle is classically represented as a pseudovector r \u00d7 p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics. Unlike linear momentum, angular momentum depends on where this origin is chosen, since the particle's position is measured from it. Angular momentum is an extensive quantity; that is, the total angular momentum of any composite system is the sum of the angular momenta of its constituent parts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the classical untyped lambda calculus, every function has a fixed point. A particular implementation of fix is Curry's paradoxical combinator Y, represented by Y = \u03bb f . ( \u03bb x . f ( x x ) ) ( \u03bb x .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Dominican Republic, number portability in both mobile and local telephony was launched September 30, 2009. In March, 2009, the Dominican Telecommunications Institute (INDOTEL) selected Inform\u00e1tica El Corte Ingl\u00e9s to administer the number portability.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above UML class diagram, the Client class refers (1) to the Aggregate interface for creating an Iterator object (createIterator()) and (2) to the Iterator interface for traversing an Aggregate object (next(),hasNext()). The Iterator1 class implements the Iterator interface by accessing the Aggregate1 class. The UML sequence diagram shows the run-time interactions: The Client object calls createIterator() on an Aggregate1 object, which creates an Iterator1 object and returns it to the Client. The Client uses then Iterator1 to traverse the elements of the Aggregate1 object.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the only way the process can use or set '-' values in its VAS is to ask the OS to map them to bytes from a file. A common way to use VAS memory in this way is to map it to the page file. The page file is a single file, but multiple distinct sets of contiguous bytes can be mapped into a VAS: 0 4 GiB VAS |---vvv--------vvvvvv---vvvv----vv---v----vvv--| mapping ||| |||||| |||| || | ||| file bytes app kernel user system_page_file And different parts of the page file can map into the VAS of different processes: 0 4 GiB VAS 1 |---vvvv-------vvvvvv---vvvv----vv---v----vvv--| mapping |||| |||||| |||| || | ||| file bytes app1 app2 kernel user system_page_file mapping |||| |||||| |||| || | VAS 2 |--------vvvv--vvvvvv---vvvv-------vv---v------| On Microsoft Windows 32-bit, by default, only 2 GiB are made available to processes for their own use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real-time computing, priority inheritance is a method for eliminating unbounded priority inversion. Using this programming method, a process scheduling algorithm increases the priority of a process (A) to the maximum priority of any other process waiting for any resource on which A has a resource lock (if it is higher than the original priority of A). The basic idea of the priority inheritance protocol is that when a job blocks one or more high-priority jobs, it ignores its original priority assignment and executes its critical section at an elevated priority level. After executing its critical section and releasing its locks, the process returns to its original priority level.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"World's first GSM call was actually made by me. I called Marjo Jousinen, in Salo. \", Lonka informed. The following year saw the sending of the first short messaging service (SMS or \"text message\") message, MS and Vodafone UK and Telecom Finland signed the first international roaming agreement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many digital modulation methods such as COFDM use the electromagnetic spectrum very efficiently, allowing for a very tight spectral mask. This allows placement of broadcast stations or other transmissions on channels right next to each other without interference, allowing for an increase in a band's total capacity. Conversely, it is allowing the U.S. to eliminate TV channels 52 to 69, freeing up 108 MHz (from approximately 700 to 800 MHz) for emergency services and to be auctioned off to the highest bidder, while still retaining (although moving) all existing TV stations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result, students inherit all the attributes common to all persons. Additionally, students have unique attributes that other persons don't have. Object-oriented languages model subset/superset relationships using inheritance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The driving force for the cathodic protection current is the difference in electrode potential between the anode and the cathode. During the initial phase of high current, the potential of the steel surface is polarized (pushed) more negative protecting the steel which hydroxide ion generation at the steel surface and ionic migration restore the concrete environment. Over time the galvanic anode continues to corrode, consuming the anode material until eventually it must be replaced.Galvanic or sacrificial anodes are made in various shapes and sizes using alloys of zinc, magnesium, and aluminum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then [0, 1\u20442) is open in S but not in R {\\displaystyle \\mathbb {R} } . Likewise [1\u20442, 1) is closed in S but not in R {\\displaystyle \\mathbb {R} } . S is both open and closed as a subset of itself but not as a subset of R {\\displaystyle \\mathbb {R} } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, there is varying degree of accuracy when it comes to locating a person using cell phone data. These datasets are anonymized by the phone companies so as to hide and protect the identity of actual users. As example of its usage, researchers used the trajectory of 100,000 cell phone users within a period of six months, while in much larger scale trajectories of three million cell phone users were analyzed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variables and a finite number of constraints. In the former case the constraints are typically parameterized.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. Statistical manifolds provide a setting for the field of information geometry. The Fisher information metric provides a metric on these manifolds. Following this definition, the log-likelihood function is a differentiable map and the score is an inclusion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Herzog\u2013Sch\u00f6nheim conjecture is a combinatorial problem in the area of group theory, posed by Marcel Herzog and Jochanan Sch\u00f6nheim in 1974.Let G {\\displaystyle G} be a group, and let A = { a 1 G 1 , \u2026 , a k G k } {\\displaystyle A=\\{a_{1}G_{1},\\ \\ldots ,\\ a_{k}G_{k}\\}} be a finite system of left cosets of subgroups G 1 , \u2026 , G k {\\displaystyle G_{1},\\ldots ,G_{k}} of G {\\displaystyle G} . Herzog and Sch\u00f6nheim conjectured that if A {\\displaystyle A} forms a partition of G {\\displaystyle G} with k > 1 {\\displaystyle k>1} , then the (finite) indices  , \u2026 ,  {\\displaystyle ,\\ldots ,} cannot be distinct. In contrast, if repeated indices are allowed, then partitioning a group into cosets is easy: if H {\\displaystyle H} is any subgroup of G {\\displaystyle G} with index k =  < \u221e {\\displaystyle k=<\\infty } then G {\\displaystyle G} can be partitioned into k {\\displaystyle k} left cosets of H {\\displaystyle H} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On the other hand, if the running time of the algorithm is much smaller than D communication rounds, then the nodes in the network must produce their output without having the possibility to obtain information about distant parts of the network. In other words, the nodes must make globally consistent decisions based on information that is available in their local D-neighbourhood. Many distributed algorithms are known with the running time much smaller than D rounds, and understanding which problems can be solved by such algorithms is one of the central research questions of the field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to implement a successful PAT project, a combination of three main PAT tools is essential: Multivariate data acquisition and data analysis tools: usually advanced software packages which aid in design of experiments, collection of raw data and statistically analyzing this data in order to determine what parameters are CPP. Process analytical chemistry (PAC) tools: in-line and on-line analytical instruments used to measure those parameters that have been defined as CPP. These include mainly near infrared spectroscopy (NIRS); but also include biosensors, Raman spectroscopy, fiber optics and others. Continuous improvement and/or knowledge management tools: paper systems or software packages which accumulate Quality Control data acquired over time for specific processes with the aim of defining process weaknesses and implementing and monitoring process improvement initiatives. These products may be the same or separated from the statistical analysis tools above.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, a number of commentators have called for legislative reforms to the state secrets privilege. These reforms center around several ideas: Requiring judges to review each piece of evidence that the executive claims is subject to the privilege. Requiring the executive to craft alternative evidence that is not subject to the privilege, for the opposing party to use in place of the original, privileged evidence. Such substitute evidence should only be required when it is possible to do so without harming national security.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Call Center space, the following type of call transfers can be undertaken and take on a slightly different meaning: Warm transfer: (also known as a live or hot transfer) the call center operator dials a number and talks to the person who has picked up the call before transferring the caller over to them. This could also be a three-way conference before the call center operator drops-off. One common example of a warm transfer is when a receptionist or virtual receptionist takes a call for the business and notifies the party attempting to be reached who the person is and the nature of their call. Tepid transfer: This involves the call center operator dialing a number and transferring the caller on to the called number without conferencing or speaking to the third party.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each language had its own format for passing parameters into procedure calls, the file formats that they generated were often quite different. In general terms, it was not always possible to write different portions of a program in different languages, although doing so often has real utility.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the Azuma\u2013Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences. Suppose { X k: k = 0 , 1 , 2 , 3 , \u2026 } {\\displaystyle \\{X_{k}:k=0,1,2,3,\\dots \\}} is a martingale (or super-martingale) and | X k \u2212 X k \u2212 1 | \u2264 c k , {\\displaystyle |X_{k}-X_{k-1}|\\leq c_{k},\\,} almost surely. Then for all positive integers N and all positive reals \u03f5 {\\displaystyle \\epsilon } , P ( X N \u2212 X 0 \u2265 \u03f5 ) \u2264 exp \u2061 ( \u2212 \u03f5 2 2 \u2211 k = 1 N c k 2 ) . {\\displaystyle {\\text{P}}(X_{N}-X_{0}\\geq \\epsilon )\\leq \\exp \\left({-\\epsilon ^{2} \\over 2\\sum _{k=1}^{N}c_{k}^{2}}\\right).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While there is ongoing debate on whether checkpointing is the dominating I/O workload on distributed computing systems, there is general consensus that checkpointing is one of the major I/O workloads.There are two main approaches for checkpointing in the distributed computing systems: coordinated checkpointing and uncoordinated checkpointing. In the coordinated checkpointing approach, processes must ensure that their checkpoints are consistent. This is usually achieved by some kind of two-phase commit protocol algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The driven exam can be completed in the Class B bus the driver wishes to operate. It is common for restrictions to be issued on the driver's license disallowing them to operate higher classes of vehicles than they tested on. A common restriction is a driver with a Class B CDL that performs their P endorsement test on a class B bus, resulting in their license bearing the \"no class A passenger vehicle\" restriction, which is notated with an 'M', in addition to their P endorsement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is not stable if: In other words, a matching is stable when there does not exist any pair (A, B) which both prefer each other to their current partner under the matching.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum computing, the threshold theorem (or quantum fault-tolerance theorem) states that a quantum computer with a physical error rate below a certain threshold can, through application of quantum error correction schemes, suppress the logical error rate to arbitrarily low levels. This shows that quantum computers can be made fault-tolerant, as an analogue to von Neumann's threshold theorem for classical computation. This result was proven (for various error models) by the groups of Dorit Aharanov and Michael Ben-Or; Emanuel Knill, Raymond Laflamme, and Wojciech Zurek; and Alexei Kitaev independently. These results built off a paper of Peter Shor, which proved a weaker version of the threshold theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a symmetric probability distribution is a probability distribution\u2014an assignment of probabilities to possible occurrences\u2014which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some value of the random variable represented by the distribution. This vertical line is the line of symmetry of the distribution. Thus the probability of being any given distance on one side of the value about which symmetry occurs is the same as the probability of being the same distance on the other side of that value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In project management; Risks that are external to the project and the project manager cannot control. Good examples of external risks are changes in government legislation, changes in strategy from senior managers, and the economy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of representation scenarios, design knowledge can also be categorized into off-line and on-line knowledge. Design process knowledge can be categorized into ontologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Drazin inverse, named after Michael P. Drazin, is a kind of generalized inverse of a matrix. Let A be a square matrix. The index of A is the least nonnegative integer k such that rank(Ak+1) = rank(Ak).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This led MIT Technology Review to name it 'the machine that saved Moore's law'. The first prototype in 2006 produced one wafer in 23 hours.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Coin errors that occur on the die are generally more desirable than errors made at the time of the strike. For example, a doubled die, where a date or another device appears twice slightly offset, is often a highly desired error. Strike errors are generally unique, whereas all coins struck with an error die will have the same characteristic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language design, there are a wide variety of factors to consider. Some factors may be mutually exclusive (e.g. security versus speed). It may be necessary to consider whether a programming language will perform better interpreted, or compiled, if a language should be dynamically or statically typed, if inheritance will be in a language, and the general syntax of the language. Many factors involved with the design of a language can be decided on by the goals behind the language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a client may receive an event stating that a given key has been pressed while the Shift modifier was down. If this key would normally generate the character \"a\", the client (and not the server) associates this event to the character \"A\". While the translation from keycodes to keysyms is done by the client, the table that represents this association is maintained by the server.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle {\\sigma ^{2}+\\left({\\frac {\\text{Third central moment}}{2\\sigma ^{2}}}\\right)^{2}}\\leq {\\frac {1}{4}}(M-m)^{2}.} If one additionally assumes knowledge of the expectation, then the stronger Bhatia\u2013Davis inequality holds \u03c3 2 \u2264 ( M \u2212 \u03bc ) ( \u03bc \u2212 m ) {\\displaystyle \\sigma ^{2}\\leq (M-\\mu )(\\mu -m)} where \u03bc is the expectation of the random variable.In the case of an independent sample of n observations from a bounded probability distribution, the von Szokefalvi Nagy inequality gives a lower bound to the variance of the sample mean: \u03c3 2 \u2265 ( M \u2212 m ) 2 2 n . {\\displaystyle \\sigma ^{2}\\geq {\\frac {(M-m)^{2}}{2n}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-processor systems (more than one Opteron on a single motherboard), the CPUs communicate using the Direct Connect Architecture over high-speed HyperTransport links. Each CPU can access the main memory of another processor, transparent to the programmer. The Opteron approach to multi-processing is not the same as standard symmetric multiprocessing; instead of having one bank of memory for all CPUs, each CPU has its own memory. Thus the Opteron is a Non-Uniform Memory Access (NUMA) architecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to extract the desired distortion information, at any given location in the spherical coordinate system, the values of K {\\displaystyle K} can be computed directly. The Jacobian, J {\\displaystyle J} , can be computed analytically from the mapping function itself, but it is often simpler to numerically approximate the values at any location on the map using central differences. Once these values are computed, SVD can be applied to each transformation matrix to extract the local distortion information. Remember that, because distortion is local, every location on the map will have its own transformation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These probabilities are used to determine what the target is using a maximum likelihood decision. This method has been shown to be able to distinguish between vehicle types (wheeled vs tracked vehicles for example), and even decide how many people are present up to three people with a high probability of success.CNN-Based Target Recognition Convolutional neural network (CNN)-based target recognition is able to outperform the conventional methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For these reasons, constant interfaces may be considered an anti-pattern. Use of this pattern has a few other downsides: It pollutes the class namespace with read-only variables that may not be of use. Contrary to the compile-time tactical utility of implementing a constant interface, the incidental run-time artifacts have little practical purpose (cf. marker interfaces which also have no methods but are useful at run-time).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As x and y must be rational, the square of \u00b1 2 x y {\\displaystyle \\pm 2{\\sqrt {xy}}} must be rational. This implies that \u03b1 = 0 {\\displaystyle \\alpha =0} in the expression of \u00b1 2 x y {\\displaystyle \\pm 2{\\sqrt {xy}}} as \u03b1 + \u03b2 c . {\\displaystyle \\alpha +\\beta {\\sqrt {c}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phrase structure grammars such as generative grammar, the verb phrase is one headed by a verb. It may be composed of only a single verb, but typically it consists of combinations of main and auxiliary verbs, plus optional specifiers, complements (not including subject complements), and adjuncts. For example: Yankee batters hit the ball well enough to win their first World Series since 2000. Mary saw the man through the window.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, to improve the usability and reliability of keys, many single-access keys incorporate reticulation, changing the tree structure into a directed acyclic graph. Single-access keys have been in use for several hundred years. They may be printed in various styles (e. g., linked, nested, indented, graphically branching) or used as interactive, computer-aided keys.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first two of these were to resolve the continuum hypothesis and prove the consistency of elementary arithmetic, respectively; the tenth was to produce a method that could decide whether a multivariate polynomial equation over the integers has a solution. Subsequent work to resolve these problems shaped the direction of mathematical logic, as did the effort to resolve Hilbert's Entscheidungsproblem, posed in 1928. This problem asked for a procedure that would decide, given a formalized mathematical statement, whether the statement is true or false.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the three classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and later generations of Greek mathematicians because of their importance in geometry and music.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The cosets of Inn(G) with respect to outer automorphisms are then the elements of Out(G); this is an instance of the fact that quotients of groups are not, in general, (isomorphic to) subgroups. If the inner automorphism group is trivial (when a group is abelian), the automorphism group and outer automorphism group are naturally identified; that is, the outer automorphism group does act on the group. For example, for the alternating group, An, the outer automorphism group is usually the group of order 2, with exceptions noted below. Considering An as a subgroup of the symmetric group, Sn, conjugation by any odd permutation is an outer automorphism of An or more precisely \"represents the class of the (non-trivial) outer automorphism of An\", but the outer automorphism does not correspond to conjugation by any particular odd element, and all conjugations by odd elements are equivalent up to conjugation by an even element.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A second publication from 1968 described the theory and the technical details of the instrument and had Hadravsk\u00fd and Robert Galambos, the head of the group at Yale, as additional authors. In 1970 the US patent was granted. It was filed in 1967.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As an example, given a PostBQP algorithm A with success probability 2/3, we can construct another algorithm which runs three independent copies of A, outputs a postselection bit equal to the conjunction of the three \"inner\" ones, and outputs an output bit equal to the majority of the three \"inner\" ones; the new algorithm will be correct with conditional probability ( 2 / 3 ) 3 + 3 ( 1 / 3 ) ( 2 / 3 ) 2 = 20 / 27 {\\displaystyle (2/3)^{3}+3(1/3)(2/3)^{2}=20/27} , greater than the original 2/3. PostBQP is closed under intersection. Suppose we have PostBQP circuit families for two languages L 1 {\\displaystyle L_{1}} and L 2 {\\displaystyle L_{2}} , with respective postselection qubits and output qubits P 1 , P 2 , Q 1 , Q 2 {\\displaystyle P_{1},P_{2},Q_{1},Q_{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the von Staudt\u2013Clausen theorem is a result determining the fractional part of Bernoulli numbers, found independently by Karl von Staudt (1840) and Thomas Clausen (1840). Specifically, if n is a positive integer and we add 1/p to the Bernoulli number B2n for every prime p such that p \u2212 1 divides 2n, we obtain an integer, i.e., B 2 n + \u2211 ( p \u2212 1 ) | 2 n 1 p \u2208 Z . {\\displaystyle B_{2n}+\\sum _{(p-1)|2n}{\\frac {1}{p}}\\in \\mathbb {Z} .} This fact immediately allows us to characterize the denominators of the non-zero Bernoulli numbers B2n as the product of all primes p such that p \u2212 1 divides 2n; consequently the denominators are square-free and divisible by 6. These denominators are 6, 30, 42, 30, 66, 2730, 6, 510, 798, 330, 138, 2730, 6, 870, 14322, 510, 6, 1919190, 6, 13530, ... (sequence A002445 in the OEIS).The sequence of integers B 2 n + \u2211 ( p \u2212 1 ) | 2 n 1 p {\\displaystyle B_{2n}+\\sum _{(p-1)|2n}{\\frac {1}{p}}} is 1, 1, 1, 1, 1, 1, 2, -6, 56, -528, 6193, -86579, 1425518, -27298230, ... (sequence A000146 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let \u03c0 ( x ) {\\displaystyle \\pi (x)} , the prime-counting function, denote the number of primes less than or equal to x {\\displaystyle x} . If q {\\displaystyle q} is a positive integer and a {\\displaystyle a} is coprime to q {\\displaystyle q} , we let \u03c0 ( x ; q , a ) {\\displaystyle \\pi (x;q,a)} denote the number of primes less than or equal to x {\\displaystyle x} which are equal to a {\\displaystyle a} modulo q {\\displaystyle q} . Dirichlet's theorem on primes in arithmetic progressions then tells us that \u03c0 ( x ; q , a ) \u2248 \u03c0 ( x ) \u03c6 ( q ) {\\displaystyle \\pi (x;q,a)\\approx {\\frac {\\pi (x)}{\\varphi (q)}}} where \u03c6 {\\displaystyle \\varphi } is Euler's totient function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Barzilai and Borwein proved their method converges R-superlinearly for quadratic minimization in two dimensions. Raydan demonstrates convergence in general for quadratic problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major unresolved challenge is to determine if the problem admits a polynomial time algorithm; that is, whether the problem lies in the complexity class P.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If portfolio weights are largely a function of estimation errors, then Ex-post performance of a growth-optimal portfolio may differ fantastically from the ex-ante prediction. Parameter uncertainty and estimation errors are a large topic in portfolio theory. An approach to counteract the unknown risk is to invest less than the Kelly criterion (e.g., half).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Every finite distributive lattice can be represented as a lattice of stable matchings. The number of elements in the lattice can vary from an average case of e \u2212 1 n ln \u2061 n {\\displaystyle e^{-1}n\\ln n} to a worst-case of exponential. Computing the number of elements is #P-complete.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Atlantis, is continued. Ais and her crew face many other challenges, most notably internal problems, caused first by the rebellion of one of the deputies, and then by open warfare led by the non-Delosiani Dr. Satham, a scrupulous scientist and his henchmen.While the uplift experiment seems to progress, eventually the Great Brain, the highest authority on Des (Delos), decides to stop and destroy the work of Ais and her colleagues. However, Ais and some of her subordinates questioned (\u2192 reflection) the strange order and refuse to abandon the uplift (whether the command actually came directly from the Great Brain is not known.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Heilbronn triangle problem, throw n {\\displaystyle n} points in the unit square and determine the maximum of the minimal area of a triangle formed by three of the points over all possible arrangements. This problem was solved for small arrangements, and much work was done on asymptotic expression as a function of n {\\displaystyle n} . The original conjecture of Heilbronn was O ( 1 / n 2 ) {\\displaystyle O(1/n^{2})} during the early 1950s. Paul Erd\u0151s proved that this bound is correct for n {\\displaystyle n} , a prime number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "He invented the Adams operations in K-theory, which are derived from the exterior powers; they are now also widely used in purely algebraic contexts. Adams introduced them in a 1962 paper to solve the famous vector fields on spheres problem. Subsequently he used them to investigate the Adams conjecture, which is concerned (in one instance) with the image of the J-homomorphism in the stable homotopy groups of spheres.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other projects the need to move into Prolog was considered unnecessary because the printed logico-linguistic models provided an easy to use guide to decision making. For example, a system for mortgage loan approval", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of data race detection for programs using lock based synchronization, lockset-based techniques provide an unsound, yet lightweight mechanism for detecting data races. These techniques primarily detect violations of the lockset principle. which says that all accesses of a given memory location must be protected by a common lock. Such techniques are also used to filter out candidate race reports in more expensive analyses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Seven dogs were missed (false negatives), and seven cats were correctly excluded (true negatives). The program's precision is then 5/8 (true positives / selected elements) while its recall is 5/12 (true positives / relevant elements). Adopting a hypothesis-testing approach from statistics, in which, in this case, the null hypothesis is that a given item is irrelevant (i.e., not a dog), absence of type I and type II errors (i.e., perfect specificity and sensitivity of 100% each) corresponds respectively to perfect precision (no false positive) and perfect recall (no false negative).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "And if you cannot do that, simplify your design until you can.\u201dAt a SIGPLAN symposium in 1973, Tony Hoare discussed various language aspects in some detail. He also identifies a number of shortcomings in (then) current programming languages.\u201ca programming language is a tool which should assist the programmer in the most difficult aspects of his art, namely program design, documentation, and debugging.\u201d\u201cobjective criteria for good language design may be summarized in five catch phrases: simplicity, security, fast translation, efficient object code, and readability.\u201d \"It is absurd to make elaborate security checks on debugging runs, when no trust is put in the results, and then remove them in production runs, when an erroneous result could be expensive or disastrous.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance. It has applications in the analysis of time series. It was introduced by David Brillinger.It is most transparent when stated in its most general form, for joint cumulants, rather than for cumulants of a specified order for just one random variable. In general, we have \u03ba ( X 1 , \u2026 , X n ) = \u2211 \u03c0 \u03ba ( \u03ba ( X i: i \u2208 B \u2223 Y ): B \u2208 \u03c0 ) , {\\displaystyle \\kappa (X_{1},\\dots ,X_{n})=\\sum _{\\pi }\\kappa (\\kappa (X_{i}:i\\in B\\mid Y):B\\in \\pi ),} where \u03ba(X1, ..., Xn) is the joint cumulant of n random variables X1, ..., Xn, and the sum is over all partitions \u03c0 {\\displaystyle \\pi } of the set { 1, ..., n } of indices, and \"B \u2208 \u03c0;\" means B runs through the whole list of \"blocks\" of the partition \u03c0, and \u03ba(Xi: i \u2208 B | Y) is a conditional cumulant given the value of the random variable Y. It is therefore a random variable in its own right\u2014a function of the random variable Y.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using a car as an analogy, if the user steps on the gas without first starting the engine, the car does not crash, fail, or throw an exception - it simply fails to accelerate. Sequential coupling can be refactored with the template method pattern to overcome the problems posed by the usage of this anti-pattern. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial cones, and these become proper simplices with an additional constraint. The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the constraints applied to the objective function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In all page table formats supported by x86 and x86-64, the 12 least significant bits of the page table entry are either interpreted by the memory management unit or are reserved for operating system use. In processors that implement the \"no-execute\" or \"execution disable\" feature, the most significant bit (bit 63) is the NX bit. The next eleven most significant bits (bits 52 through 62) are reserved for operating system use by both Intel and AMD's architecture specifications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, commercial truck classification is determined based on the vehicle's gross vehicle weight rating (GVWR). The classes are numbered 1 through 8. Trucks are also classified more broadly by the Federal Highway Administration (FHWA), which groups classes 1 and 2 as light duty, 3 through 6 as medium duty, and 7 and 8 as heavy duty. The Environmental Protection Agency (EPA) has a separate system of emissions classifications for trucks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In any case, such definitions (also called bridge laws or correspondence rules) were held to serve three important purposes. In the first place, by connecting the uninterpreted formalism with the observation language, they permit the assignment of synthetic content to theories. In the second, according to whether they express a factual or a purely conventional content, they allow for the subdivision of science into two parts: one factual and independent of human conventions, the other non-empirical and conventional.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In contrast, a program where both Stack and Queue are subclasses of a type Bag, whose specification for get is merely that it removes some element, does satisfy behavioral subtyping and allows clients to safely reason about correctness based on the presumed types of the objects they interact with. Indeed, any object that satisfies the Stack or Queue specification also satisfies the Bag specification. It is important to stress that whether a type S is a behavioral subtype of a type T depends only on the specification (i.e. the documentation) of type T; the implementation of type T, if it has any, is completely irrelevant to this question.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model checking, a subfield of computer science, a timed word is an extension of the notion of words, in a formal language, in which each letter is associated with a positive time tag. The sequence of time tags must be non-decreasing, which intuitively means that letters are received. For example, a system receiving a word over a network may associate to each letter the time at which the letter is received. The non-decreasing condition here means that the letters are received in the correct order. A timed language is a set of timed words.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Fido is a dog. Therefore Fido is a mammal.\" Formally, the rule as an axiom schema is given as \u2200 x A \u21d2 A { x \u21a6 a } , {\\displaystyle \\forall x\\,A\\Rightarrow A\\{x\\mapsto a\\},} for every formula A and every term a, where A { x \u21a6 a } {\\displaystyle A\\{x\\mapsto a\\}} is the result of substituting a for each free occurrence of x in A. A { x \u21a6 a } {\\displaystyle \\,A\\{x\\mapsto a\\}} is an instance of \u2200 x A .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, focused proofs are a family of analytic proofs that arise through goal-directed proof-search, and are a topic of study in structural proof theory and reductive logic. They form the most general definition of goal-directed proof-search\u2014in which someone chooses a formula and performs hereditary reductions until the result meets some condition. The extremal case where reduction only terminates when axioms are reached forms the sub-family of uniform proofs.A sequent calculus is said to have the focusing property when focused proofs are complete for some terminating condition. For System LK, System LJ, and System LL, uniform proofs are focused proofs where all the atoms are assigned negative polarity. Many other sequent calculi has been shown to have the focusing property, notably the nested sequent calculi of both the classical and intuitionistic variants of the modal logics in the S5 cube.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is generally called roaming from a customer perspective, but also called visiting when describing the underlying technical process. Each geographic area has a database called the Visitor Location Register (VLR), which contains details of all the mobiles currently in that area. Whenever a phone attaches, or visits, a new area, the Visitor Location Register must contact the Home Location Register to obtain the details for that phone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical finite group theory, the Brauer\u2013Fowler theorem, proved by Brauer & Fowler (1955), states that if a group G has even order g > 2 then it has a proper subgroup of order greater than g1/3. The technique of the proof is to count involutions (elements of order 2) in G. Perhaps more important is another result that the authors derive from the same count of involutions, namely that up to isomorphism there are only a finite number of finite simple groups with a given centralizer of an involution. This suggested that finite simple groups could be classified by studying their centralizers of involutions, and it led to the discovery of several sporadic groups. Later it motivated a part of the classification of finite simple groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics the mean squared prediction error (MSPE), also known as mean squared error of the predictions, of a smoothing, curve fitting, or regression procedure is the expected value of the squared prediction errors (PE), the square difference between the fitted values implied by the predictive function g ^ {\\displaystyle {\\widehat {g}}} and the values of the (unobservable) true value g. It is an inverse measure of the explanatory power of g ^ , {\\displaystyle {\\widehat {g}},} and can be used in the process of cross-validation of an estimated model. Knowledge of g would be required in order to calculate the MSPE exactly; in practice, MSPE is estimated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, under this assumption, a poset may be defined as a small posetal category, a distributive lattice as a small posetal distributive category, a Heyting algebra as a small posetal finitely cocomplete cartesian closed category, and a Boolean algebra as a small posetal finitely cocomplete *-autonomous category. Conversely, categories, distributive categories, finitely cocomplete cartesian closed categories, and finitely cocomplete *-autonomous categories can be considered the respective categorifications of posets, distributive lattices, Heyting algebras, and Boolean algebras. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hardy\u2013Ramanujan\u2013Littlewood circle method is a technique of analytic number theory. It is named for G. H. Hardy, S. Ramanujan, and J. E. Littlewood, who developed it in a series of papers on Waring's problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Unary relations can be viewed as a collection of members (such as the collection of Nobel laureates) having some property (such as that of having been awarded the Nobel prize). Binary relations are the most commonly studied form of finitary relations. When X1 = X2 it is called a homogeneous relation, for example: Equality and inequality, denoted by signs such as = and < in statements such as \"5 < 12\", or Divisibility, denoted by the sign | in statements such as \"13|143\".Otherwise it is a heterogeneous relation, for example: Set membership, denoted by the sign \u2208 in statements such as \"1 \u2208 N\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct Boolean-valued models of set theory in the theory of forcing. Every Boolean algebra A has an essentially unique completion, which is a complete Boolean algebra containing A such that every element is the supremum of some subset of A. As a partially ordered set, this completion of A is the Dedekind\u2013MacNeille completion. More generally, if \u03ba is a cardinal then a Boolean algebra is called \u03ba-complete if every subset of cardinality less than \u03ba has a supremum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In QCA's next step, inferential logic or Boolean algebra is used to simplify or reduce the number of inferences to the minimum set of inferences supported by the data. This reduced set of inferences is termed the \"prime implicates\" by QCA adherents. For instance, if the presence of conditions A and B is always associated with the presence of a particular value of D, regardless of the observed value of C, then the value that C takes is irrelevant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, aspect and time are very clearly separated, making them much more distinct to their speakers. There are a number of languages that mark aspect much more saliently than time. Prominent in this category are Chinese and American Sign Language, which both differentiate many aspects but rely exclusively on optional time-indicating terms to pinpoint an action with respect to time. In other language groups, for example in most modern Indo-European languages (except Slavic languages and some Indo-Aryan languages like Hindi), aspect has become almost entirely conflated, in the verbal morphological system, with time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications networks, a node (Latin: nodus, \u2018knot\u2019) is either a redistribution point or a communication endpoint. The definition of a node depends on the network and protocol layer referred to. A physical network node is an electronic device that is attached to a network, and is capable of creating, receiving, or transmitting information over a communication channel. A passive distribution point such as a distribution frame or patch panel is consequently not a node.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Rete II gives about a 100 to 1 order of magnitude performance improvement in more complex problems as shown by KnowledgeBased Systems Corporation benchmarks. Rete II can be characterized by two areas of improvement; specific optimizations relating to the general performance of the Rete network (including the use of hashed memories in order to increase performance with larger sets of data), and the inclusion of a backward chaining algorithm tailored to run on top of the Rete network. Backward chaining alone can account for the most extreme changes in benchmarks relating to Rete vs. Rete II. Rete II is implemented in the commercial product Advisor from FICO, formerly called Fair Isaac Jess (at least versions 5.0 and later) also adds a commercial backward chaining algorithm on top of the Rete network, but it cannot be said to fully implement Rete II, in part due to the fact that no full specification is publicly available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and decision theory, a frequently used loss function is the 0-1 loss function L ( y ^ , y ) =  {\\displaystyle L({\\hat {y}},y)=\\left} using Iverson bracket notation, i.e. it evaluates to 1 when y ^ \u2260 y {\\displaystyle {\\hat {y}}\\neq y} , and 0 otherwise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, fn is any of jn, yn, h(1)n, h(2)n for n = 0, \u00b11, \u00b12, ...", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle y^{2}=x(x-a^{n})(x+b^{n}).\\,} Such an elliptic curve would enjoy very special properties, which are due to the appearance of high powers of integers in its equation and the fact that an + bn = cn is an nth power as well. In the summer of 1986, Ken Ribet demonstrated that, just as Gerhard Frey had anticipated, a special case of the Taniyama\u2013Shimura conjecture (still not proved at the time), together with the now proved epsilon conjecture, implies Fermat's Last Theorem. Thus, if the Taniyama\u2013Shimura conjecture is true for semistable elliptic curves, then Fermat's Last Theorem would be true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most Forth systems, the body of a code definition consists of either machine language, or some form of threaded code. The original Forth which follows the informal FIG standard (Forth Interest Group), is a TIL (Threaded Interpretive Language). This is also called indirect-threaded code, but direct-threaded and subroutine threaded Forths have also become popular in modern times. The fastest modern Forths, such as SwiftForth, VFX Forth, and iForth, compile Forth to native machine code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz (Schwartz distributions) have a two-variable theory that includes all reasonable bilinear forms on the space D {\\displaystyle {\\mathcal {D}}} of test functions. The space D {\\displaystyle {\\mathcal {D}}} itself consists of smooth functions of compact support.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Different classification methods may have different percentages of error for a given classification project. It is important that the remote sensor chooses a classification method that works best with the number of classifications used while providing the least amount of error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In prior versions of C++, only functions, classes or type aliases could be templated. C++14 allows the creation of variables that are templated. An example given in the proposal is a variable pi that can be read to get the value of pi for various types (e.g., 3 when read as an integral type; the closest value possible with float, double or long double precision when read as float, double or long double, respectively; etc.). The usual rules of templates apply to such declarations and definitions, including specialization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For almost all tournaments, the size is at least ( n 2 ) / 2 \u2212 1.73 n 3 / 2 {\\displaystyle {\\tbinom {n}{2}}/2-1.73n^{3/2}} . Every directed acyclic graph D {\\displaystyle D} can be embedded as a subgraph of a larger tournament graph, in such a way that D {\\displaystyle D} is the unique minimum feedback arc set of the tournament. The size of this tournament has been defined as the \"reversing number\" of D {\\displaystyle D} , and among directed acyclic graphs with the same number of vertices it is largest when D {\\displaystyle D} is itself an (acyclic) tournament.A directed graph has an Euler tour whenever it is strongly connected and each vertex has equal numbers of incoming and outgoing edges.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mechanics, the eigenvectors of the moment of inertia tensor define the principal axes of a rigid body. The tensor of moment of inertia is a key quantity required to determine the rotation of a rigid body around its center of mass.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some versions of Ring-LWE there is a security reduction to the shortest-vector problem (SVP) in a lattice as a lower bound on the security. The SVP is known to be NP-hard. Specific ring-LWE systems that have provable security reductions include a variant of Lyubashevsky's ring-LWE signatures defined in a paper by G\u00fcneysu, Lyubashevsky, and P\u00f6ppelmann.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer. In other words, there are infinitely many primes that are congruent to a modulo d. The numbers of the form a + nd form an arithmetic progression a , a + d , a + 2 d , a + 3 d , \u2026 , {\\displaystyle a,\\ a+d,\\ a+2d,\\ a+3d,\\ \\dots ,\\ } and Dirichlet's theorem states that this sequence contains infinitely many prime numbers. The theorem, named after Peter Gustav Lejeune Dirichlet, extends Euclid's theorem that there are infinitely many prime numbers. Stronger forms of Dirichlet's theorem state that for any such arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges and that different such arithmetic progressions with the same modulus have approximately the same proportions of primes. Equivalently, the primes are evenly distributed (asymptotically) among the congruence classes modulo d containing a's coprime to d.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When one processor is taken out then the other processor operates independently. When the faulty processor is repaired and brought in service then memory contents of the active processor are copied into its memory and the two are synchronized and comparator is enabled. It is possible that a comparator fault occurs only due to transient failure which is not shown even when check out program is run.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Erd\u0151s\u2013Ko\u2013Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common. Paul Erd\u0151s, Chao Ko, and Richard Rado proved the theorem in 1938, but did not publish it until 1961. It is part of the field of combinatorics, and one of the central results of extremal set theory. The theorem applies to families of sets that all have the same size, r {\\displaystyle r} , and are all subsets of some larger set of size n {\\displaystyle n} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most modern operating systems (OSs), a large body of reusable code is provided to simplify the programmer's job. This code is typically provided as a set of dynamically loadable libraries that applications can call at runtime. Because the Java platform is not dependent on any specific operating system, applications cannot rely on any of the pre-existing OS libraries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Difficulties with such dependencies can be easily avoided if we reinsert the upper unit node \u03b7 \u2032 {\\displaystyle \\eta ^{\\prime }} after reinserting the unit node \u03b7 {\\displaystyle \\eta } (i.e. after reinsertion, \u03b7 \u2032 {\\displaystyle \\eta ^{\\prime }} must appear below \u03b7 {\\displaystyle \\eta } , to cancel the extra literal \u2113 \u00af {\\displaystyle {\\overline {\\ell }}} from \u03b7 {\\displaystyle \\eta } \u2019s clause). This can be ensured by collecting the unit nodes in a queue during a bottom-up traversal of the proof and reinserting them in the order they were queued. The algorithm for fixing a proof containing many roots performs a top-down traversal of the proof, recomputing the resolvents and replacing broken nodes (e.g. nodes having deletedNodeMarker as one of their parents) by their surviving parents (e.g. the other parent, in case one parent was deletedNodeMarker). When unit nodes are collected and removed from a proof of a clause \u03ba {\\displaystyle \\kappa } and the proof is fixed, the clause \u03ba \u2032 {\\displaystyle \\kappa ^{\\prime }} in the root node of the new proof is not equal to \u03ba {\\displaystyle \\kappa } anymore, but contains (some of) the duals of the literals of the unit clauses that have been removed from the proof. The reinsertion of unit nodes at the bottom of the proof resolves \u03ba \u2032 {\\displaystyle \\kappa ^{\\prime }} with the clauses of (some of) the collected unit nodes, in order to obtain a proof of \u03ba {\\displaystyle \\kappa } again.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then the new state is ( a 1 , a 2 , \u2026 , a r ; z \u2032 ) {\\displaystyle (a_{1},a_{2},\\dots ,a_{r};z')} . By iterating the state change an FCSR generates an infinite, eventually periodic sequence of numbers in S {\\displaystyle S} . FCSRs have been used in the design of stream ciphers (such as the F-FCSR generator), in the cryptanalysis of the summation combiner stream cipher (the reason Goresky and Klapper invented them), and in generating pseudorandom numbers for quasi-Monte Carlo (under the name Multiply With Carry (MWC) generator - invented by Couture and L'Ecuyer,) generalizing work of Marsaglia and Zaman.FCSRs are analyzed using number theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities. This greatly simplifies operations such as finding the maximum or minimum of a multivariate function and solving systems of differential equations. The notation used here is commonly used in statistics and engineering, while the tensor index notation is preferred in physics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most traditional PCRs the resulting products are analyzed after the PCR has been completed. This is called end-point analysis and is normally qualitative of nature rather than being quantitative. For this sort of analysis, products are mostly analyzed on an agarose gel and visualized using ethidium bromide as a fluorescent dye. Direct correlation between signal strength and initial sample concentration is not possible using end-point analysis since PCR efficiency decreases as the reaction nears the plateau phase.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the branch of abstract algebra known as ring theory, a left primitive ring is a ring which has a faithful simple left module. Well known examples include endomorphism rings of vector spaces and Weyl algebras over fields of characteristic zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "+ 1 {\\displaystyle (p-1)!+1} . Both are named for 18th-century English mathematician John Wilson; in 1770, Edward Waring credited the theorem to Wilson, although it had been stated centuries earlier by Ibn al-Haytham.The only known Wilson primes are 5, 13, and 563 (sequence A007540 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result, the vast majority of a program's time was being spent in only five instructions. Further, even when the program called one of those five instructions, the microcode required a finite time to decode it, even if it was just to call the internal hardware. On faster machines, this overhead was considerable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This becomes important, for example, when the Levene's test fails to satisfy the rather generous conditions for normality associated with that test and is a default alternative under those conditions for certain statistical software programs like the VarianceEquivalenceTest routine in Mathematica. In addition to Levene's test, other parametric tests for equality of variance include the Bartlett, Brown-Forsythe, and Fisher Ratio tests. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This permits the existence of directory hierarchies, i.e., directories containing sub-directories. A name that refers to a file within a directory must be typically unique. In other words, there must be no identical names within a directory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory and combinatorics, a multipartition of a positive integer n is a way of writing n as a sum, each element of which is in turn a partition. The concept is also found in the theory of Lie algebras.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle H_{D}(x,R)=-\\sum _{i\\in (1\\dots r)}P_{D}(d_{i},x,R)\\log P_{D}(d_{i},x,R).} Using this entropy equation we can further calculate H D ( x , R ) {\\displaystyle H_{D}(x,R)} for every point x {\\displaystyle x} and region shape R {\\displaystyle R} . A more complex region, like the eye region, has a more complex distributor and hence higher entropy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is essential in assuring that a transmission stays within its channel. An FM radio station, for example, must attenuate everything beyond \u00b175kHz from the center frequency by a few decibels, and anything beyond \u00b1100 kHz (the channel boundary) by much more. Emissions on further adjacent channels must be reduced to almost zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle K_{1}K_{2}\\cdots K_{M}.} A conditional probability table can be put into matrix form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to prevent adaptive-chosen-ciphertext attacks, it is necessary to use an encryption or encoding scheme that limits ciphertext malleability and a proof of security of the system. After the theoretical and foundation level development of CCA secure systems, a number of systems have been proposed in the Random Oracle model: the most common standard for RSA encryption is Optimal Asymmetric Encryption Padding (OAEP). Unlike improvised schemes such as the padding used in the early versions of PKCS#1, OAEP has been proven secure in the random oracle model, OAEP was incorporated into PKCS#1 as of version 2.0 published in 1998 as the now-recommended encoding scheme, with the older scheme still supported but not recommended for new applications. However, the golden standard for security is to show the system secure without relying on the Random Oracle idealization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series. It depends on the quantity lim sup n \u2192 \u221e | a n | n , {\\displaystyle \\limsup _{n\\rightarrow \\infty }{\\sqrt{|a_{n}|}},} where a n {\\displaystyle a_{n}} are the terms of the series, and states that the series converges absolutely if this quantity is less than one, but diverges if it is greater than one. It is particularly useful in connection with power series.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music, a reduction is an arrangement or transcription of an existing score or composition in which complexity is lessened to make analysis, performance, or practice easier or clearer; the number of parts may be reduced or rhythm may be simplified, such as through the use of block chords.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to avoid regressions being seen by the end-user after release, developers regularly run regression tests after changes are introduced to the software. These tests can include unit tests to catch local regressions as well as integration tests to catch remote regressions. Regression testing techniques often leverage existing test cases to minimize the effort involved in creating them. However, due to the volume of these existing tests, it is often necessary to select a representative subset, using techniques such as test-case prioritization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of university records, authorities both on the state and federal level have shown an awareness about issues of privacy in education and a distaste for institutions' disclosure of information. The U.S. Department of Education has provided guidance about data discourse and identification, instructing educational institutions to be sensitive to the risk of re-identification of anonymous data by cross-referencing with auxiliary data, to minimize the amount of data in the public domain by decreasing publication of directory information about students and institutional personnel, and to be consistent in the processes of de-identification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The statement is relative easy to prove by induction on the dimension of Z (even for Y=Z, X=0, c=1) with a K that depends only on N; the point of the theorem is that K is independent of N. In fact, the constant c can be made arbitrarily close to 1, at the expense of the constant K becoming large. The original proof allowed c ( K ) \u2248 1 \u2212 const / log \u2061 log \u2061 K . {\\displaystyle c(K)\\approx 1-{\\text{const}}/\\log \\log K.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A porous barrier or ceramic disk may be used to separate the two solutions while allowing the flow of sulfate ions. When the half cells are placed in two entirely different and separate containers, a salt bridge is often used to connect the two cells. The salt bridge typically contains a high concentration of potassium nitrate (a salt that will not interfere chemically with the reaction in either half-cell).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen to be as short as possible. For example, if one chooses to take commutativity for granted, an axiom with six NAND operations and three variables is equivalent to Boolean algebra: ( ( a \u2223 b ) \u2223 c ) \u2223 ( a \u2223 ( ( a \u2223 c ) \u2223 a ) ) = c {\\displaystyle ((a\\mid b)\\mid c)\\mid (a\\mid ((a\\mid c)\\mid a))=c} where the vertical bar represents the NAND logical operation (also known as the Sheffer stroke). It is one of 25 candidate axioms for this property identified by Stephen Wolfram, by enumerating the Sheffer identities of length less or equal to 15 elements (excluding mirror images) that have no noncommutative models with four or fewer variables, and was first proven equivalent by William McCune, Branden Fitelson, and Larry Wos. MathWorld, a site associated with Wolfram, has named the axiom the \"Wolfram axiom\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of a cache miss, the purpose of using such a structure will be rendered useless and the computer will have to go to the main memory to fetch the required data. However, with a multiple-level cache, if the computer misses the cache closest to the processor (level-one cache or L1) it will then search through the next-closest level(s) of cache and go to main memory only if these methods fail. The general trend is to keep the L1 cache small and at a distance of 1\u20132 CPU clock cycles from the processor, with the lower levels of caches increasing in size to store more data than L1, hence being more distant but with a lower miss rate. This results in a better AAT. The number of cache levels can be designed by architects according to their requirements after checking for trade-offs between cost, AATs, and size.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In previous work, according to Chi (2000), \"researchers have attempted to construct taxonomies of information visualization techniques by examining the data domains that are compatible with these techniques. This is useful because implementers can quickly identify various techniques that can be applied to their domain of interest. However, these taxonomies do not help the implementers understand how to apply and implement these techniques\".According to Chi (2000), he and J.T.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to treat very large problems, the structure of hierarchical matrices can be improved: H2-matrices replace the general low-rank structure of the blocks by a hierarchical representation closely related to the fast multipole method in order to reduce the storage complexity to O ( n k ) {\\displaystyle O(nk)} . In the context of boundary integral operators, replacing the fixed rank k {\\displaystyle k} by block-dependent ranks leads to approximations that preserve the rate of convergence of the underlying boundary element method at a complexity of O ( n ) . {\\displaystyle O(n).} Arithmetic operations like multiplication, inversion, and Cholesky or LR factorization of H2-matrices can be implemented based on two fundamental operations: the matrix-vector multiplication with submatrices and the low-rank update of submatrices. While the matrix-vector multiplication is straightforward, implementing efficient low-rank updates with adaptively optimized cluster bases poses a significant challenge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Khoisan languages and the International Phonetic Alphabet, the vertical bar is used to write the dental click (\u01c0). A double vertical bar is used to write the alveolar lateral click (\u01c1). Since these are technically letters, they have their own Unicode code points in the Latin Extended-B range: U+01C0 for the single bar and U+01C1 for the double bar.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the new memory layout, the ensemble dimension is added to the lowest dimension to reduce possible branch divergence. The impact of the unavoidable branch divergence from data irregularity, caused by the noise, is minimized via a regularization technique using the on-chip memory. Moreover, the cache memory is utilized to amortize unavoidable uncoalesced memory accesses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, division by two or halving has also been called mediation or dimidiation. The treatment of this as a different operation from multiplication and division by other numbers goes back to the ancient Egyptians, whose multiplication algorithm used division by two as one of its fundamental steps. Some mathematicians as late as the sixteenth century continued to view halving as a separate operation, and it often continues to be treated separately in modern computer programming. Performing this operation is simple in decimal arithmetic, in the binary numeral system used in computer programming, and in other even-numbered bases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle x^{*}(p_{1},p_{2},I)=\\left({\\frac {Ip_{1}^{\\epsilon -1}}{p_{1}^{\\epsilon }+p_{2}^{\\epsilon }}},{\\frac {Ip_{2}^{\\epsilon -1}}{p_{1}^{\\epsilon }+p_{2}^{\\epsilon }}}\\right),\\quad {\\text{with}}\\quad \\epsilon ={\\frac {\\delta }{\\delta -1}}.} In both cases, the preferences are strictly convex, the demand is unique and the demand function is continuous. 3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "On the probability space we define the space X = { X } {\\displaystyle {\\mathcal {X}}=\\{X\\}} of random variables with values in measurable metric space ( U , d u ) {\\displaystyle (U,d_{u})} and the space Y = { Y } {\\displaystyle {\\mathcal {Y}}=\\{Y\\}} of random variables with values in measurable metric space ( V , d v ) {\\displaystyle (V,d_{v})} . By characterizations of probability distributions we understand general problems of description of some set C {\\displaystyle {\\mathcal {C}}} in the space X {\\displaystyle {\\mathcal {X}}} by extracting the sets A \u2286 X {\\displaystyle {\\mathcal {A}}\\subseteq {\\mathcal {X}}} and B \u2286 Y {\\displaystyle {\\mathcal {B}}\\subseteq {\\mathcal {Y}}} which describe the properties of random variables X \u2208 A {\\displaystyle X\\in {\\mathcal {A}}} and their images Y = F X \u2208 B {\\displaystyle Y=\\mathbf {F} X\\in {\\mathcal {B}}} , obtained by means of a specially chosen mapping F: X \u2192 Y {\\displaystyle \\mathbf {F} :{\\mathcal {X}}\\to {\\mathcal {Y}}} . The description of the properties of the random variables X {\\displaystyle X} and of their images Y = F X {\\displaystyle Y=\\mathbf {F} X} is equivalent to the indication of the set A \u2286 X {\\displaystyle {\\mathcal {A}}\\subseteq {\\mathcal {X}}} from which X {\\displaystyle X} must be taken and of the set B \u2286 Y {\\displaystyle {\\mathcal {B}}\\subseteq {\\mathcal {Y}}} into which its image must fall.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Snippets are similar to having static preprocessing included in the editor, and do not require support by a compiler. On the flip side, this means that snippets cannot be invariably modified after the fact, and thus is vulnerable to all of the problems of copy and paste programming. For this reason snippets are primarily used for simple sections of code (with little logic), or for boilerplate, such as copyright notices, function prototypes, common control structures, or standard library imports.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A number of dimensional models have been produced, differing in the way in which they are constructed and the way in which they are intended to be interpreted. There are four broad types of dimensional representation, although others also exist: Dimensional representation of the original DSM categories of personality disorders; Dimensional representation based on identification of latent traits with the DSM disorders; Dimensional representation based on the traits from normal personality research; Representation based on integration of dimensional modals, e.g. by using network analysis.The dimensional approach is included in Section III (\"Emerging Measures and Models\") of the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5), where it is described as an \"Alternative DSM-5 Model for Personality Disorders. \": p.761\u2013781 The decision to retain the old DSM-IV categorical model of personality disorders in DSM-5 was controversial, and efforts continue to persuade the American Psychiatric Association to replace it with the dimensional model in DSM 5.1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the U.S., the calculation and disclosure of APR is governed by the Truth in Lending Act (which is implemented by the Consumer Financial Protection Bureau (CFPB) in Regulation Z of the Act). In general, APR in the United States is expressed as the periodic (for instance, monthly) interest rate times the number of compounding periods in a year (also known as the nominal interest rate); since the APR must include certain non-interest charges and fees, it requires more detailed calculation. The APR must be disclosed to the borrower within 3 days of applying for a mortgage. This information is typically mailed to the borrower and the APR is found on the truth in lending disclosure statement, which also includes an amortization schedule.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the content is deemed dangerous or inappropriate, its spread could be curbed immediately.Understandably, methods for countering disinformation that involve algorithmic governance raise ethical concerns. The use of technologies that track and manipulate information raises questions about \"who is accountable for their operation, whether they can create injustices and erode civic norms, and how we should resolve their (un)intended consequences\".A study from the Pew Research Center reports that public support for restriction of disinformation by both technology companies and government increased among Americans from 2018-2021. However, views on whether government and technology companies should take such steps became increasingly partisan and polarized during the same time period.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming (OOP), an instance is a concrete occurrence of any object, existing usually during the runtime of a computer program. Formally, \"instance\" is synonymous with \"object\" as they are each a particular value (realization), and these may be called an instance object; \"instance\" emphasizes the distinct identity of the object. The creation of an instance is called instantiation. An object may be varied in a number of ways.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some hackathons, all work is on a single application, such as an operating system, programming language, or content management system. Such events are often known as \"code sprints\", and are especially popular for open source software projects, where such events are sometimes the only opportunity for developers to meet face-to-face.Code sprints typically last from one week to three weeks and often take place near conferences at which most of the team attend. Unlike other hackathons, these events rarely include a competitive element. The annual hackathon to work on the operating system OpenBSD, held since 1999, is one such event; it may have originated the word \"hackathon\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\u03b7 . {\\displaystyle \\eta ^{\\prime }S.\\eta .} See: distributive law between monads. A generalized distributive law has also been proposed in the area of information theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other methods of defining the correspondence include a nondeterministic algorithm in terms of jeu de taquin. The bijective nature of the correspondence relates it to the enumerative identity \u2211 \u03bb \u2208 P n ( t \u03bb ) 2 = n ! {\\displaystyle \\sum _{\\lambda \\in {\\mathcal {P}}_{n}}(t_{\\lambda })^{2}=n!} where P n {\\displaystyle {\\mathcal {P}}_{n}} denotes the set of partitions of n (or of Young diagrams with n squares), and t\u03bb denotes the number of standard Young tableaux of shape \u03bb.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Before virtual memory could be implemented in mainstream operating systems, many problems had to be addressed. Dynamic address translation required expensive and difficult-to-build specialized hardware; initial implementations slowed down access to memory slightly. There were worries that new system-wide algorithms utilizing secondary storage would be less effective than previously used application-specific algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "0 K m , n =  {\\displaystyle 0_{K_{m,n}}={\\begin{bmatrix}0_{K}&0_{K}&\\cdots &0_{K}\\\\0_{K}&0_{K}&\\cdots &0_{K}\\\\\\vdots &\\vdots &&\\vdots \\\\0_{K}&0_{K}&\\cdots &0_{K}\\end{bmatrix}}} The zero matrix is the additive identity in K m , n {\\displaystyle K_{m,n}} . That is, for all A \u2208 K m , n {\\displaystyle A\\in K_{m,n}}: 0 K m , n + A = A + 0 K m , n = A {\\displaystyle 0_{K_{m,n}}+A=A+0_{K_{m,n}}=A} There is exactly one zero matrix of any given size m \u00d7 n (with entries from a given ring), so when the context is clear, one often refers to the zero matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The relative point of view is that much of algebraic geometry should be developed for a morphism X \u2192 Y of schemes (called a scheme X over Y), rather than for an individual scheme. For example, in studying algebraic surfaces, it can be useful to consider families of algebraic surfaces over any scheme Y. In many cases, the family of all varieties of a given type can itself be viewed as a variety or scheme, known as a moduli space. For some of the detailed definitions in the theory of schemes, see the glossary of scheme theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, MDP allowed the protocol to be optionally configured to send proactive repair packets in the original data transmission block. MDP was a direct predecessor to NORM, with an initial IETF draft published in November 1996. The National Aeronautics and Space Administration (NASA) adopted MDP for reliable file transfers during space missions., and the U.S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Hall's conjecture is an open question, as of 2015, on the differences between perfect squares and perfect cubes. It asserts that a perfect square y2 and a perfect cube x3 that are not equal must lie a substantial distance apart. This question arose from consideration of the Mordell equation in the theory of integer points on elliptic curves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a nonempty subset S of a group G is said to be symmetric if it contains the inverses of all of its elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, the term \"algebraic statistics\" has been used more restrictively, to label the use of algebraic geometry and commutative algebra to study problems related to discrete random variables with finite state spaces. Commutative algebra and algebraic geometry have applications in statistics because many commonly used classes of discrete random variables can be viewed as algebraic varieties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The load step becomes a separate instruction, and that instruction is statically scheduled much earlier in the code sequence. The compiler puts independent steps in between. Scheduling memory accesses requires explicit, spare registers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as \"there exists\", \"there is at least one\", or \"for some\". It is usually denoted by the logical operator symbol \u2203, which, when used together with a predicate variable, is called an existential quantifier (\"\u2203x\" or \"\u2203(x)\" or \"(\u2203x)\"). Existential quantification is distinct from universal quantification (\"for all\"), which asserts that the property or relation holds for all members of the domain. Some sources use the term existentialization to refer to existential quantification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A surrogate key may be used as the primary key to avoid giving one candidate key artificial primacy over the others. Since primary keys exist primarily as a convenience to the programmer, surrogate primary keys are often used, in many cases exclusively, in database application design. Due to the popularity of surrogate primary keys, many developers and in some cases even theoreticians have come to regard surrogate primary keys as an inalienable part of the relational data model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Ammunition and canisters which replenish shields or oxygen can be found while exploring the game's environments, as well as various temporary power-ups. Single-player level objectives can include exterminating all hostile creatures, rescuing civilians, retrieving certain items, or exploring certain locations. Most levels contain platforms, stairs, doors, and liquids which players can control by activating switches.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Cantelli's inequality (also called the Chebyshev-Cantelli inequality and the one-sided Chebyshev inequality) is an improved version of Chebyshev's inequality for one-sided tail bounds. The inequality states that, for \u03bb > 0 , {\\displaystyle \\lambda >0,} Pr ( X \u2212 E  \u2265 \u03bb ) \u2264 \u03c3 2 \u03c3 2 + \u03bb 2 , {\\displaystyle \\Pr(X-\\mathbb {E} \\geq \\lambda )\\leq {\\frac {\\sigma ^{2}}{\\sigma ^{2}+\\lambda ^{2}}},} where X {\\displaystyle X} is a real-valued random variable, Pr {\\displaystyle \\Pr } is the probability measure, E  {\\displaystyle \\mathbb {E} } is the expected value of X {\\displaystyle X} , \u03c3 2 {\\displaystyle \\sigma ^{2}} is the variance of X {\\displaystyle X} .Applying the Cantelli inequality to \u2212 X {\\displaystyle -X} gives a bound on the lower tail, Pr ( X \u2212 E  \u2264 \u2212 \u03bb ) \u2264 \u03c3 2 \u03c3 2 + \u03bb 2 . {\\displaystyle \\Pr(X-\\mathbb {E} \\leq -\\lambda )\\leq {\\frac {\\sigma ^{2}}{\\sigma ^{2}+\\lambda ^{2}}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "REBOL reifies code as data and vice versa. Many languages, such as Lisp, JavaScript, and Curl, provide an eval or evaluate procedure that effectively reifies the language interpreter. The Logtalk framework for Prolog offers a means to explore reification in the context of logic programming. Smalltalk and Actor languages permit the reification of blocks and messages, which are equivalent of lambda expressions in Lisp, and thisContext in Smallltalk, which is a reification of the current executing block. Homoiconic languages reify the syntax of the language itself in the form of an abstract syntax tree, typically together with eval.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This was still a vast amount of memory at the time, but because of this limitation, architectures since have included various steps away from the original 26-bit design. The ARM architecture version 3 introduced a 32-bit PC and separate PSR, as well as a 32-bit address bus, allowing 4 GiB of memory to be addressed. The change in the PC/PSR layout caused incompatibility with code written for previous architectures, so the processor also included a 26-bit compatibility mode which used the old PC/PSR combination.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set notation a subset S {\\displaystyle S} of a group G {\\displaystyle G} is called symmetric if whenever s \u2208 S {\\displaystyle s\\in S} then the inverse of s {\\displaystyle s} also belongs to S . {\\displaystyle S.} So if G {\\displaystyle G} is written multiplicatively then S {\\displaystyle S} is symmetric if and only if S = S \u2212 1 {\\displaystyle S=S^{-1}} where S \u2212 1 := { s \u2212 1: s \u2208 S } . {\\displaystyle S^{-1}:=\\left\\{s^{-1}:s\\in S\\right\\}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the concept of an inverse element generalises the concepts of opposite (\u2212x) and reciprocal (1/x) of numbers. Given an operation denoted here \u2217, and an identity element denoted e, if x \u2217 y = e, one says that x is a left inverse of y, and that y is a right inverse of x. (An identity element is an element such that x * e = x and e * y = y for all x and y for which the left-hand sides are defined.) When the operation \u2217 is associative, if an element x has both a left inverse and a right inverse, then these two inverses are equal and unique; they are called the inverse element or simply the inverse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nature, species do not evolve in isolation but in large networks of interacting species. One of the main goals in evolutionary ecology is to disentangle the evolutionary mechanisms that shape and are shaped by patterns of interaction between species. A particularly important question concerns how coevolution, the reciprocal evolutionary change in local populations of interacting species driven by natural selection, is shaped by the architecture of food webs, plant-animal mutualistic networks, and host-parasite communities. The concept of diffuse coevolution, where adaptation is in response to a suite of biotic interactions, was the first step towards a framework unifying relevant theories in community ecology and coevolution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of mathematical logic and computer science known as type theory, a type constructor is a feature of a typed formal language that builds new types from old ones. Basic types are considered to be built using nullary type constructors. Some type constructors take another type as an argument, e.g., the constructors for product types, function types, power types and list types. New types can be defined by recursively composing type constructors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One can then also calculate the mean square of the model by dividing the sum of squares of the model minus the degrees of freedom, which is just the number of parameters. Then the F value can be calculated by dividing the mean square of the model by the mean square of the error, and we can then determine significance (which is why you want the mean squares to begin with. ).However, because of the behavior of the process of regression, the distributions of residuals at different data points (of the input variable) may vary even if the errors themselves are identically distributed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some countries, declining satisfaction with the urban environment is held to blame for continuing migration to smaller towns and rural areas (so-called urban exodus). Successful urban planning supported Regional planning can bring benefits to a much larger hinterland or city region and help to reduce both congestion along transport routes and the wastage of energy implied by excessive commuting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is widely used in a Filipino youth subculture known as Jejemons. kkkk: in Somali and Ethiopian languages spoken in the Horn of Africa, iterations of the letter \"k\", usually ranging between 2 and 8 k's, are used as a variation of LOL. These iterations are also used by Shona, Ndebele and other Zimbabwean languages speakers, with the longer variant being \"kikiki\" (emulating a laughing sound).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The number of trailing zeros in a non-zero base-b integer n equals the exponent of the highest power of b that divides n. For example, 14000 has three trailing zeros and is therefore divisible by 1000 = 103, but not by 104. This property is useful when looking for small factors in integer factorization. Some computer architectures have a count trailing zeros operation in their instruction set for efficiently determining the number of trailing zero bits in a machine word.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matroid theory, an Eulerian matroid is a matroid whose elements can be partitioned into a collection of disjoint circuits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the geometric topology is a topology one can put on the set H of hyperbolic 3-manifolds of finite volume.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Sim\u00e9on Denis Poisson (; French pronunciation: \u200b). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In stop/step mode debugging, the core/microcontroller is stopped through the use of breakpoints and then \"single-stepped\" through the code by executing instructions one at a time. If the other cores/microcontrollers of the SoC have finished synchronously, the overall state of the system can be examined. Stop/step mode debugging includes control/configure techniques, run control of a core/microcontroller, start/stop synchronization with other cores, memory and register access, and additional debug features such as performance counter and run-time memory access.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the autumn of 1884, K\u00e1roly Zipernowsky, Ott\u00f3 Bl\u00e1thy and Miksa D\u00e9ri (ZBD), three Hungarian engineers associated with the Ganz Works, had determined that open-core devices were impracticable, as they were incapable of reliably regulating voltage. In their joint 1885 patent applications for novel transformers (later called ZBD transformers), they described two designs with closed magnetic circuits where copper windings were either wound around an iron wire ring core or surrounded by an iron wire core. The two designs were the first application of the two basic transformer constructions in common use to this day, termed \"core form\" or \"shell form\" . The Ganz factory had also in the autumn of 1884 made delivery of the world's first five high-efficiency AC transformers, the first of these units having been shipped on September 16, 1884.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consider for example the random variable of the number of items in a shopper's basket at a supermarket checkout line. Presumably a shopper does not stand in line with nothing to buy (i.e., the minimum purchase is 1 item), so this phenomenon may follow a ZTP distribution.Since the ZTP is a truncated distribution with the truncation stipulated as k > 0, one can derive the probability mass function g(k;\u03bb) from a standard Poisson distribution f(k;\u03bb) as follows: g ( k ; \u03bb ) = P ( X = k \u2223 X > 0 ) = f ( k ; \u03bb ) 1 \u2212 f ( 0 ; \u03bb ) = \u03bb k e \u2212 \u03bb k ! ( 1 \u2212 e \u2212 \u03bb ) = \u03bb k ( e \u03bb \u2212 1 ) k ! {\\displaystyle g(k;\\lambda )=P(X=k\\mid X>0)={\\frac {f(k;\\lambda )}{1-f(0;\\lambda )}}={\\frac {\\lambda ^{k}e^{-\\lambda }}{k!\\left(1-e^{-\\lambda }\\right)}}={\\frac {\\lambda ^{k}}{(e^{\\lambda }-1)k!}}} The mean is E \u2061  = \u03bb 1 \u2212 e \u2212 \u03bb = \u03bb e \u03bb e \u03bb \u2212 1 {\\displaystyle \\operatorname {E} ={\\frac {\\lambda }{1-e^{-\\lambda }}}={\\frac {\\lambda e^{\\lambda }}{e^{\\lambda }-1}}} and the variance is Var \u2061  = \u03bb + \u03bb 2 1 \u2212 e \u2212 \u03bb \u2212 \u03bb 2 ( 1 \u2212 e \u2212 \u03bb ) 2 = E \u2061  ( 1 + \u03bb \u2212 E \u2061  ) {\\displaystyle \\operatorname {Var} ={\\frac {\\lambda +\\lambda ^{2}}{1-e^{-\\lambda }}}-{\\frac {\\lambda ^{2}}{(1-e^{-\\lambda })^{2}}}=\\operatorname {E} (1+\\lambda -\\operatorname {E} )}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a bracketing strategy, in each iteration the ITP queries the value of the function on one point and discards the part of the interval between two points where the function value shares the same sign. The queried point is calculated with three steps: it interpolates finding the regula falsi estimate, then it perturbes/truncates the estimate (similar to Regula falsi \u00a7 Improvements in regula falsi) and then projects the perturbed estimate onto an interval in the neighbourhood of the bisection midpoint. The neighbourhood around the bisection point is calculated in each iteration in order to guarantee minmax optimality (Theorem 2.1 of ). The method depends on three hyper-parameters \u03ba 1 \u2208 ( 0 , \u221e ) , \u03ba 2 \u2208 [ 1 , 1 + \u03d5 ) {\\displaystyle \\kappa _{1}\\in (0,\\infty ),\\kappa _{2}\\in \\left[1,1+\\phi \\right)} and n 0 \u2208 [ 0 , \u221e ) {\\displaystyle n_{0}\\in [0,\\infty )} where \u03d5 {\\displaystyle \\phi } is the golden ratio 1 2 ( 1 + 5 ) {\\displaystyle {\\tfrac {1}{2}}(1+{\\sqrt {5}})}: the first two control the size of the truncation and the third is a slack variable that controls the size of the interval for the projection step.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "First, since the self-improvement through learning is more direct and rapid than the evolution process, the social learning algorithm can improve the efficiency of the algorithms mimicking natural evolution. Second, compared with the interaction and learning behaviors in animal groups, the social learning process of human beings exhibits a higher level of intelligence. By emulating human learning behaviors, it is possible to arrive at more effective optimizers than existing swarm intelligence algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word collision refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force.In physics, collisions can be classified by the change in the total kinetic energy of the system before and after the collision: If most or all of the total kinetic energy is lost (dissipated as heat, sound, etc. or absorbed by the objects themselves), the collision is said to be inelastic; such collisions involve objects coming to a full stop. An example of such a collision is a car crash, as cars crumple inward when crashing, rather than bouncing off of each other. This is by design, for the safety of the occupants and bystanders should a crash occur - the frame of the car absorbs the energy of the crash instead.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These relations set strong limitations for the nonexistence of common eigenstates for incompatible observables. The Maccone\u2013Pati uncertainty relations have been experimentally tested for qutrit systems. The new uncertainty relations not only capture the incompatibility of observables but also of quantities that are physically measurable (as variances can be measured in the experiment).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to run safely on multiprocessor machines, access to shared resources (like files, data structures) must be serialized so that threads or processes do not attempt to modify the same resource at the same time. In order to prevent multiple threads from accessing or modifying a shared resource simultaneously, DragonFly employs critical sections, and serializing tokens to prevent concurrent access. While both Linux and FreeBSD 5 employ fine-grained mutex models to achieve higher performance on multiprocessor systems, DragonFly does not. Until recently, DragonFly also employed spls, but these were replaced with critical sections.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the modern demarcation point is a device defined by FCC rules (47 C.F.R. Part 68) to allow safe connection of third-party telephone customer-premises equipment and wiring to the Public Switched Telephone Network (PSTN). The modern demarcation point is the network interface device (NID) or intelligent network interface device (INID) also known as a \"smartjack\". The NID is the telco's property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When information is transferred across time, often to specific points in time, the process is known as forecasting. Forecasting usually requires time series methods, while prediction is often performed on cross-sectional data. Statistical techniques used for prediction include regression and its various sub-categories such as linear regression, generalized linear models (logistic regression, Poisson regression, Probit regression), etc. In case of forecasting, autoregressive moving average models and vector autoregression models can be utilized.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With no differing information to counter the untruths or the general agreement within isolated social clusters, some argue the outcome is an absence of a collective reality. Although social media sites have changed their algorithms to prevent the spread of fake news, the problem still exists. Furthermore, research has shown that while people may know what the scientific community has proved as a fact, they may still refuse to accept it as such.Researchers fear that misinformation in social media is \"becoming unstoppable.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In microbiology, genes can move freely even between distantly related bacteria, possibly extending to the whole bacterial domain. As a rule of thumb, microbiologists have assumed that kinds of Bacteria or Archaea with 16S ribosomal RNA gene sequences more similar than 97% to each other need to be checked by DNA-DNA hybridisation to decide if they belong to the same species or not. This concept was narrowed in 2006 to a similarity of 98.7%.DNA-DNA hybridisation is outdated, and results have sometimes led to misleading conclusions about species, as with the pomarine and great skua. Modern approaches compare sequence similarity using computational methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Microsoft .NET Framework, XML Literal allows a computer program to include XML directly in the code. It is currently only supported in VB.NET 9.0 and VB.NET 10.0. When a Visual Basic expression is embedded in an XML literal, the application creates a LINQ-to-XML object for each literal at run time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the scalar projection of a vector a {\\displaystyle \\mathbf {a} } on (or onto) a vector b , {\\displaystyle \\mathbf {b} ,} also known as the scalar resolute of a {\\displaystyle \\mathbf {a} } in the direction of b , {\\displaystyle \\mathbf {b} ,} is given by: s = \u2016 a \u2016 cos \u2061 \u03b8 = a \u22c5 b ^ , {\\displaystyle s=\\left\\|\\mathbf {a} \\right\\|\\cos \\theta =\\mathbf {a} \\cdot \\mathbf {\\hat {b}} ,} where the operator \u22c5 {\\displaystyle \\cdot } denotes a dot product, b ^ {\\displaystyle {\\hat {\\mathbf {b} }}} is the unit vector in the direction of b , {\\displaystyle \\mathbf {b} ,} \u2016 a \u2016 {\\displaystyle \\left\\|\\mathbf {a} \\right\\|} is the length of a , {\\displaystyle \\mathbf {a} ,} and \u03b8 {\\displaystyle \\theta } is the angle between a {\\displaystyle \\mathbf {a} } and b {\\displaystyle \\mathbf {b} } . The term scalar component refers sometimes to scalar projection, as, in Cartesian coordinates, the components of a vector are the scalar projections in the directions of the coordinate axes. The scalar projection is a scalar, equal to the length of the orthogonal projection of a {\\displaystyle \\mathbf {a} } on b {\\displaystyle \\mathbf {b} } , with a negative sign if the projection has an opposite direction with respect to b {\\displaystyle \\mathbf {b} } . Multiplying the scalar projection of a {\\displaystyle \\mathbf {a} } on b {\\displaystyle \\mathbf {b} } by b ^ {\\displaystyle \\mathbf {\\hat {b}} } converts it into the above-mentioned orthogonal projection, also called vector projection of a {\\displaystyle \\mathbf {a} } on b {\\displaystyle \\mathbf {b} } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If K = R {\\displaystyle \\mathbb {K} =\\mathbb {R} } , then A \u2217 = A T {\\displaystyle A^{*}=A^{\\textsf {T}}} . For A \u2208 K m \u00d7 n {\\displaystyle A\\in \\mathbb {K} ^{m\\times n}} , ran \u2061 ( A ) {\\displaystyle \\operatorname {ran} (A)} (standing for \"range\") denotes the column space (image) of A {\\displaystyle A} (the space spanned by the column vectors of A {\\displaystyle A} ) and ker \u2061 ( A ) {\\displaystyle \\ker(A)} denotes the kernel (null space) of A {\\displaystyle A} . Finally, for any positive integer n {\\displaystyle n} , I n \u2208 K n \u00d7 n {\\displaystyle I_{n}\\in \\mathbb {K} ^{n\\times n}} denotes the n \u00d7 n {\\displaystyle n\\times n} identity matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some software originating on big-endian machines such as Silicon Graphics, colors were stored in 32 bits similar to ARGB32, but with the alpha in the bottom 8 bits rather than the top. For example, 808000FF would be Red and Green:50.2%, Blue:0% and Alpha:100%, a brown. This is what you would get if RGBA8888 data was read as words on these machines. It is used in Portable Arbitrary Map and in FLTK, but in general it is rare. The bytes are stored in memory on a little-endian machine in the order ABGR.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The requirements for the United States are covered in Title 47 of the Code of Federal Regulations, part 97.119. Land mobile two-way (including public safety and business mobile) require station identifications by call sign. In the case of the GMRS service, this is to be done by each station in a similar manner to the amateur practice, though the time limit is fifteen minutes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Numerical semigroups are commutative monoids and are also known as numerical monoids.The definition of numerical semigroup is intimately related to the problem of determining nonnegative integers that can be expressed in the form x1n1 + x2 n2 + ... + xr nr for a given set {n1, n2, ..., nr} of positive integers and for arbitrary nonnegative integers x1, x2, ..., xr. This problem had been considered by several mathematicians like Frobenius (1849\u20131917) and Sylvester (1814\u20131897) at the end of the 19th century. During the second half of the twentieth century, interest in the study of numerical semigroups resurfaced because of their applications in algebraic geometry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Schedule 1 drugs have little or no medical benefit, hence their limitations on prescribing. District nurses and health visitors have had limited prescribing rights since the mid-1990s; until then, prescriptions for dressings and simple medicines had to be signed by a doctor. Once issued, a prescription is taken by the patient to a pharmacy, which dispenses the medicine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With thirty diverse bidders unable to communicate about strategy except through their bids, forming such unanimous agreement is difficult at best.\" Nevertheless, Federal Communications Commission (FCC) experimented with precautions for spectrum auctions like restricting visibility of bids, limiting the number of bids and anonymous bidding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To have a lack-of-fit sum of squares that differs from the residual sum of squares, one must observe more than one y-value for each of one or more of the x-values. One then partitions the \"sum of squares due to error\", i.e., the sum of squares of residuals, into two components: sum of squares due to error = (sum of squares due to \"pure\" error) + (sum of squares due to lack of fit).The sum of squares due to \"pure\" error is the sum of squares of the differences between each observed y-value and the average of all y-values corresponding to the same x-value. The sum of squares due to lack of fit is the weighted sum of squares of differences between each average of y-values corresponding to the same x-value and the corresponding fitted y-value, the weight in each case being simply the number of observed y-values for that x-value. Because it is a property of least squares regression that the vector whose components are \"pure errors\" and the vector of lack-of-fit components are orthogonal to each other, the following equality holds: \u2211 ( observed value \u2212 fitted value ) 2 (error) = \u2211 ( observed value \u2212 local average ) 2 (pure error) + \u2211 weight \u00d7 ( local average \u2212 fitted value ) 2 (lack of fit) {\\displaystyle {\\begin{aligned}&\\sum ({\\text{observed value}}-{\\text{fitted value}})^{2}&&{\\text{(error)}}\\\\&\\qquad =\\sum ({\\text{observed value}}-{\\text{local average}})^{2}&&{\\text{(pure error)}}\\\\&\\qquad \\qquad {}+\\sum {\\text{weight}}\\times ({\\text{local average}}-{\\text{fitted value}})^{2}&&{\\text{(lack of fit)}}\\end{aligned}}} Hence the residual sum of squares has been completely decomposed into two components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, testing measures are never perfectly consistent. Theories of test reliability have been developed to estimate the effects of inconsistency on the accuracy of measurement. The basic starting point for almost all theories of test reliability is the idea that test scores reflect the influence of two sorts of factors:1. Consistency factors: stable characteristics of the individual or the attribute that one is trying to measure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. It assumes that the expected returns are known and is optimal for a bettor who values their wealth logarithmically. J. L. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This technique was developed by C E Wynn-Williams at The Cavendish Laboratory and first published in 1932. The original counters used a cascade of \"Eccles-Jordan\" divide-by-two circuits, today known as flip flops. Early count readings were therefore binary numbers and had to be manually re-calculated into decimal values. Later, with the development of electronic indicators, which started with the introduction of the Dekatron readout tube in the 1950s, and culminating in the modern digital indicator, totalised readings came to be directly indicated in decimal notation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1 cosh \u2061 t = 2 e t + e \u2212 t = \u2211 n = 0 \u221e E n n ! \u22c5 t n {\\displaystyle {\\frac {1}{\\cosh t}}={\\frac {2}{e^{t}+e^{-t}}}=\\sum _{n=0}^{\\infty }{\\frac {E_{n}}{n! }}\\cdot t^{n}} ,where cosh \u2061 ( t ) {\\displaystyle \\cosh(t)} is the hyperbolic cosine function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the finding of a pathognomonic sign or symptom it is almost certain that the target condition is present, and in the absence of finding a sine qua non sign or symptom it is almost certain that the target condition is absent. In reality, however, the subjective probability of the presence of a condition is never exactly 100% or 0%, so tests are rather aimed at estimating a post-test probability of a condition or other entity. Most diagnostic tests basically use a reference group to establish performance data such as predictive values, likelihood ratios and relative risks, which are then used to interpret the post-test probability for an individual. In monitoring tests of an individual, the test results from previous tests on that individual may be used as a reference to interpret subsequent tests.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the positive remainder is always chosen, but in computing, programming languages choose depending on the language and the signs of a or n. Standard Pascal and ALGOL 68, for example, give a positive remainder (or 0) even for negative divisors, and some programming languages, such as C90, leave it to the implementation when either of n or a is negative (see the table under \u00a7 In programming languages for details). a modulo 0 is undefined in most systems, although some do define it as a. As described by Leijen, Boute argues that Euclidean division is superior to the other ones in terms of regularity and useful mathematical properties, although floored division, promoted by Knuth, is also a good definition. Despite its widespread use, truncated division is shown to be inferior to the other definitions. However, truncated division satisfies the identity ( \u2212 a ) / b = \u2212 ( a / b ) = a / ( \u2212 b ) {\\displaystyle ({-a})/b={-(a/b)}=a/({-b})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scholarly writing, an important objective of classifying sources is to determine their independence and reliability. In contexts such as historical writing, it is almost always advisable to use primary sources and that \"if none are available, it is only with great caution that  may proceed to make use of secondary sources.\" Sreedharan believes that primary sources have the most direct connection to the past and that they \"speak for themselves\" in ways that cannot be captured through the filter of secondary sources.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this sense the solution represents the unbounded \u03bc operator that can, if necessary, hunt ad infinitum along the unbounded string of registers until it finds what it is looking for. The pointer register is exactly like any other register with one exception: under the circumstances called \"indirect addressing\" it provides its contents, rather than the address-operand in the state machine's TABLE, to be the address of the target register (including possibly itself! ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most programming languages, even those with no explicit Boolean type, have support for Boolean algebraic operations such as conjunction (AND, &, *), disjunction (OR, |, +), equivalence (EQV, =, ==), exclusive or/non-equivalence (XOR, NEQV, ^, !=, \u00ac), and negation (NOT, ~, !, \u00ac). In some languages, like Ruby, Smalltalk, and Alice the true and false values belong to separate classes, e.g., True and False, respectively, so there is no one Boolean type. In SQL, which uses a three-valued logic for explicit comparisons because of its special treatment of Nulls, the Boolean data type (introduced in SQL:1999) is also defined to include more than two truth values, so that SQL Booleans can store all logical values resulting from the evaluation of predicates in SQL. A column of Boolean type can be restricted to just TRUE and FALSE though.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In marketing research, the most frequently used types of observational techniques are: Personal observation observing products in use to detect usage patterns and problems observing license plates in store parking lots determining the socio-economic status of shoppers determining the level of package scrutiny determining the time it takes to make a purchase decision Mechanical observationeye-tracking analysis while subjects watch advertisements oculometers \u2013 what the subject is looking at pupilometers \u2013 how interested is the viewer electronic checkout scanners \u2013 records purchase behaviour on-site cameras in stores people meters (as in monitoring television viewing) e.g.Nielsen box voice pitch meters \u2013 measures emotional reactions psychogalvanometer \u2013 measures galvanic skin response Auditsretail audits to determine the quality of service in stores inventory audits to determine product acceptance shelf space audits scanner based audits Trace Analysiscredit card records computer cookie records garbology \u2013 looking for traces of purchase patterns in garbage detecting store traffic patterns by observing the wear in the floor (long term) or the dirt on the floor (short term) exposure to advertisements Content analysisobserve the content of magazines, television broadcasts, radio broadcasts, or newspapers, either articles, programs, or advertisements", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a covering set for a sequence of integers refers to a set of prime numbers such that every term in the sequence is divisible by at least one member of the set. The term \"covering set\" is used only in conjunction with sequences possessing exponential growth.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C99 version of the C programming language and the C++11 version of C++, a long long type is supported that has double the minimum capacity of the standard long. This type is not supported by compilers that require C code to be compliant with the previous C++ standard, C++03, because the long long type did not exist in C++03. For an ANSI/ISO compliant compiler, the minimum requirements for the specified ranges, that is, \u2212(263\u22121) to 263\u22121 for signed and 0 to 264\u22121 for unsigned, must be fulfilled; however, extending this range is permitted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the above algorithm is typically iterated to produce a sequence x n {\\displaystyle \\mathbf {x} _{n}} , n = 1 , 2 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, The Poisson scatter theorem describes a probability model of random scattering. It implies that the number of points in a fixed region will follow a Poisson distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks. A major theme in the mathematical and computational analysis of GDSs is to relate their structural properties (e.g. the network connectivity) and the global dynamics that result. The work on GDSs considers finite graphs and finite state spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i.e., if there exists a Turing machine which will enumerate all valid strings of the language. Recursively enumerable languages are known as type-0 languages in the Chomsky hierarchy of formal languages. All regular, context-free, context-sensitive and recursive languages are recursively enumerable. The class of all recursively enumerable languages is called RE.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These terms in biology contain no judgement about the sophistication, superiority, value or adaptiveness of the named trait. \"Primitive\" in biology means only that the character appeared first in the common ancestor of a clade group and has been passed on largely intact to more recent members of the clade.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, the image and the codomain of the function are equal. A surjective function is a surjection. Notationally: \u2200 y \u2208 Y , \u2203 x \u2208 X such that y = f ( x ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sets and possibles alike make for a crowded ontology. Sets and possibles alike raise questions we have no way to answer. I propose to be equally undisturbed by these equally mysterious mysteries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a logical system has the soundness property if every formula that can be proved in the system is logically valid with respect to the semantics of the system. In most cases, this comes down to its rules having the property of preserving truth. The converse of soundness is known as completeness. A logical system with syntactic entailment \u22a2 {\\displaystyle \\vdash } and semantic entailment \u22a8 {\\displaystyle \\models } is sound if for any sequence A 1 , A 2 , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the CbD approach, developed by Ehtibar Dzhafarov, Janne Kujala, and colleagues, (non)contextuality is treated as a property of any system of random variables, defined as a set R = { R q c: q \u2208 Q , q \u227a c , c \u2208 C } {\\displaystyle {\\mathcal {R}}=\\left\\{R_{q}^{c}:q\\in Q,q\\prec c,c\\in C\\right\\}} in which each random variable R q c {\\displaystyle R_{q}^{c}} is labeled by its content q {\\displaystyle q} , the property it measures, and its context c {\\displaystyle c} , the set of recorded circumstances under which it is recorded (including but not limited to which other random variables it is recorded together with); q \u227a c {\\displaystyle q\\prec c} stands for \" q {\\displaystyle q} is measured in c {\\displaystyle c} \". The variables within a context are jointly distributed, but variables from different contexts are stochastically unrelated, defined on different sample spaces. A (probabilistic) coupling of the system R {\\displaystyle {\\mathcal {R}}} is defined as a system S {\\displaystyle S} in which all variables are jointly distributed and, in any context c {\\displaystyle c} , R c = { R q c: q \u2208 Q , q \u227a c } {\\displaystyle R^{c}=\\left\\{R_{q}^{c}:q\\in Q,q\\prec c\\right\\}} and S c = { S q c: q \u2208 Q , q \u227a c } {\\displaystyle S^{c}=\\left\\{S_{q}^{c}:q\\in Q,q\\prec c\\right\\}} are identically distributed. The system is considered noncontextual if it has a coupling S {\\displaystyle S} such that the probabilities Pr  {\\displaystyle \\Pr \\left} are maximal possible for all contexts c , c \u2032 {\\displaystyle c,c'} and contents q {\\displaystyle q} such that q \u227a c , c \u2032 {\\displaystyle q\\prec c,c'} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode, the algorithm may be expressed as: function CountingSort(input, k) count \u2190 array of k + 1 zeros output \u2190 array of same length as input for i = 0 to length(input) - 1 do j = key(input) count = count + 1 for i = 1 to k do count = count + count for i = length(input) - 1 down to 0 do j = key(input) count = count - 1 output] = input return output Here input is the input array to be sorted, key returns the numeric key of each item in the input array, count is an auxiliary array used first to store the numbers of items with each key, and then (after the second loop) to store the positions where items with each key should be placed, k is the maximum value of the non-negative key values and output is the sorted output array. In summary, the algorithm loops over the items in the first loop, computing a histogram of the number of times each key occurs within the input collection. After that in the second loop, it performs a prefix sum computation on count in order to determine, for each key, the position range where the items having that key should be placed; i.e. items of key i {\\displaystyle i} should be placed starting in position count. Finally, in the third loop, it loops over the items of input again, but in reverse order, moving each item into its sorted position in the output array.The relative order of items with equal keys is preserved here; i.e., this is a stable sort.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Berkeley RISC design, only eight registers out of a total of 64 are visible to the programs. The complete set of registers are known as the register file, and any particular set of eight as a window. The file allows up to eight procedure calls to have their own register sets. As long as the program does not call down chains longer than eight calls deep, the registers never have to be spilled, i.e. saved out to main memory or cache which is a slow process compared to register access.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the configuration model, a giant component (GC) exists if \u27e8 k 2 \u27e9 \u2212 2 \u27e8 k \u27e9 > 0 , {\\displaystyle \\langle k^{2}\\rangle -2\\langle k\\rangle >0,} where \u27e8 k \u27e9 {\\displaystyle \\langle k\\rangle } and \u27e8 k 2 \u27e9 {\\displaystyle \\langle k^{2}\\rangle } are the first and second moments of the degree distribution. That means that, the critical threshold solely depends on quantities which are uniquely determined by the degree distribution p k {\\displaystyle p_{k}} . Configuration model generates locally tree-like networks, meaning that any local neighborhood in such a network takes the form of a tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 19th century, Carl Friedrich Gauss observed that non-zero integer solutions to homogeneous polynomial equations with rational coefficients exist if non-zero rational solutions exist.In the 1850s, Leopold Kronecker formulated the Kronecker\u2013Weber theorem, introduced the theory of divisors, and made numerous other connections between number theory and algebra. He then conjectured his \"liebster Jugendtraum\" (\"dearest dream of youth\"), a generalization that was later put forward by Hilbert in a modified form as his twelfth problem, which outlines a goal to have number theory operate only with rings that are quotients of polynomial rings over the integers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of computer science, a pre-topological order or pre-topological ordering of a directed graph is a linear ordering of its vertices such that if there is a directed path from vertex u to vertex v and v comes before u in the ordering, then there is also a directed path from vertex v to vertex u.If the graph is a directed acyclic graph (DAG), topological orderings are pre-topological orderings and vice versa. In other cases, any pre-topological ordering gives a partial order. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, this case is easy to detect and correct. With the modulus out of the way, the asymptotic complexity of the algorithm only depends on the multiplication algorithm used to square s at each step. The simple \"grade-school\" algorithm for multiplication requires O(p2) bit-level or word-level operations to square a p-bit number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of telegraphy and radiotelegraphy, individual countries, and sometimes individual states, sometimes set their own regulations. For example, in the period around 1909, California required that \"messages must, if practicable, be transmitted immediately on and in order of receipt; if not practicable, then in the following order:\" Messages from public agents of the State or of the United States on public business. Messages for immediate publication in newspapers, and not for any secret use. Message relating to sickness or death. Other messages in the order of filing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Performing this calculation in any software that used the floating-point coprocessor, such as Windows Calculator, would allow users to discover whether their Pentium chip was affected.The correct value of the calculation is: When converted to the hexadecimal value used by the processor, 4,195,835 = 0x4005FB and 3,145,727 = 0x2FFFFF. The '5' in 0x4005FB triggers the access to the 'empty' array cells. As a result, the value returned by a flawed Pentium processor is incorrect at or beyond four digits: which is actually the value of 4,195,579/3,145,727 =4,195,835 - 256/3,145,727.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in particular in computational algebra, the Berlekamp\u2013Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus. As a consequence of Gauss's lemma, this amounts to solving the problem also over the rationals. The algorithm starts by finding factorizations over suitable finite fields using Hensel's lemma to lift the solution from modulo a prime p to a convenient power of p. After this the right factors are found as a subset of these. The worst case of this algorithm is exponential in the number of factors. Van Hoeij (2002) improved this algorithm by using the LLL algorithm, substantially reducing the time needed to choose the right subsets of mod p factors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Every (conditional) line has zero or more asserted propositions on the right.In other words, natural deduction and sequent calculus systems are particular distinct kinds of Gentzen-style systems. Hilbert-style systems typically have a very small number of inference rules, relying more on sets of axioms. Gentzen-style systems typically have very few axioms, if any, relying more on sets of rules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, the mapping information exists as set and it has a pair for each element in the domain. Of course for any set from some class, there is always the unique element of the singleton 1 {\\displaystyle 1} , and so merely a chosen range being a set does not suffice to be granted a function set. In summary, in the set theory context the focus is on capturing particular total relations that are functional.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s, Plantronics created a line of cordless products using infrared technology. Though the technology utilized was the same one being used by television remote controls, the link did not require a Federal Communications Commission (FCC) telecommunications approval. One of the first products used the infrared beam to create a communications link between a small transmitter and a base unit which was connected to the telephone network. This product was the first \"echo-free\" speakerphone for use in conference rooms. The small transmitter could be handheld or clipped to clothing to ensure a good pickup of the speaker's voice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. Random projection methods are known for their power, simplicity, and low error rates when compared to other methods. According to experimental results, random projection preserves distances well, but empirical results are sparse. They have been applied to many natural language tasks under the name random indexing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the system is described by a matrix rather than a vector, this problem can be written as min X \u2016 A X \u2212 Y \u2016 2 + \u03bb \u2016 X \u2016 2 , {\\displaystyle \\min _{X}\\|AX-Y\\|^{2}+\\lambda \\|X\\|^{2},} where the vector norm enforcing a regularization penalty on x {\\displaystyle x} has been extended to a matrix norm on X {\\displaystyle X} . Matrix regularization has applications in matrix completion, multivariate regression, and multi-task learning. Ideas of feature and group selection can also be extended to matrices, and these can be generalized to the nonparametric case of multiple kernel learning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Gauss\u2013Kuzmin distribution is a discrete probability distribution that arises as the limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1). The distribution is named after Carl Friedrich Gauss, who derived it around 1800, and Rodion Kuzmin, who gave a bound on the rate of convergence in 1929. It is given by the probability mass function p ( k ) = \u2212 log 2 \u2061 ( 1 \u2212 1 ( 1 + k ) 2 ) . {\\displaystyle p(k)=-\\log _{2}\\left(1-{\\frac {1}{(1+k)^{2}}}\\right)~.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Slutsky\u2019s theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables.The theorem was named after Eugen Slutsky. Slutsky's theorem is also attributed to Harald Cram\u00e9r.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle e\\cdot e=e.