In modular arithmetic, the integers coprime (relatively prime) to n from the set { 0 , 1 , … , n − 1 } {\displaystyle \{0,1,\dots ,n-1\}} of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n. Hence another name is the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. Here units refers to elements with a multiplicative inverse, which, in this ring, are exactly those coprime to n. This quotient group, usually denoted ( Z / n Z ) × {\displaystyle (\mathbb {Z} /n\mathbb {Z} )^{\times }} , is fundamental in number theory. It is used in cryptography, integer factorization, and primality testing. It is an abelian, finite group whose order is given by Euler's totient function: | ( Z / n Z ) × | = φ ( n ) . {\displaystyle |(\mathbb {Z} /n\mathbb {Z} )^{\times }|=\varphi (n).} For prime n the group is cyclic, and in general the structure is easy to describe, but no simple general formula for finding generators is known.


In the field of bioinformatics, clustering is used for a number of applications. One use is as a pattern recognition technique to analyze gene expression data from RNA-sequencing data or other technologies. In this case, genes with similar expression patterns are grouped into the same cluster, and different clusters display distinct, well-separated patterns of expression. Use of clustering can provide insight into gene function and regulation.


This assertion, which uses set-builder notation, means that if the elements satisfying the property P ( x ) {\displaystyle P(x)} are the same as the elements satisfying Q ( x ) , {\displaystyle Q(x),} then the two uses of the set-builder notation define the same set. This property is often expressed as "two sets that have the same elements are equal." It is one of the usual axioms of set theory, called axiom of extensionality.


In much of probability, especially when conditional expectation is involved, one is concerned with sets that represent only part of all the possible information that can be observed. This partial information can be characterized with a smaller σ-algebra which is a subset of the principal σ-algebra; it consists of the collection of subsets relevant only to and determined only by the partial information. A simple example suffices to illustrate this idea. Imagine you and another person are betting on a game that involves flipping a coin repeatedly and observing whether it comes up Heads ( H {\displaystyle H} ) or Tails ( T {\displaystyle T} ).


In statistics, single-linkage clustering is one of several methods of hierarchical clustering. It is based on grouping clusters in bottom-up fashion (agglomerative clustering), at each step combining two clusters that contain the closest pair of elements not yet belonging to the same cluster as each other. This method tends to produce long thin clusters in which nearby elements of the same cluster have small distances, but elements at opposite ends of a cluster may be much farther from each other than two elements of other clusters. For some classes of data, this may lead to difficulties in defining classes that could usefully subdivide the data. However, it is popular in astronomy for analyzing galaxy clusters, which may often involve long strings of matter; in this application, it is also known as the friends-of-friends algorithm.


Often, the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown. In the case of two variables, each solution may be interpreted as the Cartesian coordinates of a point of the Euclidean plane. The solutions of a linear equation form a line in the Euclidean plane, and, conversely, every line can be viewed as the set of all solutions of a linear equation in two variables.


Similarly, the WMB maintains program order only among writes. The SPARC V9 RMO model provides a MEMBAR instruction which can be customised to order previous reads and writes with respect to future read and write operations. There is no need for using read-modify-writes to achieve this order because the MEMBAR instruction can be used to order a write with respect to a succeeding read.


(Roughly speaking, Girard found pure systems in which one can express the sentence "the types form a type".) Furthermore, all known examples of pure type systems that are not strongly normalizing are not even (weakly) normalizing: they contain expressions that do not have normal forms, just like the untyped lambda calculus. It is a major open problem in the field whether this is always the case, i.e. whether a (weakly) normalizing PTS always has the strong normalization property. This is known as the Barendregt–Geuvers–Klop conjecture (named after Henk Barendregt, Herman Geuvers, and Jan Willem Klop).


In probability theory, Kolmogorov's Three-Series Theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite series of random variables in terms of the convergence of three different series involving properties of their probability distributions. Kolmogorov's three-series theorem, combined with Kronecker's lemma, can be used to give a relatively easy proof of the Strong Law of Large Numbers.


A wide variety of mathematical theories to understand and analyze message-passing systems are available, including the actor model, and various process calculi. Message passing can be efficiently implemented via symmetric multiprocessing, with or without shared memory cache coherence.Shared memory and message passing concurrency have different performance characteristics. Typically (although not always), the per-process memory overhead and task switching overhead is lower in a message passing system, but the overhead of message passing is greater than for a procedure call. These differences are often overwhelmed by other performance factors.


In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past. For instance, a machine may have two states, A and E. When it is in state A, there is a 40% chance of it moving to state E and a 60% chance of it remaining in state A. When it is in state E, there is a 70% chance of it moving to A and a 30% chance of it staying in E. The sequence of states of the machine is a Markov chain. If we denote the chain by X 0 , X 1 , X 2 , .


Since the minimum Hamming weight of ( 7 , 4 , 3 ) {\displaystyle (7,4,3)} Hamming Code is 3, d H ( x 1 , x 2 ) ≥ 3 {\displaystyle d_{H}(\mathbf {x_{1}} ,\mathbf {x_{2}} )\geq 3} . Therefore, the input x {\displaystyle \mathbf {x} } can be recovered since d H ( x , y ) ≤ 1 {\displaystyle d_{H}(\mathbf {x} ,\mathbf {y} )\leq 1} . Similarly, the bits distribution with R X = 7 {\displaystyle R_{X}=7} , R Y = 3 {\displaystyle R_{Y}=3} can be achieved by reversing the roles of X {\displaystyle X} and Y {\displaystyle Y} .


A different ontology arises if we need to attend to the electrodynamics in the device: Here signals propagate at finite speed and an object (like a resistor) that was previously viewed as a single component with an I/O behavior may now have to be thought of as an extended medium through which an electromagnetic wave flows. Ontologies can of course be written down in a wide variety of languages and notations (e.g., logic, LISP, etc.); the essential information is not the form of that language but the content, i.e., the set of concepts offered as a way of thinking about the world. Simply put, the important part is notions like connections and components, not the choice between writing them as predicates or LISP constructs.


S = ∅ , T = ∅ S ≠ ∅ , T ≠ ∅ , S ⊂ T S = ∅ , T ≠ ∅ S ≠ ∅ , T ≠ ∅ , T ⊂ S S ≠ ∅ , T = ∅ S ≠ ∅ , T ≠ ∅ , T = S S ≠ ∅ , T ≠ ∅ , S ∩ T = ∅ S ≠ ∅ , T ≠ ∅ , S ∩ T ≠ ∅ , ¬ ( S ⊆ T ) , ¬ ( T ⊆ S ) , S ≠ T {\displaystyle {\begin{array}{l|l}S=\emptyset ,T=\emptyset &S\neq \emptyset ,T\neq \emptyset ,S\subset T\\\hline S=\emptyset ,T\neq \emptyset &S\neq \emptyset ,T\neq \emptyset ,T\subset S\\\hline S\neq \emptyset ,T=\emptyset &S\neq \emptyset ,T\neq \emptyset ,T=S\\\hline S\neq \emptyset ,T\neq \emptyset ,S\cap T=\emptyset &S\neq \emptyset ,T\neq \emptyset ,S\cap T\neq \emptyset ,\lnot (S\subseteq T),\lnot (T\subseteq S),S\neq T\end{array}}} As can be noticed, standard partitions might change according to how much testing the engineer wants to perform. Sub-domain Propagation (SDP). This tactic is applied to expressions containing: Two or more mathematical operators for which there are already defined standard partitions, or Mathematical operators which are defined in terms of other mathematical operators.In any of these cases, the standard partitions of the operators appearing in the expression or in the definition of a complex one, are combined to produce a partition for the expression.


In the United States, most cities have zoning codes that set the minimum size for a housing unit (often 400 square feet) as well as the number of non-related persons who can live together in one unit.In June 2016, New York City got its first microapartment building, Carmel Place, with 55 units that are as small as 250 square feet (23 m2) and ceilings from nine to ten feet (2.7 to 3.0 m). Common's Williamsburg in Brooklyn rents single rooms where tenants share a kitchen for $2,050 per month; The Guardian states that "ingle room occupancy housing is obviously not a new concept, however, the genius of late capitalism is that it has made it desirable" to high-income renters".In 2017, California passed a law that encourages development of "efficiency units" of at least 150 sq ft by disallowing localities from limiting their numbers near public universities and public transportation. : 1 In San Francisco, Starcity is converting unused parking garages, commercial spaces and offices into single room residential units, where tenants (tech professionals are the typical renter) get a furnished bedroom and access to wifi, janitor services and common kitchens and lounges for $1,400 to $2,400 per month, an approach that has been called "dorm living for grown ups".Boston's first microapartment building opened in August 2016, on Commonwealth Avenue in Packard's Corner. As the largest microapartment building in the United States, the building is currently being leased by Boston University to house 341 students during the renovation of another university residence.


In percolation theory one examines a finite or infinite graph and removes edges (or links) randomly. Thus the Erdős–Rényi process is in fact unweighted link percolation on the complete graph. (One refers to percolation in which nodes and/or links are removed with heterogeneous weights as weighted percolation). As percolation theory has much of its roots in physics, much of the research done was on the lattices in Euclidean spaces.


