In programming languages with Hindley-Milner type inference and imperative features, in particular the ML programming language family, the value restriction means that declarations are only polymorphically generalized if they are syntactic values (also called non-expansive). The value restriction prevents reference cells from holding values of different types and preserves type safety.


Increasing return loss corresponds to lower SWR. Return loss is a measure of how well devices or lines are matched. A match is good if the return loss is high.


Among popular ones are syntactic closures, explicit renaming macros and define-macro, a non-hygienic macro system similar to defmacro system provided in Common Lisp. The inability to specify whether or not a macro is hygienic is one of the shortcomings of the macro system. Alternative models for expansion such as scope sets provide a potential solution.


In number theory, Lagrange's theorem is a statement named after Joseph-Louis Lagrange about how frequently a polynomial over the integers may evaluate to a multiple of a fixed prime. More precisely, it states that if p is a prime number, x ∈ Z / p Z {\displaystyle x\in \mathbb {Z} /p\mathbb {Z} } , and f ( x ) ∈ Z  {\displaystyle \textstyle f(x)\in \mathbb {Z} } is a polynomial with integer coefficients, then either: every coefficient of f(x) is divisible by p, or f(x) ≡ 0 (mod p) has at most deg f(x) solutionswhere deg f(x) is the degree of f(x). If the modulus is not prime, then it is possible for there to be more than deg f(x) solutions.


In the context of text indexing, RMQs can be used to find the LCP (longest common prefix), where LCPT(i, j) computes the LCP of the suffixes that start at indexes i and j in T. To do this we first compute the suffix array A, and the inverse suffix array A−1. We then compute the LCP array H giving the LCP of adjacent suffixes in A. Once these data structures are computed, and RMQ preprocessing is complete, the length of the general LCP can be computed in constant time by the formula: LCP(i, j) = RMQH(A-1 + 1, A-1), where we assume for simplicity that A-1 + 1 <= A-1 (otherwise swap).


Dimensionality reduction using PCA has also been explored.Another line of approximate solution techniques for solving POMDPs relies on using (a subset of) the history of previous observations, actions and rewards up to the current time step as a pseudo-state. Usual techniques for solving MDPs based on these pseudo-states can then be used (e.g. Q-learning). Ideally the pseudo-states should contain the most important information from the whole history (to reduce bias) while being as compressed as possible (to reduce overfitting).


In other languages which use writing systems with lowercases and uppercases, adjectives derived from proper nouns are commonly not capitalized.


The tee symbol ⊤ {\displaystyle \top } is sometimes used to denote an arbitrary tautology, with the dual symbol ⊥ {\displaystyle \bot } (falsum) representing an arbitrary contradiction; in any symbolism, a tautology may be substituted for the truth value "true", as symbolized, for instance, by "1".Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A key property of tautologies in propositional logic is that an effective method exists for testing whether a given formula is always satisfied (equiv., whether its negation is unsatisfiable). The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of propositional logic.


Sometimes, a set is endowed with more than one feature simultaneously, which allows mathematicians to study the interaction between the different structures more richly. For example, an ordering imposes a rigid form, shape, or topology on the set, and if a set has both a topology feature and a group feature, such that these two features are related in a certain way, then the structure becomes a topological group.Mappings between sets which preserve structures (i.e., structures in the domain are mapped to equivalent structures in the codomain) are of special interest in many fields of mathematics. Examples are homomorphisms, which preserve algebraic structures; homeomorphisms, which preserve topological structures; and diffeomorphisms, which preserve differential structures.


In probability theory: Branching process, a Markov process that models a population Diffusion process, a solution to a stochastic differential equation Empirical process, a stochastic process that describes the proportion of objects in a system in a given state Lévy process, a stochastic process with independent, stationary increments Poisson process, a point process consisting of randomly located points on some underlying space Predictable process, a stochastic process whose value is knowable Stochastic process, a random process, as opposed to a deterministic process Wiener process, a continuous-time stochastic process Process calculus, a diverse family of related approaches for formally modeling concurrent systems Process function, a mathematical concept used in thermodynamics


In mathematics, the Itô isometry, named after Kiyoshi Itô, is a crucial fact about Itô stochastic integrals. One of its main applications is to enable the computation of variances for random variables that are given as Itô integrals. Let W:  × Ω → R {\displaystyle W:\times \Omega \to \mathbb {R} } denote the canonical real-valued Wiener process defined up to time T > 0 {\displaystyle T>0} , and let X:  × Ω → R {\displaystyle X:\times \Omega \to \mathbb {R} } be a stochastic process that is adapted to the natural filtration F ∗ W {\displaystyle {\mathcal {F}}_{*}^{W}} of the Wiener process. Then E   = E   , {\displaystyle \operatorname {E} \left=\operatorname {E} \left,} where E {\displaystyle \operatorname {E} } denotes expectation with respect to classical Wiener measure.


In quantum theory, an experimental setup is described by the observable A {\displaystyle A} to be measured, and the state σ {\displaystyle \sigma } of the system. The expectation value of A {\displaystyle A} in the state σ {\displaystyle \sigma } is denoted as ⟨ A ⟩ σ {\displaystyle \langle A\rangle _{\sigma }} . Mathematically, A {\displaystyle A} is a self-adjoint operator on a Hilbert space. In the most commonly used case in quantum mechanics, σ {\displaystyle \sigma } is a pure state, described by a normalized vector ψ {\displaystyle \psi } in the Hilbert space.


In the BB84 scheme, Alice wishes to send a private key to Bob. She begins with two strings of bits, a {\displaystyle a} and b {\displaystyle b} , each n {\displaystyle n} bits long. She then encodes these two strings as a tensor product of n {\displaystyle n} qubits: | ψ ⟩ = ⨂ i = 1 n | ψ a i b i ⟩ , {\displaystyle |\psi \rangle =\bigotimes _{i=1}^{n}|\psi _{a_{i}b_{i}}\rangle ,} where a i {\displaystyle a_{i}} and b i {\displaystyle b_{i}} are the i {\displaystyle i} -th bits of a {\displaystyle a} and b {\displaystyle b} respectively. Together, a i b i {\displaystyle a_{i}b_{i}} give us an index into the following four qubit states: | ψ 00 ⟩ = | 0 ⟩ , {\displaystyle |\psi _{00}\rangle =|0\rangle ,} | ψ 10 ⟩ = | 1 ⟩ , {\displaystyle |\psi _{10}\rangle =|1\rangle ,} | ψ 01 ⟩ = | + ⟩ = 1 2 | 0 ⟩ + 1 2 | 1 ⟩ , {\displaystyle |\psi _{01}\rangle =|+\rangle ={\frac {1}{\sqrt {2}}}|0\rangle +{\frac {1}{\sqrt {2}}}|1\rangle ,} | ψ 11 ⟩ = | − ⟩ = 1 2 | 0 ⟩ − 1 2 | 1 ⟩ .


16 × 8 equals 128, therefore, each module has two ranks of 64 bits each. So, from the MCH point of view there are four 1 GB modules.


More generally, a linear differential operator of order k, sending sections of a vector bundle E → M {\displaystyle E\rightarrow M} to sections of another bundle F → M {\displaystyle F\rightarrow M} is seen to be an R {\displaystyle \mathbb {R} } -linear map Δ: Γ ( E ) → Γ ( F ) {\displaystyle \Delta :\Gamma (E)\to \Gamma (F)} between the associated modules, such that for any k + 1 {\displaystyle k+1} elements f 0 , … , f k ∈ A {\displaystyle f_{0},\ldots ,f_{k}\in A}: where the bracket : Γ ( E ) → Γ ( F ) {\displaystyle :\Gamma (E)\to \Gamma (F)} is defined as the commutator Denoting the set of k {\displaystyle k} th order linear differential operators from an A {\displaystyle A} -module P {\displaystyle P} to an A {\displaystyle A} -module Q {\displaystyle Q} with D i f f k ( P , Q ) {\displaystyle \mathrm {Diff} _{k}(P,Q)} we obtain a bi-functor with values in the category of A {\displaystyle A} -modules. Other natural concepts of calculus such as jet spaces, differential forms are then obtained as representing objects of the functors D i f f k {\displaystyle \mathrm {Diff} _{k}} and related functors. Seen from this point of view calculus may in fact be understood as the theory of these functors and their representing objects.


Sometimes, the components of the covector v ⋅ {\displaystyle \mathbf {v} \ \cdot } are referred to as the covariant components of v {\displaystyle \mathbf {v} } , although this is potentially misleading, (due to a vector having components that always vary in the contravariant sense). Despite potential confusion, this is what will be meant when the "covariant components of a vector" are referred to herein. The gradient is often cited as an example of a covector, but this is incorrect.


G L 4 ( F 2 ) {\displaystyle 2^{4\,. }\mathrm {GL} _{4}(\mathbb {F} _{2})} is a maximal subgroup of the sporadic Conway group Co3. The nonsplit extension 2 5 . G L 5 ( F 2 ) {\displaystyle 2^{5\,. }\mathrm {GL} _{5}(\mathbb {F} _{2})} is a maximal subgroup of the Thompson sporadic group Th.


As a special case, for C = π/2, then cos C = 0, and one obtains the spherical analogue of the Pythagorean theorem: If the law of cosines is used to solve for c, the necessity of inverting the cosine magnifies rounding errors when c is small. In this case, the alternative formulation of the law of haversines is preferable.A variation on the law of cosines, the second spherical law of cosines, (also called the cosine rule for angles) states: where A and B are the angles of the corners opposite to sides a and b, respectively. It can be obtained from consideration of a spherical triangle dual to the given one.


