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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.
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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.
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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: ответ ('answer') vs. ответить ('to answer') несу (' carry') vs. несёт ('carries') голод ('hunger') vs. голоден ('hungry' masc.)
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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.
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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—that 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—that 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.
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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.
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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.
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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.
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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 Martínez, Gloria Gutiérrez & 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.
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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 → 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 → 0 {\displaystyle s\rightarrow 0} has been criticized on diverse grounds.
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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.
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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 − β {\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 β {\displaystyle \beta } of making a type II error by wrongly failing to reject the null hypothesis decreases.
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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).
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, FN), and let Q {\displaystyle \mathbb {Q} } denote an equivalent martingale measure. Let U = (U0, U1, . .
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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.
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In mathematical cryptography, a Kleinian integer is a complex number of the form m + n 1 + − 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 ( − 7 ) {\displaystyle \mathbb {Q} ({\sqrt {-7}})} . This ring is a unique factorization domain.
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In some jurisdictions, false statement is a crime similar to perjury.
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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.
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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.
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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.
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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.
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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.
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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.
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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 ⟨k⟩ and aspirated ⟨kʰ⟩. An old symbol for light aspiration was ⟨ʻ⟩, but this is now obsolete.
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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).
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In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant.
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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 ∣ 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}}} .
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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.
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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.
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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.
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Thus for some rational number β . {\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 Δ = a 2 − c = d 2 > 0 {\displaystyle ~\Delta =a^{2}-c=d^{2}>0~} (≠ 0, otherwise c would be the square of a), hence x and y must be and a − a 2 − c 2 .
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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.
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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.
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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 ) = − 1. {\displaystyle \left({\frac {a}{p}}\right)=-1.}
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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.
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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.
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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.
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Vector processors use this technique with one additional trick. Because the data layout is in a known format — a set of numbers arranged sequentially in memory — 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.
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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.
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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.
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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.
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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.
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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 − λ λ n + r ( n + r ) ! ⋅ 1 I ( r , λ ) , n = 0 , 1 , 2 , … if r ≥ 0 e − λ λ n + r ( n + r ) ! ⋅ 1 I ( r + s , λ ) , n = s , s + 1 , s + 2 , … otherwise {\displaystyle P(X=n)={\begin{cases}e^{-\lambda }{\dfrac {\lambda ^{n+r}}{\left(n+r\right)!
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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.
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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.
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In mathematics, the language of ordered abelian groups has one constant symbol 0, one unary function symbol −, one binary function symbol +, and one binary relation symbol ≤. Then: The expressions +(x, y) and +(x, +(y, −(z))) are terms. These are usually written as x + y and x + y − z. The expressions +(x, y) = 0 and ≤(+(x, +(y, −(z))), +(x, y)) are atomic formulas. These are usually written as x + y = 0 and x + y − z ≤ x + y. The expression ( ∀ x ∀ y {\displaystyle (\forall x\forall y\,} is a formula, which is usually written as ∀ x ∀ y ( x + y ≤ z ) → ∀ x ∀ y ( x + y = 0 ) .
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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.
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In software engineering, an entity–relationship model (ERM) is an abstract and conceptual representation of data. Entity–relationship 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–relationship 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.
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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.
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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.
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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.
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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 − 1 e {\displaystyle 1-{1 \over e}} for values of k ≥ 3 {\displaystyle k\geq 3} . This is the best possible approximation ratio unless N P ⊆ D T I M E ( n O ( log log n ) ) {\displaystyle NP\subseteq DTIME(n^{O(\log \log n)})} .
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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.
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. {\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).
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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.
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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.
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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.
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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–value 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.
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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 — indeed in any area where fields appear prominently.
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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 Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is π(N) ~ N/log(N), where π(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).
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Yet Gödel 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–Fraenkel set theory as shown by Cohen.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Calculate an − 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 × 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In numerical linear algebra, the Gauss–Seidel 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In terms of the Hilbert symbol, Hilbert's reciprocity law for an algebraic number field states that ∏ 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 ) ∞ ( 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)∞ is 1 if one of p and q is positive and –1 otherwise, and (p,q)2 is (–1)(p–1)(q–1)/4. So for p and q positive odd primes Hilbert's law is the law of quadratic reciprocity.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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—and the basic components of the system had been known since the 1960s DNA synthesis work of Har Gobind Khorana—making "who invented PCR?" a complicated question.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In the above formulation, if the bit rate constraint is neglected by setting λ {\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–distortion 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 = ⌈ log 2 M ⌉ {\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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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—at least to "some interesting extent"—fulfill certain properties: Domain specificity: modules only operate on certain kinds of inputs—they 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—information encapsulation—stands 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 Müller-Lyer illusion is an illusion does not correct visual processing.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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{\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×M transpose is an M×N transpose, although it is also easy to show explicitly that P−1 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−1,M−1), 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).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 Δ 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 Évariste 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).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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For example, giving the structure of the simply-typed λ-calculus at the type level requires binding, or higher-order, type operators. These binding type operators correspond to the 2nd axis of the λ-cube, and type theories such as the simply-typed λ-calculus with type operators, λω. Combining type operators with the polymorphic λ-calculus (System F) yields System Fω.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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}}.}
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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In mathematics, a Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 /ð/ 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).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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–Howard correspondence. To be sound, such a system must have uninhabited types.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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, 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 − 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).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 Plücker embedding.For given d ≤ n we define as formal variables the brackets with the λ taken from {1,...,n}, subject to = − and similarly for other transpositions. The set Λ(n,d) of size ( n d ) {\displaystyle {\binom {n}{d}}} generates a polynomial ring K over a field K. There is a homomorphism Φ(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 λ. The bracket ring B(n,d) is the image of Φ. The kernel I(n,d) of Φ 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−d)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).
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 ∣ B ) = P ( B ∣ 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.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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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 “Natural Language” or LexisNexis' Headnote searches.
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https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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