Note that this implies that p {\displaystyle p} is contained in β {\displaystyle \beta } and γ {\displaystyle \gamma } (with opposite polarity) and q {\displaystyle q} is contained in δ {\displaystyle \delta } and α {\displaystyle \alpha } (also with opposite polarity). The table below shows the rewriting rules proposed by Simone et al.. The idea of the algorithm is to reduce proof size by opportunistically applying these rules. The first five rules were introduced in an earlier paper.


In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology. A splicing language is a language generated by iterated application of a splicing rule: the splicing languages form a proper subset of the regular languages.


In the context of healthcare in the United States, a pre-existing condition is a medical condition that started before a person's health insurance went into effect. Before 2014, some insurance policies would not cover expenses due to pre-existing conditions. These exclusions by the insurance industry were meant to cope with adverse selection by potential customers. Such exclusions have been prohibited since January 1, 2014, by the Patient Protection and Affordable Care Act. According to the Kaiser Family Foundation, more than a quarter of adults below the age of 65 (approximately 52 million people) had pre-existing conditions in 2016.


Fourth, the "trialability" of an innovation; that is, whether it can be tested without commitment for a period of time. An innovation that has an available trial period provides less uncertainty to the group member who will be trying it. Lastly, whether there are observable results with use of the innovation. The more positive and visible results, the higher the likelihood it gets adopted as a permanent idea for the group.


In mathematics, given a collection S of subsets of a set X, an exact hitting set X* is a subset of X such that each subset in S contains exactly one element in X*. One says that each subset in S is hit by exactly one element in X*. In computer science, the exact hitting set problem is a decision problem to find an exact hitting set or else determine none exists. The exact hitting set problem is an abstract exact cover problem.


The technique is also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov. The theoretical basis for the method was developed by the French mathematician Georges Matheron based on the Master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes.


In mathematics, the notion of cancellativity (or cancellability) is a generalization of the notion of invertibility. An element a in a magma (M, ∗) has the left cancellation property (or is left-cancellative) if for all b and c in M, a ∗ b = a ∗ c always implies that b = c. An element a in a magma (M, ∗) has the right cancellation property (or is right-cancellative) if for all b and c in M, b ∗ a = c ∗ a always implies that b = c. An element a in a magma (M, ∗) has the two-sided cancellation property (or is cancellative) if it is both left- and right-cancellative. A magma (M, ∗) has the left cancellation property (or is left-cancellative) if all a in the magma are left cancellative, and similar definitions apply for the right cancellative or two-sided cancellative properties. A left-invertible element is left-cancellative, and analogously for right and two-sided. If a⁻¹ is the inverse of a, then a ∗ b = a ∗ c implies a⁻¹ ∗ a ∗ b = a⁻¹ ∗ a ∗ c which implies b = c. For example, every quasigroup, and thus every group, is cancellative.


In natural language processing, a sentence embedding refers to a numeric representation of a sentence in the form of a vector of real numbers which encodes meaningful semantic information.State of the art embeddings are based on the learned hidden layer representation of dedicated sentence transformer models. BERT pioneered an approach involving the use of a dedicated  token preprended to the beginning of each sentence inputted into the model; the final hidden state vector of this token encodes information about the sentence and can be fine-tuned for use in sentence classification tasks. In practice however, BERT's sentence embedding with the  token achieves poor performance, often worse than simply averaging non-contextual word embeddings. SBERT later achieved superior sentence embedding performance by fine tuning BERT's  token embeddings through the usage of a siamese neural network architecture on the SNLI dataset.


In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form x2 + bx + c = 0with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers. Common examples of quadratic integers are the square roots of rational integers, such as √2, and the complex number i = √−1, which generates the Gaussian integers.


Adolescents and adults who know the rule are faster than those who do not. In the learning of a second language the correction of errors remains a controversial topic with many differing schools of thought. Throughout the last century much advancement has been made in research on the correction of students' errors.


In mathematics and group theory, the term multiplicative group refers to one of the following concepts: the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is (F ∖ {0}, •), where 0 refers to the zero element of F and the binary operation • is the field multiplication, the algebraic torus GL(1)..


In network science, reciprocity is a measure of the likelihood of vertices in a directed network to be mutually linked. Like the clustering coefficient, scale-free degree distribution, or community structure, reciprocity is a quantitative measure used to study complex networks.


Showing this with hundreds of pages of hand analysis, Appel and Haken concluded that no smallest counterexample exists because any must contain, yet do not contain, one of these 1,936 maps. This contradiction means there are no counterexamples at all and that the theorem is therefore true. Initially, their proof was not accepted by mathematicians at all because the computer-assisted proof was infeasible for a human to check by hand. However, the proof has since then gained wider acceptance, although doubts still remain.


In mathematics parity can refer to the evenness or oddness of an integer, which, when written in its binary form, can be determined just by examining only its least significant bit. In information technology parity refers to the evenness or oddness, given any set of binary digits, of the number of those bits with value one. Because parity is determined by the state of every one of the bits, this property of parity—being dependent upon all the bits and changing its value from even to odd parity if any one bit changes—allows for its use in error detection and correction schemes. In telecommunications the parity referred to by some protocols is for error-detection.


The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.


In order to achieve the highest level of privacy and protection when calculating and transmitting sensitive information, biometric tokenization leverages existing encryption algorithms, authentication protocols, as well as hardware trust zones. Combining some or all of these methods maximizes the level of protection needed to uphold the integrity of the process and security of data that could otherwise expose users to a breach of trust on a mass scale.


It must be sensitive to differences between MT systems and reliable in that MT systems that score similarly should be expected to perform similarly. Finally, the metric must be general, that is it should work with different text domains, in a wide range of scenarios and MT tasks. The aim of this subsection is to give an overview of the state of the art in automatic metrics for evaluating machine translation.


People interested in building a small home can encounter institutional “discrimination” when building codes require minimum size well above the size of a small home. Also, neighbors may be hostile because they fear negative impacts on their property values and have concerns about increased taxes.More broadly, these sentiments of "othering" homeless and unhoused persons have culminated into a broader movement of NIMBY-ism, or "Not in My Backyard."


The use of this feature by programmers led to the Gate A20 compatibility issues in later CPU generations, where the linear address space was expanded past 20 bits. In 16-bit real mode, enabling applications to make use of multiple memory segments (in order to access more memory than available in any one 64K-segment) is quite complex, but was viewed as a necessary evil for all but the smallest tools (which could do with less memory). The root of the problem is that no appropriate address-arithmetic instructions suitable for flat addressing of the entire memory range are available.


In modular arithmetic, the set of available numbers is restricted to a finite subset of the integers, and addition "wraps around" when reaching a certain value, called the modulus. For example, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory. The set of integers modulo 2 has just two elements; the addition operation it inherits is known in Boolean logic as the "exclusive or" function. A similar "wrap around" operation arises in geometry, where the sum of two angle measures is often taken to be their sum as real numbers modulo 2π. This amounts to an addition operation on the circle, which in turn generalizes to addition operations on many-dimensional tori.


In other programming languages such as Pascal, indices may start at 1, so indexing in a block of memory can be changed to fit a start-at-1 addressing scheme by a simple linear transformation – in this scheme, the memory location of the ith element with base address b and element size s is b + (i − 1)s.


In statistical classification, the Fisher kernel, named after Ronald Fisher, is a function that measures the similarity of two objects on the basis of sets of measurements for each object and a statistical model. In a classification procedure, the class for a new object (whose real class is unknown) can be estimated by minimising, across classes, an average of the Fisher kernel distance from the new object to each known member of the given class. The Fisher kernel was introduced in 1998. It combines the advantages of generative statistical models (like the hidden Markov model) and those of discriminative methods (like support vector machines): generative models can process data of variable length (adding or removing data is well-supported) discriminative methods can have flexible criteria and yield better results.


Furthermore, the warranty of habitability generally cannot be disclaimed.Contractual language can also limit the remedies available for breach of an implied warranty such as by capping recoverable damages or limiting the legal remedy to a replacement of a defective item. However, such a term can be found to be unconscionable. For example, if a defective product causes a personal injury, a contractual provision limiting recovery in such a case will be deemed prima facie unconscionable. UCC § 2-719(3)


In model checking, a field of computer science, a difference bound matrix (DBM) is a data structure used to represent some convex polytopes called zones. This structure can be used to efficiently implement some geometrical operations over zones, such as testing emptyness, inclusion, equality, and computing the intersection and the sum of two zones. It is, for example, used in the Uppaal model checker; where it is also distributed as an independent library.More precisely, there is a notion of canonical DBM; there is a one-to-one relation between canonical DBMs and zones and from each DBM a canonical equivalent DBM can be efficiently computed. Thus, equality of zone can be tested by checking for equality of canonical DBMs.


In probability theory, events E1, E2, ..., En are said to be mutually exclusive if the occurrence of any one of them implies the non-occurrence of the remaining n − 1 events. Therefore, two mutually exclusive events cannot both occur. Formally said, the intersection of each two of them is empty (the null event): A ∩ B = ∅.


. . , n + 1 , {\displaystyle v_{k}=\mathrm {constant} \ \forall \ k=0,...,n+1,} and this corresponds to eigenvalue 0 {\displaystyle 0} .