All registered healthcare professionals must abide by these standards and if they are found to have breached confidentiality, they can face disciplinary action. A healthcare worker shares confidential information with someone else who is, or is about to, provide the patient directly with healthcare to make sure they get the best possible treatment. They only share information that is relevant to their care in that instance, and with consent.


A related concept is the role of "recommendation engines", which give a user recommendations based on his/her previous online activity. Discoverability applies to computers and devices that can access the Internet, including various console video game systems and mobile devices such as tablets and smartphones. When producers make an effort to promote content (e.g., a TV show, film, song, or video game), they can use traditional marketing (billboards, TV ads, radio ads) and digital ads (pop-up ads, pre-roll ads, etc.), or a mix of traditional and digital marketing.


There are debates if increasing the number of taxa sampled improves phylogenetic accuracy more than increasing the number of genes sampled per taxon. Differences in each method's sampling impact the number of nucleotide sites utilized in a sequence alignment, which may contribute to disagreements. For example, phylogenetic trees constructed utilizing a more significant number of total nucleotides are generally more accurate, as supported by phylogenetic trees' bootstrapping replicability from random sampling.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 67, 167, 467, and 1467 are the patterns related to Braille pattern dots-35, since the two additional dots of kantenji patterns 035, 357, and 0357 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In processor design, microcode serves as an intermediary layer situated between the central processing unit (CPU) hardware and the programmer-visible instruction set architecture of a computer. It consists of a set of hardware-level instructions that implement higher-level machine code instructions or control internal finite-state machine sequencing in many digital processing components. While microcode is utilized in general-purpose CPUs in contemporary desktops, it also functions as a fallback path for scenarios that the faster hardwired control unit is unable to manage.Housed in special high-speed memory, microcode translates machine instructions, state machine data, or other input into sequences of detailed circuit-level operations. It separates the machine instructions from the underlying electronics, thereby enabling greater flexibility in designing and altering instructions.


In the following piece of Java code, the Java keyword synchronized makes the method thread-safe: In the C programming language, each thread has its own stack. However, a static variable is not kept on the stack; all threads share simultaneous access to it. If multiple threads overlap while running the same function, it is possible that a static variable might be changed by one thread while another is midway through checking it. This difficult-to-diagnose logic error, which may compile and run properly most of the time, is called a race condition.


In priority-based scheduling algorithms, a major problem is indefinite block, or starvation. A process that is ready to run but waiting for the CPU can be considered blocked. A priority scheduling algorithm can leave some low-priority processes waiting indefinitely. A steady stream of higher-priority processes can prevent a low-priority process from ever getting the CPU.


Although the distance update is still correct with the help of synchronization, the resource is wasted. In fact, to find the vertices for the next frontier, each unvisited vertex only need to check if any its neighbor vertex is in the frontier. This is also the core idea for direction optimization.


Instead, the method of assessment should be changed so that this requirement is met, in the same way that a weighing scale should be rectified if it gives different comparisons between objects upon separate measurements of the objects. Data analysed using the model are usually responses to conventional items on tests, such as educational tests with right/wrong answers. However, the model is a general one, and can be applied wherever discrete data are obtained with the intention of measuring a quantitative attribute or trait.


In statistics, expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance (ANOVA). They can be used for ascertaining which statistic should appear in the denominator in an F-test for testing a null hypothesis that a particular effect is absent.


In the category of sets, the coequalizer of two functions f, g: X → Y is the quotient of Y by the smallest equivalence relation ∼ {\displaystyle \sim } such that for every x ∈ X {\displaystyle x\in X} , we have f ( x ) ∼ g ( x ) {\displaystyle f(x)\sim g(x)} . In particular, if R is an equivalence relation on a set Y, and r1, r2 are the natural projections (R ⊂ Y × Y) → Y then the coequalizer of r1 and r2 is the quotient set Y/R. (See also: quotient by an equivalence relation.) The coequalizer in the category of groups is very similar.


Hence if it's possible to polynomial-time assign weights from a field of characteristic 2 to a digraph's arcs that make its weighted adjacency matrix unitary and having a non-zero Hamiltonian cycle polynomial then the digraph is Hamiltonian. Therefore the Hamiltonian cycle problem is computable on such graphs in polynomial time. In characteristic 2, the Hamiltonian cycle polynomial of an n×n-matrix is zero if n > 2k where k is its rank or if it's involutory and n > 2.


Annotea is an extensible standard and is designed to work with other W3C standards when possible. For instance, Annotea uses an RDF Schema for describing annotations as metadata and XPointer for locating the annotations in the annotated document. Similarly a bookmark schema describes the bookmark and topic metadata.


However, static typing does imply static name resolution. Static name resolution catches, at compile time, use of variables that are not in scope; preventing programmer errors. Languages with dynamic scope resolution sacrifice this safety for more flexibility; they can typically set and get variables in the same scope at runtime.


In the Base vector, the new metrics User Interaction (UI) and Privileges Required (PR) were added to help distinguish vulnerabilities that required user interaction or user or administrator privileges to be exploited. Previously, these concepts were part of the Access Vector metric of CVSSv2. The Base vector also saw the introduction of the new Scope (S) metric, which was designed to make clear which vulnerabilities may be exploited and then used to attack other parts of a system or network. These new metrics allow the Base vector to more clearly express the type of vulnerability being evaluated.


As in prior designs, instructions were "stuffed" into words, with each instruction taking up either 16- or 32-bits (up from 15/30). The 8600 no longer used the A or B registers as in previous designs, and included a set of 16 general-purpose X registers instead.


In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model. The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution function at neighbouring data points. The concept underlying the method is based on the probability integral transform, in that a set of independent random samples derived from any random variable should on average be uniformly distributed with respect to the cumulative distribution function of the random variable. The MPS method chooses the parameter values that make the observed data as uniform as possible, according to a specific quantitative measure of uniformity.


For example: The code rate of a convolutional code will typically be 1⁄2, 2⁄3, 3⁄4, 5⁄6, 7⁄8, etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that 204 − 188 = 16 redundant octets (or bytes) are added to each block of 188 octets of useful information. A few error correction codes do not have a fixed code rate—rateless erasure codes. Note that bit/s is a more widespread unit of measurement for the information rate, implying that it is synonymous with net bit rate or useful bit rate exclusive of error-correction codes.


In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. For example, the integers are nowhere dense among the reals, whereas the interval (0, 1) is not nowhere dense. A countable union of nowhere dense sets is called a meagre set. Meagre sets play an important role in the formulation of the Baire category theorem, which is used in the proof of several fundamental results of functional analysis.


The denominator is the sample size reduced by the number of model parameters estimated from the same data, (n−p) for p regressors or (n−p−1) if an intercept is used (see errors and residuals in statistics for more details). Although the MSE (as defined in this article) is not an unbiased estimator of the error variance, it is consistent, given the consistency of the predictor. In regression analysis, "mean squared error", often referred to as mean squared prediction error or "out-of-sample mean squared error", can also refer to the mean value of the squared deviations of the predictions from the true values, over an out-of-sample test space, generated by a model estimated over a particular sample space.


In order of increasing strength, i.e., decreasing sets of pairs, three of the possible orders on the Cartesian product of two totally ordered sets are: Lexicographical order: (a,b) ≤ (c,d) if and only if a < c or (a = c and b ≤ d). This is a total order. (a,b) ≤ (c,d) if and only if a ≤ c and b ≤ d (the product order). This is a partial order.


In the case of 3 events—A, B, and C—it can be shown that:


In territories such as the UK a core function of a DMS has always been to support safe switching and work on the networks. Control engineers prepare switching schedules to isolate and make safe a section of network before work is carried out, and the DMS validates these schedules using its network model. Switching schedules can combine telecontrolled and manual (on-site) switching operations. When the required section has been made safe, the DMS allows a Pemit To Work (PTW) document to be issued.


In mathematics, the Marcinkiewicz–Zygmund inequality, named after Józef Marcinkiewicz and Antoni Zygmund, gives relations between moments of a collection of independent random variables. It is a generalization of the rule for the sum of variances of independent random variables to moments of arbitrary order. It is a special case of the Burkholder-Davis-Gundy inequality in the case of discrete-time martingales.


A lockstep fault-tolerant machine uses replicated elements operating in parallel. At any time, all the replications of each element should be in the same state. The same inputs are provided to each replication, and the same outputs are expected.


In mathematical logic, the primitive recursive functionals are a generalization of primitive recursive functions into higher type theory. They consist of a collection of functions in all pure finite types. The primitive recursive functionals are important in proof theory and constructive mathematics. They are a central part of the Dialectica interpretation of intuitionistic arithmetic developed by Kurt Gödel. In recursion theory, the primitive recursive functionals are an example of higher-type computability, as primitive recursive functions are examples of Turing computability.


In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation on a set is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication.


In mathematics, specifically in algebraic topology and algebraic geometry, an inverse image functor is a contravariant construction of sheaves; here “contravariant” in the sense given a map f: X → Y {\displaystyle f:X\to Y} , the inverse image functor is a functor from the category of sheaves on Y to the category of sheaves on X. The direct image functor is the primary operation on sheaves, with the simplest definition. The inverse image exhibits some relatively subtle features.


In operating systems, memory management is the function responsible for managing the computer's primary memory. : 105–208 The memory management function keeps track of the status of each memory location, either allocated or free. It determines how memory is allocated among competing processes, deciding which gets memory, when they receive it, and how much they are allowed. When memory is allocated it determines which memory locations will be assigned. It tracks when memory is freed or unallocated and updates the status. This is distinct from application memory management, which is how a process manages the memory assigned to it by the operating system.