} The similarly defined trivial monoid is also a group since its only element is its own inverse, and is hence the same as the trivial group. The trivial group is distinct from the empty set, which has no elements, hence lacks an identity element, and so cannot be a group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and especially game theory, the airport problem is a type of fair division problem in which it is decided how to distribute the cost of an airport runway among different players who need runways of different lengths. The problem was introduced by S. C. Littlechild and G. Owen in 1973. Their proposed solution is: Divide the cost of providing the minimum level of required facility for the smallest type of aircraft equally among the number of landings of all aircraft Divide the incremental cost of providing the minimum level of required facility for the second smallest type of aircraft (above the cost of the smallest type) equally among the number of landings of all but the smallest type of aircraft. Continue thus until finally the incremental cost of the largest type of aircraft is divided equally among the number of landings made by the largest aircraft type.The authors note that the resulting set of landing charges is the Shapley value for an appropriately defined game.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fields of computational linguistics and natural language processing (NLP), esp. corpus linguistics and machine-learned NLP, it is common to disregard hapax legomena (and sometimes other infrequent words), as they are likely to have little value for computational techniques. This disregard has the added benefit of significantly reducing the memory use of an application, since, by Zipf's law, many words are hapax legomena.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mobile telecommunications, inter-cell interference coordination (ICIC) techniques apply restrictions to the radio resource management (RRM) block, improving favorable channel conditions across subsets of users that are severely impacted by the interference, and thus attaining high spectral efficiency. This coordinated resource management can be achieved through fixed, adaptive or real-time coordination with the help of additional inter-cell signaling in which the signaling rate can vary accordingly. In general, inter-cell signaling refers to the communication interface among neighboring cells and the received measurement message reports from user equipments (UEs).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, a file system may not make use of a storage device but can be used to organize and represent access to any data, whether it is stored or dynamically generated (e.g. procfs).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first step, messages are passed inwards: starting at the leaves, each node passes a message along the (unique) edge towards the root node. The tree structure guarantees that it is possible to obtain messages from all other adjoining nodes before passing the message on. This continues until the root has obtained messages from all of its adjoining nodes. The second step involves passing the messages back out: starting at the root, messages are passed in the reverse direction. The algorithm is completed when all leaves have received their messages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can also be seen as a methodology for writing and structuring large theories: start with a theory, T 0 {\\displaystyle T_{0}} , that is known (or assumed) to be consistent, and successively build conservative extensions T 1 {\\displaystyle T_{1}} , T 2 {\\displaystyle T_{2}} , ... of it. Recently, conservative extensions have been used for defining a notion of module for ontologies: if an ontology is formalized as a logical theory, a subtheory is a module if the whole ontology is a conservative extension of the subtheory. An extension which is not conservative may be called a proper extension.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some models (standard linear regression, in particular), the equations for each of the data points i = 1, ..., n are stacked together and written in vector form as y = X \u03b2 + \u03b5 , {\\displaystyle \\mathbf {y} =\\mathbf {X} {\\boldsymbol {\\beta }}+{\\boldsymbol {\\varepsilon }},\\,} where y = ( y 1 y 2 \u22ee y n ) , X = ( x 1 \u2032 x 2 \u2032 \u22ee x n \u2032 ) = ( x 11 \u22ef x 1 p x 21 \u22ef x 2 p \u22ee \u22f1 \u22ee x n 1 \u22ef x n p ) , \u03b2 = ( \u03b2 1 \u22ee \u03b2 p ) , \u03b5 = ( \u03b5 1 \u03b5 2 \u22ee \u03b5 n ) . {\\displaystyle \\mathbf {y} ={\\begin{pmatrix}y_{1}\\\\y_{2}\\\\\\vdots \\\\y_{n}\\end{pmatrix}},\\quad \\mathbf {X} ={\\begin{pmatrix}\\mathbf {x} '_{1}\\\\\\mathbf {x} '_{2}\\\\\\vdots \\\\\\mathbf {x} '_{n}\\end{pmatrix}}={\\begin{pmatrix}x_{11}&\\cdots &x_{1p}\\\\x_{21}&\\cdots &x_{2p}\\\\\\vdots &\\ddots &\\vdots \\\\x_{n1}&\\cdots &x_{np}\\end{pmatrix}},\\quad {\\boldsymbol {\\beta }}={\\begin{pmatrix}\\beta _{1}\\\\\\vdots \\\\\\beta _{p}\\end{pmatrix}},\\quad {\\boldsymbol {\\varepsilon }}={\\begin{pmatrix}\\varepsilon _{1}\\\\\\varepsilon _{2}\\\\\\vdots \\\\\\varepsilon _{n}\\end{pmatrix}}.} The matrix X is known as the design matrix and encodes all known information about the independent variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-exponential fitting, the time-resolved curves are fitted with an exponential decay model to determine the decay constants. While this method is straightforward, it has low accuracy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler.Uses of Lagrange polynomials include the Newton\u2013Cotes method of numerical integration, Shamir's secret sharing scheme in cryptography, and Reed\u2013Solomon error correction in coding theory. For equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, multidimensional signal processing covers all signal processing done using multidimensional signals and systems. While multidimensional signal processing is a subset of signal processing, it is unique in the sense that it deals specifically with data that can only be adequately detailed using more than one dimension. In m-D digital signal processing, useful data is sampled in more than one dimension. Examples of this are image processing and multi-sensor radar detection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and natural language processing, a topic model is a type of statistical model for discovering the abstract \"topics\" that occur in a collection of documents. Topic modeling is a frequently used text-mining tool for discovery of hidden semantic structures in a text body. Intuitively, given that a document is about a particular topic, one would expect particular words to appear in the document more or less frequently: \"dog\" and \"bone\" will appear more often in documents about dogs, \"cat\" and \"meow\" will appear in documents about cats, and \"the\" and \"is\" will appear approximately equally in both. A document typically concerns multiple topics in different proportions; thus, in a document that is 10% about cats and 90% about dogs, there would probably be about 9 times more dog words than cat words.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Hamiltonian cycle polynomial of an n\u00d7n-matrix is a polynomial in its entries, defined as ham \u2061 ( A ) = \u2211 \u03c3 \u2208 H n \u220f i = 1 n a i , \u03c3 ( i ) {\\displaystyle \\operatorname {ham} (A)=\\sum _{\\sigma \\in H_{n}}\\prod _{i=1}^{n}a_{i,\\sigma (i)}} where H n {\\displaystyle H_{n}} is the set of n-permutations having exactly one cycle. This is an algebraic option useful, in a number of cases, for determining the existence of a Hamiltonian cycle in a directed graph. It is a generalization of the number of Hamiltonian cycles of a digraph as the sum of the products of its Hamiltonian cycles' arc weights (all of which equal unity) for weighted digraphs with arc weights taken from a given commutative ring. In the meantime, for an undirected weighted graph the sum of the products of the edge weights of its Hamiltonian cycles containing any fixed edge (i,j) can be expressed as the product of the weight of (i,j) and the Hamiltonian cycle polynomial of a matrix received from its weighted adjacency matrix via subjecting its rows and columns to any permutation mapping i to 1 and j to 2 and then removing its 1-st row and 2-nd column.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a k-th percentile, also known as percentile score or centile, is a score below which a given percentage k of scores in its frequency distribution falls (\"exclusive\" definition) or a score at or below which a given percentage falls (\"inclusive\" definition). Percentiles are expressed in the same unit of measurement as the input scores, not in percent; for example, if the scores refer to human weight, the corresponding percentiles will be expressed in kilograms or pounds. In the limit of an infinite sample size, the percentile approximates the percentile function, the inverse of the cumulative distribution function. Percentiles are a type of quantiles, obtained adopting a subdivision into 100 groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The improvements included magnetic (non-mercury) core memory of 2000 to 10000 words, UNISERVO II tape drives, which could use either the old UNIVAC I metal tapes or the new PET film tapes, and some circuits that were transistorized (although it was still a vacuum-tube computer). It was fully compatible with existing UNIVAC I programs for both code and data. The UNIVAC II also added some instructions to the UNIVAC I's instruction set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "x {\\displaystyle \\exists !x} means \"there exists exactly one x\".In any case (for any function), the following holds: \u2200 x \u2208 X , \u2203 ! y \u2208 Y such that y = f ( x ) . {\\displaystyle \\forall x\\in X,\\exists !y\\in Y{\\text{ such that }}y=f(x).} An injective function need not be surjective (not all elements of the codomain may be associated with arguments), and a surjective function need not be injective (some images may be associated with more than one argument). The four possible combinations of injective and surjective features are illustrated in the adjacent diagrams.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonetics, a tilde is used as a diacritic that is placed above a letter, below it or superimposed onto the middle of it: A tilde above a letter indicates nasalization, e.g. , . A tilde superimposed onto the middle of a letter indicates velarization or pharyngealization, e.g. , . If no precomposed Unicode character exists, the Unicode character U+0334 \u25cc\u0334 COMBINING TILDE OVERLAY can be used to generate one. A tilde below a letter indicates laryngealisation, e.g. . If no precomposed Unicode character exists, the Unicode character U+0330 \u25cc\u0330 COMBINING TILDE BELOW can be used to generate one.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory, a branch of mathematical logic, proof mining (or proof unwinding) is a research program that studies or analyzes formalized proofs, especially in analysis, to obtain explicit bounds, ranges or rates of convergence from proofs that, when expressed in natural language, appear to be nonconstructive. This research has led to improved results in analysis obtained from the analysis of classical proofs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 2015, the IETF upgraded its weak \"informational\" recommendation of 1998, that datagram switching nodes perform active queue management (AQM), to make it a stronger and more detailed \"best current practice\" recommendation. While the initial datagram queueing model was simple to implement and needed no more tuning than queue lengths, support of more sophisticated and parametrized mechanisms were found necessary \"to improve and preserve Internet performance\" (RED, ECN etc.). Further research on the subject was also called for, with a list of identified items.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That is, for any property P ( k ) {\\displaystyle P(k)} of the integer k {\\displaystyle k} , one can rewrite the restricted sum \u2211 k: P ( k ) f ( k ) {\\displaystyle \\sum _{k:P(k)}f(k)} in the unrestricted form \u2211 k f ( k ) \u22c5  {\\displaystyle \\sum _{k}f(k)\\cdot } . With this convention, f ( k ) {\\displaystyle f(k)} does not need to be defined for the values of k for which the Iverson bracket equals 0; that is, a summand f ( k )  {\\displaystyle f(k)} must evaluate to 0 regardless of whether f ( k ) {\\displaystyle f(k)} is defined. The notation was originally introduced by Kenneth E. Iverson in his programming language APL, though restricted to single relational operators enclosed in parentheses, while the generalisation to arbitrary statements, notational restriction to square brackets, and applications to summation, was advocated by Donald Knuth to avoid ambiguity in parenthesized logical expressions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This was demonstrated more formally and in greater detail by Xavier D\u00e9fago, et al.A fundamental result in distributed computing is that achieving consensus in asynchronous systems in which even one crash failure can occur is impossible in the most general case. This was shown in 1985 by Michael J. Fischer, Nancy Lynch, and Mike Paterson, and is sometimes called the FLP result. Since consensus and atomic broadcast are equivalent, FLP applies also to atomic broadcast. The FLP result does not prohibit the implementation of atomic broadcast in practice, but it does require making less stringent assumptions than FLP in some respect, such as about processor and communication timings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, the inventory is grouped into three categories (A, B, and C) in order of their estimated importance. 'A' items are very important for an organization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of queries that read data from the database, the SPARQL language specifies four different query variations for different purposes. SELECT query Used to extract raw values from a SPARQL endpoint, the results are returned in a table format. CONSTRUCT query Used to extract information from the SPARQL endpoint and transform the results into valid RDF.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Commodore 64 used x5C (ASCII: \\) while the Oric used x5F (ASCII: _). IBM's EBCDIC code page 037 uses xB1 for the \u00a3 while its code page 285 uses x5B. ICL's 1900-series mainframes used a six-bit (64-position character set) encoding for characters, loosely based on BS 4730, with the \u00a3 symbol represented as octal 23 (hex 13, dec 19).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "r is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface). \u2113 is the length of the object to or over which the torque is being applied. \u03c6 (phi) is the angle of twist in radians. G is the shear modulus, also called the modulus of rigidity, and is usually given in gigapascals (GPa), lbf/in2 (psi), or lbf/ft2 or in ISO units N/mm2. The product JTG is called the torsional rigidity wT.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Jessen\u2013Wintner theorem, introduced by Jessen and Wintner (1935), asserts that a random variable of Jessen\u2013Wintner type, meaning the sum of an almost surely convergent series of independent discrete random variables, is of pure type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Celtic languages there is a distinction between the so-called substantive verb, used when the predicate is an adjective phrase or prepositional phrase, and the so-called copula, used when the predicate is a noun. The conjugation of the Old Irish and Middle Welsh verbs is as follows: The forms of the Old Irish present tense of the substantive verb, as well as Welsh taw, come from the PIE root *st\u0101-. The other forms are from the roots *es- and *bh\u016b-. Welsh mae originally meant \"here is\" (cf. yma 'here').", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the perfect fifth with ratio 3/2 (equivalent to 31/ 21) and the perfect fourth with ratio 4/3 (equivalent to 22/ 31) are Pythagorean intervals. All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system. However, some Pythagorean intervals are also used in other tuning systems. For instance, the above-mentioned Pythagorean perfect fifth and fourth are also used in just intonation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a normalizing constant is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e.g., to make it a probability density function or a probability mass function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and machine learning, double descent is the phenomenon where a statistical model with a small number of parameters and a model with an extremely large number of parameters have a small error, but a model whose number of parameters is about the same as the number of data points used to train the model will have a large error. It was discovered around 2018 when researchers were trying to reconcile the bias-variance tradeoff in classical statistics, which states that having too many parameters will yield an extremely large error, with the 2010s empirical observation of machine learning practitioners that the larger models are, the better they work. The scaling behavior of double descent has been found to follow a broken neural scaling law functional form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "19. Specifying a series of logical operators or inferential system which captures all or most cases to which the concept applies (algorithm). 20.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter \u03b8 of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized by the statistician Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A sticking knife scores points. The thrower must be standing at least a set distance away from the target, with higher distances for more challenging events. IKTHOF keeps a ranking of its members based on their performance during these sponsored competitions. EuroThrowers maintains a register of the world records, and for each championship publishes the full scores together with the meetings' reports.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of sieve theory the Tur\u00e1n sieve is of combinatorial type: deriving from a rudimentary form of the inclusion\u2013exclusion principle. The result gives an upper bound for the size of the sifted set. Let A be a set of positive integers \u2264 x and let P be a set of primes. For each p in P, let Ap denote the set of elements of A divisible by p and extend this to let Ad be the intersection of the Ap for p dividing d, when d is a product of distinct primes from P. Further let A1 denote A itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, the term means a record of both completed and attempted accesses and service, or data forming a logical path linking a sequence of events, used to trace the transactions that have affected the contents of a record. In information or communications security, information audit means a chronological record of system activities to enable the reconstruction and examination of the sequence of events and/or changes in an event. Information put away or transmitted in paired structure that might be depended upon in court. An audit trail is a progression of records of computer data about a working framework, an application, or client exercises.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This choice is motivated by their status as the driving force behind the development of algebraic number theory. Since the late nineteenth century, binary quadratic forms have given up their preeminence in algebraic number theory to quadratic and more general number fields, but advances specific to binary quadratic forms still occur on occasion. Pierre Fermat stated that if p is an odd prime then the equation p = x 2 + y 2 {\\displaystyle p=x^{2}+y^{2}} has a solution iff p \u2261 1 ( mod 4 ) {\\displaystyle p\\equiv 1{\\pmod {4}}} , and he made similar statement about the equations p = x 2 + 2 y 2 {\\displaystyle p=x^{2}+2y^{2}} , p = x 2 + 3 y 2 {\\displaystyle p=x^{2}+3y^{2}} , p = x 2 \u2212 2 y 2 {\\displaystyle p=x^{2}-2y^{2}} and p = x 2 \u2212 3 y 2 {\\displaystyle p=x^{2}-3y^{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nonstandard analysis, a hyperinteger n is a hyperreal number that is equal to its own integer part. A hyperinteger may be either finite or infinite. A finite hyperinteger is an ordinary integer. An example of an infinite hyperinteger is given by the class of the sequence (1, 2, 3, ...) in the ultrapower construction of the hyperreals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Scarf's fixed-point method was a break-through in the mathematics of computation generally, and specifically in optimization and computational economics. Later researchers continued to develop iterative methods for computing fixed-points, both for topological models like Scarf's and for models described by functions with continuous second derivatives or convexity or both. Of course, \"global Newton methods\" for essentially convex and smooth functions and path-following methods for diffeomorphisms converged faster than did robust algorithms for continuous functions, when the smooth methods are applicable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of computational discourse, the study of discourse relations was closely entangled with the study of discourse structure, so that theories such as RST and SDRT effectively postulate tree structures. (SDRT permits relations between independent nodes in a tree, but the tree still defines accessibility domains.) For practical annotation, however, this was felt to be a disadvantage because discourse relations could only be annotated after the global coherence of a particular text has been understood, and annotators disagreed widely (as already observed by Mann and Thompson 1987). For theoretical reasons, the tree model was criticized because at least some types of discourse relations (especially what Hobbs referred to as elaboration) was apparently not constrained by tree structures but could connect elements disconnected in the tree (Knott et al. 2001).This has been the motivation to perform the annotation of discourse relations independently from discourse structure, and this \"shallow\" model of discourse coherence could be annotated from local context alone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems design, a fail-fast system is one which immediately reports at its interface any condition that is likely to indicate a failure. Fail-fast systems are usually designed to stop normal operation rather than attempt to continue a possibly flawed process. Such designs often check the system's state at several points in an operation, so any failures can be detected early. The responsibility of a fail-fast module is detecting errors, then letting the next-highest level of the system handle them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the name Schubfachprinzip (\"drawer principle\" or \"shelf principle\").The principle has several generalizations and can be stated in various ways. In a more quantified version: for natural numbers k and m, if n = km + 1 objects are distributed among m sets, then the pigeonhole principle asserts that at least one of the sets will contain at least k + 1 objects. For arbitrary n and m, this generalizes to k + 1 = \u230a ( n \u2212 1 ) / m \u230b + 1 = \u2308 n / m \u2309 , {\\displaystyle k+1=\\lfloor (n-1)/m\\rfloor +1=\\lceil n/m\\rceil ,} where \u230a \u22ef \u230b {\\displaystyle \\lfloor \\cdots \\rfloor } and \u2308 \u22ef \u2309 {\\displaystyle \\lceil \\cdots \\rceil } denote the floor and ceiling functions, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some covering problems, the covering should satisfy some additional requirements. In particular, in the rainbow covering problem, each of the original objects has a \"color\", and it is required that the covering contains exactly one (or at most one) object of each color. Rainbow covering was studied e.g. for covering points by intervals: There is a set J of n colored intervals on the real line, and a set P of points on the real line. A subset Q of J is called a rainbow set if it contains at most a single interval of each color.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some theories of formal semantics, including David Dowty's, stative verbs have a logical form that is the lambda expression \u03bb ( x ):  {\\displaystyle \\lambda (x):\\ } Apart from Dowty, Z. Vendler and C. S. Smith have also written influential work on aspectual classification of verbs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, bit inversion means the changing of the state of a bit to the opposite state, i.e. the changing of a 0 bit to 1 or of a 1 bit to 0. It also refers to the changing of a state representing a given bit to the opposite state. Source: Federal Standard 1037C and MIL-STD-188", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If they have the representation I \u2261 \u27e8 f 1 , \u2026 , f p \u27e9 {\\displaystyle I\\equiv \\langle f_{1},\\ldots ,f_{p}\\rangle } and J \u2261 \u27e8 g 1 , \u2026 , g q \u27e9 , {\\displaystyle J\\equiv \\langle g_{1},\\ldots ,g_{q}\\rangle ,} f i {\\displaystyle f_{i}} , g j \u2208 D {\\displaystyle g_{j}\\in {\\mathcal {D}}} for all i {\\displaystyle i} and j {\\displaystyle j} , the sum is generated by the union of the generators of I {\\displaystyle I} and J {\\displaystyle J} . The solution space of the equations corresponding to Gcrd \u2061 ( I , J ) {\\displaystyle \\operatorname {Gcrd} (I,J)} is the intersection of the solution spaces of its arguments. The least common left multiple (Lclm) or left intersection of two ideals I {\\displaystyle I} and J {\\displaystyle J} is the largest ideal with the property that it is contained both in I {\\displaystyle I} and J {\\displaystyle J} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a logical matrix may be described as d-disjunct and/or d-separable. These concepts play a pivotal role in the mathematical area of non-adaptive group testing. In the mathematical literature, d-disjunct matrices may also be called super-imposed codes or d-cover-free families.According to Chen and Hwang (2006), A matrix is said to be d-separable if no two sets of d columns have the same boolean sum. A matrix is said to be d \u00af {\\displaystyle {\\overline {d}}} -separable (that's d with an overline) if no two sets of d-or-fewer columns have the same boolean sum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to ensure that CDSs are of high quality, multiple quality assurance (QA) tests are performed (Table 1). All tests are performed following the annotation comparison step of each CCDS build and are independent of individual annotation group QA tests performed prior to the annotation comparison. Annotations that fail QA tests undergo a round of manual checking that may improve results or reach a decision to reject annotation matches based on QA failure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The statement has a short proof in a more powerful system: in fact the proof given in the previous paragraph is a proof in the system of Peano arithmetic plus the statement \"Peano arithmetic is consistent\" (which, per the incompleteness theorem, cannot be proved in Peano arithmetic). In this argument, Peano arithmetic can be replaced by any more powerful consistent system, and a googolplex can be replaced by any number that can be described concisely in the system. Harvey Friedman found some explicit natural examples of this phenomenon, giving some explicit statements in Peano arithmetic and other formal systems whose shortest proofs are ridiculously long (Smory\u0144ski 1982).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The simulation presumed a complete graph with random relations having a random unbalanced triad selected for transformation. The evolution of the signed graph with N nodes under this process is studied and simulated to describe the stationary density of friendly links. Balance theory has been severely challenged, especially in its application to large systems, on the theoretical ground that friendly relations tie a society together, while a society divided into two camps of enemies would be highly unstable. Experimental studies have also provided only weak confirmation of the predictions of structural balance theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a twisted polynomial is a polynomial over a field of characteristic p {\\displaystyle p} in the variable \u03c4 {\\displaystyle \\tau } representing the Frobenius map x \u21a6 x p {\\displaystyle x\\mapsto x^{p}} . In contrast to normal polynomials, multiplication of these polynomials is not commutative, but satisfies the commutation rule \u03c4 x = x p \u03c4 {\\displaystyle \\tau x=x^{p}\\tau } for all x {\\displaystyle x} in the base field. Over an infinite field, the twisted polynomial ring is isomorphic to the ring of additive polynomials, but where multiplication on the latter is given by composition rather than usual multiplication. However, it is often easier to compute in the twisted polynomial ring \u2014 this can be applied especially in the theory of Drinfeld modules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is famous as the Molloy-Reed criterion. The intuition behind this criterion is that if the giant component (GC) exists, then the average degree of a randomly chosen vertex i {\\displaystyle i} in a connected component should be at least 2. Molloy-Reed criterion can also be expressed as: \u2211 i k i ( k i \u2212 2 ) > 0 , {\\displaystyle \\sum _{i}k_{i}(k_{i}-2)>0,} which implies that, although the size of the GC may depend on p 0 {\\displaystyle p_{0}} and p 2 {\\displaystyle p_{2}} , the number of nodes of degree 0 and 2 have no contribution in the existence of the giant component.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Having arisen from the fields of knowledge representation, description logic and formal ontology, Semantic Web languages have a closer relationship to philosophical ontology than do conventional programming languages such as Java or Python. Accordingly, the nature of metaclasses is informed by philosophical notions such as abstract objects, the abstract and concrete, and type-token distinction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metadata, a vocabulary-based transformation (VBT) is a transformation aided by the use of a semantic equivalence statements within a controlled vocabulary. Many organizations today require communication between two or more computers. Although many standards exist to exchange data between computers such as HTML or email, there is still much structured information that needs to be exchanged between computers that is not standardized. The process of mapping one source of data into another is often a slow and labor-intensive process. VBT is a possible way to avoid much of the time and cost of manual data mapping using traditional extract, transform, load technologies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to sterilize items effectively, it is important to use optimal parameters when running an autoclave cycle. A 2017 study performed by the Johns Hopkins Hospital biocontainment unit tested the ability of pass-through autoclaves to decontaminate loads of simulated biomedical waste when run on the factory default setting. The study found that 18 of 18 (100%) mock patient loads (6 PPE, 6 linen, and 6 liquid loads) passed sterilization tests with the optimized parameters compared to only 3 of 19 (16%) mock loads that passed with use of the factory default settings.There are physical, chemical, and biological indicators that can be used to ensure that an autoclave reaches the correct temperature for the correct amount of time. If a non-treated or improperly treated item can be confused for a treated item, then there is the risk that they will become mixed up, which, in some areas such as surgery, is critical.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, 0.999... (also written as 0.9 or 0..9) denotes the repeating decimal consisting of an unending sequence of 9s after the decimal point. This repeating decimal represents the smallest number no less than every decimal number in the sequence (0.9, 0.99, 0.999, ...); that is, the supremum of this sequence. This number is equal to 1. In other words, \"0.999...\" is not \"almost exactly\" or \"very, very nearly but not quite\" 1 \u2013 rather, \"0.999...\" and \"1\" represent exactly the same number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Property B is a certain set theoretic property. Formally, given a finite set X, a collection C of subsets of X has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z. The property gets its name from mathematician Felix Bernstein, who first introduced the property in 1908.Property B is equivalent to 2-coloring the hypergraph described by the collection C. A hypergraph with property B is also called 2-colorable. : 468 Sometimes it is also called bipartite, by analogy to the bipartite graphs. Property B is often studied for uniform hypergraphs (set systems in which all subsets of the system have the same cardinality) but it has also been considered in the non-uniform case.The problem of checking whether a collection C has Property B is called the set splitting problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Otherwise, the jurisdiction must vote to update its code and bring its inspectors up to date on the changes being made to the code. Most jurisdictions update their codes regularly to avoid backlash from architects and building contractors who respond to outdated codes by seeking variances to permit the use of more efficient design solutions and technologies accepted in areas using more modern codes. The model codes may either be adopted outright as the building codes for a jurisdiction, or they may be adopted with amendments or additional rules.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terrestrial radio and television broadcasting, centralcasting refers to the use of systems automation by which customised signals for broadcast by multiple individual stations may be created at one central facility.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hartmanis' model \u2013 quite similar to Melzak's (1961) model \u2013 uses two and three-register adds and subtracts and two parameter copies; Cook and Reckhow's model reduce the number of parameters (registers called out in the program instructions) to one call-out by use of an accumulator \"AC\". The solution in a nutshell: Design our machine/model with unbounded indirection \u2013 provide an unbounded \"address\" register that can potentially name (call out) any register no matter how many there are. For this to work, in general, the unbounded register requires an ability to be cleared and then incremented (and, possibly, decremented) by a potentially infinite loop.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 3578, 13578, 34578, and 134578 are the patterns related to Braille pattern dots-2346, since the two additional dots of kantenji patterns 02346, 23467, and 023467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Femtocells are an alternative way to deliver the benefits of fixed\u2013mobile convergence (FMC). The distinction is that most FMC architectures require a new dual-mode handset which works with existing unlicensed spectrum home/enterprise wireless access points, while a femtocell-based deployment will work with existing handsets but requires the installation of a new access point that uses licensed spectrum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T: X \u2192 Y {\\displaystyle T:X\\rightarrow Y} acting between Hilbert spaces X {\\displaystyle X} and Y {\\displaystyle Y} , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator T \u2217 T {\\displaystyle T^{*}T} (where T \u2217 {\\displaystyle T^{*}} denotes the adjoint of T {\\displaystyle T} ). The singular values are non-negative real numbers, usually listed in decreasing order (\u03c31(T), \u03c32(T), \u2026). The largest singular value \u03c31(T) is equal to the operator norm of T (see Min-max theorem). If T acts on Euclidean space R n {\\displaystyle \\mathbb {R} ^{n}} , there is a simple geometric interpretation for the singular values: Consider the image by T {\\displaystyle T} of the unit sphere; this is an ellipsoid, and the lengths of its semi-axes are the singular values of T {\\displaystyle T} (the figure provides an example in R 2 {\\displaystyle \\mathbb {R} ^{2}} ).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the course of time many network queueing disciplines have been developed. Each of these provides specific reordering or dropping of network packets inside various transmit or receive buffers. Queuing disciplines are commonly used as attempts to compensate for various networking conditions, like reducing the latency for certain classes of network packets, and are generally used as part of QoS measures.Examples of algorithms suitable for managing network traffic include: Several of the above have been implemented as Linux kernel modules and are freely available.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the diagrams, P is used for N\u2019s parent, G for the grandparent, and U will denote N\u2019s uncle. The diagrams show the parent node P as the left child of its parent G even though it is possible for P to be on either side. The sample code covers both possibilities by means of the side variable dir. N is the insertion node, but as the operation proceeds also other nodes may become current (see case I2).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This made it harder to interface other processors. Upgrading to a more powerful processor would subtly change the timings, and timing restraints were not always tightly specified. Nor were electrical parameters and physical dimensions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reality, initial exponential growth is often not sustained forever. After some period, it will be slowed by external or environmental factors. For example, population growth may reach an upper limit due to resource limitations. In 1845, the Belgian mathematician Pierre Fran\u00e7ois Verhulst first proposed a mathematical model of growth like this, called the \"logistic growth\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The total time for his algorithm is O(m log m). For planar graphs with maximum degree \u0394 \u2265 7, the optimal number of colors is again exactly \u0394. With the stronger assumption that \u0394 \u2265 9, it is possible to find an optimal edge coloring in linear time (Cole & Kowalik 2008). For d-regular graphs which are pseudo-random in the sense that their adjacency matrix has second largest eigenvalue (in absolute value) at most d1\u2212\u03b5, d is the optimal number of colors (Ferber & Jain 2020).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first RSA numbers generated, from RSA-100 to RSA-500, were labeled according to their number of decimal digits. Later, beginning with RSA-576, binary digits are counted instead. An exception to this is RSA-617, which was created before the change in the numbering scheme. The numbers are listed in increasing order below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most cases, ELM is used as a single hidden layer feedforward network (SLFN) including but not limited to sigmoid networks, RBF networks, threshold networks, fuzzy inference networks, complex neural networks, wavelet networks, Fourier transform, Laplacian transform, etc. Due to its different learning algorithm implementations for regression, classification, sparse coding, compression, feature learning and clustering, multi ELMs have been used to form multi hidden layer networks, deep learning or hierarchical networks.A hidden node in ELM is a computational element, which need not be considered as classical neuron. A hidden node in ELM can be classical artificial neurons, basis functions, or a subnetwork formed by some hidden nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. G\u00f6del's incompleteness theorems, published in 1931, showed that Hilbert's program was unattainable for key areas of mathematics. In his first theorem, G\u00f6del showed that any consistent system with a computable set of axioms which is capable of expressing arithmetic can never be complete: it is possible to construct a statement that can be shown to be true, but that cannot be derived from the formal rules of the system. In his second theorem, he showed that such a system could not prove its own consistency, so it certainly cannot be used to prove the consistency of anything stronger with certainty. This refuted Hilbert's assumption that a finitistic system could be used to prove the consistency of itself, and therefore could not prove everything else.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Factorization may also refer to more general decompositions of a mathematical object into the product of smaller or simpler objects. For example, every function may be factored into the composition of a surjective function with an injective function. Matrices possess many kinds of matrix factorizations. For example, every matrix has a unique LUP factorization as a product of a lower triangular matrix L with all diagonal entries equal to one, an upper triangular matrix U, and a permutation matrix P; this is a matrix formulation of Gaussian elimination.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, if A {\\displaystyle A} is a subset of B , {\\displaystyle B,} then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \u03b9 {\\displaystyle \\iota } that sends each element x {\\displaystyle x} of A {\\displaystyle A} to x , {\\displaystyle x,} treated as an element of B: {\\displaystyle B:} A \"hooked arrow\" (U+21AA \u21aa RIGHTWARDS ARROW WITH HOOK) is sometimes used in place of the function arrow above to denote an inclusion map; thus: (However, some authors use this hooked arrow for any embedding.) This and other analogous injective functions from substructures are sometimes called natural injections. Given any morphism f {\\displaystyle f} between objects X {\\displaystyle X} and Y {\\displaystyle Y} , if there is an inclusion map into the domain \u03b9: A \u2192 X , {\\displaystyle \\iota :A\\to X,} then one can form the restriction f \u03b9 {\\displaystyle f\\,\\iota } of f . {\\displaystyle f.} In many instances, one can also construct a canonical inclusion into the codomain R \u2192 Y {\\displaystyle R\\to Y} known as the range of f . {\\displaystyle f.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 2005 Star Trek: Enterprise episode \"The Aenar\", it was used in the Aenar city.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One downside to the RISC design was that the programs that run on them tend to be larger. This is because compilers must generate longer sequences of the simpler instructions to perform the same results. Since these instructions must be loaded from memory anyway, the larger code offsets some of the RISC design's fast memory handling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In psycholinguistics, semantic processing is the stage of language processing that occurs after one hears a word and encodes its meaning: the mind relates the word to other words with similar meanings. Once a word is perceived, it is placed in a context mentally that allows for a deeper processing. Therefore, semantic processing produces memory traces that last longer than those produced by shallow processing, since shallow processing produces fragile memory traces that decay rapidly. Semantic processing is the deepest level of processing and it requires the listener to think about the meaning of the cue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "2(2). In computer science terms, programming in the large can refer to programming code that represents the high-level state transition logic of a system. This logic encodes information such as when to wait for messages, when to send messages, when to compensate for failed non-ACID transactions, etc. A language that was designed to explicitly support programming in the large is BPEL.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Conversely, a group of participants can atomically broadcast messages by achieving consensus regarding the first message to be received, followed by achieving consensus on the next message, and so forth until all the messages have been received. Thus, atomic broadcast reduces to consensus.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Northeast Caucasian languages, such as Tsez, the dative also takes the functions of the lative case in marking the direction of an action. By some linguists, they are still regarded as two separate cases in those languages, although the suffixes are exactly the same for both cases. Other linguists list them separately only for the purpose of separating syntactic cases from locative cases. An example with the ditransitive verb \"show\" (literally: \"make see\") is given below: The dative/lative is also used to indicate possession, as in the example below, because there is no such verb as \"to have\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of computing, CPU time was expensive, and peripherals were very slow. When the computer ran a program that needed access to a peripheral, the central processing unit (CPU) would have to stop executing program instructions while the peripheral processed the data. This was usually very inefficient. The first computer using a multiprogramming system was the British Leo III owned by J. Lyons and Co.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These scores, based on a normal curve, are known as \"scaled\" scores. Because of their grounding in this model, scaled MAT scores of 500-600 are extremely rare, as they would be more than four standard deviations above the norm of 400.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The order of a hypergraph ( X , E ) {\\displaystyle (X,E)} is the number of vertices in X {\\displaystyle X} . The size of the hypergraph is the number of edges in E {\\displaystyle E} . The order of an edge e = ( D , C ) {\\displaystyle e=(D,C)} in a directed hypergraph is | e | = ( | D | , | C | ) {\\displaystyle |e|=(|D|,|C|)}: that is, the number of vertices in its tail followed by the number of vertices in its head.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The new networks have higher download speeds, with a peak speed of 10 gigabits per second (Gbit/s) when there is only one user in the network. 5G has higher bandwidth to deliver faster speeds than 4G and can thus connect more different devices, improving the quality of Internet services in crowded areas. Due to the increased bandwidth, it is expected the 5G networks will increasingly be used as general internet service providers (ISPs), competing with existing ISPs such as cable internet, and also will make possible new applications in internet-of-things (IoT) and machine-to-machine areas. Cellphones with 4G capability alone are not able to use the 5G networks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, the distances between consecutive occurrences of the strings are likely to be multiples of the length of the keyword. Thus finding more repeated strings narrows down the possible lengths of the keyword, since we can take the greatest common divisor of all the distances. The reason this test works is that if a repeated string occurs in the plaintext, and the distance between corresponding characters is a multiple of the keyword length, the keyword letters will line up in the same way with both occurrences of the string.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily a surjection. The composition of surjective functions is always surjective. Any function can be decomposed into a surjection and an injection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Read before write, read after read and write before write ordering is still preserved in this model. The processor consistency model is similar to the PRAM consistency model with a stronger condition that defines all writes to the same memory location must be seen in the same sequential order by all other processes. Processor consistency is weaker than sequential consistency but stronger than the PRAM consistency model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By B\u00e9zout's identity, there are r and s such that r n + s a = 1. {\\displaystyle rn+sa=1.} Multiply both sides by b: r n b + s a b = b . {\\displaystyle rnb+sab=b.} The first term on the left is divisible by n, and the second term is divisible by ab, which by hypothesis is divisible by n. Therefore their sum, b, is also divisible by n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W states in that it is more difficult to eliminate quantum entanglement (via projective measurements) in the case of cluster states.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Concurrent schedules often induce rapid alternation between the keys. To prevent this, a \"changeover delay\" is commonly introduced: each schedule is inactivated for a brief period after the subject switches to it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Ng5 f5 11. g3 Nh6 12. Bd3 Nf7 13. Bxf5?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted Z n {\\displaystyle \\mathbb {Z} ^{n}} , is the lattice in the Euclidean space R n {\\displaystyle \\mathbb {R} ^{n}} whose lattice points are n-tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. Z n {\\displaystyle \\mathbb {Z} ^{n}} is the simplest example of a root lattice. The integer lattice is an odd unimodular lattice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Stack machines can work around the memory delay by either having a deep out-of-order execution pipeline covering many instructions at once, or more likely, they can permute the stack such that they can work on other workloads while the load completes, or they can interlace the execution of different program threads, as in the Unisys A9 system. Today's increasingly parallel computational loads suggests, however, this might not be the disadvantage it's been made out to be in the past. Stack machines can omit the operand fetching stage of a register machine. For example, in the Java Optimized Processor (JOP) microprocessor the top 2 operands of stack directly enter a data forwarding circuit that is faster than the register file.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to build the classification models, the samples belonging to each class need to be analysed using principal component analysis (PCA); only the significant components are retained. For a given class, the resulting model then describes either a line (for one Principal Component or PC), plane (for two PCs) or hyper-plane (for more than two PCs). For each modelled class, the mean orthogonal distance of training data samples from the line, plane, or hyper-plane (calculated as the residual standard deviation) is used to determine a critical distance for classification. This critical distance is based on the F-distribution and is usually calculated using 95% or 99% confidence intervals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The contraction generated by the cooling supposedly produced the high pressure required to transform graphite into diamond. Moissan published his work in a series of articles in the 1890s.Many other scientists tried to replicate his experiments. Sir William Crookes claimed success in 1909.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In attributive sentences (see below), as well as agreement in person and number between the subject and the verb, there is also agreement of gender and number between the subject and the head of the attribute when it is a noun or an adjective. In Catalan there are four main types of sentence: Predicative sentences, consisting of a subject, a verb and some complements. En Jordi va collir tres roses per a la N\u00faria (Jordi picked three roses for N\u00faria).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A variant of this problem gives the total number of travelers available, and asks for the maximum distance that can be reached. In the cars across the desert problem, the starting base has unlimited units of fuel. Each car can carry at most 1 unit of supplies at any time, and can travel 1 unit of distance on 1 unit of fuel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sometimes schools do half-day in-service days in which students are dismissed early, rather than full-day holidays. Unplanned interruptions in schooling (such as weather events like heavy snow) can extend the school year on occasion. Such calendar extensions, as well as the initial cancellations, are decided by each local administration and announced to the parents in as timely manner as possible.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To show that a system S is required to prove a theorem T, two proofs are required. The first proof shows T is provable from S; this is an ordinary mathematical proof along with a justification that it can be carried out in the system S. The second proof, known as a reversal, shows that T itself implies S; this proof is carried out in the base system. The reversal establishes that no axiom system S\u2032 that extends the base system can be weaker than S while still proving T.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to say something about the security properties of the above explained XTR encryption scheme, first it is important to check the security of the XTR group, which means how hard it is to solve the Discrete Logarithm problem there. The next part will then state the equivalency between the Discrete Logarithm problem in the XTR group and the XTR version of the discrete logarithm problem, using only the traces of elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice this becomes computationally onerous as k {\\displaystyle ~k~} and N {\\displaystyle ~N~} increase so it is probably only worth using exact tests for small samples. For larger samples, asymptotic approximations are accurate enough and easier to calculate. One of these approximations is the likelihood ratio.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of server consolidation, many small physical servers can be replaced by one larger physical server to decrease the need for more (costly) hardware resources such as CPUs, and hard drives. Although hardware is consolidated in virtual environments, typically OSs are not. Instead, each OS running on a physical server is converted to a distinct OS running inside a virtual machine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Thue\u2013Morse sequence or Prouhet\u2013Thue\u2013Morse sequence or parity sequence is the binary sequence (an infinite sequence of 0s and 1s) obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. The first few steps of this procedure yield the strings 0 then 01, 0110, 01101001, 0110100110010110, and so on, which are prefixes of the Thue\u2013Morse sequence. The full sequence begins: 01101001100101101001011001101001.... The sequence is named after Axel Thue and Marston Morse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, qualitative comparative analysis (QCA) is a data analysis based on set theory to examine the relationship of conditions to outcome. QCA describes the relationship in terms of necessary conditions and sufficient conditions. The technique was originally developed by Charles Ragin in 1987 to study data sets that are too small for linear regression analysis but large for cross-case analysis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Below is the example that compares SPARQL and SQL queries for medications that treats \"TB of vertebra\". SELECT ?medication WHERE { ?diagnosis a example:Diagnosis . ?diagnosis example:name \u201cTB of vertebra\u201d . ?medication example:canTreat ?diagnosis . } SELECT DRUG.medID FROM DIAGNOSIS, DRUG, DRUG_DIAGNOSIS WHERE DIAGNOSIS.diagnosisID=DRUG_DIAGNOSIS.diagnosisID AND DRUG.medID=DRUG_DIAGNOSIS.medID AND DIAGNOSIS.name=\u201dTB of vertebra\u201d", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The reason is that if V {\\displaystyle V} is an F {\\displaystyle F} -vector space and q: V \u2192 F {\\displaystyle q:V\\to F} is a quadratic form and v {\\displaystyle v} is an element of V {\\displaystyle V} such that q ( v ) = a \u2208 F \u00d7 {\\displaystyle q(v)=a\\in F^{\\times }} , then for all u \u2208 F \u00d7 {\\displaystyle u\\in F^{\\times }} , q ( u v ) = a u 2 {\\displaystyle q(uv)=au^{2}} and thus it is sometimes more convenient to talk about the square classes which the quadratic form represents. Every element of the square class group is an involution. It follows that, if the number of square classes of a field is finite, it must be a power of two. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Greek, for example, the imperfective sometimes adds the notion of \"try to do something\" (the so-called conative imperfect); hence, the same verb, in the imperfective (present or imperfect) and aorist, respectively, is used to convey look and see, search and find, listen and hear. (For example, \u1f20\u03ba\u03bf\u03cd\u03bf\u03bc\u03b5\u03bd (\u0113kouomen, \"we listened\") vs. \u1f20\u03ba\u03bf\u03cd\u03c3\u03b1\u03bc\u03b5\u03bd (\u0113kousamen, \"we heard\").) Spanish has similar pairs for certain verbs, such as (imperfect and preterite, respectively) sab\u00eda (\"I knew\") vs. supe (\"I found out\"), pod\u00eda (\"I was able to\") vs. pude (\"I succeeded (in doing something)\"), quer\u00eda (\"I wanted to\") vs. quise (\"I tried to\"), and no quer\u00eda (\"I did not want to\") vs. no quise (\"I refused (to do something)\"). Such differences are often highly language-specific.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some communication systems, a receiver can achieve character synchronization from an undifferentiated bit stream, or start-of-header synchronization from a byte stream, without the overhead of an explicit syncword. For example, the FSK441 protocol achieves character synchronization by synchronizing on any \"space\" characters in the message\u200d\u2014\u200cin effect, every \"space\" character in the message does double duty as a syncword. For example, CRC-based framing achieves character and start-of-header synchronization. In a self-synchronizing code, every character is, in effect, a syncword, and can be used to achieve character synchronization in an undifferentiated bit stream.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the age of advanced mobile devices, there is some disadvantage in using phonewords. Devices with physical keyboards such as BlackBerry and some other smartphones do not have the apportioned letters on the keys used for dialing, so one is unable to do alphabetic dialing without some other cross-reference to the actual phone number. This can be overcome by phonewords also being accompanied by the actual numeric phone number, allowing users of such smartphones to dial using the numeric phone number. However, devices which have virtual keyboards, including iOS and Android devices, will translate phoneword phone numbers in webpages and SMS messages to their proper digits within a hyperlink leading to that device's phone app, and their keypads show the appropriate local mapping of letters within their virtual dialpad.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. It is thus related to the chi-squared distribution by describing the distribution of the positive square roots of a variable obeying a chi-squared distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a fluid limit, fluid approximation or fluid analysis of a stochastic model is a deterministic real-valued process which approximates the evolution of a given stochastic process, usually subject to some scaling or limiting criteria. Fluid limits were first introduced by Thomas G. Kurtz publishing a law of large numbers and central limit theorem for Markov chains. It is known that a queueing network can be stable, but have an unstable fluid limit. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of machine learning, the exploration-exploitation tradeoff is often encountered in reinforcement learning, a type of machine learning that involves training agents to make decisions based on feedback from the environment. The agent must decide whether to exploit the current best-known policy or explore new policies to improve its performance. Various algorithms have been developed to address this challenge, such as epsilon-greedy, Thompson sampling, and the upper confidence bound. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the main application of the Peano kernel theorem is to bound the error of an approximation that is exact for all f \u2208 P \u03bd {\\displaystyle f\\in \\mathbb {P} _{\\nu }} . The theorem above follows from the Taylor polynomial for f {\\displaystyle f} with integral remainder: f ( x ) = f ( a ) + ( x \u2212 a ) f \u2032 ( a ) + ( x \u2212 a ) 2 2 f \u2033 ( a ) + \u22ef \u22ef + ( x \u2212 a ) \u03bd \u03bd ! f ( \u03bd ) ( a ) + 1 \u03bd ! \u222b a x ( x \u2212 \u03b8 ) \u03bd f ( \u03bd + 1 ) ( \u03b8 ) d \u03b8 , {\\displaystyle {\\begin{aligned}f(x)=f(a)+{}&(x-a)f'(a)+{\\frac {(x-a)^{2}}{2}}f''(a)+\\cdots \\\\&\\cdots +{\\frac {(x-a)^{\\nu }}{\\nu ! }}f^{(\\nu )}(a)+{\\frac {1}{\\nu ! }}\\int _{a}^{x}(x-\\theta )^{\\nu }f^{(\\nu +1)}(\\theta )\\,d\\theta ,\\end{aligned}}} defining L ( f ) {\\displaystyle L(f)} as the error of the approximation, using the linearity of L {\\displaystyle L} together with exactness for f \u2208 P \u03bd {\\displaystyle f\\in \\mathbb {P} _{\\nu }} to annihilate all but the final term on the right-hand side, and using the ( \u22c5 ) + {\\displaystyle (\\cdot )_{+}} notation to remove the x {\\displaystyle x} -dependence from the integral limits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of group theory, a sequence G 0 \u2192 f 1 G 1 \u2192 f 2 G 2 \u2192 f 3 \u22ef \u2192 f n G n {\\displaystyle G_{0}\\;{\\xrightarrow {f_{1}}}\\;G_{1}\\;{\\xrightarrow {f_{2}}}\\;G_{2}\\;{\\xrightarrow {f_{3}}}\\;\\cdots \\;{\\xrightarrow {f_{n}}}\\;G_{n}} of groups and group homomorphisms is called exact if the image of each homomorphism is equal to the kernel of the next: i m ( f k ) = k e r ( f k + 1 ) . {\\displaystyle \\mathrm {im} (f_{k})=\\mathrm {ker} (f_{k+1}).\\!} Note that the sequence of groups and homomorphisms may be either finite or infinite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of topology, a circle is not limited to the geometric concept, but to all of its homeomorphisms. Two topological circles are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an ambient isotopy).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In several fields, especially computing, deprecation is the discouragement of use of some terminology, feature, design, or practice, typically because it has been superseded or is no longer considered efficient or safe, without completely removing it or prohibiting its use. Typically, deprecated materials are not completely removed to ensure legacy compatibility or back up practice in case new methods are not functional in an odd scenario. It can also imply that a feature, design, or practice will be removed or discontinued entirely in the future.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most computationally expensive component of the best predictor formula is inverting the covariance matrix \u03a3 {\\displaystyle \\mathbf {\\Sigma } } , which has cubic complexity O ( n 3 ) {\\displaystyle {\\mathcal {O}}(n^{3})} . Similarly, evaluating likelihood involves both calculating \u03a3 \u2212 1 {\\displaystyle \\mathbf {\\Sigma } ^{-1}} and the determinant det ( \u03a3 ) {\\displaystyle \\det(\\mathbf {\\Sigma } )} which has the same cubic complexity. Gaussian process approximations can often be expressed in terms of assumptions on y {\\displaystyle y} under which log \u2061 \u2113 ( y ) {\\displaystyle \\log \\ell (\\mathbf {y} )} and \u03bc y \u2217 {\\displaystyle \\mathbf {\\mu } _{\\mathbf {y} }^{*}} can be calculated with much lower complexity. Since these assumptions are generally not believed to reflect reality, the likelihood and the best predictor obtained in this way are not exact, but they are meant to be close to their original values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In non-smooth method, unilateral interactions between bodies are fundamentally modelled by the Signorini condition for non-penetration, and impact laws are used to define the impact process. The Signorini condition can be expressed as the complementarity problem: g \u2265 0 , \u03bb \u2265 0 , \u03bb \u22a5 g {\\displaystyle g\\geq 0,\\quad \\lambda \\geq 0,\\quad \\lambda \\perp g} , where g {\\displaystyle g} denotes the distance between two bodies and \u03bb {\\displaystyle \\lambda } denotes the contact force generated by the unilateral constraints, as shown in the figure below. Moreover, in terms of the concept of proximal point of convex theory, the Signorini condition can be equivalently expressed as: \u03bb = p r o j R + ( \u03bb \u2212 \u03c1 g ) {\\displaystyle \\lambda ={\\rm {proj}}_{\\mathbb {R} ^{+}}(\\lambda -\\rho g)} , where \u03c1 > 0 {\\displaystyle \\rho >0} denotes an auxiliary parameter, and p r o j C ( x ) {\\displaystyle {\\rm {proj}}_{\\bf {C}}(x)} represents the proximal point in the set C {\\displaystyle C} to the variable x {\\displaystyle x} , defined as: p r o j C ( x ) = a r g m i n y \u2208 C \u2016 y \u2212 x \u2016 {\\displaystyle {\\rm {proj}}_{\\bf {C}}(x)={\\rm {argmin}}_{y\\in C}\\|y-x\\|} . Both the expressions above represent the dynamic behaviour of unilateral constraints: on the one hand, when the normal distance g N {\\displaystyle g_{\\rm {N}}} is above zero, the contact is open, which means that there is no contact force between bodies, \u03bb = 0 {\\displaystyle \\lambda =0} ; on the other hand, when the normal distance g N {\\displaystyle g_{\\rm {N}}} is equal to zero, the contact is closed, resulting in \u03bb \u2265 0 {\\displaystyle \\lambda \\geq 0} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the participant makes a mistake, the experimenter prompts them to start again. The threat of negative evaluation is the social stressor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The choice of loss function here gives rise to several well-known learning algorithms such as regularized least squares and support vector machines. A purely online model in this category would learn based on just the new input ( x t + 1 , y t + 1 ) {\\displaystyle (x_{t+1},y_{t+1})} , the current best predictor f t {\\displaystyle f_{t}} and some extra stored information (which is usually expected to have storage requirements independent of training data size). For many formulations, for example nonlinear kernel methods, true online learning is not possible, though a form of hybrid online learning with recursive algorithms can be used where f t + 1 {\\displaystyle f_{t+1}} is permitted to depend on f t {\\displaystyle f_{t}} and all previous data points ( x 1 , y 1 ) , \u2026 , ( x t , y t ) {\\displaystyle (x_{1},y_{1}),\\ldots ,(x_{t},y_{t})} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Designed by PLP Architecture, the development has 546 rooms with most units grouped into \"twodios\" \u2013 two en-suite bedrooms that share a small kitchenette. There are also some private suites. The units sizes range from 9.2 square metres (99 sq ft) for an ensuite rooms with a 5.8 square metres (62 sq ft) shared kitchenette, to 12 square metres (130 sq ft) for a shared ensuite and 16.5 square metres (178 sq ft) shared ensuite with kitchenette. Each floor features one larger kitchen with a dining table, which is shared between 30 and 70 residents, and themed communal living spaces such as a games room, a cinema, a 'disco-launderette', a hidden garden and a spa. A restaurant, gym and co-working spaces are located in the lower floors of the building.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the generalized taxicab number Taxicab(k, j, n) is the smallest number \u2014 if it exists \u2014 that can be expressed as the sum of j kth positive powers in n different ways. For k = 3 and j = 2, they coincide with taxicab number. T a x i c a b ( 1 , 2 , 2 ) = 4 = 1 + 3 = 2 + 2. {\\displaystyle \\mathrm {Taxicab} (1,2,2)=4=1+3=2+2.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The UNIVAC 1232 was a military version of the 490. The UNIVAC 492 is similar to the UNIVAC 490, but with extended memory to 64K 30-bit words. The UNIVAC 494 was a 30-bit word machine and successor to the UNIVAC 490/492 with faster CPU and 131K (later 262K) core memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In support vector machines (SVMs), the formulating the primal problem of SVMs as the dual problem can be used to implement Kernel trick, but the latter has higher time complexity in the historical cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically additive number theory, Romanov's theorem is a mathematical theorem proved by Nikolai Pavlovich Romanov. It states that given a fixed base b, the set of numbers that are the sum of a prime and a positive integer power of b has a positive lower asymptotic density.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In remote sensing, \"ground truth\" refers to information collected at the imaged location. Ground truth allows image data to be related to real features and materials on the ground. The collection of ground truth data enables calibration of remote-sensing data, and aids in the interpretation and analysis of what is being sensed. Examples include cartography, meteorology, analysis of aerial photographs, satellite imagery and other techniques in which data are gathered at a distance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of business process integration (see figure), data modeling complements business process modeling, and ultimately results in database generation.The process of designing a database involves producing the previously described three types of schemas - conceptual, logical, and physical. The database design documented in these schemas are converted through a Data Definition Language, which can then be used to generate a database. A fully attributed data model contains detailed attributes (descriptions) for every entity within it. The term \"database design\" can describe many different parts of the design of an overall database system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Simon Tatham's contribution, based on Duff's device, is a notable example of the genre, and is the basis for Protothreads and similar implementations. In addition to Duff's objections, Tatham's own comments provide a frank evaluation of the limitations of this approach: \"As far as I know, this is the worst piece of C hackery ever seen in serious production code.\" The main shortcomings of this approximation are that, in not maintaining a separate stack frame for each coroutine, local variables are not preserved across yields from the function, it is not possible to have multiple entries to the function, and control can only be yielded from the top-level routine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, one can define a product of group subsets in a natural way. If S and T are subsets of a group G, then their product is the subset of G defined by S T = { s t: s \u2208 S and t \u2208 T } . {\\displaystyle ST=\\{st:s\\in S{\\text{ and }}t\\in T\\}.} The subsets S and T need not be subgroups for this product to be well defined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In optimization, a self-concordant function is a function f: R \u2192 R {\\displaystyle f:\\mathbb {R} \\rightarrow \\mathbb {R} } for which | f \u2034 ( x ) | \u2264 2 f \u2033 ( x ) 3 / 2 {\\displaystyle |f'''(x)|\\leq 2f''(x)^{3/2}} or, equivalently, a function f: R \u2192 R {\\displaystyle f:\\mathbb {R} \\rightarrow \\mathbb {R} } that, wherever f \u2033 ( x ) > 0 {\\displaystyle f''(x)>0} , satisfies | d d x 1 f \u2033 ( x ) | \u2264 1 {\\displaystyle \\left|{\\frac {d}{dx}}{\\frac {1}{\\sqrt {f''(x)}}}\\right|\\leq 1} and which satisfies f \u2034 ( x ) = 0 {\\displaystyle f'''(x)=0} elsewhere. More generally, a multivariate function f ( x ): R n \u2192 R {\\displaystyle f(x):\\mathbb {R} ^{n}\\rightarrow \\mathbb {R} } is self-concordant if d d \u03b1 \u2207 2 f ( x + \u03b1 y ) | \u03b1 = 0 \u2aaf 2 y T \u2207 2 f ( x ) y \u2207 2 f ( x ) {\\displaystyle \\left. {\\frac {d}{d\\alpha }}\\nabla ^{2}f(x+\\alpha y)\\right|_{\\alpha =0}\\preceq 2{\\sqrt {y^{T}\\nabla ^{2}f(x)\\,y}}\\,\\nabla ^{2}f(x)} or, equivalently, if its restriction to any arbitrary line is self-concordant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, multiple correspondence analysis (MCA) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a low-dimensional Euclidean space. The procedure thus appears to be the counterpart of principal component analysis for categorical data. MCA can be viewed as an extension of simple correspondence analysis (CA) in that it is applicable to a large set of categorical variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While we cannot do this by simply rearranging the quantifiers, we show that it is yet enough to prove the theorem for sentences of that form. Finally we prove the theorem for sentences of that form. This is done by first noting that a sentence such as B = \u2200x1\u2200x2...\u2200xk \u2203y1\u2203y2...\u2203ym \u03c6(x1...xk, y1...ym) is either refutable (its negation is always true) or satisfiable, i.e. there is some model in which it holds (it might even be always true, i.e. a tautology); this model is simply assigning truth values to the subpropositions from which B is built.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the IBM System/370 models with virtual storage (DAT) and 24-bit addresses, control register 0 specifies a segment size of either 64 KiB or 1 MiB and a page size of either 2 KiB or 4 KiB; control register 1 contains a Segment Table Designator (STD), which specifies the length and real address of the segment table. Each segment table entry contains a page table location, a page table length and an invalid bit. IBM later expanded the address size to 31 bits and added two bits to the segment table entries: Segment-protection bit Segment is read-only Common-segment bit The segment is shared between address spaces; this bit is set to optimize TLB useEach of IBM's DAT implementations includes a translation cache, which IBM called a Translation Lookaside Buffer (TLB).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 19th century new developments such as the discovery of photography, Rowland's invention of the concave diffraction grating, and Schumann's works on discovery of vacuum ultraviolet (fluorite for prisms and lenses, low-gelatin photographic plates and absorption of UV in air below 185 nm) made advance to shorter wavelengths very fast. At the same time Dewar observed series in alkali spectra, Hartley found constant wave-number differences, Balmer discovered a relation connecting wavelengths in the visible hydrogen spectrum, and finally Rydberg derived a formula for wave-numbers of spectral series. Meanwhile, the substantial summary of past experiments performed by Maxwell (1873), resulted in his equations of electromagnetic waves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One says also a is prime to b or a is coprime with b. The numbers 8 and 9 are coprime, despite the fact that neither considered individually is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1970s, Diffie worked with Martin Hellman to develop the fundamental ideas of dual-key, or public key, cryptography. They published their results in 1976\u2014solving one of the fundamental problems of cryptography, key distribution\u2014and essentially broke the monopoly that had previously existed where government entities controlled cryptographic technology and the terms on which other individuals could have access to it. \"From the moment Diffie and Hellman published their findings..., the National Security Agency's crypto monopoly was effectively terminated. ... Every company, every citizen now had routine access to the sorts of cryptographic technology that not many years ago ranked alongside the atom bomb as a source of power.\" The solution has become known as Diffie\u2013Hellman key exchange.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This bias is especially prevalent in group settings where one thinks the collective opinion of their own group matches that of the larger population. Since the members of a group reach a consensus and rarely encounter those who dispute it, they tend to believe that everybody thinks the same way. The false-consensus effect is not restricted to cases where people believe that their values are shared by the majority, but it still manifests as an overestimate of the extent of their belief.Additionally, when confronted with evidence that a consensus does not exist, people often assume that those who do not agree with them are defective in some way.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, following a known software design structure, such as client and broker, can help in designing a well-built structure with a solid foundation. Furthermore, if the software is to be modified in the future, it is even more important that it follows a logical foundation of separation between the client and server. This is because if a programmer comes in and cannot clearly understand the dynamics of the program, they may end up adding or changing something that can add a security flaw. Even with the best design, this is always a possibility, but the better the standardization of the design, the less chance there is of this occurring.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, print carries the individuating power of the phonetic alphabet much further than manuscript culture could ever do. Print is the technology of individualism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the affected program is running with special privileges, or accepts data from untrusted network hosts (e.g. a webserver) then the bug is a potential security vulnerability. If the stack buffer is filled with data supplied from an untrusted user then that user can corrupt the stack in such a way as to inject executable code into the running program and take control of the process. This is one of the oldest and more reliable methods for attackers to gain unauthorized access to a computer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, rational reconstruction is a method that allows one to recover a rational number from its value modulo a sufficiently large integer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A continuum of complex morphology of language may be adopted. The three models of morphology stem from attempts to analyze languages that more or less match different categories in this typology. The item-and-arrangement approach fits very naturally with agglutinative languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that: Each element of the Boolean algebra can be expressed as a finite combination of generators, using the Boolean operations, and The generators are as independent as possible, in the sense that there are no relationships among them (again in terms of finite expressions using the Boolean operations) that do not hold in every Boolean algebra no matter which elements are chosen.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For the Bluetooth Low Energy stack, according to Bluetooth 4.0 a special set of profiles applies. A host Operating System can expose a basic set of profiles (namely OBEX, HID and Audio Sink) and manufacturers can add additional profiles to its driver and stack to enhance what their Bluetooth device can do. Devices such as mobile phones can expose additional profiles by installing appropriate apps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 57, 157, 457, and 1457 are the patterns related to Braille pattern dots-34, since the two additional dots of kantenji patterns 034, 347, and 0347 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development and product management, a user story is an informal, natural language description of features of a software system. They are written from the perspective of an end user or user of a system, and may be recorded on index cards, Post-it notes, or digitally in project management software. Depending on the project, user stories may be written by different stakeholders like client, user, manager, or development team. User stories are a type of boundary object. They facilitate sensemaking and communication; and may help software teams document their understanding of the system and its context.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In signal processing, the above definition is often used without the normalization, that is, without subtracting the mean and dividing by the variance. When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the autocorrelation coefficient or autocovariance function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as 5/6 = 1/2 + 1/3. As the name indicates, these representations have been used as long ago as ancient Egypt, but the first published systematic method for constructing such expansions was described in 1202 in the Liber Abaci of Leonardo of Pisa (Fibonacci). It is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that can be used in any representation of the remaining fraction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In these scenarios, modularity is an abstraction of the 2nd Isomorphism Theorem. For example, the subspaces of a vector space (and more generally the submodules of a module over a ring) form a modular lattice. In a not necessarily modular lattice, there may still be elements b for which the modular law holds in connection with arbitrary elements x and a (for a \u2264 b).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\operatorname {disc} ({\\mathcal {H}}):=\\min _{\\chi :V\\rightarrow \\{-1,+1\\}}\\operatorname {disc} ({\\mathcal {H}},\\chi ).} These notions as well as the term 'discrepancy' seem to have appeared for the first time in a paper of Beck.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the counter-electronic codebook mode, the Cascaded Cipher uses full strength AES-128 in counter mode to generate a secure key stream and supplies this key-stream to a reduced round Serpent in electronic codebook mode to encrypt each plaintext block. To increase performance, each inner key stream block is reused several times to encrypt multiple blocks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "And here, Kant says, we are liable to error in two ways. The first type of error consists in trying to attract students into being moral by providing them examples in which morality and self-love coincide. The second type of error consists in trying to emotionally arouse the students about morality by providing examples of extraordinary moral heroism, above what morality normally requires.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Babenko\u2013Beckner inequality (after K. Ivan Babenko and William E. Beckner) is a sharpened form of the Hausdorff\u2013Young inequality having applications to uncertainty principles in the Fourier analysis of Lp spaces. The (q, p)-norm of the n-dimensional Fourier transform is defined to be \u2016 F \u2016 q , p = sup f \u2208 L p ( R n ) \u2016 F f \u2016 q \u2016 f \u2016 p , where 1 < p \u2264 2 , and 1 p + 1 q = 1. {\\displaystyle \\|{\\mathcal {F}}\\|_{q,p}=\\sup _{f\\in L^{p}(\\mathbb {R} ^{n})}{\\frac {\\|{\\mathcal {F}}f\\|_{q}}{\\|f\\|_{p}}},{\\text{ where }}1", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In stage two, testers will recruit test subjects across a broad spectrum of abilities. For example, in one study, experienced users showed no problem using any design, from the first to the last, while naive users and self-identified power users both failed repeatedly. Later on, as the design smooths out, users should be recruited from the target population.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Petersburg paradox.In microbiology, the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth. During this bacterial growth phase, the number of new cells appearing is proportional to the population. This terminological confusion between logarithmic growth and exponential growth may be explained by the fact that exponential growth curves may be straightened by plotting them using a logarithmic scale for the growth axis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The command will be applied to all unit codes sent. It is also possible to send a message with no unit codes, just a house code and a command code. This will apply to the command to the last group of units codes previously sent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the category of graphs, the product is the tensor product of graphs. In the category of relations, the product is given by the disjoint union. (This may come as a bit of a surprise given that the category of sets is a subcategory of the category of relations.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Conway\u2013Maxwell\u2013Poisson (CMP or COM\u2013Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Sim\u00e9on Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion. It is a member of the exponential family, has the Poisson distribution and geometric distribution as special cases and the Bernoulli distribution as a limiting case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This raises the question of how to implement this randomized allocation in practice? One cannot just randomize for each object separately, since this may result in allocations in which some people get many objects while other people get no objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The modern formulation of the conjecture relates arithmetic data associated with an elliptic curve E over a number field K to the behaviour of the Hasse\u2013Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that the rank of the abelian group E(K) of points of E is the order of the zero of L(E, s) at s = 1, and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K (Wiles 2006). The conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, which has offered a $1,000,000 prize for the first correct proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented jargon, abstract datatypes are called classes. However, a class is only a definition; no memory is allocated. When memory is allocated to a class, it's called an object.Object-oriented imperative languages developed by combining the need for classes and the need for safe functional programming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Seidel matrix of G is also the adjacency matrix of a signed complete graph KG in which the edges of G are negative and the edges not in G are positive. It is also the adjacency matrix of the two-graph associated with G and KG. The eigenvalue properties of the Seidel matrix are valuable in the study of strongly regular graphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These would be rendered at the same width as the other single-byte characters, making them half-width kana characters rather than normally proportioned kana. Although the JIS X 0201 standard itself did not specify half-width display for katakana, this became the visually distinguishing feature in Shift JIS between the single-byte JIS X 0201 and double-byte JIS X 0208 katakana. Some IBM code pages used a similar treatment for Korean jamo, based on the N-byte Hangul code and its EBCDIC translation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, the Data Protection Acts and later the Freedom of Information Act 2000 gave patients or their representatives the right to a copy of their record, except where information breaches confidentiality (e.g., information from another family member or where a patient has asked for information not to be disclosed to third parties) or would be harmful to the patient's wellbeing (e.g., some psychiatric assessments). Also, the legislation gives patients the right to check for any errors in their record and insist that amendments be made if required.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The sole aim of the design was to eliminate the mains transformer. The lower cost of transformerless designs remained popular with manufacturers long after DC power distribution had disappeared.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a coded set is a set of elements onto which another set of elements has been mapped according to a code. Examples of coded sets include the list of names of airports that is mapped onto a set of corresponding three-letter representations of airport names, the list of classes of emission that is mapped onto a set of corresponding standard symbols, and the names of the months of the year mapped onto a set of two-digit decimal numbers. This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first section, Christian interweaves discussions of the history of artificial intelligence research, particularly the machine learning approach of artificial neural networks such as the Perceptron and AlexNet, with examples of how AI systems can have unintended behavior. He tells the story of Julia Angwin, a journalist whose ProPublica investigation of the COMPAS algorithm, a tool for predicting recidivism among criminal defendants, led to widespread criticism of its accuracy and bias towards certain demographics. One of AI's main alignment challenges is its black box nature (inputs and outputs are identifiable but the transformation process in between is undetermined). The lack of transparency makes it difficult to know where the system is going right and where it is going wrong.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", x 1 , y i \u2212 1 , y i \u2212 2 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming, a docstring is a string literal specified in source code that is used, like a comment, to document a specific segment of code. Unlike conventional source code comments, or even specifically formatted comments like docblocks, docstrings are not stripped from the source tree when it is parsed and are retained throughout the runtime of the program. This allows the programmer to inspect these comments at run time, for instance as an interactive help system, or as metadata. Languages that support docstrings include Python, Lisp, Elixir, Clojure, Gherkin, Julia and Haskell.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(1964\u20131977). By the early 2010s videotelephony and videophones had become commonplace and unremarkable in various forms of media, in part due to their real and ubiquitous presence in common electronic devices and laptop computers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It depends on the models, which one to use and requires experience to choose the right one. In most cases, the goal is to estimate the state sequence from the measurements. In other cases, one can use the description to estimate the parameters of a noise process for example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics the symmetrization methods are algorithms of transforming a set A \u2282 R n {\\displaystyle A\\subset \\mathbb {R} ^{n}} to a ball B \u2282 R n {\\displaystyle B\\subset \\mathbb {R} ^{n}} with equal volume vol \u2061 ( B ) = vol \u2061 ( A ) {\\displaystyle \\operatorname {vol} (B)=\\operatorname {vol} (A)} and centered at the origin. B is called the symmetrized version of A, usually denoted A \u2217 {\\displaystyle A^{*}} . These algorithms show up in solving the classical isoperimetric inequality problem, which asks: Given all two-dimensional shapes of a given area, which of them has the minimal perimeter (for details see Isoperimetric inequality). The conjectured answer was the disk and Steiner in 1838 showed this to be true using the Steiner symmetrization method (described below).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matroid theory, a field within mathematics, a gammoid is a certain kind of matroid, describing sets of vertices that can be reached by vertex-disjoint paths in a directed graph. The concept of a gammoid was introduced and shown to be a matroid by Hazel Perfect (1968), based on considerations related to Menger's theorem characterizing the obstacles to the existence of systems of disjoint paths. Gammoids were given their name by Pym (1969) and studied in more detail by Mason (1972).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following the Ranked pairs winner for the first group of voters is determined. The results would be tabulated as follows:  indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption  indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column captionThe sorted list of victories would be: Result: B > C and A > B are locked in first (and C > A can't be locked in after that), so the full ranking is A > B > C. Thus, A is elected Ranked pairs winner by the first group of voters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel computing, folded cube graphs have been studied as a potential network topology, as an alternative to the hypercube. Compared to a hypercube, a folded cube with the same number of nodes has nearly the same vertex degree but only half the diameter. Efficient distributed algorithms (relative to those for a hypercube) are known for broadcasting information in a folded cube.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is a tool that postal management uses to redistribute and eliminate overtime costs, based on consultation with the carrier about his/her estimated workload for the day and mail volume projections from the DOIS (Delivery Operations Information System) computer program. Routes are adjusted and/or eliminated based on information (length, time, and overall workload) also controlled by this program, consultations with the carrier assigned to the route, and a current PS Form 3999 (street observation by a postal supervisor to determine accurate times spent on actual delivery of mail). Rural carriers are under a form of salary called \"evaluated hours\", usually with overtime built into their pay.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement. An experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on. Experimental uncertainty estimates are needed to assess the confidence in the results. A related field is design of experiments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In fact, subjects actually named predictable words faster than they did unpredictable words. Whittlesea was able to conclude from this study that subjects misattributed their fast responses for highly predictable words as an indication that they had previously experienced the word whereas in fact that was incorrect. As a result, the fluency of processing caused the subjects to misinterpret their quickness as a case of familiarity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers. For \"pure\" vector spaces, the concept has been introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most tabletop role-playing games, die rolls required by the system are given in the form AdX. A and X are variables, separated by the letter d, which stands for die or dice. The letter d is most commonly lower-case, but some forms of notation use upper-case D (non-English texts can use the equivalent form of the first letter of the given language's word for \"dice\", but also often use the English \"d\"). A is the number of dice to be rolled (usually omitted if 1).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Sylvester's sequence is an integer sequence in which each term is the product of the previous terms, plus one. The first few terms of the sequence are 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 (sequence A000058 in the OEIS).Sylvester's sequence is named after James Joseph Sylvester, who first investigated it in 1880. Its values grow doubly exponentially, and the sum of its reciprocals forms a series of unit fractions that converges to 1 more rapidly than any other series of unit fractions. The recurrence by which it is defined allows the numbers in the sequence to be factored more easily than other numbers of the same magnitude, but, due to the rapid growth of the sequence, complete prime factorizations are known only for a few of its terms. Values derived from this sequence have also been used to construct finite Egyptian fraction representations of 1, Sasakian Einstein manifolds, and hard instances for online algorithms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mid-2001, the Xeon brand was introduced (\"Pentium\" was dropped from the name). The initial variant that used the new NetBurst microarchitecture, \"Foster\", was slightly different from the desktop Pentium 4 (\"Willamette\"). It was a decent chip for workstations, but for server applications it was almost always outperformed by the older Cascades cores with a 2 MB L2 cache and AMD's Athlon MP. Combined with the need to use expensive Rambus Dynamic RAM, the Foster's sales were somewhat unimpressive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the easiest way to find an optimal BFS is to use the simplex algorithm. It keeps, at each point of its execution, a \"current basis\" B (a subset of m out of n variables), a \"current BFS\", and a \"current tableau\". The tableau is a representation of the linear program where the basic variables are expressed in terms of the non-basic ones:: 65 where x B {\\displaystyle x_{B}} is the vector of m basic variables, x N {\\displaystyle x_{N}} is the vector of n non-basic variables, and z {\\displaystyle z} is the maximization objective. Since non-basic variables equal 0, the current BFS is p {\\displaystyle p} , and the current maximization objective is z 0 {\\displaystyle z_{0}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Division by a power of 2 is often written as a right-shift, not for optimization as might be assumed, but because the floor of negative results is required. Assuming such shifts are \"premature optimization\" and replacing them with division can break software.Many programming languages (including C, C++, C#, Java, PHP, R, and Python) provide standard functions for floor and ceiling, usually called floor and ceil, or less commonly ceiling. The language APL uses \u230ax for floor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix A satisfying the equation A*A = AA* is diagonalizable. The converse does not hold because diagonalizable matrices may have non-orthogonal eigenspaces. The left and right singular vectors in the singular value decomposition of a normal matrix A = U \u03a3 V \u2217 {\\displaystyle \\mathbf {A} =\\mathbf {U} {\\boldsymbol {\\Sigma }}\\mathbf {V} ^{*}} differ only in complex phase from each other and from the corresponding eigenvectors, since the phase must be factored out of the eigenvalues to form singular values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Compound or \"query-based\" operations on groups of identifiers, based on the namespaces in which they are declared, are rendered unwieldy or unfeasible. In languages with restricted identifier length, the use of prefixes limits the number of characters that can be used to identify what the function does. This is a particular problem for packages originally written in FORTRAN 77, which offered only 6 characters per identifier.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Square matrices are often used to represent simple linear transformations, such as shearing or rotation. For example, if R {\\displaystyle R} is a square matrix representing a rotation (rotation matrix) and v {\\displaystyle \\mathbf {v} } is a column vector describing the position of a point in space, the product R v {\\displaystyle R\\mathbf {v} } yields another column vector describing the position of that point after that rotation. If v {\\displaystyle \\mathbf {v} } is a row vector, the same transformation can be obtained using v R T {\\displaystyle \\mathbf {v} R^{\\mathsf {T}}} , where R T {\\displaystyle R^{\\mathsf {T}}} is the transpose of R {\\displaystyle R} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Examples are \"sales department\", \"procurement department\", etc. It is represented as an ellipse with a vertical line.Information, material, or resource object In the event-driven process chain, the information, material, or resource objects portray objects in the real world, for example business objects, entities, etc., which can be input data serving as the basis for a function, or output data produced by a function. Examples are \"material\", \"order\", etc. In the EPC graph such an object is represented as rectangle.Logical connector In the event-driven process chain the logical relationships between elements in the control flow, that is, events and functions are described by logical connectors. With the help of logical connectors it is possible to split the control flow from one flow to two or more flows and to synchronize the control flow from two or more flows to one flow.Logical relationshipsThere are three kinds of logical relationships defined in event-driven process chains:Branch/Merge: Branch and merge correspond to making decision of which path to choose among several control flows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Richardson's theorem establishes the undecidability of the equality of real numbers defined by expressions involving integers, \u03c0, ln \u2061 2 , {\\displaystyle \\ln 2,} and exponential and sine functions. It was proved in 1968 by mathematician and computer scientist Daniel Richardson of the University of Bath. Specifically, the class of expressions for which the theorem holds is that generated by rational numbers, the number \u03c0, the number ln 2, the variable x, the operations of addition, subtraction, multiplication, composition, and the sin, exp, and abs functions. For some classes of expressions (generated by other primitives than in Richardson's theorem) there exist algorithms that can determine whether an expression is zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, it is easy to calculate t(G) directly: If G is itself a tree, then t(G) = 1. When G is the cycle graph Cn with n vertices, then t(G) = n. For a complete graph with n vertices, Cayley's formula gives the number of spanning trees as nn \u2212 2. If G is the complete bipartite graph K p , q {\\displaystyle K_{p,q}} ,then t ( G ) = p q \u2212 1 q p \u2212 1 {\\displaystyle t(G)=p^{q-1}q^{p-1}} . For the n-dimensional hypercube graph Q n {\\displaystyle Q_{n}} , the number of spanning trees is t ( G ) = 2 2 n \u2212 n \u2212 1 \u220f k = 2 n k ( n k ) {\\displaystyle t(G)=2^{2^{n}-n-1}\\prod _{k=2}^{n}k^{n \\choose k}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Paley\u2013Zygmund inequality bounds the probability that a positive random variable is small, in terms of its first two moments. The inequality was proved by Raymond Paley and Antoni Zygmund. Theorem: If Z \u2265 0 is a random variable with finite variance, and if 0 \u2264 \u03b8 \u2264 1 {\\displaystyle 0\\leq \\theta \\leq 1} , then P \u2061 ( Z > \u03b8 E \u2061  ) \u2265 ( 1 \u2212 \u03b8 ) 2 E \u2061  2 E \u2061  . {\\displaystyle \\operatorname {P} (Z>\\theta \\operatorname {E} )\\geq (1-\\theta )^{2}{\\frac {\\operatorname {E} ^{2}}{\\operatorname {E} }}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is very difficult to support new peers joining part-way through a game. Each peer must communicate with all other peers, limiting the number of connected players. Each peer must wait for every other peer's message before simulating the next \"network frame\", resulting in all players experiencing the same latency as the player with the worst connection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When n = 2 r {\\displaystyle n=2r} there are other equally-large families, but for larger values of n {\\displaystyle n} only the families constructed in this way can be largest. The Erd\u0151s\u2013Ko\u2013Rado theorem can also be described in terms of hypergraphs or independent sets in Kneser graphs. Several analogous theorems apply to other kinds of mathematical object than sets, including linear subspaces, permutations, and strings. They again describe the largest possible intersecting families as being formed by choosing an element and forming the family of all objects that contain the chosen element.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "}}\\right)\\\\\\\\&{}=\\lambda e^{-\\lambda t}-e^{-\\lambda t}\\sum _{u=1}^{x-1}\\left({\\frac {\\lambda ^{u}t^{u-1}}{(u-1)! }}-{\\frac {\\lambda ^{u+1}t^{u}}{u! }}\\right)\\end{aligned}}} The sum telescopes, leaving f ( t ) = \u03bb x t x \u2212 1 e \u2212 \u03bb t ( x \u2212 1 ) ! . {\\displaystyle f(t)={\\frac {\\lambda ^{x}t^{x-1}e^{-\\lambda t}}{(x-1)!}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A field has a consistent tensorial character wherever it is defined: i.e. a field cannot be a scalar field somewhere and a vector field somewhere else. For example, the Newtonian gravitational field is a vector field: specifying its value at a point in spacetime requires three numbers, the components of the gravitational field vector at that point. Moreover, within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively. In this theory an equivalent representation of field is a field particle, for instance a boson.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So, 30 Z {\\displaystyle 30\\mathbb {Z} } is a semiprime ideal of the integers (because 30 = 2 \u00d7 3 \u00d7 5, with no repeated prime factors), but 12 Z {\\displaystyle 12\\mathbb {Z} \\,} is not (because 12 = 22 \u00d7 3, with a repeated prime factor). The class of semiprime rings includes semiprimitive rings, prime rings and reduced rings. Most definitions and assertions in this article appear in (Lam 1999) and (Lam 2001).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Euler's idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as x2 \u00b1 Dy2 (where x2 is relatively prime to Dy2) is a prime power or twice a prime power. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing infinitely many primes and missing infinitely many other primes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Unicode standard, the symbol \u00a3 is called POUND SIGN, and the symbol \u20a4 is the LIRA SIGN. These have respective code points: U+00A3 \u00a3 POUND SIGN (\u00a3 \u00b7 inherited from Latin-1) U+20A4 \u20a4 LIRA SIGNUnicode notes that the \"lira sign\" is not widely used and was added due to both it and the pound sign being available on HP printers.The encoding of the \u00a3 symbol in position xA3 (16310) was first standardised by ISO Latin-1 (an \"extended ASCII\") in 1985. Position xA3 was used by the Digital Equipment Corporation VT220 terminal, Mac OS Roman, Amstrad CPC, Amiga, and Acorn Archimedes. Many early computers (limited to a 7-bit, 128-position character set) used a variant of ASCII with one of the less-frequently used characters replaced by the \u00a3.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In netstalking, there are two general methods for finding unusual information: a deli-search and a net-random. Deli-search, or \"deliberated search\", is a targeted search for objects of interest whose characteristics are already known. This method usually uses the language of search queries and web archives, with which one can view old or deleted versions of these pages. Net-random searches for hidden and unknown information through the process of trial and error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The b {\\displaystyle b} on the right-hand side can also be written as b 1 {\\displaystyle b^{1}} , giving b r + r = b 1 {\\displaystyle b^{r+r}=b^{1}} . Equating the exponents on both sides, we have r + r = 1 {\\displaystyle r+r=1} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the age of information, the amount of the written material we encounter each day is simply beyond our processing capacity. Topic models can help to organize and offer insights for us to understand large collections of unstructured text bodies. Originally developed as a text-mining tool, topic models have been used to detect instructive structures in data such as genetic information, images, and networks. They also have applications in other fields such as bioinformatics and computer vision.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the components of the gradient of a function f {\\displaystyle f} , ( \u2207 f ) i {\\displaystyle (\\nabla f)^{i}} , are expressed in terms of a given basis, e i {\\displaystyle \\mathbf {e} _{i}} , then these components will in fact still vary oppositely to that of the basis vectors, as can be seen by observing (using the Einstein summation convention): where \u03b4 j i {\\displaystyle \\delta _{j}^{i}} is the kronecker delta symbol, and ( T ) k i {\\displaystyle (T)_{k}^{i}} represents the components of some transformation matrix corresponding to the transformation T {\\displaystyle T} . As can be seen, whatever transformation acts on the basis vectors, the inverse transformation must act on the components. A third concept related to covariance and contravariance is invariance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the free matroid over a given ground-set E is the matroid in which the independent sets are all subsets of E. It is a special case of a uniform matroid. The unique basis of this matroid is the ground-set itself, E. Among matroids on E, the free matroid on E has the most independent sets, the highest rank, and the fewest circuits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, mobile phone network providers are not obliged to provide unlocking, even after the end of the contract. Ofcom, UK's telecom regulator, allowed 3 UK to sell a mobile phone with the SIM card permanently superglued to the phone. Most operators offer some form of unlocking service, depending on the state of the contract and the model of phone, but usually for a charge. The full Oftel 2002 SIM-lock position paper specifies that there is no SIM-locking law in the UK; the regulator wants only \"consumer awareness\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Following is another example: TABLE 1 The join dependencies of the table are {medic name, occupation}, {medic name, practice in years} and {medic name, type}. Hence we could see that such table is 2NF (due to the appearance of transitive dependency). The following tables try to bring it to 6NF: TABLE 2.1 TABLE 2.2 TABLE 2.3 TABLE 2.4", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory, parametricity is an abstract uniformity property enjoyed by parametrically polymorphic functions, which captures the intuition that all instances of a polymorphic function act the same way.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In simple cases, the user can compute the path delay between elements manually. If the design is more than a dozen or so elements this is impractical. For example, the time delay along a path from the output of a D-Flip Flop, through combinatorial logic gates, then into the next D-Flip Flop input must satisfy (be less than) the time period between synchronizing clock pulses to the two flip flops. When the delay through the elements is greater than the clock cycle time, the elements are said to be on the critical path.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years the model formulating approach of considering a \"typical user\" in cellular (or other) networks has been used considerably. This is, however, just a first approach which allows one to characterize only the spectral efficiency (or information rate) of the network. In other words, this approach captures the best possible service that can be given to a single user who does not need to share wireless network resources with other users. Models beyond the typical user approach have been proposed with the aim of analyzing QoS metrics of a population of users, and not just a single user.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Over a perfect field of non-zero characteristic p, this quotient is the product of the a i {\\displaystyle a_{i}} such that i is not a multiple of p. Further GCD computations and exact divisions allow computing the square-free factorization (see square-free factorization over a finite field). In characteristic zero, a better algorithm is known, Yun's algorithm, which is described below. Its computational complexity is, at most, twice that of the GCD computation of the input polynomial and its derivative. More precisely, if T n {\\displaystyle T_{n}} is the time needed to compute the GCD of two polynomials of degree n {\\displaystyle n} and the quotient of these polynomial by the GCD, then 2 T n {\\displaystyle 2T_{n}} is an upper bound for the time needed to compute the square free decomposition. There are also known algorithms for the computation of the square-free decomposition of multivariate polynomials, that proceed generally by considering a multivariate polynomial as a univariate polynomial with polynomial coefficients, and applying recursively a univariate algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, the size of each table does not change, so both table and directory now have only 512 entries. Because this allows only one half of the entries of the original scheme, an extra level of hierarchy has been added, so CR3 now points physically to a Page Directory Pointer Table, a short table containing four pointers to page directories. Supporting 64 bit addresses in the page-table is a significant change as this enables two changes to the processor addressing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially homotopy theory, the mapping cone is a construction C f {\\displaystyle C_{f}} of topology, analogous to a quotient space. It is also called the homotopy cofiber, and also notated C f {\\displaystyle Cf} . Its dual, a fibration, is called the mapping fibre. The mapping cone can be understood to be a mapping cylinder M f {\\displaystyle Mf} , with one end of the cylinder collapsed to a point. Thus, mapping cones are frequently applied in the homotopy theory of pointed spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of Information theory Shannon entropy is defined to quantify the complexity of a distribution p as p log \u2061 p {\\displaystyle p\\log p\\,} . Therefore, higher entropy means p is more complex hence more unpredictable. To measure the complexity of an image region { x , R } {\\displaystyle \\{x,R\\}} around point x {\\displaystyle x} with shape R {\\displaystyle R} , a descriptor D {\\displaystyle D} that takes on values d 1 , \u2026 , d r {\\displaystyle {d_{1},\\dots ,d_{r}}} (e.g., in an 8 bit grey level image, D would range from 0 to 255 for each pixel) is defined so that P D ( d i , x , R ) {\\displaystyle P_{D}(d_{i},x,R)} , the probability of descriptor value d i {\\displaystyle d_{i}} occurs in region { x , R } {\\displaystyle \\{x,R\\}} can be computed. Further, the entropy of image region R x {\\displaystyle R_{x}} can compute as H D ( x , R ) = \u2212 \u2211 i \u2208 ( 1 \u2026 r ) P D ( d i , x , R ) log \u2061 P D ( d i , x , R ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, it is conventional to denote a Lorentz transformation \u039b \u2208 SO + \u2061 ( 1 , 3 ) {\\displaystyle \\Lambda \\in \\operatorname {SO} ^{+}(1,3)} as \u039b \u03bc \u03bd , {\\displaystyle {\\Lambda ^{\\mu }}_{\\nu }~,} thus showing the matrix with spacetime indexes \u03bc , \u03bd = 0 , 1 , 2 , 3. {\\displaystyle \\mu ,\\nu =0,1,2,3.} A four-vector can be created from the Pauli matrices in two different ways: as \u03c3 \u03bc = ( I , \u03c3 \u2192 ) {\\displaystyle \\sigma ^{\\mu }=(I,{\\vec {\\sigma }})} and as \u03c3 \u00af \u03bc = ( I , \u2212 \u03c3 \u2192 ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional or planar space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a branch of mathematics, the Carmichael function \u03bb(n) of a positive integer n is the smallest positive integer m such that a m \u2261 1 ( mod n ) {\\displaystyle a^{m}\\equiv 1{\\pmod {n}}} holds for every integer a coprime to n. In algebraic terms, \u03bb(n) is the exponent of the multiplicative group of integers modulo n. The Carmichael function is named after the American mathematician Robert Carmichael who defined it in 1910. It is also known as Carmichael's \u03bb function, the reduced totient function, and the least universal exponent function. The following table compares the first 36 values of \u03bb(n) (sequence A002322 in the OEIS) with Euler's totient function \u03c6 (in bold if they are different; the ns such that they are different are listed in OEIS: A033949).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most prominent of these models has been the Penn Discourse Treebank (PDTB). PDTB is focusing on the annotation of discourse cues (discourse markers, discourse connectives), which are assigned an internal argument (to which the discourse marker is attached), an external argument (target or attachment point of the relation) and a sense (discourse relation). Both arguments are defined as the smallest string that expresses the meaning of the utterances to be connected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was an upgrade path for users who had outgrown the IBM System/3. It ran Cobol-74, RPG2, Fortran, and Assembler. The instruction set of the 90/xx series was implemented in microcode and was loaded into control storage as part of the boot up process, before loading the operating system.Shortly after the 90/30 was introduced, Sperry Univac introduced the 90/25 which was the same basic hardware, however had an option for a smaller 80 column card reader and was a bit slower.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A common variant on the RISC design employs the Harvard architecture, versus Von Neumann architecture or stored program architecture common to most other designs. In a Harvard Architecture machine, the program and data occupy separate memory devices and can be accessed simultaneously. In Von Neumann machines, the data and programs are mixed in one memory device, requiring sequential accessing which produces the so-called Von Neumann bottleneck.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In these examples, the ranks are assigned to values in ascending order. (In some other cases, descending ranks are used.) Ranks are related to the indexed list of order statistics, which consists of the original dataset rearranged into ascending order.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to factor using algebra tiles, one has to start out with a set of tiles that the student combines into a rectangle, this may require the use of adding zero pairs in order to make the rectangular shape. An example would be where one is given one positive x2 tile, three positive x tiles, and two positive unit tiles. The student forms the rectangle by having the x2 tile in the upper right corner, then one has two x tiles on the right side of the x2 tile, one x tile underneath the x2 tile, and two unit tiles are in the bottom right corner.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to bound the time complexity of the algorithm, we must analyze the number of push and relabel operations which occur within the main loop. The numbers of relabel, saturating push and nonsaturating push operations are analyzed separately. In the algorithm, the relabel operation can be performed at most (2| V | \u2212 1)(| V | \u2212 2) < 2| V |2 times. This is because the labeling \ud835\udcc1(u) value for any node u can never decrease, and the maximum label value is at most 2| V | \u2212 1 for all nodes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "And edges connect different types of nodes (i.e. actors to movies) if they have a relationship (actors in a movie). Initially the network was found to have a small-world property. Afterwards, it was discovered that it exhibits a scale-free (power-law) behavior.The parlor game of Six Degrees of Kevin Bacon involves finding paths in this network from specified actors to Kevin Bacon.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of integer operations, the PRISM architecture was similar to the MIPS designs. Of the 32-bits in the instructions, the 6 highest and 5 lowest bits were the instruction, leaving the other 21 bits of the word for encoding either a constant or register locations. Sixty-four 32-bit registers were included, as opposed to thirty-two in the MIPS, but usage was otherwise similar. PRISM and MIPS both lack the register windows that were a hallmark of the other major RISC design, Berkeley RISC.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the domain of computer vision, efforts have been made to model the mechanism of human attention, especially the bottom-up intentional mechanism and its semantic significance in classification of video contents. Both spatial attention and temporal attention have been incorporated in such classification efforts. Generally speaking, there are two kinds of models to mimic the bottom-up salience mechanism in static images.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of components, let A = A i d x i , {\\displaystyle A=A_{i}dx^{i},} where d x i {\\displaystyle dx^{i}} is the standard one-form coordinate bases on the cotangent bundle T*M. Inserting into the above, and expanding, one obtains (using the summation convention): F = 1 2 ( \u2202 A j \u2202 x i \u2212 \u2202 A i \u2202 x j +  ) d x i \u2227 d x j . {\\displaystyle F={\\frac {1}{2}}\\left({\\frac {\\partial A_{j}}{\\partial x^{i}}}-{\\frac {\\partial A_{i}}{\\partial x^{j}}}+\\right)dx^{i}\\wedge dx^{j}.} Keep in mind that for an n-dimensional vector space, each A i {\\displaystyle A_{i}} is an n\u00d7n matrix, the indices of which have been suppressed, whereas the indices i and j run over 1,...,m, with m being the dimension of the underlying manifold. Both of these indices can be made simultaneously manifest, as shown in the next section. The notation presented here is that which is commonly used in physics; for example, it can be immediately recognizable as the gluon field strength tensor. For the abelian case, n=1, and the vector bundle is one-dimensional; the commutator vanishes, and the above can then be recognized as the electromagnetic tensor in more or less standard physics notation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, they are only assumed identical or nearly identical in musical set theory. Sets are said to be inversionally symmetrical if they map onto themselves under inversion. The pitch that the sets must be inverted around is said to be the axis of symmetry (or center).