होना ہونا (honā) is the only verb in Hindi-Urdu to have the present indicative, imperfect indicative, presumptive mood and the present subjunctive conjugations, and all the other verbs in Hindi-Urdu lack them.The verb होना / ہونا (honā) can be translated as "to be", "to exist", "to happen" or "to have" depending on the context, and when used in the third person it could also be translated as "there is/are". Many verbs conjugations in Hindi-Urdu are derived from participles and hence are gendered and numbered, and they agree with either the object or the subject of the sentence depending on the grammatical case of the subject of the sentence. When the subject is in the ergative or the dative case (seeː dative construction & quirky subject) the verb agrees in gender and number with the object of the sentence and with the subject when the subject is in the nominative case.


In the above no-tyranny scenario, suppose no floor federation, but (only) a room with some local governance. Suppose that the gym room is not used by all, but there is a "community" of regulars, there is a grouping of voters by its activity as speed-cyclists (illustrated as spiked hair), that have the gym room key for some activities on Sundays. They are acting collectively to preserve the gym room for a local cyclists group. In this situation the following facts hold: There is a subset of voters and some collective action, uniting them, making them a cohesive group.


In the case of a speech signal, inputs are spectral coefficients over time. In order to learn critical acoustic-phonetic features (for example formant transitions, bursts, frication, etc.) without first requiring precise localization, the TDNN is trained time-shift-invariantly. Time-shift invariance is achieved through weight sharing across time during training: Time shifted copies of the TDNN are made over the input range (from left to right in Fig.1). Backpropagation is then performed from an overall classification target vector (see TDNN diagram, three phoneme class targets (/b/, /d/, /g/) are shown in the output layer), resulting in gradients that will generally vary for each of the time-shifted network copies.


In Haskell, there is no variable assignment; but operations similar to assignment (like assigning to a field of an array or a field of a mutable data structure) usually evaluate to the unit type, which is represented as (). This type has only one possible value, therefore containing no information. It is typically the type of an expression that is evaluated purely for its side effects.


In the matrix equation case in which A is a square matrix, eigenvalues λ {\displaystyle \lambda } may be found by setting the determinant of the matrix equal to zero, i.e. finding where the matrix has no inverse. (Such a square matrix is said to be singular.) Finite matrices have only a finite number of eigenvalues/eigenvectors, whereas linear operators can have a countably infinite number of eigenvalues/eigenfunctions (in confined regions) or uncountably infinite (continuous) spectra of solutions, as in unbounded regions.


Alternatively, the elements of a free abelian group may be thought of as signed multisets containing finitely many elements of B {\displaystyle B} , with the multiplicity of an element in the multiset equal to its coefficient in the formal sum. Another way to represent an element of a free abelian group is as a function from B {\displaystyle B} to the integers with finitely many nonzero values; for this functional representation, the group operation is the pointwise addition of functions. Every set B {\displaystyle B} has a free abelian group with B {\displaystyle B} as its basis.


In the Microsoft document "Output Content Protection and Windows Vista", it is claimed that: "The security level achieved for typical video data is estimated to be approaching that of regular AES. This assertion is being tested by Intel putting its Cascaded Cipher out to the cryptography community to get their security assessment — that is, to see if they can break it." The security of the system requires that it is impossible to recover the currently active inner key from the output of the reduced round Serpent encrypted video stream. Furthermore, the security of this method is highly sensitive to the number of rounds used in Serpent, the mode of operation described in the patent application, and the number of times the inner key is reused.


In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such that a k ≡ 1 ( mod n ) {\textstyle a^{k}\ \equiv \ 1{\pmod {n}}} .In other words, the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the integers modulo n. The order of a modulo n is sometimes written as ord n  ( a ) {\displaystyle \operatorname {ord} _{n}(a)} .


In number theory, the Dedekind psi function is the multiplicative function on the positive integers defined by ψ ( n ) = n ∏ p | n ( 1 + 1 p ) , {\displaystyle \psi (n)=n\prod _{p|n}\left(1+{\frac {1}{p}}\right),} where the product is taken over all primes p {\displaystyle p} dividing n . {\displaystyle n.} (By convention, ψ ( 1 ) {\displaystyle \psi (1)} , which is the empty product, has value 1.) The function was introduced by Richard Dedekind in connection with modular functions.


In mathematics, the Feit–Thompson conjecture is a conjecture in number theory, suggested by Walter Feit and John G. Thompson (1962). The conjecture states that there are no distinct prime numbers p and q such that p q − 1 p − 1 {\displaystyle {\frac {p^{q}-1}{p-1}}} divides q p − 1 q − 1 {\displaystyle {\frac {q^{p}-1}{q-1}}} .If the conjecture were true, it would greatly simplify the final chapter of the proof (Feit & Thompson 1963) of the Feit–Thompson theorem that every finite group of odd order is solvable. A stronger conjecture that the two numbers are always coprime was disproved by Stephens (1971) with the counterexample p = 17 and q = 3313 with common factor 2pq + 1 = 112643. It is known that the conjecture is true for q = 3 (Le 2012). Informal probability arguments suggest that the "expected" number of counterexamples to the Feit–Thompson conjecture is very close to 0, suggesting that the Feit–Thompson conjecture is likely to be true.


Additionally, in the United States, progress reports may be issued to track a student's performance in between report cards. They are typically issued at the midpoint of a grading period, (for example: 4½ weeks into a nine-week grading period, or three weeks into a six-week grading period) and contain virtually the same information as the report card. These reports allow students and their parents to see if school performance is slipping and if intervention is required to bring up the grade.


These logarithms are equally spaced along a vertical line in the complex plane. A complex-valued function log: U → C {\displaystyle \log \colon U\to \mathbb {C} } , defined on some subset U {\displaystyle U} of the set C ∗ {\displaystyle \mathbb {C} ^{*}} of nonzero complex numbers, satisfying e log  z = z {\displaystyle e^{\log z}=z} for all z {\displaystyle z} in U {\displaystyle U} . Such complex logarithm functions are analogous to the real logarithm function ln: R > 0 → R {\displaystyle \ln \colon \mathbb {R} _{>0}\to \mathbb {R} } , which is the inverse of the real exponential function and hence satisfies eln x = x for all positive real numbers x. Complex logarithm functions can be constructed by explicit formulas involving real-valued functions, by integration of 1 / z {\displaystyle 1/z} , or by the process of analytic continuation.There is no continuous complex logarithm function defined on all of C ∗ {\displaystyle \mathbb {C} ^{*}} . Ways of dealing with this include branches, the associated Riemann surface, and partial inverses of the complex exponential function. The principal value defines a particular complex logarithm function Log: C ∗ → C {\displaystyle \operatorname {Log} \colon \mathbb {C} ^{*}\to \mathbb {C} } that is continuous except along the negative real axis; on the complex plane with the negative real numbers and 0 removed, it is the analytic continuation of the (real) natural logarithm.


In the early 20th century, it was common for weather maps to be hand drawn. The symbols for cloud cover on these maps, like the modern symbols, were drawn inside the circle marking the position of the weather station making the measurements. Unlike the modern symbols, these ones consisted of straight lines only rather than filled in blocks which would have been less practical on a hand drawing. A reduced set of these symbols were used on teleprinters used for distributing weather information and warnings. These machines were 5-bit teleprinters using a modified version of the Baudot-Murray code.


In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass-filtered signal at a sample rate below its Nyquist rate (twice the upper cutoff frequency), but is still able to reconstruct the signal. When one undersamples a bandpass signal, the samples are indistinguishable from the samples of a low-frequency alias of the high-frequency signal. Such sampling is also known as bandpass sampling, harmonic sampling, IF sampling, and direct IF-to-digital conversion.


In some situations, one can avoid using the transpose A ⊤ {\displaystyle A^{\top }} , as proposed by Mikhail Lavrentyev. For example, if A {\displaystyle A} is symmetric positive definite, i.e. A = A ⊤ > 0 {\displaystyle A=A^{\top }>0} , so is its inverse A − 1 {\displaystyle A^{-1}} , which can thus be used to set up the weighted norm squared ‖ x ‖ P 2 = x ⊤ A − 1 x {\displaystyle \|x\|_{P}^{2}=x^{\top }A^{-1}x} in the generalized Tikhonov regularization, leading to minimizing ‖ A x − b ‖ A − 1 2 + ‖ x − x 0 ‖ Q 2 {\displaystyle \|Ax-b\|_{A^{-1}}^{2}+\|x-x_{0}\|_{Q}^{2}} or, equivalently up to a constant term, x ⊤ ( A + Q ) x − 2 x ⊤ ( b + Q x 0 ) {\displaystyle x^{\top }(A+Q)x-2x^{\top }(b+Qx_{0})} .This minimization problem has an optimal solution x ∗ {\displaystyle x^{*}} which can be written explicitly using the formula x ∗ = ( A + Q ) − 1 ( b + Q x 0 ) {\displaystyle x^{*}=(A+Q)^{-1}(b+Qx_{0})} ,which is nothing but the solution of the generalized Tikhonov problem where A = A ⊤ = P − 1 . {\displaystyle A=A^{\top }=P^{-1}.} The Lavrentyev regularization, if applicable, is advantageous to the original Tikhonov regularization, since the Lavrentyev matrix A + Q {\displaystyle A+Q} can be better conditioned, i.e., have a smaller condition number, compared to the Tikhonov matrix A ⊤ A + Γ ⊤ Γ . {\displaystyle A^{\top }A+\Gamma ^{\top }\Gamma .}


In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted to study of properties of the noncommutative rings, including the properties that apply also to commutative rings.