A weaker three-sigma rule can be derived from Chebyshev's inequality, stating that even for non-normally distributed variables, at least 88.8% of cases should fall within properly calculated three-sigma intervals. For unimodal distributions, the probability of being within the interval is at least 95% by the Vysochanskij–Petunin inequality. There may be certain assumptions for a distribution that force this probability to be at least 98%.


In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes). It is a weakened form of Goldbach's conjecture, which states that every even number is the sum of two primes.


In mathematics, a greatest common divisor matrix (sometimes abbreviated as GCD matrix) is a matrix.


In the bin covering problem, there are n items with different sizes. The goal is to pack the items into a maximum number of bins, where each bin should contain at least B. A natural configuration LP for this problem could be: maximize 1 ⋅ x s.t. A x ≤ n and x ≥ 0 {\displaystyle {\text{maximize}}~~\mathbf {1} \cdot \mathbf {x} ~~~{\text{s.t. }}~~A\mathbf {x} \leq \mathbf {n} ~~~{\text{and}}~~\mathbf {x} \geq 0} where A represents all configurations of items with sum at least B (one can take only the inclusion-minimal configurations).


In mathematics, a congruence is an equivalence relation on the integers. The following sections list important or interesting prime-related congruences.


In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one. For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution. In Bayes' theorem, a normalizing constant is used to ensure that the sum of all possible hypotheses equals 1. Other uses of normalizing constants include making the value of a Legendre polynomial at 1 and in the orthogonality of orthonormal functions. A similar concept has been used in areas other than probability, such as for polynomials.


Factorization was first considered by ancient Greek mathematicians in the case of integers. They proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1.


Terms that are usually considered primitive in other notations (such as integers, booleans, pairs, lists, and tagged unions) are mapped to higher-order functions under Church encoding. The Church-Turing thesis asserts that any computable operator (and its operands) can be represented under Church encoding. In the untyped lambda calculus the only primitive data type is the function.


If at phase i, V has an incorrect value for f i − 1 ( r 1 , … ) {\displaystyle f_{i-1}(r_{1},\dots )} then f i ( r 1 , … , 0 ) {\displaystyle f_{i}(r_{1},\dots ,0)} and f i ( r 1 , … , 1 ) {\displaystyle f_{i}(r_{1},\dots ,1)} will likely also be incorrect, and so forth. The probability for P ~ {\displaystyle {\tilde {P}}} to get lucky on some random r is at most the degree of the polynomial divided by the field size: n / n 4 {\displaystyle n/n^{4}} . The protocol runs through O(n2) phases, so the probability that P ~ {\displaystyle {\tilde {P}}} gets lucky at some phase is ≤ 1/n.


But the CFC industry did not give up that easily. As late as 1986, the Alliance for Responsible CFC Policy (an association representing the CFC industry founded by DuPont) was still arguing that the science was too uncertain to justify any action. In 1987, DuPont testified before the US Congress that "We believe there is no imminent crisis that demands unilateral regulation."


{\displaystyle \mathbb {R} \cup \left\{-\infty ,+\infty \right\}.} It is the Dedekind–MacNeille completion of the real numbers. When the meaning is clear from context, the symbol + ∞ {\displaystyle +\infty } is often written simply as ∞ . {\displaystyle \infty .} There is also the projectively extended real line where + ∞ {\displaystyle +\infty } and − ∞ {\displaystyle -\infty } are not distinguished so the infinity is denoted by only ∞ {\displaystyle \infty } .


The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects). For example, the ordered triple (a,b,c) can be defined as (a, (b,c)), i.e., as one pair nested in another. In the ordered pair (a, b), the object a is called the first entry, and the object b the second entry of the pair. Alternatively, the objects are called the first and second components, the first and second coordinates, or the left and right projections of the ordered pair. Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs, cf. picture.


In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean. Specifically, no more than 1/k2 of the distribution's values can be k or more standard deviations away from the mean (or equivalently, at least 1 − 1/k2 of the distribution's values are less than k standard deviations away from the mean). The rule is often called Chebyshev's theorem, about the range of standard deviations around the mean, in statistics.


In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms. Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions.


In the 1st edition of his well-known work, Phaselock Techniques, Floyd M. Gardner introduced a lock-in concept: If, for some reason, the frequency difference between input and VCO is less than the loop bandwidth, the loop will lock up almost instantaneously without slipping cycles. The maximum frequency difference for which this fast acquisition is possible is called the lock-in frequency. His notion of the lock-in frequency and corresponding definition of the lock-in range have become popular and nowadays are given in various engineering publications. However, since even for zero frequency difference there may exist initial states of loop such that cycle slipping may take place during the acquisition process, the consideration of initial state of the loop is of utmost importance for the cycle slip analysis and, therefore, Gardner’s concept of lock-in frequency lacked rigor and required clarification. In the 2nd edition of his book, Gardner stated: "there is no natural way to define exactly any unique lock-in frequency", and he wrote that "despite its vague reality, lock-in range is a useful concept".


In mathematics, the Hilbert projection theorem is a famous result of convex analysis that says that for every vector x {\displaystyle x} in a Hilbert space H {\displaystyle H} and every nonempty closed convex C ⊆ H , {\displaystyle C\subseteq H,} there exists a unique vector m ∈ C {\displaystyle m\in C} for which ‖ c − x ‖ {\displaystyle \|c-x\|} is minimized over the vectors c ∈ C {\displaystyle c\in C} ; that is, such that ‖ m − x ‖ ≤ ‖ c − x ‖ {\displaystyle \|m-x\|\leq \|c-x\|} for every c ∈ C . {\displaystyle c\in C.}


In telecommunication, a dial plan (or dialing plan) establishes the permitted sequences of digits dialed by telephone subscriber and the manner in which a telephone switch interprets these digits within the definitions of the prevailing telephone numbering plan. Dial plans in the public switched telephone network referred to as dialing procedures.The collection of permissible digit patterns, so called digit-maps, for a private telephone system or for customer premise equipment, such as an analog telephone adapter (ATA) or an IP phone, is sometimes also called dial plan. A pattern may be as short as a single digit, e.g. for reaching an operator, or as long as a complete international telephone number, including trunk prefixes and international prefixes.


The method became known as the Diffie-Hellman key exchange. RSA (Rivest–Shamir–Adleman) is another notable public-key cryptosystem.


Each time this (latter) magnitude comprises a half, a third, or a quarter of the given magnitude (of the unit), or, compared with (the unit), comprises three, five, or three-fifths, it is a rational magnitude. And, in general, each magnitude that corresponds to this magnitude (i.e. to the unit), as one number to another, is rational. If, however, a magnitude cannot be represented as a multiple, a part (1/n), or parts (m/n) of a given magnitude, it is irrational, i.e. it cannot be expressed other than by means of roots."


In the field of machine learning and specifically the problem of statistical classification, a confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one; in unsupervised learning it is usually called a matching matrix. Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa – both variants are found in the literature. The name stems from the fact that it makes it easy to see whether the system is confusing two classes (i.e. commonly mislabeling one as another). It is a special kind of contingency table, with two dimensions ("actual" and "predicted"), and identical sets of "classes" in both dimensions (each combination of dimension and class is a variable in the contingency table).


In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature. F-algebras can also be used to represent data structures used in programming, such as lists and trees. The main related concepts are initial F-algebras which may serve to encapsulate the induction principle, and the dual construction F-coalgebras.


Faraday created this concept by impression of Roger Boscovich, a physicist that impacted Maxwell's work as well. In 1856, he published his 1st paper in electromagnetism: On Faraday's Lines of Force. He tried to use the analogy of incompressible fluid flow to model the magnetic lines of forces.


In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. A simple random sample is an unbiased sampling technique. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods.


In number theory, an n-Knödel number for a given positive integer n is a composite number m with the property that each i < m coprime to m satisfies i m − n ≡ 1 ( mod m ) {\displaystyle i^{m-n}\equiv 1{\pmod {m}}} . The concept is named after Walter Knödel.The set of all n-Knödel numbers is denoted Kn. The special case K1 is the Carmichael numbers. There are infinitely many n-Knödel numbers for a given n. Due to Euler's theorem every composite number m is an n-Knödel number for n = m − φ ( m ) {\displaystyle n=m-\varphi (m)} where φ {\displaystyle \varphi } is Euler's totient function.


In the context of digital privacy, information privacy is the idea that individuals should have the freedom to determine how their digital information is collected and used. This is particularly relevant for personally identifiable information. The concept of information privacy has evolved in parallel to the evolution of the field of Information Technology (IT). The rise of networking and computing led to the dramatic change in the ways of information exchange.


In statistical hypothesis testing, a null result occurs when an experimental result is not significantly different from what is to be expected under the null hypothesis; its probability (under the null hypothesis) does not exceed the significance level, i.e., the threshold set prior to testing for rejection of the null hypothesis. The significance level varies, but common choices include 0.10, 0.05, and 0.01.As an example in physics, the results of the Michelson–Morley experiment were of this type, as it did not detect the expected velocity relative to the postulated luminiferous aether. This experiment's famous failed detection, commonly referred to as the null result, contributed to the development of special relativity. The experiment did appear to measure a non-zero "drift", but the value was far too small to account for the theoretically expected results; it is generally thought to be inside the noise level of the experiment.


In engineering there are multiple types of failure based upon the application of the material. In many machine applications any change in the part due to yielding will result in the machine piece needing to be replaced. Although this deformation or weakening of the material is not the technical definition of ultimate failure, the piece has failed.