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Find k \u2208 Z {\\displaystyle k\\in \\mathbb {Z} } such that p = r + k \u22c5 q {\\displaystyle p=r+k\\cdot q} is a P {\\displaystyle P} -bit prime with p \u2261 2 mod 3 {\\displaystyle p\\equiv 2\\ {\\text{mod}}\\ 3} .Correctness of Algorithm A:It remains to check that q \u2223 p 2 \u2212 p + 1 {\\displaystyle q\\mid p^{2}-p+1} because all the other necessary properties are obviously satisfied per definition of p {\\displaystyle p} and q {\\displaystyle q} . We easily see that p 2 \u2212 p + 1 = r 2 + 2 r k q + k 2 q 2 \u2212 r \u2212 k q + 1 = r 2 \u2212 r + 1 + q ( 2 r k + k 2 q \u2212 k ) = q ( 1 + 2 r k + k 2 q \u2212 k ) {\\displaystyle p^{2}-p+1=r^{2}+2rkq+k^{2}q^{2}-r-kq+1=r^{2}-r+1+q(2rk+k^{2}q-k)=q(1+2rk+k^{2}q-k)} which implies that q \u2223 p 2 \u2212 p + 1 {\\displaystyle q\\mid p^{2}-p+1} .Algorithm A is very fast and can be used to find primes p {\\displaystyle p} that satisfy a degree-two polynomial with small coefficients. Such p {\\displaystyle p} lead to fast arithmetic operations in G F ( p ) {\\displaystyle GF(p)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the background there is an update stream that runs a series of insert/delete operations (one pair for each query user). The choice of the number of users is at the discretion of the test sponsor. The throughput metric is computed as the total amount of work (S\u00d717), converted to hours from seconds (3600 seconds per hour), scaled by the database volume (SF) and divided by the total elapsed time (Ts) required between the first query starting and the last query or update function completing. Therefore, the complete formulation is: Q t h D = S \u00d7 17 \u00d7 3600 T s \u00d7 S F {\\displaystyle {\\mathit {QthD}}={\\frac {S\\times 17\\times 3600}{T_{s}}}\\times {\\mathit {SF}}} == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To generate this distribution experimentally, we have to repeat the experiment until it happens to give n balls. If we want to fix the value of n prior to the experiment then we have to take the balls one by one until we have n balls. The balls are therefore no longer independent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots. In statistics, the normal distribution is used in classical multivariate analysis, while elliptical distributions are used in generalized multivariate analysis, for the study of symmetric distributions with tails that are heavy, like the multivariate t-distribution, or light (in comparison with the normal distribution). Some statistical methods that were originally motivated by the study of the normal distribution have good performance for general elliptical distributions (with finite variance), particularly for spherical distributions (which are defined below). Elliptical distributions are also used in robust statistics to evaluate proposed multivariate-statistical procedures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Hermite polynomial Hen(x) of variance 1, the absolute value of the coefficient of xk is the number of (unordered) partitions of an n-element set into k singletons and n \u2212 k/2 (unordered) pairs. Equivalently, it is the number of involutions of an n-element set with precisely k fixed points, or in other words, the number of matchings in the complete graph on n vertices that leave k vertices uncovered (indeed, the Hermite polynomials are the matching polynomials of these graphs). The sum of the absolute values of the coefficients gives the total number of partitions into singletons and pairs, the so-called telephone numbers 1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496,... (sequence A000085 in the OEIS).This combinatorial interpretation can be related to complete exponential Bell polynomials as where xi = 0 for all i > 2. These numbers may also be expressed as a special value of the Hermite polynomials:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While classes are suitable to represent a population of individuals, metaclasses can, as one of their feature, be used to represent the conceptual dimension of an ontology. Metaclasses are supported in the ontology language OWL and the data-modeling vocabulary RDFS. Metaclasses are often modeled by setting them as the object of claims involving rdf:type and rdfs:subClassOf\u2014built-in properties commonly referred to as instance of and subclass of.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, the term \"back-to-back agreement\" refers to an NDA entered into with a third party who legitimately receives confidential information, putting them under similar non-disclosure obligations as the initial party granted the information. Case law in a 2013 Court of Appeal decision (Dorchester Project Management v BNP Paribas) confirmed that a confidentiality agreement will be interpreted as a contract subject to the rules of contractual interpretation which generally apply in the English courts.NDAs are often used as a condition of a financial settlement in an attempt to silence whistleblowing employees from making public the misdeeds of their former employers. There is law, the Public Interest Disclosure Act 1998, which allows \"protected disclosure\" despite the existence of an NDA, although employers sometimes intimidate the former employee into silence despite this.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fields of computational linguistics and applied linguistics, a morphological dictionary is a linguistic resource that contains correspondences between surface form and lexical forms of words. Surface forms of words are those found in natural language text. The corresponding lexical form of a surface form is the lemma followed by grammatical information (for example the part of speech, gender and number).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Store: Data-collection or some sort of material. Flow: Movement of data or material in the process. External Entity: External to the modeled system, but interacts with it.Now, with these symbols, a process can be represented as a network of these symbols. This decomposed process is a DFD, data flow diagram. In Dynamic Enterprise Modeling a division is made in the Control model, Function Model, Process model and Organizational model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With object-oriented programming the memory objects are often stored dynamically on the heap but modern operating systems use address space layout randomization (ASLR). Therefore, the only way to modify such memory in a reproducible manner is to get information from inside the game process. This requires reverse engineering methods like API hooking of malloc() and free(), code injection or searching for static access pointers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This problem has initialized a significant effort in developing automated detection methods for misinformation on social media platforms.Social media platforms allow for easy spread of misinformation. The specific reasons why misinformation spreads through social media so easily remain unknown. A 2018 study of Twitter determined that, compared to accurate information, false information spread significantly faster, further, deeper, and more broadly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Kuiper's theorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H. It states that the space GL(H) of invertible bounded endomorphisms of H is such that all maps from any finite complex Y to GL(H) are homotopic to a constant, for the norm topology on operators. A significant corollary, also referred to as Kuiper's theorem, is that this group is weakly contractible, ie. all its homotopy groups are trivial. This result has important uses in topological K-theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, the strength notated as si of a node i is defined as si = \u03a3jwij, where wij is the weight of the link between i and j. In order to apply the disparity filter algorithm without overlooking nodes with low strength, a normalized weight pij is defined as pij = wij/si. In the null model, the normalized weights of a certain node with degree k is generated like this: k \u2212 1 pins are randomly assigned between the interval 0 and 1. The interval is then divided into k subintervals. The length of the subinterval represents the normalized weight of each link in the null model. Consecutively, and based on the null model, we can derive that the normalized weight distribution of a node with degree k follows \u03c1 ( x ) d x = ( k \u2212 1 ) ( 1 \u2212 x ) k \u2212 2 d x {\\displaystyle \\rho (x)\\,dx=(k-1)(1-x)^{k-2}\\,dx} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where a parametrized family has a location parameter, a slightly different definition is often used as follows. If we denote the location parameter by m {\\displaystyle m} , and the scale parameter by s {\\displaystyle s} , then we require that F ( x ; s , m , \u03b8 ) = F ( ( x \u2212 m ) / s ; 1 , 0 , \u03b8 ) {\\displaystyle F(x;s,m,\\theta )=F((x-m)/s;1,0,\\theta )} where F ( x , s , m , \u03b8 ) {\\displaystyle F(x,s,m,\\theta )} is the cmd for the parametrized family. This modification is necessary in order for the standard deviation of a non-central Gaussian to be a scale parameter, since otherwise the mean would change when we rescale x {\\displaystyle x} . However, this alternative definition is not consistently used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the examination of individual scripts, the study of writing systems has developed along partially independent lines. Thus, the terminology employed differs somewhat from field to field.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some terminals and editing programs could not deal with double-byte characters starting at odd columns, only even ones (some could not even put double-byte and single-byte characters in the same line). So the DBCS sets generally included Roman characters and digits also, for use alongside the CJK characters in the same line. On the other hand, early Japanese computing used a single-byte code page called JIS X 0201 for katakana.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, these activities are known as software maintenance (cf. ISO/IEC 9126). Closely related concepts in the software engineering domain are evolvability, modifiability, technical debt, and code smells. The maintainability index is calculated with certain formulae from lines-of-code measures, McCabe measures and Halstead complexity measures. The measurement and tracking of maintainability are intended to help reduce or reverse a system's tendency toward \"code entropy\" or degraded integrity, and to indicate when it becomes cheaper and/or less risky to rewrite the code than it is to change it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In proof theory, the semantic tableau (; plural: tableaux, also called truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. An analytic tableau is a tree structure computed for a logical formula, having at each node a subformula of the original formula to be proved or refuted. Computation constructs this tree and uses it to prove or refute the whole formula. The tableau method can also determine the satisfiability of finite sets of formulas of various logics. It is the most popular proof procedure for modal logics (Girle 2000).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An algorithm is a formal procedure in which each step is clearly defined. It guarantees success if applied correctly. The long multiplication usually taught in school is an example of an algorithm for solving the problem of multiplying big numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a ranked partially ordered set or ranked poset may be either: a graded poset, or a poset with the property that for every element x, all maximal chains among those with x as greatest element have the same finite length, or a poset in which all maximal chains have the same finite length.The second definition differs from the first in that it requires all minimal elements to have the same rank; for posets with a least element, however, the two requirements are equivalent. The third definition is even more strict in that it excludes posets with infinite chains and also requires all maximal elements to have the same rank. Richard P. Stanley defines a graded poset of length n as one in which all maximal chains have length n. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many other shock-related changes take place within both impactor and target as the shock wave passes through, and some of these changes can be used as diagnostic tools to determine whether particular geological features were produced by impact cratering.As the shock wave decays, the shocked region decompresses towards more usual pressures and densities. The damage produced by the shock wave raises the temperature of the material. In all but the smallest impacts this increase in temperature is sufficient to melt the impactor, and in larger impacts to vaporize most of it and to melt large volumes of the target. As well as being heated, the target near the impact is accelerated by the shock wave, and it continues moving away from the impact behind the decaying shock wave.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In occupational health and safety, a tagging system is a system of recording and displaying the status of a machine or equipment, enabling staff to view whether it is in working order. It is a product of industry-specific legislation which sets safety standards for a particular piece of equipment, involving inspection, record-keeping, and repair. This sets standardized umbrella terms for equipment and machinery (e.g. machinery, scaffolding, forklift, cherry picker) to be deemed 'safe to use'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some circumstances, the \"pre-\" in preadaptation can be interpreted as applying, for non-teleological reasons, prior to the adaptation itself, creating a meaning for the term that is distinct from exaptation. For example, future environments (say, hotter or drier ones), may resemble those already encountered by a population at one of its current spatial or temporal margins. This is not actual foresight, but rather the luck of having adapted to a climate which later becomes more prominent. Cryptic genetic variation may have the most strongly deleterious mutations purged from it, leaving an increased chance of useful adaptations, but this represents selection acting on current genomes with consequences for the future, rather than foresight. Function may not always come before form: developed structures could change or alter the primary functions they were intended for due to some structural or historical cause.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle n=1,2,...} , to converge to a minimum, provided such a minimum exists and p n {\\displaystyle \\mathbf {p} _{n}} is selected appropriately in each step. For gradient descent, p n {\\displaystyle \\mathbf {p} _{n}} is selected as \u2212 \u2207 f ( x n ) {\\displaystyle -\\nabla f(\\mathbf {x} _{n})} . The value of \u03b1 j {\\displaystyle \\alpha _{j}} for the j {\\displaystyle j} that fulfills the Armijo\u2013Goldstein condition depends on x {\\displaystyle \\mathbf {x} } and p {\\displaystyle \\mathbf {p} } , and is thus denoted below by \u03b1 ( x , p ) {\\displaystyle \\alpha (\\mathbf {x} ,\\mathbf {p} )} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A page table maps virtual memory to physical memory. There may be a single page table, a page table for each process, a page table for each segment, or a hierarchy of page tables, depending on the architecture and the OS. The page tables are usually invisible to the process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In subjective testing, implicit learning occurs when participants who show above chance performance have no knowledge of their judgements. Subjects who are theorized to have no knowledge of their judgements generally are convinced that their judgements are guesses and will have an accuracy rate that has little correlation with their ratings of confidence they assigned to each of their judgements. In artificial grammar learning and sequence learning participants showed higher than chance performance. These participants were convinced that they were only making assumptions and had no real knowledge of the subject. Results usually showed that in reality, they had gained implicit knowledge throughout the experiment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, the Schur complement method, named after Issai Schur, is the basic and the earliest version of non-overlapping domain decomposition method, also called iterative substructuring. A finite element problem is split into non-overlapping subdomains, and the unknowns in the interiors of the subdomains are eliminated. The remaining Schur complement system on the unknowns associated with subdomain interfaces is solved by the conjugate gradient method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Zsigmondy's theorem, named after Karl Zsigmondy, states that if a > b > 0 {\\displaystyle a>b>0} are coprime integers, then for any integer n \u2265 1 {\\displaystyle n\\geq 1} , there is a prime number p (called a primitive prime divisor) that divides a n \u2212 b n {\\displaystyle a^{n}-b^{n}} and does not divide a k \u2212 b k {\\displaystyle a^{k}-b^{k}} for any positive integer k < n {\\displaystyle k 1 {\\displaystyle n>1} and n {\\displaystyle n} is not equal to 6, then 2 n \u2212 1 {\\displaystyle 2^{n}-1} has a prime divisor not dividing any 2 k \u2212 1 {\\displaystyle 2^{k}-1} with k < n {\\displaystyle k", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values. As well as substituting individual objects such as Alice, the number 1, the tallest building in London etc. for x, we may substitute both Alice and Bob, or all the numbers between 0 and 10, or all the buildings in London over 20 stories. The point of the theory is to give first-order logic the power of set theory, but without any \"existential commitment\" to such objects as sets. The classic expositions are Boolos 1984 and Lewis 1991.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against cryptanalysis by quantum computers and also to provide the basis for homomorphic encryption. Public-key cryptography relies on construction of mathematical problems that are believed to be hard to solve if no further information is available, but are easy to solve if some information used in the problem construction is known. Some problems of this sort that are currently used in cryptography are at risk of attack if sufficiently large quantum computers can ever be built, so resistant problems are sought.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are two main approaches. In languages with declaration-site variance annotations (e.g., C#), the programmer annotates the definition of a generic type with the intended variance of its type parameters. With use-site variance annotations (e.g., Java), the programmer instead annotates the places where a generic type is instantiated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The main reasons for unsuccessful call setups in mobile networks are lack of radio coverage (either in the downlink or the uplink), radio interference between different subscribers, imperfections in the functioning of the network (such as failed call setup redirect procedures), overload of the different elements of the network (such as cells), etc. The call setup success rate is one of the key performance indicators (KPIs) used by the network operators to assess the performance of their networks. It is assumed to have direct influence on the customer satisfaction with the service provided by the network and its operator. The call setup success rate is usually included, together with other technical parameters of the network, in a key performance indicator known as service accessibility. The operators of telecommunication networks aim at increasing the call setup success rate as much as practical and affordable. In mobile networks this is achieved by improving radio coverage, expanding the capacity of the network and optimising the performance of its elements, all of which may require considerable effort and significant investments on the part of the network operator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the order polytope of a finite partially ordered set is a convex polytope defined from the set. The points of the order polytope are the monotonic functions from the given set to the unit interval, its vertices correspond to the upper sets of the partial order, and its dimension is the number of elements in the partial order. The order polytope is a distributive polytope, meaning that coordinatewise minima and maxima of pairs of its points remain within the polytope. The order polytope of a partial order should be distinguished from the linear ordering polytope, a polytope defined from a number n {\\displaystyle n} as the convex hull of indicator vectors of the sets of edges of n {\\displaystyle n} -vertex transitive tournaments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This smaller design, the Cell Broadband Engine or Cell/BE was fabricated using a 90 nm SOI process.In March 2007, IBM announced that the 65 nm version of Cell/BE is in production at its plant (at the time, now GlobalFoundries') in East Fishkill, New York, with Bandai Namco Entertainment using the Cell/BE processor for their 357 arcade board as well as the subsequent 369. In February 2008, IBM announced that it would begin to fabricate Cell processors with the 45 nm process.In May 2008, IBM introduced the high-performance double-precision floating-point version of the Cell processor, the PowerXCell 8i, at the 65 nm feature size. In May 2008, an Opteron- and PowerXCell 8i-based supercomputer, the IBM Roadrunner system, became the world's first system to achieve one petaFLOPS, and was the fastest computer in the world until third quarter 2009. The world's three most energy-efficient supercomputers, as represented by the Green500 list, are similarly based on the PowerXCell 8i. In August 2009 the 45 nm Cell processor was introduced in concert with Sony's PlayStation 3 Slim.By November 2009, IBM had discontinued the development of a Cell processor with 32 APUs but was still developing other Cell products.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more advanced areas of mathematics, when viewing Euclidean space as a vector space, its distance is associated with a norm called the Euclidean norm, defined as the distance of each vector from the origin. One of the important properties of this norm, relative to other norms, is that it remains unchanged under arbitrary rotations of space around the origin. By Dvoretzky's theorem, every finite-dimensional normed vector space has a high-dimensional subspace on which the norm is approximately Euclidean; the Euclidean norm is the only norm with this property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The practice of integrity management consultancy combines numerous disciplines including established Knowledge Acquisition Methodologies, Public Relations Practices, Business Risk Management techniques, Corporate Social Responsibility (CSR), Compliance functions, Insider Threat detection and Financial expertise to help clients make responsible and ethical business decisions. Integrity management consultancies offer services such as: Identifying potential reputational and ethical threats for clients Developing practical recommendations to mitigate these threats Making recommendations for, and carrying out due diligence on local professional service suppliers Providing advice on accessing a local pool of talent and addressing cultural considerations for building an effective local workforce Conducting detailed investigations into proposed local partners and key employees Preparing community needs reviews for better targeting of CSR programmes and; Administering anti and counter-corruption trainingMany also offer general ethics audits so that companies can obtain independent verification to attest to the high standard of their corporate ethics. Of course, this is not an exhaustive list as each consultancy offers different services.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Box\u2013Cox distribution (also known as the power-normal distribution) is the distribution of a random variable X for which the Box\u2013Cox transformation on X follows a truncated normal distribution. It is a continuous probability distribution having probability density function (pdf) given by f ( y ) = 1 ( 1 \u2212 I ( f < 0 ) \u2212 sgn \u2061 ( f ) \u03a6 ( 0 , m , s ) ) 2 \u03c0 s 2 exp \u2061 { \u2212 1 2 s 2 ( y f f \u2212 m ) 2 } {\\displaystyle f(y)={\\frac {1}{\\left(1-I(f<0)-\\operatorname {sgn}(f)\\Phi (0,m,{\\sqrt {s}})\\right){\\sqrt {2\\pi s^{2}}}}}\\exp \\left\\{-{\\frac {1}{2s^{2}}}\\left({\\frac {y^{f}}{f}}-m\\right)^{2}\\right\\}} for y > 0, where m is the location parameter of the distribution, s is the dispersion, \u0192 is the family parameter, I is the indicator function, \u03a6 is the cumulative distribution function of the standard normal distribution, and sgn is the sign function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a 2-valued morphism is a homomorphism that sends a Boolean algebra B onto the two-element Boolean algebra 2 = {0,1}. It is essentially the same thing as an ultrafilter on B, and, in a different way, also the same things as a maximal ideal of B. 2-valued morphisms have also been proposed as a tool for unifying the language of physics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multithreaded computing, the ABA problem occurs during synchronization, when a location is read twice, has the same value for both reads, and the read value being the same twice is used to conclude that nothing has happened in the interim; however, another thread can execute between the two reads and change the value, do other work, then change the value back, thus fooling the first thread into thinking nothing has changed even though the second thread did work that violates that assumption. The ABA problem occurs when multiple threads (or processes) accessing shared data interleave. Below is a sequence of events that illustrates the ABA problem: Process P 1 {\\displaystyle P_{1}} reads value A from some shared memory location, P 1 {\\displaystyle P_{1}} is preempted, allowing process P 2 {\\displaystyle P_{2}} to run, P 2 {\\displaystyle P_{2}} writes value B to the shared memory location P 2 {\\displaystyle P_{2}} writes value A to the shared memory location P 2 {\\displaystyle P_{2}} is preempted, allowing process P 1 {\\displaystyle P_{1}} to run, P 1 {\\displaystyle P_{1}} reads value A from the shared memory location, P 1 {\\displaystyle P_{1}} determines that the shared memory value has not changed and continues.Although P 1 {\\displaystyle P_{1}} can continue executing, it is possible that the behavior will not be correct due to the \"hidden\" modification in shared memory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If that sum of squares is divided by n, the number of observations, the result is the mean of the squared residuals. Since this is a biased estimate of the variance of the unobserved errors, the bias is removed by dividing the sum of the squared residuals by df = n \u2212 p \u2212 1, instead of n, where df is the number of degrees of freedom (n minus the number of parameters (excluding the intercept) p being estimated - 1). This forms an unbiased estimate of the variance of the unobserved errors, and is called the mean squared error.Another method to calculate the mean square of error when analyzing the variance of linear regression using a technique like that used in ANOVA (they are the same because ANOVA is a type of regression), the sum of squares of the residuals (aka sum of squares of the error) is divided by the degrees of freedom (where the degrees of freedom equal n \u2212 p \u2212 1, where p is the number of parameters estimated in the model (one for each variable in the regression equation, not including the intercept)).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If neighborhood searched is limited to just one or a very small number of changes from the current solution, then it can be difficult to escape from local minima, even with additional meta-heuristic techniques such as Simulated Annealing or Tabu search. In large neighborhood search techniques, the possible changes from one solution to its neighbor may allow tens or hundreds of values to change, and this means that the size of the neighborhood may itself be sufficient to allow the search process to avoid or escape local minima, though additional meta-heuristic techniques can still improve performance. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An example from linear algebra is the multiplicative monoid of real square matrices of order n (called the full linear monoid). The map which sends a matrix to its transpose is an involution because the transpose is well defined for any matrix and obeys the law (AB)T = BTAT, which has the same form of interaction with multiplication as taking inverses has in the general linear group (which is a subgroup of the full linear monoid). However, for an arbitrary matrix, AAT does not equal the identity element (namely the diagonal matrix).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For each unit, its duties and responsibilities in response to each command are specified. This is analogous to establishing a work breakdown structure for a development project, or defining an organizational chart for a business or military operation. Step 3 specifies the processing that is triggered within each unit upon receipt of an input command.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In military munitions, a fuze (sometimes fuse) is the part of the device that initiates function. In some applications, such as torpedoes, a fuze may be identified by function as the exploder. The relative complexity of even the earliest fuze designs can be seen in cutaway diagrams.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Are the preconditions each necessary and collectively sufficient to reach the long-term outcomes and ultimate impact? Are there gaps in the logic?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the decision phase the following approaches are usually used: Fixed Threshold \u2013 In this approach, the scores are compared to a threshold which was set previously and if the score is higher than the threshold a cut is declared. Adaptive Threshold \u2013 In this approach, the scores are compared to a threshold which considers various scores in the video to adapt the threshold to the properties of the current video. Like in the previous case, if the score is higher than the corresponding threshold a cut is declared. Machine Learning - Machine learning techniques can be applied also to the decision process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ": ch1 Four-vectors describe, for instance, position x\u03bc in spacetime modeled as Minkowski space, a particle's four-momentum p\u03bc, the amplitude of the electromagnetic four-potential A\u03bc(x) at a point x in spacetime, and the elements of the subspace spanned by the gamma matrices inside the Dirac algebra. The Lorentz group may be represented by 4\u00d74 matrices \u039b. The action of a Lorentz transformation on a general contravariant four-vector X (like the examples above), regarded as a column vector with Cartesian coordinates with respect to an inertial frame in the entries, is given by (matrix multiplication) where the components of the primed object refer to the new frame. Related to the examples above that are given as contravariant vectors, there are also the corresponding covariant vectors x\u03bc, p\u03bc and A\u03bc(x).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum physics, the mathematical notion is usually applied to representations of the gauge group. For example, an SU ( 2 ) {\\displaystyle {\\text{SU}}(2)} gauge theory will have multiplets which are fields whose representation of SU ( 2 ) {\\displaystyle {\\text{SU}}(2)} is determined by the single half-integer number s =: n / 2 {\\displaystyle s=:n/2} , the isospin. Since irreducible SU ( 2 ) {\\displaystyle {\\text{SU}}(2)} representations are isomorphic to the n {\\displaystyle n} th symmetric power of the fundamental representation, every field has n {\\displaystyle n} symmetrized internal indices. Fields also transform under representations of the Lorentz group SO ( 1 , 3 ) {\\displaystyle {\\text{SO}}(1,3)} , or more generally its spin group Spin ( 1 , 3 ) {\\displaystyle {\\text{Spin}}(1,3)} which can be identified with SL ( 2 , C ) {\\displaystyle {\\text{SL}}(2,\\mathbb {C} )} due to an exceptional isomorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to transmit information, the continuous wave must be turned off and on with a telegraph key to produce the different length pulses, \"dots\" and \"dashes\", that spell out text messages in Morse code, so a \"continuous wave\" radiotelegraphy signal consists of pulses of sine waves with a constant amplitude interspersed with gaps of no signal. In on-off carrier keying, if the carrier wave is turned on or off abruptly, communications theory can show that the bandwidth will be large; if the carrier turns on and off more gradually, the bandwidth will be smaller. The bandwidth of an on-off keyed signal is related to the data transmission rate as: B n = B K {\\displaystyle B_{n}=BK} where B n {\\displaystyle B_{n}} is the necessary bandwidth in hertz, B {\\displaystyle B} is the keying rate in signal changes per second (baud rate), and K {\\displaystyle K} is a constant related to the expected radio propagation conditions; K=1 is difficult for a human ear to decode, K=3 or K=5 is used when fading or multipath propagation is expected.The spurious noise emitted by a transmitter which abruptly switches a carrier on and off is called key clicks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a group G is called the direct sum of two normal subgroups with trivial intersection if it is generated by the subgroups. In abstract algebra, this method of construction of groups can be generalized to direct sums of vector spaces, modules, and other structures; see the article direct sum of modules for more information. A group which can be expressed as a direct sum of non-trivial subgroups is called decomposable, and if a group cannot be expressed as such a direct sum then it is called indecomposable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This theorem is one of the main reasons why 1 is not considered a prime number: if 1 were prime, then factorization into primes would not be unique; for example, 2 = 2 \u22c5 1 = 2 \u22c5 1 \u22c5 1 = \u2026 {\\displaystyle 2=2\\cdot 1=2\\cdot 1\\cdot 1=\\ldots } The theorem generalizes to other algebraic structures that are called unique factorization domains and include principal ideal domains, Euclidean domains, and polynomial rings over a field. However, the theorem does not hold for algebraic integers. This failure of unique factorization is one of the reasons for the difficulty of the proof of Fermat's Last Theorem. The implicit use of unique factorization in rings of algebraic integers is behind the error of many of the numerous false proofs that have been written during the 358 years between Fermat's statement and Wiles's proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Common proof rules used are modus ponens and universal instantiation.In contrast, an indirect proof may begin with certain hypothetical scenarios and then proceed to eliminate the uncertainties in each of these scenarios until an inescapable conclusion is forced. For example, instead of showing directly p \u21d2 q, one proves its contrapositive ~q \u21d2 ~p (one assumes ~q and shows that it leads to ~p). Since p \u21d2 q and ~q \u21d2 ~p are equivalent by the principle of transposition (see law of excluded middle), p \u21d2 q is indirectly proved. Proof methods that are not direct include proof by contradiction, including proof by infinite descent. Direct proof methods include proof by exhaustion and proof by induction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Cantor cube is a topological group of the form {0, 1}A for some index set A. Its algebraic and topological structures are the group direct product and product topology over the cyclic group of order 2 (which is itself given the discrete topology). If A is a countably infinite set, the corresponding Cantor cube is a Cantor space. Cantor cubes are special among compact groups because every compact group is a continuous image of one, although usually not a homomorphic image.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory and Boolean algebra, it is often stated as \"union and intersection interchange under complementation\", which can be formally expressed as: A \u222a B \u00af = A \u00af \u2229 B \u00af , A \u2229 B \u00af = A \u00af \u222a B \u00af , {\\displaystyle {\\begin{aligned}{\\overline {A\\cup B}}&={\\overline {A}}\\cap {\\overline {B}},\\\\{\\overline {A\\cap B}}&={\\overline {A}}\\cup {\\overline {B}},\\end{aligned}}} where: A \u00af {\\displaystyle {\\overline {A}}} is the negation of A {\\displaystyle A} , the overline being written above the terms to be negated, \u2229 {\\displaystyle \\cap } is the intersection operator (AND), \u222a {\\displaystyle \\cup } is the union operator (OR).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a burst transmission or data burst is the broadcast of a relatively high-bandwidth transmission over a short period. Burst transmission can be intentional, broadcasting a compressed message at a very high data signaling rate within a very short transmission time. In the 1980s, the term \"data burst\" (and \"info burst\") was used for a technique used by some United Kingdom and South African TV programmes to transmit large amounts of primarily textual information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Multibrot set is the set of values in the complex plane whose absolute value remains below some finite value throughout iterations by a member of the general monic univariate polynomial family of recursions. The name is a portmanteau of multiple and Mandelbrot set. The same can be applied to the Julia set, this being called Multijulia set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For simple patterns, summation of long sequences may be represented with most summands replaced by ellipses. For example, summation of the first 100 natural numbers may be written as 1 + 2 + 3 + 4 + \u22ef + 99 + 100. Otherwise, summation is denoted by using \u03a3 notation, where \u2211 {\\textstyle \\sum } is an enlarged capital Greek letter sigma.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Of these, the addresses of the 16 general-purpose registers (R0-R15) are not fixed. Instead, the R0 register is located at the address pointed to by the \"Context Pointer\" (CP) register, and the remaining 15 registers follow sequentially thereafter.Register windows also provide an easy upgrade path. Since the additional registers are invisible to the programs, additional windows can be added at any time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Near set theory provides a formal basis for the observation, comparison, and classification of elements in sets based on their closeness, either spatially or descriptively. Near sets offer a framework for solving problems based on human perception that arise in areas such as image processing, computer vision as well as engineering and science problems. Near sets have a variety of applications in areas such as topology, pattern detection and classification, abstract algebra, mathematics in computer science, and solving a variety of problems based on human perception that arise in areas such as image analysis, image processing, face recognition, ethology, as well as engineering and science problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of selection principles, Tsaban devised the method of omission of intervals for establishing covering properties of sets of real numbers that have certain combinatorial structures. In nonabelian cryptology he devised the algebraic span method that solved a number of computational problems that underlie a number of proposals for nonabelian public-key cryptographic schemes (such as the commutator key exchange).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This allowed the STAR to use vectors of length not limited by the length of registers, making it highly flexible. Unfortunately, the pipeline had to be very long in order to allow it to have enough instructions in flight to make up for the slow memory. That meant the machine incurred a high cost when switching from processing vectors to performing operations on non-vector operands. Additionally, the low scalar performance of the machine meant that after the switch had taken place and the machine was running scalar instructions, the performance was quite poor. The result was rather disappointing real-world performance, something that could, perhaps, have been forecast by Amdahl's law.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While it is possible to write computer programs as long lists of numbers (machine language) and while this technique was used with many early computers, it is extremely tedious and potentially error-prone to do so in practice, especially for complicated programs. Instead, each basic instruction can be given a short name that is indicative of its function and easy to remember \u2013 a mnemonic such as ADD, SUB, MULT or JUMP. These mnemonics are collectively known as a computer's assembly language. Converting programs written in assembly language into something the computer can actually understand (machine language) is usually done by a computer program called an assembler.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In secure computing terms, because access to a resource via a handle is mediated by another system, a handle functions as a capability: it not only identifies an object, but also associates access rights. For example, while a filename is forgeable (it is just a guessable identifier), a handle is given to a user by an external system, and thus represents not just identity, but also granted access. For example, if a program wishes to read the system password file (/etc/passwd) in read/write mode (O_RDWR), it could try to open the file via the following call: This call asks the operating system to open the specified file with the specified access rights. If the OS allows this, then it opens the file (creates an entry in the per-process file descriptor table) and returns a handle (file descriptor, index into this table) to the user: the actual access is controlled by the OS, and the handle is a token of that.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order-theoretic mathematics, a series-parallel partial order is a partially ordered set built up from smaller series-parallel partial orders by two simple composition operations.The series-parallel partial orders may be characterized as the N-free finite partial orders; they have order dimension at most two. They include weak orders and the reachability relationship in directed trees and directed series\u2013parallel graphs. The comparability graphs of series-parallel partial orders are cographs.Series-parallel partial orders have been applied in job shop scheduling, machine learning of event sequencing in time series data, transmission sequencing of multimedia data, and throughput maximization in dataflow programming.Series-parallel partial orders have also been called multitrees; however, that name is ambiguous: multitrees also refer to partial orders with no four-element diamond suborder and to other structures formed from multiple trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is common in economic models that involve decision-making over time to assume that decision-makers are exponential discounters. Exponential discounting posits that the decision maker assigns future utility of any good according to the formula U ( t ) = U ( 0 ) e \u2212 \u03c1 t {\\displaystyle U(t)=U(0)e^{-\\rho t}} where t = 0 {\\displaystyle t=0} is the present, U ( 0 ) {\\displaystyle U(0)} is the utility assigned to the good if it were consumed immediately, and \u03c1 {\\displaystyle \\rho } is the \"discount factor\", which is the same for all goods and constant over time. Mathematically, it is the unique continuous function that satisfies the equation U ( t 1 ) / U ( t 2 ) = U ( t 1 + c ) / U ( t 2 + c ) ; {\\displaystyle U(t_{1})/U(t_{2})=U(t_{1}+c)/U(t_{2}+c);} that is, the ratio of utility values for a good at two different moments of time only depends on the interval between these times, but not on their choice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Working in the opposite direction, the second expression asserts that A is false and B is false (or equivalently that \"not A\" and \"not B\" are true). Knowing this, a disjunction of A and B must be false also. The negation of said disjunction must thus be true, and the result is identical to the first claim.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a cyclic graph may mean a graph that contains a cycle, or a graph that is a cycle, with varying definitions of cycles. See: Cycle (graph theory), a cycle in a graph Forest (graph theory), an undirected graph with no cycles Biconnected graph, an undirected graph in which every edge belongs to a cycle Directed acyclic graph, a directed graph with no cycles Strongly connected graph, a directed graph in which every edge belongs to a cycle Aperiodic graph, a directed graph in which the cycle lengths have no nontrivial common divisor Pseudoforest, a directed or undirected graph in which every connected component includes at most one cycle Cycle graph, a graph that has the structure of a single cycle Pancyclic graph, a graph that has cycles of all possible lengths Cycle detection (graph theory), the algorithmic problem of finding cycles in graphsOther similarly-named concepts include Cycle graph (algebra), a graph that illustrates the cyclic subgroups of a group Circulant graph, a graph with an automorphism which permutes its vertices cyclically.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1890s Michelson built a mechanical device called the harmonic analyzer, for computing coefficients of Fourier series and drawing graphs of their partial sums. He and S. W. Stratton published a paper about this machine in the American Journal of Science in 1898.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Prices of $60 for keyboards were achieved, and Key Tronic rapidly became the largest independent keyboard manufacturer. Meanwhile, IBM made their own keyboards, using their own patented technology: Keys on older IBM keyboards were made with a \"buckling spring\" mechanism, in which a coil spring under the key buckles under pressure from the user's finger, triggering a hammer that presses two plastic sheets (membranes) with conductive traces together, completing a circuit. This produces a clicking sound and gives physical feedback for the typist, indicating that the key has been depressed.The first electronic keyboards had a typewriter key travel distance of 0.187 inches (4.75 mm), keytops were a half-inch (12.7 mm) high, and keyboards were about two inches (5 cm) thick.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Transportation modes are an essential component of transport systems since they are the means by which mobility is supported. Geographers consider a wide range of modes that may be grouped into three broad categories based on the medium they exploit: land, water and air. Each mode has its own requirements and features, and is adapted to serve the specific demands of freight and passenger traffic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 17th century, European mathematicians Isaac Barrow, Ren\u00e9 Descartes, Pierre de Fermat, Blaise Pascal, John Wallis and others discussed the idea of a derivative. In particular, in Methodus ad disquirendam maximam et minima and in De tangentibus linearum curvarum distributed in 1636, Fermat introduced the concept of adequality, which represented equality up to an infinitesimal error term. This method could be used to determine the maxima, minima, and tangents to various curves and was closely related to differentiation.Isaac Newton would later write that his own early ideas about calculus came directly from \"Fermat's way of drawing tangents.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In regular expressions, the period (., also called \"dot\") is the wildcard pattern which matches any single character. Combined with the asterisk operator . * it will match any number of any characters. In this case, the asterisk is also known as the Kleene star.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, falsing is a signaling error condition when a signal decoder detects a valid input although the implied protocol function was not intended. This is also known as a false decode. Other forms are referred to as talk-off.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some computer programming languages, the size in bits of certain data types 16-bit computing A 16-bit integer can represent up to 65,536 values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Declare a new variable in the procedure (called L for reference). On each remaining unconnected exit path, add a statement that sets L to the label value on that path. Combine the resulting programs into a selection statement that executes the program with the entry path label indicated by L Construct a loop that executes this selection statement as long as L is not 0. Construct a sequence that initializes L to 1 and executes the loop.Note that this construction can be improved by converting some cases of the selection statement into subprocedures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, list edge-coloring is a type of graph coloring that combines list coloring and edge coloring. An instance of a list edge-coloring problem consists of a graph together with a list of allowed colors for each edge. A list edge-coloring is a choice of a color for each edge, from its list of allowed colors; a coloring is proper if no two adjacent edges receive the same color.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In punctuation, a word divider is a form of glyph which separates written words. In languages which use the Latin, Cyrillic, and Arabic alphabets, as well as other scripts of Europe and West Asia, the word divider is a blank space, or whitespace. This convention is spreading, along with other aspects of European punctuation, to Asia and Africa, where words are usually written without word separation.In computing, the word \"delimiter\" refers to a character that separates two words. In character encoding, word segmentation depends on which characters are defined as word dividers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety but different schemes) and allowing \"varieties\" defined over any commutative ring (for example, Fermat curves are defined over the integers). Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise \"\u00c9l\u00e9ments de g\u00e9om\u00e9trie alg\u00e9brique\"; one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne). Strongly based on commutative algebra, scheme theory allows a systematic use of methods of topology and homological algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 23578, 123578, 234578, and 1234578 are the patterns related to Braille pattern dots-12346, since the two additional dots of kantenji patterns 012346, 123467, and 0123467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In stream ciphers, IVs are loaded into the keyed internal secret state of the cipher, after which a number of cipher rounds are executed prior to releasing the first bit of output. For performance reasons, designers of stream ciphers try to keep that number of rounds as small as possible, but because determining the minimal secure number of rounds for stream ciphers is not a trivial task, and considering other issues such as entropy loss, unique to each cipher construction, related-IVs and other IV-related attacks are a known security issue for stream ciphers, which makes IV loading in stream ciphers a serious concern and a subject of ongoing research.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "where F\u00d7 is the multiplicative group of F (that is, F excluding 0). These elements are \"special\" in that they form an algebraic subvariety of the general linear group \u2013 they satisfy a polynomial equation (since the determinant is polynomial in the entries). When F is a finite field of order q, the notation SL(n, q) is sometimes used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a primary cyclic group is a group that is both a cyclic group and a p-primary group for some prime number p. That is, it is a cyclic group of order pm, Cpm, for some prime number p, and natural number m. Every finite abelian group G may be written as a finite direct sum of primary cyclic groups, as stated in the fundamental theorem of finite abelian groups: G = \u2a01 1 \u2264 i \u2264 n C p i m i . {\\displaystyle G=\\bigoplus _{1\\leq i\\leq n}\\mathrm {C} _{{p_{i}}^{m_{i}}}.} This expression is essentially unique: there is a bijection between the sets of groups in two such expressions, which maps each group to one that is isomorphic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The question then becomes: on which level of iterated logarithms do to compare two numbers? There is a sense in which one may want to consider 10 10 10 {\\displaystyle 10^{10^{10}}} and 10 10 9 {\\displaystyle 10^{10^{9}}} to be \"close in magnitude\". The relative error between these two numbers is large, and the relative error between their logarithms is still large; however, the relative error in their second-iterated logarithms is small: log 10 \u2061 ( log 10 \u2061 ( 10 10 10 ) ) = 10 {\\displaystyle \\log _{10}(\\log _{10}(10^{10^{10}}))=10} and log 10 \u2061 ( log 10 \u2061 ( 10 10 9 ) ) = 9 {\\displaystyle \\log _{10}(\\log _{10}(10^{10^{9}}))=9} Such comparisons of iterated logarithms are common, e.g., in analytic number theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Like for conic sections, a line cuts this oval at, at most, two points. A non-singular plane cubic defines an elliptic curve, over any field K for which it has a point defined. Elliptic curves are now normally studied in some variant of Weierstrass's elliptic functions, defining a quadratic extension of the field of rational functions made by extracting the square root of a cubic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Column 3 - F = Furniture Vans, Carriages, Motor Cars, Portable Engines and Machines on Wheels. Column 4 - L = Livestock Column 5 - H = Horse Boxes and Prize Cattle Vans. Column 6 - C = Carriages and Motor Cars by Passenger or Parcels Train. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In random graphs the sizes of components are given by a random variable, which, in turn, depends on the specific model of how random graphs are chosen. In the G ( n , p ) {\\displaystyle G(n,p)} version of the Erd\u0151s\u2013R\u00e9nyi\u2013Gilbert model, a graph on n {\\displaystyle n} vertices is generated by choosing randomly and independently for each pair of vertices whether to include an edge connecting that pair, with probability p {\\displaystyle p} of including an edge and probability 1 \u2212 p {\\displaystyle 1-p} of leaving those two vertices without an edge connecting them. The connectivity of this model depends on p {\\displaystyle p} , and there are three different ranges of p {\\displaystyle p} with very different behavior from each other. In the analysis below, all outcomes occur with high probability, meaning that the probability of the outcome is arbitrarily close to one for sufficiently large values of n {\\displaystyle n} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a hereditary property is a property of an object that is inherited by all of its subobjects, where the meaning of subobject depends on the context. These properties are particularly considered in topology and graph theory, but also in set theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, average bitrate (ABR) refers to the average amount of data transferred per unit of time, usually measured per second, commonly for digital music or video. An MP3 file, for example, that has an average bit rate of 128 kbit/s transfers, on average, 128,000 bits every second. It can have higher bitrate and lower bitrate parts, and the average bitrate for a certain timeframe is obtained by dividing the number of bits used during the timeframe by the number of seconds in the timeframe. Bitrate is not reliable as a standalone measure of audio or video quality, since more efficient compression methods use lower bitrates to encode material at a similar quality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, he proved there is no odd perfect number with fewer than four prime factors. In algebra, he was notable for the study of associative algebras. He first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the Peirce decomposition. In the philosophy of mathematics, he became known for the statement that \"Mathematics is the science that draws necessary conclusions\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In systems theory, it involves the description of a network whose components are compartments that represent a population of elements that are equivalent with respect to the manner in which they process input signals to the compartment. Instant homogeneous distribution of materials or energies within a \"compartment.\" The exchange rate of materials or energies among the compartments is related to the densities of these compartments. Usually, it is desirable that the materials do not undergo chemical reactions while transmitting among the compartments. When concentration of the cell is of interest, typically the volume is assumed to be constant over time, though this may not be totally true in reality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In short, it is a cartesian product and it corresponds to a product in the category of types. Most functional programming languages have a primitive notion of product type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the CS reconstruction models using constrained \u2113 1 {\\displaystyle \\ell _{1}} minimization, larger coefficients are penalized heavily in the \u2113 1 {\\displaystyle \\ell _{1}} norm. It was proposed to have a weighted formulation of \u2113 1 {\\displaystyle \\ell _{1}} minimization designed to more democratically penalize nonzero coefficients. An iterative algorithm is used for constructing the appropriate weights. Each iteration requires solving one \u2113 1 {\\displaystyle \\ell _{1}} minimization problem by finding the local minimum of a concave penalty function that more closely resembles the \u2113 0 {\\displaystyle \\ell _{0}} norm. An additional parameter, usually to avoid any sharp transitions in the penalty function curve, is introduced into the iterative equation to ensure stability and so that a zero estimate in one iteration does not necessarily lead to a zero estimate in the next iteration. The method essentially involves using the current solution for computing the weights to be used in the next iteration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to capture sufficient thermoacoustic data to form an accurate 3D map of electromagnetic absorption, it is necessary to surround the anatomy being imaged with a 2D array of transducers. The world's first 3D thermoacoustic animal scanner (Fig. 8: left panel) accomplished this by combining a cylindrical array of 128 transducers (Fig. 8: center panel) with rotation of the animal being imaged about the vertical axis. The net result was to capture thermoacoustic data over the surface of a sphere surrounding the animal being imaged (Fig. 8: right panel). This device was capable of visualizing structures as small as 1/3 millimeter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Applied to a function with one variable, the Y combinator usually does not terminate. More interesting results are obtained by applying the Y combinator to functions of two or more variables. The additional variables may be used as a counter, or index.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "New centers were then chosen to better represent the cluster. This process was repeated until the centers at the start matched the centers at the end. When the cluster centers have not changed, it could be interpreted that this means proper clusters have been chosen.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the diagrams below, P is used for N\u2019s parent, S for the sibling of N, C (meaning close nephew) for S\u2019s child in the same direction as N, and D (meaning distant nephew) for S\u2019s other child (S cannot be a NIL node in the first iteration, because it must have black height one, which was the black height of N before its deletion, but C and D may be NIL nodes). The diagrams show the current node N as the left child of its parent P even though it is possible for N to be on either side. The code samples cover both possibilities by means of the side variable dir. At the beginning (in the first iteration) of removal, N is the NIL node replacing the node to be deleted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Testers debug materials and procedures. The team reviews and revises the project according to feedback. After completing the development of the course material, the designers should conduct an imperative pilot test; this can be carried out by involving key stakeholders and rehearsing the course material.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into the space of all possible words. It gives an important limitation on the efficiency with which any error-correcting code can utilize the space in which its code words are embedded. A code that attains the Hamming bound is said to be a perfect code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. Preorders are more general than equivalence relations and (non-strict) partial orders, both of which are special cases of a preorder: an antisymmetric (or skeletal) preorder is a partial order, and a symmetric preorder is an equivalence relation. The name preorder comes from the idea that preorders (that are not partial orders) are 'almost' (partial) orders, but not quite; they are neither necessarily antisymmetric nor asymmetric. Because a preorder is a binary relation, the symbol \u2264 {\\displaystyle \\,\\leq \\,} can be used as the notational device for the relation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Whether or not a name is well-formed depends on the type of computer system being used. Early computers permitted only a few letters or digits in the name of a file, but modern computers allow long names (some up to 255 characters) containing almost any combination of unicode letters or unicode digits, making it easier to understand the purpose of a file at a glance. Some computer systems allow file names to contain spaces; others do not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "We may assume by probability amplification that both circuit families have success probability at least 5/6. Then we create a composite algorithm where the circuits for L 1 {\\displaystyle L_{1}} and L 2 {\\displaystyle L_{2}} are run independently, and we set P to the conjunction of P 1 {\\displaystyle P_{1}} and P 2 {\\displaystyle P_{2}} , and Q to the conjunction of Q 1 {\\displaystyle Q_{1}} and Q 2 {\\displaystyle Q_{2}} . It is not hard to see by a union bound that this composite algorithm correctly decides membership in L 1 \u2229 L 2 {\\displaystyle L_{1}\\cap L_{2}} with (conditional) probability at least 2/3.More generally, combinations of these ideas show that PostBQP is closed under union and BQP truth-table reductions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Tunnell's theorem gives a partial resolution to the congruent number problem, and under the Birch and Swinnerton-Dyer conjecture, a full resolution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1992 article \"Extending and Formalizing the Framework for Information Systems Architecture\" John F. Sowa and John Zachman present the framework and its recent extensions and show how it can be formalized in the notation of conceptual graphs. Also in 1992: John Zachman's co-author John Sowa proposed the additions of the Scope perspective of the \u2018planner\u2019 (bounding lists common to the enterprise and its environment) and the Detailed Representation perspective of the \u2018sub-contractor\u2019 (being the out-of-context vendor solution components). The Who, When and Why columns were brought into public view, the notion of the four levels of metaframeworks and a depiction of integration associations across the perspectives were all outlined in the paper. Keri Anderson Healey assisted by creating a model of the models (the framework metamodel) which was also included in the article. Later during the 1990s Methodologists like Clive Finkelstein refocused on the top two framework rows which he labeled Enterprise Engineering and has one of the most successful methods for converging the business needs with information technology engineering implementation, and determining a logical build sequence of the pieces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Piotrowski law is a case of the so-called logistic model (cf. logistic equation). It was shown that it covers also language acquisition processes (cf. language acquisition law). Text block law: Linguistic units (e.g. words, letters, syntactic functions and constructions) show a specific frequency distribution in equally large text blocks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A symplectomorphism is an isomorphism of symplectic manifolds. A permutation is an automorphism of a set. In geometry, isomorphisms and automorphisms are often called transformations, for example rigid transformations, affine transformations, projective transformations.Category theory, which can be viewed as a formalization of the concept of mapping between structures, provides a language that may be used to unify the approach to these different aspects of the basic idea.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the prime omega functions \u03c9 ( n ) {\\displaystyle \\omega (n)} and \u03a9 ( n ) {\\displaystyle \\Omega (n)} count the number of prime factors of a natural number n . {\\displaystyle n.} Thereby \u03c9 ( n ) {\\displaystyle \\omega (n)} (little omega) counts each distinct prime factor, whereas the related function \u03a9 ( n ) {\\displaystyle \\Omega (n)} (big omega) counts the total number of prime factors of n , {\\displaystyle n,} honoring their multiplicity (see arithmetic function). That is, if we have a prime factorization of n {\\displaystyle n} of the form n = p 1 \u03b1 1 p 2 \u03b1 2 \u22ef p k \u03b1 k {\\displaystyle n=p_{1}^{\\alpha _{1}}p_{2}^{\\alpha _{2}}\\cdots p_{k}^{\\alpha _{k}}} for distinct primes p i {\\displaystyle p_{i}} ( 1 \u2264 i \u2264 k {\\displaystyle 1\\leq i\\leq k} ), then the respective prime omega functions are given by \u03c9 ( n ) = k {\\displaystyle \\omega (n)=k} and \u03a9 ( n ) = \u03b1 1 + \u03b1 2 + \u22ef + \u03b1 k {\\displaystyle \\Omega (n)=\\alpha _{1}+\\alpha _{2}+\\cdots +\\alpha _{k}} . These prime factor counting functions have many important number theoretic relations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, a sanity test (a form of software testing which offers \"quick, broad, and shallow testing\") evaluates the result of a subset of application functionality to determine whether it is possible and reasonable to proceed with further testing of the entire application. Sanity tests may sometimes be used interchangeably with smoke tests insofar as both terms denote tests which determine whether it is possible and reasonable to continue testing further. On the other hand, a distinction is sometimes made that a smoke test is a non-exhaustive test that ascertains whether the most crucial functions of a programme work before proceeding with further testing whereas a sanity test refers to whether specific functionality such as a particular bug fix works as expected without testing the wider functionality of the software. In other words, a sanity test determines whether the intended result of a code change works correctly while a smoke test ensures that nothing else important was broken in the process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The resulting conditional probability distribution is a parametrized family of probability measures called a Markov kernel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model theory, a branch of mathematical logic, and in algebra, the reduced product is a construction that generalizes both direct product and ultraproduct. Let {Si | i \u2208 I} be a family of structures of the same signature \u03c3 indexed by a set I, and let U be a filter on I. The domain of the reduced product is the quotient of the Cartesian product \u220f i \u2208 I S i {\\displaystyle \\prod _{i\\in I}S_{i}} by a certain equivalence relation ~: two elements (ai) and (bi) of the Cartesian product are equivalent if { i \u2208 I: a i = b i } \u2208 U {\\displaystyle \\left\\{i\\in I:a_{i}=b_{i}\\right\\}\\in U} If U only contains I as an element, the equivalence relation is trivial, and the reduced product is just the original Cartesian product. If U is an ultrafilter, the reduced product is an ultraproduct. Operations from \u03c3 are interpreted on the reduced product by applying the operation pointwise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, Bartlett's theorem gives the distribution of the number of customers in a given part of a system at a fixed time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Euclidean algorithm for computing the greatest common divisor of two integers is one example. Given two integers a {\\displaystyle a} and b {\\displaystyle b} , the algorithm performs O ( log \u2061 a + log \u2061 b ) {\\displaystyle O(\\log a+\\log b)} arithmetic operations on numbers with at most O ( log \u2061 a + log \u2061 b ) {\\displaystyle O(\\log a+\\log b)} bits. At the same time, the number of arithmetic operations cannot be bounded by the number of integers in the input (which is constant in this case, there are always only two integers in the input).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The computation of the USPCA and CSPCA solutions is demanding when the data matrix is large. With Projection SPCA (PSPCA) approximate CSPCA solutions can computed much more efficiently by simply projecting the current first PC onto subsets of the variables. This means that the solutions can be computed with efficient linear regression routines. PSPCA is fast and can be shown to explain a proportion of the variance of the dataset comparable with that explained by CSPCA.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Cash prizes of varying size, up to US$200,000 (and prizes up to $20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Hooley's delta function ( \u0394 ( n ) {\\displaystyle \\Delta (n)} ), also called Erd\u0151s--Hooley delta-function, defines the maximum number of divisors of n {\\displaystyle n} in  {\\displaystyle } for all u {\\displaystyle u} , where e {\\displaystyle e} is the Euler's number. The first few terms of this sequence are 1 , 2 , 1 , 2 , 1 , 2 , 1 , 2 , 1 , 2 , 1 , 3 , 1 , 2 , 2 , 2 , 1 , 2 , 1 , 3 , 2 , 2 , 1 , 4 {\\displaystyle 1,2,1,2,1,2,1,2,1,2,1,3,1,2,2,2,1,2,1,3,2,2,1,4} (sequence A226898 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hans van der Laan: Modern Primitive. The sequence was described by Ian Stewart in his Scientific American column Mathematical Recreations in June 1996.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In pseudocode the algorithm can be expressed as (0-based array):", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Specialized hobbyist websites (like Geocaching.com) FAQ and its Benchmark Hunting forum can provide more information. Some of these marks have precise \"adjusted\" coordinates (latitude and longitude). The adjusted coordinates are precise to sub-centimeter accuracy, while others, typically true elevation Bench Marks, have only coordinates scaled from a map.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "C variables are used directly while register names are quoted as string literals. __asm in Microsoft Visual C++ (MSVC), Borland/Embarcadero C compiler, and descendents. This syntax is not based on ISO rules at all; programmers simply write ASM inside a block without needing to conform to C syntax.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The dispatch has all these three services combined into one dispatch for the best multi-coordinated response to an incident or an emergency. And also facilitates in information management, emergency communication and care of citizens. These services are the main structure for a response to an emergency. It can happen that, for a specific emergency, the co-operation with another service is needed, for instance the Ministry of Defence, water board(s) or Rijkswaterstaat. The safety region can integrate these other services into their structure by adding them to specific conferences on operational or administrative level.All regions operate according to the Coordinated Regional Incident Management system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The statement that two sets A and B are equinumerous is usually denoted A \u2248 B {\\displaystyle A\\approx B\\,} or A \u223c B {\\displaystyle A\\sim B} , or | A | = | B | . {\\displaystyle |A|=|B|.} The definition of equinumerosity using bijections can be applied to both finite and infinite sets, and allows one to state whether two sets have the same size even if they are infinite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is possible and sometimes desirable for the condition to always evaluate to be true. This creates an infinite loop. When an infinite loop is created intentionally there is usually another control structure that allows termination of the loop.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Note that the four points x {\\displaystyle x} , y {\\displaystyle y} , x \u2227 y {\\displaystyle x\\wedge y} , and x \u2228 y {\\displaystyle x\\vee y} form a rectangle in Euclidean space (in the sense that x \u2227 y \u2212 x = y \u2212 x \u2228 y {\\displaystyle x\\wedge y-x=y-x\\vee y} , x \u2212 x \u2228 y = x \u2227 y \u2212 y {\\displaystyle x-x\\vee y=x\\wedge y-y} , and x \u2227 y \u2212 x {\\displaystyle x\\wedge y-x} and x \u2212 x \u2228 y {\\displaystyle x-x\\vee y} are orthogonal). On the other hand, supermodularity and concavity together guarantee that u ( x \u2228 y \u2212 \u03bb v ) \u2212 u ( y ) \u2265 u ( x ) \u2212 u ( x \u2227 y + \u03bb v ) . {\\displaystyle u(x\\vee y-\\lambda v)-u(y)\\geq u(x)-u(x\\wedge y+\\lambda v).} for any \u03bb \u2208  {\\displaystyle \\lambda \\in } , where v = y \u2212 x \u2227 y = x \u2228 y \u2212 x {\\displaystyle v=y-x\\wedge y=x\\vee y-x} . In this case, crucially, the four points x {\\displaystyle x} , y {\\displaystyle y} , x \u2228 y \u2212 \u03bb v {\\displaystyle x\\vee y-\\lambda v} , and x \u2227 y + \u03bb v {\\displaystyle x\\wedge y+\\lambda v} form a backward-leaning parallelogram in Euclidean space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The standard specifies that the correct encoding of a code point uses only the minimum number of bytes required to hold the significant bits of the code point. Longer encodings are called overlong and are not valid UTF-8 representations of the code point. This rule maintains a one-to-one correspondence between code points and their valid encodings, so that there is a unique valid encoding for each code point. This ensures that string comparisons and searches are well-defined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In morphology, a null morpheme or zero morpheme is a morpheme that has no phonetic form. In simpler terms, a null morpheme is an \"invisible\" affix. It is a concept useful for analysis, by contrasting null morphemes with alternatives that do have some phonetic realization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That cannot be your task. There is no such thing as valid jury nullification. You would violate your oath and the law if you willfully brought a verdict contrary to the law given to you in this case.\" The Ninth Circuit upheld the first three sentences of the jury's instruction and overruled the remainder but deemed that instruction a harmless error and affirmed the conviction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Again, it depends on the context how exactly the word \"filtration\" is to be understood. Descending filtrations are not to be confused with the dual notion of cofiltrations (which consist of quotient objects rather than subobjects). Filtrations are widely used in abstract algebra, homological algebra (where they are related in an important way to spectral sequences), and in measure theory and probability theory for nested sequences of \u03c3-algebras. In functional analysis and numerical analysis, other terminology is usually used, such as scale of spaces or nested spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In BNPF encoding, a single byte (8 bits) would be represented by a highly redundant character framing sequence starting with a single ASCII \"B\", eight ASCII characters where a \"0\" would be represented by a \"N\" and a \"1\" would be represented by a \"P\", followed by an ending ASCII \"F\". These ten-character ASCII sequences were separated by one or more whitespace characters, therefore using at least eleven ASCII characters for each byte stored (9% efficiency). The ASCII \"N\" and \"P\" characters differed in four bit positions, providing excellent protection from single punch errors. Alternative schemes were also available where \"L\" and \"H\" or \"0\" and \"1\" were also available to represent data bits, but in both of these encoding schemes, the two data-bearing ASCII characters differ in only one bit position, providing very poor single punch error detection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following definitions, x T {\\displaystyle \\mathbf {x} ^{\\textsf {T}}} is the transpose of x {\\displaystyle \\mathbf {x} } , x \u2217 {\\displaystyle \\mathbf {x} ^{*}} is the conjugate transpose of x {\\displaystyle \\mathbf {x} } and 0 {\\displaystyle \\mathbf {0} } denotes the n-dimensional zero-vector.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alice sends | \u03c8 \u27e9 {\\displaystyle |\\psi \\rangle } over a public and authenticated quantum channel E {\\displaystyle {\\mathcal {E}}} to Bob. Bob receives a state E ( \u03c1 ) = E ( | \u03c8 \u27e9 \u27e8 \u03c8 | ) {\\displaystyle {\\mathcal {E}}(\\rho )={\\mathcal {E}}(|\\psi \\rangle \\langle \\psi |)} , where E {\\displaystyle {\\mathcal {E}}} represents both the effects of noise in the channel and eavesdropping by a third party we'll call Eve. After Bob receives the string of qubits, both Bob and Eve have their own states.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early days of computing the total capacity of HDDs was specified in seven to nine decimal digits frequently truncated with the idiom millions. By the 1970s, the total capacity of HDDs was given by manufacturers using SI decimal prefixes such as megabytes (1 MB = 1,000,000 bytes), gigabytes (1 GB = 1,000,000,000 bytes) and terabytes (1 TB = 1,000,000,000,000 bytes). However, capacities of memory are usually quoted using a binary interpretation of the prefixes, i.e. using powers of 1024 instead of 1000.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The formula is used in calculating the frequency of each note in the piece. The values are then added together and divided by the number of notes. This is the average frequency of those notes. It is said that such techniques were used by classical composers, especially those who involved mathematics heavily in their music.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The general number field sieve, on the other hand, manages to search for smooth numbers that are subexponential in the size of n. Since these numbers are smaller, they are more likely to be smooth than the numbers inspected in previous algorithms. This is the key to the efficiency of the number field sieve. In order to achieve this speed-up, the number field sieve has to perform computations and factorizations in number fields. This results in many rather complicated aspects of the algorithm, as compared to the simpler rational sieve. The size of the input to the algorithm is log2 n or the number of bits in the binary representation of n. Any element of the order nc for a constant c is exponential in log n. The running time of the number field sieve is super-polynomial but sub-exponential in the size of the input.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular arithmetic, any unit fraction can be converted into an equivalent whole number using the extended Euclidean algorithm. This conversion can be used to perform modular division: dividing by a number x {\\displaystyle x} , modulo y {\\displaystyle y} , can be performed by converting the unit fraction 1 / x {\\displaystyle 1/x} into an equivalent whole number modulo y {\\displaystyle y} , and then multiplying by that number.In more detail, suppose that x {\\displaystyle x} is relatively prime to y {\\displaystyle y} (otherwise, division by x {\\displaystyle x} is not defined modulo y {\\displaystyle y} ). The extended Euclidean algorithm for the greatest common divisor can be used to find integers a {\\displaystyle a} and b {\\displaystyle b} such that B\u00e9zout's identity is satisfied: In modulo- y {\\displaystyle y} arithmetic, the term b y {\\displaystyle by} can be eliminated as it is zero modulo y {\\displaystyle y} . This leaves That is, a {\\displaystyle a} is the modular inverse of x {\\displaystyle x} , the number that when multiplied by x {\\displaystyle x} produces one. Equivalently, Thus division by x {\\displaystyle x} (modulo y {\\displaystyle y} ) can instead be performed by multiplying by the integer a {\\displaystyle a} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1760s, Johann Heinrich Lambert was the first to prove that the number \u03c0 is irrational, meaning it cannot be expressed as a fraction a / b {\\displaystyle a/b} , where a {\\displaystyle a} and b {\\displaystyle b} are both integers. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With some luck it will be the target of the search. If the target is not found by the time the search pattern has reached maximum convenient radius, the centre point may be shifted and another search started. This can be repeated as often as necessary, but the positions of the centre points must be chosen to allow the full search area to be covered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(where \u03c6 ( \u03b2 / \u03b1 ) {\\displaystyle \\varphi (\\beta /\\alpha )} denotes the formula formed by substituting all free occurrences of the variable \u03b1 {\\displaystyle \\alpha } in \u03c6 {\\displaystyle \\varphi } by \u03b2 {\\displaystyle \\beta } .) Likewise, finding a counterexample disproves (proves the negation of) a universal conclusion. This is used in a proof by contradiction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Even the \"system specific\" code needs modification only slightly from implementation to implementation. The result is great amounts of implementation work saved while porting the system. Finally, it was an error to enter into a second round of optimization before bootstrapping the compiler.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a differential invariant is an invariant for the action of a Lie group on a space that involves the derivatives of graphs of functions in the space. Differential invariants are fundamental in projective differential geometry, and the curvature is often studied from this point of view. Differential invariants were introduced in special cases by Sophus Lie in the early 1880s and studied by Georges Henri Halphen at the same time. Lie (1884) was the first general work on differential invariants, and established the relationship between differential invariants, invariant differential equations, and invariant differential operators.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to understand how sounds are made, experimental procedures are often adopted. Palatography is one of the oldest instrumental phonetic techniques used to record data regarding articulators. In traditional, static palatography, a speaker's palate is coated with a dark powder. The speaker then produces a word, usually with a single consonant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s, the term double dabble was also used for a different mental algorithm, used by programmers to convert a binary number to decimal. It is performed by reading the binary number from left to right, doubling if the next bit is zero, and doubling and adding one if the next bit is one. In the example above, 11110011, the thought process would be: \"one, three, seven, fifteen, thirty, sixty, one hundred twenty-one, two hundred forty-three\", the same result as that obtained above.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Using matrices, this formula can be written x o l d = A x n e w , {\\displaystyle \\mathbf {x} _{\\mathrm {old} }=A\\,\\mathbf {x} _{\\mathrm {new} },} where \"old\" and \"new\" refer respectively to the firstly defined basis and the other basis, x o l d {\\displaystyle \\mathbf {x} _{\\mathrm {old} }} and x n e w {\\displaystyle \\mathbf {x} _{\\mathrm {new} }} are the column vectors of the coordinates of the same vector on the two bases, and A {\\displaystyle A} is the change-of-basis matrix (also called transition matrix), which is the matrix whose columns are the coordinate vectors of the new basis vectors on the old basis. This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical analysis, Agmon's inequalities, named after Shmuel Agmon, consist of two closely related interpolation inequalities between the Lebesgue space L \u221e {\\displaystyle L^{\\infty }} and the Sobolev spaces H s {\\displaystyle H^{s}} . It is useful in the study of partial differential equations. Let u \u2208 H 2 ( \u03a9 ) \u2229 H 0 1 ( \u03a9 ) {\\displaystyle u\\in H^{2}(\\Omega )\\cap H_{0}^{1}(\\Omega )} where \u03a9 \u2282 R 3 {\\displaystyle \\Omega \\subset \\mathbb {R} ^{3}} . Then Agmon's inequalities in 3D state that there exists a constant C {\\displaystyle C} such that \u2016 u \u2016 L \u221e ( \u03a9 ) \u2264 C \u2016 u \u2016 H 1 ( \u03a9 ) 1 / 2 \u2016 u \u2016 H 2 ( \u03a9 ) 1 / 2 , {\\displaystyle \\displaystyle \\|u\\|_{L^{\\infty }(\\Omega )}\\leq C\\|u\\|_{H^{1}(\\Omega )}^{1/2}\\|u\\|_{H^{2}(\\Omega )}^{1/2},} and \u2016 u \u2016 L \u221e ( \u03a9 ) \u2264 C \u2016 u \u2016 L 2 ( \u03a9 ) 1 / 4 \u2016 u \u2016 H 2 ( \u03a9 ) 3 / 4 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the numbers of the form x2 + xy + y2 for integer x, y are called the L\u00f6schian numbers (or Loeschian numbers). These numbers are named after August L\u00f6sch. They are the norms of the Eisenstein integers. They are a set of whole numbers, including zero, and having prime factorization in which all primes congruent to 2 mod 3 have even powers (there is no restriction of primes congruent to 0 or 1 mod 3).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Heyting implication, Y \u21d2 Z {\\displaystyle Y\\Rightarrow Z} , is an alternative notation for Z Y {\\displaystyle Z^{Y}} . The above adjunction results translate to implication ( \u21d2: H \u00d7 H \u2192 H {\\displaystyle \\Rightarrow :H\\times H\\to H} ) being right adjoint to meet ( \u2227: H \u00d7 H \u2192 H {\\displaystyle \\wedge :H\\times H\\to H} ). This adjunction can be written as ( \u2212 \u2227 Y ) \u22a3 ( Y \u21d2 \u2212 ) {\\displaystyle (-\\wedge Y)\\dashv (Y\\Rightarrow -)} , or more fully as: In the category of topological spaces, the exponential object Z Y {\\displaystyle Z^{Y}} exists provided that Y {\\displaystyle Y} is a locally compact Hausdorff space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the European Union, RRM data analysis showed that authentic information was \"de-contextualized\", \"manipulated\" and \"distorted\", then used by \"questionable\" writers on \"untrustworthy\" sites to \"seed conversations\", which were then \"framed using a divisive and inflammatory narrative.\" These would reference the original authentic source. In a \"coordinated fashion\" the information would be \"amplified\" with the most \"susceptible communities\" targeted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In elliptic geometry, an elliptic rectangle is a figure in the elliptic plane whose four edges are elliptic arcs which meet at equal angles greater than 90\u00b0. Opposite arcs are equal in length. In hyperbolic geometry, a hyperbolic rectangle is a figure in the hyperbolic plane whose four edges are hyperbolic arcs which meet at equal angles less than 90\u00b0. Opposite arcs are equal in length.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, transmission is the process of sending or propagating an analog or digital signal via a medium that is wired, wireless, or fiber-optic.Transmission system technologies typically refer to physical layer protocol duties such as modulation, demodulation, line coding, equalization, error control, bit synchronization and multiplexing, but it may also involve higher-layer protocol duties, for example, digitizing an analog signal, and data compression. Transmission of a digital message, or of a digitized analog signal, is known as data transmission. Examples of transmission are the sending of signals with limited duration, for example, a block or packet of data, a phone call, or an email.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the binary octahedral group, name as 2O or \u27e82,3,4\u27e9 is a certain nonabelian group of order 48. It is an extension of the chiral octahedral group O or (2,3,4) of order 24 by a cyclic group of order 2, and is the preimage of the octahedral group under the 2:1 covering homomorphism Spin \u2061 ( 3 ) \u2192 SO \u2061 ( 3 ) {\\displaystyle \\operatorname {Spin} (3)\\to \\operatorname {SO} (3)} of the special orthogonal group by the spin group. It follows that the binary octahedral group is a discrete subgroup of Spin(3) of order 48. The binary octahedral group is most easily described concretely as a discrete subgroup of the unit quaternions, under the isomorphism Spin \u2061 ( 3 ) \u2245 Sp \u2061 ( 1 ) {\\displaystyle \\operatorname {Spin} (3)\\cong \\operatorname {Sp} (1)} where Sp(1) is the multiplicative group of unit quaternions. (For a description of this homomorphism see the article on quaternions and spatial rotations.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The optional Selector Channel also enabled the use of other high speed devices such as the 1200 lpm 0776 printer or the 2000 lpm 0770 printer. The machine had either 4K or 16K memory chips, and typical machines had between 128 and 512 KiB memory. It ran an OS called OS/3, and could run up to 7 jobs at one time, not counting various OS extensions such as the print spooler and telecommunications access (ICAM).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Lastly, the difference between the two highest values of FEV1 should also be within 150 mL. The highest FVC and FEV1 may be used from each different test. Until the results of three tests meet the criteria of reproducibility, the test can be repeated up to eight times. If it is still not possible to get accurate results, the best three tests are used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, right triangles, isosceles triangles and equilateral triangles are non-generic and non-degenerate. In fact, degenerate cases often correspond to singularities, either in the object or in some configuration space. For example, a conic section is degenerate if and only if it has singular points (e.g., point, line, intersecting lines).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These incorrect responses often matched the incorrect response of the majority group (i.e., actors). Overall, 75% of participants gave at least one incorrect answer out of the 12 critical trials. In his opinion regarding the study results, Asch put it this way: \"That intelligent, well-meaning, young people are willing to call white black is a matter of concern.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "397-398).Cook and Reckhow (1973) say it most succinctly: The indirect instructions are necessary in order for a fixed program to access an unbounded number of registers as the inputs vary.\" (p. 73)Unbounded capacities of registers versus bounded capacities of state-machine instructions: The so-called finite state part of the machine is supposed to be \u2013 by the normal definition of algorithm \u2013 very finite both in the number of \"states\" (instructions) and the instructions' sizes (their capacity to hold symbols/signs).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure and almost twice the number of parameters. Random vectors with a GD distribution are completely neutral.The density function of p 1 , \u2026 , p k \u2212 1 {\\displaystyle p_{1},\\ldots ,p_{k-1}} is  \u2212 1 p k b k \u2212 1 \u2212 1 \u220f i = 1 k \u2212 1  {\\displaystyle \\left^{-1}p_{k}^{b_{k-1}-1}\\prod _{i=1}^{k-1}\\left} where we define p k = 1 \u2212 \u2211 i = 1 k \u2212 1 p i {\\textstyle p_{k}=1-\\sum _{i=1}^{k-1}p_{i}} . Here B ( x , y ) {\\displaystyle B(x,y)} denotes the Beta function. This reduces to the standard Dirichlet distribution if b i \u2212 1 = a i + b i {\\displaystyle b_{i-1}=a_{i}+b_{i}} for 2 \u2a7d i \u2a7d k \u2212 1 {\\displaystyle 2\\leqslant i\\leqslant k-1} ( b 0 {\\displaystyle b_{0}} is arbitrary).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. For example, {1, 2, 3} and {4, 5, 6} are disjoint sets, while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets is called disjoint if any two distinct sets of the collection are disjoint.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The child element is within the parent element, such as in a Venn diagram. This structure is most effective in representing simple hierarchical relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, modes of variation are a continuously indexed set of vectors or functions that are centered at a mean and are used to depict the variation in a population or sample. Typically, variation patterns in the data can be decomposed in descending order of eigenvalues with the directions represented by the corresponding eigenvectors or eigenfunctions. Modes of variation provide a visualization of this decomposition and an efficient description of variation around the mean. Both in principal component analysis (PCA) and in functional principal component analysis (FPCA), modes of variation play an important role in visualizing and describing the variation in the data contributed by each eigencomponent. In real-world applications, the eigencomponents and associated modes of variation aid to interpret complex data, especially in exploratory data analysis (EDA).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of the leaky bucket algorithm as a queue, the only defined limit for this algorithm is the bandwidth of its output.The bandwidth 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.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern mathematics, one often studies spaces whose points are themselves mathematical objects. A distance function on such a space generally aims to measure the dissimilarity between two objects. Here are some examples: Functions to a metric space. If X is any set and M is a metric space, then the set of all bounded functions f: X \u2192 M {\\displaystyle f\\colon X\\to M} (i.e. those functions whose image is a bounded subset of M {\\displaystyle M} ) can be turned into a metric space by defining the distance between two bounded functions f and g to be This metric is called the uniform metric or supremum metric.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, the Official Charts Company compiles a weekly compilation albums chart, limited to various artists compilations and soundtrack compilations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events, hence the name.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Here, the word \"broadcast\" is used in the sense of conveying the state to two or more recipients. For multiple recipients to each receive the state, there must be, in some sense, a way of duplicating the state. The no-broadcast theorem generalizes the no-cloning theorem for mixed states.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Later releases added the ability to write unformatted dumps, called at that time core image dumps. In modern operating systems, a process address space may contain gaps, and it may share pages with other processes or files, so more elaborate representations are used; they may also include other information about the state of the program at the time of the dump. In Unix-like systems, core dumps generally use the standard executable image-format: a.out in older versions of Unix, ELF in modern Linux, System V, Solaris, and BSD systems, Mach-O in macOS, etc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Various multi-compartment models can be used in the areas of pharmacokinetics and pharmacology, in the support of efforts in drug discovery, and in environmental science. In humans and related organisms, there are five major body compartments: the blood plasma, interstitial fluids, fat tissues, intracellular fluids, and transcellular fluids, the latter of which includes fluids in the pleural (peritoneal) cavity. The relative percents of body mass of these are included in the following table.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, intra-rater reliability is the degree of agreement among repeated administrations of a diagnostic test performed by a single rater. Intra-rater reliability and inter-rater reliability are aspects of test validity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It not only breaks the isolation that operating systems should provide between programs and hardware, raising both stability and security concerns, but also could leave the graphics hardware in an inconsistent state if two or more user space programs try to do the mode-setting at the same time. To avoid these conflicts, the X Server became in practice the only user space program that performed mode-setting operations; the remainder user space programs relied on the X Server to set the appropriate mode and to handle any other operation involving mode-setting. Initially the mode-setting was performed exclusively during the X Server startup process, but later the X Server gained the ability to do it while running.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle {\\frac {\\sum _{v}d(v)^{2}}{2|E|}}={\\frac {|V|}{2|E|}}(\\mu ^{2}+\\sigma ^{2})={\\frac {\\mu ^{2}+\\sigma ^{2}}{\\mu }}=\\mu +{\\frac {\\sigma ^{2}}{\\mu }}.} For a graph that has vertices of varying degrees (as is typical for social networks), \u03c3 2 {\\displaystyle {\\sigma }^{2}} is strictly positive, which implies that the average degree of a friend is strictly greater than the average degree of a random node.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The consumer has income I {\\displaystyle I} , and hence a budget set of affordable packages B ( p , I ) = { x: p \u22c5 x \u2264 I } , {\\displaystyle B(p,I)=\\{x:p\\cdot x\\leq I\\},} where p \u22c5 x = \u2211 i L p i x i {\\displaystyle p\\cdot x=\\sum _{i}^{L}p_{i}x_{i}} is the dot product of the price and quantity vectors. The consumer has a utility function u: R + L \u2192 R . {\\displaystyle u:\\mathbb {R} _{+}^{L}\\rightarrow \\mathbb {R} .} The consumer's Marshallian demand correspondence is defined to be x \u2217 ( p , I ) = argmax x \u2208 B ( p , I ) \u2061 u ( x ) {\\displaystyle x^{*}(p,I)=\\operatorname {argmax} _{x\\in B(p,I)}u(x)}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In business telephony, a telephone extension may refer to a phone on an internal telephone line attached to a private branch exchange (PBX) or Centrex system. The PBX operates much as a community switchboard does for a geographic telephone numbering plan and allows multiple lines inside the office to connect without each phone requiring a separate outside line. In these systems, one usually has to dial a number (typically 9 in North America, 0 in Europe) to tell the PBX to connect with an outside landline (also called DDCO, or Direct Dial Central Office) to dial an external number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to use a hurricane tracking chart, one needs access to latitude/longitude pairs of the cyclone's center and maximum sustained wind information in order to know which symbol to depict. New tropical cyclone information is available at least every twelve hours in the Southern Hemisphere and at least every six hours in the Northern Hemisphere from Regional Specialized Meteorological Centers and Tropical Cyclone Warning Centers.In decades past, newspaper, television, and radio (including weather radio) were primary sources for this information. Local television stations within threatened markets would advertise tropical cyclone positions within the morning, evening, and nightly news during their weather segments. The Weather Channel includes the information within their tropical updates every hour during the Atlantic and Pacific hurricane seasons. Starting in the mid 1990s, the World Wide Web allowed for the development of ftp and web sites by the Bureau of Meteorology in Australia, Canadian Hurricane Centre, Central Pacific Hurricane Center, the Nadi Tropical Cyclone Centre/Fiji Meteorological Service, Japan Meteorological Agency, Joint Typhoon Warning Center, M\u00e9t\u00e9o-France La R\u00e9union, National Hurricane Center, and the Philippine Atmospheric, Geophysical and Astronomical Services Administration which allows the end user to get their information from their official products.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern usage, metric is used almost exclusively in commercial transactions. These units are mostly historical, although they are still used in some limited contexts and in Maltese idioms and set phrases. Many of these terms are directly related to Arabic units and some to Sicilian units. The Weights and Measures Ordinance of 1921 established uniformity in the conversion of such weights and measures. All these measures were defined as simple multiples of the Imperial units then in use in Britain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Chung\u2013Fuchs theorem, named after Chung Kai-lai and Wolfgang Heinrich Johannes Fuchs, states that for a particle undergoing a random walk in m-dimensions, it is certain to come back infinitely often to any neighborhood of the origin on a one-dimensional line (m = 1) or two-dimensional plane (m = 2), but in three or more dimensional spaces it will leave to infinity. Specifically, if a position of the particle is described by the vector X n {\\displaystyle X_{n}}: where Z 1 , Z 2 , \u2026 , Z n {\\displaystyle Z_{1},Z_{2},\\dots ,Z_{n}} are independent m-dimensional vectors with a given multivariate distribution, then if m = 1 {\\displaystyle m=1} , E ( | Z i | ) < \u221e {\\displaystyle E(|Z_{i}|)<\\infty } and E ( Z i ) = 0 {\\displaystyle E(Z_{i})=0} , or if m = 2 {\\displaystyle m=2} E ( | Z i 2 | ) < \u221e {\\displaystyle E(|Z_{i}^{2}|)<\\infty } and E ( Z i ) = 0 {\\displaystyle E(Z_{i})=0} , the following holds: However, for m \u2265 3 {\\displaystyle m\\geq 3} ,", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That means we can compute and store f {\\displaystyle f} on all the possible values in T = ( log \u2061 log \u2061 q ) m {\\displaystyle T=(\\log \\log q)^{m}} time and space. If we take d = log \u2061 q {\\displaystyle d=\\log q} , we get m = log \u2061 n log \u2061 log \u2061 q {\\displaystyle m={\\tfrac {\\log n}{\\log \\log q}}} , so the time/space requirement is just n log \u2061 log \u2061 q log \u2061 log \u2061 log \u2061 q . {\\displaystyle n^{\\frac {\\log \\log q}{\\log \\log \\log q}}.} Kedlaya and Umans further show how to combine this preprocessing with fast (FFT) multipoint evaluation. This allows optimal algorithms for many important algebraic problems, such as polynomial modular composition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bot is a natural type for the \"null pointer\" value (a pointer which does not point to any object) of languages like Java: in Java, the null type is the universal subtype of reference types. null is the only value of the null type; and it can be cast to any reference type. However, the null type is not a bottom type as described above, it is not a subtype of int and other primitive types. A type system including both Top and Bot seems to be a natural target for type inference, allowing the constraints on an omitted type parameter to be captured by a pair of bounds: we write S<:X<:T to mean \"the value of X must lie somewhere between S and T.\" In such a scheme, a completely unconstrained parameter is bounded below by Bot and above by Top.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the remainder of this article, base ten is assumed. The single-digit final state reached in the process of calculating an integer's additive persistence is its digital root. Put another way, a number's additive persistence counts how many times we must sum its digits to arrive at its digital root.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the board game industry, playtesting applies both to feedback gathered during the early design process as well as late stage exposure to the target audience by a game's publisher. Major types of boardgame testing include local testing \u2014 where a designer, developer, or publisher representative moderates the test in person, and remote testing, where groups receive copies of the game or files to assemble their own version.Wizards of the Coast ran a public playtest of their new Dungeon Command miniatures game. In this case, they used the feedback generated on the rules to improve the game but also used feedback on the playtest itself to improve logistics on the D&D Next playtest.Steve Jackson Games uses Munchkin players from the area around their offices to test new cards and expansions, as well as distributing playtest packages at conventions. According to the SJG website, this is done \"so we  can observe carefully which cards work well, which jokes aren't as funny as we thought, and so on.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, the XML document and the ASCII tree have the same structure. XML Trees do not show the content in an Instance document, only the structure of the document. In this example Product is the Root Element of the tree and the two child nodes of Product are Name and Details. Details contains two child nodes, Description and Price. The tree command in Windows and *nix also produce a similar tree structure and path.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for a table to be in sixth normal form, it has to be in fifth normal form first and then it requires that each table satisfies only trivial join dependencies. Let\u2019s take a simple example with a table already in 5NF: Here, in the users table, every attribute is non null and the primary key is the username: Users_table This table is in 5NF because each join dependency is implied by the unique candidate key of the table (Username). More specifically, the only possible join dependencies are: {username, status}, {username, department}. The 6NF version would look like this: Users Users_dept So, from one table in 5NF, 6NF produces two tables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements. Another variant, widely used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences, to which the lexicographical order is applied. A generalization defines an order on a Cartesian product of partially ordered sets; this order is a total order if and only if all factors of the Cartesian product are totally ordered.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By 1995, the Internet was fully commercialized in the U.S. when the NSFNet was decommissioned, removing the last restrictions on use of the Internet to carry commercial traffic. As technology advanced and commercial opportunities fueled reciprocal growth, the volume of Internet traffic started experiencing similar characteristics as that of the scaling of MOS transistors, exemplified by Moore's law, doubling every 18 months.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In standard truth-functional propositional logic, distribution in logical proofs uses two valid rules of replacement to expand individual occurrences of certain logical connectives, within some formula, into separate applications of those connectives across subformulas of the given formula. The rules are where \" \u21d4 {\\displaystyle \\Leftrightarrow } \", also written \u2261 , {\\displaystyle \\,\\equiv ,\\,} is a metalogical symbol representing \"can be replaced in a proof with\" or \"is logically equivalent to\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini\u2013Study metric when restricted to the pure states alone.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The cylinder was rotated every 24 hours, providing an approximate time for a given quake.Luigi Palmieri, influenced by Mallet's 1848 paper, invented a seismometer in 1856 that could record the time of an earthquake. This device used metallic pendulums which closed an electric circuit with vibration, which then powered an electromagnet to stop a clock.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(e.g. in a claim Bob instance of Human, Bob is the subject and an Instance, while the object, Human, is an ordinary class; but a further claim that Human instance of Animal species makes \"Animal species\" a metaclass because it has a member, \"Human\", that is also a Class). OWL 2 DL supports metaclasses by a feature called punning, in which one entity is interpreted as two different types of thing\u2014a class and an individual\u2014depending on its syntactic context. For example, through punning, an ontology could have a concept hierarchy such as Harry the eagle instance of golden eagle, golden eagle subclass of bird, and golden eagle instance of species.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and its applications, the root mean square of a set of numbers x i {\\displaystyle x_{i}} (abbreviated as RMS, RMS or rms and denoted in formulas as either x R M S {\\displaystyle x_{\\mathrm {RMS} }} or R M S x {\\displaystyle \\mathrm {RMS} _{x}} ) is defined as the square root of the mean square (the arithmetic mean of the squares) of the set. The RMS is also known as the quadratic mean (denoted M 2 {\\displaystyle M_{2}} ) and is a particular case of the generalized mean. The RMS of a continuously varying function (denoted f R M S {\\displaystyle f_{\\mathrm {RMS} }} ) can be defined in terms of an integral of the squares of the instantaneous values during a cycle. For alternating electric current, RMS is equal to the value of the constant direct current that would produce the same power dissipation in a resistive load. In estimation theory, the root-mean-square deviation of an estimator is a measure of the imperfection of the fit of the estimator to the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This could be confused with the Greek letter Theta on a badly focused display, but in practice there was no confusion because theta was not (then) a displayable character and very little used anyway. An alternative, the slashed zero (looking similar to the letter O except for the slash), was primarily used in hand-written coding sheets before transcription to punched cards or tape, and is also used in old-style ASCII graphic sets descended from the default typewheel on the Teletype Model 33 ASR. This form is similar to the symbol \u2205 {\\displaystyle \\emptyset } , or \"\u2205\" (Unicode character U+2205), representing the empty set, as well as to the letter \u00d8 used in several Scandinavian languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In processor design, there are two ways to increase on-chip parallelism with fewer resource requirements: one is superscalar technique which tries to exploit instruction-level parallelism (ILP); the other is multithreading approach exploiting thread-level parallelism (TLP). Superscalar means executing multiple instructions at the same time while thread-level parallelism (TLP) executes instructions from multiple threads within one processor chip at the same time. There are many ways to support more than one thread within a chip, namely: Interleaved multithreading: Interleaved issue of multiple instructions from different threads, also referred to as temporal multithreading. It can be further divided into fine-grained multithreading or coarse-grained multithreading depending on the frequency of interleaved issues.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consequently, an irreducible ideal of a Noetherian ring is primary. Various methods of generalizing primary ideals to noncommutative rings exist, but the topic is most often studied for commutative rings. Therefore, the rings in this article are assumed to be commutative rings with identity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a sampling frame is the source material or device from which a sample is drawn. It is a list of all those within a population who can be sampled, and may include individuals, households or institutions.Importance of the sampling frame is stressed by Jessen and Salant and Dillman. In many practical situations the frame is a matter of choice to the survey planner, and sometimes a critical one. Some very worthwhile investigations are not undertaken at all because of the lack of an apparent frame; others, because of faulty frames, have ended in a disaster or in cloud of doubt.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Kochen\u2013Specker article the possibility is discussed that the value attribution v ( A ) {\\displaystyle v(\\mathbf {A} )} may be context-dependent, i.e. observables corresponding to equal vectors in different columns of the table need not have equal values because different columns correspond to different measurement arrangements. Since subquantum reality (as described by the hidden-variable theory) may be dependent on the measurement context, it is possible that relations between quantum-mechanical observables and hidden variables are just homomorphic rather than isomorphic. This would make obsolete the requirement of a context-independent value attribution. Hence, the KS theorem only excludes noncontextual hidden-variable theories. The possibility of contextuality has given rise to the so-called modal interpretations of quantum mechanics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, finite-dimensional distributions are a tool in the study of measures and stochastic processes. A lot of information can be gained by studying the \"projection\" of a measure (or process) onto a finite-dimensional vector space (or finite collection of times).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the SubBytes step, each byte a i , j {\\displaystyle a_{i,j}} in the state array is replaced with a SubByte S ( a i , j ) {\\displaystyle S(a_{i,j})} using an 8-bit substitution box. Note that before round 0, the state array is simply the plaintext/input. This operation provides the non-linearity in the cipher.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group G and a positive integer n, one asks for the smallest value of k such that every sequence of elements of G of size k contains n terms that sum to 0. The classic result in this area is the 1961 theorem of Paul Erd\u0151s, Abraham Ginzburg, and Abraham Ziv. They proved that for the group Z / n Z {\\displaystyle \\mathbb {Z} /n\\mathbb {Z} } of integers modulo n, Explicitly this says that any multiset of 2n \u2212 1 integers has a subset of size n the sum of whose elements is a multiple of n, but that the same is not true of multisets of size 2n \u2212 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In physics, Averroes did not adopt the inductive method that was being developed by Al-Biruni in the Islamic world and is closer to today's physics. Rather, he was\u2014in the words of historian of science Ruth Glasner\u2014a \"exegetical\" scientist who produced new theses about nature through discussions of previous texts, especially the writings of Aristotle. because of this approach, he was often depicted as an unimaginative follower of Aristotle, but Glasner argues that Averroes's work introduced highly original theories of physics, especially his elaboration of Aristotle's minima naturalia and on motion as forma fluens, which were taken up in the west and are important to the overall development of physics. Averroes also proposed a definition of force as \"the rate at which work is done in changing the kinetic condition of a material body\"\u2014a definition close to that of power in today's physics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a typical server runs at 425 W and VMware estimates a hardware reduction ratio of up to 15:1. A virtual machine (VM) can be more easily controlled and inspected from a remote site than a physical machine, and the configuration of a VM is more flexible. This is very useful in kernel development and for teaching operating system courses, including running legacy operating systems that do not support modern hardware.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-stage job scheduling problems, there are other options for the machine environments: O: Open-shop problem. Every job j {\\displaystyle j} consists of m {\\displaystyle m} operations O i j {\\displaystyle O_{ij}} for i = 1 , \u2026 , m {\\displaystyle i=1,\\ldots ,m} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In response, the field of integrity management has been born to help clients conduct business, even in the most challenging of markets, without compromising their ethics. With the help of expert advice, companies can go beyond abiding by the law to taking a voluntary, proactive approach to ensuring a company's activities promote behaving responsibly, with fairness, sustainability, and cultural sensitivity in the communities in which they operate. It is very different in this respect from the more reactive field of risk management, although some risk management companies have attempted to embrace ethical risk as an area of specialism. Many risk management consultancies are adjuncts to private security companies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle ~-2\\ln()=-2\\;\\sum _{i=1}^{k}x_{i}\\ln \\left({\\frac {\\pi _{i}}{p_{i}}}\\right)~.} (The factor \u2212 2 {\\displaystyle ~-2~} is chosen to make the statistic asymptotically chi-squared distributed, for convenient comparison to a familiar statistic commonly used for the same application.) If the null hypothesis is true, then as N {\\displaystyle ~N~} increases, the distribution of \u2212 2 ln \u2061 (  ) {\\displaystyle ~-2\\ln()~} converges to that of chi-squared with k \u2212 1 {\\displaystyle ~k-1~} degrees of freedom.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Legendre's formula describes the exponents of the prime numbers in a prime factorization of the factorials, and can be used to count the trailing zeros of the factorials. Daniel Bernoulli and Leonhard Euler interpolated the factorial function to a continuous function of complex numbers, except at the negative integers, the (offset) gamma function. Many other notable functions and number sequences are closely related to the factorials, including the binomial coefficients, double factorials, falling factorials, primorials, and subfactorials. Implementations of the factorial function are commonly used as an example of different computer programming styles, and are included in scientific calculators and scientific computing software libraries. Although directly computing large factorials using the product formula or recurrence is not efficient, faster algorithms are known, matching to within a constant factor the time for fast multiplication algorithms for numbers with the same number of digits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras, although Euclid did not represent distances as numbers, and the connection from the Pythagorean theorem to distance calculation was not made until the 18th century.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates. In modern geometry, Euclidean spaces are often defined by using vector spaces. In this case, the dot product is used for defining lengths (the length of a vector is the square root of the dot product of the vector by itself) and angles (the cosine of the angle between two vectors is the quotient of their dot product by the product of their lengths). The name \"dot product\" is derived from the centered dot \" \u00b7 \" that is often used to designate this operation; the alternative name \"scalar product\" emphasizes that the result is a scalar, rather than a vector (as with the vector product in three-dimensional space).