In the exploit, bidirectional characters are abused to visually reorder text in source code so that later execution occurs in a different order. Bidirectional characters can be inserted in areas of source code where string literals are allowed. This often applies to documentation, variables, or comments.


In the Philippines, the Philippine Atmospheric, Geophysical and Astronomical Services Administration (PAGASA) branch of the Department of Science and Technology (DOST) issues general flood advisory (for non-telemetered river basins whenever there is a significant amount of rainfall recorded).


In some programming languages, the maximum size of the call stack is much less than the space available in the heap, and recursive algorithms tend to require more stack space than iterative algorithms. Consequently, these languages sometimes place a limit on the depth of recursion to avoid stack overflows; Python is one such language. Note the caveat below regarding the special case of tail recursion.


Creating a measure or scale of the degree to which the concept applies (metrology). 18. Examining the distribution patterns or distributional frequency of (possibly different) uses of the concept (statistics).


In some circumstances the natural key that uniquely identifies a tuple in a relation may be cumbersome to use for software development. For example, it may involve multiple columns or large text fields. In such cases, a surrogate key can be used instead as the primary key. In other situations there may be more than one candidate key for a relation, and no candidate key is obviously preferred.


The processors ran at 20 MHz in the integer units and 40 MHz for the FPUs, with the intention being to increase this to 50 MHz by the time it shipped. At about 12 Mflops peak per CU, the machine as a whole would deliver up to 1.5 Gflops, although due to the memory latencies this was typically closer to 250 Mflops. While this was fast for a CMOS machine processor of the time, it was hardly competitive for a supercomputer.


In the 1990s the chip design and fabrication process grew to the point where it was possible to build a commodity processor with every potential feature built into it. To improve performance, CPU designs started adding internal parallelism, becoming "superscalar". In any program there are instructions that work on unrelated data, so by adding more functional units these instructions can be run at the same time. A new portion of the CPU, the scheduler, looks for these independent instructions and feeds them into the units, taking their outputs and re-ordering them so externally it appears they ran in succession.


In order to use the above mentioned models efficiently, it is important to have a large amount of data. However, as users, we are stuck with limited data i.e. the original image. In order to compensate for these issues, we employ tricks such as random cropping. Random cropping refers to the act of randomly choosing certain sub images from the existing original image.


In mathematics, symbolic dynamics is the practice of modeling a topological or smooth dynamical system by a discrete space consisting of infinite sequences of abstract symbols, each of which corresponds to a state of the system, with the dynamics (evolution) given by the shift operator. Formally, a Markov partition is used to provide a finite cover for the smooth system; each set of the cover is associated with a single symbol, and the sequences of symbols result as a trajectory of the system moves from one covering set to another.


In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle. If a given particle is taken to be at the origin O, and if ρ = N / V {\displaystyle \rho =N/V} is the average number density of particles, then the local time-averaged density at a distance r {\displaystyle r} from O is ρ g ( r ) {\displaystyle \rho g(r)} . This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below.


However, issues may arise that complicate the process. In 1992, Christel and Kang identified problems that indicate the challenges for requirements elicitation: 'Problems of scope'. The boundary of the system is ill-defined or the customers/users specify unnecessary technical details that may confuse, rather than clarify, overall system objectives.


In mathematics, a family F {\displaystyle {\mathcal {F}}} of sets is of finite character if for each A {\displaystyle A} , A {\displaystyle A} belongs to F {\displaystyle {\mathcal {F}}} if and only if every finite subset of A {\displaystyle A} belongs to F {\displaystyle {\mathcal {F}}} . That is, For each A ∈ F {\displaystyle A\in {\mathcal {F}}} , every finite subset of A {\displaystyle A} belongs to F {\displaystyle {\mathcal {F}}} . If every finite subset of a given set A {\displaystyle A} belongs to F {\displaystyle {\mathcal {F}}} , then A {\displaystyle A} belongs to F {\displaystyle {\mathcal {F}}} .


In category theory, the empty semigroup is always admitted. It is the unique initial object of the category of semigroups. A semigroup with no elements is an inverse semigroup, since the necessary condition is vacuously satisfied.


For constant k, this is in the same complexity class as the Lucas-Lehmer test. In practice however, the cost of doing many iterations and other differences leads to worse performance for Miller–Rabin. The most efficient deterministic primality test for any n-digit number, the AKS primality test, requires Õ(n6) bit operations in its best known variant and is extremely slow even for relatively small values.


In mathematics, and disciplines in which mathematics plays a major role, hand-waving refers to either absence of formal proof or methods that do not meet mathematical rigor. In practice, it often involves the use of unrepresentative examples, unjustified assumptions, key omissions and faulty logic, and while these may be useful in expository papers and seminar presentations, they ultimately fall short of the standard of proof needed to establish a result. The mathematical profession tends to be receptive to informed critiques from any listener, and a claimant to a new result is expected to be able to answer any such question with a logical argument, up to a full proof. Should a speaker apparently fail to give such an answer, anyone in the audience who can supply the needed demonstration may sometimes upstage the speaker.


In mathematics and economics, a corner solution is a special solution to an agent's maximization problem in which the quantity of one of the arguments in the maximized function is zero. In non-technical terms, a corner solution is when the chooser is either unwilling or unable to make a trade-off between goods.


In relational grammar, constituents that serve as the arguments to predicates are numbered in what is called the grammatical relations (GR) hierarchy. This numbering system corresponds loosely to the notions of subject, direct object and indirect object. The numbering scheme is subject → (1), direct object → (2) and indirect object → (3).


In practice, many screens that almost comply with part F of the standard deviate in various minor ways, and most brands of compliant brackets are designed to handle these deviations with little or no trouble for the end user: Non-square patterns, such as 600 × 200 mm and 600 x 400 mm and 800 × 400 mm. These were apparently permitted by the version 1 (2002) standard. : vii–viii The labeling for these may have been "MIS-F, width, height" e.g. "MIS-F, 600, 200" for 600 × 200 mm. A somewhat strange pattern of 280 × 150 mm. Various protrusions on the screen extending a few millimeters further back than the mounting surfaces.


(Fuzzy extractors convert biometric data into secret, uniformly random, and reliably reproducible random strings.) These techniques can also have other broader applications for other type of noisy inputs such as approximative data from human memory, images used as passwords, and keys from quantum channels. Fuzzy extractors also have applications in the proof of impossibility of the strong notions of privacy with regard to statistical databases.


In number theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares, such that n = a2 + b2 for some integers a, b. An integer greater than one can be written as a sum of two squares if and only if its prime decomposition contains no factor pk, where prime p ≡ 3 ( mod 4 ) {\displaystyle p\equiv 3{\pmod {4}}} and k is odd. In writing a number as a sum of two squares, it is allowed for one of the squares to be zero, or for both of them to be equal to each other, so all squares and all doubles of squares are included in the numbers that can be represented in this way. This theorem supplements Fermat's theorem on sums of two squares which says when a prime number can be written as a sum of two squares, in that it also covers the case for composite numbers. A number may have multiple representations as a sum of two squares, counted by the sum of squares function; for instance, every Pythagorean triple a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} gives a second representation for c 2 {\displaystyle c^{2}} beyond the trivial representation c 2 + 0 2 {\displaystyle c^{2}+0^{2}} .


Bg2 Kd4 2. Kd2 Ke5 3. Ke3 Kf5 4.


When an individual algorithm is profiled, as with complexity analysis, memory and cache considerations are often more significant than instruction counts or clock cycles; however, the profiler's findings can be considered in light of how the algorithm accesses data rather than the number of instructions it uses.Profiling may provide intuitive insight into an algorithm's behavior by revealing performance findings as a visual representation. Performance profiling has been applied, for example, during the development of algorithms for matching wildcards. Early algorithms for matching wildcards, such as Rich Salz' wildmat algorithm, typically relied on recursion, a technique criticized on grounds of performance.


In probability theory, a fair coin is defined as a probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} , which is in turn defined by the sample space, event space, and probability measure. Using H {\displaystyle H} for heads and T {\displaystyle T} for tails, the sample space of a coin is defined as: The event space for a coin includes all sets of outcomes from the sample space which can be assigned a probability, which is the full power set 2 Ω {\displaystyle 2^{\Omega }} . Thus, the event space is defined as: { } {\displaystyle \{\}} is the event where neither outcome happens (which is impossible and can therefore be assigned 0 probability), and { H , T } {\displaystyle \{H,T\}} is the event where either outcome happens, (which is guaranteed and can be assigned 1 probability). Because the coin is fair, the possibility of any single outcome is 50-50.


In some languages, infinitives may be marked for grammatical categories like voice, aspect, and to some extent tense. This may be done by inflection, as with the Latin perfect and passive infinitives, or by periphrasis (with the use of auxiliary verbs), as with the Latin future infinitives or the English perfect and progressive infinitives. Latin has present, perfect and future infinitives, with active and passive forms of each. For details see Latin conjugation § Infinitives.


A complete version of the theorem with a self-contained proof was given by M.W. Liebeck, Cheryl Praeger and Jan Saxl. The theorem is now a standard part of textbooks on permutation groups.


This is signified by the 'always false' proposition, called the "falsum", denoted "⊥". Since the consequence is false, at least one of the antecedents must be false. Thus for example, ' A1, A2 ⊢ ' means that at least one of the antecedents A1 and A2 must be false.