. . δ i k p k M  ( l − 2 ) ⟩ ⟩ {\displaystyle {\hat {T}}r\left\langle \left\langle \delta _{i_{1}p_{1}}...\delta _{i_{k}p_{k}}\mathbf {M} _{i_{1}p_{1}}^{(l)}\right\rangle \right\rangle =(2l+2k+1)\left\langle \left\langle \delta _{i_{2}p_{2}}...\delta _{i_{k}p_{k}}\mathbf {M} _{}^{(l-2)}\right\rangle \right\rangle } .Calculating the trace reduces the number of the Kronecker symbols by one, and the rank of the harmonic tensor on the right-hand side of the equation decreases by two.


In mathematics, and especially general topology, the interlocking interval topology is an example of a topology on the set S := R+ \ Z+, i.e. the set of all positive real numbers that are not positive whole numbers. To give the set S a topology means to say which subsets of S are "open", and to do so in a way that the following axioms are met: The union of open sets is an open set. The finite intersection of open sets is an open set. S and the empty set ∅ are open sets.


In some languages, gender is determined by strictly semantic criteria, but in other languages, semantic criteria only partially determine gender.


In order to effectively manage all the documentation required to care for collections, organized systems are necessary. In the early days of museum registration simple paper ledgers were used to track objects, and documentation was stored in file cabinets. Since computers became more commonplace however, practices have evolved and very technologically advanced systems now exist to manage all aspects of collection management in one place.


Primary rules require individuals to act or not act in certain ways and create duties for the governed to obey. Secondary rules are rules that confer authority to create new primary rules or modify existing ones. Secondary rules are divided into rules of adjudication (how to resolve legal disputes), rules of change (how laws are amended), and the rule of recognition (how laws are identified as valid).


In nursing, a study has been conducted of the impact of interruptions on nurses in a trauma center. Another study has been done on the interruption rates of nurses and doctors.Interruption caused by smartphone use in health-care settings can be deadly. Hence, it may be worthwhile for health care organizations to craft effective cellphone usage policies to maximize technological benefits and minimize unnecessary distraction associated with smartphone use.


The elements l i ∈ D {\displaystyle l_{i}\in {\mathcal {D}}} are applied to a single differential indeterminate z {\displaystyle z} . In this way the ideal I = ⟨ l 1 , l 2 , … ⟩ {\displaystyle I=\langle l_{1},l_{2},\ldots \rangle } corresponds to the system of PDEs l 1 z = 0 {\displaystyle l_{1}z=0} , l 2 z = 0 , … {\displaystyle l_{2}z=0,\ldots } for the single function z {\displaystyle z} . The generators of an ideal are highly non-unique; its members may be transformed in infinitely many ways by taking linear combinations of them or its derivatives without changing the ideal.


From this matrix, the probability of being in a particular state n steps in the future can be calculated. A Markov chain's state space can be partitioned into communicating classes that describe which states are reachable from each other (in one transition or in many). Each state can be described as transient or recurrent, depending on the probability of the chain ever returning to that state.


In quantum neural networks programmed on gate-model quantum computers, based on quantum perceptrons instead of variational quantum circuits, the non-linearity of the activation function can be implemented with no need of measuring the output of each perceptron at each layer. The quantum properties loaded within the circuit such as superposition can be preserved by creating the Taylor series of the argument computed by the perceptron itself, with suitable quantum circuits computing the powers up to a wanted approximation degree. Because of the flexibility of such quantum circuits, they can be designed in order to approximate any arbitrary classical activation function.


Although not perfect, these frequencies can usually provide some clues about the topic of the document. And sometimes it is also useful to weight the term frequencies by the inverse document frequencies. See tf-idf for detailed discussions.


In telecommunications, communications protection is the application of communications security (COMSEC) measures to telecommunications systems in order to: (a) deny unauthorized access to sensitive unclassified information of value, (b) prevent disruption of telecommunications services, or (c) ensure the authenticity of information handled by telecommunications systems.


In practice, researchers attempt to fit appropriate model parameters to the data corpus using one of several heuristics for maximum likelihood fit. A survey by D. Blei describes this suite of algorithms. Several groups of researchers starting with Papadimitriou et al. have attempted to design algorithms with provable guarantees.


In physics, the no-broadcasting theorem is a result of quantum information theory. In the case of pure quantum states, it is a corollary of the no-cloning theorem. The no-cloning theorem for pure states says that it is impossible to create two copies of an unknown state given a single copy of the state. Since quantum states cannot be copied in general, they cannot be broadcast.


In software engineering, the Extract Class refactoring is applied when a class becomes overweight with too many methods and its purpose becomes unclear. Extract Class refactoring involves creating a new class and moving methods and/or data to the new class.


In situation theory, situation semantics (pioneered by Jon Barwise and John Perry in the early 1980s) attempts to provide a solid theoretical foundation for reasoning about common-sense and real world situations, typically in the context of theoretical linguistics, theoretical philosophy, or applied natural language processing,


In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions. Comparison of sum-of-squares with degrees-of-freedom is no longer meaningful, and software may report certain fractional 'degrees of freedom' in these cases. Such numbers have no genuine degrees-of-freedom interpretation, but are simply providing an approximate chi-squared distribution for the corresponding sum-of-squares. The details of such approximations are beyond the scope of this page.


In the United States, seven frequency bands have been allocated by the Federal Communications Commission for uses that include cordless phones. These are: 1.7 MHz (1.665–1.770 MHz, narrow-band FM) Cordless phones manufactured after October 1, 1984, are not allowed to use this band and were required to use the newer (higher) 43-50 MHz frequencies, although older telephones, on the older frequency pairs, could still be used. 27 MHz, near the Citizens Band (CB) Radio service with some frequencies being 26.010, 26.050, 26.380, 26.419 and 27.095 MHz. These were initially paired with the 1.7 MHz frequencies, then, later, with the 49 MHz frequencies.


Among other things, the use of serializing tokens prevents many of the situations that could result in deadlocks and priority inversions when using mutexes, as well as greatly simplifying the design and implementation of a many-step procedure that would require a resource to be shared among multiple threads. The serializing token code is evolving into something quite similar to the "Read-copy-update" feature now available in Linux. Unlike Linux's current RCU implementation, DragonFly's is being implemented such that only processors competing for the same token are affected rather than all processors in the computer.DragonFly switched to multiprocessor safe slab allocator, which requires neither mutexes nor blocking operations for memory assignment tasks. It was eventually ported into standard C library in the userland, where it replaced FreeBSD's malloc implementation.


In organizational development (OD), performance can be thought of as Actual Results vs Desired Results. Any discrepancy, where Actual is less than Desired, could constitute the performance improvement zone. Performance management and improvement can be thought of as a cycle: Performance planning where goals and objectives are established Performance coaching where a manager intervenes to give feedback and adjust performance Performance appraisal where individual performance is formally documented and feedback deliveredA performance problem is any gap between Desired Results and Actual Results. Performance improvement is any effort targeted at closing the gap between Actual Results and Desired Results.Other organizational development definitions are slightly different. The U.S. Office of Personnel Management (OPM) indicates that Performance Management consists of a system or process whereby: Work is planned and expectations are set Performance of work is monitored Staff ability to perform is developed and enhanced Performance is rated or measured and the ratings summarized Top performance is rewarded.


In the United States, even if an artifact or process is protected by trade secrets, reverse-engineering the artifact or process is often lawful if it has been legitimately obtained.Reverse engineering of computer software often falls under both contract law as a breach of contract as well as any other relevant laws. That is because most end-user license agreements specifically prohibit it, and US courts have ruled that if such terms are present, they override the copyright law that expressly permits it (see Bowers v. Baystate Technologies). According to Section 103(f) of the Digital Millennium Copyright Act (17 U.S.C. § 1201 (f)), a person in legal possession of a program may reverse-engineer and circumvent its protection if that is necessary to achieve "interoperability", a term that broadly covers other devices and programs that can interact with it, make use of it, and to use and transfer data to and from it in useful ways. A limited exemption exists that allows the knowledge thus gained to be shared and used for interoperability purposes.


In the quantum world, however, the conservation of quantum information should mean that information cannot be created nor destroyed. This concept stems from two fundamental theorems of quantum mechanics: the no-cloning theorem and the no-deleting theorem. But the no-hiding theorem is a more general proof of conservation of quantum information which originates from the proof of conservation of wave function in quantum theory.


These facilities tend to vary drastically between languages, but in general each can achieve anything that is possible with any of the others. A great many operation overloads, data type by data type, can have the same effect at compile-time as any degree of inheritance or other means to achieve polymorphism. The class notation is simply a coder's convenience.


Within the PBX, the user merely dials the extension number to reach any other user directly. For inbound calls, a switchboard operator or automated attendant may request the number of the desired extension or the call may be completed with direct inbound dialing, if outside numbers are assigned to individual extensions. An off-premises extension, where a worker at a remote location employs a telephone configured to appear as if it were an extension located at the main business site, may be created in analog telephony by using a leased line to connect the extension to the main enterprise system. Voice over IP makes the creation of off-premises extensions inexpensive and trivial as broadband Internet and virtual private networking can extend local network access anywhere in the world. In either system, an off-premises extension is reachable from within the same enterprise simply by calling its extension number directly; for inbound and outgoing calls, it functions as if it were located at the main place of business.


In the Turing test, the conversation is conducted via keyboards and the challenge for the AI community is to produce a computer that can give answers that are indistinguishable from those produced by a real human. Given that such interactions are by their very nature open-ended and context-dependent Collins argues that only a fully socialised intelligence will be able to respond appropriately to any of the new and potentially unknown sentences directed to it. Although the argument was not made in these terms at the time, the concept of interactional expertise is important here.