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such dogmatic assertions can't be proved. The statements are not based on possible experience. In section II, the discipline of pure reason in polemics, Kant argues strongly against the polemical use of pure reason.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If one requires a more differentiated hierarchy of animals \u2013 to differentiate, say, those who provide milk from those who provide nothing except meat at the end of their lives \u2013 that is an intermediary level of abstraction, probably DairyAnimal (cows, goats) who would eat foods suitable to giving good milk, and MeatAnimal (pigs, steers) who would eat foods to give the best meat-quality. Such an abstraction could remove the need for the application coder to specify the type of food, so they could concentrate instead on the feeding schedule. The two classes could be related using inheritance or stand alone, and the programmer could define varying degrees of polymorphism between the two types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the U.S., SMS is often charged both at the sender and at the destination, but, unlike phone calls, it cannot be rejected or dismissed. The reasons for lower uptake than other countries are varied. Many users have unlimited \"mobile-to-mobile\" minutes, high monthly minute allotments, or unlimited service.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place. Just as a binary relation is formally defined as a set of pairs, i.e. a subset of the Cartesian product A \u00d7 B of some sets A and B, so a ternary relation is a set of triples, forming a subset of the Cartesian product A \u00d7 B \u00d7 C of three sets A, B and C. An example of a ternary relation in elementary geometry can be given on triples of points, where a triple is in the relation if the three points are collinear. Another geometric example can be obtained by considering triples consisting of two points and a line, where a triple is in the ternary relation if the two points determine (are incident with) the line.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spatial statistics and stochastic geometry, to measure the statistical correlation relationship between points of a point process, the pair correlation function of a point process N {\\displaystyle {N}} is defined as: \u03c1 ( x 1 , x 2 ) = \u03bc ( 2 ) ( x 1 , x 2 ) \u03bc ( 1 ) ( x 1 ) \u03bc ( 1 ) ( x 2 ) , {\\displaystyle \\rho (x_{1},x_{2})={\\frac {\\mu ^{(2)}(x_{1},x_{2})}{\\mu ^{(1)}(x_{1})\\mu ^{(1)}(x_{2})}},} where the points x 1 , x 2 \u2208 R d {\\displaystyle x_{1},x_{2}\\in R^{d}} . In general, \u03c1 ( x 1 , x 2 ) \u2265 0 {\\displaystyle \\rho (x_{1},x_{2})\\geq 0} whereas \u03c1 ( x 1 , x 2 ) = 1 {\\displaystyle \\rho (x_{1},x_{2})=1} corresponds to no correlation (between points) in the typical statistical sense.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s, the object-oriented programming paradigm was applied to database technology, creating a new database model known as object databases. This aims to avoid the object\u2013relational impedance mismatch \u2013 the overhead of converting information between its representation in the database (for example as rows in tables) and its representation in the application program (typically as objects). Even further, the type system used in a particular application can be defined directly in the database, allowing the database to enforce the same data integrity invariants. Object databases also introduce the key ideas of object programming, such as encapsulation and polymorphism, into the world of databases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The second and third columns would give, (1,1), (2,1), (2,2) and (1,2); again, all possible ordered pairs each appearing once. The same statement would hold had the first and second columns been used. This is thus an orthogonal array of strength two.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States the majority of smartphones use IPv6, but only a small percent of computers and tablets use IPv6. As of April 2022, 46.2% of Google users in the US use IPv6.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages that support generics (a.k.a. parametric polymorphism), the programmer can extend the type system with new constructors. For example, a C# interface like IList makes it possible to construct new types like IList or IList . The question then arises what the variance of these type constructors should be.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At each single observation in the sequence, probabilities to be used for calculations at the next observation are computed. The smoothing step can be calculated simultaneously during the backward pass. This step allows the algorithm to take into account any past observations of output for computing more accurate results. The forward\u2013backward algorithm can be used to find the most likely state for any point in time. It cannot, however, be used to find the most likely sequence of states (see Viterbi algorithm).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem. A missing solution is a solution that is a valid solution to the problem, but disappeared during the process of solving the problem. Both are frequently the consequence of performing operations that are not invertible for some or all values of the variables, which prevents the chain of logical implications in the proof from being bidirectional.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the distributed approach, each developer works directly with their own local repository, and changes are shared between repositories as a separate step.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a ground term of a formal system is a term that does not contain any variables. Similarly, a ground formula is a formula that does not contain any variables. In first-order logic with identity with constant symbols a {\\displaystyle a} and b {\\displaystyle b} , the sentence Q ( a ) \u2228 P ( b ) {\\displaystyle Q(a)\\lor P(b)} is a ground formula. A ground expression is a ground term or ground formula.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\ln(m_{i}!)} is a constant, it will not give any additional information regarding the position of the maximum, so let's consider \u03b1 ( m | E ) = \u2211 i K  {\\displaystyle \\alpha (m\\vert E)=\\sum _{i}^{K}\\left} where \u03b1 {\\displaystyle \\alpha } is something that shares the same maximum position as P ( m | E ) {\\displaystyle P(m\\vert E)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All diagonal elements M i i {\\displaystyle M_{ii}} in a tuned filter are equal to zero because a susceptance vanishes at the resonant frequency. Important merit of the matrix M {\\displaystyle \\mathbf {M} } is the fact that it allows to directly compute the frequency response of the equivalent network having the inductively coupled resonant circuits,. Therefore it is convenient to use this matrix when designing the cross-coupled filters. The coupling matrices M {\\displaystyle \\mathbf {M} } , in particular, are used as coarse models of filters. Utilization of a coarse model allows to quicken filter optimization manyfold because of computation of the frequency response for the coarse model does not consume CPU time with respect to computation for the real filter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain shadowy techniques used to \"prove\" them. These techniques were introduced by John Blissard and are sometimes called Blissard's symbolic method. They are often attributed to \u00c9douard Lucas (or James Joseph Sylvester), who used the technique extensively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of indivisible items, we have the following strong versions of the two welfare theorems: Any competitive equilibrium maximizes the social welfare (the sum of utilities), not only over all realistic assignments of items, but also over all fractional assignments of items. I.e., even if we could assign fractions of an item to different people, we couldn't do better than a competitive equilibrium in which only whole items are assigned. If there is an integral assignment (with no fractional assignments) that maximizes the social welfare, then there is a competitive equilibrium with that assignment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a matroid oracle is a subroutine through which an algorithm may access a matroid, an abstract combinatorial structure that can be used to describe the linear dependencies between vectors in a vector space or the spanning trees of a graph, among other applications. The most commonly used oracle of this type is an independence oracle, a subroutine for testing whether a set of matroid elements is independent. Several other types of oracle have also been used; some of them have been shown to be weaker than independence oracles, some stronger, and some equivalent in computational power.Many algorithms that perform computations on matroids have been designed to take an oracle as input, allowing them to run efficiently without change on many different kinds of matroids, and without additional assumptions about what kind of matroid they are using. For instance, given an independence oracle for any matroid, it is possible to find the minimum weight basis of the matroid by applying a greedy algorithm that adds elements to the basis in sorted order by weight, using the independence oracle to test whether each element can be added.In computational complexity theory, the oracle model has led to unconditional lower bounds proving that certain matroid problems cannot be solved in polynomial time, without invoking unproved assumptions such as the assumption that P \u2260 NP. Problems that have been shown to be hard in this way include testing whether a matroid is binary or uniform, or testing whether it contains certain fixed minors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Priority inversion can also reduce the perceived performance of the system. Low-priority tasks usually have a low priority because it is not important for them to finish promptly (for example, they might be a batch job or another non-interactive activity).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Chv\u00e1tal\u2013Sankoff constants are mathematical constants that describe the lengths of longest common subsequences of random strings. Although the existence of these constants has been proven, their exact values are unknown. They are named after V\u00e1clav Chv\u00e1tal and David Sankoff, who began investigating them in the mid-1970s.There is one Chv\u00e1tal\u2013Sankoff constant \u03b3 k {\\displaystyle \\gamma _{k}} for each positive integer k, where k is the number of characters in the alphabet from which the random strings are drawn. The sequence of these numbers grows inversely proportionally to the square root of k. However, some authors write \"the Chv\u00e1tal\u2013Sankoff constant\" to refer to \u03b3 2 {\\displaystyle \\gamma _{2}} , the constant defined in this way for the binary alphabet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In bifurcating (fully resolved) trees, each internal branch induces a quartet whose leaves are either subtrees of the original tree or actual leaves of the original tree. If the topology of a quartet extracted from the reference species tree is embedded in the gene tree, the quartet is compatible with the gene tree. Conversely, incompatible strongly supported quartets indicate potential HGT events. Quartet mapping methods are much more computationally efficient and naturally handle heterogeneous representation of taxa among gene families, making them a good basis for developing large-scale scans for HGT, looking for highways of gene sharing in databases of hundreds of complete genomes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to assess whether financial management for IT services has been successfully deployed, the following key performance indicators may be examined: do the predicted budgets match the actual expenditure? has user behavior changed to follow the corporate IT goals? are charges seen by users and customers to be simple, fair and in line with organisational goals?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, an incomplete Cholesky factorization of a symmetric positive definite matrix is a sparse approximation of the Cholesky factorization. An incomplete Cholesky factorization is often used as a preconditioner for algorithms like the conjugate gradient method. The Cholesky factorization of a positive definite matrix A is A = LL* where L is a lower triangular matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a specific example, the goal of Verschelde, et al. was the integration of several different ontology libraries into a larger one that contained more definitions of different subspecialties (medical, molecular biological, etc.) and was able to distinguish between ambiguous tags; the result was a data-warehouse like effect, with easy access to multiple databases through the use of ontologies. In a separate project, Bertens, et al. constructed a lattice work of three ontologies (for anatomy and development of model organisms) on a novel framework ontology of generic organs. For example, results from a search of \u2018heart\u2019 in this ontology would return the heart plans for each of the vertebrate species whose ontologies were included. The stated goal of the project is to facilitate comparative and evolutionary studies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early years, ACAR was mainly used to investigate the physics of the electron-positron annihilation process. In the 1930s several annihilation mechanism were discussed. Otto Klemperer could show with his angular correlation setup that the electron-positron pairs annihilate mainly into two gamma quanta which are emitted anti-parallel. In the 1950s, it was realized that by measuring the deviation from collinearity of the annihilation radiation information about the electronic structure of a solid can be obtained.During this time mainly setups with 'long slit geometry' were used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The same heuristic renumbering algorithm that reduce the bandwidth are also used to reduce the skyline. The basic and one of the earliest algorithms to do that is reverse Cuthill\u2013McKee algorithm. However, skyline storage is not as popular for very large systems (many millions of equations) because skyline Cholesky is not so easily adapted for massively parallel computing, and general sparse methods, which store only the nonzero entries of the matrix, become more efficient for very large problems due to much less fill-in.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Richard Cole and Uzi Vishkin show that there is a distributed algorithm that reduces the number of colors from n to O(log n) in one synchronous communication step. By iterating the same procedure, it is possible to obtain a 3-coloring of an n-cycle in O(log* n) communication steps (assuming that we have unique node identifiers). The function log*, iterated logarithm, is an extremely slowly growing function, \"almost constant\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical optimization, the Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon\u2013Fletcher\u2013Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so by gradually improving an approximation to the Hessian matrix of the loss function, obtained only from gradient evaluations (or approximate gradient evaluations) via a generalized secant method.Since the updates of the BFGS curvature matrix do not require matrix inversion, its computational complexity is only O ( n 2 ) {\\displaystyle {\\mathcal {O}}(n^{2})} , compared to O ( n 3 ) {\\displaystyle {\\mathcal {O}}(n^{3})} in Newton's method. Also in common use is L-BFGS, which is a limited-memory version of BFGS that is particularly suited to problems with very large numbers of variables (e.g., >1000). The BFGS-B variant handles simple box constraints.The algorithm is named after Charles George Broyden, Roger Fletcher, Donald Goldfarb and David Shanno.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In morpheme-based morphology, word forms are analyzed as arrangements of morphemes. A morpheme is defined as the minimal meaningful unit of a language. In a word such as independently, the morphemes are said to be in-, de-, pend, -ent, and -ly; pend is the (bound) root and the other morphemes are, in this case, derivational affixes. In words such as dogs, dog is the root and the -s is an inflectional morpheme.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: \u1f34\u03c3\u03bf\u03c2 isos \"equal\", and \u03bc\u03bf\u03c1\u03c6\u03ae morphe \"form\" or \"shape\". The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hardware execution of Java bytecode, such as that offered by ARM's Jazelle, was also explored to offer significant performance improvements. The performance of a Java bytecode compiled Java program depends on how optimally its given tasks are managed by the host Java virtual machine (JVM), and how well the JVM exploits the features of the computer hardware and operating system (OS) in doing so. Thus, any Java performance test or comparison has to always report the version, vendor, OS and hardware architecture of the used JVM. In a similar manner, the performance of the equivalent natively compiled program will depend on the quality of its generated machine code, so the test or comparison also has to report the name, version and vendor of the used compiler, and its activated compiler optimization directives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, an evaluation is done to determine the fit of a development proposal within its environment. It also allows comparison of alternatives. Another purpose is to seek the best use of resources to maximize economic vitality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Sophie Germain's theorem is a statement about the divisibility of solutions to the equation x p + y p = z p {\\displaystyle x^{p}+y^{p}=z^{p}} of Fermat's Last Theorem for odd prime p {\\displaystyle p} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Sastry automorphism, is an automorphism of a field of characteristic 2 satisfying some rather complicated conditions related to the problem of embedding Ree groups of type 2F4 into Chevalley groups of type F4. They were introduced by Sastry (1995), and named and classified by Bombieri (2002) who showed that there are 22 families of Sastry automorphisms, together with 22 exceptional ones over some finite fields of orders up to 210.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle (\\neg A)\\wedge (\\neg B).} If either A or B were true, then the disjunction of A and B would be true, making its negation false. Presented in English, this follows the logic that \"since two things are both false, it is also false that either of them is true\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each returning traveler must have enough supplies on the way back. The problem asks for the minimum number of accompanying travelers needed to reach the other base.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consider a function f \u2208 K \u00af ( C ) \u2217 {\\displaystyle f\\in {\\overline {K}}(C)^{*}} , then we can look at the formal sum div ( f ) = \u2211 P \u2208 C o r d P ( f )  {\\textstyle (f)=\\sum _{P\\in C}{\\mathrm {ord} _{P}(f)}} . Here o r d P ( f ) {\\displaystyle \\mathrm {ord} _{P}(f)} denotes the order of f {\\displaystyle f} at P {\\displaystyle P} . We have that ord P ( f ) < 0 {\\displaystyle _{P}(f)<0} if f {\\displaystyle f} has a pole of order \u2212 o r d P ( f ) {\\displaystyle -\\mathrm {ord} _{P}(f)} at P {\\displaystyle P} , o r d P ( f ) = 0 {\\displaystyle \\mathrm {ord} _{P}(f)=0} if f {\\displaystyle f} is defined and non-zero at P {\\displaystyle P} and o r d P ( f ) > 0 {\\displaystyle \\mathrm {ord} _{P}(f)>0} if f {\\displaystyle f} has a zero of order o r d P ( f ) {\\displaystyle \\mathrm {ord} _{P}(f)} at P {\\displaystyle P} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recursion theory, \u03d5 e {\\displaystyle \\phi _{e}} denotes the computable function with index (program) e in some standard numbering of computable functions, and \u03d5 e B {\\displaystyle \\phi _{e}^{B}} denotes the eth computable function using a set B of natural numbers as an oracle. A set A of natural numbers is Turing reducible to a set B if there is a computable function that, given an oracle for set B, computes the characteristic function \u03c7A of the set A. That is, there is an e such that \u03c7 A = \u03d5 e B {\\displaystyle \\chi _{A}=\\phi _{e}^{B}} . This relationship is denoted A \u2264T B; the relation \u2264T is a preorder. Two sets of natural numbers are Turing equivalent if each is Turing reducible to the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a primorial prime is a prime number of the form pn# \u00b1 1, where pn# is the primorial of pn (i.e. the product of the first n primes).Primality tests show that pn# \u2212 1 is prime for n = 2, 3, 5, 6, 13, 24, ... (sequence A057704 in the OEIS) pn# + 1 is prime for n = 0, 1, 2, 3, 4, 5, 11, ... (sequence A014545 in the OEIS)The first term of the second sequence is 0 because p0# = 1 is the empty product, and thus p0# + 1 = 2, which is prime. Similarly, the first term of the first sequence is not 1, because p1# = 2, and 2 \u2212 1 = 1 is not prime. The first few primorial primes are 2, 3, 5, 7, 29, 31, 211, 2309, 2311, 30029, 200560490131, 304250263527209, 23768741896345550770650537601358309 (sequence A228486 in the OEIS)As of October 2021, the largest known primorial prime (of the form pn# \u2212 1) is 3267113# \u2212 1 (n = 234,725) with 1,418,398 digits, found by the PrimeGrid project.As of 2022, the largest known prime of the form pn# + 1 is 392113# + 1 (n = 33,237) with 169,966 digits, found in 2001 by Daniel Heuer. Euclid's proof of the infinitude of the prime numbers is commonly misinterpreted as defining the primorial primes, in the following manner: Assume that the first n consecutive", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a category is distributive if it has finite products and finite coproducts and such that for every choice of objects A , B , C {\\displaystyle A,B,C} , the canonical map : A \u00d7 B + A \u00d7 C \u2192 A \u00d7 ( B + C ) {\\displaystyle :A\\!\\times \\!B\\,+A\\!\\times \\!C\\to A\\!\\times \\! (B+C)} is an isomorphism, and for all objects A {\\displaystyle A} , the canonical map 0 \u2192 A \u00d7 0 {\\displaystyle 0\\to A\\times 0} is an isomorphism (where 0 denotes the initial object). Equivalently, if for every object A {\\displaystyle A} the endofunctor A \u00d7 \u2212 {\\displaystyle A\\times -} defined by B \u21a6 A \u00d7 B {\\displaystyle B\\mapsto A\\times B} preserves coproducts up to isomorphisms f {\\displaystyle f} . It follows that f {\\displaystyle f} and aforementioned canonical maps are equal for each choice of objects. In particular, if the functor A \u00d7 \u2212 {\\displaystyle A\\times -} has a right adjoint (i.e., if the category is cartesian closed), it necessarily preserves all colimits, and thus any cartesian closed category with finite coproducts (i.e., any bicartesian closed category) is distributive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, an informed user is one who can protect and achieve the best security out of the system they use. Because of the importance of end-user security and the impact it can have on organisations the UK government set out a guidance for the public sector, to help civil servants learn how to be more security aware when using government networks and computers. While this is targeted to a certain sector, this type of educational effort can be informative to any type of user. This helps developers meet security norms and end users be aware of the risks involved. Reimers and Andersson have conducted a number of studies on end user security habits and found that the same type of repeated education/training in security \"best practices\" can have a marked effect on the perception of compliance with good end user network security habits, especially concerning malware and ransomware.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Alternatively, one can visualize infinitely many 3-dimensional planes that go through N = 2 {\\displaystyle N=2} fixed points. More generally, to estimate a least squares model with k {\\displaystyle k} distinct parameters, one must have N \u2265 k {\\displaystyle N\\geq k} distinct data points. If N > k {\\displaystyle N>k} , then there does not generally exist a set of parameters that will perfectly fit the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1980s, researchers at UC Berkeley and IBM both discovered that most computer language compilers and interpreters used only a small subset of the instructions of complex instruction set computing (CISC). Much of the power of the CPU was being ignored in real-world use. They realized that by making the computer simpler and less orthogonal, they could make it faster and less costly at the same time. At the same time, CPU calculation became faster in relation to the time for needed memory accesses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems, write barrier is a mechanism for enforcing a particular ordering in a sequence of writes to a storage system in a computer system. For example, a write barrier in a file system is a mechanism (program logic) that ensures that in-memory file system state is written out to persistent storage in the correct order.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This ensures semantically rigorous designs, preserving identical semantics throughout the chip design flow, which included extensive use of formal verification techniques. Without such attention, integrating an ARM11 with third-party designs could risk exposing hard-to-find latent bugs. Due to ARM cores being integrated into many different designs, using a variety of logic synthesis tools and chip manufacturing processes, the impact of its register-transfer level (RTL) quality is magnified many times. The ARM11 generation focused more on synthesis than previous generations, making such concerns more of an issue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Timing Advance is significant for privacy and communications security, as its combination with other variables can allow GSM localization to find the device's position and track the mobile phone user. TA is also used to adjust transmission power in space-division multiple access systems. This limited the original range of a GSM cell site to 35 km as mandated by the duration of the standard timeslots defined in the GSM specification.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "DECT phones use allocated spectrum outside the ISM bands that differs in Europe and North America. Ultra-wideband LANs require more spectrum than the ISM bands can provide, so the relevant standards such as IEEE 802.15.4a are designed to make use of spectrum outside the ISM bands. Despite the fact that these additional bands are outside the official ITU-R ISM bands, because they are used for the same types of low power personal communications, they are sometimes incorrectly referred to as ISM bands as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the analysis of algorithms, the input to breadth-first search is assumed to be a finite graph, represented as an adjacency list, adjacency matrix, or similar representation. However, in the application of graph traversal methods in artificial intelligence the input may be an implicit representation of an infinite graph. In this context, a search method is described as being complete if it is guaranteed to find a goal state if one exists. Breadth-first search is complete, but depth-first search is not. When applied to infinite graphs represented implicitly, breadth-first search will eventually find the goal state, but depth first search may get lost in parts of the graph that have no goal state and never return.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the category of sets, the morphisms between sets X and Y are the functions from X to Y. It results that the set of the functions from X to Y that is denoted Y X {\\displaystyle Y^{X}} in the preceding section can also be denoted hom \u2061 ( X , Y ) . {\\displaystyle \\hom(X,Y).} The isomorphism ( S T ) U \u2245 S T \u00d7 U {\\displaystyle (S^{T})^{U}\\cong S^{T\\times U}} can be rewritten hom \u2061 ( U , S T ) \u2245 hom \u2061 ( T \u00d7 U , S ) . {\\displaystyle \\hom(U,S^{T})\\cong \\hom(T\\times U,S).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These are called supplementary services and are commonly invoked by a Vertical service code. Examples include \"Call waiting\", \"Call forward on busy\" etc. Call control software, because of its central place in the operation of the telephone network, is marked by both complexity and reliability. Call control systems will typically require many thousands of person years in development.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a complete set of invariants for a classification problem is a collection of maps f i: X \u2192 Y i {\\displaystyle f_{i}:X\\to Y_{i}} (where X {\\displaystyle X} is the collection of objects being classified, up to some equivalence relation \u223c {\\displaystyle \\sim } , and the Y i {\\displaystyle Y_{i}} are some sets), such that x \u223c x \u2032 {\\displaystyle x\\sim x'} if and only if f i ( x ) = f i ( x \u2032 ) {\\displaystyle f_{i}(x)=f_{i}(x')} for all i {\\displaystyle i} . In words, such that two objects are equivalent if and only if all invariants are equal.Symbolically, a complete set of invariants is a collection of maps such that ( \u220f f i ): ( X / \u223c ) \u2192 ( \u220f Y i ) {\\displaystyle \\left(\\prod f_{i}\\right):(X/\\sim )\\to \\left(\\prod Y_{i}\\right)} is injective. As invariants are, by definition, equal on equivalent objects, equality of invariants is a necessary condition for equivalence; a complete set of invariants is a set such that equality of these is also sufficient for equivalence. In the context of a group action, this may be stated as: invariants are functions of coinvariants (equivalence classes, orbits), and a complete set of invariants characterizes the coinvariants (is a set of defining equations for the coinvariants).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The unit of measurement for the log-odds scale is called a logit, from logistic unit, hence the alternative names. See \u00a7 Background and \u00a7 Definition for formal mathematics, and \u00a7 Example for a worked example. Binary variables are widely used in statistics to model the probability of a certain class or event taking place, such as the probability of a team winning, of a patient being healthy, etc. (see \u00a7 Applications), and the logistic model has been the most commonly used model for binary regression since about 1970.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1840s, mathematicians were generally unprepared to understand Grassmann's ideas. In the 1860s and 1870s various mathematicians came to ideas similar to that of Grassmann's, but Grassmann himself was not interested in mathematics anymore. : 46 Adh\u00e9mar Jean Claude Barr\u00e9 de Saint-Venant developed a vector calculus similar to that of Grassmann, which he published in 1845. He then entered into a dispute with Grassmann about which of the two had thought of the ideas first.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the algebra of sets, not to be confused with the mathematical structure of an algebra of sets, defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations. Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator being union, the meet operator being intersection, the complement operator being set complement, the bottom being \u2205 {\\displaystyle \\varnothing } and the top being the universe set under consideration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance\u2013covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions. As an example, the variation in a collection of random points in two-dimensional space cannot be characterized fully by a single number, nor would the variances in the x {\\displaystyle x} and y {\\displaystyle y} directions contain all of the necessary information; a 2 \u00d7 2 {\\displaystyle 2\\times 2} matrix would be necessary to fully characterize the two-dimensional variation. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). The covariance matrix of a random vector X {\\displaystyle \\mathbf {X} } is typically denoted by K X X {\\displaystyle \\operatorname {K} _{\\mathbf {X} \\mathbf {X} }} , \u03a3 {\\displaystyle \\Sigma } or S {\\displaystyle S} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "GO TOs were largely replaced by the PERFORM statement and procedures, which promoted modular programming and gave easy access to powerful looping facilities. However, PERFORM could be used only with procedures so loop bodies were not located where they were used, making programs harder to understand.COBOL programs were infamous for being monolithic and lacking modularization. COBOL code could be modularized only through procedures, which were found to be inadequate for large systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a version control system is used to keep track of versions of a set of files, usually to allow multiple developers to collaborate on a project. The repository keeps track of the files in the project, which is represented as a graph. A Distributed version control system is made up of central and branch repositories. A central repository exists on the server. To make changes to it, a developer first works on a branch repository, and proceeds to commit the change to the former.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a full reptend prime, full repetend prime, proper prime: 166 or long prime in base b is an odd prime number p such that the Fermat quotient q p ( b ) = b p \u2212 1 \u2212 1 p {\\displaystyle q_{p}(b)={\\frac {b^{p-1}-1}{p}}} (where p does not divide b) gives a cyclic number. Therefore, the base b expansion of 1 / p {\\displaystyle 1/p} repeats the digits of the corresponding cyclic number infinitely, as does that of a / p {\\displaystyle a/p} with rotation of the digits for any a between 1 and p \u2212 1. The cyclic number corresponding to prime p will possess p \u2212 1 digits if and only if p is a full reptend prime. That is, the multiplicative order ordp b = p \u2212 1, which is equivalent to b being a primitive root modulo p. The term \"long prime\" was used by John Conway and Richard Guy in their Book of Numbers. Confusingly, Sloane's OEIS refers to these primes as \"cyclic numbers\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null evaluate to false, and strings with content (like \"abc\"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called \"truthy\" and \"falsy\" / \"false\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and information theory, the variation of information or shared information distance is a measure of the distance between two clusterings (partitions of elements). It is closely related to mutual information; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual information, however, the variation of information is a true metric, in that it obeys the triangle inequality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one possible description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to facilitate the development of applications for mobile devices, and consistency thereof, various approaches have been taken. Most companies that ship a product (e.g. Apple, iPod/iPhone/iPad) provide an official software development kit (SDK). They may also opt to provide some form of Testing and/or Quality Assurance (QA). In exchange for being provided the SDK or other tools, it may be necessary for a prospective developer to sign a some form of non-disclosure agreement, or NDA, which restricts the sharing of privileged information.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spectral graph theory, the Alon\u2013Boppana bound provides a lower bound on the second-largest eigenvalue of the adjacency matrix of a d {\\displaystyle d} -regular graph, meaning a graph in which every vertex has degree d {\\displaystyle d} . The reason for the interest in the second-largest eigenvalue is that the largest eigenvalue is guaranteed to be d {\\displaystyle d} due to d {\\displaystyle d} -regularity, with the all-ones vector being the associated eigenvector. The graphs that come close to meeting this bound are Ramanujan graphs, which are examples of the best possible expander graphs. Its discoverers are Noga Alon and Ravi Boppana.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sound and music, sampling is the reuse of a portion (or sample) of a sound recording in another recording. Samples may comprise elements such as rhythm, melody, speech, sound effects or longer portions of music, and may be layered, equalized, sped up or slowed down, repitched, looped, or otherwise manipulated. They are usually integrated using electronic music instruments (samplers) or software such as digital audio workstations. A process similar to sampling originated in the 1940s with musique concr\u00e8te, experimental music created by splicing and looping tape.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "k is then the Gaussian curvature of the space at the time when a(t) = 1. r is sometimes called the reduced circumference because it is equal to the measured circumference of a circle (at that value of r), centered at the origin, divided by 2\u03c0 (like the r of Schwarzschild coordinates). Where appropriate, a(t) is often chosen to equal 1 in the present cosmological era, so that d \u03a3 {\\displaystyle \\mathrm {d} \\mathbf {\\Sigma } } measures comoving distance. Alternatively, k may be taken to belong to the set {\u22121 ,0, +1} (for negative, zero, and positive curvature respectively).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern grammar, a particle is a function word that must be associated with another word or phrase to impart meaning, i.e., it does not have its own lexical definition. According to this definition, particles are a separate part of speech and are distinct from other classes of function words, such as articles, prepositions, conjunctions and adverbs. Languages vary widely in how much they use particles, some using them extensively and others more commonly using alternative devices such as prefixes/suffixes, inflection, auxiliary verbs and word order. Particles are typically words that encode grammatical categories (such as negation, mood, tense, or case), clitics, fillers or (oral) discourse markers such as well, um, etc. Particles are never inflected.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, examiners usually follow guidelines issued by the Association of Chief Police Officers (ACPO) for the authentication and integrity of evidence. They were updated to Version 5 in October 2011 when computer based evidence was replaced with digital evidence reflecting the development of investigating information security incidents in a wider context. The guidelines consist of four principles: Principle 1: No action taken by law enforcement agencies, persons employed within those agencies or their agents should change data which may subsequently be relied upon in court. Principle 2: In circumstances where a person finds it necessary to access original data, that person must be competent to do so and be able to give evidence explaining the relevance and the implications of their actions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Finally, the dissemination of foreign intelligence information needed for an approved purpose . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonetics and linguistics, a phone is any distinct speech sound or gesture, regardless of whether the exact sound is critical to the meanings of words. In contrast, a phoneme is a speech sound in a given language that, if swapped with another phoneme, could change one word to another. Phones are absolute and are not specific to any language, but phonemes can be discussed only in reference to specific languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of DIKW, information meets the definition for knowledge by description (\"information is contained in descriptions\"), and is differentiated from data in that it is \"useful\". \"Information is inferred from data\", in the process of answering interrogative questions (e.g., \"who\", \"what\", \"where\", \"how many\", \"when\"), thereby making the data useful for \"decisions and/or action\". \"Classically,\" states a 2007 text, \"information is defined as data that are endowed with meaning and purpose.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(See example below.) After their introduction in the 1968 ALGOL 68 \"Final Report\", W-grammars were widely considered as too powerful and unconstrained to be practical.This was partly a consequence of the way in which they had been applied; the 1973 ALGOL 68 \"Revised Report\" contains a much more readable grammar, without modifying the W-grammar formalism itself. Meanwhile, it became clear that W-grammars, when used in their full generality, are indeed too powerful for such practical purposes as serving as the input for a parser generator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In military acquisition, full operating capability or full operational capability (FOC) is the completion of a development effort. This is usually preceded by an initial operating capability or initial operational capability (IOC) phase. For the United States Department of Defense military acquisition FOC is defined as \"in general attained when all units and/or organizations in the force structure scheduled to receive a system have received it and have the ability to employ and maintain it. The specifics for any particular system FOC are defined in that system\u2019s Capability Development Document (CDD) and Capability Production Document (CPD).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Attention to the location of items in the search can be used to guide visual searches. This was demonstrated by valid cues improving the identification of targets relative to the invalid and neutral conditions. A visual search display can also influence how fast an observer responds to a spatial probe.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For vitamin C, vitamin D, vitamin E, vitamin K, calcium, phosphorus, magnesium, and manganese, the current highest RDAs are up to 50% higher than the older Daily Values used in labeling, whereas for other nutrients the recommended needs have gone down. A side-by-side table of the old and new adult Daily Values is provided at Reference Daily Intake. As of October 2010, the only micronutrients that are required to be included on all labels are vitamin A, vitamin C, calcium, and iron.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "ASHRAE Guideline 4-2014 provides performance indices criteria for model calibration. The performance indices used are normalized mean bias error (NMBE), coefficient of variation (CV) of the root mean square error (RMSE), and R2 (coefficient of determination). ASHRAE recommends a R2 greater than 0.75 for calibrated models. The criteria for NMBE and CV RMSE depends on if measured data is available at a monthly or hourly timescale.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the event of an attack from an aggressor, a state would massively retaliate by using a force disproportionate to the size of the attack. The aim of massive retaliation is to deter another state from attacking first. For such a strategy to work, it must be made public knowledge to all possible aggressors. The aggressor also must believe that the state announcing the policy has the ability to maintain second-strike capability in the event of an attack.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The MIPS design team that designed the R4300i started the company SandCraft, which designed the R5432 for NEC and later produced the SR71000, one of the first out-of-order execution processors for the embedded market. The original DEC StrongARM team eventually split into two MIPS-based start-ups: SiByte which produced the SB-1250, one of the first high-performance MIPS-based systems-on-a-chip (SOC); while Alchemy Semiconductor (later acquired by AMD) produced the Au-1000 SoC for low-power uses. Lexra used a MIPS-like architecture and added DSP extensions for the audio chip market and multithreading support for the networking market.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If these decisions change later in the project then the cone will widen. Original research for engineering and construction in the chemical industry demonstrated that actual final costs often exceeded the earliest \"base\" estimate by as much as 100% (or underran by as much as 50%). Research in the software industry on the Cone of Uncertainty stated that in the beginning of the project life cycle (i.e. before gathering of requirements) estimates have in general an uncertainty of factor 4 on both the high side and the low side. This means that the actual effort or scope can be 4 times or 1/4 of the first estimates. This uncertainty tends to decrease over the course of a project, although that decrease is not guaranteed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some networks, routing is complicated by the fact that no single entity is responsible for selecting paths; instead, multiple entities are involved in selecting paths or even parts of a single path. Complications or inefficiency can result if these entities choose paths to optimize their own objectives, which may conflict with the objectives of other participants. A classic example involves traffic in a road system, in which each driver picks a path that minimizes their travel time. With such routing, the equilibrium routes can be longer than optimal for all drivers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Later work by Kummer and others always divided the problem into first and second cases. Sophie Germain primes and safe primes have applications in public key cryptography and primality testing. It has been conjectured that there are infinitely many Sophie Germain primes, but this remains unproven.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more recent times, the term bit slicing was reused by Matthew Kwan to refer to the technique of using a general-purpose CPU to implement multiple parallel simple virtual machines using general logic instructions to perform single-instruction multiple-data (SIMD) operations. This technique is also known as SIMD within a register (SWAR). This was initially in reference to Eli Biham's 1997 article A Fast New DES Implementation in Software, which achieved significant gains in performance of DES by using this method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following query, four different types of data are retrieved from a single table (status) and for a single user (\"me\"): This query can run by querying the Facebook graph endpoint /fql with the parameters set to q=", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For the 1991 and 1992 seasons, this meant potentially severe angles for short field goal attempts, since the hashmark width remained at 53 ft 4 in (16.26 m). In 1993, the NCAA narrowed the distance between the hashmarks to 40 ft (12.19 m), matching what was the width of hashmarks in the NFL from 1945 through 1971; as mentioned above, the NFL narrowed the hashmarks in 1972 to goalpost width at 18.5 feet (5.64 m). Canadian hash marks in amateur play are 51 feet (16 m) apart, 24 yards from each sideline.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. For a given natural number k, a number n is called k-perfect (or k-fold perfect) if the sum of all positive divisors of n (the divisor function, \u03c3(n)) is equal to kn; a number is thus perfect if and only if it is 2-perfect. A number that is k-perfect for a certain k is called a multiply perfect number. As of 2014, k-perfect numbers are known for each value of k up to 11.It is unknown whether there are any odd multiply perfect numbers other than 1. The first few multiply perfect numbers are: 1, 6, 28, 120, 496, 672, 8128, 30240, 32760, 523776, 2178540, 23569920, 33550336, 45532800, 142990848, 459818240, ... (sequence A007691 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scientific inquiry and academic research, data fabrication is the intentional misrepresentation of research results. As with other forms of scientific misconduct, it is the intent to deceive that marks fabrication as unethical, and thus different from scientists deceiving themselves. There are many ways data can be fabricated. Experimental data can be fabricated by reporting experiments that were never conducted, and accurate data can be manipulated or misrepresented to suit a desired outcome.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This rule not only replaces the representation of a monophthong with that of a diphthong, but it also destroys the reversibility of any capitalization process in digital environments, as the combination of uppercase letter and uppercase iota would normally be converted back to lowercase letter and lowercase iota. It is therefore strongly recommended, both for the integrity of text and for the practical compatibility with digital environments, that lowercase letter and iota subscript should be capitalized in all situations and contexts as uppercase letter and iota adscript. A future revision of the above-mentioned Unicode stipulation is linguistically stipulated and digitally inevitable, as its application is both destructive to the text and impractical in digital applications. In the ASCII-based encoding standard Beta Code, the iota subscript is represented by the pipe character \"|\" placed after the letter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, computational complexity theory, and computer science, the existential theory of the reals is the set of all true sentences of the form where the variables X i {\\displaystyle X_{i}} are interpreted as having real number values, and where F ( X 1 , \u2026 X n ) {\\displaystyle F(X_{1},\\dots X_{n})} is a quantifier-free formula involving equalities and inequalities of real polynomials. A sentence of this form is true if it is possible to find values for all of the variables that, when substituted into formula F {\\displaystyle F} , make it become true.The decision problem for the existential theory of the reals is the problem of finding an algorithm that decides, for each such sentence, whether it is true or false. Equivalently, it is the problem of testing whether a given semialgebraic set is non-empty. This decision problem is NP-hard and lies in PSPACE, giving it significantly lower complexity than Alfred Tarski's quantifier elimination procedure for deciding statements in the first-order theory of the reals without the restriction to existential quantifiers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus in the sentence Here is the big house, both house and big house are N-bars, while the big house is a noun phrase. In the sentence I like big houses, both houses and big houses are N-bars, but big houses also functions as a noun phrase (in this case without an explicit determiner). In some modern theories of syntax, however, what are called \"noun phrases\" above are no longer considered to be headed by a noun, but by the determiner (which may be null), and they are thus called determiner phrases (DP) instead of noun phrases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Given a finite group G = \u27e8S\u27e9 and g \u2208 G, find a straight-line program computing g over S. The constructive membership problem is often studied in the setting of black box groups. The elements are encoded by bit strings of a fixed length. Three oracles are provided for the group-theoretic functions of multiplication, inversion, and checking for equality with the identity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reverse mathematics, Brouwer's theorem can be proved in the system WKL0, and conversely over the base system RCA0 Brouwer's theorem for a square implies the weak K\u0151nig's lemma, so this gives a precise description of the strength of Brouwer's theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, a strict adherence to the basic three-structure template of structured programming yields highly nested code, due to inability to exit a structured unit prematurely, and a combinatorial explosion with quite complex program state data to handle all possible conditions. Two solutions have been generally adopted: a way to exit a structured unit prematurely, and more generally exceptions \u2013 in both cases these go up the structure, returning control to enclosing blocks or functions, but do not jump to arbitrary code locations. These are analogous to the use of a return statement in non-terminal position \u2013 not strictly structured, due to early exit, but a mild relaxation of the strictures of structured programming. In C, break and continue allow one to terminate a loop or continue to the next iteration, without requiring an extra while or if statement.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If \u03c41,...,\u03c4m,\u03c31,...,\u03c3n are ramified types then as in simple type theory there is a type (\u03c41,...,\u03c4m,\u03c31,...,\u03c3n) of \"predicative\" propositional functions of \u03c41,...,\u03c4m,\u03c31,...,\u03c3n. However, there are also ramified types (\u03c41,...,\u03c4m|\u03c31,...,\u03c3n) that can be thought of as the classes of propositional functions of \u03c41,...\u03c4m obtained from propositional functions of type (\u03c41,...,\u03c4m,\u03c31,...,\u03c3n) by quantifying over \u03c31,...,\u03c3n. When n=0 (so there are no \u03c3s) these propositional functions are called predicative functions or matrices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In such a cyberattack the attacker places malware within the networks through a variety of methods (malware-laden website, targeted email, infected USB stick, socially engineered access, etc.) and then the malware propagates within the network. Most of the time existing cyber defenses clear the attacker tools from standard serves and IT workstations (IT endpoints) but the cyber defense software cannot access the embedded processors within medical devices. Most of the embedded operating systems within medical devices are running on Microsoft Windows 7 and Windows XP. The security in these operating systems is no longer supported.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Additionally, unlike bounds on the total time, it is a suitable form of analysis even for algorithms that produce an infinite sequence of outputs. The notion of polynomial delay was first introduced by David S. Johnson, Mihalis Yannakakis and Christos Papadimitriou. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, communications survivability is the ability of communications systems to continue to operate effectively under adverse conditions, though portions of the system may be damaged or destroyed. Various methods may be used to maintain communications services, such as using alternate routing, different transmission media or methods, redundant equipment, and sites and equipment that are radiation hardened.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An even nontotient may be one more than a prime number, but never one less, since all numbers below a prime number are, by definition, coprime to it. To put it algebraically, for p prime: \u03c6(p) = p \u2212 1. Also, a pronic number n(n \u2212 1) is certainly not a nontotient if n is prime since \u03c6(p2) = p(p \u2212 1). If a natural number n is a totient, it can be shown that n \u00b7 2k is a totient for all natural number k. There are infinitely many even nontotient numbers: indeed, there are infinitely many distinct primes p (such as 78557 and 271129, see Sierpinski number) such that all numbers of the form 2ap are nontotient, and every odd number has an even multiple which is a nontotient.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and psychometrics, reliability is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions:\"It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The theorem also includes a converse: if two quantum states do commute, there is a method for broadcasting them: they must have a common basis of eigenstates diagonalizing them simultaneously, and the map that clones every state of this basis is a legitimate quantum operation, requiring only physical resources independent of the input state to implement\u2014a completely positive map. A corollary is that there is a physical process capable of broadcasting every state in some set of quantum states if, and only if, every pair of states in the set commutes. This broadcasting map, which works in the commuting case, produces an overall state in which the two copies are perfectly correlated in their eigenbasis. Remarkably, the theorem does not hold if more than one copy of the initial state is provided: for example, broadcasting six copies starting from four copies of the original state is allowed, even if the states are drawn from a non-commuting set. The purity of the state can even be increased in the process, a phenomenon known as superbroadcasting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, in the context of stockholder lawsuits, typically relating to the sale or merger of a public company, the Delaware Court of Chancery has required sufficient disclosures be made to a board of directors and shareholders to \u201cprovide a balanced, truthful account of all matters\u201d and said \u201cWhen a document ventures into certain subjects, it must do so in a manner that is materially complete and unbiased by the omission of material facts.\u201d In a Memorandum Opinion in the CheckFree/Fiserv merger Chancellor Chandler underlined that the earlier In re Pure Resources Court had established the proper frame of analysis for disclosure of financial data: \u201ctockholders are entitled to a fair summary of the substantive work performed by the investment bankers upon whose advice the recommendations of their board as to how to vote on a merger or tender rely.\u201d According to the certification hypothesis fairness opinions may also serve the interest of the shareholders by mitigating informational asymmetries in corporate transactions. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a generating set \u0393 of a module M over a ring R is a subset of M such that the smallest submodule of M containing \u0393 is M itself (the smallest submodule containing a subset is the intersection of all submodules containing the set). The set \u0393 is then said to generate M. For example, the ring R is generated by the identity element 1 as a left R-module over itself. If there is a finite generating set, then a module is said to be finitely generated. This applies to ideals, which are the submodules of the ring itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The pseudo code stores the prefix sum in variable x {\\displaystyle x} and the sum over all nodes in a sub cube in variable \u03c3 {\\displaystyle \\sigma } . This makes it possible for all nodes in 1-sub cube to receive the sum over the 0-sub cube in every step. This results in a factor of log \u2061 p {\\displaystyle \\log p} for T start {\\displaystyle T_{\\text{start}}} and a factor of n log \u2061 p {\\displaystyle n\\log p} for T byte {\\displaystyle T_{\\text{byte}}}: T ( n , p ) = ( T start + n T byte ) log \u2061 p {\\displaystyle T(n,p)=(T_{\\text{start}}+nT_{\\text{byte}})\\log p} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "RMO and PowerPC allow reordering of reads to the same location. These models violate sequential order in examples A and B. An additional relaxation allowed in these models is that memory operations following a read operation can be overlapped and reordered with respect to the read. Alpha and RMO allow a read to return the value of another processor's early write. From a programmer's perspective these models must maintain the illusion of write atomicity even though they allow the processor to read its own write early.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Dialling 123 from a few mobile services, such as O2, also obtains a speaking clock service. The Giffgaff network uses the same service as O2. The service is not available on the 3 mobile telephone network, as they use 123 as the number for their voicemail services.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Pocklington\u2013Lehmer primality test is a primality test devised by Henry Cabourn Pocklington and Derrick Henry Lehmer. The test uses a partial factorization of N \u2212 1 {\\displaystyle N-1} to prove that an integer N {\\displaystyle N} is prime. It produces a primality certificate to be found with less effort than the Lucas primality test, which requires the full factorization of N \u2212 1 {\\displaystyle N-1} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this way, the first path will be drawn as an x-monotone polyline, a type of curve that is automatically non-self-crossing, and the second path will similarly be drawn as a y-monotone polyline. This type of drawing places the vertices in an integer lattice of dimensions linear in the graph sizes. Similarly defined layouts also work, with larger but still linear grid sizes, when both graphs are caterpillars or when both are cycle graphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After returning from these recursive calls, vertex 2 is added to X and removed from P. The iteration of the inner loop of the algorithm for v = 4 makes a recursive call to the algorithm with R = {4}, P = {3,5,6}, and X = \u00d8 (although vertex 2 belongs to the set X in the outer call to the algorithm, it is not a neighbor of v and is excluded from the subset of X passed to the recursive call). This recursive call will end up making three second-level recursive calls to the algorithm that report the three cliques {3,4}, {4,5}, and {4,6}. Then, vertex 4 is added to X and removed from P. In the third and final iteration of the inner loop of the algorithm, for v = 6, there is a recursive call to the algorithm with R = {6}, P = \u00d8, and X = {4}.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is also generally an expectation that there be a close resemblance between the real world and the features of the model in an ontology.In theory, an ontology is a \"formal, explicit specification of a shared conceptualisation\". An ontology renders shared vocabulary and taxonomy which models a domain with the definition of objects and/or concepts and their properties and relations.Ontologies are the structural frameworks for organizing information and are used in artificial intelligence, the Semantic Web, systems engineering, software engineering, biomedical informatics, library science, enterprise bookmarking, and information architecture as a form of knowledge representation about the world or some part of it. The creation of domain ontologies is also essential to the definition and use of an enterprise architecture framework.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, housing segregation is the practice of denying African Americans and other minority groups equal access to housing through the process of misinformation, denial of realty and financing services, and racial steering. Housing policy in the United States has influenced housing segregation trends throughout history. Key legislation include the National Housing Act of 1934, the G.I. Bill, and the Fair Housing Act.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This has enabled download speeds in excess of 100 Mbit/s, over distances up to 35 miles (56 km) from the transmission site. In the early days of MMDS, it was known as \"wireless cable\" and was used in a variety of investment scams that still surface today. Frequent solicitations of wireless cable fraud schemes were often heard on talk radio shows like The Sonny Bloch Show in the mid-1990s.Several US telephone companies attempted television services via this system in the mid-1990s \u2013 the Tele-TV venture of Bell Atlantic, NYNEX and Pacific Bell; and the rival Americast consortium of Ameritech, BellSouth, SBC, SNET and GTE.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance. A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An IBM MPIC was also used in the RS/6000 7046 Model B50.The Apple Hydra Mac I/O (MIO) chip (from the 1990s classic Mac OS era) implemented a MPIC alongside a SCSI controller, ADB controller, GeoPort controller, and timers. The Apple implementation of \"Open PIC\" (as the Apple documentation of this era spells it) in their first MIO chip for the Common Hardware Reference Platform was based on version 1.2 of the register specification and supported up to two processors and up to 20 interrupt sources. A MPIC was also incorporated in the newer K2 I/O controller used in the Power Mac G5s.Freescale also uses a MPIC (\"compatible with the Open PIC\") on all its PowerQUICC and QorIQ processors. The Linux Kernel-based Virtual Machine (KVM) supports a virtualized MPIC with up to 256 interrupts, based on the Freescale variants.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory, subtyping (also subtype polymorphism or inclusion polymorphism) is a form of type polymorphism in which a subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements, typically subroutines or functions, written to operate on elements of the supertype can also operate on elements of the subtype. If S is a subtype of T, the subtyping relation (written as S <: T, S \u2291 T, or S \u2264: T ) means that any term of type S can safely be used in any context where a term of type T is expected. The precise semantics of subtyping here crucially depends on the particulars of how \"safely be used\" and \"any context\" are defined by a given type formalism or programming language. The type system of a programming language essentially defines its own subtyping relation, which may well be trivial, should the language support no (or very little) conversion mechanisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus the seeming contradiction is that a model that is itself countable, and which therefore contains only countable sets, satisfies the first-order sentence that intuitively states \"there are uncountable sets\". A mathematical explanation of the paradox, showing that it is not a contradiction in mathematics, was given by Skolem (1922). Skolem's work was harshly received by Ernst Zermelo, who argued against the limitations of first-order logic, but the result quickly came to be accepted by the mathematical community.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are also several methods to approximate a shortest addition chain, and which often require fewer multiplications than binary exponentiation; binary exponentiation itself is a suboptimal addition-chain algorithm. The optimal algorithm choice depends on the context (such as the relative cost of the multiplication and the number of times a given exponent is re-used).The problem of finding the shortest addition chain cannot be solved by dynamic programming, because it does not satisfy the assumption of optimal substructure. That is, it is not sufficient to decompose the power into smaller powers, each of which is computed minimally, since the addition chains for the smaller powers may be related (to share computations). For example, in the shortest addition chain for a15 above, the subproblem for a6 must be computed as (a3)2 since a3 is re-used (as opposed to, say, a6 = a2(a2)2, which also requires three multiplies).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The category of pointed sets and pointed maps has both products and coproducts, but it is not a distributive category. It is also an example of a category where 0 \u00d7 A {\\displaystyle 0\\times A} is not isomorphic to 0 {\\displaystyle 0} .Many algebraic structures are pointed sets in a rather trivial way. For example, groups are pointed sets by choosing the identity element as the basepoint, so that group homomorphisms are point-preserving maps. : 24 This observation can be restated in category theoretic terms as the existence of a forgetful functor from groups to pointed sets. : 582 A pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element.As \"rooted set\" the notion naturally appears in the study of antimatroids and transportation polytopes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The range of colors, sizes and shapes is far wider than in those grown or sold in Africa, Europe or the Americas. Southeast Asian languages do not make the distinction between \"bananas\" and \"plantains\" that is made in English (and Spanish). Thus both Cavendish cultivars, the classic yellow dessert bananas, and Saba cultivars, used mainly for cooking, are called pisang in Malaysia and Indonesia, kluai in Thailand and chu\u1ed1i in Vietnam.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The treaty stipulated that the use of cryptography with short key-lengths (56-bit for symmetric encryption, 512-bit for RSA) would no longer be export-controlled. Cryptography exports from the US became less strictly regulated as a consequence of a major relaxation in 2000; there are no longer very many restrictions on key sizes in US-exported mass-market software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space. Metric spaces are an important class of topological spaces where a real, non-negative distance, also called a metric, can be defined on pairs of points in the set. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For how long? When do they regress to already seen words?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While the algorithmic complexity implies a deterministic description of an object (it measures the information content of an individual sequence), the statistical complexity, like forecasting complexity, implies a statistical description, and refers to an ensemble of sequences generated by a certain source. Formally, the statistical complexity reconstructs a minimal model comprising the collection of all histories sharing a similar probabilistic future, and measures the entropy of the probability distribution of the states within this model. It is a computable and observer-independent measure based only on the internal dynamics of the system, and has been used in studies of emergence and self-organization.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates (all twelve tones). Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create \"two aggregates, between the first hexachords of each, and the second hexachords of each, respectively. \"Combinatoriality is a side effect of derived rows, where the initial segment or set may be combined with its transformations (T,R,I,RI) to create an entire row.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the compact disc system, cross-interleaved Reed\u2013Solomon code (CIRC) provides error detection and error correction. CIRC adds to every three data bytes one redundant parity byte.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2567, 12567, 24567, and 124567 are the patterns related to Braille pattern dots-1345, since the two additional dots of kantenji patterns 01345, 13457, and 013457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\sum _{v}\\left({\\frac {d(v)}{|E|}}{\\frac {1}{2}}\\right)d(v)={\\frac {\\sum _{v}d(v)^{2}}{2|E|}}.} We know from the definition of variance that \u2211 v d ( v ) 2 | V | = \u03bc 2 + \u03c3 2 , {\\displaystyle {\\frac {\\sum _{v}d(v)^{2}}{|V|}}=\\mu ^{2}+\\sigma ^{2},} where \u03c3 2 {\\displaystyle \\sigma ^{2}} is the variance of the degrees in the graph. This allows us to compute the desired expected value as \u2211 v d ( v ) 2 2 | E | = | V | 2 | E | ( \u03bc 2 + \u03c3 2 ) = \u03bc 2 + \u03c3 2 \u03bc = \u03bc + \u03c3 2 \u03bc .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most programming languages, the simplest method to convert a floating point number to an integer does not do floor or ceiling, but truncation. The reason for this is historical, as the first machines used ones' complement and truncation was simpler to implement (floor is simpler in two's complement). FORTRAN was defined to require this behavior and thus almost all processors implement conversion this way. Some consider this to be an unfortunate historical design decision that has led to bugs handling negative offsets and graphics on the negative side of the origin.A bit-wise right-shift of a signed integer x {\\displaystyle x} by n {\\displaystyle n} is the same as \u230a x 2 n \u230b {\\displaystyle \\left\\lfloor {\\frac {x}{2^{n}}}\\right\\rfloor } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, time-sharing was new ground. Many of the concepts involved, such as virtual memory, remained unproven. For example: At the time, nobody could explain why the troubled Manchester/Ferranti Atlas virtual memory \"didn't work\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of economics, for example, this is usually economic cost or regret. In classification, it is the penalty for an incorrect classification of an example. In actuarial science, it is used in an insurance context to model benefits paid over premiums, particularly since the works of Harald Cram\u00e9r in the 1920s. In optimal control, the loss is the penalty for failing to achieve a desired value. In financial risk management, the function is mapped to a monetary loss.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers. Since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their least common denominator, a quadratic irrational is an irrational root of some quadratic equation with integer coefficients. The quadratic irrational numbers, a subset of the complex numbers, are algebraic numbers of degree 2, and can therefore be expressed as a + b c d , {\\displaystyle {a+b{\\sqrt {c}} \\over d},} for integers a, b, c, d; with b, c and d non-zero, and with c square-free. When c is positive, we get real quadratic irrational numbers, while a negative c gives complex quadratic irrational numbers which are not real numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These often arise when discretising one-dimensional problems.Problems in higher dimensions also lead to banded matrices, in which case the band itself also tends to be sparse. For instance, a partial differential equation on a square domain (using central differences) will yield a matrix with a bandwidth equal to the square root of the matrix dimension, but inside the band only 5 diagonals are nonzero. Unfortunately, applying Gaussian elimination (or equivalently an LU decomposition) to such a matrix results in the band being filled in by many non-zero elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An early version was demonstrated to a special committee of the society, the Recording Group, and this was later presented to the AIA. This was favourably received and the database has been in development ever since. In 2002 the society received an award from the AIA.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle 480=2!\\cdot 2!\\cdot 5!} . Every tree has a number of symmetries that is a Jordan\u2013P\u00f3lya number, and every Jordan\u2013P\u00f3lya number arises in this way as the order of an automorphism group of a tree. These numbers are named after Camille Jordan and George P\u00f3lya, who both wrote about them in the context of symmetries of trees.These numbers grow more quickly than polynomials but more slowly than exponentials. As well as in the symmetries of trees, they arise as the numbers of transitive orientations of comparability graphs and in the problem of finding factorials that can be represented as products of smaller factorials.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The paper is also darkened in proportion to its exposure to light, so a second reversal results which restores light and dark to their normal order.Negatives were once commonly made on a thin sheet of glass rather than a plastic film, and some of the earliest negatives were made on paper.Transparent positive prints can be made by printing a negative onto special positive film, as is done to make traditional motion picture film prints for use in theaters. Some films used in cameras are designed to be developed by reversal processing, which produces the final positive, instead of a negative, on the original film. Positives on film or glass are known as transparencies or diapositives, and if mounted in small frames designed for use in a slide projector or magnifying viewer they are commonly called slides.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The image on the right shows the permutohedron of order 4, which is the truncated octahedron. Its vertices are the 24 permutations of (1, 2, 3, 4). Parallel edges have the same edge color. The 6 edge colors correspond to the 6 possible transpositions of 4 elements, i.e. they indicate in which two places the connected permutations differ. (E.g. red edges connect permutations that differ in the last two places.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Once researchers determine their preferred statistical model, different forms of regression analysis provide tools to estimate the parameters \u03b2 {\\displaystyle \\beta } . For example, least squares (including its most common variant, ordinary least squares) finds the value of \u03b2 {\\displaystyle \\beta } that minimizes the sum of squared errors \u2211 i ( Y i \u2212 f ( X i , \u03b2 ) ) 2 {\\displaystyle \\sum _{i}(Y_{i}-f(X_{i},\\beta ))^{2}} . A given regression method will ultimately provide an estimate of \u03b2 {\\displaystyle \\beta } , usually denoted \u03b2 ^ {\\displaystyle {\\hat {\\beta }}} to distinguish the estimate from the true (unknown) parameter value that generated the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another category of bug is called a race condition that may occur when programs have multiple components executing at the same time. If the components interact in a different order than the developer intended, they could interfere with each other and stop the program from completing its tasks. These bugs may be difficult to detect or anticipate, since they may not occur during every execution of a program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fair cake-cutting problem, classic allocation rules such as divide and choose are not RM. Several rules are known to be RM: When the pieces may be disconnected, any allocation rule maximizing a concave welfare function of the absolute (not normalized) utilities is RM. In particular, the Nash-optimal rule, absolute-leximin rule and absolute-utilitarian rule are all RM. However, if the maximization uses the relative utilities (utilities divided by total cake value) then most of these rules are not RM; the only one that remains RM is the Nash-optimal rule.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The most common and challenging criticism to metalinguistic description theories was put forth by Kripke himself: they seem to be an ad hoc explanation of a single linguistic phenomenon. Why should there be a metalinguistic theory for proper nouns (like names) but not for common nouns, count nouns, verbs, predicates, indexicals and other parts of speech. Another recent approach is two-dimensional semantics. The motivations for this approach are rather different from those that inspired other forms of descriptivism, however. Two-dimensional approaches are usually motivated by a sense of dissatisfaction with the causal theorist explanation of how it is that a single proposition can be both necessary and a posteriori or contingent and a priori.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The log-logistic distribution is the probability distribution of a random variable whose logarithm has a logistic distribution. It is similar in shape to the log-normal distribution but has heavier tails. Unlike the log-normal, its cumulative distribution function can be written in closed form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since there can be various levels of data classification and user clearances, this implies a quantified scale for robustness. For example, more robustness is indicated for system environments containing classified Top Secret information and uncleared users than for one with Secret information and users cleared to at least Confidential. To promote consistency and eliminate subjectivity in degrees of robustness, an extensive scientific analysis and risk assessment of the topic produced a landmark benchmark standardization quantifying security robustness capabilities of systems and mapping them to the degrees of trust warranted for various security environments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case where all the matrices are Hermitian positive definite and all the eigenvalues are distinct, \u03bb i = \u03bb 0 i + x 0 i \u22a4 ( \u03b4 K \u2212 \u03bb 0 i \u03b4 M ) x 0 i x i = x 0 i ( 1 \u2212 1 2 x 0 i \u22a4 \u03b4 M x 0 i ) + \u2211 j = 1 j \u2260 i N x 0 j \u22a4 ( \u03b4 K \u2212 \u03bb 0 i \u03b4 M ) x 0 i \u03bb 0 i \u2212 \u03bb 0 j x 0 j {\\displaystyle {\\begin{aligned}\\lambda _{i}&=\\lambda _{0i}+\\mathbf {x} _{0i}^{\\top }\\left(\\delta \\mathbf {K} -\\lambda _{0i}\\delta \\mathbf {M} \\right)\\mathbf {x} _{0i}\\\\\\mathbf {x} _{i}&=\\mathbf {x} _{0i}\\left(1-{\\tfrac {1}{2}}\\mathbf {x} _{0i}^{\\top }\\delta \\mathbf {M} \\mathbf {x} _{0i}\\right)+\\sum _{j=1 \\atop j\\neq i}^{N}{\\frac {\\mathbf {x} _{0j}^{\\top }\\left(\\delta \\mathbf {K} -\\lambda _{0i}\\delta \\mathbf {M} \\right)\\mathbf {x} _{0i}}{\\lambda _{0i}-\\lambda _{0j}}}\\mathbf {x} _{0j}\\end{aligned}}} for infinitesimal \u03b4 K {\\displaystyle \\delta \\mathbf {K} } and \u03b4 M {\\displaystyle \\delta \\mathbf {M} } (the higher order terms in (3) being neglected). So far, we have not proved that these higher order terms may be neglected. This point may be derived using the implicit function theorem; in next section, we summarize the use of this theorem in order to obtain a first order expansion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability a quasi-stationary distribution is a random process that admits one or several absorbing states that are reached almost surely, but is initially distributed such that it can evolve for a long time without reaching it. The most common example is the evolution of a population: the only equilibrium is when there is no one left, but if we model the number of people it is likely to remain stable for a long period of time before it eventually collapses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical research, it is an aim to measure the magnitudes of phenomena. For this purpose, phenomena have to be grouped and categorized, so that distinct and discrete counting units can be defined. It must be possible to allocate all observations to mutually exclusive categories, so that they are properly quantifiable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts. It is the mean absolute error of the forecast values, divided by the mean absolute error of the in-sample one-step naive forecast. It was proposed in 2005 by statistician Rob J. Hyndman and Professor of Decision Sciences Anne B. Koehler, who described it as a \"generally applicable measurement of forecast accuracy without the problems seen in the other measurements.\" The mean absolute scaled error has favorable properties when compared to other methods for calculating forecast errors, such as root-mean-square-deviation, and is therefore recommended for determining comparative accuracy of forecasts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can be viewed as a special case of the result relating two minimal Stinespring representations. Alternatively, there is an isometry scalar matrix {uij}ij \u2208 Cnm \u00d7 nm such that A i = \u2211 j = 1 u i j B j . {\\displaystyle A_{i}=\\sum _{j=1}u_{ij}B_{j}.} This follows from the fact that for two square matrices M and N, M M* = N N* if and only if M = N U for some unitary U.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A measurement system can be accurate but not precise, precise but not accurate, neither, or both. For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from the flawed experiment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most of these systems, the hardware is not open to run general purpose applications. Bare machine computing originated with the application object (AO) concept invented by Karne at Towson University. It evolved over the years into dispersed operating systems (DOSC), and eventually into the BMC paradigm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In category theory, a map may refer to a morphism. The term transformation can be used interchangeably, but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the foundations of mathematics, formalism is associated with a certain rigorous mathematical method: see formal system. In common usage, a formalism means the out-turn of the effort towards formalisation of a given limited area. In other words, matters can be formally discussed once captured in a formal system, or commonly enough within something formalisable with claims to be one. Complete formalisation is in the domain of computer science. Formalism also more precisely refers to a certain school in the philosophy of mathematics, stressing axiomatic proofs through theorems, specifically associated with David Hilbert. In the philosophy of mathematics, therefore, a formalist is a person who belongs to the school of formalism, which is a certain mathematical-philosophical doctrine descending from Hilbert.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The original, strong, form of the conjecture with exponent 1/2 has never been disproved, although it is no longer believed to be true and the term Hall's conjecture now generally means the version with the \u03b5 in it. For example, in 1998, Noam Elkies found the example 4478849284284020423079182 - 58538865167812233 = -1641843, for which compatibility with Hall's conjecture would require C to be less than .0214 \u2248 1/50, so roughly 10 times smaller than the original choice of 1/5 that Hall suggested. The weak form of Hall's conjecture would follow from the ABC conjecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, for given real numbers a and b, the logarithm logb a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that bk = a. In number theory, the more commonly used term is index: we can write x = indr a (mod m) (read \"the index of a to the base r modulo m\") for rx \u2261 a (mod m) if r is a primitive root of m and gcd(a,m) = 1. Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. Several important algorithms in public-key cryptography, such as ElGamal, base their security on the assumption that the discrete logarithm problem (DLP) over carefully chosen groups has no efficient solution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In relationally synthesized Odia words, base morphemes (root words) join with bound morphemes to express grammatical function. The Odia language has a tendency for commonly used words to have a 2:1 morpheme-word ratio i.e. on average; there are two morphemes in a single word. Because of this tendency, Odia is said to \"possess morphology\" since almost each used word has an internal compositional structure in terms of morphemes. In the Odia language, generally, separate words are used to express syntactic relationships which imparts an isolating tendency, while using inflectional morphology could have made the language more synthetic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number a is equal to itself (reflexive).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a concrete category is a category that is equipped with a faithful functor to the category of sets (or sometimes to another category, see Relative concreteness below). This functor makes it possible to think of the objects of the category as sets with additional structure, and of its morphisms as structure-preserving functions. Many important categories have obvious interpretations as concrete categories, for example the category of topological spaces and the category of groups, and trivially also the category of sets itself. On the other hand, the homotopy category of topological spaces is not concretizable, i.e. it does not admit a faithful functor to the category of sets. A concrete category, when defined without reference to the notion of a category, consists of a class of objects, each equipped with an underlying set; and for any two objects A and B a set of functions, called morphisms, from the underlying set of A to the underlying set of B. Furthermore, for every object A, the identity function on the underlying set of A must be a morphism from A to A, and the composition of a morphism from A to B followed by a morphism from B to C must be a morphism from A to C.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming, users can inherit the properties and behaviour of a superclass in subclasses. A subclass can override methods of its superclass, substituting its own implementation of the method for the superclass's implementation. Sometimes the overriding method will completely replace the corresponding functionality in the superclass, while in other cases the superclass's method must still be called from the overriding method. Therefore, most programming languages require that an overriding method must explicitly call the overridden method on the superclass for it to be executed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the absence of intervention in the foreign exchange market by national government authorities, the exchange rate of a country's currency is determined, in general, by market forces of supply and demand at a point in time. Government authorities may intervene in the market from time to time to achieve specific policy objectives, such as maintaining its balance of trade or to give its exporters a competitive advantage in international trade.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\mathbf {y} =\\mathbf {X} \\mathbf {\\beta } +\\mathbf {\\varepsilon } ,\\qquad \\operatorname {E} =0,\\ \\operatorname {Cov} =\\mathbf {\\Omega } .} Here \u03b2 \u2208 R k {\\displaystyle \\beta \\in \\mathbb {R} ^{k}} is a vector of unknown constants (known as \u201cregression coefficients\u201d) that must be estimated from the data. Suppose b {\\displaystyle \\mathbf {b} } is a candidate estimate for \u03b2 {\\displaystyle \\mathbf {\\beta } } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statically typed languages (such as C++ and Java), the term generic functions refers to a mechanism for compile-time polymorphism (static dispatch), specifically parametric polymorphism. These are functions defined with TypeParameters, intended to be resolved with compile time type information. The compiler uses these types to instantiate suitable versions, resolving any function overloading appropriately.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a fork\u2013join queue is a queue where incoming jobs are split on arrival for service by numerous servers and joined before departure. The model is often used for parallel computations or systems where products need to be obtained simultaneously from different suppliers (in a warehouse or manufacturing setting). : 78\u201380 The key quantity of interest in this model is usually the time taken to service a complete job. The model has been described as a \"key model for the performance analysis of parallel and distributed systems.\" Few analytical results exist for fork\u2013join queues, but various approximations are known. The situation where jobs arrive according to a Poisson process and service times are exponentially distributed is sometimes referred to as a Flatto\u2013Hahn\u2013Wright model or FHW model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G. In connected graphs where shortest paths are well-defined (i.e. where there are no negative-length cycles), we may construct a shortest-path tree using the following algorithm: Compute dist(u), the shortest-path distance from root v to vertex u in G using Dijkstra's algorithm or Bellman\u2013Ford algorithm. For all non-root vertices u, we can assign to u a parent vertex pu such that pu is connected to u, and that dist(pu) + edge_dist(pu,u) = dist(u). In case multiple choices for pu exist, choose pu for which there exists a shortest path from v to pu with as few edges as possible; this tie-breaking rule is needed to prevent loops when there exist zero-length cycles.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These include, among others: the \"is greater than\", \"is equal to\", and \"divides\" relations in arithmetic; the \"is congruent to\" relation in geometry; the \"is adjacent to\" relation in graph theory; the \"is orthogonal to\" relation in linear algebra.A function may be defined as a special kind of binary relation. Binary relations are also heavily used in computer science.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to identify which transitions must be made, the protocol detects sharing using a special bus line named CopiesExist. All other caches snoop all memory operations and raise the CopiesExist(C) if they detect a \"snoop hit\", i.e. if they have a copy of the data in their own cache. An arrow that goes from nowhere to a state represents a newly loaded block.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The weights used are usually based on the aggregate input shares either factor earns. This ratio is often quoted as: 33% return to capital and 67% return to labor (in Western nations).In a growing economy, capital is accumulated faster than people are born, so the denominator in the growth function under the MFP calculation is growing faster than in the ALP calculation. Hence, MFP growth is almost always lower than ALP growth. (Therefore, measuring in ALP terms increases the apparent capital deepening effect.) MFP is measured by the \"Solow residual\", not ALP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The problem is to approximate the integral of a function f as the average of the function evaluated at a set of points x1, ..., xN: \u222b  s f ( u ) d u \u2248 1 N \u2211 i = 1 N f ( x i ) . {\\displaystyle \\int _{^{s}}f(u)\\,{\\rm {d}}u\\approx {\\frac {1}{N}}\\,\\sum _{i=1}^{N}f(x_{i}).} Since we are integrating over the s-dimensional unit cube, each xi is a vector of s elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Values also have types, which can be checked and queried at runtime. Typing of variables also allows polymorphisms to be resolved at compile time. However, this is different from the polymorphism used in object-oriented function calls (referred to as virtual functions in C++) which resolves the call based on the value type as opposed to the supertypes the variable is allowed to have.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following soft clustering example, the reference vector Y {\\displaystyle Y\\,} contains sample categories and the joint probability p ( X , Y ) {\\displaystyle p(X,Y)\\,} is assumed known. A soft cluster c k {\\displaystyle c_{k}\\,} is defined by its probability distribution over the data samples x i: p ( c k | x i ) {\\displaystyle x_{i}:\\,\\,\\,p(c_{k}|x_{i})} . Tishby et al. presented the following iterative set of equations to determine the clusters which are ultimately a generalization of the Blahut-Arimoto algorithm, developed in rate distortion theory. The application of this type of algorithm in neural networks appears to originate in entropy arguments arising in the application of Gibbs Distributions in deterministic annealing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So we must sum over all these possibilities: Pr ( Median = v ) = \u2211 i = 0 n \u2211 k = 0 n N ! i ! ( N \u2212 i \u2212 k ) !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most computers organize files into hierarchies using folders, directories, or catalogs. The concept is the same irrespective of the terminology used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the 68\u201395\u201399.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively. In mathematical notation, these facts can be expressed as follows, where Pr() is the probability function, \u03a7 is an observation from a normally distributed random variable, \u03bc (mu) is the mean of the distribution, and \u03c3 (sigma) is its standard deviation: The usefulness of this heuristic especially depends on the question under consideration. In the empirical sciences, the so-called three-sigma rule of thumb (or 3\u03c3 rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.In the social sciences, a result may be considered \"significant\" if its confidence level is of the order of a two-sigma effect (95%), while in particle physics, there is a convention of a five-sigma effect (99.99994% confidence) being required to qualify as a discovery.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first version of the above-cited paper, the authors proved the asymptotic time complexity of the algorithm to be O ~ ( log \u2061 ( n ) 12 ) {\\displaystyle {\\tilde {O}}(\\log(n)^{12})} (using \u00d5 from big O notation)\u2014the twelfth power of the number of digits in n times a factor that is polylogarithmic in the number of digits. However, this upper bound was rather loose; a widely-held conjecture about the distribution of the Sophie Germain primes would, if true, immediately cut the worst case down to O ~ ( log \u2061 ( n ) 6 ) {\\displaystyle {\\tilde {O}}(\\log(n)^{6})} . In the months following the discovery, new variants appeared (Lenstra 2002, Pomerance 2002, Berrizbeitia 2002, Cheng 2003, Bernstein 2003a/b, Lenstra and Pomerance 2003), which improved the speed of computation greatly. Owing to the existence of the many variants, Crandall and Papadopoulos refer to the \"AKS-class\" of algorithms in their scientific paper \"On the implementation of AKS-class primality tests\", published in March 2003.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early years of knowledge-based systems the knowledge-bases were fairly small. The knowledge-bases that were meant to actually solve real problems rather than do proof of concept demonstrations needed to focus on well defined problems. So for example, not just medical diagnosis as a whole topic, but medical diagnosis of certain kinds of diseases. As knowledge-based technology scaled up, the need for larger knowledge bases and for modular knowledge bases that could communicate and integrate with each other became apparent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In doctoral mathematics departments, however, only about 58% of statistics course instructors had at least a master\u2019s degree in statistics or biostatistics as their highest degree earned. In master\u2019s-level mathematics departments, the corresponding percentage was near 44%, and in bachelor\u2019s-level departments only 19% of statistics course instructors had at least a master\u2019s degree in statistics or biostatistics as their highest degree earned. As we expected, a large majority of instructors in statistics departments (83% for doctoral departments and 62% for master\u2019s departments) held doctoral degrees in either statistics or biostatistics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more modern terms, a crypt is most often a stone chambered burial vault used to store the deceased. Placing a corpse into a crypt can be called immurement, and is a method of final disposition, as an alternative to, for example, cremation. Crypts are usually found in cemeteries and under public religious buildings, such as churches or cathedrals, but are also occasionally found beneath mausolea or chapels on personal estates. Wealthy or prestigious families will often have a 'family crypt' or 'vault,' in which all members of the family are interred.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "According to the TCP specification, that first sequence number sent by an endpoint can be any value as decided by that endpoint. As the sequence number is chosen by the sender, returned by the recipient, and has no otherwise-defined internal structure, it can be overloaded to carry additional data. The following describes one possible implementation, however as there is no public standard to follow, the order, length, and semantics of the fields may differ between SYN cookie implementations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When using a file transfer protocol, the packets themselves offer their own framing. The packets will always send a continuous stream of data, so the clock cannot \"drift\" in the same way that it could for data being sent by a user typing on a keyboard. By turning off these framing bits when operating on an error-corrected link, that 20% overhead can be eliminated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In stratigraphic excavation, the goal is to remove some or, preferably, all archaeological deposits and features in the reverse order they were created and construct a Harris matrix as a chronological record or \"sequence\" of the site. This Harris matrix is used for interpretation and combining contexts into ever larger units of understanding. This stratigraphic removal of the site is crucial for understanding the chronology of events on site. Stratigraphic excavation involves a process of cleaning or \"troweling back\" the surface of the site and isolating contexts and edges which are definable as either: Discrete, discernible \"edges\" that are formed by being completely separated from the surrounding surface and therefore stratigraphically later than its surroundings Discrete, discernible \"edges\" (as in 1.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an edge cycle cover (sometimes called simply cycle cover) of a graph is a family of cycles which are subgraphs of G and contain all edges of G. If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. In this case, the set of the cycles constitutes a spanning subgraph of G. If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the chain rule (also called the general product rule) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities. The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus the number \u22121,234,567 is 7 digits wide and is encoded as: 0001 0010 0011 0100 0101 0110 0111 1101 1 2 3 4 5 6 7 \u2212 Like character strings, the first byte of the packed decimal \u2013 that with the most significant two digits \u2013 is usually stored in the lowest address in memory, independent of the endianness of the machine. In contrast, a 4-byte binary two's complement integer can represent values from \u22122,147,483,648 to +2,147,483,647. While packed BCD does not make optimal use of storage (using about 20% more memory than binary notation to store the same numbers), conversion to ASCII, EBCDIC, or the various encodings of Unicode is made trivial, as no arithmetic operations are required.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language theory and type theory, polymorphism is the provision of a single interface to entities of different types or the use of a single symbol to represent multiple different types. The concept is borrowed from a principle in biology where an organism or species can have many different forms or stages.The most commonly recognized major classes of polymorphism are: Ad hoc polymorphism: defines a common interface for an arbitrary set of individually specified types. Parametric polymorphism: not specifying concrete types and instead use abstract symbols that can substitute for any type. Subtyping (also called subtype polymorphism or inclusion polymorphism): when a name denotes instances of many different classes related by some common superclass.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, considerable effort has been put into improving the performance of existing algorithms. Among them are CLARANS, and BIRCH. With the recent need to process larger and larger data sets (also known as big data), the willingness to trade semantic meaning of the generated clusters for performance has been increasing. This led to the development of pre-clustering methods such as canopy clustering, which can process huge data sets efficiently, but the resulting \"clusters\" are merely a rough pre-partitioning of the data set to then analyze the partitions with existing slower methods such as k-means clustering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Though the transportation network does not depend on the power network to function, the communications network does. Thus the deactivation of a critical number of nodes in either the power network or the communication network can lead to a series of cascading failures across the system with potentially catastrophic repercussions. If the two networks were treated in isolation, this important feedback effect would not be seen and predictions of network robustness would be greatly overestimated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, given two groups, (G, \u2217) and (H, \u00b7), a group homomorphism from (G, \u2217) to (H, \u00b7) is a function h: G \u2192 H such that for all u and v in G it holds that h ( u \u2217 v ) = h ( u ) \u22c5 h ( v ) {\\displaystyle h(u*v)=h(u)\\cdot h(v)} where the group operation on the left side of the equation is that of G and on the right side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, h ( e G ) = e H {\\displaystyle h(e_{G})=e_{H}} and it also maps inverses to inverses in the sense that h ( u \u2212 1 ) = h ( u ) \u2212 1 . {\\displaystyle h\\left(u^{-1}\\right)=h(u)^{-1}.\\,} Hence one can say that h \"is compatible with the group structure\". Older notations for the homomorphism h(x) may be xh or xh, though this may be confused as an index or a general subscript. In automata theory, sometimes homomorphisms are written to the right of their arguments without parentheses, so that h(x) becomes simply x h {\\displaystyle xh} .In areas of mathematics where one considers groups endowed with additional structure, a homomorphism sometimes means a map which respects not only the group structure (as above) but also the extra structure. For example, a homomorphism of topological groups is often required to be continuous.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, attack time is the time between the instant that a signal at the input of a device or circuit exceeds the activation threshold of the device or circuit and the instant that the device or circuit reacts in a specified manner, or to a specified degree, to the input. Attack time occurs in devices such as clippers, peak limiters, compressors, and voxes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Equipment will search for a bit which has the correct pattern, and will align its framing based on that bit. The pattern sent is 12 bits long, so every group of 12 frames is called a superframe. The pattern used in the 193rd bit is 100011 011100.Each channel sends two bits of call supervision data during each superframe using robbed-bit signaling during frames 6 and 12 of the superframe. More specifically, after the 6th and 12th bit in the superframe pattern, the least significant data bit of each channel (bit 8; T1 data is sent big-endian and uses 1-origin numbering) is replaced by a \"channel-associated signalling\" bit (bits A and B, respectively).Superframe remained in service in many places through the turn of the century, replaced by the improved extended superframe (ESF) of the 1980s in applications where its additional features were desired.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The cases (x, y, z) = (n, n, 2) and all its permutations were proven for n \u2265 4 by Darmon and Merel in 1995 following work from Euler and Poonen. The cases (x, y, z) = (n, n, 3) and all its permutations were proven for n \u2265 3 by \u00c9douard Lucas, Bjorn Poonen, and Darmon and Merel. The case (x, y, z) = (2n, 2n, 5) and all its permutations were proven for n \u2265 2 by Bennett in 2006.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The second expression is evaluated prior to each iteration and the loop is terminated if it evaluates to false. The third expression is evaluated after each iteration, prior to deciding whether to perform the next. This for loop is the only looping construct that can not have a continue block, but expr3 is functionally equivalent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the two coordinate-free definitions described above are rarely used because in virtually all cases, the curl operator can be applied using some set of curvilinear coordinates, for which simpler representations have been derived. The notation \u2207 \u00d7 F has its origins in the similarities to the 3-dimensional cross product, and it is useful as a mnemonic in Cartesian coordinates if \u2207 is taken as a vector differential operator del. Such notation involving operators is common in physics and algebra. Expanded in 3-dimensional Cartesian coordinates (see Del in cylindrical and spherical coordinates for spherical and cylindrical coordinate representations),\u2207 \u00d7 F is, for F composed of  (where the subscripts indicate the components of the vector, not partial derivatives): \u2207 \u00d7 F = | \u0131 ^ \u0237 ^ k ^ \u2202 \u2202 x \u2202 \u2202 y \u2202 \u2202 z F x F y F z | {\\displaystyle \\nabla \\times \\mathbf {F} ={\\begin{vmatrix}{\\boldsymbol {\\hat {\\imath }}}&{\\boldsymbol {\\hat {\\jmath }}}&{\\boldsymbol {\\hat {k}}}\\\\{\\dfrac {\\partial }{\\partial x}}&{\\dfrac {\\partial }{\\partial y}}&{\\dfrac {\\partial }{\\partial z}}\\\\F_{x}&F_{y}&F_{z}\\end{vmatrix}}} where i, j, and k are the unit vectors for the x-, y-, and z-axes, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the eighth chapter titled \"The explanatory power of linguistic theory\", Chomsky writes a linguistic theory cannot content itself by just generating valid grammatical sentences. It also has to account for other structural phenomena at different levels of linguistic representation. At a certain linguistic level, there can be two items which can be understood having different meanings but they are structurally indistinguishable within that level. This is called a \u201cconstructional homonymity\u201d .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{ x \u2223 P ( x ) } = { x \u2223 Q ( x ) } {\\displaystyle \\{x\\mid P(x)\\}=\\{x\\mid Q(x)\\}} if and only if P ( x ) \u21d4 Q ( x ) . {\\displaystyle P(x)\\Leftrightarrow Q(x).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, the Doob\u2013Dynkin lemma, named after Joseph L. Doob and Eugene Dynkin, characterizes the situation when one random variable is a function of another by the inclusion of the \u03c3 {\\displaystyle \\sigma } -algebras generated by the random variables. The usual statement of the lemma is formulated in terms of one random variable being measurable with respect to the \u03c3 {\\displaystyle \\sigma } -algebra generated by the other. The lemma plays an important role in the conditional expectation in probability theory, where it allows replacement of the conditioning on a random variable by conditioning on the \u03c3 {\\displaystyle \\sigma } -algebra that is generated by the random variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public key infrastructure, a validation authority (VA) is an entity that provides a service used to verify the validity or revocation status of a digital certificate per the mechanisms described in the X.509 standard and RFC 5280 (page 69).The dominant method used for this purpose is to host a certificate revocation list (CRL) for download via the HTTP or LDAP protocols. To reduce the amount of network traffic required for certificate validation, the OCSP protocol may be used instead. While a validation authority is capable of responding to a network-based request for a CRL, it lacks the ability to issue or revoke certificates. It must be continuously updated with current CRL information from a certificate authority which issued the certificates contained within the CRL.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It shows that it is impossible to express the square root of 2 as a ratio of two integers. Another consequential proof of impossibility was Ferdinand von Lindemann's proof in 1882, which showed that the problem of squaring the circle cannot be solved because the number \u03c0 is transcendental (i.e., non-algebraic), and that only a subset of the algebraic numbers can be constructed by compass and straightedge. Two other classical problems\u2014trisecting the general angle and doubling the cube\u2014were also proved impossible in the 19th century, and all of these problems gave rise to research into more complicated mathematical structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols \"0\"\u2013\"9\" to represent values 0 to 9, and \"A\"\u2013\"F\" (or alternatively \"a\"\u2013\"f\") to represent values from ten to fifteen. Software developers and system designers widely use hexadecimal numbers because they provide a human-friendly representation of binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Previous studies have been conducted, focusing on priming effects having a rapid rise time and a hasty decay time. For example, an experiment by Donald Foss researched the decay time of semantic facilitation in lists and sentences. Three experiments were conducted and it was found that semantic relationships within words differs when words occur in sentences rather than lists. Thus, supporting the ongoing discourse model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to abstract the concept of orientation on the edges of a graph to sets, one needs the ability to assign \"direction\" to the elements of a set. The way this achieved is with the following definition of signed sets. A signed set, X {\\displaystyle X} , combines a set of objects, X _ {\\displaystyle {\\underline {X}}} , with a partition of that set into two subsets: X + {\\displaystyle X^{+}} and X \u2212 {\\displaystyle X^{-}} .The members of X + {\\displaystyle X^{+}} are called the positive elements; members of X \u2212 {\\displaystyle X^{-}} are the negative elements.The set X _ = X + \u222a X \u2212 {\\displaystyle {\\underline {X}}=X^{+}\\cup X^{-}} is called the support of X {\\displaystyle X} . The empty signed set, \u2205 {\\displaystyle \\emptyset } , is defined as the empty set \u2205 _ {\\displaystyle {\\underline {\\emptyset }}} combined with a \"partition\" of it into two empty sets: \u2205 + {\\displaystyle \\emptyset ^{+}} and \u2205 \u2212 {\\displaystyle \\emptyset ^{-}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multiprocessor systems, a processor may send an interrupt request to another processor via inter-processor interrupts (IPI).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "MDP also used packet-level forward error correction coding concepts as a repair mechanism. Encoded parity repair packets were generally sent in response to repair requests by receivers. In this way no additional protocol overhead was added above selective retransmission methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a channel bank is a device that performs multiplexing or demultiplexing (\"demux\") of a group of communications channels, such as analog or digital telephone lines, into one channel of higher bandwidth or higher digital bit rate, such as a DS-1 (T1) circuit, so that all the channels can be sent simultaneously over a single cable called a trunkline. A channel bank may be located in a telephone exchange, or in an enterprise's telephone closet or enclosure where it \"breaks out\" individual telephone lines from a high-capacity telephone trunk line connected to the central telephone office, or the enterprise's PBX system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one of Google's promotional videos for search published in the summer of 2010, the majority of the links available were reported to be produced at content farms. In late February 2011, Google announced it was adjusting search algorithms significantly to \"provide better rankings for high-quality sites\u2014sites with original content and information such as research, in-depth reports, thoughtful analysis and so on.\" This was reported to be a reaction to content farms and an attempt to reduce their effectiveness in manipulating search result rankings.The privacy-focused search engine DuckDuckGo does not show results from content farms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Construct the shortest-path tree using the edges between each node and its parent.The above algorithm guarantees the existence of shortest-path trees. Like minimum spanning trees, shortest-path trees in general are not unique. In graphs for which all edge weights are equal, shortest path trees coincide with breadth-first search trees.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is also Bell's theorem: no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. While an impossibility assertion in natural science can never be absolutely proved, it could be refuted by the observation of a single counterexample. Such a counterexample would require that the assumptions underlying the theory that implied the impossibility be re-examined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, the term terminal equipment has the following meanings: Communications equipment at either end of a communications link, used to permit the stations involved to accomplish the mission for which the link was established. In radio-relay systems, equipment used at points where data are inserted or derived, as distinct from equipment used only to relay a reconstituted signal. Telephone and telegraph switchboards and other centrally located equipment at which communications circuits are terminated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For the source and destination of every flight i, one adds two nodes to V, node si as the source and node di as the destination node of flight i. One also adds the following edges to E: An edge with capacity  between s and each si. An edge with capacity  between each di and t. An edge with capacity  between each pair of si and di. An edge with capacity  between each di and sj, if source sj is reachable with a reasonable amount of time and cost from the destination of flight i. An edge with capacity  between s and t.In the mentioned method, it is claimed and proved that finding a flow value of k in G between s and t is equal to finding a feasible schedule for flight set F with at most k crews.Another version of airline scheduling is finding the minimum needed crews to perform all the flights.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line. There are several more precise definitions, depending on the context and the mathematical tools that are used for the study. The simplest mathematical surfaces are planes and spheres in the Euclidean 3-space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a result, it is common for researchers working in the majority of languages with only one type or the other to simply use the alveolar symbols indifferently for both types, unless they specifically want to call attention to the distinction. The most common sounds are the stops  and . More generally, several kinds are distinguished: , voiceless dental plosive , voiced dental plosive , dental ejective , voiced dental implosive == Notes ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a ternary operation is an n-ary operation with n = 3. A ternary operation on a set A takes any given three elements of A and combines them to form a single element of A. In computer science, a ternary operator is an operator that takes three arguments as input and returns one output.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, in each convolutional layer, each neuron takes input from a larger area in the input than previous layers. This is due to applying the convolution over and over, which takes the value of a pixel into account, as well as its surrounding pixels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semantics, the most well-known types of semantic equivalence are dynamic equivalence and formal equivalence (coined by Eugene Nida) are associated with two dissimilar translation approaches that are employed to achieve different levels of literalness between the source and target text, as evidenced in biblical translation. The two have been understood basically, with dynamic equivalence as sense-for-sense translation (translating the meanings of phrases or whole sentences) with readability in mind, and with formal equivalence as word-for-word translation (translating the meanings of words and phrases in a more literal way), keeping literal fidelity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering and hardware engineering, serviceability (also known as supportability) is one of the -ilities or aspects (from IBM's RAS(U) (Reliability, Availability, Serviceability, and Usability)). It refers to the ability of technical support personnel to install, configure, and monitor computer products, identify exceptions or faults, debug or isolate faults to root cause analysis, and provide hardware or software maintenance in pursuit of solving a problem and restoring the product into service. Incorporating serviceability facilitating features typically results in more efficient product maintenance and reduces operational costs and maintains business continuity. Examples of features that facilitate serviceability include: Help desk notification of exceptional events (e.g., by electronic mail or by sending text to a pager) Network monitoring Documentation Event logging / Tracing (software) Logging of program state, such as Execution path and/or local and global variables Procedure entry and exit, optionally with incoming and return variable values (see: subroutine) Exception block entry, optionally with local state (see: exception handling) Software upgrade Graceful degradation, where the product is designed to allow recovery from exceptional events without intervention by technical support staff Hardware replacement or upgrade planning, where the product is designed to allow efficient hardware upgrades with minimal computer system downtime (e.g., hotswap components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the Zipf\u2013Mandelbrot law is a discrete probability distribution. Also known as the Pareto\u2013Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf who suggested a simpler distribution called Zipf's law, and the mathematician Benoit Mandelbrot, who subsequently generalized it. The probability mass function is given by: f ( k ; N , q , s ) = 1 / ( k + q ) s H N , q , s {\\displaystyle f(k;N,q,s)={\\frac {1/(k+q)^{s}}{H_{N,q,s}}}} where H N , q , s {\\displaystyle H_{N,q,s}} is given by: H N , q , s = \u2211 i = 1 N 1 ( i + q ) s {\\displaystyle H_{N,q,s}=\\sum _{i=1}^{N}{\\frac {1}{(i+q)^{s}}}} which may be thought of as a generalization of a harmonic number. In the formula, k {\\displaystyle k} is the rank of the data, and q {\\displaystyle q} and s {\\displaystyle s} are parameters of the distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UML Superstructure 2.4.1 Specification Document the following definition is given: The notion of power type was inspired by the notion of power set. A power set is defined as a set whose instances are subsets. In essence, then, a power type is a class whose instances are subclasses. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results from the high number of fundamental properties of commutative rings that do not extend to noncommutative rings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In symbols, one writes \u03c6 i ( n ) = { \u03c6 ( n ) , if i = 1 \u03c6 ( \u03c6 i \u2212 1 ( n ) ) , if i \u2265 2 {\\displaystyle \\varphi ^{i}(n)={\\begin{cases}\\varphi (n),&{\\text{ if }}i=1\\\\\\varphi (\\varphi ^{i-1}(n)),&{\\text{ if }}i\\geq 2\\end{cases}}} for the iterated totient function. Then if c is the integer such that \u03c6 c ( n ) = 2 , {\\displaystyle \\displaystyle \\varphi ^{c}(n)=2,} one has that n is a perfect totient number if n = \u2211 i = 1 c + 1 \u03c6 i ( n ) . {\\displaystyle n=\\sum _{i=1}^{c+1}\\varphi ^{i}(n).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, Canonical Schema is a design pattern, applied within the service-orientation design paradigm, which aims to reduce the need for performing data model transformation when services exchange messages that reference the same data model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The small Veblen ordinal \u03b8 \u03a9 \u03c9 ( 0 ) {\\displaystyle \\theta _{\\Omega ^{\\omega }}(0)} or \u03c8 ( \u03a9 \u03a9 \u03c9 ) {\\displaystyle \\psi (\\Omega ^{\\Omega ^{\\omega }})} is the limit of ordinals that can be described using a version of Veblen functions with finitely many arguments. It is the ordinal that measures the strength of Kruskal's theorem. It is also the ordinal type of a certain ordering of rooted trees (Jervell 2005).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Lovelace went on to write one of history's earliest computer programs that aided Babbage in the design of the Analytical Engine, a machine capable of running programs automatically. Lovelace's work with Babbage positioned her as a significant pioneer in the field of cybersecurity. Kevin Kelly, the co-founder of Wired magazine, once stated that Lovelace played a major role in the invention of computer science, and there are more lines of code written in languages that she created than in C++, Java, JavaScript, or Python combined.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a priority interrupt system, the FLIH also (briefly) masks other interrupts of equal or lesser priority. A SLIH completes long interrupt processing tasks similarly to a process. SLIHs either have a dedicated kernel thread for each handler, or are executed by a pool of kernel worker threads.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Extended real-valued function for which the minimization problem is not solved by any one of these three trivial cases are exactly those that are called proper. Many (although not all) results whose hypotheses require that the function be proper add this requirement specifically to exclude these trivial cases. If the problem is instead a maximization problem (which would be clearly indicated, such as by the function being concave rather than convex) then the definition of \"proper\" is defined in an analogous (albeit technically different) manner but with the same goal: to exclude cases where the maximization problem can be answered immediately. Specifically, a concave function g {\\displaystyle g} is called proper if its negation \u2212 g , {\\displaystyle -g,} which is a convex function, is proper in the sense defined above.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, the identity channel is a noise-free quantum channel. That is, the channel outputs exactly what was put in.The identity channel is commonly denoted as I {\\displaystyle I} , i d {\\displaystyle {\\mathsf {id}}} or I {\\displaystyle \\mathbb {I} } . == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of the original Gr\u00e4tzel and O'Regan design, the cell has 3 primary parts. On top is a transparent anode made of fluoride-doped tin dioxide (SnO2:F) deposited on the back of a (typically glass) plate. On the back of this conductive plate is a thin layer of titanium dioxide (TiO2), which forms into a highly porous structure with an extremely high surface area. The (TiO2) is chemically bound by a process called sintering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle FSK can be implemented by using completely independent free-running oscillators, and switching between them at the beginning of each symbol period. In general, independent oscillators will not be at the same phase and therefore the same amplitude at the switch-over instant, causing sudden discontinuities in the transmitted signal. In practice, many FSK transmitters use only a single oscillator, and the process of switching to a different frequency at the beginning of each symbol period preserves the phase. The elimination of discontinuities in the phase (and therefore elimination of sudden changes in amplitude) reduces sideband power, reducing interference with neighboring channels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "with Since f {\\displaystyle f} does not appear explicitly in L , {\\displaystyle L,} the first term in the Euler\u2013Lagrange equation vanishes for all f ( x ) {\\displaystyle f(x)} and thus, Substituting for L {\\displaystyle L} and taking the derivative, Thus for some constant c . {\\displaystyle c.} Then where Solving, we get which implies that is a constant and therefore that the shortest curve that connects two points ( x 1 , y 1 ) {\\displaystyle \\left(x_{1},y_{1}\\right)} and ( x 2 , y 2 ) {\\displaystyle \\left(x_{2},y_{2}\\right)} is and we have thus found the extremal function f ( x ) {\\displaystyle f(x)} that minimizes the functional A  {\\displaystyle A} so that A  {\\displaystyle A} is a minimum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, Bland's rule (also known as Bland's algorithm, Bland's anti-cycling rule or Bland's pivot rule) is an algorithmic refinement of the simplex method for linear optimization. With Bland's rule, the simplex algorithm solves feasible linear optimization problems without cycling.The original simplex algorithm starts with an arbitrary basic feasible solution, and then changes the basis in order to decrease the minimization target and find an optimal solution. Usually, the target indeed decreases in every step, and thus after a bounded number of steps an optimal solution is found. However, there are examples of degenerate linear programs, on which the original simplex algorithm cycles forever.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Brocard's conjecture is the conjecture that there are at least four prime numbers between (pn)2 and (pn+1)2, where pn is the nth prime number, for every n \u2265 2. The conjecture is named after Henri Brocard. It is widely believed that this conjecture is true.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more generally, members of a vector space. For representing a vector, the common typographic convention is lower case, upright boldface type, as in v. The International Organization for Standardization (ISO) recommends either bold italic serif, as in v, or non-bold italic serif accented by a right arrow, as in v \u2192 {\\displaystyle {\\vec {v}}} .In advanced mathematics, vectors are often represented in a simple italic type, like any variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The member also has duties to the tax authorities, notably of compliance with the law and the honest presentation of his client's circumstances. It is the taxpayer's responsibility to ensure that returns made to the tax authorities are correct and complete. It is for the member to assist him to decide on the extent and manner of disclosure of facts in relation to his tax affairs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Phenotypic correlations between psychological traits show significant and substantial genetic mediation.\" \"The heritability of intelligence increases throughout development.\" \"Age-to-age stability is mainly due to genetics.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This does not allow for full cross-referencing of information and, according to P. Simon and J. Stavo-Debauge, produces the opposite effect by creating a quasi-hierarchy, with foreigners from outside the European Union making up the group with the most difficulties. Paradoxically, a highly aggregated country classification is more evocative of ethnic discrimination than a country-level classification. Other organizations redact variables such as nationality, necessary for the proper processing of their files, when publishing data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some text messaging software products, an ellipsis is displayed while the interlocutor is typing characters. The feature has been referred to as a \"typing awareness indicator\", for which patents have been filed since the 1990s.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the classification of finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic. The proof consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004. Simple groups can be seen as the basic building blocks of all finite groups, reminiscent of the way the prime numbers are the basic building blocks of the natural numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the commutative diagrams of a category are interpreted as a typed equational theory whose objects are the types, a codiscrete posetal category corresponds to an inconsistent theory understood as one satisfying the axiom x = y at all types. Viewing a 2-category as an enriched category whose hom-objects are categories, the hom-objects of any extension of a posetal category to a 2-category having the same 1-cells are monoids. Some lattice-theoretic structures are definable as posetal categories of a certain kind, usually with the stronger assumption of being skeletal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and precision.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "s . {\\displaystyle \\mathbb {E} \\left=0,a.s.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Subshells are usually identified by their n {\\displaystyle n} - and \u2113 {\\displaystyle \\ell } -values. n {\\displaystyle n} is represented by its numerical value, but \u2113 {\\displaystyle \\ell } is represented by a letter as follows: 0 is represented by 's', 1 by 'p', 2 by 'd', 3 by 'f', and 4 by 'g'. For instance, one may speak of the subshell with n = 2 {\\displaystyle n=2} and \u2113 = 0 {\\displaystyle \\ell =0} as a '2s subshell'.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that prime, with constant difference between them that is equal to that prime. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". (  (  (  (  (  P +  P ) +  P ) +  P ) + \u2026 ) \u22ef +  P ) +  P =  P +  P + \u22ef +  P +  P {\\displaystyle (....(((((P+P)+P)+P)+\\dots )\\dots +P)+P=P+P+\\dots +P+P} . Note that, this simple algorithm takes at most 2l steps and each step consists of a doubling and (if ki \u2260 0) adding two points. So, this is one of the reasons why addition and doubling formulas are defined. Furthermore, this method is applicable to any group and if the group law is written multiplicatively, the double-and-add algorithm is instead called square-and-multiply algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an associative algebra A is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field K. The addition and multiplication operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a vector space over K. In this article we will also use the term K-algebra to mean an associative algebra over the field K. A standard first example of a K-algebra is a ring of square matrices over a field K, with the usual matrix multiplication. A commutative algebra is an associative algebra that has a commutative multiplication, or, equivalently, an associative algebra that is also a commutative ring. In this article associative algebras are assumed to have a multiplicative identity, denoted 1; they are sometimes called unital associative algebras for clarification. In some areas of mathematics this assumption is not made, and we will call such structures non-unital associative algebras.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Lehmann\u2013Scheff\u00e9 theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. The theorem states that any estimator which is unbiased for a given unknown quantity and that depends on the data only through a complete, sufficient statistic is the unique best unbiased estimator of that quantity. The Lehmann\u2013Scheff\u00e9 theorem is named after Erich Leo Lehmann and Henry Scheff\u00e9, given their two early papers.If T is a complete sufficient statistic for \u03b8 and E(g(T)) = \u03c4(\u03b8) then g(T) is the uniformly minimum-variance unbiased estimator (UMVUE) of \u03c4(\u03b8).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nonlinear optimization, quasiconvex programming studies iterative methods that converge to a minimum (if one exists) for quasiconvex functions. Quasiconvex programming is a generalization of convex programming. Quasiconvex programming is used in the solution of \"surrogate\" dual problems, whose biduals provide quasiconvex closures of the primal problem, which therefore provide tighter bounds than do the convex closures provided by Lagrangian dual problems. In theory, quasiconvex programming and convex programming problems can be solved in reasonable amount of time, where the number of iterations grows like a polynomial in the dimension of the problem (and in the reciprocal of the approximation error tolerated); however, such theoretically \"efficient\" methods use \"divergent-series\" stepsize rules, which were first developed for classical subgradient methods. Classical subgradient methods using divergent-series rules are much slower than modern methods of convex minimization, such as subgradient projection methods, bundle methods of descent, and nonsmooth filter methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It takes inspiration from NUSAP, a method used to qualify the worth (quality) of quantitative information with the generation of `Pedigrees' of numbers. Likewise, sensitivity auditing has been developed to provide pedigrees of models and model-based inferences.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The notion of a replicating portfolio is fundamental to rational pricing, which assumes that market prices are arbitrage-free \u2013 concretely, arbitrage opportunities are exploited by constructing a replicating portfolio. In practice, replicating portfolios are seldom, if ever, exact replications. Most significantly, unless they are claims against the same counterparties, there is credit risk. Further, dynamic replication is invariably imperfect, since actual price movements are not infinitesimal \u2013 they may in fact be large \u2013 and transaction costs to change the hedge are not zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of biometric systems, presentation attacks may also be called \"spoofing attacks\". As per the recent ISO/IEC 30107 standard, presentation attacks are defined as \"presentation to the biometric capture subsystem with the goal of interfering with the operation of the biometric system\". These attacks can be either impersonation or obfuscation attacks.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: A simple base case (or cases) \u2014 a terminating scenario that does not use recursion to produce an answer A recursive step \u2014 a set of rules that reduces all successive cases toward the base case.For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or One's parent's ancestor (recursive step).The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as base case 1,Fib(1) = 1 as base case 2,For all integers n > 1, Fib(n) = Fib(n \u2212 1) + Fib(n \u2212 2).Many mathematical axioms are based upon recursive rules. For example, the formal definition of the natural numbers by the Peano axioms can be described as: \"Zero is a natural number, and each natural number has a successor, which is also a natural number.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 2000s, scholars noted a lack of theory and conceptual frameworks to inform and guide research and teacher preparation in technology integration. The classic definition of PCK proposed by Shulman included one dynamic and complex relationship between two different knowledge bodies: content knowledge and pedagogical knowledge. Shulman defined PCK as the blend between content and pedagogy, highlighting the teacher's comprehension of how specific topics are organized, adapted, and represented according to students' diverse interests and capabilities. For five years, Mishra & Koehler participated in a design experiment whose focus was to understand P-20 educators\u2019 professional development of rich technology uses as well as helping them develop their teaching with technology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s and early 1980s, the cost of making a phone call decreased and more business communication was done by phone. As corporations grew and labor rates increased, the ratio of secretaries to employees decreased. The initial solution to the phone communication problem for businesses was the \u201cmessage center.\u201d A message center or \u201cmessage desk\u201d was a centralized, manual answering service inside a company manned by a few people answering everyone's phones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In planar graphs, the maximum independent set may be approximated to within any approximation ratio c < 1 in polynomial time; similar polynomial-time approximation schemes exist in any family of graphs closed under taking minors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to fully specify the Bayesian network and thus fully represent the joint probability distribution, it is necessary to specify for each node X the probability distribution for X conditional upon X's parents. The distribution of X conditional upon its parents may have any form. It is common to work with discrete or Gaussian distributions since that simplifies calculations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In other parts of the world, similar concepts have been created to define standards for electronic signatures. In Switzerland, the digital signing standard ZertES has comparable standards that address the conformity and regulation of trust service providers who product digital certificates.In the United States, the NIST Digital Signature Standard (DSS) does not provide a comparable standard for regulating qualified certificates that would address non-repudiation of a signatory's qualified certificate. An amendment to NIST DSS is currently being discussed that would be more in-line with how eIDAS and ZertES handle trusted services.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 17th century, European mathematicians started using infinite numbers and infinite expressions in a systematic fashion. In 1655, John Wallis first used the notation \u221e {\\displaystyle \\infty } for such a number in his De sectionibus conicis, and exploited it in area calculations by dividing the region into infinitesimal strips of width on the order of 1 \u221e . {\\displaystyle {\\tfrac {1}{\\infty }}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the EQP phase of SLQP, the search direction d k {\\displaystyle d_{k}} of the step is obtained by solving the following equality-constrained quadratic program: min d f ( x k ) + \u2207 f ( x k ) T d + 1 2 d T \u2207 x x 2 L ( x k , \u03bb k , \u03c3 k ) d s . t . b A k ( x k ) + \u2207 b A k ( x k ) T d = 0 c A k ( x k ) + \u2207 c A k ( x k ) T d = 0. {\\displaystyle {\\begin{array}{rl}\\min \\limits _{d}&f(x_{k})+\\nabla f(x_{k})^{T}d+{\\tfrac {1}{2}}d^{T}\\nabla _{xx}^{2}{\\mathcal {L}}(x_{k},\\lambda _{k},\\sigma _{k})d\\\\\\mathrm {s.t.} &b_{{\\cal {A}}_{k}}(x_{k})+\\nabla b_{{\\cal {A}}_{k}}(x_{k})^{T}d=0\\\\&c_{{\\cal {A}}_{k}}(x_{k})+\\nabla c_{{\\cal {A}}_{k}}(x_{k})^{T}d=0.\\end{array}}} Note that the term f ( x k ) {\\displaystyle f(x_{k})} in the objective functions above may be left out for the minimization problems, since it is constant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each element of the queue is a pair of symbols (terminals or previously defined pairs) that occur consecutively in the sequence. The priority of a pair is given by the number of occurrences of the pair in the remaining sequence. Each time a new pair is created, the priority queue is updated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In symmetric case, what we want is equal bitrate for the two sources: 5 bits each with separate encoder and joint decoder. We still use linear codes for this system, as we used for asymmetric case. The basic idea is similar, but in this case, we need to do coset partition for both sources, while for a pair of received syndromes (corresponds to one coset), only one pair of input variables are possible given the correlation between two sources. Suppose we have a pair of linear code C 1 {\\displaystyle \\mathbf {C_{1}} } and C 2 {\\displaystyle \\mathbf {C_{2}} } and an encoder-decoder pair based on linear codes which can achieve symmetric coding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of its application to a disjunction, consider the following claim: \"it is false that either of A or B is true\", which is written as: \u00ac ( A \u2228 B ) . {\\displaystyle \\neg (A\\lor B).} In that it has been established that neither A nor B is true, then it must follow that both A is not true and B is not true, which may be written directly as: ( \u00ac A ) \u2227 ( \u00ac B ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Selecting the references can be done manually ( \u03a6 1 , \u03a6 2 , \u03a6 5 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(See also the A-theory and the B-theory of time.) Chalmers also considers negative facts. For example, a statement like \"there do not exist nonphysical angels.\" If in fact true, it does not seem that this logically follows from any of the physical facts by themselves; but, he argues, it would follow if one added a \"That is all\" statement at the end of the list of all the physical facts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, a unimodal probability distribution or unimodal distribution is a probability distribution which has a single peak. The term \"mode\" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called \"unimodal\". If it has more modes it is \"bimodal\" (2), \"trimodal\" (3), etc., or in general, \"multimodal\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scores for sporting events, in particular tennis and association football, the number 0 has the very specialized names \"love\" and \"nil\". This can cause difficulty for radio and television newsreaders, because the reader must be aware of which name to use, when the score is often written as the digit \"0\" in the script. (McLeish recommends to readers that they write the number out on the script in words if necessary.) In cricket, a batsman who is out without scoring is said to have scored \"a duck\", but \"duck\" is not used as a synonym for zero in the same way that \"love\" or \"nil\" are: it is always accompanied by the indefinite article and is not usually used in a formal reading of a team's scoresheet.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In nonlinear programming, the constraints are not necessarily linear. Nonetheless, many of the same principles apply. To ensure that the global maximum of a non-linear problem can be identified easily, the problem formulation often requires that the functions be convex and have compact lower level sets. This is the significance of the Karush\u2013Kuhn\u2013Tucker conditions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, film classification is a voluntary process with the ratings issued by the Motion Picture Association (MPA) via the Classification and Rating Administration (CARA). The system was established in 1968, but the version listed below is the most recent revision, having been in effect since 1990. An unrated film is often informally denoted by \"NR\" in newspapers and so forth. G (General Audiences) \u2013 All ages admitted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "are: write performance increases linearly with the number of connected devices in the cluster. while the storage cluster is partitioned, all parts remain responsive. There is a risk of conflicting updates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since the method employs a selector variable (a factor introduced for each element to permit a counting procedure) the method is also known as the Darwin\u2013Fowler method of selector variables. Note that a distribution function is not the same as the probability \u2013 cf. Maxwell\u2013Boltzmann distribution, Bose\u2013Einstein distribution, Fermi\u2013Dirac distribution. Also note that the distribution function f i {\\displaystyle f_{i}} which is a measure of the fraction of those states which are actually occupied by elements, is given by f i = n i / g i {\\displaystyle f_{i}=n_{i}/g_{i}} or n i = f i g i {\\displaystyle n_{i}=f_{i}g_{i}} , where g i {\\displaystyle g_{i}} is the degeneracy of energy level i {\\displaystyle i} of energy \u03b5 i {\\displaystyle \\varepsilon _{i}} and n i {\\displaystyle n_{i}} is the number of elements occupying this level (e.g. in Fermi\u2013Dirac statistics 0 or 1).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Folders can be named just as files can (except for the root folder, which often does not have a name). The use of folders makes it easier to organize files in a logical way. When a computer allows the use of folders, each file and folder has not only a name of its own, but also a path, which identifies the folder or folders in which a file or folder resides.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the branch of mathematics known as order theory, a semimodular lattice, is a lattice that satisfies the following condition: Semimodular law a \u2227 b <: a implies b <: a \u2228 b.The notation a <: b means that b covers a, i.e. a < b and there is no element c such that a < c < b. An atomistic semimodular bounded lattice is called a matroid lattice because such lattices are equivalent to (simple) matroids. An atomistic semimodular bounded lattice of finite length is called a geometric lattice and corresponds to a matroid of finite rank.Semimodular lattices are also known as upper semimodular lattices; the dual notion is that of a lower semimodular lattice. A finite lattice is modular if and only if it is both upper and lower semimodular. A finite lattice, or more generally a lattice satisfying the ascending chain condition or the descending chain condition, is semimodular if and only if it is M-symmetric. Some authors refer to M-symmetric lattices as semimodular lattices.A semimodular lattice is one kind of algebraic lattice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All the nodes on average are the same in degree therefore attacking one shouldn't cause anymore damage than attacking another. As the number of attacks go up and more nodes are removed, we observe that S decreases non-linearly and acts as if a threshold exists when a fraction of the nodes (f) has been removed, (f\u2248.28). At this point, S goes to zero. The average size of the isolated clusters behaves opposite, increasing exponentially to = 2, also approaching the threshold line f\u2248.28, except decreases back to 1 after. This model was tested for a large range of nodes and proven to maintain the same pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, effective data transfer rate is the average number of units of data, such as bits, characters, blocks, or frames, transferred per unit time from a source and accepted as valid by a sink. Note: The effective data transfer rate is usually expressed in bits, characters, blocks, or frames per second. The effective data transfer rate may be averaged over a period of seconds, minutes, or hours.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The amount of parallelism that can be extracted in superscalar designs is limited by the number of instructions that the scheduler can examine for interdependencies. Examining a greater number of instructions can improve the chance of finding an instruction that can be run in parallel, but only at the cost of increasing the complexity of the scheduler itself. Despite massive efforts, CPU designs using classic RISC or CISC ISA's have plateaued at about three or four functional units.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The anode is specially designed to dissipate the heat and wear resulting from this intense focused barrage of electrons. The anode is precisely angled at 1-20 degrees off perpendicular to the electron current so as to allow the escape of some of the X-ray photons which are emitted perpendicular to the direction of the electron current. The anode is usually made out of tungsten or molybdenum. The tube has a window designed for escape of the generated X-ray photons. The power of a Coolidge tube usually ranges from 0.1 to 18 kW.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Idle wait is instead not convenient in case of a kernel critical section for device management, present in monolithic kernels only. A microkernel instead falls on just the first two of the above cases. In a multiprocessor system, most of the conflicts are kernel-level conflicts, due to the access to the kernel level critical sections, and thus the idle wait periods generated by them have a major impact in performance degradation. This idle wait time increases the average number of idle processors and thus decreases scalability and relative efficiency.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reality, radio propagation changes along with the weather and tropospheric ducting, and occasionally along with other upper-atmospheric phenomena like sunspots and even meteor showers. Thus, while a broadcasting authority might fix the range to an area with exact boundaries (defined as a series of vectors), this is rarely if ever true. When a broadcast reaches well outside of its intended range due to unusual conditions, DXing is possible. The local terrain can also play a major role in limiting broadcast range.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Programmable tools vs. \u2018fixed function\u2019 tools. Some tools can be altered to get varying amounts of data, at varying times. Some tools have only a fixed function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In talent scheduling problem, we can prove that is NP-hard by a reduction from the optimal linear arrangement(OLA) problem. And in this problem, even we restrict each actor is needed for just two days and all actors' salaries are 1, it's still polynomially reducible to the OLA problem. Thus, this problem is unlikely to have pseudo-polynomial algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The radiographer (also known as a radiologic technologist) is usually responsible for acquiring medical images of diagnostic quality; although other professionals may train in this area, notably some radiological interventions performed by radiologists are done so without a radiographer. As a field of scientific investigation, medical imaging constitutes a sub-discipline of biomedical engineering, medical physics or medicine depending on the context: Research and development in the area of instrumentation, image acquisition (e.g., radiography), modeling and quantification are usually the preserve of biomedical engineering, medical physics, and computer science; Research into the application and interpretation of medical images is usually the preserve of radiology and the medical sub-discipline relevant to medical condition or area of medical science (neuroscience, cardiology, psychiatry, psychology, etc.) under investigation. Many of the techniques developed for medical imaging also have scientific and industrial applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The physical addresses are 32-bit on the 386, but can be larger on newer processors which support Physical Address Extension. The 80386 also introduced two new general-purpose data segment registers, FS and GS, to the original set of four segment registers (CS, DS, ES, and SS). A 386 CPU can be put back into real mode by clearing a bit in the CR0 control register, however this is a privileged operation in order to enforce security and robustness. By way of comparison, a 286 could only be returned to real mode by forcing a processor reset, e.g. by a triple fault or using external hardware.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom, the Financial Conduct Authority functions as the national competent authority for the regulation of financial markets; the definition in its Handbook of the term \"security\" applies only to equities, debentures, alternative debentures, government and public securities, warrants, certificates representing certain securities, units, stakeholder pension schemes, personal pension schemes, rights to or interests in investments, and anything that may be admitted to the Official List. In the United States, a \"security\" is a tradable financial asset of any kind. Securities can be broadly categorized into: debt securities (e.g., banknotes, bonds, and debentures) equity securities (e.g., common stocks) derivatives (e.g., forwards, futures, options, and swaps).The company or other entity issuing the security is called the issuer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Developing enough shared vocabulary to communicate can often take a while. The same knowledge can be included in different domain knowledge. Knowledge which may be applicable across a number of domains is called domain-independent knowledge, for example logics and mathematics. Operations on domain knowledge are performed by meta-knowledge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The high-order byte of the instruction specifies the operation. Bits 9 through 15 are the op-code, and bit 8 is the value of the condition code calculation which results in the branch being taken. The low-order byte is a signed word offset relative to the current location of the program counter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming language syntax, spaces are frequently used to explicitly separate tokens. In most languages multiple whitespace characters are treated the same as a single whitespace character (outside of quoted strings); such languages are called free-form. In a few languages, including Haskell, occam, ABC, and Python, whitespace and indentation are used for syntactical purposes. In the satirical language called Whitespace, whitespace characters are the only valid characters for programming, while any other characters are ignored.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s, most real-time applications did not use operating systems because the latter were perceived as adding too much overhead. Typical computers of the time had barely enough computing power to handle the tasks at hand. Moreover, most software of this type was written in assembly language. As a consequence, real-time systems were classic examples of spaghetti code: complex masses of assembly language software using all sorts of machine-dependent tricks to achieve maximum performance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One of the processor actually controls the exchange, but other is synchronized with the former but does not participate in the exchange control. If a fault is detected by the comparator the processors are decoupled and a check-out program is run independently to find faulty processor. This process runs without disturbing the call processing which is suspended temporarily.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to use Dantzig\u2013Wolfe decomposition, the constraint matrix of the linear program must have a specific form. A set of constraints must be identified as \"connecting\", \"coupling\", or \"complicating\" constraints wherein many of the variables contained in the constraints have non-zero coefficients. The remaining constraints need to be grouped into independent submatrices such that if a variable has a non-zero coefficient within one submatrix, it will not have a non-zero coefficient in another submatrix. This description is visualized below: The D matrix represents the coupling constraints and each Fi represents the independent submatrices. Note that it is possible to run the algorithm when there is only one F submatrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, 6b/8b is a line code that expands 6-bit codes to 8-bit symbols for the purposes of maintaining DC-balance in a communications system.The 6b/8b encoding is a balanced code -- each 8-bit output symbol contains 4 zero bits and 4 one bits. So the code can, like a parity bit, detect all single-bit errors. The number of 8-bit patterns with 4 bits set is the binomial coefficient ( 8 4 ) {\\displaystyle {\\tbinom {8}{4}}} = 70. Further excluding the patterns 11110000 and 00001111, this allows 68 coded patterns: 64 data codes, plus 4 additional control codes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus it can be expressed as the vector \u27e8 x 11 , x 22 , x 12 \u27e9 {\\displaystyle \\langle x_{11},x_{22},x_{12}\\rangle } .As another example: The stress tensor (in matrix notation) is given as \u03c3 =  . {\\displaystyle {\\boldsymbol {\\sigma }}=\\left.} In Voigt notation it is simplified to a 6-dimensional vector: \u03c3 ~ = ( \u03c3 x x , \u03c3 y y , \u03c3 z z , \u03c3 y z , \u03c3 x z , \u03c3 x y ) \u2261 ( \u03c3 1 , \u03c3 2 , \u03c3 3 , \u03c3 4 , \u03c3 5 , \u03c3 6 ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Universal Mobile Telecommunications System (UMTS) and 3GPP Long Term Evolution (LTE), user equipment (UE) is any device used directly by an end-user to communicate. It can be a hand-held telephone, a laptop computer equipped with a mobile broadband adapter, or any other device. It connects to the base station Node B/eNodeB as specified in the ETSI 125/136-series and 3GPP 25/36-series of specifications. It roughly corresponds to the mobile station (MS) in GSM systems. The radio interface between the UE and the Node B is called Uu.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, dependency injection is a programming technique in which an object or function receives other objects or functions that it requires, as opposed to creating them internally. Dependency injection aims to separate the concerns of constructing objects and using them, leading to loosely coupled programs. The pattern ensures that an object or function which wants to use a given service should not have to know how to construct those services.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The geometric mean is often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as a set of growth figures: values of the human population or interest rates of a financial investment over time. It also applies to benchmarking, where it is particularly useful for computing means of speedup ratios: since the mean of 0.5x (half as fast) and 2x (twice as fast) will be 1 (i.e., no speedup overall). The geometric mean can be understood in terms of geometry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Similarly, a high-priority task has a high priority because it is more likely to be subject to strict time constraints\u2014it may be providing data to an interactive user, or acting subject to real-time response guarantees. Because priority inversion results in the execution of a lower-priority task blocking the high-priority task, it can lead to reduced system responsiveness or even the violation of response time guarantees. A similar problem called deadline interchange can occur within earliest deadline first scheduling (EDF).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Alpha architecture, a byte is defined as an 8-bit datum (octet), a word as a 16-bit datum, a longword as a 32-bit datum, a quadword as a 64-bit datum, and an octaword as a 128-bit datum. The Alpha architecture originally defined six data types: Quadword (64-bit) integer Longword (32-bit) integer IEEE T-floating-point (double precision, 64-bit) IEEE S-floating-point (single precision, 32-bit)To maintain a level of compatibility with the VAX, the 32-bit architecture that preceded the Alpha, two other floating-point data types are included: VAX G-floating point (double precision, 64-bit) VAX F-floating point (single precision, 32-bit) VAX H-floating point (quad precision, 128-bit) was not supported, but another 128-bit floating-point option, X-floating point, is available on Alpha, but not VAX.H and X have been described as similar, but not identical. Software emulation for H-floating is available from DEC, as is a source-code level converter named DECmigrate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, the typeface \"Bauer Bodoni\" (sample shown here) includes fonts \"Roman\" (or \"Regular\"), \"Bold\" and \"Italic\"; each of these exists in a variety of sizes. The term \"font\" is correctly applied to any one of these alone but may be seen used loosely to refer to the whole typeface. When used in computers, each style is in a separate digital \"font file\". In both traditional typesetting and computing, the word \"font\" refers to the delivery mechanism of the typeface. In traditional typesetting, the font would be made from metal or wood type: to compose a page may require multiple fonts or even multiple typefaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Perhaps the simplest model of distributed computing is a synchronous system where all nodes operate in a lockstep fashion. This model is commonly known as the LOCAL model. During each communication round, all nodes in parallel (1) receive the latest messages from their neighbours, (2) perform arbitrary local computation, and (3) send new messages to their neighbors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, when viewing content on the Internet (the channel), a web browser (a communicating party) would use the HTTP (the communication protocol) to request a web page from the server (another communicating party), and then render the returned data into its visual form. This is how the request\u2013response messaging pattern operates. Alternatively, in computer networking, we have the UDP network protocol. It is used with the one-way messaging pattern, where the sending party is not interested whether the message arrives to any receiving party, nor it expects any of the receiving parties to produce an \"answering\" message.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the L\u00e9vy distribution, named after Paul L\u00e9vy, is a continuous probability distribution for a non-negative random variable. In spectroscopy, this distribution, with frequency as the dependent variable, is known as a van der Waals profile. It is a special case of the inverse-gamma distribution. It is a stable distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most telecommunications organizations, a virtual channel is a method of remapping the program number as used in H.222 Program Association Tables and Program Mapping Tables to a channel number that can be entered as digits on a receiver's remote control. Often, virtual channels are implemented in digital television to help users to go to channels easily and in general to ease the transition from analogue to digital broadcasting. Assigning virtual channels is most common in parts of the world where TV stations were colloquially named after the RF channel they were transmitting on (\"Channel 6 Springfield\"), as was common in North America during the analogue TV era. In other parts of the world, such as Europe, virtual channels are rarely used or needed, because TV stations there identify themselves by name, not by RF channel or callsign.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical mathematics, the Uzawa iteration is an algorithm for solving saddle point problems. It is named after Hirofumi Uzawa and was originally introduced in the context of concave programming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Annotea is part of the W3C Semantic Web efforts. An example implementation of Annotea is W3C's Amaya editor/browser. The current Amaya user interface for annotations is presented in the Amaya documentation. Other projects consists of Plugins for Firefox/Mozilla or Annotatio Client which interacts with most browsers per JavaScript.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the expressions in this article, is the standard normal probability density function, is the corresponding cumulative distribution function (where erf is the error function), and is Owen's T function. Owen has an extensive list of Gaussian-type integrals; only a subset is given below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. For instance, a strictly convex function on an open set has no more than one minimum. Even in infinite-dimensional spaces, under suitable additional hypotheses, convex functions continue to satisfy such properties and as a result, they are the most well-understood functionals in the calculus of variations. In probability theory, a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function of the random variable. This result, known as Jensen's inequality, can be used to deduce inequalities such as the arithmetic\u2013geometric mean inequality and H\u00f6lder's inequality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The definition of theorems as sentences of a formal language is useful within proof theory, which is a branch of mathematics that studies the structure of formal proofs and the structure of provable formulas. It is also important in model theory, which is concerned with the relationship between formal theories and structures that are able to provide a semantics for them through interpretation. Although theorems may be uninterpreted sentences, in practice mathematicians are more interested in the meanings of the sentences, i.e. in the propositions they express.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also generalizes the concepts of a Markov chain and of a subshift of finite type. The languages recognized by probabilistic automata are called stochastic languages; these include the regular languages as a subset.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modular programming, modularity refers to the compartmentalization and interrelation of the parts of a software package. In software design, modularity refers to a logical partitioning of the \"software design\" that allows complex software to be manageable for the purpose of implementation and maintenance. The logic of partitioning may be based on related functions, implementation considerations, data links, or other criteria. In self-reconfiguring modular robotics, modularity refers to the ability of the robotic system to automatically achieve different morphologies to execute the task at hand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The limit of 17 planes is due to UTF-16, which can encode 220 code points (16 planes) as pairs of words, plus the BMP as a single word. UTF-8 was designed with a much larger limit of 231 (2,147,483,648) code points (32,768 planes), and would still be able to encode 221 (2,097,152) code points (32 planes) even under the current limit of 4 bytes.The 17 planes can accommodate 1,114,112 code points. Of these, 2,048 are surrogates (used to make the pairs in UTF-16), 66 are non-characters, and 137,468 are reserved for private use, leaving 974,530 for public assignment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "After receiving Alice's qubit, operating on the pair and measuring both, Bob obtains two classical bits of information. It is worth stressing that if Alice and Bob do not pre-share entanglement, then the superdense protocol is impossible, as this would violate Holevo's theorem. Superdense coding is the underlying principle of secure quantum secret coding. The necessity of having both qubits to decode the information being sent eliminates the risk of eavesdroppers intercepting messages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A black box algorithm is one which uses only these oracles. Hence, straight-line programs for black box groups are black box algorithms. Explicit straight-line programs are given for a wealth of finite simple groups in the online ATLAS of Finite Groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, however, confusion of the term \"dollar cost averaging\" with what Vanguard call a systematic implementation plan has arisen. The term \"dollar cost averaging\" is used to describe a delayed and staged investment strategy used in the situation where the investor has a windfall gain such as an insurance payout or inheritance, as opposed to the immediate investment of the entire sum. The delayed, staged strategy seems preferable for the investor who is concerned with avoiding timing risk (the risk of missing out in beneficial movements in price due to an error in market timing) then instead of investing the entire sum immediately, or waiting for the (mythical) ideal time to invest the entire sum, the investor spreads their investment of the windfall sum into the market over time in a staged way, which appears similar to dollar cost averaging. This behaviour is driven by the fear that volatility in the market could cause a significant drop in the value of the investment immediately after the investment is made.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Functional programming languages often allow the subtyping of records. Consequently, simply typed lambda calculus extended with record types is perhaps the simplest theoretical setting in which a useful notion of subtyping may be defined and studied. Because the resulting calculus allows terms to have more than one type, it is no longer a \"simple\" type theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying \"discrete uniform distribution\" would be \"a known, finite number of outcomes equally likely to happen\". A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Substituting into the first equation relating P ( s 1 ) , P ( s 2 ) {\\displaystyle P(s_{1}),\\;P(s_{2})}: P ( s 1 ) P ( s 2 ) = e \u2212 E ( s 1 ) / k T e \u2212 E ( s 2 ) / k T , {\\displaystyle {\\frac {P(s_{1})}{P(s_{2})}}={\\frac {e^{-E(s_{1})/kT}}{e^{-E(s_{2})/kT}}},} which implies, for any state s of the system P ( s ) = 1 Z e \u2212 E ( s ) / k T , {\\displaystyle P(s)={\\frac {1}{Z}}e^{-E(s)/kT},} where Z is an appropriately chosen \"constant\" to make total probability 1. (Z is constant provided that the temperature T is invariant.) Z = \u2211 s e \u2212 E ( s ) / k T , {\\displaystyle Z=\\sum _{s}e^{-E(s)/kT},} where the index s runs through all microstates of the system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to get more stable results and use all valuable data for training, a data set can be repeatedly split into several training and a validation datasets. This is known as cross-validation. To confirm the model's performance, an additional test data set held out from cross-validation is normally used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In packed pixel or chunky framebuffer organization, the bits defining each pixel are clustered and stored consecutively. For example, if there are 16 bits per pixel, each pixel is represented in two consecutive (contiguous) 8-bit bytes in the framebuffer. If there are 4 bits per pixel, each framebuffer byte defines two pixels, one in each nibble. The latter example is as opposed to storing a single 4-bit pixel in a byte, leaving 4 bits of the byte unused.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Modularity\u2014the ability to define boundaries around specific domains and problem spaces\u2014is essential for these languages because as stated by Tom Gruber, \"Every ontology is a treaty- a social agreement among people with common motive in sharing.\" There are always many competing and differing views that make any general-purpose ontology impossible. A general-purpose ontology would have to be applicable in any domain and different areas of knowledge need to be unified.There is a long history of work attempting to build ontologies for a variety of task domains, e.g., an ontology for liquids, the lumped element model widely used in representing electronic circuits (e.g.,), as well as ontologies for time, belief, and even programming itself.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In standard multiple regression, each predictor is multiplied by a number that is called the beta weight, regression weight or weighted regression coefficients (denoted \u03b2W or BW). The prediction is obtained by adding these products along with a constant. When the weights are chosen to give the best prediction by some criterion, the model referred to as a proper linear model. Therefore, multiple regression is a proper linear model. By contrast, unit-weighted regression is called an improper linear model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All matrices are assumed to have coefficients in the complex numbers. For the equation to make sense, the matrices must have appropriate sizes, for example they could all be square matrices of the same size. But more generally, A and B must be square matrices of sizes n and m respectively, and then X and C both have n rows and m columns.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some settings it is natural to consider primitive recursive functions that take as inputs tuples that mix numbers with truth values (that is t for true and f for false), or that produce truth values as outputs. This can be accomplished by identifying the truth values with numbers in any fixed manner. For example, it is common to identify the truth value t with the number 1 and the truth value f with the number 0. Once this identification has been made, the characteristic function of a set A, which always returns 1 or 0, can be viewed as a predicate that tells whether a number is in the set A. Such an identification of predicates with numeric functions will be assumed for the remainder of this article.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is used in order to create input at exactly a specific time, seen as how one can find a particular moment simply by checking every frame at one's leisure. Glitch An unintentional feature in a game \u2014 usually considered an error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Related to the diatonic modes are the eight church modes or Gregorian modes, in which authentic and plagal forms of scales are distinguished by ambitus and tenor or reciting tone. Although both diatonic and gregorian modes borrow terminology from ancient Greece, the Greek tonoi do not otherwise resemble their mediaeval/modern counterparts. In the Middle Ages the term modus was used to describe both intervals and rhythm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, anonymous work is legally defined as \"a work on the copies or phonorecords of which no natural person is identified as author.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one rearrangement proof, two squares are used whose sides have a measure of a + b {\\displaystyle a+b} and which contain four right triangles whose sides are a, b and c, with the hypotenuse being c. In the square on the right side, the triangles are placed such that the corners of the square correspond to the corners of the right angle in the triangles, forming a square in the center whose sides are length c. Each outer square has an area of ( a + b ) 2 {\\displaystyle (a+b)^{2}} as well as 2 a b + c 2 {\\displaystyle 2ab+c^{2}} , with 2 a b {\\displaystyle 2ab} representing the total area of the four triangles. Within the big square on the left side, the four triangles are moved to form two similar rectangles with sides of length a and b. These rectangles in their new position have now delineated two new squares, one having side length a is formed in the bottom-left corner, and another square of side length b formed in the top-right corner. In this new position, this left side now has a square of area ( a + b ) 2 {\\displaystyle (a+b)^{2}} as well as 2 a b + a 2 + b 2 {\\displaystyle 2ab+a^{2}+b^{2}} . Since both squares have the area of ( a + b ) 2 {\\displaystyle (a+b)^{2}} it follows that the other measure of the square area also equal each other such that 2 a b + c 2 {\\displaystyle 2ab+c^{2}} = 2 a b + a 2 + b 2 {\\displaystyle 2ab+a^{2}+b^{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle ~\\operatorname {\\mathbb {P} } \\left(\\mathbf {x} \\right)_{0}=N!\\,\\prod _{i=1}^{k}{\\frac {\\pi _{i}^{x_{i}}}{x_{i}!}}~.} The significance probability for the test is the probability of occurrence of the data set observed, or of a data set less likely than that observed, if the null hypothesis is true. Using an exact test, this is calculated as p  = \u2211 y: P \u2061 ( y ) \u2264 P \u2061 ( x ) 0 P \u2061 ( y ) {\\displaystyle ~p_{\\mathcal {}}=\\sum _{\\mathbf {y} \\,:\\;\\operatorname {\\mathbb {P} } \\left(\\mathbf {y} \\right)\\,\\leq \\,\\operatorname {\\mathbb {P} } \\left(\\mathbf {x} \\right)_{0}}\\operatorname {\\mathbb {P} } \\left(\\mathbf {y} \\right)~} where the sum ranges over all outcomes as likely as, or less likely than, that observed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this way, the tester determines whether the particular device under test meets the device specifications. While packaged as a wafer, automatic test equipment (ATE) can connect to the individual units using a set of microscopic needles. Once the chips are sawn apart and packaged, test equipment can connect to the chips using ZIF sockets (sometimes called contactors).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These maximal hypotheses essentially constitute a (optimistic) claim that the true concept is defined just by the negative data already observed: Thus, if a novel (never-before-seen) data point is observed, it should be assumed to be positive. (I.e., if data has not previously been ruled out, then it's ruled in.) Thus, during learning, the version space (which itself is a set \u2013 possibly infinite \u2013 containing all consistent hypotheses) can be represented by just its lower and upper bounds (maximally general and maximally specific hypothesis sets), and learning operations can be performed just on these representative sets. After learning, classification can be performed on unseen examples by testing the hypothesis learned by the algorithm. If the example is consistent with multiple hypotheses, a majority vote rule can be applied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a filter or order filter is a special subset of a partially ordered set (poset), describing \"large\" or \"eventual\" elements. Filters appear in order and lattice theory, but also topology, whence they originate. The notion dual to a filter is an order ideal. Special cases of filters include ultrafilters, which are filters that cannot be enlarged, and describe nonconstructive techniques in mathematical logic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In older literature on mathematical logic, the period glyph used to indicate how expressions should be bracketed (see Glossary of Principia Mathematica).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was characteristic of logical positivism to consider a scientific theory to be nothing more than a set of sentences, subdivided into the class of theoretical sentences, the class of observational sentences, and the class of mixed sentences. The first class contains terms which refer to theoretical entities, that is to entities not directly observable such as electrons, atoms and molecules; the second class contains terms which denote quantities or observable entities, and the third class consists of precisely the coordinative definitions which contain both types of terms because they connect the theoretical terms with empirical procedures of measurement or with observable entities. For example, the interpretation of \"the geodesic between two points\" as correspondent to \"the path of a light ray in a vacuum\" provides a coordinative definition.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The deterministic behavior is desired and expected in compiling programming languages. In natural language processing, it was thought for a long time that deterministic parsing is impossible due to ambiguity inherent in natural languages (many sentences have more than one plausible parse). Thus, non-deterministic approaches such as the chart parser had to be applied. However, Mitch Marcus proposed in 1978 the Parsifal parser that was able to deal with ambiguities while still keeping the deterministic behavior.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the inverse heat equation, deducing a previous distribution of temperature from final data, is not well-posed in that the solution is highly sensitive to changes in the final data. Continuum models must often be discretized in order to obtain a numerical solution. While solutions may be continuous with respect to the initial conditions, they may suffer from numerical instability when solved with finite precision, or with errors in the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plain English, a hierarchy can be thought of as a set in which: No element is superior to itself, and One element, the (apex or hierarch), is superior to all of the other elements in the set.The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive. The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predicate logic, existential instantiation (also called existential elimination) is a rule of inference which says that, given a formula of the form ( \u2203 x ) \u03d5 ( x ) {\\displaystyle (\\exists x)\\phi (x)} , one may infer \u03d5 ( c ) {\\displaystyle \\phi (c)} for a new constant symbol c. The rule has the restrictions that the constant c introduced by the rule must be a new term that has not occurred earlier in the proof, and it also must not occur in the conclusion of the proof. It is also necessary that every instance of x {\\displaystyle x} which is bound to \u2203 x {\\displaystyle \\exists x} must be uniformly replaced by c. This is implied by the notation P ( a ) {\\displaystyle P\\left({a}\\right)} , but its explicit statement is often left out of explanations. In one formal notation, the rule may be denoted by \u2203 x P ( x ) \u27f9 P ( a ) {\\displaystyle \\exists xP\\left({x}\\right)\\implies P\\left({a}\\right)} where a is a new constant symbol that has not appeared in the proof.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the MixColumns step, the four bytes of each column of the state are combined using an invertible linear transformation. The MixColumns function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes. Together with ShiftRows, MixColumns provides diffusion in the cipher.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some \"cost\" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predicate calculus, a Henkin witness for a sentence \u2203 x \u03c6 ( x ) {\\displaystyle \\exists x\\,\\varphi (x)} in a theory T is a term c such that T proves \u03c6(c) (Hinman 2005:196). The use of such witnesses is a key technique in the proof of G\u00f6del's completeness theorem presented by Leon Henkin in 1949.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Moreover, it's worth mentioning that if we carry forward the same line of thinking, something fascinating emerges. When we take infinity and divide it by a regular number like 10, the result still holds true: it's infinity. This adds another layer of insight to our mathematical journey, underscoring the depth of what we're uncovering here.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus the total demand for page file-backed virtual memory must exceed 250% of the computer's physical memory before the page file will expand. The fragmentation of the page file that occurs when it expands is temporary. As soon as the expanded regions are no longer in use (at the next reboot, if not sooner) the additional disk space allocations are freed and the page file is back to its original state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In fact, a stronger result is true: the number of permutations of length n with major index k and i inversions is the same as the number of permutations of length n with major index i and k inversions, that is, the two statistics are equidistributed. For example, the number of permutations of length 4 with given major index and number of inversions is given in the table below. 0 1 2 3 4 5 6 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 2 0 1 2 1 1 0 0 3 0 1 1 2 1 1 0 4 0 0 1 1 2 1 0 5 0 0 0 1 1 1 0 6 0 0 0 0 0 0 1 {\\displaystyle {\\begin{array}{c|ccccccc}&0&1&2&3&4&5&6\\\\\\hline 0&1&0&0&0&0&0&0\\\\1&0&1&1&1&0&0&0\\\\2&0&1&2&1&1&0&0\\\\3&0&1&1&2&1&1&0\\\\4&0&0&1&1&2&1&0\\\\5&0&0&0&1&1&1&0\\\\6&0&0&0&0&0&0&1\\end{array}}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social psychology, signed graphs have been used to model social situations, with positive edges representing friendships and negative edges enmities between nodes, which represent people. Then, for example, a positive 3-cycle is either three mutual friends, or two friends with a common enemy; while a negative 3-cycle is either three mutual enemies, or two enemies who share a mutual friend. According to balance theory, positive cycles are balanced and supposed to be stable social situations, whereas negative cycles are unbalanced and supposed to be unstable. According to the theory, in the case of three mutual enemies, this is because sharing a common enemy is likely to cause two of the enemies to become friends.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of networks, social capital exists where people have an advantage because of their location in a network. Contacts in a network provide information, opportunities and perspectives that can be beneficial to the central player in the network. Most social structures tend to be characterized by dense clusters of strong connections. Information within these clusters tends to be rather homogeneous and redundant.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social cataloging much like social bookmarking, this software is aimed towards academics. It allows the user to post a citation for an article found on the internet or a website, online database like Academic Search Premier or LexisNexis Academic University, a book found in a library catalog and so on. These citations can be organized into predefined categories, or a new category defined by the user through the use of tags. This method allows academics researching or interested in similar areas to connect and share resources.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Wasserstein distance between two measures is, roughly speaking, the cost of transporting one to the other. The set of all m by n matrices over some field is a metric space with respect to the rank distance d ( A , B ) = r a n k ( B \u2212 A ) {\\displaystyle d(A,B)=\\mathrm {rank} (B-A)} . The Helly metric in game theory measures the difference between strategies in a game.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From this definition the following standard definition of a let expression, as used in a functional language may be derived. x \u2209 FV \u2061 ( y ) \u27f9 ( let \u2061 x: x = y in \u2061 z ) = z  = ( \u03bb x . z ) y {\\displaystyle x\\not \\in \\operatorname {FV} (y)\\implies (\\operatorname {let} x:x=y\\operatorname {in} z)=z=(\\lambda x.z)\\ y} For simplicity the marker specifying the existential variable, x: {\\displaystyle x:} , will be omitted from the expression where it is clear from the context. x \u2209 FV \u2061 ( y ) \u27f9 ( let \u2061 x = y in \u2061 z ) = z  = ( \u03bb x . z ) y {\\displaystyle x\\not \\in \\operatorname {FV} (y)\\implies (\\operatorname {let} x=y\\operatorname {in} z)=z=(\\lambda x.z)\\ y}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Investigations into home primes make up a minor side issue in number theory. Its questions have served as test fields for the implementation of efficient algorithms for factoring composite numbers, but the subject is really one in recreational mathematics. The outstanding computational problem as of 2016 is whether HP(49) = HP(77) can be calculated in practice.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Line 2: Second matrix-valued set of conditional probabilities. By definition p ( y i | c k ) = \u2211 j p ( y i | x j ) p ( x j | c k ) = \u2211 j p ( y i | x j ) p ( x j , c k ) / p ( c k ) = \u2211 j p ( y i | x j ) p ( c k | x j ) p ( x j ) / p ( c k ) {\\displaystyle {\\begin{aligned}p(y_{i}|c_{k})&=\\sum _{j}p(y_{i}|x_{j})p(x_{j}|c_{k})\\\\&=\\sum _{j}p(y_{i}|x_{j})p(x_{j},c_{k}){\\big /}p(c_{k})\\\\&=\\sum _{j}p(y_{i}|x_{j})p(c_{k}|x_{j})p(x_{j}){\\big /}p(c_{k})\\\\\\end{aligned}}} where the Bayes identities p ( a , b ) = p ( a | b ) p ( b ) = p ( b | a ) p ( a ) {\\displaystyle p(a,b)=p(a|b)p(b)=p(b|a)p(a)\\,} are used. Line 3: this line finds the marginal distribution of the clusters c {\\displaystyle c\\,} p ( c i ) = \u2211 j p ( c i , x j ) = \u2211 j p ( c i | x j ) p ( x j ) {\\displaystyle {\\begin{aligned}p(c_{i})&=\\sum _{j}p(c_{i},x_{j})&=\\sum _{j}p(c_{i}|x_{j})p(x_{j})\\end{aligned}}} This is a standard result.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Traditional single-dispatch OO languages make it trivial to add new datatypes but not new functions; traditional functional languages tend to have the opposite effect, and multiple dispatch, if implemented correctly, allows both. It is desirable for an implementation of multiple dispatch to have the following properties: It is possible to define different \"cases\" of a multi-method from within different packages without modifying the source of a base package. Inclusion of another package in the program should not change the behavior of a given multi-method call, when the call does not use any datatypes defined in the package. Conversely, if a datatype is defined in a given package, and a multi-method extension using that type is also defined in the same package, and a value of that type is passed (through a base type reference or into a generic function) into another package with no dependency on that package, and then the multi-method is invoked with that value as an argument, the multi-method case defined in the package which includes the type should be employed. To put it another way--within a given program, the same multi-method invoked with the same set of arguments should resolve to the same implementation, regardless of the location of the call site, and whether or not a given definition is \"in scope\" or \"visible\" at the point of the method call.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An examination of the development in artificial intelligence that has followed reveals that the learning machine did take the abstract path suggested by Turing as in the case of Deep Blue, a chess playing computer developed by IBM and one which defeated the world champion Garry Kasparov (though, this too is controversial) and the numerous computer chess games which can outplay most amateurs. As for the second suggestion Turing makes, it has been likened by some authors as a call to finding a simulacrum of human cognitive development. And such attempts at finding the underlying algorithms by which children learn of the features of the world around them are only beginning to be made.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Johnson\u2013Lindenstrauss lemma is a result named after William B. Johnson and Joram Lindenstrauss concerning low-distortion embeddings of points from high-dimensional into low-dimensional Euclidean space. The lemma states that a set of points in a high-dimensional space can be embedded into a space of much lower dimension in such a way that distances between the points are nearly preserved. The map used for the embedding is at least Lipschitz, and can even be taken to be an orthogonal projection. The lemma has applications in compressed sensing, manifold learning, dimensionality reduction, and graph embedding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the C, C++, and D programming languages, a type qualifier is a keyword that is applied to a type, resulting in a qualified type. For example, const int is a qualified type representing a constant integer, while int is the corresponding unqualified type, simply an integer. In D these are known as type constructors, by analogy with constructors in object-oriented programming. Type qualifiers are a way of expressing additional information about a value through the type system, and ensuring correctness in the use of the data. Type qualifiers are not generally used outside the C/C++ family of languages: many languages have a notation of constants, but express this by the name binding being constant (a \"variable that doesn't vary\"), rather than through the type system; see alternatives, below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some contexts one considers the more general notion of order-indiscernibles, and the term sequence of indiscernibles often refers implicitly to this weaker notion. In our example of binary formulas, to say that the triple (a, b, c) of distinct elements is a sequence of indiscernibles implies (  \u2228  ) \u2227 (  \u2228  ) . {\\displaystyle (\\lor )\\land (\\lor )\\,.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine. Linear regression has many practical uses. Most applications fall into one of the following two broad categories: If the goal is error reduction in prediction or forecasting, linear regression can be used to fit a predictive model to an observed data set of values of the response and explanatory variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The improved coloring with ColorSort algorithm takes in consideration the above observation. Each vertex is assigned to a color class Ck. If k < |Qmax| \u2212 |Q| + 1 the vertex is moved to R (behind the last vertex in R).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The fastest 3G-based standard in the UMTS family is the HSPA+ standard, which has been commercially available since 2009 and offers 21 Mbit/s downstream (11 Mbit/s upstream) without MIMO, i.e. with only one antenna, and in 2011 accelerated up to 42 Mbit/s peak bit rate downstream using either DC-HSPA+ (simultaneous use of two 5 MHz UMTS carriers) or 2x2 MIMO. In theory speeds up to 672 Mbit/s are possible, but have not been deployed yet. The fastest 3G-based standard in the CDMA2000 family is the EV-DO Rev. B, which is available since 2010 and offers 15.67 Mbit/s downstream.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a square root of a number x is a number y such that y 2 = x {\\displaystyle y^{2}=x} ; in other words, a number y whose square (the result of multiplying the number by itself, or y \u22c5 y {\\displaystyle y\\cdot y} ) is x. For example, 4 and \u22124 are square roots of 16 because 4 2 = ( \u2212 4 ) 2 = 16 {\\displaystyle 4^{2}=(-4)^{2}=16} . Every nonnegative real number x has a unique nonnegative square root, called the principal square root or simply the square root (with a definite article, see below), which is denoted by x , {\\displaystyle {\\sqrt {x}},} where the symbol \" {\\displaystyle {\\sqrt {~^{~}}}} \" is called the radical sign or radix. For example, to express the fact that the principal square root of 9 is 3, we write 9 = 3 {\\displaystyle {\\sqrt {9}}=3} . The term (or number) whose square root is being considered is known as the radicand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says something like \"3 + 4 = 4 + 3\" or \"2 \u00d7 5 = 5 \u00d7 2\", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it (for example, \"3 \u2212 5 \u2260 5 \u2212 3\"); such operations are not commutative, and so are referred to as noncommutative operations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The above results may be summarized in the following table. Each cell represents a subshell, and lists the values of m \u2113 {\\displaystyle m_{\\ell }} available in that subshell. Empty cells represent subshells that do not exist.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Teamwork offers different perspectives, and each member may have a different way of handling the project. By sharing ideas, teams can produce better quality work than if the project was done by an individual.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such a combination of proteins is also called a light-harvesting complex.Although all cells in the green parts of a plant have chloroplasts, the majority of those are found in specially adapted structures called leaves. Certain species adapted to conditions of strong sunlight and aridity, such as many Euphorbia and cactus species, have their main photosynthetic organs in their stems. The cells in the interior tissues of a leaf, called the mesophyll, can contain between 450,000 and 800,000 chloroplasts for every square millimeter of leaf. The surface of the leaf is coated with a water-resistant waxy cuticle that protects the leaf from excessive evaporation of water and decreases the absorption of ultraviolet or blue light to minimize heating. The transparent epidermis layer allows light to pass through to the palisade mesophyll cells where most of the photosynthesis takes place.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the Scott\u2013Curry theorem is a result in lambda calculus stating that if two non-empty sets of lambda terms A and B are closed under beta-convertibility then they are recursively inseparable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s, Noam Elkies, followed by A. O. L. Atkin, devised improvements to Schoof's basic algorithm by restricting the set of primes S = { l 1 , \u2026 , l s } {\\displaystyle S=\\{l_{1},\\ldots ,l_{s}\\}} considered before to primes of a certain kind. These came to be called Elkies primes and Atkin primes respectively. A prime l {\\displaystyle l} is called an Elkies prime if the characteristic equation: \u03d5 2 \u2212 t \u03d5 + q = 0 {\\displaystyle \\phi ^{2}-t\\phi +q=0} splits over F l {\\displaystyle \\mathbb {F} _{l}} , while an Atkin prime is a prime that is not an Elkies prime. Atkin showed how to combine information obtained from the Atkin primes with the information obtained from Elkies primes to produce an efficient algorithm, which came to be known as the Schoof\u2013Elkies\u2013Atkin algorithm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics \u2014 specifically, in Riemannian geometry \u2014 geodesic convexity is a natural generalization of convexity for sets and functions to Riemannian manifolds. It is common to drop the prefix \"geodesic\" and refer simply to \"convexity\" of a set or function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Finally, supervenience claims typically involve some modal force, however, the way that modal force is specified depends on which more specific variety of supervenience one decides upon (see below). (1) and (2) are sometimes called \"schemata\" because they do not correspond to actual supervenience relations until the sets of properties A and B, the domain of entities to which those properties apply, and a modal force have been specified. For modal forms of supervenience, the modal strength of the relation is usually taken to be a parameter (that is, the possible worlds appealed to may be physically possible, logically possible, etc.). Also, note that in the early literature properties were not always central, and there remain some who prefer to frame the relation in terms of predicates, facts, or entities instead, for example.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This was the beginning of a new field of mathematics now called analysis. Though not itself a branch of geometry, it is applicable to geometry, and it solved two families of problems that had long been almost intractable: finding tangent lines to odd curves, and finding areas enclosed by those curves. The methods of calculus reduced these problems mostly to straightforward matters of computation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, there are five levels of flooding.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cultures of the South Pacific, life is believed to leave a person's body when they are sick or asleep, making for multiple \"deaths\" in the span of one lifetime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In media where italicization is not possible, alternatives are used as substitutes: In typewritten or handwritten text, underlining is typically used. In plain-text computer files, including e-mail communication, italicised words are often indicated by surrounding them with slashes or other matched delimiters. For example: I was /really/ annoyed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, it must be relatively prime to the order of the group, if the group is finite. If the group is abelian, any powering index works. If the powering index 2 or -1 works, then the group is abelian.The group of power automorphisms commutes with the group of inner automorphisms when viewed as subgroups of the automorphism group. Thus, in particular, power automorphisms that are also inner must arise as conjugations by elements in the second group of the upper central series.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, mean absolute error (MAE) is a measure of errors between paired observations expressing the same phenomenon. Examples of Y versus X include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. MAE is calculated as the sum of absolute errors divided by the sample size:It is thus an arithmetic average of the absolute errors | e i | = | y i \u2212 x i | {\\displaystyle |e_{i}|=|y_{i}-x_{i}|} , where y i {\\displaystyle y_{i}} is the prediction and x i {\\displaystyle x_{i}} the true value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many X10 protocol charts represent this start code as \"1110\", but it is important to realize that is in terms of zero crossings, not data bits. Immediately after the start code, a 4-bit house code (normally represented by the letters A to P on interface units) appears, and after the house code comes a 5-bit function code. Function codes may specify a unit number code (1\u201316) or a command code.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Finally, eight registers (g0 through g7) are globally visible to all procedure levels. The AMD 29000 improved the design by allowing the windows to be of variable size, which helps utilization in the common case where fewer than eight registers are needed for a call. It also separated the registers into a global set of 64, and an additional 128 for the windows.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fields of science and engineering, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's true value. The precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. Although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method. The field of statistics, where the interpretation of measurements plays a central role, prefers to use the terms bias and variability instead of accuracy and precision: bias is the amount of inaccuracy and variability is the amount of imprecision.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For two groups with general monotone valuations, there always exists a 1/2-democratic envy-free-except-1 allocation, and it can be found by an efficient algorithm. For three or more groups with binary additive valuations, there always exists a 1/k-democratic envy-free-except-1 allocation; with general monotone valuations, there always exists a 1/k-democratic envy-free-except-2 allocation. The factor 1/k is tight for envy-free-except-c allocation for any constant c. If envy-freeness is relaxed to proportionality or maximin-share, then similar guarantees can be attained using a polynomial-time algorithm. For groups with additive valuations, a variant of round-robin item allocation can be used to find a 1/3-democratic 1-out-of-best-k allocation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 7, 17, 47, and 147 are the patterns related to Braille pattern dots-3, since the two additional dots of kantenji patterns 03, 37, and 037 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope. A uniform polypeton is vertex-transitive, and all facets are uniform 5-polytopes. The complete set of convex uniform 6-polytopes has not been determined, but most can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations of rings of the Coxeter-Dynkin diagrams. Each combination of at least one ring on every connected group of nodes in the diagram produces a uniform 6-polytope. The simplest uniform polypeta are regular polytopes: the 6-simplex {3,3,3,3,3}, the 6-cube (hexeract) {4,3,3,3,3}, and the 6-orthoplex (hexacross) {3,3,3,3,4}.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More precisely, if you start at any node in the network and form the set of all nodes at distance d {\\displaystyle d} or less from that starting node, the set will, with probability tending to 1 as n \u2192 \u221e, take the form of a tree. In tree-like structures, the number of second neighbors averaged over the whole network, c 2 {\\displaystyle c_{2}} , is: c 2 = \u27e8 k 2 \u27e9 \u2212 \u27e8 k \u27e9 . {\\displaystyle c_{2}=\\langle k^{2}\\rangle -\\langle k\\rangle .}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of coding theory, D KL ( P \u2225 Q ) {\\displaystyle D_{\\text{KL}}(P\\parallel Q)} can be constructed by measuring the expected number of extra bits required to code samples from P {\\displaystyle P} using a code optimized for Q {\\displaystyle Q} rather than the code optimized for P {\\displaystyle P} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In supervised learning, one is given a set of training examples X 1 \u2026 X n {\\displaystyle X_{1}\\ldots X_{n}} with labels y 1 \u2026 y n {\\displaystyle y_{1}\\ldots y_{n}} , and wishes to predict y n + 1 {\\displaystyle y_{n+1}} given X n + 1 {\\displaystyle X_{n+1}} . To do so one forms a hypothesis, f {\\displaystyle f} , such that f ( X n + 1 ) {\\displaystyle f(X_{n+1})} is a \"good\" approximation of y n + 1 {\\displaystyle y_{n+1}} . A \"good\" approximation is usually defined with the help of a loss function, \u2113 ( y , z ) {\\displaystyle \\ell (y,z)} , which characterizes how bad z {\\displaystyle z} is as a prediction of y {\\displaystyle y} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, Welch's t-test, or unequal variances t-test, is a two-sample location test which is used to test the (null) hypothesis that two populations have equal means. It is named for its creator, Bernard Lewis Welch, is an adaptation of Student's t-test, and is more reliable when the two samples have unequal variances and possibly unequal sample sizes. These tests are often referred to as \"unpaired\" or \"independent samples\" t-tests, as they are typically applied when the statistical units underlying the two samples being compared are non-overlapping. Given that Welch's t-test has been less popular than Student's t-test and may be less familiar to readers, a more informative name is \"Welch's unequal variances t-test\" \u2014 or \"unequal variances t-test\" for brevity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In robotics, the manipulability ellipsoid is the geometric interpretation of the scaled eigenvectors resulting from the singular value decomposition of the jacobian that describes a robot's motion.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming, instrumentation means: Profiling: measuring dynamic program behaviors during a training run with a representative input. This is useful for properties of a program that cannot be analyzed statically with sufficient precision, such as alias analysis. Inserting timers into functions. Logging major events such as crashes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer points the polytope contains. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem in the Euclidean plane. These polynomials are named after Eug\u00e8ne Ehrhart who studied them in the 1960s.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Remote call forwarding is also a means for a suburban business to obtain a city-centre local number (with its full large-city coverage area) for inbound calls; while cheaper than a foreign exchange line, this can reduce long-distance telephony costs in markets where local calls are flat-rated but trunk calls are expensive. One alternative to RCF is Caller Redirect whereby callers simply hear an intercept message notifying them that the number has changed. Another alternative is to port the existing number to a voice over IP carrier, which is not tied to a single physical location as the subscriber may be anywhere on broadband Internet. However, not all phone numbers can be ported.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, on the System/370 Model 158, the keyboard sequence 0-7-X (zero, seven and X, in that order) results in an IPL from the device address which was keyed into the input area. The Amdahl 470V/6 and related CPUs supported four hexadecimal digits on those CPUs which had the optional second channel unit installed, for a total of 32 channels.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A formal language begins with different types of symbols. These types can include variables, operators, function symbols, predicate (or relation) symbols, quantifiers, and propositional constants. (Grouping symbols such as delimiters are often added for convenience in using the language, but do not play a logical role.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In prose writing, twelve, being the last single-syllable numeral, is sometimes taken as the last number to be written as a word, and 13 the first to be written using digits. This is not a binding rule, and in English language tradition, it is sometimes recommended to spell out numbers up to and including either nine, ten or twelve, or even ninety-nine or one hundred. Another system spells out all numbers written in one or two words (sixteen, twenty-seven, fifteen thousand, but 372 or 15,001). In German orthography, there used to be the widely followed (but unofficial) rule of spelling out numbers up to twelve (zw\u00f6lf). The Duden (the German standard dictionary) mentions this rule as outdated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This random tree has several equivalent definitions and constructions: using sub-trees generated by finitely many leaves, using a Brownian excursion, Poisson separating a straight line or as a limit of Galton-Watson trees. Intuitively, the Brownian tree is a binary tree whose nodes (or branching points) are dense in the tree; which is to say that for any distinct two points of the tree, there will always exist a node between them. It is a fractal object which can be approximated with computers or by physical processes with dendritic structures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Researchers note that a password based protocol with mutual authentication is important because user identities and passwords are still protected, as the messages are only readable to the two parties involved.However, a negative aspect about password-based authentication is that password tables can take up a lot of memory space. One way around using a lot of memory during a password-based authentication scheme is to implement one-time passwords (OTP), which is a password sent to the user via SMS or email. OTPs are time-sensitive, which means that they will expire after a certain amount of time and that memory does not need to be stored.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This would give a model perplexity of 2190 per sentence. However, it is more common to normalize for sentence length. Thus, if the test sample's sentences comprised a total of 1,000 words, and could be coded using 7.95 bits per word, one could report a model perplexity of 27.95 = 247 per word. In other words, the model is as confused on test data as if it had to choose uniformly and independently among 247 possibilities for each word.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of deconvolution of seismic data, the original unknown signal is made of spikes hence is possible to characterize with sparsity constraints or regularizations such as l1 norm/l2 norm norm ratios, suggested by W. C. Gray in 1978.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The spectral characteristics of these areas are used to train the remote sensing software using decision rules for classifying the rest of the image. These decision rules such as Maximum Likelihood Classification, Parallelopiped Classification, and Minimum Distance Classification offer different techniques to classify an image. Additional ground truth sites allow the remote sensor to establish an error matrix that validates the accuracy of the classification method used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The general linear groups PGL(2,q) are imperfect for q an odd prime power. For any group H, the wreath product H wr Sym2 of H with the symmetric group on two points is imperfect. In particular, every group can be embedded as a two-step subnormal subgroup of an imperfect group of roughly the same cardinality (2|H|2).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to substantiate an athlete's or team's improvements, progress must be monitored. During the monitoring step feedback is provided and the necessary adjustments follow thereafter. It is important to remember this is a feedback loop and operates in a manner that the feedback feeds into adjustments made and vice versa.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Due to the nature of our value function\u2019s different slopes for gains and losses, our utility is maximized in different ways, depending on how we code the four kinds of transactions x {\\displaystyle x} and y {\\displaystyle y} (as gains or as losses):1) Multiple gains: x {\\displaystyle x} and y {\\displaystyle y} are both considered gains. Here, we see that V a l u e ( x ) + V a l u e ( y ) > V a l u e ( x + y ) {\\displaystyle Value(x)+Value(y)>Value(x+y)} . Thus, we want to segregate multiple gains.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one sense, DRT offers a variation of first-order predicate calculus\u2014its forms are pairs of first-order formulae and the free variables that occur in them. In traditional natural language semantics, only individual sentences are examined, but the context of a dialogue plays a role in meaning as well. For example, anaphoric pronouns such as he and she rely upon previously introduced individual constants in order to have meaning. DRT uses variables for every individual constant in order to account for this problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers \"yes\" or \"no\" according to whether the statement is universally valid, i.e., valid in every structure satisfying the axioms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Subscribing organisations are expected to provide relevant data to maintain the common data pool.Credit reference agencies are bound by the Data Protection Act 2018, which requires that data relating to identifiable individuals must be accurate, relevant, held for a proper purpose and not out-of-date, and gives individuals the legal right to access data held on them. Credit agencies are therefore required under law to provide an individual with a copy of their consumer credit report upon request. Most agencies also provide online services for ongoing access to reports.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is one case where they go beyond merely ensuring integrity, and with some reactive security mechanisms, may actually prevent the malicious activity, e.g. by dropping all packets containing the honeytoken at the router. However, such mechanisms have pitfalls because it might cause serious problems if the honeytoken was poorly chosen and appeared in otherwise legitimate network traffic, which was then dropped. The term was first coined by Augusto Paes de Barros in 2003.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The \"topics\" produced by topic modeling techniques are clusters of similar words. A topic model captures this intuition in a mathematical framework, which allows examining a set of documents and discovering, based on the statistics of the words in each, what the topics might be and what each document's balance of topics is. Topic models are also referred to as probabilistic topic models, which refers to statistical algorithms for discovering the latent semantic structures of an extensive text body.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group. It is a central tool in combinatorial and geometric group theory. The structure and symmetry of Cayley graphs makes them particularly good candidates for constructing families of expander graphs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a closure operator on a set S is a function cl: P ( S ) \u2192 P ( S ) {\\displaystyle \\operatorname {cl} :{\\mathcal {P}}(S)\\rightarrow {\\mathcal {P}}(S)} from the power set of S to itself that satisfies the following conditions for all sets X , Y \u2286 S {\\displaystyle X,Y\\subseteq S} Closure operators are determined by their closed sets, i.e., by the sets of the form cl(X), since the closure cl(X) of a set X is the smallest closed set containing X. Such families of \"closed sets\" are sometimes called closure systems or \"Moore families\". A set together with a closure operator on it is sometimes called a closure space. Closure operators are also called \"hull operators\", which prevents confusion with the \"closure operators\" studied in topology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Numerous methods exist to compute descent directions, all with differing merits, such as gradient descent or the conjugate gradient method. More generally, if P {\\displaystyle P} is a positive definite matrix, then p k = \u2212 P \u2207 f ( x k ) {\\displaystyle p_{k}=-P\\nabla f(x_{k})} is a descent direction at x k {\\displaystyle x_{k}} . This generality is used in preconditioned gradient descent methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scrum, the term developer or team member refers to anyone who plays a role in the development and support of the product and can include researchers, architects, designers, programmers, etc.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, a realizer for the proposition \"A implies B\" is a computable function that takes a realizer for A, and uses it to compute a realizer for B. Realizability models characterize realizers for propositions in terms of their visible behavior, and not in terms of their internal structure. Girard shows that for second-order affine linear logic, given a computational system with nontermination and error stops as effects, realizability and focalization give the same meaning to types. Ludics was proposed by the logician Jean-Yves Girard.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the efforts-expended method, the share of effort consumed to date is compared to the total effort expected for the project. For example, the completion percentage may be established on direct work hours, machine hours, or quantities of material.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", which at least chooses a minimum-expected-loss action \u03b4 ( x ) {\\displaystyle \\delta (x)\\!\\,} for those x {\\displaystyle x\\,\\!} for which a finite-expected-loss action does exist. In addition, a generalized Bayes rule may be desirable because it must choose a minimum-expected-loss action \u03b4 ( x ) {\\displaystyle \\delta (x)\\,\\!}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, descriptions of the elements of a smart television can be found in public discourse from the beginning of the 1980s, if not earlier, with the introduction of videotex services, particularly teletext information for reception by television sets, leading commentators to consider that televisions and accessories would evolve to encompass a range of related activities. In the words of one commentator: \"In the long run, this machine is likely to develop into a multi-purpose receiver, for electronic mail, dealing with the bank, calculations, remote information - and 'Not the nine o'clock news' or 'Casablanca' on video. \"The mass acceptance of digital television in the mid-late 2000s and early 2010s greatly improved Smart TVs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern Gaelic, person inflections have almost disappeared, but the negative and interrogative are marked by distinctive forms. In Irish, particularly in the south, person inflections are still very common for the t\u00e1/bh\u00ed series.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A similar system, known as Emergency Alert, is used in Australia to notify the public of impending disasters through both SMS and landline phone calls. These messages can be sent based on either the location of the phone or the address to which the handset is registered. In the early 2020s, device manufacturers have begun to integrate satellite messaging connectivity and satellite emergency services into conventional mobile phones for use in remote regions, where there is no reliable terrestrial cellular network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The purpose of this directive is to prevent the production of waste electronics and also to encourage reuse and recycling of such waste. The directive requires the Member States to encourage design and production methods that take into account the future dismantling and recovery of their products. These take-back programs have been adopted in nearly every OECD country. In the United States, most of these policies have been implemented at the state level.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The motive behind the project was to provide the utility of a smartphone in a simplistic and less dynamic delivery. Moreover, other projects have focused on building second phones with less functionality, or putting human nature and design above technology. Some critics disagree with Google's approach to the digital detox phenomenon, however, and instead argue that harmony between technology use and well-being can be achieved. Additionally, these critics suggest that the best way to digitally detox is to be mindful of the amount of time that is being spent on a digital device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to prove the HSW coding theorem, we really just need a few basic things from quantum mechanics. First, a quantum state is a unit trace, positive operator known as a density operator. Usually, we denote it by \u03c1 {\\displaystyle \\rho } , \u03c3 {\\displaystyle \\sigma } , \u03c9 {\\displaystyle \\omega } , etc. The simplest model for a quantum channel is known as a classical-quantum channel: The meaning of the above notation is that inputting the classical letter x {\\displaystyle x} at the transmitting end leads to a quantum state \u03c1 x {\\displaystyle \\rho _{x}} at the receiving end. It is the task of the receiver to perform a measurement to determine the input of the sender.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more precisely in formal language theory, the profinite words are a generalization of the notion of finite words into a complete topological space. This notion allows the use of topology to study languages and finite semigroups. For example, profinite words are used to give an alternative characterization of the algebraic notion of a variety of finite semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical statistics, a random variable X is standardized by subtracting its expected value E \u2061  {\\displaystyle \\operatorname {E} } and dividing the difference by its standard deviation \u03c3 ( X ) = Var \u2061 ( X ): {\\displaystyle \\sigma (X)={\\sqrt {\\operatorname {Var} (X)}}:} Z = X \u2212 E \u2061  \u03c3 ( X ) {\\displaystyle Z={X-\\operatorname {E}  \\over \\sigma (X)}} If the random variable under consideration is the sample mean of a random sample X 1 , \u2026 , X n {\\displaystyle \\ X_{1},\\dots ,X_{n}} of X: X \u00af = 1 n \u2211 i = 1 n X i {\\displaystyle {\\bar {X}}={1 \\over n}\\sum _{i=1}^{n}X_{i}} then the standardized version is Z = X \u00af \u2212 E \u2061  \u03c3 ( X ) / n . {\\displaystyle Z={\\frac {{\\bar {X}}-\\operatorname {E} }{\\sigma (X)/{\\sqrt {n}}}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sometimes it is enough to prove negligence, while in other cases a more serious fault is required. Thus, anyone who unlawfully interferes, intentionally or through recklessness, with the life, body, health, freedom or property of others is liable to others to repair the resulting damage. On the other hand, less protection is granted in the event of damage to purely intangible interests, nicht-gegenst\u00e4ndliche Interessen, that is to say when the victim only suffers purely economic or moral damage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the learner knows the conditional probability, then one solution is: C ^ B ( x ) = arg \u2061 max k \u2208 { 1... K } P ( C k | X = x ) {\\displaystyle {\\hat {C}}_{B}(x)=\\arg \\max _{k\\in \\{1...K\\}}P(C_{k}|X=x)} This solution is known as the Bayes classifier. The corresponding expected Prediction Error is called the Bayes error rate: B E = E x  = E x  = E x  {\\displaystyle BE=E_{x}=E_{x}=E_{x}} ,where the sum can be omitted in the last step due to considering the counter event. By the definition of the Bayes classifier, it maximizes P ( C ^ B ( x ) | x ) {\\displaystyle P({\\hat {C}}_{B}(x)|x)} and, therefore, minimizes the Bayes error BE. The Bayes error is non-zero if the classification labels are not deterministic, i.e., there is a non-zero probability of a given instance belonging to more than one class.. In a regression context with squared error, the Bayes error is equal to the noise variance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum mechanics, the Kochen\u2013Specker (KS) theorem, also known as the Bell\u2013Kochen\u2013Specker theorem, is a \"no-go\" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved by Kochen and Specker also gave an explicit example for this constraint in terms of a finite number of state vectors. The theorem is a complement to Bell's theorem (to be distinguished from the (Bell\u2013)Kochen\u2013Specker theorem of this article).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, an equidigital number is a natural number in a given number base that has the same number of digits as the number of digits in its prime factorization in the given number base, including exponents but excluding exponents equal to 1. For example, in base 10, 1, 2, 3, 5, 7, and 10 (2 \u00d7 5) are equidigital numbers (sequence A046758 in the OEIS). All prime numbers are equidigital numbers in any base. A number that is either equidigital or frugal is said to be economical.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some versions of coordinate descent randomly pick a different coordinate direction each iteration. Random-restart hill climbing is a meta-algorithm built on top of the hill climbing algorithm. It is also known as Shotgun hill climbing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social network analysis and mathematical sociology, interpersonal ties are defined as information-carrying connections between people. Interpersonal ties, generally, come in three varieties: strong, weak or absent. Weak social ties, it is argued, are responsible for the majority of the embeddedness and structure of social networks in society as well as the transmission of information through these networks. Specifically, more novel information flows to individuals through weak rather than strong ties.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In political/economic theory, notably socialist, Marxist, and many anarchist philosophies, the distinction between private and personal property is an important one. In capitalism private and personal property are considered to be of equal importance and significance without the need for making a distinction. Personal property, or possessions, includes \"items intended for personal use\" (e.g., one's toothbrush, clothes, and vehicles, and rarely money). It must be gained in a \"fair\" manner according to socialist doctrine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Bonse's inequality, named after H. Bonse, relates the size of a primorial to the smallest prime that does not appear in its prime factorization. It states that if p1, ..., pn, pn+1 are the smallest n + 1 prime numbers and n \u2265 4, then p n # = p 1 \u22ef p n > p n + 1 2 . {\\displaystyle p_{n}\\#=p_{1}\\cdots p_{n}>p_{n+1}^{2}.} (the middle product is short-hand for the primorial p n # {\\displaystyle p_{n}\\#} of pn) Mathematician Denis Hanson showed an upper bound where n # \u2264 3 n {\\displaystyle n\\#\\leq 3^{n}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is an example of an algorithm, a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly linear algebra, a zero matrix is a matrix with all its entries being zero. It is alternately denoted by the symbol O {\\displaystyle O} . Some examples of zero matrices are 0 1 , 1 =  , 0 2 , 2 =  , 0 2 , 3 =  , {\\displaystyle 0_{1,1}={\\begin{bmatrix}0\\end{bmatrix}},\\ 0_{2,2}={\\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}},\\ 0_{2,3}={\\begin{bmatrix}0&0&0\\\\0&0&0\\end{bmatrix}},\\ } The set of m \u00d7 n matrices with entries in a ring K forms a module K m , n {\\displaystyle K_{m,n}} . The zero matrix 0 K m , n {\\displaystyle 0_{K_{m,n}}} in K m , n {\\displaystyle K_{m,n}} is the matrix with all entries equal to 0 K {\\displaystyle 0_{K}} , where 0 K {\\displaystyle 0_{K}} is the additive identity in K.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of a pointwise convergent sequence of random variables defined on a common probability space. It is named for the Soviet mathematician A. V. Skorokhod.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Neumann (1935), G.A. Miller (1935), and J.A. de S\u00e9guier (1904).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In either case, the PC would display an error message and halt. Some later PC clones used an NMI to conceal the hardware differences from that of a standard PC. On such computers, an NMI would be generated when a program attempted to access incompatible hardware.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the tests are run once or twice per week during the entire development cycle, using three to five test subjects per round, and with the results delivered within 24 hours to the designers. The number of users actually tested over the course of the project can thus easily reach 50 to 100 people. Research shows that user testing conducted by organisations most commonly involves the recruitment of 5-10 participants.In the early stage, when users are most likely to immediately encounter problems that stop them in their tracks, almost anyone of normal intelligence can be used as a test subject.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of the elements of a set J, then J is an index set. The indexing consists of a surjective function from J onto A, and the indexed collection is typically called an indexed family, often written as {Aj}j\u2208J.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some examples of algorithms used are Filterbank, adjacent orientation vector (AOV) system, and correlation-filter. Filterbank requires whole fingerprints and cannot identify just the tips of the finger since it uses both the local and overall structure. The algorithm works by selecting a region of interest and dividing it into sectors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, topology (from the Greek words \u03c4\u03cc\u03c0\u03bf\u03c2, 'place, location', and \u03bb\u03cc\u03b3\u03bf\u03c2, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Categorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data. More specifically, categorical data may derive from observations made of qualitative data that are summarised as counts or cross tabulations, or from observations of quantitative data grouped within given intervals. Often, purely categorical data are summarised in the form of a contingency table.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Surveys in the academic community have shown NLP to be widely discredited among scientists. Among the reasons for considering NLP a pseudoscience are that evidence in favor of it is limited to anecdotes and personal testimony, that it is not informed by scientific understanding of neuroscience and linguistics, and that the name \"neuro-linguistic programming\" uses jargon words to impress readers and obfuscate ideas, whereas NLP itself does not relate any phenomena to neural structures and has nothing in common with linguistics or programming. In fact, in education, NLP has been used as a key example of pseudoscience.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The two codes C 1 {\\displaystyle \\mathbf {C_{1}} } and C 2 {\\displaystyle \\mathbf {C_{2}} } can be constructed as subcodes of the ( 7 , 4 , 3 ) {\\displaystyle (7,4,3)} Hamming code and thus has minimum distance of 3 {\\displaystyle 3} . Given the generator matrix G {\\displaystyle \\mathbf {G} } of the original Hamming code, the generator matrix G 1 {\\displaystyle \\mathbf {G_{1}} } for C 1 {\\displaystyle \\mathbf {C_{1}} } is constructed by taking any two rows from G {\\displaystyle \\mathbf {G} } , and G 2 {\\displaystyle \\mathbf {G_{2}} } is constructed by the remaining two rows of G {\\displaystyle \\mathbf {G} } . The corresponding ( 5 \u00d7 7 ) {\\displaystyle (5\\times 7)} parity-check matrix for each sub-code can be generated according to the generator matrix and used to generate syndrome bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, a pointer can reference executable code, i.e., it can point to a function, method, or procedure. A function pointer will store the address of a function to be invoked. While this facility can be used to call functions dynamically, it is often a favorite technique of virus and other malicious software writers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Unlike other Indo-European languages, in Slavic languages tense is independent of aspect, with imperfective and perfective aspects being indicated instead by means of prefixes, stem changes, or suppletion. In many West Slavic and East Slavic languages, the early Slavic past tenses have largely merged into a single past tense. In both West and East Slavic, verbs in the past tense are conjugated for gender (masculine, feminine, neuter) and number (singular, plural).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Bayesian network below, X {\\displaystyle X\\,\\!} and Y {\\displaystyle Y\\,\\!} are parent variables and Z {\\displaystyle Z\\,\\!} is the child variable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element. More precisely, if A is a finite set of generators for G then the word problem is the membership problem for the formal language of all words in A and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on A to the group G. If B is another finite generating set for G, then the word problem over the generating set B is equivalent to the word problem over the generating set A. Thus one can speak unambiguously of the decidability of the word problem for the finitely generated group G. The related but different uniform word problem for a class K of recursively presented groups is the algorithmic problem of deciding, given as input a presentation P for a group G in the class K and two words in the generators of G, whether the words represent the same element of G. Some authors require the class K to be definable by a recursively enumerable set of presentations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The theorems are those formulae B {\\displaystyle B} such that \u22a2 B {\\displaystyle \\vdash B} (with an empty left-hand side) is the conclusion of a valid proof. (In some presentations of natural deduction, the A i {\\displaystyle A_{i}} s and the turnstile are not written down explicitly; instead a two-dimensional notation from which they can be inferred is used.) The standard semantics of a judgment in natural deduction is that it asserts that whenever A 1 {\\displaystyle A_{1}} , A 2 {\\displaystyle A_{2}} , etc., are all true, B {\\displaystyle B} will also be true. The judgments A 1 , \u2026 , A n \u22a2 B {\\displaystyle A_{1},\\ldots ,A_{n}\\vdash B} and \u22a2 ( A 1 \u2227 \u22ef \u2227 A n ) \u2192 B {\\displaystyle \\vdash (A_{1}\\land \\cdots \\land A_{n})\\rightarrow B} are equivalent in the strong sense that a proof of either one may be extended to a proof of the other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of telephony, quality of service was defined by the ITU in 1994. Quality of service comprises requirements on all the aspects of a connection, such as service response time, loss, signal-to-noise ratio, crosstalk, echo, interrupts, frequency response, loudness levels, and so on. A subset of telephony QoS is grade of service (GoS) requirements, which comprises aspects of a connection relating to capacity and coverage of a network, for example guaranteed maximum blocking probability and outage probability.In the field of computer networking and other packet-switched telecommunication networks, teletraffic engineering refers to traffic prioritization and resource reservation control mechanisms rather than the achieved service quality. Quality of service is the ability to provide different priorities to different applications, users, or data flows, or to guarantee a certain level of performance to a data flow.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the area of modern algebra known as group theory, the McLaughlin group McL is a sporadic simple group of order 27 \u22c5 36 \u22c5 53 \u22c5 7 \u22c5 11 = 898,128,000 \u2248 9\u00d7108.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Bayesian version of binary hypothesis testing one is interested in minimizing the average error probability under both hypothesis, assuming a prior probability of occurrence on each hypothesis. Let \u03c0 0 {\\displaystyle \\pi _{0}} denote the prior probability of hypothesis H 0 {\\displaystyle H_{0}} . In this case the average error probability is given by P ave = \u03c0 0 P ( error \u2223 H 0 ) + ( 1 \u2212 \u03c0 0 ) P ( error \u2223 H 1 ) {\\displaystyle P_{\\text{ave}}=\\pi _{0}P({\\text{error}}\\mid H_{0})+(1-\\pi _{0})P({\\text{error}}\\mid H_{1})} . In this setting again a likelihood ratio test is optimal and the optimal error decays as lim n \u2192 \u221e \u2212 ln \u2061 P ave n = C ( f 0 , f 1 ) {\\displaystyle \\lim _{n\\to \\infty }{\\frac {-\\ln P_{\\text{ave}}}{n}}=C(f_{0},f_{1})} where C ( f 0 , f 1 ) {\\displaystyle C(f_{0},f_{1})} represents the Chernoff-information between the two distributions defined as C ( f 0 , f 1 ) = max \u03bb \u2208   {\\displaystyle C(f_{0},f_{1})=\\max _{\\lambda \\in }\\left} . == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In these examples, the (negative) least absolute remainder is obtained from the least positive remainder by subtracting 5, which is d. This holds in general. When dividing by d, either both remainders are positive and therefore equal, or they have opposite signs. If the positive remainder is r1, and the negative one is r2, then r1 = r2 + d.