In metaphysics, ontology is the philosophical study of being. It investigates what types of entities exist, how they are grouped into categories, and how they are related to one another on the most fundamental level. Ontologists often try to determine what the categories or highest kinds are and how they form a system of categories that encompasses the classification of all entities. Commonly proposed categories include substances, properties, relations, states of affairs, and events.


Consequently, a four-pole generator could output twice the voltage of a two-pole generator, a six-pole generator could output three times the voltage of a two-pole, and so forth. This allows output voltage to increase without also increasing the rotational rate. In a multipolar generator, the armature and field magnets are surrounded by a circular frame or "ring yoke" to which the field magnets are attached. This has the advantages of strength, simplicity, symmetrical appearance, and minimum magnetic leakage, since the pole pieces have the least possible surface and the path of the magnetic flux is shorter than in a two-pole design.


The first base 10 pandigital prime is 10123457689; OEIS: A050288 lists more. For different reasons, redundant digits are also required for a pandigital number (in any base except unary) to also be a palindromic number in that base. The smallest pandigital palindromic number in base 10 is 1023456789876543201.


The concepts of the conceptual model can be mapped into physical design or implementation constructs using either manual or automated code generation approaches. The realization of conceptual models of many domains can be combined to a coherent platform. A conceptual model can be described using various notations, such as UML, ORM or OMT for object modelling, ITE, or IDEF1X for Entity Relationship Modelling.


In mathematical analysis, epi-convergence is a type of convergence for real-valued and extended real-valued functions. Epi-convergence is important because it is the appropriate notion of convergence with which to approximate minimization problems in the field of mathematical optimization. The symmetric notion of hypo-convergence is appropriate for maximization problems. Mosco convergence is a generalization of epi-convergence to infinite dimensional spaces.


In system software, a job queue (a.k.a. batch queue, input queue), is a data structure maintained by job scheduler software containing jobs to run.Users submit their programs that they want executed, "jobs", to the queue for batch processing. The scheduler software maintains the queue as the pool of jobs available for it to run. Multiple batch queues might be used by the scheduler to differentiate types of jobs depending on parameters such as: job priority estimated execution time resource requirementsThe use of a batch queue gives these benefits: sharing of computer resources among many users time-shifts job processing to when the computer is less busy avoids idling the compute resources without minute-by-minute human supervision allows around-the-clock high utilization of expensive computing resourcesAny process that comes to the CPU should wait in a queue.


Currently, Simmons' algorithm is the only approximation algorithm for envy-free cake-cutting with connected pieces. Simmons' algorithm is one of the few fair division algorithms which have been implemented and put online.One nice thing about the algorithm is that the queries it asks the partners are very simple: they just have to decide, in each partition, which piece they prefer. This is in contrast to other algorithm, which ask numerical queries such as "cut a piece with a value of 1/3" etc.


In the field of security engineering, an oracle attack is an attack that exploits the availability of a weakness in a system that can be used as an "oracle" to give a simple go/no go indication to inform attackers how close they are to their goals. The attacker can then combine the oracle with a systematic search of the problem space to complete their attack.The padding oracle attack, and compression oracle attacks such as BREACH, are examples of oracle attacks, as was the practice of "crib-dragging" in the cryptanalysis of the Enigma machine. An oracle need not be 100% accurate: even a small statistical correlation with the correct go/no go result can frequently be enough for a systematic automated attack.


Associativity is not the same as commutativity, which addresses whether the order of two operands affects the result. For example, the order does not matter in the multiplication of real numbers, that is, a × b = b × a, so we say that the multiplication of real numbers is a commutative operation. However, operations such as function composition and matrix multiplication are associative, but not (generally) commutative.


In part one of the book, d'Alembert provides a general introduction to the origin of knowledge, which led to the works found in the Encyclopédie. He asserts that the "existence of our senses" is "indisputable," and that these senses are thus the principle of all knowledge. He links this idea to a chain of thinking and reflection that eventually leads to the need to communicate, which sets another chain of events in effect. One of his arguments for the origin of communication is that it was necessary for people to protect themselves from the evils of the world and to benefit from each other's knowledge.


Variables are available as if they are registers and some C expressions are allowed. ARM Compiler used to have a similar facility.The two families of extensions represent different understandings of division of labor in processing inline assembly. The GCC form preserves the overall syntax of the language and compartmentizes what the compiler needs to know: what is needed and what is changed.


In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized. Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied.


A Q–Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewness are similar or different in the two distributions. Q–Q plots can be used to compare collections of data, or theoretical distributions. The use of Q–Q plots to compare two samples of data can be viewed as a non-parametric approach to comparing their underlying distributions.


In the area of mathematical logic and computer science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator. A kind system is essentially a simply typed lambda calculus "one level up", endowed with a primitive type, denoted ∗ {\displaystyle *} and called "type", which is the kind of any data type which does not need any type parameters. A kind is sometimes confusingly described as the "type of a (data) type", but it is actually more of an arity specifier. Syntactically, it is natural to consider polymorphic types to be type constructors, thus non-polymorphic types to be nullary type constructors.


Such a network of co-authorship is not unusual in narrowly defined areas of science. When allegations of plagiarism in this section were examined, Wegman said that material in it had been "basically copied and pasted" by a student who was the "most knowledgeable" person about such analyses on his team, as she had taken a one-week course on network analysis with Kathleen Carley of Carnegie Mellon University. Carley described the paper based on this section as "more of an opinion piece", lacking the data needed to support its argument. The paper based on this social network analysis, published by Wegman and his former student Said, reached the conclusion that eminent scientists ought not work together, and that the findings of studies would be less biased when a "principal author tends to co-author papers with younger colleagues who were his students".


In physics, chemistry and biology, a potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux.


In mathematics, an explicit reciprocity law is a formula for the Hilbert symbol of a local field. The name "explicit reciprocity law" refers to the fact that the Hilbert symbols of local fields appear in Hilbert's reciprocity law for the power residue symbol. The definitions of the Hilbert symbol are usually rather roundabout and can be hard to use directly in explicit examples, and the explicit reciprocity laws give more explicit expressions for the Hilbert symbol that are sometimes easier to use. There are also several explicit reciprocity laws for various generalizations of the Hilbert symbol to higher local fields, p-divisible groups, and so on.


In operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.


In text retrieval, full-text search refers to techniques for searching a single computer-stored document or a collection in a full-text database. Full-text search is distinguished from searches based on metadata or on parts of the original texts represented in databases (such as titles, abstracts, selected sections, or bibliographical references). In a full-text search, a search engine examines all of the words in every stored document as it tries to match search criteria (for example, text specified by a user).


They must be able to notate and reference any problems they find in detailed reports, meet deadlines with assignments and have the skill level to complete the game titles on their most difficult settings. Most of the time the position of game tester is a highly stressful and competitive position with little pay yet is highly sought after for it serves as a doorway into the industry. Game testers are observant individuals and can spot minor defects in the game build. A common misconception is that all game testers enjoy alpha or beta version of the game and report occasionally found bugs. In contrast, game testing is highly focused on finding bugs using established and often tedious methodologies before alpha version.


In probability theory and statistics, the Exponential-Logarithmic (EL) distribution is a family of lifetime distributions with decreasing failure rate, defined on the interval [0, ∞). This distribution is parameterized by two parameters p ∈ ( 0 , 1 ) {\displaystyle p\in (0,1)} and β > 0 {\displaystyle \beta >0} .


In the airline industry a major problem is the scheduling of the flight crews. The airline scheduling problem can be considered as an application of extended maximum network flow. The input of this problem is a set of flights F which contains the information about where and when each flight departs and arrives.


In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli numbers. The first few regular odd primes are: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 109, 113, 127, 137, 139, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, ... (sequence A007703 in the OEIS).


n 3 ! ⋯ . {\displaystyle {N \choose n_{1}}{N-n_{1} \choose n_{2}}{N-n_{1}-n_{2} \choose n_{3}}\cdots ={\frac {N!}{(N-n_{1})!n_{1}!


In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic means, i.e., without quantified variables. PFL employs a small number of algebraic devices called predicate functors (or predicate modifiers) that operate on terms to yield terms. PFL is mostly the invention of the logician and philosopher Willard Quine.


In programming language theory, the call-by-push-value (CBPV) paradigm, inspired by monads, allows writing semantics for lambda-calculus without writing two variants to deal with the difference between call-by-name and call-by-value. To do so, CBPV introduces a term language that distinguishes computations and values, according to the slogan a value is, a computation does; this term language has a single evaluation order. However, to evaluate a lambda-calculus term according to either the call-by-name (CBN) or call-by-value (CBV) reduction strategy, one can translate the term to CBPV using a call-by-name or call-by-value translation strategy, which give rise to different terms. Evaluating the result of the call-by-value translation corresponds to evaluating the original term with the call-by-value strategy; evaluating the result of the call-by-name translation corresponds instead to evaluating the original term with the call-by-name strategy.


In telecommunications, an information-bearer channel is one of: A communication channel capable of transmitting all the information required for communication, such as user data, synchronizing sequences, and control signals. The information-bearer channel may operate at a higher data rate than that required for user data alone. A basic communications channel with the necessary bandwidth but without enhanced or value-added services.