The H-ternary code has also timing superiority compared to similar ternary codes. Other ternary line code such as alternate mark inversion (AMI) also lacks the timing information when a run of zeros needs to be transmitted. This drawback is partly overcome by its modified version the high density bipolar with three zeros substitution (HDB3). On the other hand, the new code has a smaller bandwidth in comparison with the polar RZ code. The latter has its frequency spectral components concentrated at twice the original binary data rate because the polar RZ code has a pulse duty cycle of 50 percent.


In one of the earliest studies involving misattribution, the Canadian cognitive psychologist Bruce Whittlesea presented subjects with a list of common words. Each word was briefly displayed to the subject. The task required the subject to judge whether a target word was semantically related to any word in the list. Unlike Whittlesea's first experiment involving the recognition of target words, this study involved the manipulation of processing fluency through the conceptual context of the target word, rather than the physical context.


The Release Management capabilities give teams the ability to perform a controlled, workflow (provided by Windows Workflow Foundation) driven release to development, test and production environments and provides dashboards for monitoring the progress of one or more releases. Microsoft has rebuilt Release Management for Visual Studio Team Services and on-premises version of TFS with the new changes in 2015 Update 2. The new version of Release Management leverages the web browser as the client and relies on the same agent architecture as Team Foundation Build. Release Management enables DevOps capabilities for Azure DevOps.


An alternative way to express this is to assume one or more solutions or examples exists, from which a smallest solution or example—a minimal counterexample—can then be inferred. Once there, one would try to prove that if a smallest solution exists, then it must imply the existence of a smaller solution (in some sense), which again proves that the existence of any solution would lead to a contradiction.


In mathematics, the Double extension set theory (DEST) is an axiomatic set theory proposed by Andrzej Kisielewicz consisting of two separate membership relations on the universe of sets, denoted here by ∈ {\displaystyle \in } and ε {\displaystyle \varepsilon } , and a set of axioms relating the two. The intention behind defining the two membership relations is to avoid the usual paradoxes of set theory, without substantially weakening the axiom of unrestricted comprehension. Intuitively, in DEST, comprehension is used to define the elements of a set under one membership relation using formulas that involve only the other membership relation. Let ϕ ( x ) {\displaystyle \phi (x)} be a first-order formula with free variable x {\displaystyle x} in the language of DEST not involving the membership relation ε {\displaystyle \varepsilon } .


Hence the expression, "counted with multiplicity". If multiplicity is ignored, this may be emphasized by counting the number of distinct elements, as in "the number of distinct roots". However, whenever a set (as opposed to multiset) is formed, multiplicity is automatically ignored, without requiring use of the term "distinct".


The study of unattested substrata often begins from the study of substrate words, which lack a clear etymology. Such words can in principle still be native inheritance, lost everywhere else in the language family; but they might in principle also originate from a substrate. The sound structure of words of unknown origin — their phonology and morphology — can often suggest hints in either direction.


In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology, as a way of measuring the complexity of rivers and streams, by Robert E. Horton (1945) and Arthur Newell Strahler (1952, 1957). In this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributaries. The same numbers also arise in the analysis of L-systems and of hierarchical biological structures such as (biological) trees and animal respiratory and circulatory systems, in register allocation for compilation of high-level programming languages and in the analysis of social networks.


The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is symmetric as two equal mathematical objects are equal regardless of their order.


In the field of generics the two languages show a superficial syntactical similarity, but they have deep underlying differences.


The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance). It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order to transform one input string into another. Simplistic string metrics such as Levenshtein distance have expanded to include phonetic, token, grammatical and character-based methods of statistical comparisons. String metrics are used heavily in information integration and are currently used in areas including fraud detection, fingerprint analysis, plagiarism detection, ontology merging, DNA analysis, RNA analysis, image analysis, evidence-based machine learning, database data deduplication, data mining, incremental search, data integration, malware detection, and semantic knowledge integration.


These are then, however, not real time capable (except one uses a really big buffer, that lowers the throughput dramatically) anymore and only sufficient for post processing. Other variants do several passes to yield a rough estimate first and then refine it by the following passes, which is inspired by video editing/transcoding.


In the field of mathematical analysis, an interpolation inequality is an inequality of the form ‖ u 0 ‖ 0 ≤ C ‖ u 1 ‖ 1 α 1 ‖ u 2 ‖ 2 α 2 … ‖ u n ‖ n α n , n ≥ 2 , {\displaystyle \|u_{0}\|_{0}\leq C\|u_{1}\|_{1}^{\alpha _{1}}\|u_{2}\|_{2}^{\alpha _{2}}\dots \|u_{n}\|_{n}^{\alpha _{n}},\quad n\geq 2,} where for 0 ≤ k ≤ n {\displaystyle 0\leq k\leq n} , u k {\displaystyle u_{k}} is an element of some particular vector space X k {\displaystyle X_{k}} equipped with norm ‖ ⋅ ‖ k {\displaystyle \|\cdot \|_{k}} and α k {\displaystyle \alpha _{k}} is some real exponent, and C {\displaystyle C} is some constant independent of u 0 , . . , u n {\displaystyle u_{0},..,u_{n}} .


In the following the Kemeny-Young winner for the first group of voters is determined. The Kemeny–Young method arranges the pairwise comparison counts in the following tally table: The ranking scores of all possible rankings are: Result: The ranking A > B > C has the highest ranking score. Thus, A wins ahead of B and C.


In order to disinfect water, such as chlorine, chlorine dioxide, and ozone are introduced which kill microorganisms.


Many older pianos only have 85 keys (seven octaves from A0 to A7). Some piano manufacturers have extended the range further in one or both directions. For example, the Imperial Bösendorfer has nine extra keys at the bass end, giving a total of 97 keys and an eight octave range.


IPS are usually defined via their Markov generator giving rise to a unique Markov process using Markov semigroups and the Hille-Yosida theorem. The generator again is given via so-called transition rates c Λ ( η , ξ ) > 0 {\displaystyle c_{\Lambda }(\eta ,\xi )>0} where Λ ⊂ G {\displaystyle \Lambda \subset G} is a finite set of sites and η , ξ ∈ Ω {\displaystyle \eta ,\xi \in \Omega } with η i = ξ i {\displaystyle \eta _{i}=\xi _{i}} for all i ∉ Λ {\displaystyle i\notin \Lambda } . The rates describe exponential waiting times of the process to jump from configuration η {\displaystyle \eta } into configuration ξ {\displaystyle \xi } .


In mathematics and optimization, a pseudo-Boolean function is a function of the form f: B n → R , {\displaystyle f:\mathbf {B} ^{n}\to \mathbb {R} ,} where B = {0, 1} is a Boolean domain and n is a nonnegative integer called the arity of the function. A Boolean function is then a special case, where the values are also restricted to 0 or 1.


More specifically, ground truth may refer to a process in which "pixels" on a satellite image are compared to what is imaged (at the time of capture) in order to verify the contents of the "pixels" in the image (noting that the concept of "pixel" is imaging-system-dependent). In the case of a classified image, supervised classification can help to determine the accuracy of the classification by the remote sensing system which can minimize error in the classification. Ground truth is usually done on site, correlating what is known with surface observations and measurements of various properties of the features of the ground resolution cells under study in the remotely sensed digital image.


In general terms the size of the CPU die has remained largely the same over time, while the size of the units within the CPU has grown much smaller as more and more units were added. That means that the relative distance between any one function unit and the global register file has grown over time. Once introduced in order to avoid delays in talking to main memory, the global register file has itself become a delay that is worth avoiding.


The machine had a two-stage assembler (SAAL – Single Address Assembly Language) which was its primary assembler; it also had a three-stage card based compiler for a programming language called SARGE. 1005s were used as some nodes on Autodin. There were actually two versions of the 1005.


The family of all rotations and their partial order can be constructed in polynomial time, leading to polynomial time solutions for other problems on stable matching including the minimum or maximum weight stable matching. The Gale–Shapley algorithm can be used to construct two special lattice elements, its top and bottom element.


In order for a CDSS to offer value, it must demonstrably improve clinical workflow or outcome. Evaluation of CDSS quantifies its value to improve a system's quality and measure its effectiveness. Because different CDSSs serve different purposes, no generic metric applies to all such systems; however, attributes such as consistency (with and with experts) often apply across a wide spectrum of systems.The evaluation benchmark for a CDSS depends on the system's goal: for example, a diagnostic decision support system may be rated based upon the consistency and accuracy of its classification of disease (as compared to physicians or other decision support systems). An evidence-based medicine system might be rated based upon a high incidence of patient improvement or higher financial reimbursement for care providers.


The second mechanism is the balancing of power generation, which is coordinated by the TSO. Depending on the energy lacks and surplus (e.g. due to power plant failures or to intermittence in the case of wind power installations), the TSO determines the penalties that will be paid by IPPs who missed in their obligations. In some cases, an intra-day market is also present, in order to take corrective actions.In order to illustrate this electricity market mechanism, consider the Dutch electricity market.


In practical electric circuits electrical breakdown is usually an unwanted occurrence, a failure of insulating material causing a short circuit, possibly resulting in a catastrophic failure of the equipment. In power circuits, the sudden drop in resistance causes a high current to flow through the material, beginning an electric arc, and if safety devices do not interrupt the current quickly the sudden extreme Joule heating may cause the insulating material or other parts of the circuit to melt or vaporize explosively, damaging the equipment and creating a fire hazard. However, external protective devices in the circuit such as circuit breakers and current limiting can prevent the high current; and the breakdown process itself is not necessarily destructive and may be reversible.