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The set of positive matrices is a subset of all non-negative matrices. While such matrices are commonly found, the term is only occasionally used due to the possible confusion with positive-definite matrices, which are different. A matrix which is both non-negative and is positive semidefinite is called a doubly non-negative matrix. A rectangular non-negative matrix can be approximated by a decomposition with two other non-negative matrices via non-negative matrix factorization. Eigenvalues and eigenvectors of square positive matrices are described by the Perron\u2013Frobenius theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since its initial sound is aspirated, it can be represented as , and the word's phonetic representation would then be . (The precise features shown in a phonetic representation depend on whether a narrow or broad transcription is used and which features the writer wishes to draw attention to in a particular context.) When phones are considered to be realizations of the same phoneme, they are called allophones of that phoneme (more information on the methods of making such assignments can be found under phoneme). In English, for example,  and  are considered allophones of a single phoneme, which is written /p/. The phonemic transcriptions of those two words is thus /sp\u026an/ and /p\u026an/, and aspiration is then no longer shown since it is not distinctive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the parity problem refers to a limitation in sieve theory that prevents sieves from giving good estimates in many kinds of prime-counting problems. The problem was identified and named by Atle Selberg in 1949. Beginning around 1996, John Friedlander and Henryk Iwaniec developed some parity-sensitive sieves that make the parity problem less of an obstacle.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Pure type systems may obscure the distinction between types and terms and collapse the type hierarchy, as is the case with the calculus of constructions, but this is not generally the case, e.g. the simply typed lambda calculus allows only terms to depend on terms. Pure type systems were independently introduced by Stefano Berardi (1988) and Jan Terlouw (1989). Barendregt discussed them at length in his subsequent papers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can make the distribution a useful overdispersed alternative to the Poisson distribution, for example for a robust modification of Poisson regression. In epidemiology, it has been used to model disease transmission for infectious diseases where the likely number of onward infections may vary considerably from individual to individual and from setting to setting. More generally, it may be appropriate where events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term. The term \"negative binomial\" is likely due to the fact that a certain binomial coefficient that appears in the formula for the probability mass function of the distribution can be written more simply with negative numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They must be fitted with a speedometer and may not be used by children under 14.All three classes may be used on footways and cycle paths. Class 2 and 3 may be used on dual carriageways with a flashing amber beacon, and otherwise must comply with most other regulations pertaining to use of vehicles on the carriageway (e.g. lights and reflectors), though they are specifically excluded from the definition of \"motor vehicle\". All are banned from motorways. None of them cover the types described in the section above, which are ordinary motor vehicles subject to all regulations applicable to such.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, obfuscation is the act of creating source or machine code that is difficult for humans or computers to understand. Like obfuscation in natural language, it may use needlessly roundabout expressions to compose statements. Programmers may deliberately obfuscate code to conceal its purpose (security through obscurity) or its logic or implicit values embedded in it, primarily, in order to prevent tampering, deter reverse engineering, or even to create a puzzle or recreational challenge for someone reading the source code. This can be done manually or by using an automated tool, the latter being the preferred technique in industry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particle physics, preons are hypothetical point particles, conceived of as sub-components of quarks and leptons. The word was coined by Jogesh Pati and Abdus Salam, in 1974. Interest in preon models peaked in the 1980s but has slowed, as the Standard Model of particle physics continues to describe physics mostly successfully, and no direct experimental evidence for lepton and quark compositeness has been found.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In bra\u2013ket notation, this is typically denoted as \u03c8 + = | + \u27e9 {\\displaystyle {\\boldsymbol {\\psi }}_{+}=|+\\rangle } , and \u03c8 \u2212 = | \u2212 \u27e9 {\\displaystyle {\\boldsymbol {\\psi }}_{-}=|-\\rangle } . As above, kets and bras with the same label are interpreted as kets and bras corresponding to each other using the inner product. In particular, when also identified with row and column vectors, kets and bras with the same label are identified with Hermitian conjugate column and row vectors. Bra\u2013ket notation was effectively established in 1939 by Paul Dirac; it is thus also known as Dirac notation, despite the notation having a precursor in Hermann Grassmann's use of  {\\displaystyle } for inner products nearly 100 years earlier.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the ideal class group (or class group) of an algebraic number field K is the quotient group JK /PK where JK is the group of fractional ideals of the ring of integers of K, and PK is its subgroup of principal ideals. The class group is a measure of the extent to which unique factorization fails in the ring of integers of K. The order of the group, which is finite, is called the class number of K. The theory extends to Dedekind domains and their fields of fractions, for which the multiplicative properties are intimately tied to the structure of the class group. For example, the class group of a Dedekind domain is trivial if and only if the ring is a unique factorization domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One approach would be to modify the program-instructions (the ones stored in the registers) so that they contain more than one command. But this too can be exhausted unless an instruction is of (potentially) unbounded size. So why not use just one \"\u00fcber-instruction\" \u2013 one really really big number \u2013 that contains all the program instructions encoded into it!", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(The above properties relating to rows may be replaced by the corresponding statements with respect to columns.) Determinants occur throughout mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, the flow-equivalent server method (also known as flow-equivalent aggregation technique, Norton's theorem for queueing networks or the Chandy\u2013Herzog\u2013Woo method) is a divide-and-conquer method to solve product form queueing networks inspired by Norton's theorem for electrical circuits. The network is successively split into two, one portion is reconfigured to a closed network and evaluated. Marie's algorithm is a similar method where analysis of the sub-network are performed with state-dependent Poisson process arrivals. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The technique was extended to unit disk graphs by Schneider et al. The fastest deterministic algorithms for (\u0394 + 1)-coloring for small \u0394 are due to Leonid Barenboim, Michael Elkin and Fabian Kuhn. The algorithm by Barenboim et al. runs in time O(\u0394) + log*(n)/2, which is optimal in terms of n since the constant factor 1/2 cannot be improved due to Linial's lower bound. Panconesi & Srinivasan (1996) use network decompositions to compute a \u0394+1 coloring in time 2 O ( log \u2061 n ) {\\displaystyle 2^{O\\left({\\sqrt {\\log n}}\\right)}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A significant invention, which later had a profound effect on electronic music, was the audion in 1906. This was the first thermionic valve, or vacuum tube and which led to the generation and amplification of electrical signals, radio broadcasting, and electronic computation, among other things. Other early synthesizers included the Telharmonium (1897), the Theremin (1919), J\u00f6rg Mager's Spharophon (1924) and Partiturophone, Taubmann's similar Electronde (1933), Maurice Martenot's ondes Martenot (\"Martenot waves\", 1928), Trautwein's Trautonium (1930).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, oracle complexity is a standard theoretical framework to study the computational requirements for solving classes of optimization problems. It is suitable for analyzing iterative algorithms which proceed by computing local information about the objective function at various points (such as the function's value, gradient, Hessian etc.). The framework has been used to provide tight worst-case guarantees on the number of required iterations, for several important classes of optimization problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The distinction between BYOD and school-issued devices became blurred when many schools started recommending devices for parents to buy (examples for both iPads and Chromebooks being used 1:1 in schools, but being paid for by parents exist, there may be similar evidence for other devices). The term 1:1 computing in education is now redefined to a situation where students have access to a device per individual that is used in the teaching as a tool for learning. Historically, the programs have centered around the following devices: Laptops (Windows and Mac) 1990s-2010. iPads (with some competing Android and Windows devices) 2010-2014 Chromebooks (2015\u2013present) (with iPad+keyboard and other laptop & tablet-computers competing).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Tuple may be formally defined from ordered pairs by recurrence by starting from ordered pairs; indeed, a n-tuple can be identified with the ordered pair of its (n \u2212 1) first elements and its nth element. Tuples are usually written by listing the elements within parentheses \"( )\", separated by a comma and a space; for example, (2, 7, 4, 1, 7) denotes a 5-tuple. Sometimes other symbols are used to surround the elements, such as square brackets \"\" or angle brackets \"\u27e8 \u27e9\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Netherlands, there is coverage on all the lines and the old system called Telerail was abandoned in favour of GSM-R in 2006.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to ensure replica convergence, a system must reconcile differences between multiple copies of distributed data. This consists of two parts: exchanging versions or updates of data between servers (often known as anti-entropy); and choosing an appropriate final state when concurrent updates have occurred, called reconciliation.The most appropriate approach to reconciliation depends on the application. A widespread approach is \"last writer wins\". Another is to invoke a user-specified conflict handler.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Be aware that roundoff errors can accumulate. If M decimal places are used in the intermediate calculation, we say there are M\u2212N guard digits. Guard digits are also used in floating point operations in most computer systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic the theory of pure equality is a first-order theory. It has a signature consisting of only the equality relation symbol, and includes no non-logical axioms at all.This theory is consistent but incomplete, as a non-empty set with the usual equality relation provides an interpretation making certain sentences true. It is an example of a decidable theory and is a fragment of more expressive decidable theories, including monadic class of first-order logic (which also admits unary predicates and is, via Skolem normal form, related to set constraints in program analysis) and monadic second-order theory of a pure set (which additionally permits quantification over predicates and whose signature extends to monadic second-order logic of k successors).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hence, it cannot account for the correct or incorrect application of a name. He claimed that there was a natural correctness to names. To do this, he pointed out that compound words and phrases have a range of correctness.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "C libraries complying to POSIX or the Single Unix Specification (SUSv3) provided such routines as getcontext, setcontext, makecontext and swapcontext, but these functions were declared obsolete in POSIX 1.2008.Once a second call stack has been obtained with one of the methods listed above, the setjmp and longjmp functions in the standard C library can then be used to implement the switches between coroutines. These functions save and restore, respectively, the stack pointer, program counter, callee-saved registers, and any other internal state as required by the ABI, such that returning to a coroutine after having yielded restores all the state that would be restored upon returning from a function call. Minimalist implementations, which do not piggyback off the setjmp and longjmp functions, may achieve the same result via a small block of inline assembly which swaps merely the stack pointer and program counter, and clobbers all other registers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the distributed environment, one might have difficulties in keeping track of everyone's workload and contribution towards the deliverable. Through adoption of agile principles and practices, the visibility is made clearer as there are multiple iterations where one can visualize the issues or criticalities on the initial stages of the project. Continuous integration of programming code, which is one of the focal pieces of agile software development, additionally serves to reduce setup of the executive issues. Adopting of agile principles appears to positively affect correspondence between groups as advancement in cycles makes it simpler for members to see the short-term objectives.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, two non-empty subsets A and B of a given metric space (X, d) are said to be positively separated if the infimum inf a \u2208 A , b \u2208 B d ( a , b ) > 0. {\\displaystyle \\inf _{a\\in A,b\\in B}d(a,b)>0.} (Some authors also specify that A and B should be disjoint sets; however, this adds nothing to the definition, since if A and B have some common point p, then d(p, p) = 0, and so the infimum above is clearly 0 in that case.) For example, on the real line with the usual distance, the open intervals (0, 2) and (3, 4) are positively separated, while (3, 4) and (4, 5) are not. In two dimensions, the graph of y = 1/x for x > 0 and the x-axis are not positively separated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Formally, given a set of data points x, the k centers ci are to be chosen so as to minimize the sum of the distances from each x to the nearest ci. The criterion function formulated in this way is sometimes a better criterion than that used in the k-means clustering algorithm, in which the sum of the squared distances is used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The programmer would change the one-word BR to the two-word JMP instruction from the next group. As JMP has no conditional forms, the programmer would change BEQ to a BNE that branched around a JMP. SOB (Subtract One and Branch) is another conditional branch instruction. The specified register is decremented by 1, and if the result is not zero, a reverse branch is taken based on the 6 bit word offset.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern operating systems, non-system (i.e. user-mode) applications are prevented from accessing any memory locations not explicitly authorized by the virtual memory controller (called memory management unit (MMU)). In addition to containing damage that may be caused by software flaws and allowing more efficient use of physical memory, this architecture forms an integral part of the security of the operating system. However, kernel-mode drivers, many hardware devices, and user-mode vulnerabilities allow direct, unimpeded access of the physical memory address space. The physical address space includes all of the main system memory, as well as memory-mapped buses and hardware devices (which are controlled by the operating system through reads and writes as if they were ordinary RAM).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a nonnegative matrix, written X \u2265 0 , {\\displaystyle \\mathbf {X} \\geq 0,} is a matrix in which all the elements are equal to or greater than zero, that is, x i j \u2265 0 \u2200 i , j . {\\displaystyle x_{ij}\\geq 0\\qquad \\forall {i,j}.} A positive matrix is a matrix in which all the elements are strictly greater than zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the EAV table itself, this is just an attribute ID, a foreign key into an Attribute Definitions table, as stated above. However, there are usually multiple metadata tables that contain attribute-related information, and these are discussed shortly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1880s Herman Hollerith invented the recording of data on a medium that could then be read by a machine. Prior uses of machine readable media had been for lists of instructions (not data) to drive programmed machines such as Jacquard looms and mechanized musical instruments. \"After some initial trials with paper tape, he settled on punched cards \".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, equation (5) applied successively, provides an algorithm to estimate our ground truth x n e w {\\displaystyle \\mathbf {x} _{new}} by ascending (since it moves in the direction of the gradient of the likelihood) in the likelihood landscape. It has not been demonstrated in this derivation that it converges and no dependence on the initial choice is shown. Note that equation (2) provides a way of following the direction that increases the likelihood but the choice of the log-derivative is arbitrary.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "More precisely, letting X = X(t,m) be the minimal number of cuts required to split the necklace. The following holds as m tends to infinity. For any s < ( t + 1 ) / 2 {\\displaystyle s<(t+1)/2} P ( X = s ) = \u0398 ( m s \u2212 ( t + 1 ) / 2 ) . {\\displaystyle \\mathbb {P} (X=s)=\\Theta {\\big (}m^{s-(t+1)/2}{\\big )}.} For any ( t + 1 ) / 2 < s \u2264 t {\\displaystyle (t+1)/2", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead of repeating step two to convergence, it may be formulated and solved as a set of linear equations. These equations are merely obtained by making s = s \u2032 {\\displaystyle s=s'} in the step two equation. Thus, repeating step two to convergence can be interpreted as solving the linear equations by relaxation. This variant has the advantage that there is a definite stopping condition: when the array \u03c0 {\\displaystyle \\pi } does not change in the course of applying step 1 to all states, the algorithm is completed. Policy iteration is usually slower than value iteration for a large number of possible states.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, Cantor's diagonal argument, also called the diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof, was published in 1891 by Georg Cantor as a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers. : 20\u2013 Such sets are now known as uncountable sets, and the size of infinite sets is now treated by the theory of cardinal numbers which Cantor began. The diagonal argument was not Cantor's first proof of the uncountability of the real numbers, which appeared in 1874.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The discrepancy (irregularity) measures how far a given distribution deviates from an ideal one. Discrepancy theory can be described as the study of inevitable irregularities of distributions, in measure-theoretic and combinatorial settings. Just as Ramsey theory elucidates the impossibility of total disorder, discrepancy theory studies the deviations from total uniformity. A significant event in the history of discrepancy theory was the 1916 paper of Weyl on the uniform distribution of sequences in the unit interval.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most dialects of American English, speakers have a process known as intervocalic alveolar flapping that changes the consonants /t/ and /d/ into a quick flap consonant () in words such as \"butter\" () and \"notable\" (). The stop consonants /t/ and /d/ only become a flap in between two vowels, where the first vowel is stressed and the second is stressless. It is common to represent phonological rules using formal rewrite rules in the most general way possible. Thus, the intervocalic alveolar flapping described above can be formalized as", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A rainbow set is a conflict-free set in the special case in which GO is made of disjoint cliques, where each clique represents a color.Conflict-free set cover is the problem of finding a conflict-free subset of O that is a covering of P. Banik, Panolan, Raman, Sahlot and Saurabh prove the following for the special case in which the conflict-graph has bounded arboricity: If the geometric cover problem is fixed-parameter tractable (FPT), then the conflict-free geometric cover problem is FPT. If the geometric cover problem admits an r-approximation algorithm, then the conflict-free geometric cover problem admits a similar approximation algorithm in FPT time. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, the Friedberg\u2013Muchnik theorem is a theorem about Turing reductions that was proven independently by Albert Muchnik and Richard Friedberg in the middle of the 1950s. It is a more general view of the Kleene\u2013Post theorem. The Kleene\u2013Post theorem states that there exist incomparable languages A and B below K. The Friedberg\u2013Muchnik theorem states that there exist incomparable, computably enumerable languages A and B. Incomparable meaning that there does not exist a Turing reduction from A to B or a Turing reduction from B to A. It is notable for its use of the priority finite injury approach.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions with probability density function f ( x ) = ( a / b ) p / 2 2 K p ( a b ) x ( p \u2212 1 ) e \u2212 ( a x + b / x ) / 2 , x > 0 , {\\displaystyle f(x)={\\frac {(a/b)^{p/2}}{2K_{p}({\\sqrt {ab}})}}x^{(p-1)}e^{-(ax+b/x)/2},\\qquad x>0,} where Kp is a modified Bessel function of the second kind, a > 0, b > 0 and p a real parameter. It is used extensively in geostatistics, statistical linguistics, finance, etc. This distribution was first proposed by \u00c9tienne Halphen. It was rediscovered and popularised by Ole Barndorff-Nielsen, who called it the generalized inverse Gaussian distribution. Its statistical properties are discussed in Bent J\u00f8rgensen's lecture notes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recreational mathematics, many problems concern the properties of numbers under concatenation of their numerals in some base. Examples include home primes (primes obtained by repeatedly factoring the increasing concatenation of prime factors of a given number), Smarandache\u2013Wellin numbers (the concatenations of the first prime numbers), and the Champernowne and Copeland\u2013Erd\u0151s constants (the real numbers formed by the decimal representations of the positive integers and the prime numbers, respectively).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Language is not an arbitrary set of conventions but a way of thinking and representing the world to oneself. It is not a conditioning process, but one in which the learner actively organizes his perceptions into linguistics concepts.The series method is a variety of the direct method in that experiences are directly connected to the target language. There are three reasons that Gouin preceded psycholinguistic theory of the 20th century.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., m \u00d7 n for an m \u00d7 n matrix) is sometimes referred to as the sparsity of the matrix.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In a completely regular semigroup, each Green H-class is a group and the semigroup is the union of these groups. Hence completely regular semigroups are also referred to as \"unions of groups\". Epigroups generalize this notion and their class includes all completely regular semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x + 3 = y {\\displaystyle x+3=y} is satisfiable because it is true when x = 3 {\\displaystyle x=3} and y = 6 {\\displaystyle y=6} , while the formula x + 1 = x {\\displaystyle x+1=x} is not satisfiable over the integers. The dual concept to satisfiability is validity; a formula is valid if every assignment of values to its variables makes the formula true. For example, x + 3 = 3 + x {\\displaystyle x+3=3+x} is valid over the integers, but x + 3 = y {\\displaystyle x+3=y} is not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In matroid theory, the dual of a matroid M {\\displaystyle M} is another matroid M \u2217 {\\displaystyle M^{\\ast }} that has the same elements as M {\\displaystyle M} , and in which a set is independent if and only if M {\\displaystyle M} has a basis set disjoint from it.Matroid duals go back to the original paper by Hassler Whitney defining matroids. They generalize to matroids the notions of plane graph duality.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the map segmentation problem is a kind of optimization problem. It involves a certain geographic region that has to be partitioned into smaller sub-regions in order to achieve a certain goal. Typical optimization objectives include: Minimizing the workload of a fleet of vehicles assigned to the sub-regions; Balancing the consumption of a resource, as in fair cake-cutting. Determining the optimal locations of supply depots; Maximizing the surveillance coverage.Fair division of land has been an important issue since ancient times, e.g. in ancient Greece.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If data models are developed on a system by system basis, then not only is the same analysis repeated in overlapping areas, but further analysis must be performed to create the interfaces between them. Most systems within an organization contain the same basic data, redeveloped for a specific purpose. Therefore, an efficiently designed basic data model can minimize rework with minimal modifications for the purposes of different systems within the organization", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1990s Sun-Joo Shin presented an extension of Existential Graphs called Venn-II. Syntax and semantics are given formally, together with a set of Rules of Transformation which are shown to be sound and complete. Proofs proceed by applying the rules (which remove or add syntactic elements to or from diagrams) sequentially. Venn-II is equivalent in expressive power to a first-order monadic language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To overcome the problems, some applications may simply attempt to replace the decomposed characters with the equivalent precomposed characters. With an incomplete font, however, precomposed characters may also be problematic \u2013 especially if they are more exotic, as in the following example (showing the reconstructed Proto-Indo-European word for \"dog\"): \u1e31\u1e77\u1e53n (U+1E31 U+1E77 U+1E53 U+006E) \u1e31\u1e77\u1e53n (U+006B U+0301 U+0075 U+032D U+006F U+0304 U+0301 U+006E)In some situations, the precomposed green k, u and o with diacritics may render as unrecognized characters, or their typographical appearance may be very different from the final letter n with no diacritic. On the second line, the base letters should at least render correctly even if the combining diacritics could not be recognized. OpenType has the ccmp \"feature tag\" to define glyphs that are compositions or decompositions involving combining characters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In painting and other visual arts, two-dimensional color wheels or three-dimensional color solids are used to represent the essential relationships between colors. The split-primary palette is a color-wheel model that attempts to explain, and to compensate for, the unsatisfactory results often produced when mixing the traditional primary colors, red, yellow, and blue. Painters have long considered red, yellow, and blue to be primary colors. In practice, however, many of the mixtures produced from these colors lack chromatic intensity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For instance, the product of type1, ..., typen is written type1*...*typen in ML and (type1,...,typen) in Haskell. In both these languages, tuples are written (v1,...,vn) and the components of a tuple are extracted by pattern-matching. Additionally, many functional programming languages provide more general algebraic data types, which extend both product and sum types. Product types are the dual of sum types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM\u2013GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same (in which case they are both that number). The simplest non-trivial case \u2013 i.e., with more than one variable \u2013 for two non-negative numbers x and y, is the statement that x + y 2 \u2265 x y {\\displaystyle {\\frac {x+y}{2}}\\geq {\\sqrt {xy}}} with equality if and only if x = y. This case can be seen from the fact that the square of a real number is always non-negative (greater than or equal to zero) and from the elementary case (a \u00b1 b)2 = a2 \u00b1 2ab + b2 of the binomial formula: 0 \u2264 ( x \u2212 y ) 2 = x 2 \u2212 2 x y + y 2 = x 2 + 2 x y + y 2 \u2212 4 x y = ( x + y ) 2 \u2212 4 x y . {\\displaystyle {\\begin{aligned}0&\\leq (x-y)^{2}\\\\&=x^{2}-2xy+y^{2}\\\\&=x^{2}+2xy+y^{2}-4xy\\\\&=(x+y)^{2}-4xy.\\end{aligned}}} Hence (x + y)2 \u2265 4xy, with equality precisely when (x \u2212 y)2 = 0, i.e. x = y. The AM\u2013GM inequality then follows from taking the positive square root of both sides and then dividing both sides by 2. For a geometrical interpretation, consider a rectangle with sides of length x and y, hence it has perimeter 2x + 2y and area xy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public policy a polycentric network is a group of distinct local, regional, or national entities that work co-operatively towards a common goal. Proponents claim that such networks can better adapt to changing issues collectively than individually, thus providing network participants better results from relevant efforts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent years, scientists and audio engineers have been developing smartphone apps to conduct sound measurements, similar to the standalone sound level meters and dosimeters. In 2014, the National Institute for Occupational Safety and Health (NIOSH) within the Centers for Disease Control and Prevention (CDC) published a study examining the efficacy of 192 sound measurement apps on Apple and Android smartphones.The authors found that only 10 apps, all of which were on the App Store, met all acceptability criteria. Of these 10 apps, only 4 apps met accuracy criteria within 2 dB(A) from the reference standard. As a result of this study, they created the NIOSH Sound Level Meter App to increase accessibility and decrease costs of monitoring noise using crowdsourcing data with a tested and highly accurate application.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, signals exhibiting cyclicity with more than one incommensurate period arise and require a generalization of the theory of cyclostationarity. Such signals are called polycyclostationary if they exhibit a finite number of incommensurate periods and almost cyclostationary if they exhibit a countably infinite number. Such signals arise frequently in radio communications due to multiple transmissions with differing sine-wave carrier frequencies and digital symbol rates. The theory was introduced in for stochastic processes and further developed in for non-stochastic time series.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mobile networks, the terminal adapter is used by the terminal equipment to access the mobile termination, using AT commands (see Hayes command set). In 2G (such as GSM or CDMA), the terminal adapter is a theoretically optional while in 3G (such as W-CDMA), the terminal adapter is mandatory and is part of the mobile termination.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most regions, Google Pay on Android permits the issuing bank to determine whether to allow its payment cards to be able to transmit when the mobile device is locked under a certain monetary amount. Issuers in Argentina, Brazil, Ecuador, Mexico, and the United States of America cannot allow locked-device payments except for select transit transactions.On Wear OS, this option is not available. All transactions for all amounts on wearable devices must be authenticated by opening the Wallet app prior to tapping.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programming languages, an implicit declaration is provided the first time such a variable is encountered at compile time. In other languages, such a usage is considered to be an error, which may result in a diagnostic message. Some languages have started out with the implicit declaration behavior, but as they matured they provided an option to disable it (e.g. Perl's \"use strict\" or Visual Basic's \"Option Explicit\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Flames' next two albums, Soundtrack to Your Escape (2004) and Come Clarity (2006), peaked at numbers 145 and 58 on the Billboard 200, respectively, with the latter album giving In Flames a Swedish Grammy Award. The Black Dahlia Murder, Arch Enemy, Children of Bodom, and Amon Amarth also enter the Billboard 200 during the 2000s decade. In the mid\u2013late 2000s, melodic metalcore became one of the most popular heavy metal genres, with bands like Killswitch Engage, Unearth, Bullet for My Valentine, All That Remains, Shadows Fall and Atreyu achieving success, headlining major festivals and selling a lot of records.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the algorithm, \u03b1k is chosen such that r k + 1 {\\displaystyle \\mathbf {r} _{k+1}} is orthogonal to r k {\\displaystyle \\mathbf {r} _{k}} . The denominator is simplified from \u03b1 k = r k T r k r k T A p k = r k T r k p k T A p k {\\displaystyle \\alpha _{k}={\\frac {\\mathbf {r} _{k}^{\\mathsf {T}}\\mathbf {r} _{k}}{\\mathbf {r} _{k}^{\\mathsf {T}}\\mathbf {A} \\mathbf {p} _{k}}}={\\frac {\\mathbf {r} _{k}^{\\mathsf {T}}\\mathbf {r} _{k}}{\\mathbf {p} _{k}^{\\mathsf {T}}\\mathbf {Ap} _{k}}}} since r k + 1 = p k + 1 \u2212 \u03b2 k p k {\\displaystyle \\mathbf {r} _{k+1}=\\mathbf {p} _{k+1}-\\mathbf {\\beta } _{k}\\mathbf {p} _{k}} . The \u03b2k is chosen such that p k + 1 {\\displaystyle \\mathbf {p} _{k+1}} is conjugate to p k {\\displaystyle \\mathbf {p} _{k}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In an adaptation of LPT called restricted LPT or RLPT, inputs are assigned in pairs - one to each machine (for m=2 machines). The resulting partition is balanced by design. Coffman, Frederickson and Lueker show that the expected largest sum of RLPT when inputs are uniformly-distributed random variables is exactly n 4 + 1 2 n + 2 {\\displaystyle {\\frac {n}{4}}+{\\frac {1}{2n+2}}} . The expected difference between the largest and smallest sum is \u0398 ( 1 / n ) {\\displaystyle \\Theta (1/n)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The unit number or command code occupies the first 4 of the 5 bits. The final bit is a 0 for a unit code and a 1 for a command code. Multiple unit codes may be transmitted in sequence before a command code is finally sent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the net gain expressed in dB is negative, it is also called the net loss. If the net gain is expressed as a ratio, and the ratio is less than unity, a net loss is indicated. The test signal must be chosen so that its power level is within the usual operating range of the circuit being tested.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Let C A {\\displaystyle C^{A}} (also written A C {\\displaystyle ^{A}C} ) denote the class of sets that fulfill the function property. This is the class of functions from A {\\displaystyle A} to C {\\displaystyle C} in a pure set theory. Below the notation x \u2192 y {\\displaystyle x\\to y} is also used for y x {\\displaystyle y^{x}} , for the sake of distinguishing it from ordinal exponentiation. When functions are understood as just function graphs as above, the membership proposition f \u2208 C A {\\displaystyle f\\in C^{A}} is also written f: A \u2192 C {\\displaystyle f\\colon A\\to C} . The boolean-valued \u03c7 B: A \u2192 { 0 , 1 } {\\displaystyle \\chi _{B}\\colon A\\to \\{0,1\\}} are among the classes discussed next.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In radio communication systems, information is carried across space using radio waves. At the sending end, the information to be sent is converted by some type of transducer to a time-varying electrical signal called the modulation signal. The modulation signal may be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal consisting of a sequence of bits representing binary data from a computer. The modulation signal is applied to a radio transmitter.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The associativity up to isomorphism is then a way of expressing that different ways of aggregating the same data\u2014such as ( ( a , b ) , c ) {\\displaystyle ((a,b),c)} and ( a , ( b , c ) ) {\\displaystyle (a,(b,c))} \u2014store the same information even though the aggregate values need not be the same. The aggregate type may be analogous to the operation of addition (type sum) or of multiplication (type product). For type product, the identity object is the unit ( ) {\\displaystyle ()} , so there is only one inhabitant of the type, and that is why a product with it is always isomorphic to the other operand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Its first known appearance in a technical paper was in a 2003 paper by Austrian researcher Leo Sauermann.Many of the existing semantic wiki applications were started in the mid-2000s, including ArtificialMemory (2004), Semantic MediaWiki (2005), Freebase (2005), and OntoWiki (2006). June 2006 saw the first meeting dedicated to semantic wikis, the \"SemWiki\" workshop, co-located with the European Semantic Web Conference in Montenegro. This workshop ran annually until 2010.The site DBpedia, launched in 2007, though not a semantic wiki, publishes structured data from Wikipedia in RDF form, which enables semantic querying of Wikipedia's data. In March 2008, Wikia, the world's largest wiki farm, made the use of Semantic MediaWiki available for all their wikis on request, thus allowing all the wikis they hosted to function as semantic wikis. However, since upgrading to version 1.19 of MediaWiki in 2013, they have stopped supporting Semantic MediaWiki for new requests on the basis of performance problem.In July 2010, Google purchased Metaweb, the company behind Freebase.In April 2012, work began on Wikidata, a collaborative, multi-language store of data, whose data could then be used within Wikipedia articles, as well as by the outside world.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of classification of groups, there is an essentially unique group containing exactly 2 elements. Similarly, there is also an essentially unique group containing exactly 3 elements: the cyclic group of order three. In fact, regardless of how one chooses to write the three elements and denote the group operation, all such groups can be shown to be isomorphic to each other, and hence are \"the same\". On the other hand, there does not exist an essentially unique group with exactly 4 elements, as there are in this case two non-isomorphic groups in total: the cyclic group of order 4 and the Klein four group.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, mirror descent is an iterative optimization algorithm for finding a local minimum of a differentiable function. It generalizes algorithms such as gradient descent and multiplicative weights.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early years, a prepaid mobile phone could only be used within the network of the operator from which the customer purchased the phone. It was not possible to roam onto other GSM networks when using the phone abroad. This was because the operator had no way to bill calls in real time from another network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a Carmichael number is a composite number n {\\displaystyle n} , which in modular arithmetic satisfies the congruence relation: b n \u2261 b ( mod n ) {\\displaystyle b^{n}\\equiv b{\\pmod {n}}} for all integers b {\\displaystyle b} . The relation may also be expressed in the form: b n \u2212 1 \u2261 1 ( mod n ) {\\displaystyle b^{n-1}\\equiv 1{\\pmod {n}}} .for all integers b {\\displaystyle b} which are relatively prime to n {\\displaystyle n} . Carmichael numbers are named after American mathematician Robert Carmichael, the term having been introduced by Nicolaas Beeger in 1950 (\u00d8ystein Ore had referred to them in 1948 as numbers with the \"Fermat property\", or \"F numbers\" for short).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators. The technique is now commonly applied to problems in physics, but has its origins in attempts to give precise meanings to ill-conditioned sums appearing in number theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Some significant work was also done on percolation on random graphs. From a physicist's point of view this would still be a mean-field model, so the justification of the research is often formulated in terms of the robustness of the graph, viewed as a communication network. Given a random graph of n \u226b 1 nodes with an average degree \u27e8 k \u27e9 {\\displaystyle \\langle k\\rangle } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Third person singular pronouns in English also have a gender feature: \"she\" is , \"he\"  and \"it . Different lexical categories realise or are specified for different grammatical features: for example, verbs in English are specified for tense, aspect and mood features, as well as person and number. The features that a category realises can also differ from language to language.There is often a correspondence between morphological and syntactic features, in that certain features, such as person, are relevant to both morphology and syntax; these are known as morphosyntactic features.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In principle, however, this could also signify that a parametric test has been employed in a situation where all parametric assumptions are fully met, but it is in most cases impossible to prove this completely in a real-world situation. Exceptions in which it is certain that parametric tests are exact include tests based on the binomial or Poisson distributions. The term permutation test is sometimes used as a synonym for exact test, but it should be kept in mind that all permutation tests are exact tests, but not all exact tests are permutation tests.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This vector corresponds to the stationary distribution of the Markov chain represented by the row-normalized adjacency matrix; however, the adjacency matrix must first be modified to ensure a stationary distribution exists. The second smallest eigenvector can be used to partition the graph into clusters, via spectral clustering. Other methods are also available for clustering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establish a general framework for these algebras, which culminated in a series of papers on rings of operators. These papers considered a special class of C*-algebras which are now known as von Neumann algebras.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another is defined the same way, but using split octonions instead of octonions. The final is constructed from the non-split octonions using a different standard involution. Over any algebraically closed field, there is just one Albert algebra, and its automorphism group G is the simple split group of type F4.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a set of natural numbers is called a K-trivial set if its initial segments viewed as binary strings are easy to describe: the prefix-free Kolmogorov complexity is as low as possible, close to that of a computable set. Solovay proved in 1975 that a set can be K-trivial without being computable. The Schnorr\u2013Levin theorem says that random sets have a high initial segment complexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United Kingdom and other parts of the Commonwealth of Nations, an equivalent service to direct distance dialing is subscriber trunk dialing (STD), and ISD for international subscriber trunk dialing. Queen Elizabeth II inaugurated STD on 5 December 1958, when she dialed a call from Bristol to Edinburgh and spoke to the Lord Provost.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the ETen (\u501a\u5929) Chinese operating system, the following code points are added, to add support for some characters present in the IBM 5550's code page but absent from generic Big5: 0xA3C0\u20130xA3E0: 33 control characters. 0xC6A1\u20130xC875: circle 1\u201310, bracket 1\u201310, Roman numerals 1\u20139 (i\u2013ix), CJK radical glyphs, Japanese hiragana, Japanese katakana, Cyrillic characters 0xF9D6\u20130xF9FE: the characters '\u7881', '\u92b9', '\u6052', '\u88cf', '\u58bb', '\u7ca7' and '\u5afa', followed by 34 additional semigraphic symbols.In some versions of ETen, there are extra graphical symbols and simplified Chinese characters.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, overhead can influence the decision whether or not to include features in new products, or indeed whether to fix bugs. A feature that has a high overhead may not be included \u2013 or needs a big financial incentive to do so. Often, even though software providers are well aware of bugs in their products, the payoff of fixing them is not worth the reward, because of the overhead. For example, an implicit data structure or succinct data structure may provide low space overhead, but at the cost of slow performance (space/time tradeoff).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the problem of non-negative least squares (NNLS) is a type of constrained least squares problem where the coefficients are not allowed to become negative. That is, given a matrix A and a (column) vector of response variables y, the goal is to find a r g m i n x \u2061 \u2016 A x \u2212 y \u2016 2 2 {\\displaystyle \\operatorname {arg\\,min} \\limits _{\\mathbf {x} }\\|\\mathbf {Ax} -\\mathbf {y} \\|_{2}^{2}} subject to x \u2265 0.Here x \u2265 0 means that each component of the vector x should be non-negative, and \u2016\u00b7\u20162 denotes the Euclidean norm. Non-negative least squares problems turn up as subproblems in matrix decomposition, e.g. in algorithms for PARAFAC and non-negative matrix/tensor factorization. The latter can be considered a generalization of NNLS.Another generalization of NNLS is bounded-variable least squares (BVLS), with simultaneous upper and lower bounds \u03b1i \u2264 xi \u2264 \u03b2i. : 291", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Doing this is only a win if the subexpression computation costs more in time than fetching from memory, which in most stack CPUs, almost always is the case. It is never worthwhile for simple variables and pointer fetches, because those already have the same cost of one data cache cycle per access. It is only marginally worthwhile for expressions such as X+1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, taxation of sodium has been proposed as a method of decreasing sodium intake and thereby improving health in countries where typical salt consumption is high. Taking an alternative view, the Salt Institute, a salt industry body based in North America, is active in promoting the use of salt, and questioning or opposing the recommended restrictions on salt intake.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the exhaustive recall method, participants are asked to record all the memories they can access before a specific age. This method, like free recall, relies on participants to come up with memories without cues. Exhaustive recall yields a better understanding than others on the number of memories surviving from early childhood but can be demanding for the subjects who often have to spend many hours trying to remember events from their childhood. No major differences among word cued, interview, focused and exhaustive recall have been found.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This problem is NP-complete, implying that neither it nor the optimization problem are expected to have polynomial time algorithms. It was one of Richard M. Karp's original set of 21 NP-complete problems; its NP-completeness was proved by Karp and Eugene Lawler by showing that inputs for another hard problem, the vertex cover problem, could be transformed (\"reduced\") into equivalent inputs to the feedback arc set decision problem.Some NP-complete problems can become easier when their inputs are restricted to special cases. But for the most important special case of the feedback arc set problem, the case of tournaments, the problem remains NP-complete.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis. Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of a clinical trial, quality typically refers to the absence of errors which can impact decision making, both during the conduct of the trial and in use of the trial results.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The main market for RISC CPUs has been systems that need low power or small size. Even some CISC processors (based on architectures that were created before RISC grew dominant), such as newer x86 processors, translate instructions internally into a RISC-like instruction set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, prediction is a part of statistical inference. One particular approach to such inference is known as predictive inference, but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides a means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as forecasting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the book that was published in 1572, entitled Algebra, Bombelli gave a comprehensive account of the algebra known at the time. He was the first European to write down the way of performing computations with negative numbers. The following is an excerpt from the text: \"Plus times plus makes plus Minus times minus makes plus Plus times minus makes minus Minus times plus makes minus Plus 8 times plus 8 makes plus 64 Minus 5 times minus 6 makes plus 30 Minus 4 times plus 5 makes minus 20 Plus 5 times minus 4 makes minus 20\" As was intended, Bombelli used simple language as can be seen above so that anybody could understand it. But at the same time, he was thorough.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\mathbb {Q} ({\\sqrt {c}}).} In this field every element may be uniquely written \u03b1 + \u03b2 c , {\\displaystyle \\alpha +\\beta {\\sqrt {c}},} with \u03b1 {\\displaystyle \\alpha } and \u03b2 {\\displaystyle \\beta } being rational numbers. This implies that \u00b1 2 x y {\\displaystyle \\pm 2{\\sqrt {xy}}} is not rational (otherwise the right-hand side of the equation would be rational; but the left-hand side is irrational).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, it is more important to minimize the total length of the cuts (e.g. to minimize the cost of performing the partition, or to minimize the amount of dust). This problem is called minimum edge-length rectangular partitioning. It was first studied by Lingas, Pinter, Rivest and Shamir in 1982. The run-time complexity of this problem crucially depends on whether the raw polygon is allowed to have holes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The NIHR Quality, Safety and Outcomes Policy Research Unit has focused on measuring and assessing the integration of services. They began by examining whether measures were available to assess processes and outcomes of integration of services. They found a very large number of available measures but the infrequent use of any common set of measures made comparisons between systems very difficult.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In model theory, the notion of an algebraic structure is generalized to structures involving both operations and relations. Let L be a signature consisting of function and relation symbols, and A, B be two L-structures. Then a homomorphism from A to B is a mapping h from the domain of A to the domain of B such that h(FA(a1,\u2026,an)) = FB(h(a1),\u2026,h(an)) for each n-ary function symbol F in L, RA(a1,\u2026,an) implies RB(h(a1),\u2026,h(an)) for each n-ary relation symbol R in L.In the special case with just one binary relation, we obtain the notion of a graph homomorphism.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the body of a generic unit, the (formal) type parameter is handled like its upper bound (expressed with extends; Object if not constrained). If the return type of a method is the type parameter, the result (e.g. of type ?) can be referenced by a variable of the type of the upper bound (or Object). In the other direction, the wildcard fits no other type, not even Object: If ?", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of two enemies sharing a friend, the shared friend is likely to choose one over the other and turn one of his or her friendships into an enemy. Antal, Krapivsky and Reder consider social dynamics as the change in sign on an edge of a signed graph. The social relations with previous friends of a divorcing couple are used to illustrate the evolution of a signed graph in society.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ": \"addictive * of biblioscopy\".) To emulate unordered search of the NEAR operator can be done using a combination of ordered searches. For example, to specify a close co-occurrence of \"house\" and \"dog\", the following search-expression could be specified: \"house dog\" OR \"dog house\" OR \"house * dog\" OR \"dog * house\" OR \"house * * dog\" OR \"dog * * house\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, the network simplex algorithm is a graph theoretic specialization of the simplex algorithm. The algorithm is usually formulated in terms of a minimum-cost flow problem. The network simplex method works very well in practice, typically 200 to 300 times faster than the simplex method applied to general linear program of same dimensions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Recursion though may be achieved by obtaining the same function passed in as an argument, and then using that argument to make the recursive call, instead of using the function's own name, as is done in languages which do support recursion natively. The Y combinator demonstrates this style of programming. An example implementation of Y combinator in two languages is presented below.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The values ISO 639-3, clergyman, clergymen are plain character strings. The value eng is taken from the list of languages as defined by ISO 639-3. With some additional information like dtdVersion and feat, the same data can be expressed by the following XML fragment: This example is rather simple, while LMF can represent much more complex linguistic descriptions the XML tagging is correspondingly complex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most cases the same mechanisms must be applied as in the positioning of an image or text content.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These occur when microorganisms only come into contact with disinfectants but are not killed by them. When ascertaining the cleanability of a surface with regard to particles, the analysis can be carried out in correlation with the surface cleanliness classes described in VDI 2083 Part 9.1. Surface roughness can be measured, for example, using profile methods (DIN EN ISO 11562) or AFM (atomic force microscope). However, no norm is currently in existence which describes a standardized AFM procedure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The request is forwarded to (performed on) all objects downwards the tree structure. The NonTerminalExpression objects (ntExpr1,ntExpr2) forward the request to their child expressions. The TerminalExpression objects (tExpr1,tExpr2,\u2026) perform the interpretation directly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, time may be required to obtain approval of the transaction by government agencies, shareholders, labor unions, lenders, or others. Until the transaction is completed, the companies involved go on about their business and are subject to risks. Contract terms that deal with material adverse changes are carefully negotiated by the parties and take into account the relevant circumstances of each party.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, as more classes are added to a program, especially during maintenance and/or refactoring, the problem of communication between these classes may become more complex. This makes the program harder to read and maintain. Furthermore, it can become difficult to change the program, since any change may affect code in several other classes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Church encoding is a means of representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named for Alonzo Church, who first encoded data in the lambda calculus this way.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "CbD essentially coincides with the probabilistic part of Abramsky's sheaf-theoretic approach if the system is strongly consistently connected, which means that the joint distributions of { R q 1 c , \u2026 , R q k c } {\\displaystyle \\left\\{R_{q_{1}}^{c},\\ldots ,R_{q_{k}}^{c}\\right\\}} and { R q 1 c \u2032 , \u2026 , R q k c \u2032 } {\\displaystyle \\left\\{R_{q_{1}}^{c'},\\ldots ,R_{q_{k}}^{c'}\\right\\}} coincide whenever q 1 , \u2026 , q k {\\displaystyle q_{1},\\ldots ,q_{k}} are measured in contexts c , c \u2032 {\\displaystyle c,c'} . However, unlike most approaches to contextuality, CbD allows for inconsistent connectedness, with R q c {\\displaystyle R_{q}^{c}} and R q c \u2032 {\\displaystyle R_{q}^{c'}} differently distributed. This makes CbD applicable to physics experiments in which no-disturbance condition is violated, as well as to human behavior where this condition is violated as a rule. In particular, Vctor Cervantes, Ehtibar Dzhafarov, and colleagues have demonstrated that random variables describing certain paradigms of simple decision making form contextual systems, whereas many other decision-making systems are noncontextual once their inconsistent connectedness is properly taken into account.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the English language, a compound sentence is composed of at least two independent clauses. It does not require a dependent clause. The clauses are joined by a coordinating conjunction, a semicolon that functions as a conjunction, a colon instead of a semicolon between two sentences when the second sentence explains or illustrates the first sentence and no coordinating conjunction is being used to connect the sentences, or a conjunctive adverb preceded by a semicolon. A conjunction can be used to make a compound sentence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum computing, Grover's algorithm, also known as the quantum search algorithm, refers to a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just O ( N ) {\\displaystyle O({\\sqrt {N}})} evaluations of the function, where N {\\displaystyle N} is the size of the function's domain. It was devised by Lov Grover in 1996.The analogous problem in classical computation cannot be solved in fewer than O ( N ) {\\displaystyle O(N)} evaluations (because, on average, one has to check half of the domain to get a 50% chance of finding the right input). Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani proved that any quantum solution to the problem needs to evaluate the function \u03a9 ( N ) {\\displaystyle \\Omega ({\\sqrt {N}})} times, so Grover's algorithm is asymptotically optimal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Modern x86 is relatively uncommon in embedded systems, however, and small low power applications (using tiny batteries), and low-cost microprocessor markets, such as home appliances and toys, lack significant x86 presence. Simple 8- and 16-bit based architectures are common here, as well as simpler RISC architectures like RISC-V, although the x86-compatible VIA C7, VIA Nano, AMD's Geode, Athlon Neo and Intel Atom are examples of 32- and 64-bit designs used in some relatively low-power and low-cost segments. There have been several attempts, including by Intel, to end the market dominance of the \"inelegant\" x86 architecture designed directly from the first simple 8-bit microprocessors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since entrenched CEO pay their workers high salaries, the CEO-worker relationship improves, making workers less likely to unionize. Often workers perceive managers' benefits to be more beneficial for them than unions. This leads us to the conclusion that entrenched CEOs have the characteristic of being very competitive when it comes to work loyalty. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In predicate logic, existential generalization (also known as existential introduction, \u2203I) is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier ( \u2203 {\\displaystyle \\exists } ) in formal proofs. Example: \"Rover loves to wag his tail. Therefore, something loves to wag its tail.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Differential equations or difference equations on such graphs can be employed to leverage the graph's structure for tasks such as image segmentation (where the vertices represent pixels and the weighted edges encode pixel similarity based on comparisons of Moore neighborhoods or larger windows), data clustering, data classification, or community detection in a social network (where the vertices represent users of the network, the edges represent links between users, and the weight function indicates the strength of interactions between users). The main advantage of finite weighted graphs is that by not being restricted to highly regular structures such as discrete regular grids, lattice graphs, or meshes, they can be applied to represent abstract data with irregular interrelationships. If a finite weighted graph is geometrically embedded in a Euclidean space, i.e., the graph vertices represent points of this space, then it can be interpreted as a discrete approximation of a related nonlocal operator in the continuum setting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(In some accounts that take this approach, the constituent lacking the determiner \u2013 that called N-bar above \u2013 may be referred to as a noun phrase.) This analysis of noun phrases is widely referred to as the DP hypothesis. It has been the preferred analysis of noun phrases in the minimalist program from its start (since the early 1990s), though the arguments in its favor tend to be theory-internal.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Likewise, lattices are directed sets both upward and downward. In topology, directed sets are used to define nets, which generalize sequences and unite the various notions of limit used in analysis. Directed sets also give rise to direct limits in abstract algebra and (more generally) category theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In several languages, the grave accent distinguishes both homophones and words that otherwise would be homographs: In Bulgarian and Macedonian, it distinguishes the conjunction \u0438 (\"and\") from the short-form feminine possessive pronoun \u045d. In Catalan, it distinguishes homophone words such as ma (\"my (f)\") and m\u00e0 (\"hand\"). In French the grave accent on the letters a and u has no effect on pronunciation and just distinguishes homonyms otherwise spelled the same, for example the preposition \u00e0 (\"to/belonging to/towards\") from the verb a (\" has\") as well as the adverb l\u00e0 (\"there\") and the feminine definite article la; it is also used in the words d\u00e9j\u00e0 (\"already\"), de\u00e7\u00e0 (preceded by en or au, and meaning \"closer than\" or \"inferior to (a given value)\"), the phrase \u00e7\u00e0 et l\u00e0 (\"hither and thither\"; without the accents, it would literally mean \"it and the\") and its functional synonym de\u00e7\u00e0, del\u00e0. It is used on the letter u only to distinguish o\u00f9 (\"where\") and ou (\"or\"). \u00c8 is rarely used to distinguish homonyms except in d\u00e8s/des (\"since/some\"), \u00e8s/es (\"in/(thou) art\"), and l\u00e8s/les (\"near/the\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. Some particular topics out of many include; operations defined on matrices (such as matrix addition, matrix multiplication and operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and cosines etc. of matrices), and the eigenvalues of matrices (eigendecomposition of a matrix, eigenvalue perturbation theory).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Recursive languages are also called decidable. The concept of decidability may be extended to other models of computation. For example, one may speak of languages decidable on a non-deterministic Turing machine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In consequence, mutually exclusive events have the property: P(A \u2229 B) = 0.For example, in a standard 52-card deck with two colors it is impossible to draw a card that is both red and a club because clubs are always black. If just one card is drawn from the deck, either a red card (heart or diamond) or a black card (club or spade) will be drawn. When A and B are mutually exclusive, P(A \u222a B) = P(A) + P(B).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This process is known as regularization. Tikhonov regularization is one of the most commonly used for regularization of linear ill-posed problems. The definition of a well-posed problem comes from the work of Jacques Hadamard on mathematical modeling of physical phenomena.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, stative and dynamic verbs will use entirely different morphological markers on the verbs themselves. For example, in the Mantauran dialect of Rukai, an indigenous language of Taiwan, the two types of verbs take different prefixes in their finite forms, with dynamic verbs taking o- and stative verbs taking ma-. Thus, the dynamic verb \"jump\" is o-coroko in the active voice, while the stative verb \"love\" is ma-\u00f0alam\u0259. This sort of marking is characteristic of other Formosan languages as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "short cable lengths and limited physical extent, avoiding signal runtime performance degradation. majority / quorum mechanisms to guarantee data consistency whenever parts of the cluster become inaccessible.Indicators for eventually consistent designs (not suitable for transactional applications!)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The residual, or error, sum-of-squares is SSE = \u2211 i = 1 n ( X i \u2212 X \u00af ) 2 + \u2211 i = 1 n ( Y i \u2212 Y \u00af ) 2 + \u2211 i = 1 n ( Z i \u2212 Z \u00af ) 2 {\\displaystyle {\\text{SSE}}=\\sum _{i=1}^{n}(X_{i}-{\\bar {X}})^{2}+\\sum _{i=1}^{n}(Y_{i}-{\\bar {Y}})^{2}+\\sum _{i=1}^{n}(Z_{i}-{\\bar {Z}})^{2}} with 3(n\u22121) degrees of freedom. Of course, introductory books on ANOVA usually state formulae without showing the vectors, but it is this underlying geometry that gives rise to SS formulae, and shows how to unambiguously determine the degrees of freedom in any given situation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, stacks of indices can count and remember what rules were applied and in which order. For example, indexed grammars can describe the context-sensitive language of word triples { www: w \u2208 {a,b}* }: A derivation of abbabbabb is then S \u21d2 S \u21d2 S \u21d2 S \u21d2 T T T \u21d2 a T T T \u21d2 ab T T T \u21d2 abb T T T \u21d2 abb T T \u21d2 ... \u21d2 abb abb T \u21d2 ... \u21d2 abb abb abb.As another example, the grammar G = \u27e8 {S,T,A,B,C}, {a,b,c}, {f,g}, P, S \u27e9 produces the language { anbncn: n \u2265 1 }, where the production set P consists of An example derivation is S \u21d2 T \u21d2 T \u21d2 A B C \u21d2 aA B C \u21d2 aA bB C \u21d2 aA bB cC \u21d2 aa bB cC \u21d2 aa bb cC \u21d2 aa bb cc.Both example languages are not context-free by the pumping lemma.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers. The challenge was ended in 2007.RSA Laboratories (which is an acronym of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In metalogic, formal languages are sometimes called object languages. The language used to make statements about an object language is called a metalanguage. This distinction is a key difference between logic and metalogic. While logic deals with proofs in a formal system, expressed in some formal language, metalogic deals with proofs about a formal system which are expressed in a metalanguage about some object language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In fact, the consecutive weightings of any digital number system can be employed since they all constitute geometric progressions. For example, the binary, ternary, octal and decimal number systems use a radix \u2018R\u2019 of 2, 3, 8 and 10 respectively. The value \u2018R\u2019 is also the common ratio of the geometric progression going up in rank order while \u2018r\u2019 is the complementary common ratio descending in rank.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "x z )  = ( \u03bb x . y z ) {\\displaystyle (\\lambda x.x\\ z)=(\\lambda x.y\\ z)} The new rules block this substitution so that it remains as, ( \u03bb x . x z )  = ( \u03bb x . x z ) {\\displaystyle (\\lambda x.x\\ z)=(\\lambda x.x\\ z)}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a trivial group or zero group is a group consisting of a single element. All such groups are isomorphic, so one often speaks of the trivial group. The single element of the trivial group is the identity element and so it is usually denoted as such: 0 , 1 , {\\displaystyle 0,1,} or e {\\displaystyle e} depending on the context. If the group operation is denoted \u22c5 {\\displaystyle \\,\\cdot \\,} then it is defined by e \u22c5 e = e .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It limits the ways that entities can use patients' personal information and protects the privacy of all medical information no matter what form it is in. Quality teleradiology must abide by important HIPAA rules to ensure patients' privacy is protected. Also State laws governing the licensing requirements and medical malpractice insurance coverage required for physicians vary from state to state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle pq-\\varphi (pq)=pq-(p-1)(q-1)=p+q-1=n-1.\\,} It is expected that every even number larger than 6 is a sum of two distinct primes, so probably no odd number larger than 5 is a noncototient. The remaining odd numbers are covered by the observations 1 = 2 \u2212 \u03d5 ( 2 ) , 3 = 9 \u2212 \u03d5 ( 9 ) {\\displaystyle 1=2-\\phi (2),3=9-\\phi (9)} and 5 = 25 \u2212 \u03d5 ( 25 ) {\\displaystyle 5=25-\\phi (25)} . For even numbers, it can be shown 2 p q \u2212 \u03c6 ( 2 p q ) = 2 p q \u2212 ( p \u2212 1 ) ( q \u2212 1 ) = p q + p + q \u2212 1 = ( p + 1 ) ( q + 1 ) \u2212 2 {\\displaystyle 2pq-\\varphi (2pq)=2pq-(p-1)(q-1)=pq+p+q-1=(p+1)(q+1)-2} Thus, all even numbers n such that n+2 can be written as (p+1)*(q+1) with p, q primes are cototients.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the ISO 5725-1 standard accuracy for measuring instruments is defined as \u201cthe closeness of agreement between a test result and the accepted reference value\u201d. This term \u201caccuracy\u201d includes both the systematic error and the bias component. Each device has its manufacturer stated accuracy specification and its tested accuracy. Uncertainty takes all the metering system factors that impact measurement accuracy into account.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "as a result. The theory is the answer the scientist creates using logic and reason to explain the phenomenon. The scientist then focuses on how to conduct experiments to test the theory incrementally and the theory is either proven to be true or false through repeatable and legitimate experimentation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus, the maximum entropy principle is not merely an alternative way to view the usual methods of inference of classical statistics, but represents a significant conceptual generalization of those methods. However these statements do not imply that thermodynamical systems need not be shown to be ergodic to justify treatment as a statistical ensemble. In ordinary language, the principle of maximum entropy can be said to express a claim of epistemic modesty, or of maximum ignorance. The selected distribution is the one that makes the least claim to being informed beyond the stated prior data, that is to say the one that admits the most ignorance beyond the stated prior data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Failing usually results in the student leaving the program or re-taking the test after some time has passed. A second failure normally guarantees dismissal from the graduate program, though progress on previous attempts may convince the student's program to grant a third, final attempt. Some schools have an intermediate category, passing at the master's level, which does not permit the student to continue doctoral study, but does allow the student to leave with a master's degree despite not having completed a thesis.In some U.S.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software engineering, a pipeline consists of a chain of processing elements (processes, threads, coroutines, functions, etc.), arranged so that the output of each element is the input of the next; the name is by analogy to a physical pipeline. Usually some amount of buffering is provided between consecutive elements. The information that flows in these pipelines is often a stream of records, bytes, or bits, and the elements of a pipeline may be called filters; this is also called the pipe(s) and filters design pattern.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Native data types can be mapped to/from Java data types. For compound types such as objects, arrays and strings the native code must explicitly convert the data by calling methods in the JNIEnv. A JNI environment pointer (JNIEnv*) is passed as an argument for each native function mapped to a Java method, allowing for interaction with the JNI environment within the native method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In morphology and syntax, words are often organized into lexical categories or word classes, such as \"noun\", \"verb\", \"adjective\", and so on. These word classes have grammatical features (also called categories or inflectional categories), which can have one of a set of potential values (also called the property, meaning, or feature of the category).For example, consider the pronoun in English. Pronouns are a lexical category. Pronouns have the person feature, which can have a value of \"first\", \"second\", or \"third\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Despite that, the purely theoretical existence results are nevertheless ubiquitous in contemporary mathematics. For example, John Nash's original proof of the existence of a Nash equilibrium in 1951 was such an existence theorem. An approach which is constructive was also later found in 1962.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, a given software system's ability to tolerate failures while still ensuring adequate quality of service\u2014often generalized as resilience\u2014is typically specified as a requirement. However, development teams often fail to meet this requirement due to factors such as short deadlines or lack of knowledge of the field. Chaos engineering is a technique to meet the resilience requirement. Chaos engineering can be used to achieve resilience against infrastructure failures, network failures, and application failures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The same convention is adopted in functional programming, particularly in Haskell. In geometry, geography and astronomy, prime and double prime are used as abbreviations for minute and second of arc (and thus latitude, longitude, elevation and right ascension). In physics, the prime is used to denote variables after an event.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Bernstein inequalities give bounds on the probability that the sum of random variables deviates from its mean. In the simplest case, let X1, ..., Xn be independent Bernoulli random variables taking values +1 and \u22121 with probability 1/2 (this distribution is also known as the Rademacher distribution), then for every positive \u03b5 {\\displaystyle \\varepsilon } , P ( | 1 n \u2211 i = 1 n X i | > \u03b5 ) \u2264 2 exp \u2061 ( \u2212 n \u03b5 2 2 ( 1 + \u03b5 3 ) ) . {\\displaystyle \\mathbb {P} \\left(\\left|{\\frac {1}{n}}\\sum _{i=1}^{n}X_{i}\\right|>\\varepsilon \\right)\\leq 2\\exp \\left(-{\\frac {n\\varepsilon ^{2}}{2(1+{\\frac {\\varepsilon }{3}})}}\\right).}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In spherical coordinates, with \u03b8 the angle with the z axis and \u03c6 the rotation around the z axis, and F again written in local unit coordinates, the divergence is div \u2061 F = \u2207 \u22c5 F = 1 r 2 \u2202 \u2202 r ( r 2 F r ) + 1 r sin \u2061 \u03b8 \u2202 \u2202 \u03b8 ( sin \u2061 \u03b8 F \u03b8 ) + 1 r sin \u2061 \u03b8 \u2202 F \u03c6 \u2202 \u03c6 . {\\displaystyle \\operatorname {div} \\mathbf {F} =\\nabla \\cdot \\mathbf {F} ={\\frac {1}{r^{2}}}{\\frac {\\partial }{\\partial r}}\\left(r^{2}F_{r}\\right)+{\\frac {1}{r\\sin \\theta }}{\\frac {\\partial }{\\partial \\theta }}(\\sin \\theta \\,F_{\\theta })+{\\frac {1}{r\\sin \\theta }}{\\frac {\\partial F_{\\varphi }}{\\partial \\varphi }}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While much of the notation may be applied with any tensors, operations relating to a differential structure are only applicable to tensor fields. Where needed, the notation extends to components of non-tensors, particularly multidimensional arrays.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more general mathematical setting, the Boltzmann distribution is also known as the Gibbs measure. In statistics and machine learning it is called a log-linear model. In deep learning the Boltzmann distribution is used in the sampling distribution of stochastic neural networks such as the Boltzmann machine.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "All bounds are asymptotically tight when the number of groups is constant. The proofs use discrepancy theory.Unanimous envy-freeness with high probability: When all k groups contain the same number of agents, and their valuations are drawn at random, an envy-free allocation exists with high probability if the number of goods is in \u03a9 ( n log \u2061 n ) {\\displaystyle \\Omega (n\\log n)} , and can be attained by a greedy algorithm that maximizes the sum of utilities. The results can be extended to two groups with different sizes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The SUS has been widely used in the evaluation of a range of systems. Bangor, Kortum and Miller have used the scale extensively over a ten-year period and have produced normative data that allow SUS ratings to be positioned relative to other systems. They propose an extension to SUS to provide an adjective rating that correlates with a given score. Based on a review of hundreds of usability studies, Sauro and Lewis proposed a curved grading scale for mean SUS scores.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of telecommunications, \"data retention\" generally refers to the storage of call detail records (CDRs) of telephony and internet traffic and transaction data (IPDRs) by governments and commercial organisations. In the case of government data retention, the data that is stored is usually of telephone calls made and received, emails sent and received, and websites visited. Location data is also collected. The primary objective in government data retention is traffic analysis and mass surveillance.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One can logically define a semigroup in which the underlying set S is empty. The binary operation in the semigroup is the empty function from S \u00d7 S to S. This operation vacuously satisfies the closure and associativity axioms of a semigroup. Not excluding the empty semigroup simplifies certain results on semigroups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the totient summatory function \u03a6 ( n ) {\\displaystyle \\Phi (n)} is a summatory function of Euler's totient function defined by: \u03a6 ( n ) := \u2211 k = 1 n \u03c6 ( k ) , n \u2208 N {\\displaystyle \\Phi (n):=\\sum _{k=1}^{n}\\varphi (k),\\quad n\\in \\mathbf {N} } It is the number of coprime integer pairs {p, q}, 1 \u2264 p \u2264 q \u2264 n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The formulation of the theorem uses the following definition. A word in two variables, say x and y, is an expression of the form W ( x , y ) = x m 1 y n 1 x m 2 y n 2 \u22ef x m p , {\\displaystyle W(x,y)=x^{m_{1}}y^{n_{1}}x^{m_{2}}y^{n_{2}}\\cdots x^{m_{p}},} where m1, n1, m2, n2, \u2026, mp are non-negative integers. The degree of this word is m 1 + n 1 + m 2 + n 2 + \u22ef + m p .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Further inputs to the algorithm are the marginal sample distribution p ( x ) {\\displaystyle p(x)\\,} which has already been determined by the dominant eigenvector of P {\\displaystyle P\\,} and the matrix valued Kullback\u2013Leibler divergence function D i , j K L = D K L  ) {\\displaystyle D_{i,j}^{KL}=D^{KL}{\\Big }{\\Big )}} derived from the sample spacings and transition probabilities. The matrix p ( y i | c j ) {\\displaystyle p(y_{i}|c_{j})\\,} can be initialized randomly or with a reasonable guess, while matrix p ( c i | x j ) {\\displaystyle p(c_{i}|x_{j})\\,} needs no prior values. Although the algorithm converges, multiple minima may exist that would need to be resolved.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Under such assumptions, the case n < m {\\displaystyle n m {\\displaystyle n>m} and { E i } {\\displaystyle \\{E_{i}\\}} does not consist of mutually orthogonal projections.For the second possibility, the problem of finding a suitable projection-valued measure now becomes the following problem. By assumption, the non-square matrix M =  {\\displaystyle M={\\begin{bmatrix}x_{1}\\cdots x_{n}\\end{bmatrix}}} is a co-isometry, that is M M \u2217 = I {\\displaystyle MM^{*}=I} . If we can find a ( n \u2212 m ) \u00d7 n {\\displaystyle (n-m)\\times n} matrix N where U =  {\\displaystyle U={\\begin{bmatrix}M\\\\N\\end{bmatrix}}} is a n \u00d7 n unitary matrix, the projection-valued measure whose elements are projections onto the column vectors of U will then have the desired properties. In principle, such a N can always be found.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the beginning of a prefix sum operation, each processing element i {\\displaystyle i} owns a message m i {\\displaystyle m_{i}} . The goal is to compute \u2a01 0 \u2264 j \u2264 i m j {\\displaystyle \\bigoplus _{0\\leq j\\leq i}m_{j}} , where \u2295 {\\displaystyle \\oplus } is an associative operation. The following pseudo code describes the algorithm. Input: message m i {\\displaystyle m_{i}} of processor i {\\displaystyle i} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In n dimensions, when all i1, ...,in, j1, ..., jn take values 1, 2, ..., n: where the exclamation mark (!) denotes the factorial, and \u03b4\u03b1...\u03b2... is the generalized Kronecker delta. For any n, the property \u2211 i , j , k , \u22ef = 1 n \u03b5 i j k \u2026 \u03b5 i j k \u2026 = n ! {\\displaystyle \\sum _{i,j,k,\\dots =1}^{n}\\varepsilon _{ijk\\dots }\\varepsilon _{ijk\\dots }=n!} follows from the facts that every permutation is either even or odd, (+1)2 = (\u22121)2 = 1, and the number of permutations of any n-element set number is exactly n!.The particular case of (8) with k = n \u2212 2 {\\textstyle k=n-2} is", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As a consequence, code quality without the context of the whole system, as W. Edwards Deming described it, has limited value.To view, explore, analyze, and communicate software quality measurements, concepts and techniques of information visualization provide visual, interactive means useful, in particular, if several software quality measures have to be related to each other or to components of a software or system. For example, software maps represent a specialized approach that \"can express and combine information about software development, software quality, and system dynamics\".Software quality also plays a role in the release phase of a software project. Specifically, the quality and establishment of the release processes (also patch processes), configuration management are important parts of an overall software engineering process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The latter usually applies to a form of argument that does not comply with the valid inference rules of logic, whereas the problematic mathematical step is typically a correct rule applied with a tacit wrong assumption. Beyond pedagogy, the resolution of a fallacy can lead to deeper insights into a subject (e.g., the introduction of Pasch's axiom of Euclidean geometry, the five colour theorem of graph theory).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the early 1990s NeXT Computer recognized that connecting to databases was essential to most businesses and yet also potentially complex. Every data source has a different data-access language (or API), driving up the costs to learn and use each vendor's product. The NeXT engineers wanted to apply the advantages of object-oriented programming, by getting objects to \"talk\" to relational databases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Items should be empirically related to one another, which leads to the second step of examining their multivariate relationships. Third, indexes scores are designed, which involves determining their score ranges and weights for the items.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Qualcomm announced a partnership that will allow supported Android phones, starting with Snapdragon 8 Gen 2 chipset, to send and receive text messages via Iridium satellites. In 2022, T-Mobile formed a partnership to use Starlink services via existing LTE/5G NR spectrum. AST SpaceMobile aims to build a cellular space network from scratch. It will allow existing, unmodified smartphones to connect to satellites in areas with coverage gaps.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Chevalley\u2013Warning theorem implies that certain polynomial equations in sufficiently many variables over a finite field have solutions. It was proved by Ewald Warning (1935) and a slightly weaker form of the theorem, known as Chevalley's theorem, was proved by Chevalley (1935). Chevalley's theorem implied Artin's and Dickson's conjecture that finite fields are quasi-algebraically closed fields (Artin 1982, page x).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One way to state the conjecture is that if R has no nil ideal, other than {0}, then it has no nil one-sided ideal, other than {0}. This question was posed in 1930 by Gottfried K\u00f6the (1905\u20131989). The K\u00f6the conjecture has been shown to be true for various classes of rings, such as polynomial identity rings and right Noetherian rings, but a general solution remains elusive.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The Hexadecimal notation for null is 00. Decoding the Base64 string AA== also yields the null character. In documentation, the null character is sometimes represented as a single-em-width symbol containing the letters \"NUL\". In Unicode, there is a character for this: U+2400 \u2400 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some games, it is possible to partition the elements of X (or a subset of them) into a set of pairwise-disjoint pairs. Under certain conditions, a player can win using the following greedy strategy: \"whenever your opponent picks an element of pair i, pick the other element of pair i\". The \"certain conditions\" are different for Maker and for Breaker; see pairing strategy.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the OMG vision of modeling, data is split into abstract models and concrete models. The abstract models represent the semantic information, whereas the concrete models represent visual diagrams. Abstract models are instances of arbitrary MOF-based modeling languages such as UML or SysML. For diagrams, the Diagram Interchange (DI, XMI) standard is used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multilevel processor sharing a finite set of thresholds are defined and jobs partitioned according to how much service they have received. The lowest level (containing jobs which have received the least service) has the highest priority and higher levels monotonically decreasing priorities. Within each level an internal discipline is used. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the National Weather Service issues flood watches and warnings for large-scale, gradual river flooding. Watches are issued when flooding is possible or expected within 12\u201348 hours, and warnings are issued when flooding over a large area or river flooding is imminent or occurring. Both can be issued on a county-by-county basis or for specific rivers or points along a river. When rapid flooding from heavy rain or a dam failure is expected, flash flood watches and warnings are issued.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Developers of mobile applications must also consider a large array of devices with different screen sizes, hardware specifications, and configurations because of intense competition in mobile hardware and changes within each of the platforms. Today, mobile apps are usually distributed via an official online outlet or marketplace (e.g. Apple - The App Store, Google - Google Play) and there is a formalized process by which developers submit their apps for approval and inclusion in those marketplaces.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, it is difficult to use Kuratowski's criterion to quickly decide whether a given graph is planar. However, there exist fast algorithms for this problem: for a graph with n vertices, it is possible to determine in time O(n) (linear time) whether the graph may be planar or not (see planarity testing). For a simple, connected, planar graph with v vertices and e edges and f faces, the following simple conditions hold for v \u2265 3: Theorem 1. e \u2264 3v \u2013 6; Theorem 2. If there are no cycles of length 3, then e \u2264 2v \u2013 4.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this context \"information\" is used to refer to all the details of the state and the statement that information must be preserved means that details corresponding to an earlier time can always be reconstructed at a later time. Mathematically, the Schr\u00f6dinger equation implies that the wavefunction at a time t1 can be related to the wavefunction at a time t2 by means of a unitary operator. Since the unitary operator is bijective, the wavefunction at t2 can be obtained from the wavefunction at t1 and vice versa.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Cantor's theorem had immediate and important consequences for the philosophy of mathematics. For instance, by iteratively taking the power set of an infinite set and applying Cantor's theorem, we obtain an endless hierarchy of infinite cardinals, each strictly larger than the one before it. Consequently, the theorem implies that there is no largest cardinal number (colloquially, \"there's no largest infinity\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician Cahit Arf (1941) when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2. The Arf invariant is the substitute, in characteristic 2, for the discriminant for quadratic forms in characteristic not 2. Arf used his invariant, among others, in his endeavor to classify quadratic forms in characteristic 2. In the special case of the 2-element field F2 the Arf invariant can be described as the element of F2 that occurs most often among the values of the form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Feasibility stage, costs of the requirements are determined. For user requirements, the current cost of work is compared to the future projected costs once the new system is in place. Questions such as these are asked: \u201cWhat are data entry errors costing us now?\u201d Or \u201cWhat is the cost of scrap due to operator error with the current interface?\u201d Actually, the need for the new tool is often recognized as these questions come to the attention of financial people in the organization. Business costs would include, \u201cWhat department has the budget for this?\u201d \u201cWhat is the expected rate of return on the new product in the marketplace?\u201d \u201cWhat\u2019s the internal rate of return in reducing costs of training and support if we make a new, easier-to-use system?\u201d Technical costs are related to software development costs and hardware costs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum information theory, the Lieb conjecture is a theorem concerning the Wehrl entropy of quantum systems for which the classical phase space is a sphere. It states that no state of such a system has a lower Wehrl entropy than the SU(2) coherent states. The analogous property for quantum systems for which the classical phase space is a plane was conjectured by Alfred Wehrl in 1978 and proven soon afterwards by Elliott H. Lieb, who at the same time extended it to the SU(2) case. The conjecture was only proven in 2012, by Lieb and Jan Philip Solovej.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages, monomorphization is a compile-time process where polymorphic functions are replaced by many monomorphic functions for each unique instantiation. It is considered beneficial to undergo the mentioned transformation because it results in the output intermediate representation (IR) having specific types, which allows for more effective optimization. Additionally, many IRs are intended to be low-level and do not accommodate polymorphism. The resulting code is generally faster than dynamic dispatch, but may require more compilation time and storage space due to duplicating the function body.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the US, the PPI was known as the Wholesale Price Index, or WPI, up to 1978. The PPI is one of the oldest continuous systems of statistical data published by the Bureau of Labor Statistics, as well as one of the oldest economic time series compiled by the Federal Government. The origins of the index can be found in an 1891 U.S. Senate resolution authorizing the Senate Committee on Finance to investigate the effects of the tariff laws \"upon the imports and exports, the growth, development, production, and prices of agricultural and manufactured articles at home and abroad\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Computations using this algorithm form part of the cryptographic protocols that are used to secure internet communications, and in methods for breaking these cryptosystems by factoring large composite numbers. The Euclidean algorithm may be used to solve Diophantine equations, such as finding numbers that satisfy multiple congruences according to the Chinese remainder theorem, to construct continued fractions, and to find accurate rational approximations to real numbers. Finally, it can be used as a basic tool for proving theorems in number theory such as Lagrange's four-square theorem and the uniqueness of prime factorizations. The original algorithm was described only for natural numbers and geometric lengths (real numbers), but the algorithm was generalized in the 19th century to other types of numbers, such as Gaussian integers and polynomials of one variable. This led to modern abstract algebraic notions such as Euclidean domains.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the Ramsey Regression Equation Specification Error Test (RESET) test is a general specification test for the linear regression model. More specifically, it tests whether non-linear combinations of the explanatory variables help to explain the response variable. The intuition behind the test is that if non-linear combinations of the explanatory variables have any power in explaining the response variable, the model is misspecified in the sense that the data generating process might be better approximated by a polynomial or another non-linear functional form. The test was developed by James B. Ramsey as part of his Ph.D. thesis at the University of Wisconsin\u2013Madison in 1968, and later published in the Journal of the Royal Statistical Society in 1969.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an orthodox semigroup is a regular semigroup whose set of idempotents forms a subsemigroup. In more recent terminology, an orthodox semigroup is a regular E-semigroup. The term orthodox semigroup was coined by T. E. Hall and presented in a paper published in 1969. Certain special classes of orthodox semigroups had been studied earlier. For example, semigroups that are also unions of groups, in which the sets of idempotents form subsemigroups were studied by P. H. H. Fantham in 1960.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above definition, we are concerned with the number of bits that must be deterministically transmitted between two parties. If both the parties are given access to a random number generator, can they determine the value of f {\\displaystyle f} with much less information exchanged? Yao, in his seminal paper answers this question by defining randomized communication complexity. A randomized protocol R {\\displaystyle R} for a function f {\\displaystyle f} has two-sided error.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following example the result of the subtraction has fewer digits than x {\\displaystyle x}: 123410  - 123401  Using the first method the sum of the nines' complement of x {\\displaystyle x} and y {\\displaystyle y} is 876589  + 123401  \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014 999990 The nines' complement of 999990 is 000009. Removing the leading zeros gives 9 the desired result. If the subtrahend, y {\\displaystyle y} , has fewer digits than the minuend, x {\\displaystyle x} , leading zeros must be added in the second method. These zeros become leading nines when the complement is taken. For example: 48032  - 391  can be rewritten 48032  - 00391  Replacing 00391 with its nines' complement and adding 1 produces the sum: 48032  + 99608  + 1 \u2014\u2014\u2014\u2014\u2014\u2014\u2014 147641 Dropping the leading 1 gives the correct answer: 47641.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to make an accurate comparison and determine if there is a match, the system requires a shape or points measurement to be compared against the information in the database. This process must be discriminating, quick to compute, concise to store, pose-independent and efficient to match.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the Padovan sequence is the sequence of integers P(n) defined by the initial values P ( 0 ) = P ( 1 ) = P ( 2 ) = 1 , {\\displaystyle P(0)=P(1)=P(2)=1,} and the recurrence relation P ( n ) = P ( n \u2212 2 ) + P ( n \u2212 3 ) . {\\displaystyle P(n)=P(n-2)+P(n-3).} The first few values of P(n) are 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ... (sequence A000931 in the OEIS)A Padovan prime is a Padovan number that is prime. The first Padovan primes are: 2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 1558877695141608507751098941899265975115403618621811951868598809164180630185566719, ... (sequence A100891 in the OEIS).The Padovan sequence is named after Richard Padovan who attributed its discovery to Dutch architect Hans van der Laan in his 1994 essay Dom.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, particularly in computer algebra, Abramov's algorithm computes all rational solutions of a linear recurrence equation with polynomial coefficients. The algorithm was published by Sergei A. Abramov in 1989.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "1 _ 01 \u03d5 0 1 _ 0 \u2192 1 _ 01 = 210 .011 \u03d5 1 1 _ 0 \u2192 001 = 1011 .011 \u03d5 200 \u2192 1001 = 1100 .100 \u03d5 011 \u2192 100 = 10000 .1 \u03d5 011 \u2192 100 {\\displaystyle {\\begin{aligned}211.0{\\underline {1}}0_{\\phi }=211&. {\\underline {1}}01_{\\phi }&0{\\underline {1}}0\\rightarrow {\\underline {1}}01\\\\=210&.011_{\\phi }&1{\\underline {1}}0\\rightarrow 001\\\\=1011&.011_{\\phi }&200\\rightarrow 1001\\\\=1100&.100_{\\phi }&011\\rightarrow 100\\\\=10000&.1_{\\phi }&011\\rightarrow 100\\\\\\end{aligned}}} Any positive number with a non-standard terminating base-\u03c6 representation can be uniquely standardized in this manner. If we get to a point where all digits are \"0\" or \"1\", except for the first digit being negative, then the number is negative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Borwein's algorithm is an algorithm devised by Jonathan and Peter Borwein to calculate the value of 1/\u03c0. They devised several other algorithms. They published the book Pi and the AGM \u2013 A Study in Analytic Number Theory and Computational Complexity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Pseudaria, an ancient lost book of false proofs, is attributed to Euclid.Mathematical fallacies exist in many branches of mathematics. In elementary algebra, typical examples may involve a step where division by zero is performed, where a root is incorrectly extracted or, more generally, where different values of a multiple valued function are equated. Well-known fallacies also exist in elementary Euclidean geometry and calculus.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are two common types of mode scramblers: the \"Step-Graded-Step\" (S-G-S) and the \"step index with bends\". The S-G-S mode scrambler is actually an assembly, a fusion-spliced concatenation of a step-index profile, a graded-index profile and another step-index profile fiber. Typically, each segment is approximately 1 meter long, and may use segments of unconventional size to produce the distribution required according to core size of fiber to be tested.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This can be proved by reduction from Planar SAT. For the case in which all holes are single points, several constant-factor approximations have been developed: A (3+sqrt(3)) approximation in time O ( n 2 ) {\\displaystyle O(n^{2})} ; A (3+sqrt(3)) approximation in time O ( n log \u2061 n ) {\\displaystyle O(n\\log {n})} ; A 4 approximation in time O ( n log \u2061 n ) {\\displaystyle O(n\\log {n})} (more generally, in d dimensions, it is a 2 d {\\displaystyle 2d} approximation in time O ( d n log \u2061 n ) {\\displaystyle O(dn\\log {n})} ), A 3 approximation in time O ( n 4 ) {\\displaystyle O(n^{4})} ; A 1.75 approximation in time O ( n 5 ) {\\displaystyle O(n^{5})} (more generally, in d dimensions, it is a 2 d \u2212 4 + 4 / d {\\displaystyle 2d-4+4/d} approximation in time O ( d n 2 d + 1 ) {\\displaystyle O(dn^{2d+1})} ); the latter approximation uses a restricted variant of the problem called guillotine partitioning, in which the cuts must be guillotine cuts (edge-to-edge cuts). Several polynomial-time approximation schemes using sophisticated guillotine cuts.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this case, the factorization can be done with root-finding algorithms. The case of polynomials with integer coefficients is fundamental for computer algebra. There are efficient computer algorithms for computing (complete) factorizations within the ring of polynomials with rational number coefficients (see factorization of polynomials).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some linear optimization problems, even though the number of constraints is exponential, one can still write a custom separation oracle that works in polynomial time. Some examples are: The minimum-cost arborescence problem: given a weighted directed graph and a vertex r in it, find a subgraph of minimum cost that contains a directed path from r to any other vertex. The problem can be presented as an LP with a constraint for each subset of vertices, which is an exponential number of constraints.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\pi \\sigma \\neq \\sigma \\pi .} As a bijection from a set to itself, a permutation is a function that performs a rearrangement of a set, and is not an arrangement itself. An older and more elementary viewpoint is that permutations are the arrangements themselves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 2378, 12378, 23478, and 123478 are the patterns related to Braille pattern dots-1236, since the two additional dots of kantenji patterns 01236, 12367, and 012367 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erd\u0151s, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is strictly greater than zero. Although the proof uses probability, the final conclusion is determined for certain, without any possible error. This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of program correctness, static analysis can discover vulnerabilities during the development phase of the program. These vulnerabilities are easier to correct than the ones found during the testing phase since static analysis leads to the root of the vulnerability. Due to many forms of static analysis being computationally undecidable, the mechanisms for doing it will not always terminate with the right answer \u2013 either because they sometimes return a false negative (\"no problems found\" when the code does in fact have problems) or a false positive, or because they never return the wrong answer but sometimes never terminate. Despite their limitations, the first type of mechanism might reduce the number of vulnerabilities, while the second can sometimes give strong assurance of the lack of a certain class of vulnerabilities.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1960s, swapping was an early virtual memory technique. An entire program or entire segment would be \"swapped out\" (or \"rolled out\") from RAM to disk or drum, and another one would be swapped in (or rolled in). A swapped-out program would be current but its execution would be suspended while its RAM was in use by another program; a program with a swapped-out segment could continue running until it needed that segment, at which point it would be suspended until the segment was swapped in. A program might include multiple overlays that occupy the same memory at different times.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The purpose of sampling is to reduce the cost and/or the amount of work that it would take to survey the entire target population. A survey that measures the entire target population is called a census. A sample refers to a group or section of a population from which information is to be obtained Survey samples can be broadly divided into two types: probability samples and super samples.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following description, the terminology used will be particular to the Windows NT operating system, but the concepts are applicable to other virtual memory operating systems.When a new application on a 32-bit OS is executed, the process has a 4 GiB VAS: each one of the memory addresses (from 0 to 232 \u2212 1) in that space can have a single byte as a value. Initially, none of them have values ('-' represents no value). Using or setting values in such a VAS would cause a memory exception. 0 4 GiB VAS |----------------------------------------------| Then the application's executable file is mapped into the VAS.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Ego integrity is the psychological concept of the ego's accumulated assurance of its capacity for order and meaning. Ego identity is the accrued confidence that the inner sameness and continuity prepared in the past are matched by the sameness and continuity of one's meaning for others, as evidenced in the promise of a career. Body and ego control organ expressions and of the other attributes of the dynamics of a physical system to face the emotions of ego death in circumstances which can summon, sometimes, anti-theonymistic self-abandonment.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The database, where all managed objects are stored, is called Management Information Base. In contrast with a CI, a managed object is \"dynamic\" and communicates with other network resources that are managed. Note: A managed object may represent a physical entity, a network service, or an abstraction of a resource that exists independently of its use in management.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the United States, the Hearing Aid Compatibility Act of 1988 requires that the Federal Communications Commission (FCC) ensure that all telephones manufactured or imported for use in the United States after August 1989, and all \"essential\" telephones, be hearing aid-compatible (through the use of a telecoil). \"Essential\" phones are defined as \"coin-operated telephones, telephones provided for emergency use, and other telephones frequently needed for use by persons using such hearing aids.\" These might include workplace telephones, telephones in confined settings (like hospitals and nursing homes), and telephones in hotel and motel rooms. Secure telephones, as well as telephones used with public mobile and private radio services, are exempt from the HAC Act.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to use InfoPath to fill in a form, a designer must develop an InfoPath template first. According to Jean Paoli, one of its developers, a key architectural design decision was \"to adhere to the XML paradigm of separating the data in a document from the formatting.\" A patent filed in 2000 by Adriana Neagu and Jean Paoli describes the technology as \"authoring XML using DHTML views and XSLT. \"All the data stored in InfoPath forms are stored in an XML format, which is referred to as the \"data source\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is intended to improve readability of the code, by ensuring that statements that are at the same level of nesting within a block are aligned to the same column. Other types of secondary notation, however, are not part of the formal notation. For example, when wrapping long lines, every line that is a continuation of a previous line can be indented arbitrarily.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phrase-based translation, the aim was to reduce the restrictions of word-based translation by translating whole sequences of words, where the lengths may differ. The sequences of words were called blocks or phrases, however, typically they were not linguistic phrases, but phrasemes that were found using statistical methods from corpora. It has been shown that restricting the phrases to linguistic phrases (syntactically motivated groups of words, see syntactic categories) decreased the quality of translation.The chosen phrases were further mapped one-to-one based on a phrase translation table, and could be reordered. This table could be learnt based on word-alignment, or directly from a parallel corpus. The second model was trained using the expectation maximization algorithm, similarly to the word-based IBM model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This replaces the instruction with a jump to a VM-safe equivalent compiled code fragment in hypervisor memory. The guest user-mode code, running in ring 3, generally runs directly on the host hardware in ring 3.In both cases, VirtualBox uses CSAM and PATM to inspect and patch the offending instructions whenever a fault occurs. VirtualBox also contains a dynamic recompiler, based on QEMU to recompile any real mode or protected mode code entirely (e.g. BIOS code, a DOS guest, or any operating system startup).Using these techniques, VirtualBox could achieve performance comparable to that of VMware in its later versions.The feature was dropped starting with VirtualBox 6.1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Euclidean relations are a class of binary relations that formalize \"Axiom 1\" in Euclid's Elements: \"Magnitudes which are equal to the same are equal to each other.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order for equation A T A v = A T b {\\displaystyle A^{T}Av=A^{T}b} to be solvable, A T A {\\displaystyle A^{T}A} should be invertible, or A T A {\\displaystyle A^{T}A} 's eigenvalues satisfy \u03bb 1 \u2265 \u03bb 2 > 0 {\\displaystyle \\lambda _{1}\\geq \\lambda _{2}>0} . To avoid noise issue, usually \u03bb 2 {\\displaystyle \\lambda _{2}} is required to not be too small. Also, if \u03bb 1 / \u03bb 2 {\\displaystyle \\lambda _{1}/\\lambda _{2}} is too large, this means that the point p {\\displaystyle p} is on an edge, and this method suffers from the aperture problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following code: a = b * c + g; d = b * c * e; it may be worth transforming the code to: tmp = b * c; a = tmp + g; d = tmp * e; if the cost of storing and retrieving tmp is less than the cost of calculating b * c an extra time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In participant governance a network is governed by its members themselves. They call such networks that involve most or all network members interacting on a relatively equal basis in the process of governance \"shared participant governance\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Periphrastic Hindi verb forms consist of two elements. The first of these two elements is the aspect marker and the second element (the copula) is the common tense/mood marker. In literary Arabic (\u0627\u0644\u0652\u0641\u064f\u0635\u0652\u062d\u064e\u0649 al-fu\u1e63\u1e25\u0101) the verb has two aspect-tenses: perfective (past), and imperfective (non-past).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of k-nearest neighbors regression, when the expectation is taken over the possible labeling of a fixed training set, a closed-form expression exists that relates the bias\u2013variance decomposition to the parameter k:: 37, 223 E \u2061  = ( f ( x ) \u2212 1 k \u2211 i = 1 k f ( N i ( x ) ) ) 2 + \u03c3 2 k + \u03c3 2 {\\displaystyle \\operatorname {E} =\\left(f(x)-{\\frac {1}{k}}\\sum _{i=1}^{k}f(N_{i}(x))\\right)^{2}+{\\frac {\\sigma ^{2}}{k}}+\\sigma ^{2}} where N 1 ( x ) , \u2026 , N k ( x ) {\\displaystyle N_{1}(x),\\dots ,N_{k}(x)} are the k nearest neighbors of x in the training set. The bias (first term) is a monotone rising function of k, while the variance (second term) drops off as k is increased. In fact, under \"reasonable assumptions\" the bias of the first-nearest neighbor (1-NN) estimator vanishes entirely as the size of the training set approaches infinity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, Kolmogorov's zero\u2013one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, namely a tail event of independent \u03c3-algebras, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one. Tail events are defined in terms of countably infinite families of \u03c3-algebras. For illustrative purposes, we present here the special case in which each sigma algebra is generated by a random variable X k {\\displaystyle X_{k}} for k \u2208 N {\\displaystyle k\\in \\mathbb {N} } . Let F {\\displaystyle {\\mathcal {F}}} be the sigma-algebra generated jointly by all of the X k {\\displaystyle X_{k}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In process improvement efforts, the process performance index is an estimate of the process capability of a process during its initial set-up, before it has been brought into a state of statistical control.Formally, if the upper and lower specifications of the process are USL and LSL, the estimated mean of the process is \u03bc ^ {\\displaystyle {\\hat {\\mu }}} , and the estimated variability of the process (expressed as a standard deviation) is \u03c3 ^ {\\displaystyle {\\hat {\\sigma }}} , then the process performance index is defined as: P ^ p k = min  {\\displaystyle {\\hat {P}}_{pk}=\\min {\\Bigg }} \u03c3 ^ {\\displaystyle {\\hat {\\sigma }}} is estimated using the sample standard deviation. Ppk may be negative if the process mean falls outside the specification limits (because the process is producing a large proportion of defective output). Some specifications may only be one sided (for example, strength). For specifications that only have a lower limit, P ^ p , l o w e r = \u03bc ^ \u2212 L S L 3 \u03c3 ^ {\\displaystyle {\\hat {P}}_{p,lower}={{\\hat {\\mu }}-LSL \\over 3{\\hat {\\sigma }}}} ; for those that only have an upper limit, P ^ p , u p p e r = U S L \u2212 \u03bc ^ 3 \u03c3 ^ {\\displaystyle {\\hat {P}}_{p,upper}={USL-{\\hat {\\mu }} \\over 3{\\hat {\\sigma }}}} . Practitioners may also encounter P ^ p = U S L \u2212 L S L 6 \u03c3 ^ {\\displaystyle {\\hat {P}}_{p}={\\frac {USL-LSL}{6{\\hat {\\sigma }}}}} , a metric that does not account for process performance not exactly centered between the specification limits, and therefore is interpreted as what the process would be capable of achieving if it could be centered and stabilized.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The reinforced concrete will continue to carry the load provided that sufficient reinforcement is present. A typical design problem is to find the smallest amount of reinforcement that can carry the stresses on a small cube (Fig. 1). This can be formulated as an optimization problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an orientation of a real vector bundle is a generalization of an orientation of a vector space; thus, given a real vector bundle \u03c0: E \u2192B, an orientation of E means: for each fiber Ex, there is an orientation of the vector space Ex and one demands that each trivialization map (which is a bundle map) \u03d5 U: \u03c0 \u2212 1 ( U ) \u2192 U \u00d7 R n {\\displaystyle \\phi _{U}:\\pi ^{-1}(U)\\to U\\times \\mathbf {R} ^{n}} is fiberwise orientation-preserving, where Rn is given the standard orientation. In more concise terms, this says that the structure group of the frame bundle of E, which is the real general linear group GLn(R), can be reduced to the subgroup consisting of those with positive determinant. If E is a real vector bundle of rank n, then a choice of metric on E amounts to a reduction of the structure group to the orthogonal group O(n). In that situation, an orientation of E amounts to a reduction from O(n) to the special orthogonal group SO(n).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It turned out that descendant trees of a particular kind, the so-called pruned coclass trees whose infinitely many vertices share a common coclass r {\\displaystyle r} , reveal a repeating finite pattern. These two crucial properties of finiteness and periodicity admit a characterization of all members of the tree by finitely many parametrized presentations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Replacing each vertex of the graph by a point and each edge of the graph by a point produces a non-Hausdorff space in which the open sets are the sets S {\\displaystyle S} with the property that, if a vertex v {\\displaystyle v} of G {\\displaystyle G} belongs to S {\\displaystyle S} , then so does every edge having v {\\displaystyle v} as one of its endpoints.In either case, every finite subgraph of G {\\displaystyle G} corresponds to a compact subspace of the topological space, and every compact subspace corresponds to a finite subgraph together with, in the Hausdorff case, finitely many compact proper subsets of edges. Thus, a graph may be covered by a nested sequence of compact sets if and only if it is locally finite, having a finite number of edges at every vertex. If a graph G {\\displaystyle G} is connected and locally finite, then it has a compact cover in which the set \u03ba i {\\displaystyle \\kappa _{i}} is the set of vertices at distance at most i {\\displaystyle i} from some arbitrarily chosen starting vertex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and more precisely in semigroup theory, a variety of finite semigroups is a class of semigroups having some nice algebraic properties. Those classes can be defined in two distinct ways, using either algebraic notions or topological notions. Varieties of finite monoids, varieties of finite ordered semigroups and varieties of finite ordered monoids are defined similarly. This notion is very similar to the general notion of variety in universal algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In symmetric cryptography, the padding oracle attack can be applied to the CBC mode of operation, where the \"oracle\" (usually a server) leaks data about whether the padding of an encrypted message is correct or not. Such data can allow attackers to decrypt (and sometimes encrypt) messages through the oracle using the oracle's key, without knowing the encryption key.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a \"false positive\" finding or conclusion; example: \"an innocent person is convicted\"), while a type II error is the failure to reject a null hypothesis that is actually false (also known as a \"false negative\" finding or conclusion; example: \"a guilty person is not convicted\"). Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility if the outcome is not determined by a known, observable causal process. By selecting a low threshold (cut-off) value and modifying the alpha (\u03b1) level, the quality of the hypothesis test can be increased. The knowledge of type I errors and type II errors is widely used in medical science, biometrics and computer science.Intuitively, type I errors can be thought of as errors of commission (i.e., the researcher unluckily concludes that something is the fact).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some jurisdictions the law also requires customers to collect the receipt and keep it at least for a short while after leaving the shop, again to check that the shop records sales, so that it cannot evade sales taxes. Often cash registers are attached to scales, barcode scanners, checkstands, and debit card or credit card terminals. Increasingly, dedicated cash registers are being replaced with general purpose computers with POS software. Today, point of sale systems scan the barcode (usually EAN or UPC) for each item, retrieve the price from a database, calculate deductions for items on sale (or, in British retail terminology, \"special offer\", \"multibuy\" or \"buy one, get one free\"), calculate the sales tax or VAT, calculate differential rates for preferred customers, actualize inventory, time and date stamp the transaction, record the transaction in detail including each item purchased, record the method of payment, keep totals for each product or type of product sold as well as total sales for specified periods, and do other tasks as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It may also result in smoother convergence, as the gradient computed at each step is averaged over more training samples. The convergence of stochastic gradient descent has been analyzed using the theories of convex minimization and of stochastic approximation. Briefly, when the learning rates \u03b7 {\\displaystyle \\eta } decrease with an appropriate rate, and subject to relatively mild assumptions, stochastic gradient descent converges almost surely to a global minimum when the objective function is convex or pseudoconvex, and otherwise converges almost surely to a local minimum. This is in fact a consequence of the Robbins\u2013Siegmund theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, one can perform multiple stochastic gradient passes (also called cycles or epochs) over the data. The algorithm thus obtained is called incremental gradient method and corresponds to an iteration w i = w i \u2212 1 \u2212 \u03b3 i \u2207 V ( \u27e8 w i \u2212 1 , x t i \u27e9 , y t i ) {\\displaystyle \\textstyle w_{i}=w_{i-1}-\\gamma _{i}\\nabla V(\\langle w_{i-1},x_{t_{i}}\\rangle ,y_{t_{i}})} The main difference with the stochastic gradient method is that here a sequence t i {\\displaystyle t_{i}} is chosen to decide which training point is visited in the i {\\displaystyle i} -th step. Such a sequence can be stochastic or deterministic.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Different from abbreviations, those are universally recognizable across language barriers as distinct and well-defined symbols. At the coding level, prosigns admit any form the Morse code can take, unlike abbreviations which have to be sent as a sequence of individual letters, like ordinary text. On the other hand, most prosigns codes are much longer than typical codes for letters and numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Table to translate raw ASCII values (A,D,M,S) to new subroutine index (1,4,3,2) in constant time using one-dimensional array (gaps in the range are shown as '..' for this example, meaning 'all hex values up to next row'. The first two columns are not part of the array) In automata-based programming and pseudoconversational transaction processing, if the number of distinct program states is small, a \"dense sequence\" control variable can be used to efficiently dictate the entire flow of the main program loop. A two byte raw data value would require a minimum table size of 65,536 bytes \u2013 to handle all input possibilities \u2013 whilst allowing just 256 different output values. However, this direct translation technique provides an extremely fast validation & conversion to a (relative) subroutine pointer if the heuristics, together with sufficient fast access memory, permits its use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, to postselect is to condition a probability space upon the occurrence of a given event. In symbols, once we postselect for an event E {\\displaystyle E} , the probability of some other event F {\\displaystyle F} changes from Pr \u2061  {\\textstyle \\operatorname {Pr} } to the conditional probability Pr \u2061  {\\displaystyle \\operatorname {Pr} } . For a discrete probability space, Pr \u2061  = Pr \u2061  Pr \u2061  {\\textstyle \\operatorname {Pr} ={\\frac {\\operatorname {Pr} }{\\operatorname {Pr} }}} , and thus we require that Pr \u2061  {\\textstyle \\operatorname {Pr} } be strictly positive in order for the postselection to be well-defined. See also PostBQP, a complexity class defined with postselection.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Regulators and carriers have also been considering blocks of the 300 MHz spectrum which is normally used for television broadcasters. If a company agrees to volunteer their spectrum, the FCC will ask for 120 MHz of it. Also, the FCC has been thinking about spectrum sharing which would allow wireless ISPs to purchase DTV licenses In January 2011, Clearwire agreed to sell off its unused spectrum in order to raise money for company spectrum and to seemingly allow other companies to pick up on some unused space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the course of its use, the Latin alphabet was adapted for use in new languages, sometimes representing phonemes not found in languages that were already written with the Roman characters. To represent these new sounds, extensions were therefore created, be it by adding diacritics to existing letters, by joining multiple letters together to make ligatures, by creating completely new forms, or by assigning a special function to pairs or triplets of letters. These new forms are given a place in the alphabet by defining an alphabetical order or collation sequence, which can vary with the particular language.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Chip-level multiprocessing (CMP or multicore): integrates two or more processors into one chip, each executing threads independently. Any combination of multithreaded/SMT/CMP.The key factor to distinguish them is to look at how many instructions the processor can issue in one cycle and how many threads from which the instructions come. For example, Sun Microsystems' UltraSPARC T1 is a multicore processor combined with fine-grain multithreading technique instead of simultaneous multithreading because each core can only issue one instruction at a time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the concept of groupoid algebra generalizes the notion of group algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Denote by C the set of different configurations (and their number). For each size s in S and configuration c in C, denote: ns - the number of items of size s. as,c - the number of occurrences of size s in configuration c. xc - a variable denoting the number of bins with configuration c. Then, the configuration LP of bin-packing is: minimize \u2211 c \u2208 C x c subject to {\\displaystyle {\\text{minimize}}~~~\\sum _{c\\in C}x_{c}~~~{\\text{subject to}}} \u2211 c \u2208 C a s , c x c \u2265 n s {\\displaystyle \\sum _{c\\in C}a_{s,c}x_{c}\\geq n_{s}} for all s in S (- all ns items of size s are packed).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "1-D structures such as this are easier to fabricate compared with constructing a rigid 2-D structure.The Symmetrical-Ring Structure is another classic example. Described by the nomenclature these are two rectangular square D type configurations, exactly the same size, lying flat, side by side, in the unit cell. Also these are not concentric.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). More specifically, PCR is used for estimating the unknown regression coefficients in a standard linear regression model. In PCR, instead of regressing the dependent variable on the explanatory variables directly, the principal components of the explanatory variables are used as regressors. One typically uses only a subset of all the principal components for regression, making PCR a kind of regularized procedure and also a type of shrinkage estimator.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Code-based modularity allows developers to reuse and repair parts of the application, but development tools are required to perform these maintenance functions (e.g. the application may need to be recompiled). Object-based modularity provides the application as a collection of separate executable files that may be independently maintained and replaced without redeploying the entire application (e.g. Microsoft's Dynamic-link library (DLL); Sun/UNIX shared object files). Some object messaging capabilities allow object-based applications to be distributed across multiple computers (e.g. Microsoft's Component Object Model (COM)).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For all possible assignments of false (\u2717) or true (\u2713) to P, Q, and R (columns 1, 3, 5), each subformula is evaluated according to the rules for material conditional, the result being shown below its main operator. Column 6 shows that the whole formula evaluates to true in every case, i.e. that it is a tautology. In fact, its antecedent (column 2) and its consequent (column 10) are even equivalent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In recent versions of Unix-like operating systems such as Linux, OpenBSD, NetBSD, Solaris and FreeBSD, up to 255-character passphrases can be used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle K(x,y;0)=\\delta (x-y)~.} As a fundamental solution, the kernel is additive, \u222b d y K ( x , y ; t ) K ( y , z ; t \u2032 ) = K ( x , z ; t + t \u2032 ) . {\\displaystyle \\int dyK(x,y;t)K(y,z;t')=K(x,z;t+t')~.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The order of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number p and every positive integer k there are fields of order pk, all of which are isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A simple solution is to simply avoid taking such unreliable words into account as well. Applying again Bayes' theorem, and assuming the classification between spam and ham of the emails containing a given word (\"replica\") is a random variable with beta distribution, some programs decide to use a corrected probability: Pr \u2032 ( S | W ) = s \u22c5 Pr ( S ) + n \u22c5 Pr ( S | W ) s + n {\\displaystyle \\Pr '(S|W)={\\frac {s\\cdot \\Pr(S)+n\\cdot \\Pr(S|W)}{s+n}}} where: Pr \u2032 ( S | W ) {\\displaystyle \\Pr '(S|W)} is the corrected probability for the message to be spam, knowing that it contains a given word ; s {\\displaystyle s} is the strength we give to background information about incoming spam ; Pr ( S ) {\\displaystyle \\Pr(S)} is the probability of any incoming message to be spam ; n {\\displaystyle n} is the number of occurrences of this word during the learning phase ; Pr ( S | W ) {\\displaystyle \\Pr(S|W)} is the spamicity of this word. (Demonstration:) This corrected probability is used instead of the spamicity in the combining formula.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The advantages of salt nitriding are: Quick processing time - usually in the order of 4 hours or so to achieve Simple operation - heat the salt and workpieces to temperature and submerge until the duration has transpired.The disadvantages are: The salts used are highly toxic - Disposal of salts are controlled by stringent environmental laws in western countries and has increased the costs involved in using salt baths. This is one of the most significant reasons the process has fallen out of favor in recent decades. Only one process possible with a particular salt type - since the nitrogen potential is set by the salt, only one type of process is possible", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Linguistic concepts take time to settle in the memory. The learner must use the new concepts frequently after presentation, either by thinking or by speaking, in order to master them. His last observation was that language was learned in sentences with the verb as the most crucial component.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sentences with Subject, Object, and Verb, any order is possible. However, some orders are more common than others. In a sample of 568 sentences of Caesar containing all three elements examined by Pinkster, the proportions were: SOV: 63% OSV: 21% OVS: 6% VOS: 5% SVO: 4% VSO: 1%An example of the typical Subject-Object-Verb (SOV) word order in Caesar is: Caesar su\u0101s c\u014dpi\u0101s in proximum collem subd\u016bcit.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Knaster's original publication on dendroids, in 1961, he posed the problem of characterizing the dendroids which can be embedded into the Euclidean plane. This problem remains open.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression. The explanatory (independent) variables resulting from the polynomial expansion of the \"baseline\" variables are known as higher-degree terms. Such variables are also used in classification settings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sensitivity auditing is especially suitable in an adversarial context, where not only the nature of the evidence, but also the degree of certainty and uncertainty associated to the evidence, is the subject of partisan interests. These are the settings considered in Post-normal science or in Mode 2 science. Post-normal science (PNS) is a concept developed by Silvio Funtowicz and Jerome Ravetz, which proposes a methodology of inquiry that is appropriate when \u201cfacts are uncertain, values in dispute, stakes high and decisions urgent\u201d (Funtowicz and Ravetz, 1992: 251\u2013273).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, common-channel signaling (CCS), or common-channel interoffice signaling (CCIS), is the transmission of control information (signaling) via a separate channel than that used for the messages, The signaling channel usually controls multiple message channels.In the public switched telephone network (PSTN) one channel of a communications link is typically used for the sole purpose of carrying signaling for establishment and tear down of telephone calls. The remaining channels are used entirely for the transmission of voice messages. In most cases, a single 64 kbit/s channel is sufficient to handle the call setup and call clear-down traffic for numerous bearer (voice and data) channels.The technical alternative to CCS is channel-associated signaling (CAS), in which each bearer channel has a dedicated signaling channel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The form that a proposition takes depends on the type of logic. The type of logic called propositional, sentential, or statement logic includes only operators and propositional constants as symbols in its language. The propositions in this language are propositional constants, which are considered atomic propositions, and composite (or compound) propositions, which are composed by recursively applying operators to propositions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consequently, descendant trees play a fundamental role in the classification of finite p-groups. By means of kernels and targets of Artin transfer homomorphisms, descendant trees can be endowed with additional structure. An important question is how the descendant tree T ( R ) {\\displaystyle {\\mathcal {T}}(R)} can actually be constructed for an assigned starting group which is taken as the root R {\\displaystyle R} of the tree. The p-group generation algorithm is a recursive process for constructing the descendant tree of a given finite p-group playing the role of the tree root. This algorithm is implemented in the computational algebra systems GAP and Magma.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Then, someone hands you a huge number of KCBS pentagrams, but at first, all of the colorings are hidden. You're told you can only uncover 2 vertices at most, and only if they share a common edge. So, for each pentagram, you randomly pick an edge and uncover the colors on its vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Two years later, Sergei Adian showed that certain Burnside groups are also counterexamples. None of these counterexamples are finitely presented, and for some years it was considered possible that the conjecture held for finitely presented groups.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "S+consonant clusters may vary between aspirated and nonaspirated depending upon if the cluster crosses a morpheme boundary or not. For instance, distend has unaspirated  since it is not analyzed as two morphemes, but distaste has an aspirated middle  because it is analyzed as dis- + taste and the word taste has an aspirated initial t. Word-final voiceless stops are sometimes aspirated. Voiceless stops in Pashto are slightly aspirated prevocalically in a stressed syllable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a sub-Gaussian distribution is a probability distribution with strong tail decay. Informally, the tails of a sub-Gaussian distribution are dominated by (i.e. decay at least as fast as) the tails of a Gaussian. This property gives sub-Gaussian distributions their name. Formally, the probability distribution of a random variable X {\\displaystyle X} is called sub-Gaussian if there is a positive constant C such that for every t \u2265 0 {\\displaystyle t\\geq 0} , P \u2061 ( | X | \u2265 t ) \u2264 2 exp \u2061 ( \u2212 t 2 / C 2 ) {\\textstyle \\operatorname {P} (|X|\\geq t)\\leq 2\\exp {(-t^{2}/C^{2})}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Regarding diagnosis, a proposed taxonomy of service tools is as follows: Level 1: Service tool that indicates if a product is functional or not functional. Describing computer servers, the states are often referred to as \u2018up\u2019 or \u2018down\u2019. This is a binary value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, the P\u00f3lya conjecture (or P\u00f3lya's conjecture) stated that \"most\" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was set forth by the Hungarian mathematician George P\u00f3lya in 1919, and proved false in 1958 by C. Brian Haselgrove. Though mathematicians typically refer to this statement as the P\u00f3lya conjecture, P\u00f3lya never actually conjectured that the statement was true; rather, he showed that the truth of the statement would imply the Riemann hypothesis. For this reason, it is more accurately called \"P\u00f3lya's problem\". The size of the smallest counterexample is often used to demonstrate the fact that a conjecture can be true for many cases and still fail to hold in general, providing an illustration of the strong law of small numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the design of programming languages, an erroneous program is one whose semantics are not well-defined, but where the language implementation is not obligated to signal an error either at compile or at execution time. For example, in Ada: In addition to bounded errors, the language rules define certain kinds of errors as leading to erroneous execution. Like bounded errors, the implementation need not detect such errors either prior to or during run time. Unlike bounded errors, there is no language-specified bound on the possible effect of erroneous execution; the effect is in general not predictable.Defining a condition as \"erroneous\" means that the language implementation need not perform a potentially expensive check (e.g. that a global variable refers to the same object as a subroutine parameter) but may nonetheless depend on a condition being true in defining the semantics of the program. == Notes ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the decimal (base-10) Hindu\u2013Arabic numeral system, each position starting from the right is a higher power of 10. The first position represents 100 (1), the second position 101 (10), the third position 102 (10 \u00d7 10 or 100), the fourth position 103 (10 \u00d7 10 \u00d7 10 or 1000), and so on. Fractional values are indicated by a separator, which can vary in different locations. Usually this separator is a period or full stop, or a comma.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In sequence design, a Feedback with Carry Shift Register (or FCSR) is the arithmetic or with carry analog of a linear-feedback shift register (LFSR). If N > 1 {\\displaystyle N>1} is an integer, then an N-ary FCSR of length r {\\displaystyle r} is a finite state device with a state ( a ; z ) = ( a 0 , a 1 , \u2026 , a r \u2212 1 ; z ) {\\displaystyle (a;z)=(a_{0},a_{1},\\dots ,a_{r-1};z)} consisting of a vector of elements a i {\\displaystyle a_{i}} in { 0 , 1 , \u2026 , N \u2212 1 } = S {\\displaystyle \\{0,1,\\dots ,N-1\\}=S} and an integer z {\\displaystyle z} . The state change operation is determined by a set of coefficients q 1 , \u2026 , q n {\\displaystyle q_{1},\\dots ,q_{n}} and is defined as follows: compute s = q r a 0 + q r \u2212 1 a 1 + \u22ef + q 1 a r \u2212 1 + z {\\displaystyle s=q_{r}a_{0}+q_{r-1}a_{1}+\\dots +q_{1}a_{r-1}+z} . Express s as s = a r + N z \u2032 {\\displaystyle s=a_{r}+Nz'} with a r {\\displaystyle a_{r}} in S {\\displaystyle S} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(binary, 6 multiplications) a 15 = (  2 \u00d7 a ) 3 {\\displaystyle a^{15}=(^{2}\\times a)^{3}\\!} (shortest addition chain, 5 multiplications). a 15 = a 3 \u00d7 (  2 ) 2 {\\displaystyle a^{15}=a^{3}\\times (^{2})^{2}\\!}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For this purpose several test procedures have been devised. The test procedure due to M.S.E (Mean Square Error/Estimator) Bartlett test is represented here. This test procedure is based on the statistic whose sampling distribution is approximately a Chi-Square distribution with (k \u2212 1) degrees of freedom, where k is the number of random samples, which may vary in size and are each drawn from independent normal distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1970s the National Bureau of Standards (NBS) defined a set of convenient numbers to ease metrication in the United States. This system of metric values was described as 1\u20132\u20135 series in reverse, with assigned preferences for those numbers which are multiples of 5, 2, and 1 (plus their powers of 10), excluding linear dimensions above 100 mm.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For many modern packet-switched communication systems, even a single uncorrected bit error is enough to cause the loss of a data packet by causing its CRC check to fail; whether that packet loss was caused by a single bit error or a hundred-bit-long error burst is irrelevant. For systems using large amounts of forward error correction, the reverse applies; a single low-level bit error will almost never occur, since any small errors will almost always be corrected, but any error sufficiently large to cause the forward error correction to fail will almost always result in a large burst error. More specialist and precise definitions of errored seconds exist in standards such as the T1 and DS1 transport systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a binary relation on a set may, or may not, hold between two given set members. For example, \"is less than\" is a relation on the set of natural numbers; it holds e.g. between 1 and 3 (denoted as 1<3) , and likewise between 3 and 4 (denoted as 3<4), but neither between 3 and 1 nor between 4 and 4. As another example, \"is sister of\" is a relation on the set of all people, it holds e.g. between Marie Curie and Bronis\u0142awa D\u0142uska, and likewise vice versa. Set members may not be in relation \"to a certain degree\" - either they are in relation or they are not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If frame pointers are being used, the prologue will typically set the new value of the frame pointer register from the stack pointer. Space on the stack for local variables can then be allocated by incrementally changing the stack pointer. The Forth programming language allows explicit winding of the call stack (called there the \"return stack\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "That may take many clock cycles, since the operand of X may in turn depend on previous instructions that fetch data from main memory.Rather than halt while waiting for X to be finished, stage A may guess whether the branch will be taken or not, and fetch the next instruction Y based on that guess. If the guess later turns out to be incorrect (hopefully rarely), the system would have to backtrack and resume with the correct choice. Namely, all the changes that were made to the machine's state by stage A and subsequent stages based on that guess would have to be undone, the instructions following X already in the pipeline would have to be flushed, and stage A would have to restart with the correct instruction pointer. This branch prediction strategy is a special case of speculative execution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "5. Clustering We can then cluster different documents based on the features we have generated. See the algorithm section in cluster analysis for different types of clustering methods.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The objective is to achieve the minimum perturbation to the item size vector so that all the items can be packed into the prescribed number of bins. In the maximum resource bin packing problem, the goal is to maximize the number of bins used, such that, for some ordering of the bins, no item in a later bin fits in an earlier bin. In a dual problem, the number of bins is fixed, and the goal is to minimize the total number or the total size of items placed into the bins, such that no remaining item fits into an unfilled bin.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations. In 1957, Hirschman considered a function f and its Fourier transform g such that g ( y ) \u2248 \u222b \u2212 \u221e \u221e exp \u2061 ( \u2212 2 \u03c0 i x y ) f ( x ) d x , f ( x ) \u2248 \u222b \u2212 \u221e \u221e exp \u2061 ( 2 \u03c0 i x y ) g ( y ) d y , {\\displaystyle g(y)\\approx \\int _{-\\infty }^{\\infty }\\exp(-2\\pi ixy)f(x)\\,dx,\\qquad f(x)\\approx \\int _{-\\infty }^{\\infty }\\exp(2\\pi ixy)g(y)\\,dy~,} where the \"\u2248\" indicates convergence in L2, and normalized so that (by Plancherel's theorem), \u222b \u2212 \u221e \u221e | f ( x ) | 2 d x = \u222b \u2212 \u221e \u221e | g ( y ) | 2 d y = 1 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Pell's equation: x 2 \u2212 P y 2 = 1 , {\\displaystyle \\ x^{2}-Py^{2}=1,} where P {\\displaystyle P} is a given integer that is not a square number, and in which the variables x {\\displaystyle x} and y {\\displaystyle y} are required to be integers. The equation of Pythagorean triples: x 2 + y 2 = z 2 , {\\displaystyle x^{2}+y^{2}=z^{2},} in which the variables x {\\displaystyle x} , y {\\displaystyle y} , and z {\\displaystyle z} are required to be positive integers. The equation of the Fermat\u2013Catalan conjecture: a m + b n = c k , {\\displaystyle a^{m}+b^{n}=c^{k},} in which the variables a {\\displaystyle a} , b {\\displaystyle b} , c {\\displaystyle c} are required to be coprime positive integers, and the variables m {\\displaystyle m} , n {\\displaystyle n} , and k {\\displaystyle k} are required to be positive integers satisfying the following equation: 1 m + 1 n + 1 k < 1. {\\displaystyle {\\frac {1}{m}}+{\\frac {1}{n}}+{\\frac {1}{k}}<1.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of complete ranks, a commonly used significance test for W against a null hypothesis of no agreement (i.e. random rankings) is given by Kendall and Gibbons (1990) \u03c7 2 = m ( n \u2212 1 ) W {\\displaystyle \\chi ^{2}=m(n-1)W} Where the test statistic takes a chi-squared distribution with d f = n \u2212 1 {\\displaystyle df=n-1} degrees of freedom. In the case of incomplete rankings (see above), this becomes \u03c7 2 = \u03bb ( n 2 \u2212 1 ) k + 1 W {\\displaystyle \\chi ^{2}={\\frac {\\lambda (n^{2}-1)}{k+1}}W} Where again, there are d f = n \u2212 1 {\\displaystyle df=n-1} degrees of freedom. Legendre compared via simulation the power of the chi-square and permutation testing approaches to determining significance for Kendall's W. Results indicated the chi-square method was overly conservative compared to a permutation test when m < 20 {\\displaystyle m<20} . Marozzi extended this by also considering the F test, as proposed in the original publication introducing the W statistic by Kendall & Babington Smith (1939): F = W ( m \u2212 1 ) 1 \u2212 W {\\displaystyle F={\\frac {W(m-1)}{1-W}}} Where the test statistic follows an F distribution with v 1 = n \u2212 1 \u2212 ( 2 / m ) {\\displaystyle v_{1}=n-1-(2/m)} and v 2 = ( m \u2212 1 ) v 1 {\\displaystyle v_{2}=(m-1)v_{1}} degrees of freedom. Marozzi found the F test performs approximately as well as the permutation test method, and may be preferred to when m {\\displaystyle m} is small, as it is computationally simpler.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunications, a protocol data unit (PDU) is a single unit of information transmitted among peer entities of a computer network. It is composed of protocol-specific control information and user data. In the layered architectures of communication protocol stacks, each layer implements protocols tailored to the specific type or mode of data exchange. For example, the Transmission Control Protocol (TCP) implements a connection-oriented transfer mode, and the PDU of this protocol is called a segment, while the User Datagram Protocol (UDP) uses datagrams as protocol data units for connectionless communication. A layer lower in the Internet protocol suite, at the Internet layer, the PDU is called a packet, irrespective of its payload type.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of computer programming, instrumentation refers to the measure of a product's performance, in order to diagnose errors and to write trace information. Instrumentation can be of two types: source instrumentation and binary instrumentation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Since, for each method of type Queue, type Stack provides a method with a matching name and signature, this check would succeed. However, clients accessing a Stack object through a reference of type Queue would, based on Queue's documentation, expect FIFO behavior but observe LIFO behavior, invalidating these clients' correctness proofs and potentially leading to incorrect behavior of the program as a whole. This example violates behavioral subtyping because type Stack is not a behavioral subtype of type Queue: it is not the case that the behavior described by the documentation of type Stack (i.e. LIFO behavior) complies with the documentation of type Queue (which requires FIFO behavior).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The fact that a map f: X \u2192 Y {\\displaystyle f:X\\rightarrow Y} is an embedding is often indicated by the use of a \"hooked arrow\" (U+21AA \u21aa RIGHTWARDS ARROW WITH HOOK); thus: f: X \u21aa Y . {\\displaystyle f:X\\hookrightarrow Y.} (On the other hand, this notation is sometimes reserved for inclusion maps.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consequently the proposition became known as a conjecture rather than a theorem. After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles and formally published in 1995.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics education, a number sentence is an equation or inequality expressed using numbers and mathematical symbols. The term is used in primary level mathematics teaching in the US, Canada, UK, Australia, New Zealand and South Africa.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random variables with finite variance are uncorrelated. A pair of random variables X and Y are independent if and only if the random vector (X, Y) with joint cumulative distribution function (CDF) F X , Y ( x , y ) {\\displaystyle F_{X,Y}(x,y)} satisfies F X , Y ( x , y ) = F X ( x ) F Y ( y ) , {\\displaystyle F_{X,Y}(x,y)=F_{X}(x)F_{Y}(y),} or equivalently, their joint density f X , Y ( x , y ) {\\displaystyle f_{X,Y}(x,y)} satisfies f X , Y ( x , y ) = f X ( x ) f Y ( y ) .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in category theory, the codensity monad is a fundamental construction associating a monad to a wide class of functors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consider the overcategory Top / X {\\displaystyle {\\text{Top}}/X} of topological spaces over X {\\displaystyle X} , that is, the category of topological spaces together with fixed continuous maps to X {\\displaystyle X} . Every object of this category is a continuous map f: Y \u2192 X {\\displaystyle f:Y\\to X} , and a morphism from Y \u2192 X {\\displaystyle Y\\to X} to Z \u2192 X {\\displaystyle Z\\to X} is a continuous map Y \u2192 Z {\\displaystyle Y\\to Z} that commutes with the two maps to X {\\displaystyle X} . There is a functor \u0393: Top / X \u2192 Sets {\\displaystyle \\Gamma :{\\text{Top}}/X\\to {\\text{Sets}}} sending an object f: Y \u2192 X {\\displaystyle f:Y\\to X} to f \u2212 1 F ( Y ) {\\displaystyle f^{-1}F(Y)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in the area of algebra known as representation theory, the representation ring (or Green ring after J. A. Green) of a group is a ring formed from all the (isomorphism classes of the) finite-dimensional linear representations of the group. Elements of the representation ring are sometimes called virtual representations. For a given group, the ring will depend on the base field of the representations. The case of complex coefficients is the most developed, but the case of algebraically closed fields of characteristic p where the Sylow p-subgroups are cyclic is also theoretically approachable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The notion of residuated map can be generalized to a binary operator (or any higher arity) via component-wise residuation. This approach gives rise to notions of left and right division in a partially ordered magma, additionally endowing it with a quasigroup structure. (One speaks only of residuated algebra for higher arities). A binary (or higher arity) residuated map is usually not residuated as a unary map.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many other disciplines use similar criteria or have specific measures geared toward the objectives of the field. Optimality criteria include maximum likelihood, Bayesian, maximum parsimony, sum of squared residuals, least absolute deviations, and many others. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Calls from mobile phones are usually routed based on the location of the base station rather than the calling party, so these (along with landline calls to non-emergency telephone numbers) must be handled manually by the telephone operator or dispatcher, determining whether the caller or incident is within a particular city limit or not so that the proper authorities may be sent. A city's limit may extend into more than one county, which can complicate certain matters of policing and taxation. (For example, sales tax revenue collected in a city by one county may not be spent in another part of the city outside that county.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , a n \u27e9 {\\displaystyle q_{1}\\cong \\langle a_{1},...,a_{n}\\rangle } q 2 \u2245 \u27e8 b 1 , .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. In particular, it can be used to evaluate hypergeometric series at rational points.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Hubs have a significantly larger number of links in comparison with other nodes in the network. The number of links (degrees) for a hub in a scale-free network is much higher than for the biggest node in a random network, keeping the size N of the network and average degree constant. The existence of hubs is the biggest difference between random networks and scale-free networks. In random networks, the degree k is comparable for every node; it is therefore not possible for hubs to emerge. In scale-free networks, a few nodes (hubs) have a high degree k while the other nodes have a small number of links.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, a hub is a node with a number of links that greatly exceeds the average. Emergence of hubs is a consequence of a scale-free property of networks. : 27 While hubs cannot be observed in a random network, they are expected to emerge in scale-free networks. The uprise of hubs in scale-free networks is associated with power-law distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern businesses, the design of file servers is complicated by competing demands for storage space, access speed, recoverability, ease of administration, security, and budget. This is further complicated by a constantly changing environment, where new hardware and technology rapidly obsolesces old equipment, and yet must seamlessly come online in a fashion compatible with the older machinery. To manage throughput, peak loads, and response time, vendors may utilize queuing theory to model how the combination of hardware and software will respond over various levels of demand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, the configuration model is a method for generating random networks from a given degree sequence. It is widely used as a reference model for real-life social networks, because it allows the modeler to incorporate arbitrary degree distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Our example is based on a modified Post\u2013Turing machine model of a Turing Machine. This model prints only the symbols 0 and 1. The blank tape is considered to be all b's.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a nonlinear eigenproblem, sometimes nonlinear eigenvalue problem, is a generalization of the (ordinary) eigenvalue problem to equations that depend nonlinearly on the eigenvalue. Specifically, it refers to equations of the form M ( \u03bb ) x = 0 , {\\displaystyle M(\\lambda )x=0,} where x \u2260 0 {\\displaystyle x\\neq 0} is a vector, and M {\\displaystyle M} is a matrix-valued function of the number \u03bb {\\displaystyle \\lambda } . The number \u03bb {\\displaystyle \\lambda } is known as the (nonlinear) eigenvalue, the vector x {\\displaystyle x} as the (nonlinear) eigenvector, and ( \u03bb , x ) {\\displaystyle (\\lambda ,x)} as the eigenpair. The matrix M ( \u03bb ) {\\displaystyle M(\\lambda )} is singular at an eigenvalue \u03bb {\\displaystyle \\lambda } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first few measured and corrected moments about the mean are then related as follows: \u03bc ^ 2 = m 2 \u2212 1 12 c 2 \u03bc ^ 3 = m 3 \u03bc ^ 4 = m 4 \u2212 1 2 m 2 c 2 + 7 240 c 4 . {\\displaystyle {\\begin{aligned}{\\hat {\\mu }}_{2}&=m_{2}-{\\frac {1}{12}}c^{2}\\\\{\\hat {\\mu }}_{3}&=m_{3}\\\\{\\hat {\\mu }}_{4}&=m_{4}-{\\frac {1}{2}}m_{2}c^{2}+{\\frac {7}{240}}c^{4}.\\end{aligned}}} When the data come from a normally distributed population, then binning and using the midpoint of the bin as the observed value results in an overestimate of the variance. That is why the correction to the variance is negative.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In post-order we always recursively traverse the current node's left subtree, next we recursively traverse the current node's right subtree and then visit the current node. Post-order traversal can be useful to get postfix expression of a binary expression tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, 21 is the GCD of 252 and 105 (as 252 = 21 \u00d7 12 and 105 = 21 \u00d7 5), and the same number 21 is also the GCD of 105 and 252 \u2212 105 = 147. Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal. When that occurs, they are the GCD of the original two numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given a set of points in d-dimensional space, a centerpoint of the set is a point such that any hyperplane that goes through that point divides the set of points in two roughly equal subsets: the smaller part should have at least a 1/(d + 1) fraction of the points. Like the median, a centerpoint need not be one of the data points. Every non-empty set of points (with no duplicates) has at least one centerpoint.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In operating systems, processes are loaded into memory, and wait for their turn to be executed by the central processing unit (CPU). CPU scheduling manages process states and decides when a process will be executed next by using the input queue.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Instead of sending the caller ID in between the first and second ring, some systems (such as in the UK) use line reversal to announce the caller ID, or caller ID signals are simply sent without any announcement. Instead of Bell 202, the European alternative V.23 is sometimes used (without the 75-baud reverse channel) or the data is sent using DTMF signalling. In general, CID as transmitted from the origin of the call is only the calling party's full phone number (including area code, and including international access code and country code if it's an international call).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If \u2211 b \u2208 A N n ( x \u2212 k \u2212 1 b ) = 0 {\\displaystyle \\sum _{b\\in A}N_{n}(x_{-k}^{-1}b)\\,=\\,0} , define p ^ n ( a \u2223 x \u2212 k \u2212 1 ) = 1 / | A | {\\displaystyle {\\hat {p}}_{n}(a\\mid x_{-k}^{-1})\\,=\\,1/|A|} . To i \u2265 1 {\\displaystyle i\\geq 1} , define \u039b n ( x \u2212 i \u2212 1 ) = 2 \u2211 y \u2208 A \u2211 a \u2208 A N n ( y x \u2212 i \u2212 1 a ) log \u2061  {\\displaystyle \\Lambda _{n}(x_{-i}^{-1})\\,=\\,2\\,\\sum _{y\\in A}\\sum _{a\\in A}N_{n}(yx_{-i}^{-1}a)\\log \\left\\,} where y x \u2212 i \u2212 1 = ( y , x \u2212 i , \u2026 , x \u2212 1 ) {\\displaystyle yx_{-i}^{-1}=(y,x_{-i},\\ldots ,x_{-1})} and p ^ n ( a \u2223 x \u2212 i \u2212 1 y ) = N n ( y x \u2212 i \u2212 1 a ) \u2211 b \u2208 A N n ( y x \u2212 i \u2212 1 b ) . {\\displaystyle {\\hat {p}}_{n}(a\\mid x_{-i}^{-1}y)={\\frac {N_{n}(yx_{-i}^{-1}a)}{\\sum _{b\\in A}N_{n}(yx_{-i}^{-1}b)}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a cocountable subset of a set X is a subset Y whose complement in X is a countable set. In other words, Y contains all but countably many elements of X. Since the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals. If the complement is finite, then one says Y is cofinite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Secondly, the FIC formulae depend on the specifics of the models used for the observed data and also on how precision is to be measured. The clearest case is where precision is taken to be mean squared error, say r j = b j 2 + \u03c4 j 2 {\\displaystyle r_{j}=b_{j}^{2}+\\tau _{j}^{2}} in terms of squared bias and variance for the estimator associated with model j {\\displaystyle j} . FIC formulae are then available in a variety of situations, both for handling parametric, semiparametric and nonparametric situations, involving separate estimation of squared bias and variance, leading to estimated precision r ^ j {\\displaystyle {\\hat {r}}_{j}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming languages that do not support higher-order functions, objects can be an effective substitute. An object's methods act in essence like functions, and a method may accept objects as parameters and produce objects as return values. Objects often carry added run-time overhead compared to pure functions, however, and added boilerplate code for defining and instantiating an object and its method(s). Languages that permit stack-based (versus heap-based) objects or structs can provide more flexibility with this method. An example of using a simple stack based record in Free Pascal with a function that returns a function: The function a() takes a Txy record as input and returns the integer value of the sum of the record's x and y fields (3 + 7).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mobile telecommunications technology, the concept of mobile signature roaming means an access point (AP) should be able to get a mobile signature from any end-user, even if the AP and the end-user have not contracted a commercial relationship with the same MSSP. Otherwise, an AP would have to build commercial terms with as many MSSPs as possible, and this might be a cost burden. This means that a mobile signature transaction issued by an application provider should be able to reach the appropriate MSSP, and this should be transparent for the AP.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In more technical terms, let us assume that we have a theory described by a certain function Z {\\displaystyle Z} of the state variables { s i } {\\displaystyle \\{s_{i}\\}} and a certain set of coupling constants { J k } {\\displaystyle \\{J_{k}\\}} . This function may be a partition function, an action, a Hamiltonian, etc. It must contain the whole description of the physics of the system. Now we consider a certain blocking transformation of the state variables { s i } \u2192 { s ~ i } {\\displaystyle \\{s_{i}\\}\\to \\{{\\tilde {s}}_{i}\\}} , the number of s ~ i {\\displaystyle {\\tilde {s}}_{i}} must be lower than the number of s i {\\displaystyle s_{i}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the majority of models, sampling fewer taxon with more sites per taxon demonstrated higher accuracy. Generally, with the alignment of a relatively equal number of total nucleotide sites, sampling more genes per taxon has higher bootstrapping replicability than sampling more taxa. However, unbalanced datasets within genomic databases make increasing the gene comparison per taxon in uncommonly sampled organisms increasingly difficult.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, tasks depend on each other. These interdependencies can be illustrated by a directed acyclic graph. Intuitively, some tasks cannot begin until others are completed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications it is useful to be able to compute the Bernoulli numbers B0 through Bp \u2212 3 modulo p, where p is a prime; for example to test whether Vandiver's conjecture holds for p, or even just to determine whether p is an irregular prime. It is not feasible to carry out such a computation using the above recursive formulae, since at least (a constant multiple of) p2 arithmetic operations would be required. Fortunately, faster methods have been developed which require only O(p (log p)2) operations (see big O notation). David Harvey describes an algorithm for computing Bernoulli numbers by computing Bn modulo p for many small primes p, and then reconstructing Bn via the Chinese remainder theorem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, incorrectly received coded data blocks are often stored at the receiver rather than discarded, and when the re-transmitted block is received, the two blocks are combined. This is called Hybrid ARQ with soft combining (Dahlman et al., p. 120).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Don't embarrass me with bad pictures\" Users may have the ability to control which pictures they post on their own Facebook page, but they do not have the ability to control what others post. Posting and \"tagging\" unflattering pictures of others may create expectancy violations. \"Don't mess up my profile\" Several participants expressed annoyance of others who alter their profiles knowing that their alterations could be perceived negatively, though they did not mention changing their passwords or protecting themselves in other ways.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "So f0 is still the truth value of \u03c8, but the Rx value produces a result that is linear in x. Also after any Q i x i {\\displaystyle {\\mathsf {Q}}_{i}x_{i}} we add R x 1 \u2026 R x i {\\displaystyle \\mathrm {R} _{x_{1}}\\dots \\mathrm {R} _{x_{i}}} in \u03c8\u2032 in order to reduce the degree down to 1 after arithmetizing Q i {\\displaystyle {\\mathsf {Q}}_{i}} . Now let's describe the protocol. If n is the length of \u03c8, all arithmetic operations in the protocol are over a field of size at least n4 where n is the length of \u03c8. Phase 0: P \u2192 V: P sends f0 to V. V checks that f0= 1 and rejects if not.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the chart below, the Carian letter for each vowel is followed by the conventional transcription with the Greek equivalent in parentheses. An epenthetic schwa to break up clusters may have been unwritten.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some programming languages, given a two-argument function f (or a binary operator), the outer product, f, of two one-dimensional arrays, A and B, is a two-dimensional array C such that C = f(A, B). This is syntactically represented in various ways: in APL, as the infix binary operator \u2218.f; in J, as the postfix adverb f/; in R, as the function outer(A, B, f) or the special %o%; in Mathematica, as Outer. In MATLAB, the function kron(A, B) is used for this product. These often generalize to multi-dimensional arguments, and more than two arguments.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In tau-square notation from N. Bourbaki's Theory of Sets, the quantifiers are defined as follows: ( \u2203 x ) A ( x ) \u2261 ( \u03c4 x ( A ) | x ) A {\\displaystyle (\\exists x)A(x)\\ \\equiv \\ (\\tau _{x}(A)|x)A} ( \u2200 x ) A ( x ) \u2261 \u00ac ( \u03c4 x ( \u00ac A ) | x ) \u00ac A \u2261 ( \u03c4 x ( \u00ac A ) | x ) A {\\displaystyle (\\forall x)A(x)\\ \\equiv \\ \\neg (\\tau _{x}(\\neg A)|x)\\neg A\\ \\equiv \\ (\\tau _{x}(\\neg A)|x)A} where A is a relation in L, x is a variable, and \u03c4 x ( A ) {\\displaystyle \\tau _{x}(A)} juxtaposes a \u03c4 {\\displaystyle \\tau } at the front of A, replaces all instances of x with \u25fb {\\displaystyle \\square } , and links them back to \u03c4 {\\displaystyle \\tau } . Then let Y be an assembly, (Y|x)A denotes the replacement of all variables x in A with Y. This notation is equivalent to the Hilbert notation and is read the same. It is used by Bourbaki to define cardinal assignment since they do not use the axiom of replacement. Defining quantifiers in this way leads to great inefficiencies. For instance, the expansion of Bourbaki's original definition of the number one, using this notation, has length approximately 4.5 \u00d7 1012, and for a later edition of Bourbaki that combined this notation with the Kuratowski definition of ordered pairs, this number grows to approximately 2.4 \u00d7 1054.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base 10 is called the decimal or common logarithm and is commonly used in science and engineering.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Several models were produced which dispensed with the power transformer, but had circuit features which only allowed operation from AC. Some early models were available in both AC-only and AC/DC versions, with the AC/DC versions sometimes slightly more expensive.Television receivers were first commercially sold in England in 1936 for the new 'Television Service' broadcast by the British Broadcasting Corporation. All pre World War II sets used mains transformers and consequently were AC only.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Negative bases are rarely used. In a system with more than | b | {\\displaystyle |b|} unique digits, numbers may have many different possible representations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from X to Y is often denoted with the notation X \u21aa Y {\\displaystyle X\\hookrightarrow Y} . In the more general setting of category theory, a monomorphism (also called a monic morphism or a mono) is a left-cancellative morphism. That is, an arrow f: X \u2192 Y such that for all objects Z and all morphisms g1, g2: Z \u2192 X, f \u2218 g 1 = f \u2218 g 2 \u27f9 g 1 = g 2 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These simpler expressions make up the majority of redundant, optimizable expressions in programs written in languages other than concatenative languages. An optimizing compiler can only win on redundancies that the programmer could have avoided in the source code.The second way leaves a computed value on the data stack, duplicating it as needed. This uses operations to copy stack entries.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particular, the convolutional neural network lends itself to eye-tracking, as it is designed for image-centric tasks. With AI, eye-tracking tasks and studies can yield additional information that may not have been detected by human observers. The practice of deep learning also allows for a given neural network to improve at a given task when given enough sample data. This requires a relatively large supply of training data, however.The potential use cases for AI in eye-tracking cover a wide range of topics from medical applications to driver safety to game theory and even education and training applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The groups Co2 of order 42,305,421,312,000 = 218 \u00b7 36 \u00b7 53 \u00b7 7 \u00b7 11 \u00b7 23and Co3 of order 495,766,656,000 = 210 \u00b7 37 \u00b7 53 \u00b7 7 \u00b7 11 \u00b7 23consist of the automorphisms of \u039b fixing a lattice vector of type 2 and type 3, respectively. As the scalar \u22121 fixes no non-zero vector, these two groups are isomorphic to subgroups of Co1. The inner product on the Leech lattice is defined as 1/8 the sum of the products of respective co-ordinates of the two multiplicand vectors; it is an integer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a function f is cofunction of a function g if f(A) = g(B) whenever A and B are complementary angles. This definition typically applies to trigonometric functions. The prefix \"co-\" can be found already in Edmund Gunter's Canon triangulorum (1620).For example, sine (Latin: sinus) and cosine (Latin: cosinus, sinus complementi) are cofunctions of each other (hence the \"co\" in \"cosine\"): The same is true of secant (Latin: secans) and cosecant (Latin: cosecans, secans complementi) as well as of tangent (Latin: tangens) and cotangent (Latin: cotangens, tangens complementi): These equations are also known as the cofunction identities.This also holds true for the versine (versed sine, ver) and coversine (coversed sine, cvs), the vercosine (versed cosine, vcs) and covercosine (coversed cosine, cvc), the haversine (half-versed sine, hav) and hacoversine (half-coversed sine, hcv), the havercosine (half-versed cosine, hvc) and hacovercosine (half-coversed cosine, hcc), as well as the exsecant (external secant, exs) and excosecant (external cosecant, exc):", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "During this time the user may be prevented from closing, resizing, or even minimizing the windows of the affected application (although moving the window is still possible in OS X, as well as previously hidden parts of the window which are usually redrawn, even when the application is otherwise unresponsive). While one application is unresponsive, typically other applications are usable. File system and network delays are another common cause.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle \\left.+\\lefte^{-ipx}\\right\\}.} Thus, \u2202 E 1 ( x ) / \u2202 x 1 + \u2202 E 2 ( x ) / \u2202 x 2 + \u2202 E 3 ( x ) / \u2202 x 3 {\\displaystyle \\partial E_{1}(x)/\\partial x_{1}+\\partial E_{2}(x)/\\partial x_{2}+\\partial E_{3}(x)/\\partial x_{3}} contains terms of the form p 1 \u03f5 1 1 ( p ) + p 2 \u03f5 2 1 ( p ) + p 3 \u03f5 3 1 ( p ) {\\displaystyle p_{1}\\epsilon _{1}^{1}(\\mathbf {p} )+p_{2}\\epsilon _{2}^{1}(\\mathbf {p} )+p_{3}\\epsilon _{3}^{1}(\\mathbf {p} )} which equate to zero by the first of Eq. (4). This gives, \u2207 \u22c5 E ( x ) = 0 , {\\displaystyle \\nabla \\cdot \\mathbf {E} (x)=0,} \u2207 \u22c5 H ( x ) = 0.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Full-text-searching techniques appeared in the 1960s, for example IBM STAIRS from 1969, and became common in online bibliographic databases in the 1990s. Many websites and application programs (such as word processing software) provide full-text-search capabilities. Some web search engines, such as the former AltaVista, employ full-text-search techniques, while others index only a portion of the web pages examined by their indexing systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It has been demonstrated for the first time in 2011 to enable better training of deeper networks, compared to the widely used activation functions prior to 2011, i.e., the logistic sigmoid (which is inspired by probability theory; see logistic regression) and its more practical counterpart, the hyperbolic tangent. A commonly used variant of the ReLU activation function is the Leaky ReLU which allows a small, positive gradient when the unit is not active: f ( x ) = { x if x > 0 , a x otherwise . {\\displaystyle f(x)={\\begin{cases}x&{\\text{if }}x>0,\\\\ax&{\\text{otherwise}}.\\end{cases}}} where x is the input to the neuron and a is a small positive constant (in the original paper the value 0.01 was used for a).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In phonology, affricates tend to behave similarly to stops, taking part in phonological patterns that fricatives do not. Kehrein (2002) analyzes phonetic affricates as phonological stops. A sibilant or lateral (and presumably trilled) stop can be realized phonetically only as an affricate and so might be analyzed phonemically as a sibilant or lateral stop. In that analysis, affricates other than sibilants and laterals are a phonetic mechanism for distinguishing stops at similar places of articulation (like more than one labial, coronal, or dorsal place).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language applications, libraries are a way to cope with thousands of details involved in syntax, lexicon, and inflection. The GF Resource Grammar Library is the standard library for Grammatical Framework. It covers the morphology and basic syntax for an increasing number of languages, currently including Afrikaans, Amharic (partial), Arabic (partial), Basque (partial), Bulgarian, Catalan, Chinese, Czech (partial), Danish, Dutch, English, Estonian, Finnish, French, German, Greek ancient (partial), Greek modern, Hebrew (fragments), Hindi, Hungarian (partial), Interlingua, Italian, Japanese, Korean (partial), Latin (partial), Latvian, Maltese, Mongolian, Nepali, Norwegian bokm\u00e5l, Norwegian nynorsk, Persian, Polish, Punjabi, Romanian, Russian, Sindhi, Slovak (partial), Slovene (partial), Somali (partial), Spanish, Swahili (fragments), Swedish, Thai, Turkish (fragments), and Urdu. In addition, 14 languages have WordNet lexicon and large-scale parsing extensions.A full API documentation of the library can be found at the RGL Synopsis page. The RGL status document gives the languages currently available in the GF Resource Grammar Library, including their maturity.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(The exception to this is when the first digit is negative one and the next two digits are one, like 1111.001=1.001.) This can be converted to the negative of a base-\u03c6 representation by negating every digit, standardizing the result, and then marking it as negative. For example, use a minus sign, or some other significance to denote negative numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For k = 1 {\\displaystyle k=1} the latter statement can be re-formulated as the # 2 {\\displaystyle _{2}} P-completeness of computing, for a given unitary n\u00d7n-matrix U {\\displaystyle U} over a field of characteristic 2, the n\u00d7n-matrix H ( U ) {\\displaystyle H(U)} whose i,j-th entry is the Hamiltonian cycle polynomial of a matrix received from U {\\displaystyle U} via subjecting its rows and columns to any permutation mapping j to 1 and i to 2 and then removing its 1-st row and 2-nd column (i.e. the sum of the products of the arc weights of the corresponding weighted digraph's Hamiltonian paths from vertex i to vertex j) for i \u2260 j and zero for i = j. This matrix satisfies the matrix equation U ( H ( U ) ) T = H ( U ) U T {\\displaystyle U(H(U))^{T}=H(U)U^{T}} , while ham \u2061 ( U U a a T 1 ) = ( a 1 2 + . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In public policy, access control to restrict access to systems (\"authorization\") or to track or monitor behavior within systems (\"accountability\") is an implementation feature of using trusted systems for security or social control.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In reduced-circumference polar coordinates the spatial metric has the form d \u03a3 2 = d r 2 1 \u2212 k r 2 + r 2 d \u03a9 2 , where d \u03a9 2 = d \u03b8 2 + sin 2 \u2061 \u03b8 d \u03d5 2 . {\\displaystyle \\mathrm {d} \\mathbf {\\Sigma } ^{2}={\\frac {\\mathrm {d} r^{2}}{1-kr^{2}}}+r^{2}\\mathrm {d} \\mathbf {\\Omega } ^{2},\\quad {\\text{where }}\\mathrm {d} \\mathbf {\\Omega } ^{2}=\\mathrm {d} \\theta ^{2}+\\sin ^{2}\\theta \\,\\mathrm {d} \\phi ^{2}.} k is a constant representing the curvature of the space. There are two common unit conventions: k may be taken to have units of length\u22122, in which case r has units of length and a(t) is unitless.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the ER model, the network generated is homogeneous, meaning each node has the same number of links. This is considered to be an exponential network. When comparing the connectivity of the ER model when it undergoes random failures vs directed attacks, we are shown that the exponential network reacts the same way to a random failure as it does to a directed attack. This is due to the homogeneity of the network, making it so that it does not matter whether a random node is selected or one is specifically targeted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, an f {\\displaystyle f} -divergence is a function D f ( P \u2016 Q ) {\\displaystyle D_{f}(P\\|Q)} that measures the difference between two probability distributions P {\\displaystyle P} and Q {\\displaystyle Q} . Many common divergences, such as KL-divergence, Hellinger distance, and total variation distance, are special cases of f {\\displaystyle f} -divergence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Pr ( S ) {\\displaystyle \\Pr(S)} can again be taken equal to 0.5, to avoid being too suspicious about incoming email. 3 is a good value for s, meaning that the learned corpus must contain more than 3 messages with that word to put more confidence in the spamicity value than in the default value. This formula can be extended to the case where n is equal to zero (and where the spamicity is not defined), and evaluates in this case to P r ( S ) {\\displaystyle Pr(S)} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most-idle hunting, calls are always delivered to whichever line has been idle the longest. This considers the length of time that the calltaker has been busy versus available. This is typically used in call centers where the calls are being answered by people, to distribute the load evenly.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistical inference, the conditional probability is an update of the probability of an event based on new information. The new information can be incorporated as follows: Let A, the event of interest, be in the sample space, say (X,P). The occurrence of the event A knowing that event B has or will have occurred, means the occurrence of A as it is restricted to B, i.e. A \u2229 B {\\displaystyle A\\cap B} . Without the knowledge of the occurrence of B, the information about the occurrence of A would simply be P(A) The probability of A knowing that event B has or will have occurred, will be the probability of A \u2229 B {\\displaystyle A\\cap B} relative to P(B), the probability that B has occurred.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following transcriptions, diacritics may be used to distinguish between apical  and laminal . The commonality of  cross-linguistically is 2% in a phonological analysis of 2155 languages", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "If the paging unit is enabled, addresses in a segment are now virtual addresses, rather than physical addresses as they were on the 80286. That is, the segment starting address, the offset, and the final 32-bit address the segmentation unit derived by adding the two are all virtual (or logical) addresses when the paging unit is enabled. When the segmentation unit generates and validates these 32-bit virtual addresses, the enabled paging unit finally translates these virtual addresses into physical addresses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The compounding corresponds to a P\u00f3lya urn scheme. It is frequently encountered in Bayesian statistics, machine learning, empirical Bayes methods and classical statistics as an overdispersed multinomial distribution. It reduces to the categorical distribution as a special case when n = 1. It also approximates the multinomial distribution arbitrarily well for large \u03b1. The Dirichlet-multinomial is a multivariate extension of the beta-binomial distribution, as the multinomial and Dirichlet distributions are multivariate versions of the binomial distribution and beta distributions, respectively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The feedback vertex set problem has applications in VLSI chip design. Another application is in complexity theory. Some computational problems on graphs are NP-hard in general, but can be solved in polynomial time for graphs with bounded FVS number. Some examples are graph isomorphism and the path reconfiguration problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive identity the ring is said to have characteristic zero. That is, char(R) is the smallest positive number n such that:(p 198, Thm. 23.14) 1 + \u22ef + 1 \u23df n summands = 0 {\\displaystyle \\underbrace {1+\\cdots +1} _{n{\\text{ summands}}}=0} if such a number n exists, and 0 otherwise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some languages, morphological features separate verbs based on their transitivity, which suggests this is a salient linguistic feature. For example, in Japanese: However, the definition of transitive verbs as those with one object is not universal, and is not used in grammars of many languages.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Bot accounts on Twitter accelerate true and fake news at the same rate. Misinformation spread by bots has been difficult for social media platforms to address.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "An implementation vulnerable to SEMA attacks will perform a different operation depending on whether the bit of the key is 0 or 1, which will use different amounts of power and/or different chip components. This method is prevalent in many different types of side-channel attacks, in particular, power analysis attacks. Thus, the attacker can observe the entire computation of encryption and can deduce the key.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, the term electromagnetic environment (EME) has the following meanings: For a telecommunications system, the spatial distribution of electromagnetic fields surrounding a given site. The electromagnetic environment may be expressed in terms of the spatial and temporal distribution of electric field strength (volts per metre), irradiance (watts per square metre), or energy density (joules per cubic metre). The resulting product of the power and time distribution, in various frequency ranges, of the radiated or conducted electromagnetic emission levels that may be encountered by a military force, system, or platform when performing its assigned mission in its intended operational environment. It is the sum of electromagnetic interference; electromagnetic pulse; hazards of electromagnetic radiation to personnel, ordnance, and volatile materials; and natural phenomena effects of lightning and p-static. All electromagnetic phenomena observable in a given location.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fields of chemistry and cheminformatics, the circuit rank of a molecular graph (the number of rings in the smallest set of smallest rings) is sometimes referred to as the Fr\u00e8rejacque number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most mainstream statically-typed languages, such as C++, C#, and Java, are manifestly typed. Complete type inference has traditionally been associated with functional languages such as Haskell and ML. However, many manifestly-typed languages support partial type inference; for example, C++, Java, and C# all infer types in certain limited cases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In monolithic kernels, a driver can write to any word of memory and thus accidentally corrupt user programs. In Minix 3, when a user expects data from, for example, the file system, it builds a descriptor telling who has access and at what addresses. It then passes an index to this descriptor to the file system, which may pass it to a driver. The file system or driver then asks the kernel to write via the descriptor, making it impossible for them to write to addresses outside the buffer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the IT Industry, deployment refers to post-sales process of guiding a client from purchase to use of the software or hardware that was purchased. This includes requirements analysis, scope analysis, customisations, systems integrations, user policies, user training and delivery. These steps are often overseen by a project manager using project management methodologies. Software Deployment involves several professionals that are relatively new to the knowledge based economy such as business analysts, software implementation specialists, solutions architects, and project managers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some applications, it is not sufficient to extract only one type of feature to obtain the relevant information from the image data. Instead two or more different features are extracted, resulting in two or more feature descriptors at each image point. A common practice is to organize the information provided by all these descriptors as the elements of one single vector, commonly referred to as a feature vector.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an ordered semigroup is a semigroup (S,\u2022) together with a partial order \u2264 that is compatible with the semigroup operation, meaning that x \u2264 y implies z\u2022x \u2264 z\u2022y and x\u2022z \u2264 y\u2022z for all x, y, z in S. An ordered monoid and an ordered group are, respectively, a monoid or a group that are endowed with a partial order that makes them ordered semigroups. The terms posemigroup, pogroup and pomonoid are sometimes used, where \"po\" is an abbreviation for \"partially ordered\". The positive integers, the nonnegative integers and the integers form respectively a posemigroup, a pomonoid, and a pogroup under addition and the natural ordering. Every semigroup can be considered as a posemigroup endowed with the trivial (discrete) partial order \"=\". A morphism or homomorphism of posemigroups is a semigroup homomorphism that preserves the order (equivalently, that is monotonically increasing).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions. It has the form minimize 1 2 x T P 0 x + q 0 T x subject to 1 2 x T P i x + q i T x + r i \u2264 0 for i = 1 , \u2026 , m , A x = b , {\\displaystyle {\\begin{aligned}&{\\text{minimize}}&&{\\tfrac {1}{2}}x^{\\mathrm {T} }P_{0}x+q_{0}^{\\mathrm {T} }x\\\\&{\\text{subject to}}&&{\\tfrac {1}{2}}x^{\\mathrm {T} }P_{i}x+q_{i}^{\\mathrm {T} }x+r_{i}\\leq 0\\quad {\\text{for }}i=1,\\dots ,m,\\\\&&&Ax=b,\\end{aligned}}} where P0, \u2026, Pm are n-by-n matrices and x \u2208 Rn is the optimization variable. If P0, \u2026, Pm are all positive semidefinite, then the problem is convex. If these matrices are neither positive nor negative semidefinite, the problem is non-convex. If P1, \u2026 ,Pm are all zero, then the constraints are in fact linear and the problem is a quadratic program.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, with introduction of font formats such as OpenType, those supplemental glyphs were merged into the main fonts, relying on specific software capabilities to access the alternate glyphs. Since Apple's and Microsoft's operating systems supported different character sets in the platform related fonts, some foundries used expert fonts in a different way. These fonts included the characters which were missing on either Macintosh or Windows computers, e.g. fractions, ligatures or some accented glyphs. The goal was to deliver the whole character set to the customer regardless of which operating system was used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The grounds advanced for the 'hypothesis' are worthless. The authors proposing such opinions might be competent, decent, honest individuals, but the views they present are demonstrably wrong.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, computational group theory is the study of groups by means of computers. It is concerned with designing and analysing algorithms and data structures to compute information about groups. The subject has attracted interest because for many interesting groups (including most of the sporadic groups) it is impractical to perform calculations by hand.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the calculus of variations the Legendre\u2013Clebsch condition is a second-order condition which a solution of the Euler\u2013Lagrange equation must satisfy in order to be a minimum. For the problem of minimizing \u222b a b L ( t , x , x \u2032 ) d t . {\\displaystyle \\int _{a}^{b}L(t,x,x')\\,dt.\\,} the condition is L x \u2032 x \u2032 ( t , x ( t ) , x \u2032 ( t ) ) \u2265 0 , \u2200 t \u2208  {\\displaystyle L_{x'x'}(t,x(t),x'(t))\\geq 0,\\,\\forall t\\in }", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Performing this operation gives us 2 1 \u00d7 0.0001 2 {\\displaystyle 2^{1}\\times 0.0001_{2}} or 2 \u2212 2 \u00d7 0.100 2 {\\displaystyle 2^{-2}\\times 0.100_{2}} . Without using a guard digit we have 2 1 \u00d7 0.100 2 \u2212 2 1 \u00d7 0.011 2 {\\displaystyle 2^{1}\\times 0.100_{2}-2^{1}\\times 0.011_{2}} , yielding 2 1 \u00d7 0.001 2 = {\\displaystyle 2^{1}\\times 0.001_{2}=} or 2 \u2212 1 \u00d7 0.100 2 {\\displaystyle 2^{-1}\\times 0.100_{2}} . This gives us a relative error of 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In networked systems where competitive decision making takes place, game theory is often used to model system dynamics, and convergence towards equilibria can be considered as a driver of topological evolution. For example, Kasthurirathna and Piraveenan have shown that when individuals in a system display varying levels of rationality, improving the overall system rationality might be an evolutionary reason for the emergence of scale-free networks. They demonstrated this by applying evolutionary pressure on an initially random network which simulates a range of classic games, so that the network converges towards Nash equilibria while being allowed to re-wire. The networks become increasingly scale-free during this process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In most cases, the annual maintenance costs dwarf the purchase price. For example, when policy servers are used (in both the plugin and proxy-based architectures), high-end hardware is needed in order to handle the workload required to run the web access management infrastructure. Centralized administration is an additional hidden cost, because customers will need to hire and train staff to exclusively manage policy entitlements for the underlying web applications. A final hidden cost relates to regulatory compliance. Since web access management is similar in concept to a firewall (more closely aligned to an application-layer firewall), it must be able to handle major audit requirements, especially for public companies subject to the Sarbanes-Oxley Act (not to mention those that are bound by the Health Insurance Portability and Accountability Act, PCI, or CPNI). Larger companies spend tremendous amounts of time and money auditing these web access management infrastructures since they are the enforcement points for many internal and external applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set; there are no unpaired elements between the two sets. In mathematical terms, a bijective function f: X \u2192 Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y. The term one-to-one correspondence must not be confused with one-to-one function (an injective function; see figures). A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and Markov modeling, an ancestral graph is a type of mixed graph to provide a graphical representation for the result of marginalizing one or more vertices in a graphical model that takes the form of a directed acyclic graph.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages, a delimited continuation, composable continuation or partial continuation, is a \"slice\" of a continuation frame that has been reified into a function. Unlike regular continuations, delimited continuations return a value, and thus may be reused and composed. Control delimiters, the basis of delimited continuations, were introduced by Matthias Felleisen in 1988 though early allusions to composable and delimited continuations can be found in Carolyn Talcott's Stanford 1984 dissertation, Felleisen et al., Felleisen's 1987 dissertation, and algorithms for functional backtracking, e.g., for pattern matching, for parsing, in the Algebraic Logic Functional programming language, and in the functional implementations of Prolog where the failure continuation is often kept implicit and the reason of being for the success continuation is that it is composable.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Due to the subtyping relation, a term may belong to more than one type. Subtyping is therefore a form of type polymorphism. In object-oriented programming the term 'polymorphism' is commonly used to refer solely to this subtype polymorphism, while the techniques of parametric polymorphism would be considered generic programming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory and statistics, a mixture is a probabilistic combination of two or more probability distributions. The concept arises mostly in two contexts: A mixture defining a new probability distribution from some existing ones, as in a mixture distribution or a compound distribution. Here a major problem often is to derive the properties of the resulting distribution. A mixture used as a statistical model such as is often used for statistical classification. The model may represent the population from which observations arise as a mixture of several components, and the problem is that of a mixture model, in which the task is to infer from which of a discrete set of sub-populations each observation originated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Mills' constant is defined as the smallest positive real number A such that the floor function of the double exponential function \u230a A 3 n \u230b {\\displaystyle \\lfloor A^{3^{n}}\\rfloor } is a prime number for all positive natural numbers n. This constant is named after William Harold Mills who proved in 1947 the existence of A based on results of Guido Hoheisel and Albert Ingham on the prime gaps. Its value is unproven, but if the Riemann hypothesis is true, it is approximately 1.3063778838630806904686144926... (sequence A051021 in the OEIS).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an evasive Boolean function \u0192 (of n variables) is a Boolean function for which every decision tree algorithm has running time of exactly n. Consequently, every decision tree algorithm that represents the function has, at worst case, a running time of n.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In military cryptography, a codress message is an encrypted message whose address is also encrypted. This is usually done to prevent traffic analysis. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Forward chaining starts with the known facts and asserts new facts. Backward chaining starts with goals, and works backward to determine what facts must be asserted so that the goals can be achieved.Additionally, the concept of 'inference' has expanded to include the process through which trained neural networks generate predictions or decisions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "With the development of formal logic, Hilbert asked whether it would be possible to prove that an axiom system is consistent by analyzing the structure of possible proofs in the system, and showing through this analysis that it is impossible to prove a contradiction. This idea led to the study of proof theory. Moreover, Hilbert proposed that the analysis should be entirely concrete, using the term finitary to refer to the methods he would allow but not precisely defining them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Engaging in a structured dialogue or repeated discussion, to exchange ideas about how to get specific about what it means and how to clear it up (scrum method). 13. Allocating different applications of the concept to different but related sets (Boolean logic).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the data warehousing strategy, the data from different sources are extracted and integrated in a single database. For example, various 'omics' datasets may be integrated to provide biological insights into biological systems. Examples include data from genomics, transcriptomics, proteomics, interactomics, metabolomics. Ideally, changes in these sources are regularly synchronized to the integrated database.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property (see definition below). This guarantees a low number of collisions in expectation, even if the data is chosen by an adversary. Many universal families are known (for hashing integers, vectors, strings), and their evaluation is often very efficient. Universal hashing has numerous uses in computer science, for example in implementations of hash tables, randomized algorithms, and cryptography.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a random minimum spanning tree may be formed by assigning random weights from some distribution to the edges of an undirected graph, and then constructing the minimum spanning tree of the graph. When the given graph is a complete graph on n vertices, and the edge weights have a continuous distribution function whose derivative at zero is D > 0, then the expected weight of its random minimum spanning trees is bounded by a constant, rather than growing as a function of n. More precisely, this constant tends in the limit (as n goes to infinity) to \u03b6(3)/D, where \u03b6 is the Riemann zeta function and \u03b6(3) is Ap\u00e9ry's constant. For instance, for edge weights that are uniformly distributed on the unit interval, the derivative is D = 1, and the limit is just \u03b6(3).In contrast to uniformly random spanning trees of complete graphs, for which the typical diameter is proportional to the square root of the number of vertices, random minimum spanning trees of complete graphs have typical diameter proportional to the cube root.Random minimum spanning trees of grid graphs may be used for invasion percolation models of liquid flow through a porous medium, and for maze generation. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While avoiding the problems of depending on delayed recordings, this method was not without its own inherent pitfalls. As the originating station was usually somewhat\u2014as far as 50\u2013100 miles (80\u2013160 km) or more\u2014the signal could frequently be degraded or interfered with by other stations on the same channel during periods of ionospheric or tropospheric disturbance. For that matter, if the originating station experienced technical difficulties and had to leave the air, the receiving station would be left without network programming during the outage as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The statement, 'If X exists, then X has most of the \u03c6's' expresses a necessary truth (in the idiolect of the speaker). (C) For any successful theory, the account must not be circular. The properties which are used in the vote must not themselves involve the notion of reference in such a way that it is ultimately impossible to eliminate.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "When the active array contains no more processes, the scheduler swaps the active and expired arrays, hence the name O(1) scheduler. In UNIX or Linux, the sar command is used to check the run queue. The vmstat UNIX or Linux command can also be used to determine the number of processes that are queued to run or waiting to run. These appear in the 'r' column. Example: $ vmstat procs -----------memory---------- ---swap-- -----io---- -system-- ------cpu----- r b swpd free buff cache si so bi bo in cs us sy id wa st 2 0 0 4579152 324416 4619528 0 0 402 236 3357 15 20 2 78 0 0 There are two models for Run queues: one that assigns a Run Queue to each physical processor, and the other has only one Run Queue in the system", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By analysing the retained data, governments can identify the locations of individuals, an individual's associates and the members of a group such as political opponents. These activities may or may not be lawful, depending on the constitutions and laws of each country. In many jurisdictions, access to these databases may be made by a government with little or no judicial oversight.In the case of commercial data retention, the data retained will usually be on transactions and web sites visited. Data retention also covers data collected by other means (e.g., by Automatic number-plate recognition systems) and held by government and commercial organisations.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p n {\\displaystyle p_{n}} , where n is its index in the ordered set of prime numbers, p n = p n \u2212 1 + p n + 1 2 . {\\displaystyle p_{n}={{p_{n-1}+p_{n+1}} \\over 2}.} For example, 53 is the sixteenth prime; the fifteenth and seventeenth primes, 47 and 59, add up to 106, and half of that is 53; thus 53 is a balanced prime.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The substitutions may be applied in any order we like, as the result will be the same. Below, the substitutions applied to the number on the previous line are on the right, the resulting number on the left. 211.0 1 _ 0 \u03d5 = 211 .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In one instance, Trojan horses were used as a targeted threat so that Israeli companies could conduct corporate espionage on each other. The Hotword Trojan, the Ginwui and the PPDropper Trojans are additional examples of Trojans used for corporate espionage. Targeted destination attacks use harvested IP addresses to send messages directly to recipients without an MX record lookup. It aims for specific sites and users by defeating hosted protection services and internal gateways to deliver e-mail with malicious payloads.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multilevel security mode of operation (also called Controlled Security Mode), all users must have: Signed NDA for ALL information on the system. Proper clearance for SOME information on the system. Formal access approval for SOME information on the system. A valid need to know for SOME information on the system.All users can access SOME data, based on their need to know, clearance and formal access approval", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At injection, the compressed air would then press the fuel through the disc-type atomisers into the combustion chamber. Manufacturing engines featuring the open nozzle design was considerably cheaper and easier than making them with a closed nozzle design. It also allows for using tar as fuel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social network analysis, betweenness centrality can have different implications. From a macroscopic perspective, bridging positions or \"structural holes\" (indicated by high betweenness centrality) reflect power, because they allow the person on the bridging position to exercise control (e.g., decide whether to share information or not) over the persons it connects between. From the microscopic perspective of ego networks (i.e., only considering first-degree connections), in online social networks a high betweenness centrality coincides with nominations of closest friends (i.e., strong interpersonal ties), because it reflects social capital investments into the relationship when distant social circles (e.g., family and university) are bridged (often resulting from an introduction by ego).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A proper treatment of this complication calls for the conception of something slightly more general than a sign relation proper, namely, a sign relational complex. In effect, expressed in the roughest practical terms, this allows for missing data in the columns of the relational database table for the sign relation in question. Typically one operates on the default assumption that all of the roles of elementary sign relations are filled, but remains wary enough of the possible exceptions to deal with them on an ad hoc basis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Analyses differ in how much they rely on morphology to explain them. Some have questioned their linguistic status, as well as the very use of the term \"classifier\". Not much is known yet about their syntax or phonology.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the construction of database applications, it can be useful to introduce an additional layer of data dictionary software, i.e. middleware, which communicates with the underlying DBMS data dictionary. Such a \"high-level\" data dictionary may offer additional features and a degree of flexibility that goes beyond the limitations of the native \"low-level\" data dictionary, whose primary purpose is to support the basic functions of the DBMS, not the requirements of a typical application. For example, a high-level data dictionary can provide alternative entity-relationship models tailored to suit different applications that share a common database. Extensions to the data dictionary also can assist in query optimization against distributed databases.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One exception to the single-entry-point paradigm is Android. Android applications do not have a single entry point \u2013 there is no special main function. Instead, they have essential components (activities and services) which the system can load and run as needed.An occasionally used technique is the fat binary, which consists of several executables for different targets packaged in a single file. Most commonly, this is implemented by a single overall entry point, which is compatible with all targets and branches to the target-specific entry point. Alternative techniques include storing separate executables in separate forks, each with its own entry point, which is then selected by the operating system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The nine lemma can be proved by direct diagram chasing, or by applying the snake lemma (to the two bottom rows in the first case, and to the two top rows in the second case). Linderholm (p.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the second sentence, \"is\" can however be interpreted as an ordinary copula and the past participle as an adjective. Sentences of the second type are called false passives by some linguists, who feel that such sentences are simply confused with the passive voice due to their outward similarity. Other linguists consider the second type to be a different kind of passive \u2013 a stative passive (rarely called statal, static, or resultative passive), in contrast to the dynamic or eventive passive illustrated by the first sentence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the quartic residue symbol, the law of quartic reciprocity for Gaussian integers states that if \u03c0 and \u03b8 are primary (congruent to 1 mod (1+i)3) Gaussian primes then   \u2212 1 = ( \u2212 1 ) N \u03c0 \u2212 1 4 N \u03b8 \u2212 1 4 . {\\displaystyle {\\Bigg }\\left^{-1}=(-1)^{{\\frac {N\\pi -1}{4}}{\\frac {N\\theta -1}{4}}}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer. For a comprehensible introduction to the topic see.Formally, cluster states | \u03d5 { \u03ba } \u27e9 C {\\displaystyle |\\phi _{\\{\\kappa \\}}\\rangle _{C}} are states which obey the set eigenvalue equations: K ( a ) | \u03d5 { \u03ba } \u27e9 C = ( \u2212 1 ) \u03ba a | \u03d5 { \u03ba } \u27e9 C {\\displaystyle K^{(a)}{\\left|\\phi _{\\{\\kappa \\}}\\right\\rangle _{C}}=(-1)^{\\kappa _{a}}{\\left|\\phi _{\\{\\kappa \\}}\\right\\rangle _{C}}} where K ( a ) {\\displaystyle K^{(a)}} are the correlation operators K ( a ) = \u03c3 x ( a ) \u2a02 b \u2208 N ( a ) \u03c3 z ( b ) {\\displaystyle K^{(a)}=\\sigma _{x}^{(a)}\\bigotimes _{b\\in \\mathrm {N} (a)}\\sigma _{z}^{(b)}} with \u03c3 x {\\displaystyle \\sigma _{x}} and \u03c3 z {\\displaystyle \\sigma _{z}} being Pauli matrices, N ( a ) {\\displaystyle N(a)} denoting the neighbourhood of a {\\displaystyle a} and { \u03ba a \u2208 { 0 , 1 } | a \u2208 C } {\\displaystyle \\{\\kappa _{a}\\in \\{0,1\\}|a\\in C\\}} being a set of binary parameters specifying the particular instance of a cluster state.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of searching for information, researchers have identified two forms of information overload: outcome overload where there are too many sources of information and textual overload where the individual sources are too long. This form of information overload may cause searchers to be less systematic. Disillusionment when a search is more challenging than expected may result in an individual being less able to search effectively. Information overload when searching can result in a satisficing strategy. : 7", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Russian peasant method, the powers of two in the decomposition of the multiplicand are found by writing it on the left and progressively halving the left column, discarding any remainder, until the value is 1 (or \u22121, in which case the eventual sum is negated), while doubling the right column as before. Lines with even numbers on the left column are struck out, and the remaining numbers on the right are added together.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Suppose we have a preparation procedure for a system in a physics lab: For example, the procedure might involve a physical apparatus and some protocols for manipulating the apparatus. As a result of this preparation procedure, some system is produced and maintained in isolation for some small period of time. By repeating this laboratory preparation procedure we obtain a sequence of systems X1, X2, ....,Xk, which in our mathematical idealization, we assume is an infinite sequence of systems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical physics, especially quantum mechanics, it is common to write the inner product between elements as \u27e8a|b\u27e9, as a short version of \u27e8a|\u00b7|b\u27e9, or \u27e8a|\u00d4|b\u27e9, where \u00d4 is an operator. This is known as Dirac notation or bra\u2013ket notation, to note vectors from the dual spaces of the Bra \u27e8A| and the Ket |B\u27e9. But there are other notations used. In continuum mechanics, chevrons may be used as Macaulay brackets.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The process of search can be divided in three parts: Generate descriptors for the media which we are going to use as query and the descriptors for the media in our database. Compare descriptors of the query and our database\u2019s media. List the media sorted by maximum coincidence.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behavior can be characterized: two readily understood behaviors are that the sequence eventually takes a constant value, and that values in the sequence continue to change but can be described by an unchanging probability distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 38, 138, 348, and 1348 are the patterns related to Braille pattern dots-26, since the two additional dots of kantenji patterns 026, 267, and 0267 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 23, 123, 234, and 1234 are the 8-dot braille patterns related to Braille pattern dots-12, since the two additional dots of kantenji patterns 012, 127, and 0127 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Further, Giles and Pulleyblank showed that if P {\\displaystyle P} is a polytope whose vertices are all integer valued, then P {\\displaystyle P} is the solution set of some TDI system A x \u2264 b {\\displaystyle Ax\\leq b} , where b {\\displaystyle b} is integer valued. Note that TDI is a weaker sufficient condition for integrality than total unimodularity. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In philosophy of science, confirmation holism, also called epistemological holism, is the view that no individual statement can be confirmed or disconfirmed by an empirical test, but rather that only a set of statements (a whole theory) can be so. It is attributed to Willard Van Orman Quine who motivated his holism through extending Pierre Duhem's problem of underdetermination in physical theory to all knowledge claims.Duhem's idea was, roughly, that no theory of any type can be tested in isolation but only when embedded in a background of other hypotheses, e.g. hypotheses about initial conditions. Quine thought that this background involved not only such hypotheses but also our whole web of belief, which, among other things, includes our mathematical and logical theories and our scientific theories. This last claim is sometimes known as the Duhem\u2013Quine thesis.A related claim made by Quine, though contested by some (see Adolf Gr\u00fcnbaum 1962), is that one can always protect one's theory against refutation by attributing failure to some other part of our web of belief. In his own words, \"Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, multinomial LR classifiers are commonly used as an alternative to naive Bayes classifiers because they do not assume statistical independence of the random variables (commonly known as features) that serve as predictors. However, learning in such a model is slower than for a naive Bayes classifier, and thus may not be appropriate given a very large number of classes to learn. In particular, learning in a Naive Bayes classifier is a simple matter of counting up the number of co-occurrences of features and classes, while in a maximum entropy classifier the weights, which are typically maximized using maximum a posteriori (MAP) estimation, must be learned using an iterative procedure; see #Estimating the coefficients.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In natural language processing, dependency-based parsing can be formulated as an ASP problem. The following code parses the Latin sentence \"Puella pulchra in villa linguam latinam discit\", \"the pretty girl is learning Latin in the villa\". The syntax tree is expressed by the arc predicates which represent the dependencies between the words of the sentence. The computed structure is a linearly ordered rooted tree.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One of the motivations of establishing a distinct, higher level of linguistic analysis is, then, to explain the structural ambiguity due to the constructional homonymities at a lower level. On the other hand, each linguistic level also captures some structural similarities within the level that are not explained in lower levels. Chomsky uses this argument as well to motivate the establishment of distinct levels of linguistic analysis.Chomsky then shows that a grammar which analyzes sentences up to the phrase structure level contains many constructional homonymities at the phrase structure level where the resulting ambiguities need to be explained at a higher level. Then he shows how his newly invented \u201ctransformational level\u201d can naturally and successfully function as that higher level. He further claims that any phrase structure grammar which cannot explain these ambiguities as successfully as transformational grammar does must be considered \"inadequate\".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, given a non-empty set of objects of finite extension in d {\\displaystyle d} -dimensional space, for example a set of points, a bounding sphere, enclosing sphere or enclosing ball for that set is an d {\\displaystyle d} -dimensional solid sphere containing all of these objects. Used in computer graphics and computational geometry, a bounding sphere is a special type of bounding volume. There are several fast and simple bounding sphere construction algorithms with a high practical value in real-time computer graphics applications.In statistics and operations research, the objects are typically points, and generally the sphere of interest is the minimal bounding sphere, that is, the sphere with minimal radius among all bounding spheres.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 368, 1368, 3468, and 13468 are the patterns related to Braille pattern dots-256, since the two additional dots of kantenji patterns 0256, 2567, and 02567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In early versions of the problem, the gambler begins with no initial knowledge about the machines. Herbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in \"some aspects of the sequential design of experiments\". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It arose in connection with James Watt's pioneering work on the steam engine. The equation of the curve can be given in polar coordinates as r 2 = b 2 \u2212  2 . {\\displaystyle r^{2}=b^{2}-\\left^{2}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Which is why it is important to consider encryption, hashing, and other security mechanisms in your design to ensure that information collected from a potential attacker won't allow access. Another key feature to client-server security design is good coding practices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Shrikhande graph, any two vertices I and J have two distinct neighbors in common (excluding the two vertices I and J themselves), which holds true whether or not I is adjacent to J. In other words, it is strongly regular and its parameters are: {16,6,2,2}, i.e., \u03bb = \u03bc = 2 {\\displaystyle \\lambda =\\mu =2} . This equality implies that the graph is associated with a symmetric BIBD. The Shrikhande graph shares these parameters with exactly one other graph, the 4\u00d74 rook's graph, i.e., the line graph L(K4,4) of the complete bipartite graph K4,4. The latter graph is the only line graph L(Kn,n) for which the strong regularity parameters do not determine that graph uniquely but are shared with a different graph, namely the Shrikhande graph (which is not a rook's graph).The Shrikhande graph is locally hexagonal; that is, the neighbors of each vertex form a cycle of six vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This was partly because differences in their architectures required these changes to optimize Unix to each architecture.Thus as general purpose operating systems became stable, supercomputers began to borrow and adapt the critical system code from them and relied on the rich set of secondary functions that came with them, not having to reinvent the wheel. However, at the same time the size of the code for general purpose operating systems was growing rapidly. By the time Unix-based code had reached 500,000 lines long, its maintenance and use was a challenge.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, the functions f {\\displaystyle f} and F {\\displaystyle F} are often not known or assumed. However, they can be estimated from an observed frequency distribution. In this section, we give an example. Consider the following table, representing a sample of 3,800 (discrete-valued) observations: Because the observations are discrete-valued, constructing the exact distribution of the median is not an immediate translation of the above expression for Pr ( Median = v ) {\\displaystyle \\Pr(\\operatorname {Median} =v)} ; one may (and typically does) have multiple instances of the median in one's sample.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Between the two extremes the realizations are discrete distributions with less and less concentration as \u03b1 {\\displaystyle \\alpha } increases. The Dirichlet process can also be seen as the infinite-dimensional generalization of the Dirichlet distribution. In the same way as the Dirichlet distribution is the conjugate prior for the categorical distribution, the Dirichlet process is the conjugate prior for infinite, nonparametric discrete distributions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are distinct because they possess a variety of desirable properties, most importantly the existence of a sufficient statistic. The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935\u20131936. Exponential families of distributions provides a general framework for selecting a possible alternative parameterisation of a parametric family of distributions, in terms of natural parameters, and for defining useful sample statistics, called the natural sufficient statistics of the family.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, only the receiving party has access to the decryption key that enables messages to be read. Public-key encryption was first described in a secret document in 1973; beforehand, all encryption schemes were symmetric-key (also called private-key). : 478 Although published subsequently, the work of Diffie and Hellman was published in a journal with a large readership, and the value of the methodology was explicitly described.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "\"Depending upon how appropriate the upgrades are considered by other owners of the same model, this may reduce or enhance the value of the car. If the car is in regular use, non-original upgrades are likely to be more acceptable; if the car is a stored collector's piece, originality would be more important. It is important as a restorer or owner to know what is acceptable to the potential market for the finished car, in order not to de-value it.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Veblen's theorem, introduced by Oswald Veblen (1912), states that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree. Thus, it is closely related to the theorem of Euler (1736) that a finite graph has an Euler tour (a single non-simple cycle that covers the edges of the graph) if and only if it is connected and every vertex has even degree. Indeed, a representation of a graph as a union of simple cycles may be obtained from an Euler tour by repeatedly splitting the tour into smaller cycles whenever there is a repeated vertex.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, \u03c6(9) = 6. As another example, \u03c6(1) = 1 since for n = 1 the only integer in the range from 1 to n is 1 itself, and gcd(1, 1) = 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The list of revisions from the start to HEAD (in graph theory terms, the unique path in the tree, which forms a linear graph as before) is the trunk or mainline. Conversely, when a revision can be based on more than one previous revision (when a node can have more than one parent), the resulting process is called a merge, and is one of the most complex aspects of revision control. This most often occurs when changes occur in multiple branches (most often two, but more are possible), which are then merged into a single branch incorporating both changes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "( z \u2208 w \u2194 ( z \u2208 x \u2228 z = y ) ) . {\\displaystyle \\forall x.\\forall y.\\exists w.\\forall z. {\\big (}z\\in w\\leftrightarrow (z\\in x\\lor z=y){\\big )}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, some Monte Carlo methods require independent observations in a sample to be drawn from a one-dimensional distribution in sorted order. In other words, all n order statistics are needed from the n observations in a sample. The naive method performs a sort and takes O(n log n) time. There are also O(n) algorithms which are better suited for large n. The special case of drawing n sorted observations from the uniform distribution on  is equivalent to drawing from the uniform distribution on an n-dimensional simplex; this task is a part of sequential importance resampling.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to represent any network, it is necessary to characterize the properties of the corresponding graph of nodes and links. Studies on the collaboration network of movie actors have been described in literature such as the work done by (Watts and Strogatz, 1998), and Barab\u00e1si and Albert in (1999) and (2000). The general characteristics are described below. According to Watts and Strogatz (1998), the movie/actor network indicated the following characteristics showing a small-world property of the underlying network:Size: 225 226 Average degree: 61 Average path length: 3.65 Clustering coefficient: 0.79Compared to a random graph of the same size and average degree, the average path length is close in value.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default. The motivation is twofold: first, maximizing entropy minimizes the amount of prior information built into the distribution; second, many physical systems tend to move towards maximal entropy configurations over time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In program analysis, shape analysis is a static code analysis technique that discovers and verifies properties of linked, dynamically allocated data structures in (usually imperative) computer programs. It is typically used at compile time to find software bugs or to verify high-level correctness properties of programs. In Java programs, it can be used to ensure that a sort method correctly sorts a list. For C programs, it might look for places where a block of memory is not properly freed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From an a-priori point of view, the main criticism is that taking s \u2192 0 {\\displaystyle s\\rightarrow 0} is far from leading to a noninformative prior. Moreover, a-posteriori, it assigns zero probability to any set that does not include the observations.The imprecise Dirichlet process has been proposed to overcome these issues. The basic idea is to fix s > 0 {\\displaystyle s>0} but do not choose any precise base measure G 0 {\\displaystyle G_{0}} . More precisely, the imprecise Dirichlet process (IDP) is defined as follows: I D P: { D P ( s , G 0 ): G 0 \u2208 P } {\\displaystyle ~~\\mathrm {IDP} :~\\left\\{\\mathrm {DP} \\left(s,G_{0}\\right):~~G_{0}\\in \\mathbb {P} \\right\\}} where P {\\displaystyle \\mathbb {P} } is the set of all probability measures. In other words, the IDP is the set of all Dirichlet processes (with a fixed s > 0 {\\displaystyle s>0} ) obtained by letting the base measure G 0 {\\displaystyle G_{0}} to span the set of all probability measures.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consider a computer program for recognizing dogs (the relevant element) in a digital photograph. Upon processing a picture which contains ten cats and twelve dogs, the program identifies eight dogs. Of the eight elements identified as dogs, only five actually are dogs (true positives), while the other three are cats (false positives).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Each bit completes a small task, which then builds up to the final bigger task. Like writing code on a computer, it is easier to write the basic smaller parts and make them work first, and then put them together to finish the larger more complicated code, instead of tackling the entire code from the very beginning. The first solution is less risky because if something goes wrong with the code, it is easier to look for the problem in the smaller bits, since the segment with the problem will be the one that does not work, while in the latter solution, the programmer may have to look through the entire code to search for a single error, which proves time-consuming.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number n such that the sum of all divisors of n (the sum-of-divisors function \u03c3(n)) is equal to 2n \u2212 1, the sum of all proper divisors of n, s(n) = \u03c3(n) \u2212 n, then being equal to n \u2212 1. The only known almost perfect numbers are powers of 2 with non-negative exponents (sequence A000079 in the OEIS). Therefore the only known odd almost perfect number is 20 = 1, and the only known even almost perfect numbers are those of the form 2k for some positive integer k; however, it has not been shown that all almost perfect numbers are of this form. It is known that an odd almost perfect number greater than 1 would have at least six prime factors.If m is an odd almost perfect number then m(2m \u2212 1) is a Descartes number. Moreover if a and b are positive odd integers such that b + 3 < a < m / 2 {\\displaystyle b+3", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a univariate polynomial has a simple root modulo a prime number p, then this root can be lifted to a unique root modulo any higher power of p. More generally, if a polynomial factors modulo p into two coprime polynomials, this factorization can be lifted to a factorization modulo any higher power of p (the case of roots corresponds to the case of degree 1 for one of the factors). By passing to the \"limit\" (in fact this is an inverse limit) when the power of p tends to infinity, it follows that a root or a factorization modulo p can be lifted to a root or a factorization over the p-adic integers. These results have been widely generalized, under the same name, to the case of polynomials over an arbitrary commutative ring, where p is replaced by an ideal, and \"coprime polynomials\" means \"polynomials that generate an ideal containing 1\". Hensel's lemma is fundamental in p-adic analysis, a branch of analytic number theory. The proof of Hensel's lemma is constructive, and leads to an efficient algorithm for Hensel lifting, which is fundamental for factoring polynomials, and gives the most efficient known algorithm for exact linear algebra over the rational numbers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the bootstrap is a method for inferring the variability of data that has an unknown distribution using pseudoreplications of the original data. For example, given a set of 100 data points, a pseudoreplicate is a data set of the same size (100 points) randomly sampled from the original data, with replacement. That is, each original data point may be represented more than once in the pseudoreplicate, or not at all. Statistical support involves evaluation of whether the original data has similar properties to a large set of pseudoreplicates.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Participants were asked to watch a 20-minute news video (half of the participants saw the negative images and the other half did not) and an additional ten-minute video. They were instructed to pay attention because they would be tested afterwards. A follow up survey was sent 6 to 7 weeks later to measure memory and recall from the news video.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, the decomposition method is an approximate method for the analysis of queueing networks where the network is broken into subsystems which are independently analyzed.The individual queueing nodes are considered to be independent G/G/1 queues where arrivals are governed by a renewal process and both service time and arrival distributions are parametrised to match the first two moments of data. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The sample code for the Banked XIOS implementation published in the MP/M II System Implementors Guide was written by Altos (and carries a disclaimer that it only works as-is with their Sun Series 8000).The \"8000\" contained in the name of Altos' first series of computer did cause some confusion in the marketplace because its name may have suggested the inclusion of the 16-bit Zilog Z8000 processor, which had just been released in 1979, although Altos' ACS-8000 did not use this processor, but the older 8-bit Z80. A 1981 review in Computerworld, comparing the ACS 8000 with other multi-user systems, found that Altos' Z80 processor was underpowered, especially for CPU-intensive tasks (most other multi-user systems used 16-bit processors by then), but the ACS-8000 was found adequate for multi-user order entry systems. A configuration with a 10-MB hard-drive plus a 1-MB 8\" floppy drive, bundled with a printer and one terminal was priced at $12,340 (the same machine but with four terminals was $15,625), which was considerably less than most other multi-user systems, which were typically priced in the $25,000\u2013$50,000 range.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ". . , N } {\\displaystyle q_{i}\\in \\{0,1,...,k\\},\\forall i\\in \\{1,2,...,N\\}} and that at least one component q i = k {\\displaystyle q_{i}=k} Let S N d {\\displaystyle S_{N}^{d}} represent a N-dimensional hypersphere with radius of d = \u2016 q \u2192 \u2016 {\\displaystyle d=\\left\\Vert {\\vec {q}}\\right\\Vert } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases a KBS could not be built because the organization did not have all the knowledge needed to support all their activities. In these cases logico-linguistic modeling showed shortcomings in the supply of information and where more was needed. For example, a planning department in a telecoms company", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it's defined by a ratio between the number of divisors an integer has and that integer raised to some positive power. For any possible exponent, whichever integer has the highest ratio is a superior highly composite number. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In telecommunication, a tactical communications system is a communications system that (a) is used within, or in direct support of, tactical forces, (b) is designed to meet the requirements of changing tactical situations and varying environmental conditions, (c) provides securable communications, such as voice, data, and video, among mobile users to facilitate command and control within, and in support of, tactical forces, and (d) usually requires extremely short installation times, usually on the order of hours, in order to meet the requirements of frequent relocation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In portfolio theory in finance, an objective often is to choose a portfolio of risky assets such that the distribution of the random portfolio return has desirable properties. For example, one might want to choose the portfolio return having the lowest variance for a given expected value. Here the random vector is the vector r {\\displaystyle \\mathbf {r} } of random returns on the individual assets, and the portfolio return p (a random scalar) is the inner product of the vector of random returns with a vector w of portfolio weights \u2014 the fractions of the portfolio placed in the respective assets. Since p = wT r {\\displaystyle \\mathbf {r} } , the expected value of the portfolio return is wTE( r {\\displaystyle \\mathbf {r} } ) and the variance of the portfolio return can be shown to be wTCw, where C is the covariance matrix of r {\\displaystyle \\mathbf {r} } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Loosely speaking, rejection of the null hypothesis implies that there is sufficient evidence against it. As a particular example, if a null hypothesis states that a certain summary statistic T {\\displaystyle T} follows the standard normal distribution N(0,1), then the rejection of this null hypothesis could mean that (i) the mean of T {\\displaystyle T} is not 0, or (ii) the variance of T {\\displaystyle T} is not 1, or (iii) T {\\displaystyle T} is not normally distributed. Different tests of the same null hypothesis would be more or less sensitive to different alternatives. However, even if we do manage to reject the null hypothesis for all 3 alternatives, and even if we know the distribution is normal and variance is 1, the null hypothesis test does not tell us which non-zero values of the mean are now most plausible. The more independent observations from the same probability distribution one has, the more accurate the test will be, and the higher the precision with which one will be able to determine the mean value and show that it is not equal to zero; but this will also increase the importance of evaluating the real-world or scientific relevance of this deviation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "+ t 2 \u2211 \u27e8 \u27e8 i , j \u27e9 \u27e9 ( c i \u03c3 \u2020 c j \u03c3 + h . c . ) + J \u2211 \u27e8 i , j \u27e9 ( S i \u22c5 S j \u2212 n i n j 4 ) \u2212 \u03bc \u2211 i n i , {\\displaystyle {\\mathcal {\\hat {H}}}=t_{1}\\sum \\limits _{\\langle i,j\\rangle }\\left(c_{i\\sigma }^{\\dagger }c_{j\\sigma }+\\mathrm {h.c.