In parallel algorithms, the list ranking problem involves determining the position, or rank, of each item in a linked list. That is, the first item in the list should be assigned the number 1, the second item in the list should be assigned the number 2, etc. Although it is straightforward to solve this problem efficiently on a sequential computer, by traversing the list in order, it is more complicated to solve in parallel. As Anderson & Miller (1990) wrote, the problem was viewed as important in the parallel algorithms community both for its many applications and because solving it led to many important ideas that could be applied in parallel algorithms more generally.


In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting.Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem. These terms could be priors, penalties, or constraints. Explicit regularization is commonly employed with ill-posed optimization problems.


Information obtained from the Atkin primes permits a further improvement which is asymptotically negligible but can be quite important in practice. The modification of Schoof's algorithm to use Elkies and Atkin primes is known as the Schoof–Elkies–Atkin (SEA) algorithm. The status of a particular prime ℓ {\displaystyle \ell } depends on the elliptic curve E / F q {\displaystyle E/\mathbb {F} _{q}} , and can be determined using the modular polynomial Ψ ℓ ( X , Y ) {\displaystyle \Psi _{\ell }(X,Y)} .


Formally, satisfiability is studied with respect to a fixed logic defining the syntax of allowed symbols, such as first-order logic, second-order logic or propositional logic. Rather than being syntactic, however, satisfiability is a semantic property because it relates to the meaning of the symbols, for example, the meaning of + {\displaystyle +} in a formula such as x + 1 = x {\displaystyle x+1=x} . Formally, we define an interpretation (or model) to be an assignment of values to the variables and an assignment of meaning to all other non-logical symbols, and a formula is said to be satisfiable if there is some interpretation which makes it true.


These numbers are equal to or slightly smaller than (n ⌈lg n⌉ − 2⌈lg n⌉ + 1), which is between (n lg n − n + 1) and (n lg n + n + O(lg n)). Merge sort's best case takes about half as many iterations as its worst case.For large n and a randomly ordered input list, merge sort's expected (average) number of comparisons approaches α·n fewer than the worst case, where α = − 1 + ∑ k = 0 ∞ 1 2 k + 1 ≈ 0.2645. {\displaystyle \alpha =-1+\sum _{k=0}^{\infty }{\frac {1}{2^{k}+1}}\approx 0.2645.}


Then, we have the following bound on the probability that the empirical measure p ^ x n {\displaystyle {\hat {p}}_{x^{n}}} of the samples falls within the set A: q n ( p ^ x n ∈ A ) ≤ ( n + 1 ) | X | 2 − n D K L ( p ∗ | | q ) {\displaystyle q^{n}({\hat {p}}_{x^{n}}\in A)\leq (n+1)^{|X|}2^{-nD_{\mathrm {KL} }(p^{*}||q)}} ,where q n {\displaystyle q^{n}} is the joint probability distribution on X n {\displaystyle X^{n}} , and p ∗ {\displaystyle p^{*}} is the information projection of q onto A.In words, the probability of drawing an atypical distribution is bounded by a function of the KL divergence from the true distribution to the atypical one; in the case that we consider a set of possible atypical distributions, there is a dominant atypical distribution, given by the information projection. Furthermore, if A is the closure of its interior, lim n → ∞ 1 n log  q n ( p ^ x n ∈ A ) = − D K L ( p ∗ | | q ) . {\displaystyle \lim _{n\to \infty }{\frac {1}{n}}\log q^{n}({\hat {p}}_{x^{n}}\in A)=-D_{\mathrm {KL} }(p^{*}||q).}


The algorithm stops when it finds the minimum, determined when no progress is made after a direction reset (i.e. in the steepest descent direction), or when some tolerance criterion is reached. Within a linear approximation, the parameters α {\displaystyle \displaystyle \alpha } and β {\displaystyle \displaystyle \beta } are the same as in the linear conjugate gradient method but have been obtained with line searches. The conjugate gradient method can follow narrow (ill-conditioned) valleys, where the steepest descent method slows down and follows a criss-cross pattern.


Instead, the Java platform provides a comprehensive set of its own standard class libraries containing many of the same reusable functions commonly found in modern operating systems. Most of the system library is also written in Java. For instance, the Swing library paints the user interface and handles the events itself, eliminating many subtle differences between how different platforms handle components.


In software, a spell checker (or spelling checker or spell check) is a software feature that checks for misspellings in a text. Spell-checking features are often embedded in software or services, such as a word processor, email client, electronic dictionary, or search engine.


In object-oriented programming, in languages such as C++, and Object Pascal, a virtual function or virtual method is an inheritable and overridable function or method for which dynamic dispatch is facilitated. This concept is an important part of the (runtime) polymorphism portion of object-oriented programming (OOP). In short, a virtual function defines a target function to be executed, but the target might not be known at compile time. Most programming languages, such as JavaScript, PHP and Python, treat all methods as virtual by default and do not provide a modifier to change this behavior. However, some languages provide modifiers to prevent methods from being overridden by derived classes (such as the final and private keywords in Java and PHP).


String?? = String? ).


In mathematics and theoretical physics, an invariant differential operator is a kind of mathematical map from some objects to an object of similar type. These objects are typically functions on R n {\displaystyle \mathbb {R} ^{n}} , functions on a manifold, vector valued functions, vector fields, or, more generally, sections of a vector bundle. In an invariant differential operator D {\displaystyle D} , the term differential operator indicates that the value D f {\displaystyle Df} of the map depends only on f ( x ) {\displaystyle f(x)} and the derivatives of f {\displaystyle f} in x {\displaystyle x} .


In number theory, Rosser's theorem states that the n {\displaystyle n} th prime number is greater than n log  n {\displaystyle n\log n} , where log {\displaystyle \log } is the natural logarithm function. It was published by J. Barkley Rosser in 1939.Its full statement is: Let p n {\displaystyle p_{n}} be the n {\displaystyle n} th prime number. Then for n ≥ 1 {\displaystyle n\geq 1} p n > n log  n . {\displaystyle p_{n}>n\log n.} In 1999, Pierre Dusart proved a tighter lower bound: p n > n ( log  n + log  log  n − 1 ) . {\displaystyle p_{n}>n(\log n+\log \log n-1).}


In number theory, there are many integer factoring algorithms that heuristically have expected running time L n  = e ( 1 + o ( 1 ) ) ( log  n ) ( log  log  n ) {\displaystyle L_{n}\left=e^{(1+o(1)){\sqrt {(\log n)(\log \log n)}}}} in little-o and L-notation. Some examples of those algorithms are the elliptic curve method and the quadratic sieve. Another such algorithm is the class group relations method proposed by Schnorr, Seysen, and Lenstra, which they proved only assuming the unproved Generalized Riemann Hypothesis (GRH).


Masking depends on the spectral composition of both masker and masking signal, and on other variations with time. The basic block diagram of a perceptual coding system is shown in the figure. The input signal is decomposed into subsampled spectral components.


A PC cannot currently contain 4 pebibytes of memory (due to the physical size of the memory chips), but AMD envisioned large servers, shared memory clusters, and other uses of physical address space that might approach this in the foreseeable future. Thus the 52-bit physical address provides ample room for expansion while not incurring the cost of implementing full 64-bit physical addresses. Similarly, the 48-bit virtual address space was designed to provide 65,536 (216) times the 32-bit limit of 4 GiB (4 × 10243 bytes), allowing room for later expansion and incurring no overhead of translating full 64-bit addresses.


This means that the code is always executed first and then the expression or test condition is evaluated. This process is repeated as long as the expression evaluates to true. If the expression is false the loop terminates.


In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor. It is common to make the additional stipulation that the ordinary least squares (OLS) method should be used: the accuracy of each predicted value is measured by its squared residual (vertical distance between the point of the data set and the fitted line), and the goal is to make the sum of these squared deviations as small as possible.


In the context of integers, subtraction of one also plays a special role: for any integer a, the integer (a − 1) is the largest integer less than a, also known as the predecessor of a.


Its cumulant generating function (logarithm of the characteristic function) is the inverse of the cumulant generating function of a Gaussian random variable. To indicate that a random variable X is inverse Gaussian-distributed with mean μ and shape parameter λ we write X ∼ IG  ( μ , λ ) {\displaystyle X\sim \operatorname {IG} (\mu ,\lambda )\,\!} .


In mathematics, a sequence transformation is an operator acting on a given space of sequences (a sequence space). Sequence transformations include linear mappings such as convolution with another sequence, and resummation of a sequence and, more generally, are commonly used for series acceleration, that is, for improving the rate of convergence of a slowly convergent sequence or series. Sequence transformations are also commonly used to compute the antilimit of a divergent series numerically, and are used in conjunction with extrapolation methods.


Faster image ingest: it will take no more than a few seconds to transfer a high-resolution RAW file from a memory card vs many minutes to scan film with a high-quality scanner. Flash: using flash in images can provide a different look such as the lighting of the image. Higher image quantity: which enables longer photography sessions without changing film rolls.


In mathematical optimization, the ordered subset expectation maximization (OSEM) method is an iterative method that is used in computed tomography. In applications in medical imaging, the OSEM method is used for positron emission tomography, for single photon emission computed tomography, and for X-ray computed tomography. The OSEM method is related to the expectation maximization (EM) method of statistics. The OSEM method is also related to methods of filtered back projection.