In mathematics, the Euclidean algorithm or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements (c. 300 BC). It is one of the oldest algorithms in common use.


In nuclear strategy, a first strike or preemptive strike is a preemptive surprise attack employing overwhelming force. First strike capability is a country's ability to defeat another nuclear power by destroying its arsenal to the point where the attacking country can survive the weakened retaliation while the opposing side is left unable to continue war. The preferred methodology is to attack the opponent's strategic nuclear weapon facilities (missile silos, submarine bases, bomber airfields), command and control sites, and storage depots first. The strategy is called counterforce.


Sachs was interested in them for their self-complementarity properties, while Erdős and Rényi studied their symmetries. Paley digraphs are directed analogs of Paley graphs that yield antisymmetric conference matrices. They were introduced by Graham & Spencer (1971) (independently of Sachs, Erdős, and Rényi) as a way of constructing tournaments with a property previously known to be held only by random tournaments: in a Paley digraph, every small subset of vertices is dominated by some other vertex.


In some cases morphemes have effectively fused and will not be recognizable as being composed of two separate morphemes.


In operator theory, a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix. It was first introduced by James Mercer in the early 20th century, in the context of solving integral operator equations. Since then, positive-definite functions and their various analogues and generalizations have arisen in diverse parts of mathematics. They occur naturally in Fourier analysis, probability theory, operator theory, complex function-theory, moment problems, integral equations, boundary-value problems for partial differential equations, machine learning, embedding problem, information theory, and other areas.


In probability theory, the Brownian web is an uncountable collection of one-dimensional coalescing Brownian motions, starting from every point in space and time. It arises as the diffusive space-time scaling limit of a collection of coalescing random walks, with one walk starting from each point of the integer lattice Z at each time.


The best-known algorithms are Shor's algorithm for factoring and Grover's algorithm for searching an unstructured database or an unordered list. Shor's algorithms runs much (almost exponentially) faster than the best-known classical algorithm for factoring, the general number field sieve. Grover's algorithm runs quadratically faster than the best possible classical algorithm for the same task, a linear search.


In mathematics, the phrase complete partial order is variously used to refer to at least three similar, but distinct, classes of partially ordered sets, characterized by particular completeness properties. Complete partial orders play a central role in theoretical computer science: in denotational semantics and domain theory.


The reason for this deviation is that standard upper limits based on a most powerful test necessarily produce empty intervals with some fixed probability when the parameter value is zero, and this property is considered undesirable by most physicists and statisticians.Upper limits derived with the CLs method always contain the zero value of the parameter and hence the coverage probability at this point is always 100%. The definition of CLs does not follow from any precise theoretical framework of statistical inference and is therefore described sometimes as ad hoc. It has however close resemblance to concepts of statistical evidence proposed by the statistician Allan Birnbaum.


The first contribution to the Lagrangian is the entropy: L e n t = − ∑ k = 1 K ∑ n = 0 N p n k ln  ( p n k ) {\displaystyle {\mathcal {L}}_{ent}=-\sum _{k=1}^{K}\sum _{n=0}^{N}p_{nk}\ln(p_{nk})} The log-likelihood is: ℓ = ∑ k = 1 K ∑ n = 0 N Δ ( n , y k ) ln  ( p n k ) {\displaystyle \ell =\sum _{k=1}^{K}\sum _{n=0}^{N}\Delta (n,y_{k})\ln(p_{nk})} Assuming the multinomial logistic function, the derivative of the log-likelihood with respect the beta coefficients was found to be: ∂ ℓ ∂ β n m = ∑ k = 1 K ( p n k x m k − Δ ( n , y k ) x m k ) {\displaystyle {\frac {\partial \ell }{\partial \beta _{nm}}}=\sum _{k=1}^{K}(p_{nk}x_{mk}-\Delta (n,y_{k})x_{mk})} A very important point here is that this expression is (remarkably) not an explicit function of the beta coefficients. It is only a function of the probabilities pnk and the data. Rather than being specific to the assumed multinomial logistic case, it is taken to be a general statement of the condition at which the log-likelihood is maximized and makes no reference to the functional form of pnk.


In programming languages that have associative arrays or comparable data structures, such as Python, Perl, PHP or Objective-C, it is idiomatic to use them to implement conditional assignment. In languages that have anonymous functions or that allow a programmer to assign a named function to a variable reference, conditional flow can be implemented by using a hash as a dispatch table.


Costa et al. write that "the case p = 5 {\displaystyle p=5} is trivial", and credit the observation that 13 is a Wilson prime to Mathews (1892). Early work on these numbers included searches by N. G. W. H. Beeger and Emma Lehmer, but 563 was not discovered until the early 1950s, when computer searches could be applied to the problem. If any others exist, they must be greater than 2 × 1013.


In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets , braces { } and angle brackets ⟨ ⟩, are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take precedence over those surrounding it. Sometimes, for the clarity of reading, different kinds of brackets are used to express the same meaning of precedence in a single expression with deep nesting of sub-expressions.Historically, other notations, such as the vinculum, were similarly used for grouping. In present-day use, these notations all have specific meanings. The earliest use of brackets to indicate aggregation (i.e. grouping) was suggested in 1608 by Christopher Clavius, and in 1629 by Albert Girard.


In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045 {\displaystyle 9045} would be 9 + 0 + 4 + 5 = 18. {\displaystyle 9+0+4+5=18.}


In statistics, per-comparison error rate (PCER) is the probability of a Type I error in the absence of any multiple hypothesis testing correction. This is a liberal error rate relative to the false discovery rate and family-wise error rate, in that it is always less than or equal to those rates. == References ==


In probability theory and statistics, the chi-squared distribution (also chi-square or χ 2 {\displaystyle \chi ^{2}} -distribution) with k {\displaystyle k} degrees of freedom is the distribution of a sum of the squares of k {\displaystyle k} independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals. This distribution is sometimes called the central chi-squared distribution, a special case of the more general noncentral chi-squared distribution. The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also use this distribution, such as Friedman's analysis of variance by ranks.


In the case of union by size, a node stores its size, which is simply its number of descendants (including the node itself). When the trees with roots x and y are merged, the node with more descendants becomes the parent. If the two nodes have the same number of descendants, then either one can become the parent. In both cases, the size of the new parent node is set to its new total number of descendants. function Union(x, y) is // Replace nodes by roots x := Find(x) y := Find(y) if x = y then return // x and y are already in the same set end if // If necessary, swap variables to ensure that // x has at least as many descendants as y if x.size < y.size then (x, y) := (y, x) end if // Make x the new root y.parent := x // Update the size of x x.size := x.size + y.size end function The number of bits necessary to store the size is clearly the number of bits necessary to store n. This adds a constant factor to the forest's required storage.


Commercial Privacy Bill of Rights Act of 2011 (Not Passed): Established parameters on the purposes for which data could be collected and placed further limitations on the length of time that data could be retained. Also established and FTC protocol that would require covered entities (those collection data on 5000+ U.S. citizens in the span of any year) to: 1) Give individuals notice about the use and storage of their personal information; 2) Provide individuals opportunities to "opt-out" of data collection, especially as used in behavioral advertising; 3) Provide avenues to fix inaccurate information; 4) Allow data points with personally identifiable characteristics to be rendered. Data Broker Accountability and Transparency Act of 2019 (Not Passed): Established requirements for entities that engage in the collections of personal data for the purposes of re-sale to third party entities. Also required that individuals be granted access to the information that is collected about themselves.


Section 4 of this act called for testing of chemicals to determine any detrimental impacts that could come as a result. A sector of the EPA focused on "compliance monitoring," which ensures that companies are following the guidelines that have been put in place by the TSCA. PCBs have been found in de-dusting agents, so the TCSA has proven important in the mitigation of this chemical in household cleaning.


This RBM is a generative stochastic feedforward neural network that can learn a probability distribution over its set of inputs. Once sufficiently many layers have been learned, the deep architecture may be used as a generative model by reproducing the data when sampling down the model (an "ancestral pass") from the top level feature activations. In 2012, Andrew Ng and Jeff Dean created an FNN that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from YouTube videos.


In the 1870s, Georg Cantor started to develop set theory and, in 1874, published a paper proving that the algebraic numbers could be put in one-to-one correspondence with the set of natural numbers, and thus that the set of transcendental numbers must be uncountable. Later, in 1891, Cantor used his more familiar diagonal argument to prove the same result. While Cantor's result is often quoted as being purely existential and thus unusable for constructing a single transcendental number, the proofs in both the aforementioned papers give methods to construct transcendental numbers.While Cantor used set theory to prove the plenitude of transcendental numbers, a recent development has been the use of model theory in attempts to prove an unsolved problem in transcendental number theory. The problem is to determine the transcendence degree of the field K = Q ( x 1 , … , x n , e x 1 , … , e x n ) {\displaystyle K=\mathbb {Q} (x_{1},\ldots ,x_{n},e^{x_{1}},\ldots ,e^{x_{n}})} for complex numbers x1, ..., xn that are linearly independent over the rational numbers.


The Guide to Legal Writing Style (2007) also does not directly address this topic.Some legal style guides do provide guidance on sentence spacing, such as the 2009 edition of the AP Stylebook and Briefing on Media Law, and the 2006 edition of The Redbook: A Manual on Legal Style—both of which state that a single space follows terminal punctuation. The Redbook provides further details on the use of this convention: "The custom during the reign of the typewriter was to insert two spaces between sentences" due to the use by typewriters of monospaced fonts that are not effective at creating readable text. It indicates that users could continue the use of two spaces if using a typewriter "or the Courier font", and espouses the advantages of widely available proportional fonts which are degraded by the use of two spaces after terminal punctuation. Of the legal style guides listed in this section, all use proportional fonts with a single space between sentences in their text.


