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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 ℵ {\displaystyle \aleph } (aleph) marked with subscript indicating their rank among the infinite cardinals. Cardinality is defined in terms of bijective functions.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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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.
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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.
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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) – a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts Boolean analysis – a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis Cluster analysis – techniques for finding groups (called clusters), based on some measure of proximity or similarity Factor analysis – 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 – combines the results of several studies that address a set of related research hypotheses Multivariate analysis – analysis of data involving several variables, such as by factor analysis, regression analysis, or principal component analysis Principal component analysis – transformation of a sample of correlated variables into uncorrelated variables (called principal components), mostly used in exploratory data analysis Regression analysis – techniques for analysing the relationships between several predictive variables and one or more outcomes in the data Scale analysis (statistics) – methods to analyse survey data by scoring responses on a numeric scale Sensitivity analysis – the study of how the variation in the output of a model depends on variations in the inputs Sequential analysis – evaluation of sampled data as it is collected, until the criterion of a stopping rule is met Spatial analysis – the study of entities using geometric or geographic properties Time-series analysis – methods that attempt to understand a sequence of data points spaced apart at uniform time intervals
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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').
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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.
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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 <:.
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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.
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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.
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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.
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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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.
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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 − 1 {\displaystyle n-1} . While L ≠ 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}}} .
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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× Platinum by Music Canada, and as of January 2013 had sold more than 476,000 copies in the country.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In the Bulgarian language the vowels а , ъ , о and е 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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Let G = Per ( 3 ) {\displaystyle G={\text{Per}}(3)} be the permutation groups in three elements. Let ρ: Per ( 3 ) → 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: ρ ( 1 , 2 ) = ( − 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 ) , ρ ( 1 , 3 ) = ( 1 2 1 2 0 0 0 1 2 − 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 ) , ρ ( 2 , 3 ) = ( 0 − 2 0 0 0 − 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\\
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Thus, A ⟶ {\displaystyle {\stackrel {\,\longrightarrow }{A}}} ⋅ B ⟶ {\displaystyle {\stackrel {\,\longrightarrow }{B}}} = | A ⟶ {\displaystyle {\stackrel {\,\longrightarrow }{A}}} | | B ⟶ {\displaystyle {\stackrel {\,\longrightarrow }{B}}} | cos θMore generally, a bilinear product in an algebra over a field. Cross product – 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.
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2) Multiple losses: x {\displaystyle x} and y {\displaystyle y} are both considered losses. 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) V a l u e ( x − y ) {\displaystyle Value(x)+Value(-y)>Value(x-y)} .
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But one really requires average numbers. These average numbers can be obtained by the Darwin–Fowler 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.
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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)
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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.
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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.
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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.
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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.
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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 ==
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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 ∈ S, W(ab) = W(b)W(a), where W(a) ≝ {x ∈ S | xax = x} is the set of weak inverses of a. == References ==
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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.
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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.
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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.
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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 '!
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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 ! ≡ − 1 mod p {\displaystyle n!\equiv -1\mod p} but p ≢ 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, Erdős, and Hardy & Subbarao.
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To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of f is the function f − 1: R → R {\displaystyle f^{-1}\colon \mathbb {R} \to \mathbb {R} } defined by f − 1 ( y ) = y + 7 5 . {\displaystyle f^{-1}(y)={\frac {y+7}{5}}.}
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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}}.}
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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.
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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.
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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.
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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.
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The generic algorithm has a strongly polynomial O(V 2E) time complexity, which is asymptotically more efficient than the O(VE 2) Edmonds–Karp 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√E) 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–relabel 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–relabel algorithm to create a variant with even higher empirical performance.
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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.
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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.
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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.
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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.
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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.
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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.
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{\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 ∧ {\displaystyle \wedge } represents the min {\displaystyle \min } operator. It is also possible to weaken the independence requirement.
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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.