{\displaystyle x=({\textbf {A}}^{\mathrm {T} }{\textbf {A}})^{-1}{\textbf {A}}^{\mathrm {T} }\phi .} Here the matrix A can be based on any set of functions mutually independent (not necessarily orthogonal) when evaluated at the sample times; functions used for spectral analysis are typically sines and cosines evenly distributed over the frequency range of interest.


1149.1-1990 after many years of initial use. In the same year, Intel released their first processor with JTAG (the 80486) which led to quicker industry adoption by all manufacturers. In 1994, a supplement that contains a description of the boundary scan description language (BSDL) was added.


Interpersonal relations may be regulated by law, custom, or mutual agreement, and form the basis of social groups and societies. They appear when people communicate or act with each other within specific social contexts, and they thrive on equitable and reciprocal compromises.Interdisciplinary analysis of relationships draws heavily upon the other social sciences, including, but not limited to: anthropology, linguistics, sociology, economics, political science, communication, mathematics, social work, communication, and cultural studies. This scientific analysis had evolved during the 1990s and has become "relationship science", through the researches of Ellen Berscheid and Elaine Hatfield. This interdisciplinary science attempts to provide evidence-based conclusions through the use of data analysis.


In statistics, Cook's distance or Cook's D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook's distance can be used in several ways: to indicate influential data points that are particularly worth checking for validity; or to indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.


In mathematics normal convergence is a type of convergence for series of functions. Like absolute-convergence, it has the useful property that it is preserved when the order of summation is changed.


k ! F ( v − 1 ) i ( 1 − F ( v ) ) k f ( v ) N − i − k {\displaystyle \Pr(\operatorname {Median} =v)=\sum _{i=0}^{n}\sum _{k=0}^{n}{\frac {N!}{i!(N-i-k)!k! }}F(v-1)^{i}(1-F(v))^{k}f(v)^{N-i-k}} Here, i is the number of points strictly less than the median and k the number strictly greater.


The biggest disadvantage is that it fails to take advantage of coefficient matrix to be a sparse matrix. The LU decomposition of a sparse matrix is usually not sparse, thus, for a large system of equations, LU decomposition may require a prohibitive amount of memory and number of arithmetical operations. In the preconditioned iterative methods, if the preconditioner matrix M is a good approximation of coefficient matrix A then the convergence is faster.


In most practical cases deterministic algorithms or randomized algorithms are discussed, although theoretical computer science also considers nondeterministic algorithms and other advanced models of computation.


The latter two cases end in -ar or -ur and -ur or -r. Irregular but not a weak noun.Most neuters are strong, and end in -s in the genitive singular with the exception of fé, genitive fjár. Although strong neuters technically only belong to one category, it is a diverse group, so about a dozen paradigms are necessary to account for varieties and exceptions. The weak neuters are so few, that a list suffices, to be found on the page for weak nouns.


If F ≤ B {\displaystyle {\mathcal {F}}\leq {\mathcal {B}}} is a sigma subalgebra of B {\displaystyle {\mathcal {B}}} , then the conditional expectation E  {\displaystyle E} is the orthogonal projection of X {\displaystyle X} onto the subspace of L 2 ( Ω , P ) {\displaystyle L^{2}(\Omega ,P)} consisting of the F {\displaystyle {\mathcal {F}}} -measurable functions. If the random variable X {\displaystyle X} in L 2 ( Ω , P ) {\displaystyle L^{2}(\Omega ,P)} is independent of the sigma algebra F {\displaystyle {\mathcal {F}}} then conditional expectation E ( X | F ) = E ( X ) {\displaystyle E(X|{\mathcal {F}})=E(X)} , i.e., its projection onto the F {\displaystyle {\mathcal {F}}} -measurable functions is constant. Equivalently, the projection of its centering is zero.


In the 1987 article "A Framework for Information Systems Architecture" Zachman noted that the term "architecture" was used loosely by information systems professionals, and meant different things to planners, designers, programmers, communication specialists, and others. In searching for an objective, independent basis upon which to develop a framework for information systems architecture, Zachman looked at the field of classical architecture, and a variety of complex engineering projects in industry. He saw a similar approach and concluded that architectures exist on many levels and involves at least three perspectives: raw material or data, function of processes, and location or networks.The Information Systems Architecture is designed to be a classification schema for organizing architecture models. It provides a synoptic view of the models needed for enterprise architecture. Information Systems Architecture does not define in detail what the models should contain, it does not enforce the modeling language used for each model, and it does not propose a method for creating these models.


In recent years, numerous studies have confirmed that by stacking several shallow structures into a single deep structure, the overall system could achieve better data representation, and, thus, more effectively deal with nonlinear and high complexity tasks. In 2018, a deep CMAC (DCMAC) framework was proposed and a backpropagation algorithm was derived to estimate the DCMAC parameters. Experimental results of an adaptive noise cancellation task showed that the proposed DCMAC can achieve better noise cancellation performance when compared with that from the conventional single-layer CMAC.


In number theory, Grimm's conjecture (named after Carl Albert Grimm, 1 April 1926 – 2 January 2018) states that to each element of a set of consecutive composite numbers one can assign a distinct prime that divides it. It was first published in American Mathematical Monthly, 76(1969) 1126-1128.


In software engineering, structured analysis (SA) and structured design (SD) are methods for analyzing business requirements and developing specifications for converting practices into computer programs, hardware configurations, and related manual procedures. Structured analysis and design techniques are fundamental tools of systems analysis. They developed from classical systems analysis of the 1960s and 1970s.


In statistics, a Tsallis distribution is a probability distribution derived from the maximization of the Tsallis entropy under appropriate constraints. There are several different families of Tsallis distributions, yet different sources may reference an individual family as "the Tsallis distribution". The q-Gaussian is a generalization of the Gaussian in the same way that Tsallis entropy is a generalization of standard Boltzmann–Gibbs entropy or Shannon entropy. Similarly, if the domain of the variable is constrained to be positive in the maximum entropy procedure, the q-exponential distribution is derived.


Each processor was about 2.5 times as fast as a 7600, so with all four running the machine as a whole would be about 10 times as fast, at about 100 MFLOPS. The government made it clear that all future computer purchases would require ASCII processing. To meet this requirement, the 8600 used a 64-bit word (eight eight-bit characters) instead of the earlier 60-bit word (ten six-bit characters) used in the 6600 and 7600.


In software engineering, a freeze is a point in time in the development process after which the rules for making changes to the source code or related resources become more strict, or the period during which those rules are applied. A freeze helps move the project forward towards a release or the end of an iteration by reducing the scale or frequency of changes, and may be used to help meet a roadmap. The exact rules depend on the type of freeze and the particular development process in use; for example, they may include only allowing changes which fix bugs, or allowing changes only after thorough review by other members of the development team.


A functional form, often linear, is hypothesized for the postulated causal relationship, and the parameters of the function are estimated from the data—that is, are chosen so as to optimize is some way the fit of the function, thus parameterized, to the data. That is the estimation step. For the prediction step, explanatory variable values that are deemed relevant to future (or current but not yet observed) values of the dependent variable are input to the parameterized function to generate predictions for the dependent variable.


In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated.


In number theory, the integer square root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal to the square root of n, For example, isqrt  ( 27 ) = ⌊ 27 ⌋ = ⌊ 5.19615242270663... ⌋ = 5. {\displaystyle \operatorname {isqrt} (27)=\lfloor {\sqrt {27}}\rfloor =\lfloor 5.19615242270663...\rfloor =5.}


In statistical physics and disordered systems, the Max Cut problem is equivalent to minimizing the Hamiltonian of a spin glass model, most simply the Ising model. For the Ising model on a graph G and only nearest-neighbor interactions, the Hamiltonian is H  = − ∑ i j ∈ E ( G ) J i j s i s j {\displaystyle H=-\sum _{ij\in E(G)}J_{ij}s_{i}s_{j}} Here each vertex i of the graph is a spin site that can take a spin value s i = ± 1. {\displaystyle s_{i}=\pm 1.} A spin configuration partitions V ( G ) {\displaystyle V(G)} into two sets, those with spin up V + {\displaystyle V^{+}} and those with spin down V − .


In software development, the term 'proof of concept' often characterizes several distinct processes with different objectives and participant roles: vendor business roles may utilize a proof of concept to establish whether a system satisfies some aspect of the purpose it was designed for. Once a vendor is satisfied, a prototype is developed which is then used to seek funding or to demonstrate to prospective customers.The US General Services Administration has a checklist for defining an Agile software proof of concept, which includes clear definitions of the problem, pre-POC input required, and output criteria (including success criteria).The key benefits of the proof of concept in software development are: The possibility to choose the best technology stack for the software (application or web platform) A higher probability of investors' interest in the future software product The ability to simplify and improve the ease of testing and validating ideas for the software's functionality Receiving valuable feedback of a target audience (users) even before building a full-scope system Onboarding first clients before an official software releaseA 'steel thread' is technical proof of concept that touches all of the technologies in a solution. By contrast, a 'proof of technology' aims to determine the solution to some technical problem (such as how two systems might integrate) or to demonstrate that a given configuration can achieve a certain throughput. No business users need be involved in a proof of technology.


In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that B = {0, 1}. Paul Halmos's name for this algebra "2" has some following in the literature, and will be employed here.