In mathematics applied to analysis of social structures, homogeneity blockmodeling is an approach in blockmodeling, which is best suited for a preliminary or main approach to valued networks, when a prior knowledge about these networks is not available. This is due to the fact, that homogeneity blockmodeling emphasizes the similarity of link (tie) strengths within the blocks over the pattern of links. In this approach, tie (link) values (or statistical data computed on them) are assumed to be equal (homogenous) within blocks.This approach to the generalized blockmodeling of valued networks was first proposed by Aleš Žiberna in 2007 with the basic idea, "that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values". The newly–formed ideal blocks, which are appropriate for blockmodeling of valued networks, are then presented together with the definitions of their block inconsistencies. Similar approach to the homogeneity blockmodeling, dealing with direct approach for structural equivalence, was previously suggested by Stephen P. Borgatti and Martin G. Everett (1992).


In the early 1980s, significant uncertainties surrounded the RISC concept. One concern involved the use of memory; a single instruction from a traditional processor like the Motorola 68k may be written out as perhaps a half dozen of the simpler RISC instructions. In theory, this could slow the system down as it spent more time fetching instructions from memory.


Search models illustrate how best to balance the cost of delay against the value of the option to try again. Mathematically, search models are optimal stopping problems. Macroeconomists have extended search theory by studying general equilibrium models in which one or more types of searchers interact. These macroeconomic theories have been called 'matching theory', or 'search and matching theory.


The relevant ambiguity can be resolved by establishing a higher level of linguistic analysis. At this higher level, the two items can be clearly shown having two different structural interpretations. In this way, constructional homonymities at the phonemic level can be resolved by establishing the level of morphology, and so forth.


In sociology, a social organization is a pattern of relationships between and among individuals and social groups.Characteristics of social organization can include qualities such as sexual composition, spatiotemporal cohesion, leadership, structure, division of labor, communication systems, and so on.And because of these characteristics of social organization, people can monitor their everyday work and involvement in other activities that are controlled forms of human interaction. These interactions include: affiliation, collective resources, substitutability of individuals and recorded control. These interactions come together to constitute common features in basic social units such as family, enterprises, clubs, states, etc. These are social organizations.Common examples of modern social organizations are government agencies, NGO's and corporations.


As a special case, an even delta-matroid is a delta-matroid in which either all sets have even number of elements, or all sets have an odd number of elements. If a constraint satisfaction problem has a Boolean variable on each edge of a planar graph, and if the variables of the edges incident to each vertex of the graph are constrained to belong to an even delta-matroid (possibly a different even delta-matroid for each vertex), then the problem can be solved in polynomial time. This result plays a key role in a characterization of the planar Boolean constraint satisfaction problems that can be solved in polynomial time. == References ==


Each of the standards has been placed in one of four fundamental categories to promote educational evaluations that are proper, useful, feasible, and accurate. In these sets of standards, validity and reliability considerations are covered under the accuracy topic. For example, the student accuracy standards help ensure that student evaluations will provide sound, accurate, and credible information about student learning and performance.


Asynchronous Transfer Mode, Frame Relay and MPLS are examples of a connection-oriented, unreliable protocol. SMTP is an example of a connection-oriented protocol in which if a message is not delivered, an error report is sent to the sender which makes SMTP a reliable protocol. Because they can keep track of a conversation, connection-oriented protocols are sometimes described as stateful.


In symmetric key cryptography, both parties must possess a secret key which they must exchange prior to using any encryption. Distribution of secret keys has been problematic until recently, because it involved face-to-face meeting, use of a trusted courier, or sending the key through an existing encryption channel. The first two are often impractical and always unsafe, while the third depends on the security of a previous key exchange. In public key cryptography, the key distribution of public keys is done through public key servers.


In order to ensure and increase the 'conformance quality' of services, that is, service delivery happening as designed, various methods are available. Some of these include Guaranteeing; Mystery Shopping; Recovering; Setting standards and measuring; Statistical process control and Customer involvement.


Humphry Davy would go on to create Decomposition Tables from his preliminary experiments on Electrolysis. The Decomposition Tables would give insight on the energies needed to break apart certain compounds.In 1817 Johan August Arfwedson determined there was another element, lithium, in some of his samples; however, he could not isolate the component. It was not until 1821 that William Thomas Brande used electrolysis to single it out.


In quantum information theory and quantum optics, the Schrödinger–HJW theorem is a result about the realization of a mixed state of a quantum system as an ensemble of pure quantum states and the relation between the corresponding purifications of the density operators. The theorem is named after physicists and mathematicians Erwin Schrödinger, Lane P. Hughston, Richard Jozsa and William Wootters. The result was also found independently (albeit partially) by Nicolas Gisin, and by Nicolas Hadjisavvas building upon work by Ed Jaynes, while a significant part of it was likewise independently discovered by N. David Mermin. Thanks to its complicated history, it is also known by various other names such as the GHJW theorem, the HJW theorem, and the purification theorem.


In statistics, the mean signed difference (MSD), also known as mean signed deviation and mean signed error, is a sample statistic that summarises how well a set of estimates θ ^ i {\displaystyle {\hat {\theta }}_{i}} match the quantities θ i {\displaystyle \theta _{i}} that they are supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error. For example, suppose a linear regression model has been estimated over a sample of data, and is then used to extrapolate predictions of the dependent variable out of sample after the out-of-sample data points have become available.


Otherwise the gap is strictly positive and weak duality holds.In general given two dual pairs separated locally convex spaces ( X , X ∗ ) {\displaystyle \left(X,X^{*}\right)} and ( Y , Y ∗ ) {\displaystyle \left(Y,Y^{*}\right)} . Then given the function f: X → R ∪ { + ∞ } {\displaystyle f:X\to \mathbb {R} \cup \{+\infty \}} , we can define the primal problem by inf x ∈ X f ( x ) . {\displaystyle \inf _{x\in X}f(x).\,} If there are constraint conditions, these can be built into the function f {\displaystyle f} by letting f = f + I constraints {\displaystyle f=f+I_{\text{constraints}}} where I {\displaystyle I} is the indicator function.


History monoids were first presented by M.W. Shields.History monoids are isomorphic to trace monoids (free partially commutative monoids) and to the monoid of dependency graphs. As such, they are free objects and are universal. The history monoid is a type of semi-abelian categorical product in the category of monoids.


Nonetheless, CI techniques are considered the more modern approach. CI jobs are often run on isolated virtual machines, and typically include automated testing as well. When someone says a developer "broke the build", they are effectively saying that a developer checked in code which might very well have compiled (and hopefully also run properly) in their account, but does not compile (and therefore, cannot be run) in anyone else's account.


In mathematics, the term "vector" is used for an element of any vector space. In physics, however, the term "vector" tends to refer almost exclusively to quantities like displacement or velocity, which have components that relate directly to the three dimensions of space, or relativistically, to the four of spacetime. Such vectors are typically denoted with over arrows ( r → {\displaystyle {\vec {r}}} ), boldface ( p {\displaystyle \mathbf {p} } ) or indices ( v μ {\displaystyle v^{\mu }} ). In quantum mechanics, a quantum state is typically represented as an element of a complex Hilbert space, for example, the infinite-dimensional vector space of all possible wavefunctions (square integrable functions mapping each point of 3D space to a complex number) or some more abstract Hilbert space constructed more algebraically.


In mathematics, a polymatroid is a polytope associated with a submodular function. The notion was introduced by Jack Edmonds in 1970. It is also described as the multiset analogue of the matroid.


In mathematics, a cancellative semigroup (also called a cancellation semigroup) is a semigroup having the cancellation property. In intuitive terms, the cancellation property asserts that from an equality of the form a·b = a·c, where · is a binary operation, one can cancel the element a and deduce the equality b = c. In this case the element being cancelled out is appearing as the left factors of a·b and a·c and hence it is a case of the left cancellation property. The right cancellation property can be defined analogously.


In other languages, verbification is a more regular process. However, such processes often do not qualify as conversion, as they involve changes in the form of the word. For example, in Esperanto, any word can be transformed into a verb, either by altering its ending to -i, or by applying suffixes such as -igi and -iĝi; and in Semitic languages, the process often involves changes of internal vowels, such as the Hebrew word "גגל" (Gigél, "He/it googled"), from the proper noun גוגל (Google). In Toki Pona, any content word may function as a noun, verb or adjective depending on syntax. For example, moku may either mean food or to eat.


In order to store volumes (axis-aligned hyper-boxes) as keys, implementations typically use corner representation which converts the two d {\displaystyle d} -dimensional minimum and maximum corners of a box into a single key with 2 ∗ d {\displaystyle 2*d} dimensions, for example by interleaving them: k = { m i n 0 , m a x 0 , m i n 1 , m a x 1 , . . . , m i n d − 1 , m a x d − 1 } {\displaystyle k=\{min_{0},max_{0},min_{1},max_{1},...,min_{d-1},max_{d-1}\}} .