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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—and sometimes on non–law enforcement agencies—to provide intelligence for their analysis.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 fε2*2 in the fast-growing hierarchy.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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–Moser notation, or Conway chained arrow notation.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 − q×s, 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematical optimization, the Klee–Minty 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–Minty 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–Minty cube. Like the simplex algorithm, the criss-cross algorithm visits all 8 corners of the three-dimensional cube in the worst case.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Consider a sequence { A k } {\displaystyle \{\mathbf {A} _{k}\}} of fixed self-adjoint matrices that satisfy ( H ( z 1 , … , z k , … , z n ) − H ( z 1 , … , z k ′ , … , z n ) ) 2 ⪯ 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 ′ {\displaystyle z'_{i}} range over all possible values of Z i {\displaystyle Z_{i}} for each index i {\displaystyle i} . Compute the variance parameter σ 2 = ‖ ∑ k A k 2 ‖ . {\displaystyle \sigma ^{2}={\bigg \Vert }\sum _{k}\mathbf {A} _{k}^{2}{\bigg \Vert }.}
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 дверь and пыль, also have a locative form that differs from the prepositional in that the stress shifts to the final syllable: "на двери́", na dverí ("on the door"), but "при две́ри", pri dvéri ("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 дом, dom (house), the second locative form is used only in certain idiomatic expressions, while the prepositional is used elsewhere. For example, "на дому́", na domu ("at the house" or "at home") would be used to describe activity that is performed at home, while "на до́ме" ("on the house") would be used to specify the location of the roof.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 − 1).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 … , x n ) {\displaystyle x=(x_{1},x_{2}\dots ,x_{n})} and weights w = ( w 1 , w 2 , … , w n ) {\displaystyle w=(w_{1},w_{2},\dots ,w_{n})} , it is calculated as: x ¯ = ( ∏ i = 1 n x i w i ) 1 / ∑ i = 1 n w i = exp ( ∑ i = 1 n w i ln x i ∑ 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Formally, a vertex conflict happens when π i = π 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 π i = π j {\displaystyle \pi _{i}=\pi _{j}} and π i = π j {\displaystyle \pi _{i}=\pi _{j}} . If vertex conflicts are not allowed, then edge conflicts cannot exist.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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A stochastic process { Z n , n = 1 , 2 , … } {\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 , … , k {\displaystyle a_{i}>0,i=1,2,\ldots ,k} and integers { 1 = M 1 < M 2 < ⋯ < M k < M k + 1 = ∞ } {\displaystyle \{1=M_{1} 0 {\displaystyle h(k)>0} for natural number k {\displaystyle k} , then { X k , k = 1 , 2 , … } {\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 , … } {\displaystyle \{X_{k},k=1,2,\dots \}} , if P { X k < x | X k − 1 = x k − 1 , … , X 1 = x 1 } = P { X k < x | X k − 1 = x k − 1 } {\displaystyle P\{X_{k}
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 ==
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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(reflexivity). (Here, id {\displaystyle \operatorname {id} } denotes the identity function on X {\displaystyle X} .) R = R − 1 {\displaystyle R=R^{-1}} (symmetry). R R ⊆ R {\displaystyle RR\subseteq R} (transitivity).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In standard NMF, matrix factor W ∈ R+m × k， 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 , … , 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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:
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval {\displaystyle } is about log log x 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 −1).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 – generally used for bus-based SMP – Symmetric Multiprocessor System/multi-core systems Directory-based – Message-passing – may be used in all systems but typically in NUMA system and in large multi-core systems Shared cache – generally used in multi-core systems
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Ramanujan–Hardy 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Invertibility: For every permutation π ∈ S n {\displaystyle \pi \in S_{n}} , there exists an inverse permutation π − 1 ∈ S n {\displaystyle \pi ^{-1}\in S_{n}} , so that π π − 1 = π − 1 π = id . {\displaystyle \pi \pi ^{-1}=\pi ^{-1}\pi =\operatorname {id} .} In general, composition of two permutations is not commutative, that is, π σ ≠ σ π .
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 ∈ N {\displaystyle \mathbb {N} } with ∀ n C ( A ↾ n ) ≤ 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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: 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In 1940 Alonzo Church (re)formulated it as simply typed lambda calculus. and examined by Gödel in 1944. A survey of these developments is found in Collins (2012).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 ==
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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