For Aristotle and Euclid, relations were conceived as whole numbers (Michell, 1993). John Wallis later conceived of ratios of magnitudes as real numbers: When a comparison in terms of ratio is made, the resultant ratio often  leaves the genus of quantities compared, and passes into the numerical genus, whatever the genus of quantities compared may have been. That is, the ratio of magnitudes of any quantity, whether volume, mass, heat and so on, is a number. Following this, Newton then defined number, and the relationship between quantity and number, in the following terms: By number we understand not so much a multitude of unities, as the abstracted ratio of any quantity to another quantity of the same kind, which we take for unity.


User input allows for the users to manipulate a system, and device's output allows the system to indicate the effects of the users' manipulation. Overall, mobile UI design's goal is mainly for an understandable, user-friendly interface. Functionality is supported by mobile enterprise application platforms or integrated development environments (IDEs).


In the case of very old works, the author's name may simply be lost over the course of history and time. In such cases the author is often referred to as Anonymus, the Latin form of "anonymous". In other cases, the creator's name is intentionally kept secret.


was a fairly full featured (for the time) spreadsheet developed for the Amiga. Organize! was a flat file database package.


In spatial analysis, the Huff model is a widely used tool for predicting the probability of a consumer visiting a site, as a function of the distance of the site, its attractiveness, and the relative attractiveness of alternatives. It was formulated by David Huff in 1963. It is used in marketing, economics, retail research and urban planning, and is implemented in several commercially available GIS systems. Its relative ease of use and applicability to a wide range of problems contribute to its enduring appeal.The formula is given as: P i j = A j α D i j − β ∑ k = 1 n A k α D i k − β {\displaystyle P_{ij}={\frac {A_{j}^{\alpha }D_{ij}^{-\beta }}{\sum _{k=1}^{n}A_{k}^{\alpha }D_{ik}^{-\beta }}}} where: A j {\displaystyle A_{j}} is a measure of attractiveness of store j D i j {\displaystyle D_{ij}} is the distance from the consumer's location, i, to store j. α {\displaystyle \alpha } is an attractiveness parameter β {\displaystyle \beta } is a distance decay parameter n {\displaystyle n} is the total number of stores, including store j == References ==


The binary search tree may be any balanced binary search tree data structure, such as a red–black tree; all that is required is that insertions, deletions, and searches take logarithmic time. Similarly, the priority queue may be a binary heap or any other logarithmic-time priority queue; more sophisticated priority queues such as a Fibonacci heap are not necessary. Note that the space complexity of the priority queue depends on the data structure used to implement it.


For distributing revocation information to clients, the timeliness of the discovery of revocation (and hence the window for an attacker to exploit a compromised certificate) trades off against resource usage in querying revocation statuses and privacy concerns. If revocation information is unavailable (either due to an accident or an attack), clients must decide whether to fail-hard and treat a certificate as if it is revoked (and so degrade availability) or to fail-soft and treat it as unrevoked (and allow attackers to sidestep revocation). Due to the cost of revocation checks and the availability impact from potentially-unreliable remote services, Web browsers limit the revocation checks they will perform, and will fail soft where they do. Certificate revocation lists are too bandwidth-costly for routine use, and the Online Certificate Status Protocol presents connection latency and privacy issues. Other schemes have been proposed but have not yet been successfully deployed to enable fail-hard checking.


In some situations, "maximal munch" leads to undesirable or unintuitive outcomes. For instance, in the C programming language, the statement x=y/*z; (without any whitespace) will probably lead to a syntax error, since the /* character sequence initiates a (unintended) comment that is either unterminated or terminated by the end token */ of some later, unrelated actual comment (comments in C do not nest). What was actually meant in the statement was to assign to the variable x the result of dividing the value in y by the value obtained by dereferencing pointer z; this would be valid code. It can be stated by making use of whitespace, or using x=y/(*z);.


In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine if a production lot of material meets the governing specifications.


This notational scheme is not strictly accurate, because the transaction counter is 21 bits, which is not an even multiple of 4 (the number of bits in a hex digit). Consequently, the transaction counter actually consumes one bit of the field that is the TRSM ID (in this example that means that the TRSM ID field can accommodate 2(5*4-1) devices, instead of 2(5*4), or about half a million). Also, it is common practice in the industry to use only 64-bits of the KSN (probably for reasons pertinent to legacy systems, and DES encryption), which would imply that the full KSN is padded to the left with four ‘f’ hex digits. The remaining 4 hex digits (16-bits) are available, nonetheless, to systems which can accommodate them. The 6-5-5 scheme mentioned above would permit about 16 million BDKs, 500,000 devices per BDK, and 1 million transactions per device.


The relationships of objects or classes through inheritance give rise to a directed acyclic graph. An inherited class is called a subclass of its parent class or super class.


Application here is simply a short way of saying that the corresponding concatenation rule has been applied. The types of logics called predicate, quantificational, or n-order logic include variables, operators, predicate and function symbols, and quantifiers as symbols in their languages. The propositions in these logics are more complex.


In programming languages, type erasure is the load-time process by which explicit type annotations are removed from a program, before it is executed at run-time. Operational semantics not requiring programs to be accompanied by types are named type-erasure semantics, in contrast with type-passing semantics. Type-erasure semantics is an abstraction principle, ensuring that the run-time execution of a program doesn't depend on type information. In the context of generic programming, the opposite of type erasure is named reification.


In semantics, words are categorized into semantic classes. Intersecting semantic classes share the same semantic features. Semantic features can include  and . These features may in some instances be realised morphologically, in which case they may also be called morphosemantic features.


In scientific visualization, image-based flow visualization (or visualisation) is a computer modelling technique developed by Jarke van Wijk to visualize two dimensional flows of liquids such as water and air, like the wind movement of a tornado. Compared with integration techniques it has the advantage of producing a whole image at every step, as the technique relies upon graphical computing methods for frame-by-frame capture of the model of advective transport of a decaying dye. It is a method from the texture advection family.


Many operators worldwide offer a femtocell service, mainly targeted at businesses but also offered to individual customers (often for a one-off fee) when they complain to the operator regarding a poor or non-existent signal at their location. Operators who have launched a femtocell service include SFR, AT&T, C Spire, Sprint Nextel, Verizon, Zain, Mobile TeleSystems, T-Mobile US, Orange, Vodafone, EE, O2, Three, and others. In 3GPP terminology, a Home NodeB (HNB) is a 3G femtocell.


Moreover, there can be many ways to test a single hypothesis from the same dataset. Although defensible, decisions in data analysis remain subjective, which can greatly affect research results. A way to counter this subjectivity is transparency. When data, analytic plans, and analytic decisions are made transparent and open access to the rest of the community, it facilitates criticism and gives the opportunity to explore alternative ways to analyse data.“Crowdsourcing the analysis of the data reveals the extent to which research conclusions are contingent on the defensible yet subjective decision made by different analysts.”—Uhlmann et al., 2019


In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), or of a less powerful theory, such as Peano arithmetic. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems.


If the raw polygon is hole-free, then an optimal partition can be found in time O ( n 4 ) {\displaystyle O(n^{4})} , where n is the number of vertices of the polygon. In the special case of a "histogram polygon", the complexity improves to O ( n 3 ) {\displaystyle O(n^{3})} . The algorithm uses dynamic programming and relies on the following fact: if the polygon is hole-free, then it has a minimum-length partition in which each maximal line-segment contains a vertex of the boundary.


Local Leakage Rate Tests (Type B or Type C testing, or LLRTs) are performed much more frequently, both to identify the possible leakage in an accident and to locate and fix leakage paths. LLRTs are performed on containment isolation valves, hatches and other appurtenances penetrating the containment.


Live media can be shared through any Internet website or application; thus, when people browse a specific website, they may find live media streams relevant to them.Live media can include coverage of various events such as concerts or live news coverage viewed using a web browser or apps such as Snapchat. James Harden and Trolli promoted an upcoming NBA All-Star Game through Snapchat. Many of LaBeouf, Rönkkö & Turner's performance art were livestreamed, such as a stream of Shia LaBeouf in a theater viewing all his movies.However, live stream commerce nowadays allows sellers to sell products by a streamer to introduce and illustrate effects (just like sales in physical stores) to motivate buyers to buy the products and services. Merritt and Zhao mention that Chinese 'live stream-based retailing’ has supported the economic growth of China and projected that about GBP 98 billion were generated from e-commerce live streaming in China. The McKinsey report also demonstrates that live stream commerce is expanding in China, the sales from live stream commerce were expected to achieve $423 billion by 2022, and the US live streaming industry was also expected to reach $25 billion by 2023.


In the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by the fact that it decomposes into a string from that same language (on the left) and a suffix (on the right). For instance, 1 + 2 + 3 {\displaystyle 1+2+3} can be recognized as a sum because it can be broken into 1 + 2 {\displaystyle 1+2} , also a sum, and + 3 {\displaystyle {}+3} , a suitable suffix. In terms of context-free grammar, a nonterminal is left-recursive if the leftmost symbol in one of its productions is itself (in the case of direct left recursion) or can be made itself by some sequence of substitutions (in the case of indirect left recursion).


Thus, each time the user compiles their program, the user is essentially recompiling numerous header libraries as well. (These would be precompiled into shared objects or dynamic link libraries in non "header" libraries.) To reduce compilation times, some compilers allow header files to be compiled into a form that is faster for the compiler to process. This intermediate form is known as a precompiled header, and is commonly held in a file named with the extension .pch or similar, such as .gch under the GNU Compiler Collection.