In mathematics, a cwatset is a set of bitstrings, all of the same length, which is closed with a twist. If each string in a cwatset, C, say, is of length n, then C will be a subset of Z 2 n {\displaystyle \mathbb {Z} _{2}^{n}} . Thus, two strings in C are added by adding the bits in the strings modulo 2 (that is, addition without carry, or exclusive disjunction). The symmetric group on n letters, Sym ( n ) {\displaystyle {\text{Sym}}(n)} , acts on Z 2 n {\displaystyle \mathbb {Z} _{2}^{n}} by bit permutation: p ( ( c 1 , … , c n ) ) = ( c p ( 1 ) , … , c p ( n ) ) , {\displaystyle p((c_{1},\ldots ,c_{n}))=(c_{p(1)},\ldots ,c_{p(n)}),} where c = ( c 1 , … , c n ) {\displaystyle c=(c_{1},\ldots ,c_{n})} is an element of Z 2 n {\displaystyle \mathbb {Z} _{2}^{n}} and p is an element of Sym ( n ) {\displaystyle {\text{Sym}}(n)} .


Starting from the root node, the left or right subtrees are traversed depending on whether the target value is less or more than the node under consideration.In the worst case, binary search makes ⌊ log 2  ( n ) + 1 ⌋ {\textstyle \lfloor \log _{2}(n)+1\rfloor } iterations of the comparison loop, where the ⌊ ⌋ {\textstyle \lfloor \rfloor } notation denotes the floor function that yields the greatest integer less than or equal to the argument, and log 2 {\textstyle \log _{2}} is the binary logarithm. This is because the worst case is reached when the search reaches the deepest level of the tree, and there are always ⌊ log 2  ( n ) + 1 ⌋ {\textstyle \lfloor \log _{2}(n)+1\rfloor } levels in the tree for any binary search. The worst case may also be reached when the target element is not in the array.


The next generation of microprocessors incorporated the clock generation on chip. The 8080 uses a 2 MHz clock but the processing throughput is similar to the 1 MHz 6800. The 8080 requires more clock cycles to execute a processor instruction.


In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f: X → Y and g: Y → Z are composed to yield a function that maps x in domain X to g(f(x)) in codomain Z. Intuitively, if z is a function of y, and y is a function of x, then z is a function of x. The resulting composite function is denoted g ∘ f: X → Z, defined by (g ∘ f )(x) = g(f(x)) for all x in X.The notation g ∘ f is read as "g of f ", "g after f ", "g circle f ", "g round f ", "g about f ", "g composed with f ", "g following f ", "f then g", or "g on f ", or "the composition of g and f ". Intuitively, composing functions is a chaining process in which the output of function f feeds the input of function g. The composition of functions is a special case of the composition of relations, sometimes also denoted by ∘ {\displaystyle \circ } . As a result, all properties of composition of relations are true of composition of functions, such as the property of associativity. Composition of functions is different from multiplication of functions (if defined at all), and has some quite different properties; in particular, composition of functions is not commutative.


After a model is obtained using the data collected, conditional probability is formed for each target contained in the training database. In this example, there are M blocks of data. This will result in a collection of M probabilities for each target in the database.


In the context of this article, a metric is a measurement. A metric that evaluates machine translation output represents the quality of the output. The quality of a translation is inherently subjective, there is no objective or quantifiable "good." Therefore, any metric must assign quality scores so they correlate with the human judgment of quality.


In addition, the semantic web approach is still considered an emerging technology and is not in wide-scale use at this time.One of the current applications of ontology-based search in the biomedical sciences is GoPubMed, which searches the PubMed database of scientific literature. Another use of ontologies is within databases such as SwissProt, Ensembl and TrEMBL, which use this technology to search through the stores of human proteome-related data for tags related to the search term.Some of the research in this field has focused on creating new and specific ontologies. Other researchers have worked on verifying the results of existing ontologies.


Alice and Bob agree that the output of the toss d is the xor of the bits a {\displaystyle a} and b, d = a ⊕ b {\displaystyle d=a\oplus b} . Alice and Bob agree on advance on the values of t0 and t1 in a common reference frame, in such a way that |t0 - t1| < t. Thus, from the principle of no superluminal signalling, at receiving a {\displaystyle a} from A0, B0 cannot send any signal that arrives to B1 before B1 gives b to A1. Therefore, Alice is guaranteed that the bit b is chosen by Bob independently of the bit a {\displaystyle a} chosen by her.


. , k } , ∀ i ∈ { 1 , 2 , .


The commitment made selecting one or another ontology can produce a sharply different view of the task at hand. Consider the difference that arises in selecting the lumped element view of a circuit rather than the electrodynamic view of the same device. As a second example, medical diagnosis viewed in terms of rules (e.g., MYCIN) looks substantially different from the same task viewed in terms of frames (e.g., INTERNIST). Where MYCIN sees the medical world as made up of empirical associations connecting symptom to disease, INTERNIST sees a set of prototypes, in particular prototypical diseases, to be matched against the case at hand.


Class B – Any single vehicle which has a gross vehicle weight rating or gross vehicle weight of 26,001 pounds (11,794 kilograms) or more, or any such vehicle towing a vehicle with a gross vehicle weight rating or gross vehicle weight that does not exceed 10,000 pounds (4,536 kilograms). Class C – Any single vehicle, or combination of vehicles, that does not meet the definition of Class A or Class B, but is either designed to transport 16 or more passengers, including the driver or is transporting material that has been designated as hazardous under 49 U.S.C. 5103 and is required to be placarded under subpart F of 49 CFR Part 172 or is transporting any quantity of a material listed as a select agent or toxin in 42 CFR Part 73.


In mathematical logic, a redundant proof is a proof that has a subset that is a shorter proof of the same result. In other words, a proof is redundant if it has more proof steps than are actually necessary to prove the result. Formally, a proof ψ {\displaystyle \psi } of κ {\displaystyle \kappa } is considered redundant if there exists another proof ψ ′ {\displaystyle \psi ^{\prime }} of κ ′ {\displaystyle \kappa ^{\prime }} such that κ ′ ⊆ κ {\displaystyle \kappa ^{\prime }\subseteq \kappa } (i.e. κ ′ subsumes κ {\displaystyle \kappa ^{\prime }\;{\text{subsumes}}\;\kappa } ) and | ψ ′ | < | ψ | {\displaystyle |\psi ^{\prime }|<|\psi |} where | φ | {\displaystyle |\varphi |} is the number of nodes in φ {\displaystyle \varphi } .


Intel said that the approach Digital Research wished to take in emulating 8086 software in protected mode differed from the original specifications; nevertheless they incorporated into the E-2 step minor changes in the microcode that allowed Digital Research to run emulation mode much faster (see LOADALL). These same limitations affected FlexOS 286 version 1.x, a reengineered derivation of Concurrent DOS 286, which was developed by Digital Research's new Flexible Automation Business Unit in Monterey, California, since 1986. Later versions added compatibility with PC DOS 2.x and 3.x. Known versions include: Concurrent DOS 286 1.0 (1985) Concurrent DOS 286 1.1 (1986-01-07) Concurrent DOS 286 1.2 (1986) FlexOS 286 1.3 (November 1986) FlexOS 286 1.31 (May 1987)


In the decade after Richards' publication, advances in the theory of distributed circuits took place mostly in Japan. K. Kuroda published these identities in 1955 in his Ph.D thesis. However, they did not appear in English until 1958 in a paper by Ozaki and Ishii on stripline filters.


In addition to placing and receiving cellular calls, the touchscreen-equipped Simon could send and receive faxes and emails. It included an address book, calendar, appointment scheduler, calculator, world time clock, and notepad, as well as other visionary mobile applications such as maps, stock reports and news.The IBM Simon was manufactured by Mitsubishi Electric, which integrated features with its own cellular radio technologies. It featured a liquid-crystal display (LCD) and PC Card support. The Simon was commercially unsuccessful, particularly due to its bulky form factor and limited battery life, using NiCad batteries rather than the nickel–metal hydride batteries commonly used in mobile phones in the 1990s, or lithium-ion batteries used in modern smartphones.The term "smart phone" was not coined until a year after the introduction of the Simon, appearing in print as early as 1995, describing AT&T's PhoneWriter Communicator. The term "smartphone" was first used by Ericsson in 1997 to describe a new device concept, the GS88.


For example, the use of upper camel case data element names is a convention used in many standard but is not specified by the XML Schema specification. Naming and Design Rules have become an important aspect of each organizations data exchange standards. Within the United States, Naming and Design Rules standards are recommended for each federal and state agency.


In modern sources, the Adian–Rabin theorem is usually stated as follows:Let P be a Markov property of finitely presentable groups. Then there does not exist an algorithm that, given a finite presentation G = ⟨ X ∣ R ⟩ {\displaystyle G=\langle X\mid R\rangle } , decides whether or not the group G {\displaystyle G} defined by this presentation has property P. The word 'algorithm' here is used in the sense of recursion theory. More formally, the conclusion of Adian–Rabin theorem means that set of all finite presentations ⟨ x 1 , x 2 , x 3 , ⋯ ∣ R ⟩ {\displaystyle \langle x_{1},x_{2},x_{3},\dots \mid R\rangle } (where x 1 , x 2 , x 3 , … {\displaystyle x_{1},x_{2},x_{3},\dots } is a fixed countably infinite alphabet, and R {\displaystyle R} is a finite set of relations in these generators and their inverses) defining groups with property P, is not a recursive set.


In programming, string concatenation generally occurs at run time, as string values are typically not known until run time. However, in the case of string literals, the values are known at compile time, and thus string concatenation can be done at compile time, either via string literal concatenation or via constant folding.


Concurrent Read Exclusive Write (CREW): The same block in main memory can be read by multiple processors concurrently. Only one processor can write to a block at a time. Exclusive Read Exclusive Write (EREW): The same block in main memory cannot be read or written by multiple processors concurrently.