} \\right)\\ +\\ t_{2}\\sum \\limits _{\\langle \\langle i,j\\rangle \\rangle }\\left(c_{i\\sigma }^{\\dagger }c_{j\\sigma }+\\mathrm {h.c.} \\right)\\ +\\ J\\sum \\limits _{\\langle i,j\\rangle }\\left(\\mathbf {S} _{i}\\cdot \\mathbf {S} _{j}-{\\frac {n_{i}n_{j}}{4}}\\right)-\\ \\mu \\sum \\limits _{i}n_{i},} where \u27e8...\u27e9 and \u27e8\u27e8...\u27e9\u27e9 denote the nearest and next-nearest neighbors, respectively, with two different values for the hopping integral (t1 and t2) and \u03bc is the chemical potential.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Ground truth also helps with atmospheric correction. Since images from satellites have to pass through the atmosphere, they can get distorted because of absorption in the atmosphere. So ground truth can help fully identify objects in satellite photos.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Permissible station content is defined by the FCC as: \"...only noncommercial voice information pertaining to traffic and road conditions, traffic hazard and travel advisories, directions, availability of lodging, rest stops and service stations, and descriptions of local points of interest. It is not permissible to identify the commercial name of any business whose service may be available within or outside the coverage area of a Travelers' Information Station. However, to facilitate announcements concerning departures/arrivals and parking areas at air, train, and bus terminals, the trade name identification of carriers is permitted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the fields of predictive modelling and probabilistic forecasting, the Markov property is considered desirable since it may enable the reasoning and resolution of the problem that otherwise would not be possible to be resolved because of its intractability. Such a model is known as a Markov model.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In polyhedral combinatorics, the hypersimplex \u0394 d , k {\\displaystyle \\Delta _{d,k}} is a convex polytope that generalizes the simplex. It is determined by two integers d {\\displaystyle d} and k {\\displaystyle k} , and is defined as the convex hull of the d {\\displaystyle d} -dimensional vectors whose coefficients consist of k {\\displaystyle k} ones and d \u2212 k {\\displaystyle d-k} zeros. Equivalently, \u0394 d , k {\\displaystyle \\Delta _{d,k}} can be obtained by slicing the d {\\displaystyle d} -dimensional unit hypercube  d {\\displaystyle ^{d}} with the hyperplane of equation x 1 + \u22ef + x d = k {\\displaystyle x_{1}+\\cdots +x_{d}=k} and, for this reason, it is a ( d \u2212 1 ) {\\displaystyle (d-1)} -dimensional polytope when 0 < k < d {\\displaystyle 0", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "must be nowhere near as talented as the devoted and serious method actors that aren't so popular like . \"In general, the reversal usually goes: Most people believe A and B are both true. B is false.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Evaluating the loop condition can have side effects, so an additional evaluation by the if construct should be compensated by replacing the while loop with a do {} while. If the code used do {} while in the first place, the whole guarding process is not needed, as the loop body is guaranteed to execute at least once. This code can be optimized further. For example, strength reduction could remove the two multiplications inside the loop (6*i and a), and induction variable elimination could then elide i completely. Since 6 * i must be in lock step with i itself, there is no need to have both.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, the cake may be the 1-dimensional interval  and each piece is an interval; or, the cake may be a rectangle cut along its longer side so that each piece is a rectangle. Every cut-set can be represented by n numbers xi, i = 1, ..., n, where xi is the length of the ith piece. We assume that the total length of the cake is 1, so x1 + ... + xn = 1.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Exact tests that are based on discrete test statistics may be conservative, indicating that the actual rejection rate lies below the nominal significance level \u03b1 {\\displaystyle \\alpha } . As an example, this is the case for Fisher's exact test and its more powerful alternative, Boschloo's test. If the test statistic is continuous, it will reach the significance level exactly.Parametric tests, such as those used in exact statistics, are exact tests when the parametric assumptions are fully met, but in practice, the use of the term exact (significance) test is reserved for non-parametric tests, i.e., tests that do not rest on parametric assumptions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied to the product ab is the sum of the values of the function applied to a and b:", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Sprague\u2013Grundy theory the minimum excluded ordinal is used to determine the nimber of a normal-play impartial game. In such a game, either player has the same moves in each position and the last player to move wins. The nimber is equal to 0 for a game that is lost immediately by the first player, and is equal to the mex of the nimbers of all possible next positions for any other game. For example, in a one-pile version of Nim, the game starts with a pile of n stones, and the player to move may take any positive number of stones.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Memory controllers such as the Intel 945 Chipset list the configurations they support: \"256-Mib, 512-Mib, and 1-Gib DDR2 technologies for \u00d78 and \u00d716 devices\", \"four ranks for all DDR2 devices up to 512-Mibit density\", \"eight ranks for 1-Gibit DDR2 devices\". As an example, take an i945 memory controller with four Kingston KHX6400D2/1G memory modules, where each module has a capacity of 1 GiB. Kingston describes each module as composed of 16 \"64M\u00d78-bit\" chips with each chip having an 8-bit-wide data bus.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Equivalent to bitwise addition without use of a carry bit. ||: Concatenation operator. Combine the strings on either side of the operator. 0a: a string of a 0 bits.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "From the 1920s through the 1970s, typing speed (along with shorthand speed) was an important secretarial qualification and typing contests were popular and often publicized by typewriter companies as promotional tools. A less common measure of the speed of a typist, CPM is used to identify the number of characters typed per minute. This is a common measurement for typing programs, or typing tutors, as it can give a more accurate measure of a person's typing speed without having to type for a prolonged period of time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The numbers less than ( n k ) {\\displaystyle {\\tbinom {n}{k}}} correspond to all k-combinations of {0, 1, ..., n \u2212 1}. The correspondence does not depend on the size n of the set that the k-combinations are taken from, so it can be interpreted as a map from N to the k-combinations taken from N; in this view the correspondence is a bijection. The number N corresponding to (ck, ..., c2, c1) is given by N = ( c k k ) + \u22ef + ( c 2 2 ) + ( c 1 1 ) {\\displaystyle N={\\binom {c_{k}}{k}}+\\cdots +{\\binom {c_{2}}{2}}+{\\binom {c_{1}}{1}}} .The fact that a unique sequence corresponds to any non-negative number N was first observed by D. H. Lehmer.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, Bertrand's postulate is a theorem stating that for any integer n > 1 {\\displaystyle n>1} , there always exists at least one prime number such that n < p < 2 n . {\\displaystyle n", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Atari's 8-bit line used a SYSTEM RESET button for this same purpose. Debugging NMIs have appeared in a number of forms, including the Apple Macintosh's \"programmers' button\", and certain key combinations on Sun workstations. With the introduction of Windows 2000, Microsoft allowed the use of an NMI to cause a system to either break into a debugger, or dump the contents of memory to disk and reboot.Debugging NMIs have also been used by devices that allow leisure users and gamers to manipulate running programs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same vector space (for example, a bilinear form or a multilinear form) that is zero whenever any pair of arguments is equal. More generally, the vector space may be a module over a commutative ring. The notion of alternatization (or alternatisation) is used to derive an alternating multilinear map from any multilinear map with all arguments belonging to the same space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In military operations, high-value targets such as command centers are frequently protected by layers of defense systems, which may in turn be protected by other systems. In order to reach a target, all of its defenses must be taken down, making it into a secondary target. Each target needs a certain amount of resources to be allocated to it in order to perform a successful attack. The optimal set of targets to attack, to obtain the most value for the resources expended, can be modeled as a closure problem.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In syntactic ambiguity, the same sequence of words is interpreted as having different syntactic structures. In contrast, in semantic ambiguity the structure remains the same, but the individual words are interpreted differently. Controlled natural languages are often designed to be unambiguous so that they can be parsed into a logical form.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of composition of the differential operator Di which takes the partial derivative with respect to xi: D i \u2218 D j = D j \u2218 D i {\\displaystyle D_{i}\\circ D_{j}=D_{j}\\circ D_{i}} .From this relation it follows that the ring of differential operators with constant coefficients, generated by the Di, is commutative; but this is only true as operators over a domain of sufficiently differentiable functions. It is easy to check the symmetry as applied to monomials, so that one can take polynomials in the xi as a domain. In fact smooth functions are another valid domain.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Category theory deals with abstract objects and morphisms between those objects. In category theory, an automorphism is an endomorphism (i.e., a morphism from an object to itself) which is also an isomorphism (in the categorical sense of the word, meaning there exists a right and left inverse endomorphism). This is a very abstract definition since, in category theory, morphisms are not necessarily functions and objects are not necessarily sets. In most concrete settings, however, the objects will be sets with some additional structure and the morphisms will be functions preserving that structure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose. Specifically, the commutation matrix K(m,n) is the nm \u00d7 mn matrix which, for any m \u00d7 n matrix A, transforms vec(A) into vec(AT): K(m,n) vec(A) = vec(AT) .Here vec(A) is the mn \u00d7 1 column vector obtain by stacking the columns of A on top of one another: vec \u2061 ( A ) =  T {\\displaystyle \\operatorname {vec} (\\mathbf {A} )=^{\\mathrm {T} }} where A = . In other words, vec(A) is the vector obtained by vectorizing A in column-major order. Similarly, vec(AT) is the vector obtaining by vectorizing A in row-major order. In the context of quantum information theory, the commutation matrix is sometimes referred to as the swap matrix or swap operator", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The maximum entropy principle is also needed to guarantee the uniqueness and consistency of probability assignments obtained by different methods, statistical mechanics and logical inference in particular. The maximum entropy principle makes explicit our freedom in using different forms of prior data. As a special case, a uniform prior probability density (Laplace's principle of indifference, sometimes called the principle of insufficient reason), may be adopted.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Active Format Description is occasionally incorrectly referred to as \"Active Format Descriptor\". There is no \"descriptor\" (descriptor has a specific meaning in ISO/IEC 13818-1, MPEG syntax). The AFD data is carried in the Video Layer of MPEG, ISO/IEC 13818-2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the book The Humane Interface, Jef Raskin championed what he termed quasimodes, which are modes that are kept in place only through some constant action on the part of the user; such modes are also called spring-loaded modes. The term quasimode is a composite of the Latin prefix quasi- (which means almost, to some degree) and the English word \"mode\". Modifier keys on the keyboard, such as the Shift key, the Alt key and the Control key, are all examples of a quasimodal interface. The application enters into that mode as long as the user is performing a conscious action, like pressing a key and keeping it pressed while invoking a command.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, if one wishes to prove that every girl in the United States (A) has brown hair (B), one can either try to directly prove A \u2192 B {\\displaystyle A\\to B} by checking that all girls in the United States do indeed have brown hair, or try to prove \u00ac B \u2192 \u00ac A {\\displaystyle \\neg B\\to \\neg A} by checking that all girls without brown hair are indeed all outside the US. In particular, if one were to find at least one girl without brown hair within the US, then one would have disproved \u00ac B \u2192 \u00ac A {\\displaystyle \\neg B\\to \\neg A} , and equivalently A \u2192 B {\\displaystyle A\\to B} . In general, for any statement where A implies B, not B always implies not A. As a result, proving or disproving either one of these statements automatically proves or disproves the other, as they are logically equivalent to each other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the era of the electrical telegraph, its principal users were post offices, railway stations, the more important governmental centers (ministries), stock exchanges, very few nationally distributed newspapers, the largest internationally important corporations, and wealthy individuals. Despite the fact that telephone devices existed before the invention of the telephone exchange, their success and economical operation would have been impossible on the same schema and structure of the contemporary telegraph, as prior to the invention of the telephone exchange switchboard, early telephones were hardwired to and communicated with only a single other telephone (such as from an individual's home to the person's business). A telephone exchange is a telephone system for a small geographic area that provides the switching (interconnection) of subscriber lines for calls made between them. Telephone exchanges replaced small telephone systems that connected its users with direct lines between each and every subscriber station.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "While such sources are still at a developmental stage QKD has been carried out successfully with them. However, as current sources operate at a low efficiency and frequency key rates and transmission distances are limited. Another solution is to modify the BB84 protocol, as is done for example in the SARG04 protocol, in which the secure key rate scales as t 3 / 2 {\\displaystyle t^{3/2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It also entails two-way explicit key confirmation, making it an authenticated key agreement with key confirmation (AKC) protocol. STS was originally presented in 1987 in the context of ISDN security (O'Higgins et al. 1987), finalized in 1989 and generally presented by Whitfield Diffie, Paul C. van Oorschot and Michael J. Wiener in 1992. The historical context for the protocol is also discussed in Diffie (1988).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The APEX API provides services to manage partitions, processes and timing, as well as partition/process communication and error handling. The partitioning environment can be implemented by using a hypervisor to map partitions to virtual machines, but this is not required. The standard is overseen by the AEEC APEX Subcommittee.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In software development, agile practices (sometimes written \"Agile\") include requirements discovery and solutions improvement through the collaborative effort of self-organizing and cross-functional teams with their customer(s)/end user(s), Popularized in the 2001 Manifesto for Agile Software Development, these values and principles were derived from and underpin a broad range of software development frameworks, including Scrum and Kanban.While there is much anecdotal evidence that adopting agile practices and values improves the effectiveness of software professionals, teams and organizations, the empirical evidence is mixed and hard to find.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In set theory, an element of a subset inherits all the attributes contained in the superset. For example, a student is a person. Therefore, the set of students is a subset of the set of persons.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is assumed that G is simple, that is, it does not contain loops or parallel edges. Let A be the adjacency matrix of G and let \u03bb i {\\displaystyle \\lambda _{i}} , i = 1 , \u2026 , n {\\displaystyle i=1,\\ldots ,n} , be the eigenvalues of A. Then the energy of the graph is defined as: E ( G ) = \u2211 i = 1 n | \u03bb i | . {\\displaystyle E(G)=\\sum _{i=1}^{n}|\\lambda _{i}|.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This necessary distributivity of \u2022 over \u2228 does not in general entail distributivity of \u2227 over \u2228, that is, a residuated lattice need not be a distributive lattice. However distributivity of \u2227 over \u2228 is entailed when \u2022 and \u2227 are the same operation, a special case of residuated lattices called a Heyting algebra. Alternative notations for x\u2022y include x\u25e6y, x;y (relation algebra), and x\u2297y (linear logic).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, addition and multiplication of real numbers is associative. By contrast, in computer science, the addition and multiplication of floating point numbers is not associative, as rounding errors are introduced when dissimilar-sized values are joined together.To illustrate this, consider a floating point representation with a 4-bit mantissa: Even though most computers compute with 24 or 53 bits of mantissa, this is an important source of rounding error, and approaches such as the Kahan summation algorithm are ways to minimise the errors. It can be especially problematic in parallel computing.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of bipartite graphs or multigraphs with maximum degree \u0394, the optimal number of colors is exactly \u0394. Cole, Ost & Schirra (2001) showed that an optimal edge coloring of these graphs can be found in the near-linear time bound O(m log \u0394), where m is the number of edges in the graph; simpler, but somewhat slower, algorithms are described by Cole & Hopcroft (1982) and Alon (2003). The algorithm of Alon (2003) begins by making the input graph regular, without increasing its degree or significantly increasing its size, by merging pairs of vertices that belong to the same side of the bipartition and then adding a small number of additional vertices and edges. Then, if the degree is odd, Alon finds a single perfect matching in near-linear time, assigns it a color, and removes it from the graph, causing the degree to become even. Finally, Alon applies an observation of Gabow (1976), that selecting alternating subsets of edges in an Euler tour of the graph partitions it into two regular subgraphs, to split the edge coloring problem into two smaller subproblems, and his algorithm solves the two subproblems recursively.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the layer cake representation of a non-negative, real-valued measurable function f {\\displaystyle f} defined on a measure space ( \u03a9 , A , \u03bc ) {\\displaystyle (\\Omega ,{\\mathcal {A}},\\mu )} is the formula f ( x ) = \u222b 0 \u221e 1 L ( f , t ) ( x ) d t , {\\displaystyle f(x)=\\int _{0}^{\\infty }1_{L(f,t)}(x)\\,\\mathrm {d} t,} for all x \u2208 \u03a9 {\\displaystyle x\\in \\Omega } , where 1 E {\\displaystyle 1_{E}} denotes the indicator function of a subset E \u2286 \u03a9 {\\displaystyle E\\subseteq \\Omega } and L ( f , t ) {\\displaystyle L(f,t)} denotes the super-level set L ( f , t ) = { y \u2208 \u03a9 \u2223 f ( y ) \u2265 t } . {\\displaystyle L(f,t)=\\{y\\in \\Omega \\mid f(y)\\geq t\\}.} The layer cake representation follows easily from observing that 1 L ( f , t ) ( x ) = 1  ( t ) {\\displaystyle 1_{L(f,t)}(x)=1_{}(t)} and then using the formula f ( x ) = \u222b 0 f ( x ) d t . {\\displaystyle f(x)=\\int _{0}^{f(x)}\\,\\mathrm {d} t.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In marketing, customers can be grouped into fuzzy clusters based on their needs, brand choices, psycho-graphic profiles, or other marketing related partitions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Other examples include the functions sin \u2061 ( x ) x {\\displaystyle {\\frac {\\sin(x)}{x}}} and x x . {\\displaystyle x^{x}.} Liouville's theorem states that elementary antiderivatives, if they exist, are in the same differential field as the function, plus possibly a finite number of applications of the logarithm function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Initially, every element in the matrix is zeros. Then for each \u201cedge\u201d point in the original space, we can formulate a circle in the parameter space and increase the voting number of the grid cell which the circle passes through. This process is called \u201cvoting\u201d. After voting, we can find local maxima in the accumulator matrix. The positions of the local maxima are corresponding to the circle centers in the original space.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sometimes the term noncommutative ring is used instead of ring to refer to an unspecified ring which is not necessarily commutative, and hence may be commutative. Generally, this is for emphasizing that the studied properties are not restricted to commutative rings, as, in many contexts, ring is used as a shorthand for commutative ring. Although some authors do not assume that rings have a multiplicative identity, in this article we make that assumption unless stated otherwise.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Such non-subclassable classes restrict reusability, particularly when developers only have access to precompiled binaries and not source code. A non-subclassable class has no subclasses, so it can be easily deduced at compile time that references or pointers to objects of that class are actually referencing instances of that class and not instances of subclasses (they don't exist) or instances of superclasses (upcasting a reference type violates the type system). Because the exact type of the object being referenced is known before execution, early binding (also called static dispatch) can be used instead of late binding (also called dynamic dispatch), which requires one or more virtual method table lookups depending on whether multiple inheritance or only single inheritance are supported in the programming language that is being used.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles: T M = Q 1 + 2 Q 2 + Q 3 4 {\\displaystyle TM={\\frac {Q_{1}+2Q_{2}+Q_{3}}{4}}} This is equivalent to the average of the median and the midhinge: T M = 1 2 ( Q 2 + Q 1 + Q 3 2 ) {\\displaystyle TM={\\frac {1}{2}}\\left(Q_{2}+{\\frac {Q_{1}+Q_{3}}{2}}\\right)} The foundations of the trimean were part of Arthur Bowley's teachings, and later popularized by statistician John Tukey in his 1977 book which has given its name to a set of techniques called exploratory data analysis. Like the median and the midhinge, but unlike the sample mean, it is a statistically resistant L-estimator with a breakdown point of 25%. This beneficial property has been described as follows: An advantage of the trimean as a measure of the center (of a distribution) is that it combines the median's emphasis on center values with the midhinge's attention to the extremes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multivariate analysis, canonical correspondence analysis (CCA) is an ordination technique that determines axes from the response data as a linear combination of measured predictors. CCA is commonly used in ecology in order to extract gradients that drive the composition of ecological communities. CCA extends Correspondence Analysis (CA) with regression, in order to incorporate predictor variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term is also used for the goal that is achieved, when such a design has reached the end of the flow and its timing requirements are satisfied. The main steps of the design flow, which may be involved in this process, are logic synthesis, placement, clock-tree synthesis and routing. A single reference clock is often cascaded and synthesized into many different output blocks of clocks resulting into a tree structure. With present technologies all of them need to be timing-aware for a design to properly meet its timing requirements, but with technologies in the range of the micrometre only logic synthesis EDA tools had such a prerequisite.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to minimize the risk of dangerous failures, safety-related electronic systems have to be developed following the applicable product liability requirements. Disregard for, or inadequate application of these standards can lead to not only personal injuries, but also severe legal and economic consequences such as product cancellations or recalls. The IEC 61508 standard, generally applicable to electrical/electronic/programmable safety-related products, is only partially adequate for automotive-development requirements.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some implementations the performance of the physical storage can actually be improved, mainly due to caching. Caching however requires the visibility of the data contained within the I/O request and so is limited to in-band and symmetric virtualization software and devices. However these implementations also directly influence the latency of an I/O request (cache miss), due to the I/O having to flow through the software or device. Assuming the software or device is efficiently designed this impact should be minimal when compared with the latency associated with physical disk accesses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The necessary conditions are sufficient for optimality if the objective function f {\\displaystyle f} of a maximization problem is a differentiable concave function, the inequality constraints g j {\\displaystyle g_{j}} are differentiable convex functions, the equality constraints h i {\\displaystyle h_{i}} are affine functions, and Slater's condition holds. Similarly, if the objective function f {\\displaystyle f} of a minimization problem is a differentiable convex function, the necessary conditions are also sufficient for optimality. It was shown by Martin in 1985 that the broader class of functions in which KKT conditions guarantees global optimality are the so-called Type 1 invex functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They are not allowed access to any identifying information, however. Risk of death or harm Information within the record can be shared with authorities without permission when failure to do so would result in death or harm, either to the patient or to others. Information cannot be used, however, to initiate or substantiate a charge unless the previous criteria are met (i.e., information from illicit drug testing cannot be used to bring charges of possession against a patient). This rule was established in the United States Supreme Court case Jaffe v. Redmond .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The first term on the right is the \"reduced correlation matrix\" and will be equal to the correlation matrix except for its diagonal values which will be less than unity. These diagonal elements of the reduced correlation matrix are called \"communalities\" (which represent the fraction of the variance in the observed variable that is accounted for by the factors): h a 2 = 1 \u2212 \u03c8 a = \u2211 j \u2113 a j \u2113 a j {\\displaystyle h_{a}^{2}=1-\\psi _{a}=\\sum _{j}\\ell _{aj}\\ell _{aj}} The sample data z a i {\\displaystyle z_{ai}} will not exactly obey the fundamental equation given above due to sampling errors, inadequacy of the model, etc. The goal of any analysis of the above model is to find the factors F p i {\\displaystyle F_{pi}} and loadings \u2113 a p {\\displaystyle \\ell _{ap}} which give a \"best fit\" to the data. In factor analysis, the best fit is defined as the minimum of the mean square error in the off-diagonal residuals of the correlation matrix: \u03b5 2 = \u2211 a \u2260 b  2 {\\displaystyle \\varepsilon ^{2}=\\sum _{a\\neq b}\\left^{2}} This is equivalent to minimizing the off-diagonal components of the error covariance which, in the model equations have expected values of zero.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle (s\\cdot f)(x)=f(xs).} It is well-defined (i.e., s \u22c5 f {\\displaystyle s\\cdot f} is R-linear) since ( s \u22c5 f ) ( r x ) = f ( r x s ) = r f ( x s ) = r ( s \u22c5 f ) ( x ) , {\\displaystyle (s\\cdot f)(rx)=f(rxs)=rf(xs)=r(s\\cdot f)(x),} and s \u22c5 f {\\displaystyle s\\cdot f} is a ring action since ( s t \u22c5 f ) ( x ) = f ( x s t ) = ( t \u22c5 f ) ( x s ) = s \u22c5 ( t \u22c5 f ) ( x ) {\\displaystyle (st\\cdot f)(x)=f(xst)=(t\\cdot f)(xs)=s\\cdot (t\\cdot f)(x)} .Note: the above verification would \"fail\" if one used the left R-action in place of the right S-action. In this sense, Hom is often said to \"use up\" the R-action. Similarly, if M is a left R-module and N is an (R, S)-module, then Hom R \u2061 ( M , N ) {\\displaystyle \\operatorname {Hom} _{R}(M,N)} is a right S-module by ( f \u22c5 s ) ( x ) = f ( x ) s {\\displaystyle (f\\cdot s)(x)=f(x)s} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The proof was accepted for publication in the Annals of Mathematics Studies series in 2015, and has been undergoing further review and revision since; fully-refereed chapters in close to final form are being made public in the process.Some state the conjecture as Every odd number greater than 7 can be expressed as the sum of three odd primes.This version excludes 7 = 2+2+3 because this requires the even prime 2. On odd numbers larger than 7 it is slightly stronger as it also excludes sums like 17 = 2+2+13, which are allowed in the other formulation. Helfgott's proof covers both versions of the conjecture. Like the other formulation, this one also immediately follows from Goldbach's strong conjecture.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and computing, the Levenberg\u2013Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss\u2013Newton algorithm (GNA) and the method of gradient descent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To support his position that methodological rules generally do not contribute to scientific success, Feyerabend analyzed counterexamples to the claim that (good) science operates according to the methodological standards invoked by philosophers during Feyerabend's time (namely, inductivism and falsificationism). Starting from episodes in science that are generally regarded as indisputable instances of progress (e.g. the Copernican revolution), he argued that these episodes violated all common prescriptive rules of science. Moreover, he claimed that applying such rules in these historical situations would actually have prevented scientific revolution. His primary case study is Galileo's hypothesis that the earth rotates on its axis.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics education at the primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method with the addition of a line separating the divisor, dividend, and partial quotients. It has a counterpart in the grid method for multiplication as well. In general, chunking is more flexible than the traditional method in that the calculation of quotient is less dependent on the place values.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the case of symmetric-key algorithm cryptosystems, an adversary must not be able to compute any information about a plaintext from its ciphertext. This may be posited as an adversary, given two plaintexts of equal length and their two respective ciphertexts, cannot determine which ciphertext belongs to which plaintext.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In music theory, the term mode or modus is used in a number of distinct senses, depending on context. Its most common use may be described as a type of musical scale coupled with a set of characteristic melodic and harmonic behaviors. It is applied to major and minor keys as well as the seven diatonic modes (including the former as Ionian and Aeolian) which are defined by their starting note or tonic. (Olivier Messiaen's modes of limited transposition are strictly a scale type.)", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, for certain systems and algorithms, complete pivoting (or maximal pivoting) may be required for acceptable accuracy. Complete pivoting interchanges both rows and columns in order to use the largest (by absolute value) element in the matrix as the pivot. Complete pivoting is usually not necessary to ensure numerical stability and, due to the additional cost of searching for the maximal element, the improvement in numerical stability that it provides is typically outweighed by its reduced efficiency for all but the smallest matrices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the context of IBM PC compatible and Wintel platforms, a 16-bit application is any software written for MS-DOS, OS/2 1.x or early versions of Microsoft Windows which originally ran on the 16-bit Intel 8088 and Intel 80286 microprocessors. Such applications used a 20-bit or 24-bit segment or selector-offset address representation to extend the range of addressable memory locations beyond what was possible using only 16-bit addresses. Programs containing more than 216 bytes (65,536 bytes) of instructions and data therefore required special instructions to switch between their 64-kilobyte segments, increasing the complexity of programming 16-bit applications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, cuckoo hashing is about 20\u201330% slower than linear probing, which is the fastest of the common approaches. The reason is that cuckoo hashing often causes two cache misses per search, to check the two locations where a key might be stored, while linear probing usually causes only one cache miss per search. However, because of its worst case guarantees on search time, cuckoo hashing can still be valuable when real-time response rates are required. One advantage of cuckoo hashing is its link-list free property, which fits GPU processing well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following examples: let F, G, H be predicate letters; let a, b, c be individual constants; let x, y, z be variables.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The technique is used frequently when a complete list of all members of the population does not exist and is inappropriate. In some cases, several levels of cluster selection may be applied before the final sample elements are reached. For example, household surveys conducted by the Australian Bureau of Statistics begin by dividing metropolitan regions into 'collection districts' and selecting some of these collection districts (first stage).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1980s the French Thomson company produced a range of 8-bit computers based on the 6809E CPU.They were released in several variations (mostly concerning the keyboard or color of the casing) covering the MO and TO series from late 1982 to 1989. While MO and TO models are incompatible in software, most of the peripherals and hardware were compatible. These machines were common in France due to the 1980s governmental educational program Computing for All (Informatique pour Tous). Around 100,000 MO5 and TO7/70 computers were ordered and installed in schools.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A document that is stored in such a database, typically would contain more than one normalized data unit and often the relationships between the units as well. If all the data units and the relationships in question are often retrieved together, then this approach optimizes the number of retrieves. It also simplifies how data gets replicated, because now there is a clearly identifiable unit of data whose consistency is self-contained.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mid-2002 the CFSCI was established as a non-membership 501(c)(3) corporation under non-profit law. The CFSCI Board of Directors and its staff comprise the CFSCI. (Subsequently, the CFSCI Board amended the bylaws to create a class of \"at-large members,\" however the at-large members have no voting rights.) The CFSCI was set up as a non-membership organization because the AAG felt it would be too cumbersome to include representatives from all local FSCs in future voting, due to how many local councils there were and how difficult it was to determine how the various FSCs would be represented, given how many different types of FSCs there were.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This architecture may replace the traditional pigment based colour filters, leading to enhanced efficiencies, viewing angles and contrast, as well as the highly saturated colour delivered by the use of QDs. The display landscape is constantly changing, but with the shift to \u03bc- and mini-LEDs, quantum dots are looking likely to provide the only solution. \u03bcLEDs are LEDs with a very small chip size (down to single digit microns) which can be directly used as pixels on a display device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The pseudoinverse facilitates the statement and proof of results in linear algebra. The pseudoinverse is defined and unique for all matrices whose entries are real or complex numbers. It can be computed using the singular value decomposition. In the special case where A {\\displaystyle A} is a normal matrix (for example, a Hermitian matrix), the pseudoinverse A + {\\displaystyle A^{+}} annihilates the kernel of A {\\displaystyle A} and acts as a traditional inverse of A {\\displaystyle A} on the subspace orthogonal to the kernel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if X {\\displaystyle X} and Y {\\displaystyle Y} are sets and L \u2286 X \u00d7 Y {\\displaystyle L\\subseteq X\\times Y} is a relation from X {\\displaystyle X} to Y , {\\displaystyle Y,} then L T {\\displaystyle L^{\\operatorname {T} }} is the relation defined so that y L T x {\\displaystyle yL^{\\operatorname {T} }x} if and only if x L y . {\\displaystyle xLy.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, given a category C, a quotient of an object X by an equivalence relation f: R \u2192 X \u00d7 X {\\displaystyle f:R\\to X\\times X} is a coequalizer for the pair of maps R \u2192 f X \u00d7 X \u2192 pr i X , i = 1 , 2 , {\\displaystyle R\\ {\\overset {f}{\\to }}\\ X\\times X\\ {\\overset {\\operatorname {pr} _{i}}{\\to }}\\ X,\\ \\ i=1,2,} where R is an object in C and \"f is an equivalence relation\" means that, for any object T in C, the image (which is a set) of f: R ( T ) = Mor \u2061 ( T , R ) \u2192 X ( T ) \u00d7 X ( T ) {\\displaystyle f:R(T)=\\operatorname {Mor} (T,R)\\to X(T)\\times X(T)} is an equivalence relation; that is, a reflexive, symmetric and transitive relation. The basic case in practice is when C is the category of all schemes over some scheme S. But the notion is flexible and one can also take C to be the category of sheaves.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In this case, the expectation value is the probability that the experiment results in \"1\", and it can be computed as In quantum theory, it is also possible for an operator to have a non-discrete spectrum, such as the position operator X {\\displaystyle X} in quantum mechanics. This operator has a completely continuous spectrum, with eigenvalues and eigenvectors depending on a continuous parameter, x {\\displaystyle x} . Specifically, the operator X {\\displaystyle X} acts on a spatial vector | x \u27e9 {\\displaystyle |x\\rangle } as X | x \u27e9 = x | x \u27e9 {\\displaystyle X|x\\rangle =x|x\\rangle } .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There is no generally agreed set of properties that make a particular trust metric better than others, as each metric is designed to serve different purposes, e.g. provides certain classification scheme for trust metrics. Two groups of trust metrics can be identified: Empirical metrics focusing on supporting the capture of values of trust in a reliable and standardized way; Formal metrics that focus on formalization leading to the ease of manipulation, processing and reasoning about trust. Formal metrics can be further classified depending on their properties.Trust metrics enable trust modelling and reasoning about trust.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the matrix t-distribution (or matrix variate t-distribution) is the generalization of the multivariate t-distribution from vectors to matrices. The matrix t-distribution shares the same relationship with the multivariate t-distribution that the matrix normal distribution shares with the multivariate normal distribution. For example, the matrix t-distribution is the compound distribution that results from sampling from a matrix normal distribution having sampled the covariance matrix of the matrix normal from an inverse Wishart distribution.In a Bayesian analysis of a multivariate linear regression model based on the matrix normal distribution, the matrix t-distribution is the posterior predictive distribution.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This tactic associates a set of constant values to a VIS' variable and generates as many test classes as elements are in the set. Each test class is characterized by a predicate of the form v a r = v a l {\\displaystyle var=val} where var is the name of the variable and val is one of the values of the set. Numeric Ranges (NR).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(See example below.) Programming languages have the analogous notions of typing and scoping. A compiler or interpreter for the language must recognize which uses of a variable belong together (refer to the same variable).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A practical implementation of these strategies with refinements is available at the ACE website. The Knuth\u2013Bendix algorithm also can perform coset enumeration, and unlike the Todd\u2013Coxeter algorithm, it can sometimes solve the word problem for infinite groups. The main practical difficulties in producing a coset enumerator are that it is difficult or impossible to predict how much memory or time will be needed to complete the process.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, \"Gray code\" almost always refers to a binary-reflected Gray code (BRGC). However, mathematicians have discovered other kinds of Gray codes. Like BRGCs, each consists of a list of words, where each word differs from the next in only one digit (each word has a Hamming distance of 1 from the next word).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the following, R {\\displaystyle \\mathbb {R} } represents the real numbers with their usual topology. The subspace topology of the natural numbers, as a subspace of R {\\displaystyle \\mathbb {R} } , is the discrete topology. The rational numbers Q {\\displaystyle \\mathbb {Q} } considered as a subspace of R {\\displaystyle \\mathbb {R} } do not have the discrete topology ({0} for example is not an open set in Q {\\displaystyle \\mathbb {Q} } ). If a and b are rational, then the intervals (a, b) and  are respectively open and closed, but if a and b are irrational, then the set of all rational x with a < x < b is both open and closed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, Twitter can use machine learning applications to flag content that does not comply with its terms of service and identify extremist posts encouraging terrorism. Facebook and Google have developed a content hierarchy system where fact-checkers can identify and de-rank possible disinformation and adjust algorithms accordingly. Companies are considering using procedural legal systems to regulate content on their platforms as well.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", a n {\\displaystyle a_{1},...,a_{n}} are attribute names. Its result is defined as the set obtained when the components of the tuples in R {\\displaystyle R} are restricted to the set { a 1 , . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the symmetric closure of a binary relation R {\\displaystyle R} on a set X {\\displaystyle X} is the smallest symmetric relation on X {\\displaystyle X} that contains R . {\\displaystyle R.} For example, if X {\\displaystyle X} is a set of airports and x R y {\\displaystyle xRy} means \"there is a direct flight from airport x {\\displaystyle x} to airport y {\\displaystyle y} \", then the symmetric closure of R {\\displaystyle R} is the relation \"there is a direct flight either from x {\\displaystyle x} to y {\\displaystyle y} or from y {\\displaystyle y} to x {\\displaystyle x} \". Or, if X {\\displaystyle X} is the set of humans and R {\\displaystyle R} is the relation 'parent of', then the symmetric closure of R {\\displaystyle R} is the relation \" x {\\displaystyle x} is a parent or a child of y {\\displaystyle y} \".", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the diagram, MGF is the mask generating function, usually MGF1, Hash is the chosen hash function, hLen is the length of the output of the hash function in bytes, k is the length of the RSA modulus n in bytes, M is the message to be padded (at most k \u2212 2 \u22c5 h L e n \u2212 2 {\\displaystyle k-2\\cdot \\mathrm {hLen} -2} bytes), L is an optional label to be associated with the message (the label is the empty string by default and can be used to authenticate data without requiring encryption), PS is a byte string of k \u2212 m L e n \u2212 2 \u22c5 h L e n \u2212 2 {\\displaystyle k-\\mathrm {mLen} -2\\cdot \\mathrm {hLen} -2} null-bytes. \u2295 is an XOR-Operation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Sometimes, a set comes equipped with a natural hierarchical structure. For example, the set of natural numbers N is equipped with a natural pre-order structure, where n \u2264 n \u2032 {\\displaystyle n\\leq n'} whenever we can find some other number m {\\displaystyle m} so that n + m = n \u2032 {\\displaystyle n+m=n'} . That is, n \u2032 {\\displaystyle n'} is bigger than n {\\displaystyle n} only because we can get to n \u2032 {\\displaystyle n'} from n {\\displaystyle n} using m {\\displaystyle m} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Consistent use of templates. Producing a consistent set of models and templates to document the requirements. Documenting dependencies.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A block is usually subjected to some type of block processing, such as multidimensional parity checking, associated with it.A block transfer attempt is a coordinated sequence of user and telecommunication system activities undertaken to effect transfer of an individual block from a source user to a destination user. A block transfer attempt begins when the first bit of the block crosses the functional interface between the source user and the telecommunication system. A block transfer attempt ends either in successful block transfer or in block transfer failure.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerically challenging applications, sophisticated preconditioners are used, which may lead to variable preconditioning, changing between iterations. Even if the preconditioner is symmetric positive-definite on every iteration, the fact that it may change makes the arguments above invalid, and in practical tests leads to a significant slow down of the convergence of the algorithm presented above. Using the Polak\u2013Ribi\u00e8re formula \u03b2 k := r k + 1 T ( z k + 1 \u2212 z k ) r k T z k {\\displaystyle \\beta _{k}:={\\frac {\\mathbf {r} _{k+1}^{\\mathsf {T}}\\left(\\mathbf {z} _{k+1}-\\mathbf {z} _{k}\\right)}{\\mathbf {r} _{k}^{\\mathsf {T}}\\mathbf {z} _{k}}}} instead of the Fletcher\u2013Reeves formula \u03b2 k := r k + 1 T z k + 1 r k T z k {\\displaystyle \\beta _{k}:={\\frac {\\mathbf {r} _{k+1}^{\\mathsf {T}}\\mathbf {z} _{k+1}}{\\mathbf {r} _{k}^{\\mathsf {T}}\\mathbf {z} _{k}}}} may dramatically improve the convergence in this case. This version of the preconditioned conjugate gradient method can be called flexible, as it allows for variable preconditioning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "One of the functions of a static map is to allow a traveler to decide upon a course of action suitable for getting from one point to another. In times of war, the terrain and the troops and weapons deployed upon it can be changed much more rapidly than cartographers can change their maps. A commander with Fingerspitzengef\u00fchl would hold such a map in their mind, and adjust it by incorporating any significant information that was received. Colonel Mehta Basti Ram was said to have Fingerspitzengef\u00fchl.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In response to escalating textbook prices, limited competition, and to provide a more efficient system to connect buyers and sellers together, online textbook exchanges were developed. Most of today's sites handle buyer and seller payments, and usually deduct a small commission only after the sale is completed. According to textbook author Henry L. Roediger (and Wadsworth Publishing Company senior editor Vicki Knight), the used textbook market is illegitimate, and entirely to blame for the rising costs of textbooks. As methods of \"dealing with this problem\", he recommends making previous editions of textbooks obsolete, binding the textbook with other materials, and passing laws to prevent the sale of used books.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Their cost function was adaptive, in that the definition of the cost function depends on the computable approximation of the \u0394 2 0 {\\displaystyle \\Delta _{2}^{0}} set being built. A cost function construction of a K-trivial computably enumerable noncomputable set first appeared in Downey et al.We say a \u0394 2 0 {\\displaystyle \\Delta _{2}^{0}} set A obeys a cost function c if there exists a computable approximation of A, \u27e8 A s: s \u2208 \u03c9 \u27e9 {\\displaystyle \\langle A_{s}:s\\in \\omega \\rangle } S = \u03a3 x , s c ( x , s )  < \u221e . {\\displaystyle S=\\Sigma _{x,s}c(x,s)[x", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As noted below, Minsky (1967) hints at the problem for a RASP but doesn't offer a solution. Elgot and Robinson (1964) proved that their RASP model P0 \u2013 it has no indirection capability \u2013 cannot compute all \"recursive sequential functions\" (ones that have parameters of arbitrary length) if it does not have the capability of modifying its own instructions, but it can via G\u00f6del numbers if it does (p. 395-397; in particular figure 2 and footnote p.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Therefore, some would-be clients are not convinced that they are best-placed to assist in the area of integrity and ethical management, because their parent companies face reputational challenges themselves. Specialist integrity management consultancy helps business leaders not only to avoid business practices that represent risk to an industry or economy, but also helps to bring such practices under scrutiny so that they can be brought to a quick end.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The terminology is also applied to indirect measurements\u2014that is, values obtained by a computational procedure from observed data. In addition to accuracy and precision, measurements may also have a measurement resolution, which is the smallest change in the underlying physical quantity that produces a response in the measurement. In numerical analysis, accuracy is also the nearness of a calculation to the true value; while precision is the resolution of the representation, typically defined by the number of decimal or binary digits. In military terms, accuracy refers primarily to the accuracy of fire (justesse de tir), the precision of fire expressed by the closeness of a grouping of shots at and around the centre of the target.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It was the first randomized polynomial time PIT algorithm to be proven correct. The larger the domain the inputs are drawn from, the less likely Schwartz\u2013Zippel is to fail. If random bits are in short supply, the Chen-Kao algorithm (over the rationals) or the Lewin-Vadhan algorithm (over any field) require fewer random bits at the cost of more required runtime.A sparse PIT has at most m {\\displaystyle m} nonzero monomial terms. A sparse PIT can be deterministically solved in polynomial time of the size of the circuit and the number m {\\displaystyle m} of monomials, see also.A low degree PIT has an upper bound on the degree of the polynomial. Any low degree PIT problem can be reduced in subexponential time of the size of the circuit to a PIT problem for depth-four circuits; therefore, PIT for circuits of depth-four (and below) is intensely studied.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical modeling of social networks, link-centric preferential attachment is a node's propensity to re-establish links to nodes it has previously been in contact with in time-varying networks. This preferential attachment model relies on nodes keeping memory of previous neighbors up to the current time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In multi-step jobs, a later step can use a referback instead of specifying in full a file which has already been specified in an earlier step. For example: Here, MYPR02 uses the file identified as NEWFILE in step MYPR01 (DSN means \"dataset name\" and specifies the name of the file; a DSN could not exceed 44 characters). In jobs which contain a mixture of job-specific JCL and procedure calls, a job-specific step can refer back to a file which was fully specified in a procedure, for example: where DSN=*.STEP01.MYPR01.NEWFILE means \"use the file identified as NEWFILE in step MYPR01 of the procedure used by step STEP01 of this job\". Using the name of the step which called the procedure rather than the name of the procedure allows a programmer to use the same procedure several times in the same job without confusion about which instance of the procedure is used in the referback.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics and statistics, sums of powers occur in a number of contexts: Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities. Faulhaber's formula expresses 1 k + 2 k + 3 k + \u22ef + n k {\\displaystyle 1^{k}+2^{k}+3^{k}+\\cdots +n^{k}} as a polynomial in n, or alternatively in terms of a Bernoulli polynomial. Fermat's right triangle theorem states that there is no solution in positive integers for a 2 = b 4 + c 4 {\\displaystyle a^{2}=b^{4}+c^{4}} and a 4 = b 4 + c 2 {\\displaystyle a^{4}=b^{4}+c^{2}} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To distinguish these concepts, subtyping is sometimes referred to as interface inheritance (without acknowledging that the specialization of type variables also induces a subtyping relation), whereas inheritance as defined here is known as implementation inheritance or code inheritance. Still, inheritance is a commonly used mechanism for establishing subtype relationships.Inheritance is contrasted with object composition, where one object contains another object (or objects of one class contain objects of another class); see composition over inheritance. Composition implements a has-a relationship, in contrast to the is-a relationship of subtyping.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, in the Python interactive REPL: However, relying on dynamic name resolution in code is discouraged by the Python community. The feature also may be removed in a later version of Python.Examples of languages that use static name resolution include C, C++, E, Erlang, Haskell, Java, Pascal, Scheme, and Smalltalk. Examples of languages that use dynamic name resolution include some Lisp dialects, Perl, PHP, Python, REBOL, and Tcl.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In perhaps the first use of substructural type theory to control resources, John C. Reynolds showed how to use an affine type theory to control aliasing and other forms of interference in Algol-like programming languages. O'Hearn used bunched type theory to extend Reynolds' system by allowing interference and non-interference to be more flexibly mixed. This resolved open problems concerning recursion and jumps in Reynolds' system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted \"+\" is defined. Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "They also arise in algebraic number theory, due to the relation of the sequence to the roots of a polynomial; in the analysis of algorithms as the running time of simple recursive functions; and in formal language theory, where they count strings up to a given length in a regular language. Constant-recursive sequences are closed under important mathematical operations such as term-wise addition, term-wise multiplication, and Cauchy product. The Skolem\u2013Mahler\u2013Lech theorem states that the zeros of a constant-recursive sequence have a regularly repeating (eventually periodic) form. On the other hand, the Skolem problem, which asks for an algorithm to determine whether a linear recurrence has at least one zero, is a famous unsolved problem in mathematics.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In real-world exploits there are a variety of challenges which need to be overcome for exploits to operate reliably. These factors include null bytes in addresses, variability in the location of shellcode, differences between environments and various counter-measures in operation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, and in particular linear algebra, the Moore\u2013Penrose inverse A + {\\displaystyle A^{+}} of a matrix A {\\displaystyle A} is the most widely known generalization of the inverse matrix. It was independently described by E. H. Moore in 1920, Arne Bjerhammar in 1951, and Roger Penrose in 1955. Earlier, Erik Ivar Fredholm had introduced the concept of a pseudoinverse of integral operators in 1903. When referring to a matrix, the term pseudoinverse, without further specification, is often used to indicate the Moore\u2013Penrose inverse.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In semantic parsing, statements in natural languages are converted into logical forms that represent their meanings.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Most phone companies sell phones from third-party manufacturers. A subscriber identity module (SIM card), which is activated by the operator once the billing relationship is established. After activation the card is then programmed with the subscriber's Mobile Subscriber Integrated Services Digital Network Number (MSISDN) (the telephone number).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "It is often more comfortable to use the notation x i = ( x i , x i \u2212 1 , x i \u2212 2 , . . .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In social networks, a link between two players is formed only if both of them decide to do so, however either of them can make the decision to delete a link without the other player\u2019s approval. The concept of Nash equilibrium has a drawback in this case since it does not take into consideration the fact that the players can discuss their decisions. To model such a situation a stability concept that takes this fact into account is required. A useful stability concept in this case is Pairwise Stability, which accounts for the mutual approval of both players.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The term isomorphism is mainly used for algebraic structures. In this case, mappings are called homomorphisms, and a homomorphism is an isomorphism if and only if it is bijective. In various areas of mathematics, isomorphisms have received specialized names, depending on the type of structure under consideration.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of the modular S-matrix, the fusion coefficients are given by N \u03bb \u03bc \u03bd = \u2211 \u03c3 S \u03bb \u03c3 S \u03bc \u03c3 S \u03c3 \u03bd \u2217 S 0 \u03c3 {\\displaystyle N_{\\lambda \\mu }^{\\nu }=\\sum _{\\sigma }{\\frac {S_{\\lambda \\sigma }S_{\\mu \\sigma }S_{\\sigma \\nu }^{*}}{S_{0\\sigma }}}} where S \u2217 {\\displaystyle S^{*}} is the component-wise complex conjugate of S {\\displaystyle S} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "By using the theory of rapidly mixing Markov chains, they show that it takes a polynomial time for the random walk to settle down to being a nearly uniform distribution. By using rejection sampling, it is possible to compare the volumes of two convex bodies, one nested within another, when their volumes are within a small factor of each other.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The algorithm runs in strongly polynomial time if: the number of operations in the arithmetic model of computation is bounded by a polynomial in the number of integers in the input instance; and the space used by the algorithm is bounded by a polynomial in the size of the input.Any algorithm with these two properties can be converted to a polynomial time algorithm by replacing the arithmetic operations by suitable algorithms for performing the arithmetic operations on a Turing machine. The second condition is strictly necessary: given the integer 2 n {\\displaystyle 2^{n}} (which takes up space proportional to n in the Turing machine model), it is possible to compute 2 2 n {\\displaystyle 2^{2^{n}}} with n multiplications using repeated squaring. However, the space used to represent 2 2 n {\\displaystyle 2^{2^{n}}} is proportional to 2 n {\\displaystyle 2^{n}} , and thus exponential rather than polynomial in the space used to represent the input.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, the pieces allocated to the partners must satisfy some geometric constraints, in addition to being fair. The most common constraint is connectivity. In case the \"cake\" is a 1-dimensional interval, this translates to the requirement that each piece is also an interval. In case the cake is a 1-dimensional circle (\"pie\"), this translates to the requirement that each piece be an arc; see fair pie-cutting.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some cases, instead of repeating digit sequences we find repeating digit patterns. For instance, the number f 3 ( 49 ) {\\displaystyle {\\sqrt {f_{3}(49)}}}: 1111111111111111111111111.1111111111111111111111111111111 01200 202020202020202020202020202020202020202020 11010102 00120012000012001200120012001200120012 0010 21120020211210002112100021121000211210 ... shows repeating digit patterns in base 3 {\\displaystyle 3} . Numbers that are schizophrenic in base b {\\displaystyle b} are also schizophrenic in base b m {\\displaystyle b^{m}} (up to a certain limit, see T\u00f3th). An example is f 3 ( 49 ) {\\displaystyle {\\sqrt {f_{3}(49)}}} above, which is still schizophrenic in base 9 {\\displaystyle 9}: 1444444444444.4444444444 350 666666666666666666666 4112 0505050505050505050 337506 75307530753075307 40552382 ...", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ", and the restriction to monadic logic means that the graph property in question may be defined in terms of sets of vertices of the given graph, but not in terms of sets of edges, or sets of tuples of vertices. As an example, the property of a graph being colorable with three colors (represented by three sets of vertices R {\\displaystyle R} , G {\\displaystyle G} , and B {\\displaystyle B} ) may be defined by the monadic second-order formula with the naming convention that uppercase variables denote sets of vertices and lowercase variables denote individual vertices (so that an explicit declaration of which is which can be omitted from the formula). The first part of this formula ensures that the three color classes cover all the vertices of the graph, and the rest ensures that they each form an independent set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the above example, vectors are represented as n \u00d7 1 matrices (column vectors), while covectors are represented as 1 \u00d7 n matrices (row covectors). When using the column vector convention: \"Upper indices go up to down; lower indices go left to right.\" \"Covariant tensors are row vectors that have indices that are below (co-row-below).\" Covectors are row vectors: Hence the lower index indicates which column you are in. Contravariant vectors are column vectors: Hence the upper index indicates which row you are in.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the European Union, (advanced) electronic signatures on legal documents are commonly performed using digital signatures with accompanying identity certificates. However, only qualified electronic signatures (which require using a qualified trust service provider and signature creation device) are given the same power as a physical signature.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the figure, we can see an example of two packets linearly combined into a new coded packet. In the example, we have two packets, namely packet f {\\displaystyle f} and packet e {\\displaystyle e} . The generation size of our example is two. We know this because each packet has two coding coefficients ( C i j {\\displaystyle C_{ij}} ) appended.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In terms of skills, software designers were expected to think out database structures in entity relationship models and functional decomposition models, then transform those models into database definitions and modules (the screens and reports). Software developers were then expected to elaborate the database definitions and modules to create working code. Finally the day to day running of the system was expected to be carried out by database administrators, who had detailed knowledge of the database internals.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1990s and early 21st century, mainstream AI achieved commercial success and academic respectability by focusing on specific sub-problems where AI can produce verifiable results and commercial applications, such as artificial neural networks and statistical machine learning. These \"applied AI\" systems are now used extensively throughout the technology industry, and research in this vein is heavily funded in both academia and industry. As of 2018 development on this field was considered an emerging trend, and a mature stage was expected to happen in more than 10 years. Most mainstream AI researchers hope that strong AI can be developed by combining programs that solve various sub-problems.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In certain special cases it is convenient to use representations which transform almost like tensors, but with an additional, nonlinear factor in the transformation. A prototypical example is a matrix representing the cross product (area of spanned parallelogram) on R 2 . {\\displaystyle \\mathbb {R} ^{2}.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This allows the procedure to access the actual variable. As a result, the variable's actual value can be changed by the procedure to which it is passed.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In queueing theory, a discipline within the mathematical theory of probability, a retrial queue is a model of a system with finite capacity, where jobs which arrive and find the system busy wait for some time before trying again to enter the system. Examples of such systems include making restaurant reservations and packet switching networks. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network science, a gradient network is a directed subnetwork of an undirected \"substrate\" network where each node has an associated scalar potential and one out-link that points to the node with the smallest (or largest) potential in its neighborhood, defined as the union of itself and its neighbors on the substrate network.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In ordinal ranking, all items receive distinct ordinal numbers, including items that compare equal. The assignment of distinct ordinal numbers to items that compare equal can be done at random, or arbitrarily, but it is generally preferable to use a system that is arbitrary but consistent, as this gives stable results if the ranking is done multiple times. An example of an arbitrary but consistent system would be to incorporate other attributes into the ranking order (such as alphabetical ordering of the competitor's name) to ensure that no two items exactly match.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, nested dissection is a divide and conquer heuristic for the solution of sparse symmetric systems of linear equations based on graph partitioning. Nested dissection was introduced by George (1973); the name was suggested by Garrett Birkhoff.Nested dissection consists of the following steps: Form an undirected graph in which the vertices represent rows and columns of the system of linear equations, and an edge represents a nonzero entry in the sparse matrix representing the system. Recursively partition the graph into subgraphs using separators, small subsets of vertices the removal of which allows the graph to be partitioned into subgraphs with at most a constant fraction of the number of vertices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of \"exponential family\", or the older term Koopman\u2013Darmois family. The terms \"distribution\" and \"family\" are often used loosely: specifically, an exponential family is a set of distributions, where the specific distribution varies with the parameter; however, a parametric family of distributions is often referred to as \"a distribution\" (like \"the normal distribution\", meaning \"the family of normal distributions\"), and the set of all exponential families is sometimes loosely referred to as \"the\" exponential family.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The ECL circuitry consumed huge amount of current at a very low voltage; the cabinets of the larger models contained extra rack space which held stacks of 400-amp power supplies, and heavy-gauge wiring leading to the backplane. In the mid-1990s, the RSX computer board featured RISC processing capabilities and high speed 75 ns static RAM design (essentially an all-cache design) while maintaining complete binary compatibility with existing programs. Gould/SEL's \"High Speed Data interface\" or HSD was considered an industry standard in the process control industry.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the 1973 article \"Flowchart techniques for structured programming\" presented at a 1973 SIGPLAN meeting Isaac Nassi and Shneiderman argued: With the advent of structured programming and GOTO-less programming a method is needed to model computation in simply ordered structures, each representing a complete thought possibly defined in terms of other thoughts as yet undefined. A model is needed which prevents unrestricted transfers of control and has a control structure closer to languages amenable to structured programming. We present an attempt at such a model. The new model technique for structured programming they presented has become known as the Nassi\u2013Shneiderman diagram; a graphical representation of the design of structured software.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This is seen when comparing system messages (natural language-like statements in the user\u2019s native language) vs. \u2018binary\u2019 storage dumps. Partial or full set of system state data: some tools collect a complete system state vs. a partial system state (user or partial \u2018binary\u2019 storage dump vs. complete system dump). Raw or analyzed data: some tools display raw data, while others analyze it (examples storage dump formatters that format data, vs. \u2018intelligent\u2019 data formatters (\u201cANALYZE\u201d is a common verb) that combine product knowledge with analysis of state variables to indicate the \u2018meaning\u2019 of the data.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In programming languages, name resolution is the resolution of the tokens within program expressions to the intended program components.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first systematic study of astroturfing in the United States, Oxford Professor Philip N. Howard argued that the internet was making it much easier for powerful lobbyists and political movements to activate small groups of aggrieved citizens to have an exaggerated importance in public policy debates. Astroturfed accounts on social media do not always require humans to write their posts; one January 2021 study detailed a \"set of human-looking bot accounts\" used to post political content, which was able to operate automatically for fourteen days (and make 1,586 posts) before being detected and suspended by Twitter. Twitter trends are often targeted by astroturfing as they are used as a proxy for popularity. A study conducted by researchers at EPFL reported that 20% of the global Twitter trends in 2019 were fake, created automatically using fake and compromised accounts which tweet in a coordinated way to mimic grassroots organizing of regular Twitter users.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a noncommutative unique factorization domain is a noncommutative ring with the unique factorization property.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These have special analysis methods. In particular linear regression techniques are much more efficient than most non-linear techniques. The model can be deterministic or stochastic (i.e. containing random components) depending on its planned use.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a pernicious number is a positive integer such that the Hamming weight of its binary representation is prime, that is, there is a prime number of 1s when it is written as a binary number.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In number theory, a provable prime is an integer that has been calculated to be prime using a primality-proving algorithm. Boot-strapping techniques using Pocklington primality test are the most common ways to generate provable primes for cryptography. Contrast with probable prime, which is likely (but not certain) to be prime, based on the output of a probabilistic primality test. In principle, every prime number can be proved to be prime in polynomial time by using the AKS primality test. Other methods which guarantee that their result is prime, but which do not work for all primes, are useful for the random generation of provable primes.Provable primes have also been generated on embedded devices.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ".These formulas are equivalent for a quadratic function, but for nonlinear optimization the preferred formula is a matter of heuristics or taste. A popular choice is \u03b2 = max { 0 , \u03b2 P R } {\\displaystyle \\displaystyle \\beta =\\max\\{0,\\beta ^{PR}\\}} , which provides a direction reset automatically.Algorithms based on Newton's method potentially converge much faster. There, both step direction and length are computed from the gradient as the solution of a linear system of equations, with the coefficient matrix being the exact Hessian matrix (for Newton's method proper) or an estimate thereof (in the quasi-Newton methods, where the observed change in the gradient during the iterations is used to update the Hessian estimate).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To illustrate this property, we shall see what happens when n = 2 (i.e. we consider 3 interpolation nodes in which case the property is not trivial). One can check that each set of (zero-symmetric) nodes of type (\u2212a, 0, a) is optimal when \u221a8/3 \u2264 a \u2264 1 (we consider only nodes in ). If we force the set of nodes to be of the type (\u22121, b, 1), then b must equal 0 (look at the Lebesgue function, whose maximum is the Lebesgue constant).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, in graph theory, the Seidel adjacency matrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex, having 0 on the diagonal, \u22121 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices. It is also called the Seidel matrix or\u2014its original name\u2014the (\u22121,1,0)-adjacency matrix. It can be interpreted as the result of subtracting the adjacency matrix of G from the adjacency matrix of the complement of G. The multiset of eigenvalues of this matrix is called the Seidel spectrum. The Seidel matrix was introduced by J. H. van Lint and Johan Jacob Seidel in 1966 and extensively exploited by Seidel and coauthors.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The closure of a subset is the result of a closure operator applied to the subset. The closure of a subset under some operations is the smallest superset that is closed under these operations. It is often called the span (for example linear span) or the generated set.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": ": 38 Qualcomm further developed the CDMA techniques for commercial use and submitted them to the Cellular Telephone Industries Association (CTIA) in 1989 as an alternative to the time-division multiple access (TDMA) standard for second-generation cell-phone networks. : 49 A few months later, CTIA officially rejected Qualcomm's CDMA standard in favor of the more established TDMA standard developed by Ericsson.At the time, CDMA wasn't considered viable in high-volume commercial applications due to the near-far field effect, whereby phones closer to a cell tower with a stronger signal drown out callers that are further away and have a weaker signal. : 54\u201355, 62\u201365 Qualcomm filed three additional patents in 1989. They were for: a power management system that adjusts the signal strength of each call to adjust for the near-far field effect; a \"soft handoff\" methodology for transferring callers from one cell-tower to the next; and a variable rate encoder, which reduces bandwidth usage when a caller isn't speaking. : 54\u201355, 62\u201365", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In scientific notation, numbers are written in the form x = a \u00d7 10 b {\\displaystyle x=a\\times 10^{b}} , where a {\\displaystyle a} is the significand and 10 b {\\displaystyle 10^{b}} is the exponential part. Addition requires two numbers in scientific notation to be represented using the same exponential part, so that the two significands can simply be added. For example: 2.34 \u00d7 10 \u2212 5 + 5.67 \u00d7 10 \u2212 6 = 2.34 \u00d7 10 \u2212 5 + 0.567 \u00d7 10 \u2212 5 = 2.907 \u00d7 10 \u2212 5 {\\displaystyle 2.34\\times 10^{-5}+5.67\\times 10^{-6}=2.34\\times 10^{-5}+0.567\\times 10^{-5}=2.907\\times 10^{-5}}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Principally, and most correctly, it can be thought of as the logical design of the base data structures used to store the data. In the relational model these are the tables and views. In an object database the entities and relationships map directly to object classes and named relationships.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "As the tree is balanced, the path from one of the input arrays to the root contains only \u0398(log k) elements. In total, there are n elements that need to be transferred. The resulting total running time is therefore in \u0398(n log k).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Historically, homographies (and projective spaces) have been introduced to study perspective and projections in Euclidean geometry, and the term homography, which, etymologically, roughly means \"similar drawing\", dates from this time. At the end of the 19th century, formal definitions of projective spaces were introduced, which differed from extending Euclidean or affine spaces by adding points at infinity. The term \"projective transformation\" originated in these abstract constructions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "A further method for the derivation of a concept hierarchy exists in the usage of several patterns that should indicate a sub- or supersumption relationship. Patterns like \u201cX, that is a Y\u201d or \u201cX is a Y\u201d indicate that X is a subclass of Y. Such pattern can be analyzed efficiently, but they often occur too infrequently to extract enough sub- or supersumption relationships. Instead, bootstrapping methods are developed, which learn these patterns automatically and therefore ensure broader coverage.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "(The expression \"a mathematical function of person and item parameters\" is analogous to Lewin's equation, B = f(P, E), which asserts that behavior is a function of the person in their environment.) The person parameter is construed as (usually) a single latent trait or dimension. Examples include general intelligence or the strength of an attitude.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the collection of these 18 problems Problem 13 is very special. In it there are 6 unknowns but only 5 equations and so Problem 13 is indeterminate and does not have a unique solution. This is the earliest known reference to a system of linear equations in which the number of unknowns exceeds the number of equations. As per a suggestion of Jean-Claude Martzloff, a historian of Chinese mathematics, Roger Hart has named this problem \"the well problem.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "And also presume that these tests have identical sensitivity and specificity. In this situation one is carried away by these findings and presume that both the tests are equivalent. However this may not be the case.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In single-linkage clustering, the distance between two clusters is determined by a single pair of elements: those two elements (one in each cluster) that are closest to each other. The shortest of these pairwise distances that remain at any step causes the two clusters whose elements are involved to be merged. The method is also known as nearest neighbour clustering. The result of the clustering can be visualized as a dendrogram, which shows the sequence in which clusters were merged and the distance at which each merge took place.Mathematically, the linkage function \u2013 the distance D(X,Y) between clusters X and Y \u2013 is described by the expression D ( X , Y ) = min x \u2208 X , y \u2208 Y d ( x , y ) , {\\displaystyle D(X,Y)=\\min _{x\\in X,y\\in Y}d(x,y),} where X and Y are any two sets of elements considered as clusters, and d(x,y) denotes the distance between the two elements x and y.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may be identified. In mathematical jargon, one says that two objects are the same up to an isomorphism.An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism between the two structures (as is the case for solutions of a universal property), or if the isomorphism is much more natural (in some sense) than other isomorphisms.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In particle physics, the hypercharge (a portmanteau of hyperonic and charge) Y of a particle is a quantum number conserved under the strong interaction. The concept of hypercharge provides a single charge operator that accounts for properties of isospin, electric charge, and flavour. The hypercharge is useful to classify hadrons; the similarly named weak hypercharge has an analogous role in the electroweak interaction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the object's vertices given some formal representation of the object. A classical example is the problem of enumeration of the vertices of a convex polytope specified by a set of linear inequalities: A x \u2264 b {\\displaystyle Ax\\leq b} where A is an m\u00d7n matrix, x is an n\u00d71 column vector of variables, and b is an m\u00d71 column vector of constants. The inverse (dual) problem of finding the bounding inequalities given the vertices is called facet enumeration (see convex hull algorithms).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In network theory, collective classification is the simultaneous prediction of the labels for multiple objects, where each label is predicted using information about the object's observed features, the observed features and labels of its neighbors, and the unobserved labels of its neighbors. Collective classification problems are defined in terms of networks of random variables, where the network structure determines the relationship between the random variables. Inference is performed on multiple random variables simultaneously, typically by propagating information between nodes in the network to perform approximate inference. Approaches that use collective classification can make use of relational information when performing inference. Examples of collective classification include predicting attributes (ex. gender, age, political affiliation) of individuals in a social network, classifying webpages in the World Wide Web, and inferring the research area of a paper in a scientific publication dataset.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In static timing analysis, the word static alludes to the fact that this timing analysis is carried out in an input-independent manner, and purports to find the worst-case delay of the circuit over all possible input combinations. The computational efficiency (linear in the number of edges in the graph) of such an approach has resulted in its widespread use, even though it has some limitations. A method that is commonly referred to as PERT is popularly used in STA. However, PERT is a misnomer, and the so-called PERT method discussed in most of the literature on timing analysis refers to the critical path method (CPM) that is widely used in project management. While the CPM-based methods are the dominant ones in use today, other methods for traversing circuit graphs, such as depth-first search, have been used by various timing analyzers.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The numeric processor also incorporated memory management and consequently employed virtual memory concepts. The memory subsystem implemented a 64 way interleaved 4-port memory. To ensure that there would be no \"hot spots\" within the memory system, the addresses to the memory were hashed to spread the accesses evenly across the 64 way memory system.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the autumn of 1884, K\u00e1roly Zipernowsky, Ott\u00f3 Bl\u00e1thy and Miksa D\u00e9ri (ZBD), three engineers associated with the Ganz Works of Budapest, determined that open-core devices were impractical, as they were incapable of reliably regulating voltage. In their joint 1885 patent applications for novel transformers (later called ZBD transformers), they described two designs with closed magnetic circuits where copper windings were either wound around a ring core of iron wires or else surrounded by a core of iron wires. In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see toroidal cores). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "{\\displaystyle f^{-}(x)=\\max(-f(x),0)=-\\min(f(x),0)={\\begin{cases}-f(x)&{\\mbox{ if }}f(x)<0\\\\0&{\\mbox{ otherwise. }}\\end{cases}}} Note that both f+ and f\u2212 are non-negative functions.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In order to support the machine translation service, a mobile device needs to be able to communicate with external computers (servers) that receive the user-input text/speech, translate it and send it back to the user. This is usually done via an Internet connection (WAP, GPRS, EDGE, UMTS, Wi-Fi) but some earlier applications used SMS to communicate with the translation server. Mobile translation is not to be confused for the user-editable (talking) dictionaries and phrase books that are already widespread and available for many hand-held devices and do not normally require internet connectivity on the mobile device.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the event calculus, fluents are reified. This means that they are not formalized by means of predicates but by means of functions. A separate predicate HoldsAt is used to tell which fluents hold at a given time point. For example, H o l d s A t ( o n ( b o x , t a b l e ) , t ) {\\displaystyle {\\mathit {HoldsAt}}(on(box,table),t)} means that the box is on the table at time t; in this formula, HoldsAt is a predicate while on is a function.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "This makes the transmission system less susceptible to noise. Despite the fact that Stibitz described this code before Gray, the reflected binary code was later named after Gray by others who used it. Two different 1953 patent applications use \"Gray code\" as an alternative name for the \"reflected binary code\"; one of those also lists \"minimum error code\" and \"cyclic permutation code\" among the names. A 1954 patent application refers to \"the Bell Telephone Gray code\". Other names include \"cyclic binary code\", \"cyclic progression code\", \"cyclic permuting binary\" or \"cyclic permuted binary\" (CPB).The Gray code is sometimes misattributed to 19th century electrical device inventor Elisha Gray.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Define the amount of elements on the hypersphere S N d {\\displaystyle S_{N}^{d}} within the neighborhood M N n {\\displaystyle M_{N}^{n}} as E {\\displaystyle E} . For a given q \u2192 {\\displaystyle {\\vec {q}}} , E {\\displaystyle E} will be equal to the amount of permutations of q \u2192 {\\displaystyle {\\vec {q}}} multiplied by the number of orthants. Let n j {\\displaystyle n_{j}} represent the amount of elements in vector q \u2192 {\\displaystyle {\\vec {q}}} which take the value j {\\displaystyle j} .", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In statistics, the bootstrap error-adjusted single-sample technique (BEST or the BEAST) is a non-parametric method that is intended to allow an assessment to be made of the validity of a single sample. It is based on estimating a probability distribution representing what can be expected from valid samples. This is done use a statistical method called bootstrapping, applied to previous samples that are known to be valid.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the base ten (decimal) number system, integer powers of 10 are written as the digit 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, 103 = 1000 and 10\u22124 = 0.0001. Exponentiation with base 10 is used in scientific notation to denote large or small numbers. For instance, 299792458 m/s (the speed of light in vacuum, in metres per second) can be written as 2.99792458\u00d7108 m/s and then approximated as 2.998\u00d7108 m/s. SI prefixes based on powers of 10 are also used to describe small or large quantities. For example, the prefix kilo means 103 = 1000, so a kilometre is 1000 m.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the century from 1832 to Noether's death in 1935, the field of mathematics \u2013 specifically algebra \u2013 underwent a profound revolution, whose reverberations are still being felt. Mathematicians of previous centuries had worked on practical methods for solving specific types of equations, e.g., cubic, quartic, and quintic equations, as well as on the related problem of constructing regular polygons using compass and straightedge. Beginning with Carl Friedrich Gauss's 1832 proof that prime numbers such as five can be factored in Gaussian integers, \u00c9variste Galois's introduction of permutation groups in 1832 (although, because of his death, his papers were published only in 1846, by Liouville), William Rowan Hamilton's discovery of quaternions in 1843, and Arthur Cayley's more modern definition of groups in 1854, research turned to determining the properties of ever-more-abstract systems defined by ever-more-universal rules. Noether's most important contributions to mathematics were to the development of this new field, abstract algebra.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In materials science, a matrix is a constituent of a composite material.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the field of security engineering, a pre-play attack is a cryptographic attack in which an attacker prepares for the attack in advance by carrying out a simulated transaction while pretending to be the device to be attacked, and then repeats the attack a second time with the real device at a time when it is likely to carry out the same series of operations as in the simulation. The technique relies on being able to guess the content of the transaction in advance, something usually made possible by a poor choice of unpredictability within the system. The name is a play on \"replay attack\". Pre-play attacks are not very effective and chances of success are slim. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In parallel computing, all-to-all (also known as index operation or total exchange) is a collective operation, where each processor sends an individual message to every other processor. Initially, each processor holds p messages of size m each, and the goal is to exchange the i-th message of processor j with the j-th message of processor i. The number of communication rounds and the overall communication volume are measures to evaluate the quality of an all-to-all algorithm. We consider a single-ported full-duplex machine throughout this article.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In 1895, the German physicist Wilhelm Conrad R\u00f6ntgen discovered and extensively studied X-rays, which were later used in X-ray spectroscopy. One year later, in 1896, French physicist Antoine Henri Becquerel discovered radioactivity, and Dutch physicist Pieter Zeeman observed spectral lines being split by a magnetic field.In 1897, theoretical physicist, Joseph Larmor explained the splitting of the spectral lines in a magnetic field by the oscillation of electrons.Physicist, Joseph Larmor, created the first solar system model of the atom in 1897. He also postulated the proton, calling it a \u201cpositive electron.\u201d He said the destruction of this type of atom making up matter \u201cis an occurrence of infinitely small probability.\u201d", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "There are many proposed implementations of programmable matter. Scale is one key differentiator between different forms of programmable matter. At one end of the spectrum reconfigurable modular robotics pursues a form of programmable matter where the individual units are in the centimeter size range.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the first phase, only the melt itself is ejected; later a depression may form in the center of the hole and gas is discharged together with the melt with a rapid decrease of pressure inside the reactor vessel; the high temperature of the melt also causes rapid erosion and enlargement of the vessel breach. If the hole is in the center of the bottom, nearly all corium can be ejected. A hole in the side of the vessel may lead to only partial ejection of corium, with a retained portion left inside the reactor vessel.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In Russian, both plain and palatalized consonant phonemes are found in words like \u0431\u043e\u043b\u044c\u0448\u043e\u0439  , \u0446\u0430\u0440\u044c  and \u041a\u0430\u0442\u044f  . In Hupa, on the other hand, the palatalization is heard as both an onglide and an offglide. In some cases, the realization of palatalization may change without any corresponding phonemic change.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The final form of Maxwell's equations was published in 1865 A Dynamical Theory of the Electromagnetic Field, in which the theory is formulated in strictly mathematical form. In 1873, Maxwell published A Treatise on Electricity and Magnetism as a summary of his work on electromagnetism. In summary, Maxwell's equations successfully unified theories of light and electromagnetism, which is one of the great unifications in physics.Later, Oliver Heaviside studied Maxwell's A Treatise on Electricity and Magnetism and employed vector calculus to synthesize Maxwell's over 20 equations into the 4 recognizable ones which modern physicists use. Maxwell's equations also inspired Albert Einstein in developing the theory of special relativity.The experimental proof of Maxwell's equations was demonstrated by Heinrich Hertz in a series of experiments in the 1890s. After that, Maxwell's equations were fully accepted by scientists.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the cycles of a permutation \u03c0 of a finite set S correspond bijectively to the orbits of the subgroup generated by \u03c0 acting on S. These orbits are subsets of S that can be written as { c1, ..., cn }, such that \u03c0(ci) = ci + 1 for i = 1, ..., n \u2212 1, and \u03c0(cn) = c1.The corresponding cycle of \u03c0 is written as ( c1 c2 ... cn ); this expression is not unique since c1 can be chosen to be any element of the orbit. The size n of the orbit is called the length of the corresponding cycle; when n = 1, the single element in the orbit is called a fixed point of the permutation. A permutation is determined by giving an expression for each of its cycles, and one notation for permutations consist of writing such expressions one after another in some order.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Chiu (1998) and DeMeza and Lockwood (1998) have extended the model by considering different bargaining games that the parties may play ex post (which can explain ownership by the less important investor). Oliver Williamson (2002) has criticized the Grossman\u2013Hart\u2013Moore model because it is focused on ex ante investment incentives, while it neglects ex post inefficiencies. Schmitz (2006) has studied a variant of the Grossman\u2013Hart\u2013Moore model in which a party may have or acquire private information about its disagreement payoff, which can explain ex post inefficiencies and ownership by the less important investor. Several variants of the Grossman\u2013Hart\u2013Moore model such as the one with private information can also explain joint ownership.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "To visualized this theorem and its conclusion, consider the particular case where K {\\displaystyle K} is a convex polygon. In this case, the corners of the polygon (which are its extreme points) are all that is needed to recover the polygon shape. The statement of the theorem is false if the polygon is not convex, as then there are many ways of drawing a polygon having given points as corners.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Combining these pieces of information gives us this table of conditional probabilities for y: With more than one conditioning variable, the table would still have one row for each potential value of the variable whose conditional probabilities are to be given, and there would be one column for each possible combination of values of the conditioning variables. Moreover, the number of columns in the table could be substantially expanded to display the probabilities of the variable of interest conditional on specific values of only some, rather than all, of the other variables. == References ==", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Many SCADA systems have been fielded up to 20 years ago have very little in the way of modern security protections that are instrumented. These types of attacks have the potential to bring a new dynamic forward in the concept of cyber warfare and the potential impact on electrical systems, financial systems, critical infrastructure, and communication systems. Though, in reality, these types of attacks may have a closer relation to espionage or idealistically driven attacks, rather than overt warfare.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In removing all non-value activities, you reduce the amount of redundant tasks performed by the bottlenecked machine and hence maximize efficiency. Removing the waste operations results in a shorter cycle time hence allowing the machine to complete each process in less time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the Japanese kantenji braille, the standard 8-dot Braille patterns 578, 1578, 4578, and 14578 are the patterns related to Braille pattern dots-346, since the two additional dots of kantenji patterns 0346, 3467, and 03467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, Tarski's plank problem is a question about coverings of convex regions in n-dimensional Euclidean space by \"planks\": regions between two hyperplanes. Tarski asked if the sum of the widths of the planks must be at least the minimum width of the convex region. The question was answered affirmatively by Th\u00f8ger Bang (1950, 1951).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The resulting configuration\u2014the number 110\u2014is the PROOF. Turing's first task had to write a generalized expression using logic symbols to express exactly what his Un(M) would do. Turing's second task is to \"G\u00f6delize\" this hugely long string-of-string-of-symbols using G\u00f6del's technique of assigning primes to the symbols and raising the primes to prime-powers, per G\u00f6del's method.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In some games such as video poker, blackjack, or Caribbean Stud Poker, it is possible to compute an optimal playing strategy based on the average payoff (the amount of payoff times the chance of payoff). Because the jackpot of a progressive game constantly grows, it sometimes exceeds the break-even point for players, such that the jackpot wager becomes a \"positive expectation bet\" for the player, with an average return to player (RTP) of greater than 100%. When the progressive jackpot is less than the break-even point, there is a negative expected value (house edge) for all players. In the long run, with optimal strategy, a player can profit by only playing progressive games when their jackpots are above the break-even point, although the \"long run\" can be quite long, tens of thousands of plays.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematical optimization, cost functions and non-linear components within can be linearized in order to apply a linear solving method such as the Simplex algorithm. The optimized result is reached much more efficiently and is deterministic as a global optimum.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The fact that a {\\displaystyle a} is false contradicts this belief, which should therefore be removed from the belief set. The result of revision is therefore { \u00ac a } {\\displaystyle \\{\\neg a\\}} in this case. The problem of using deductively closed knowledge bases is that no distinction is made between pieces of knowledge that are known by themselves and pieces of knowledge that are merely consequences of them.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In probability and statistics, a spherical contact distribution function, first contact distribution function, or empty space function is a mathematical function that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. More specifically, a spherical contact distribution function is defined as probability distribution of the radius of a sphere when it first encounters or makes contact with a point in a point process. This function can be contrasted with the nearest neighbour function, which is defined in relation to some point in the point process as being the probability distribution of the distance from that point to its nearest neighbouring point in the same point process. The spherical contact function is also referred to as the contact distribution function, but some authors define the contact distribution function in relation to a more general set, and not simply a sphere as in the case of the spherical contact distribution function. Spherical contact distribution functions are used in the study of point processes as well as the related fields of stochastic geometry and spatial statistics, which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "1 L, an alternative form, for typefaces in which these characters are difficult to distinguish, or the typeface the reader will be using is unknown. A \"script l\" in various typefaces (e.g.: 1 l) has traditionally been used in some countries to prevent confusion; however, the separate Unicode character which represents this, U+2113 \u2113 SCRIPT SMALL L, is deprecated by the SI.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "}}\\cdot {\\dfrac {1}{I\\left(r,\\lambda \\right)}},\\quad n=0,1,2,\\ldots &{\\text{if }}r\\geq 0\\\\e^{-\\lambda }{\\dfrac {\\lambda ^{n+r}}{\\left(n+r\\right)! }}\\cdot {\\dfrac {1}{I\\left(r+s,\\lambda \\right)}},\\quad n=s,s+1,s+2,\\ldots &{\\text{otherwise}}\\end{cases}}} where \u03bb > 0 {\\displaystyle \\lambda >0} and r is a new parameter; the Poisson distribution is recovered at r = 0. Here I ( r , \u03bb ) {\\displaystyle I\\left(r,\\lambda \\right)} is the Pearson's incomplete gamma function: I ( r , \u03bb ) = \u2211 y = r \u221e e \u2212 \u03bb \u03bb y y !", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Goormaghtigh conjecture is a conjecture in number theory named for the Belgian mathematician Ren\u00e9 Goormaghtigh. The conjecture is that the only non-trivial integer solutions of the exponential Diophantine equation x m \u2212 1 x \u2212 1 = y n \u2212 1 y \u2212 1 {\\displaystyle {\\frac {x^{m}-1}{x-1}}={\\frac {y^{n}-1}{y-1}}} satisfying x > y > 1 {\\displaystyle x>y>1} and n , m > 2 {\\displaystyle n,m>2} are 5 3 \u2212 1 5 \u2212 1 = 2 5 \u2212 1 2 \u2212 1 = 31 {\\displaystyle {\\frac {5^{3}-1}{5-1}}={\\frac {2^{5}-1}{2-1}}=31} and 90 3 \u2212 1 90 \u2212 1 = 2 13 \u2212 1 2 \u2212 1 = 8191. {\\displaystyle {\\frac {90^{3}-1}{90-1}}={\\frac {2^{13}-1}{2-1}}=8191.}", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In modern mapping, a topographic map or topographic sheet is a type of map characterized by large-scale detail and quantitative representation of relief features, usually using contour lines (connecting points of equal elevation), but historically using a variety of methods. Traditional definitions require a topographic map to show both natural and artificial features. A topographic survey is typically based upon a systematic observation and published as a map series, made up of two or more map sheets that combine to form the whole map.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "At that point, all of the other vendors began RISC efforts of their own. Among these were the DEC Alpha, AMD Am29000, Intel i860 and i960, Motorola 88000, IBM POWER, and, slightly later, the IBM/Apple/Motorola PowerPC. Many of these have since disappeared due to them often offering no competitive advantage over others of the same era.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "However, this may not be desirable where the programmer wishes to create closed abstractions. A pitfall of structural typing versus nominative typing is that two separately defined types intended for different purposes, but accidentally holding the same properties (e.g. both composed of a pair of integers), could be considered the same type by the type system, simply because they happen to have identical structure. One way this can be avoided is by creating one algebraic data type for each use. In 1990, Cook, et al., proved that inheritance is not subtyping in structurally-typed OO languages.Checking that two types are compatible, based on structural typing, is a non-trivial operation, e.g., requires maintaining a stack of previous checked types.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the UK planning laws, applications and restrictions delay flood mitigation work. This can be counteracted by setting up Temporary Test Dams in watercourses that can then be monitored and valued. This does however require the landowners support. TTDs have proven to be a great way to get rapid action following a flood event and a way to get communities involved in the defence against future flood events.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In program analysis, a polyvariant or context-sensitive analysis (as opposed to a monovariant or context-insensitive analysis) analyzes each function multiple times\u2014typically once at each call site\u2014to improve the precision of the analysis. Polyvariance is common in data-flow and pointer analyses. Forms of polyvariance include: Call-site sensitivity The Cartesian product algorithm Object sensitivity Type sensitivityThe first two are more often used for dataflow analyses, the latter two are more frequently used for pointer analyses.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "The norm on the space E {\\displaystyle E} is \u2016 . \u2016 E {\\displaystyle \\|.\\|_{E}} . The idea to recover the original image is to minimize the following functional for u \u2208 H 1 ( \u03a9 ) {\\displaystyle u\\in H^{1}(\\Omega )}: where C {\\displaystyle C} is a positive definite tensor.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In ontology, the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities according to Amie Thomasson. To investigate the categories of being, or simply categories, is to determine the most fundamental and the broadest classes of entities. A distinction between such categories, in making the categories or applying them, is called an ontological distinction. Various systems of categories have been proposed, they often include categories for substances, properties, relations, states of affairs or events. A representative question within the theory of categories might articulate itself, for example, in a query like, \"Are universals prior to particulars?\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In addition, \u201chierarchical organization of plans comes from the timing of behavioral sequences.\u201d The larger the phrase, the longer the response time, which factors into \u201cdecoding\u201d or \u201cunpacking\u201d hierarchical plans. Additional evidence is how easy or hard it is to learn a sequence. The mind can create a \u201cmemory for what is about to happen\u201d as well as a \u201cmemory for what has happened.\u201d The final evidence for the hierarchical organization of plans is characterized by \"chunking\". This skill combines multiple units into larger units.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "GotoBLAS's matrix-matrix multiplication routine, called GEMM in BLAS terms, is highly tuned for the x86 and AMD64 processor architectures by means of handcrafted assembly code. It follows a similar decomposition into smaller \"kernel\" routines that other BLAS implementations use, but where earlier implementations streamed data from the L1 processor cache, GotoBLAS uses the L2 cache. The kernel used for GEMM is a routine called GEBP, for \"General block-times-panel multiply\", which was experimentally found to be \"inherently superior\" over several other kernels that were considered in the design.Several other BLAS routines are, as is customary in BLAS libraries, implemented in terms of GEMM.As of January 2022, the Texas Advanced Computing Center website states that Goto BLAS in no more maintained and suggests the use of BLIS or MKL.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In plant morphology, Rolf Sattler developed a process morphology (dynamic morphology) that overcomes the structure/process (or structure/function) dualism that is commonly taken for granted in biology. According to process morphology, structures such as leaves of plants do not have processes, they are processes.In evolution and in development, the nature of the changes of biological objects are considered by many authors to be more radical than in physical systems. In biology, changes are not just changes of state in a pre-given space, instead the space and more generally the mathematical structures required to understand object change over time.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For the sequence to be sociable, the sequence must be cyclic and return to its starting point. The period of the sequence, or order of the set of sociable numbers, is the number of numbers in this cycle. If the period of the sequence is 1, the number is a sociable number of order 1, or a perfect number\u2014for example, the proper divisors of 6 are 1, 2, and 3, whose sum is again 6. A pair of amicable numbers is a set of sociable numbers of order 2. There are no known sociable numbers of order 3, and searches for them have been made up to 5 \u00d7 10 7 {\\displaystyle 5\\times 10^{7}} as of 1970.It is an open question whether all numbers end up at either a sociable number or at a prime (and hence 1), or, equivalently, whether there exist numbers whose aliquot sequence never terminates, and hence grows without bound.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In the base \u22122 representation, a signed number is represented using a number system with base \u22122. In conventional binary number systems, the base, or radix, is 2; thus the rightmost bit represents 20, the next bit represents 21, the next bit 22, and so on. However, a binary number system with base \u22122 is also possible. The rightmost bit represents (\u22122)0 = +1, the next bit represents (\u22122)1 = \u22122, the next bit (\u22122)2 = +4 and so on, with alternating sign.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Minimal algebraic notation is similar to short algebraic notation but omits the indicators for capture (\"x\"), en passant capture (\"e.p. \"), check (\"+\") and checkmate (\"#\").", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Powerful error removal methods exist. \": 5 Similarly, Davies notes on end-to-end error control, \"It is thought that all users of the network will provide themselves with some kind of error control and that without difficulty this could be made to show up a missing packet. Because of this, loss of packets, if it is sufficiently rare, can be tolerated.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the term modulo (\"with respect to a modulus of\", the Latin ablative of modulus which itself means \"a small measure\") is often used to assert that two distinct mathematical objects can be regarded as equivalent\u2014if their difference is accounted for by an additional factor. It was initially introduced into mathematics in the context of modular arithmetic by Carl Friedrich Gauss in 1801. Since then, the term has gained many meanings\u2014some exact and some imprecise (such as equating \"modulo\" with \"except for\"). For the most part, the term often occurs in statements of the form: A is the same as B modulo Cwhich means A and B are the same\u2014except for differences accounted for or explained by C.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "These phones can also make voice calls, as well as send SMS and e-mail messages, and although this requirement is no longer in force due to minimal use of the textphone feature in these phones, many of these devices remain in service, generally in populated areas.In addition, in the early 2000s BT installed a large number of 'Multiphones' that provided internet access, on top of voice, SMS, and e-mail functionality. These payphones provided these services through the use of a 2-channel ISDN2 connection, a QNX-based operating system, and a touchscreen interface to allow the user to browse websites and receive e-mail messages on a pay-per-minute basis. However, these devices have since been removed due to quickly becoming obsolete, often with the ordinary payphone previously installed in that location taking its place once again.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "See also C. Hempel, Philosophy of Natural Science 49 (1966) (he statements constituting a scientific explanation must be capable of empirical test); K. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge 37 (5th ed. 1989) (he criterion of the scientific status of a theory is its falsifiability, or refutability, or testability) (emphasis deleted). David H. Kaye said that references to the Daubert majority opinion confused falsifiability and falsification and that \"inquiring into the existence of meaningful attempts at falsification is an appropriate and crucial consideration in admissibility determinations.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or \"hat\", as in v ^ {\\displaystyle {\\hat {\\mathbf {v} }}} (pronounced \"v-hat\"). The term direction vector, commonly denoted as d, is used to describe a unit vector being used to represent spatial direction and relative direction.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "For example, in ASL, the signs for \"class\" and \"family\" are the same (a basic sign for 'group of people'), except that \"class\" is signed with a 'C' handshape, and \"family\" with an 'F' handshape. In other cases initialization is required for disambiguation, though the signs are not semantically related. For example, in ASL, \"water\" it signed with a 'W' handshape touching the mouth, while \"dentist\" is similar apart from using a 'D' handshape. In other cases initialization is not used for disambiguation; the ASL sign for \"elevator\", for example, is an 'E' handshape moving up and down along the upright index finger of the other hand. The large number of initialized signs in ASL and French Sign Language is partly a legacy of Abb\u00e9 de l'\u00c9p\u00e9e's system of Methodical Sign (les signes m\u00e9thodiques), in which the handshapes of most signs were changed to correspond to the initial letter of their translation in the local oral language, and (in the case of ASL) partly a more recent influence of Manually Coded English.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "Relations are intended to represent semantic links between words in every existing language. They can be ontological (such as \"icl\" and \"iof,\" referred to above), logical (such as \"and\" and \"or\"), and thematic (such as \"agt\" = agent, \"ins\" = instrument, \"tim\" = time, \"plc\" = place, etc.).", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In static strings method, the API caller or client embeds a string as a token in the request. This method is often referred as basic authentication. \"From a security point of view, basic authentication is not very satisfactory. It means sending the user's password over the network in clear text for every single page accessed (unless a secure lower-level protocol, like SSL, is used to encrypt all transactions). Thus the user is very vulnerable to any packet sniffers on the net.\"", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In object-oriented programming, object copying is creating a copy of an existing object, a unit of data in object-oriented programming. The resulting object is called an object copy or simply copy of the original object. Copying is basic but has subtleties and can have significant overhead. There are several ways to copy an object, most commonly by a copy constructor or cloning.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In numerical analysis, an iterative method is called locally convergent if the successive approximations produced by the method are guaranteed to converge to a solution when the initial approximation is already close enough to the solution. Iterative methods for nonlinear equations and their systems, such as Newton's method are usually only locally convergent. An iterative method that converges for an arbitrary initial approximation is called globally convergent. Iterative methods for systems of linear equations are usually globally convergent.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In mathematics, the Grothendieck group, or group of differences, of a commutative monoid M is a certain abelian group. This abelian group is constructed from M in the most universal way, in the sense that any abelian group containing a homomorphic image of M will also contain a homomorphic image of the Grothendieck group of M. The Grothendieck group construction takes its name from a specific case in category theory, introduced by Alexander Grothendieck in his proof of the Grothendieck\u2013Riemann\u2013Roch theorem, which resulted in the development of K-theory. This specific case is the monoid of isomorphism classes of objects of an abelian category, with the direct sum as its operation.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}
{"text": "In practice, document clustering often takes the following steps: 1. Tokenization Tokenization is the process of parsing text data into smaller units (tokens) such as words and phrases. Commonly used tokenization methods include Bag-of-words model and N-gram model. 2.", "source": "https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus"}