In statistical learning models, the training sample ( x i , y i ) {\displaystyle (x_{i},y_{i})} are assumed to have been drawn from the true distribution p ( x , y ) {\displaystyle p(x,y)} and the objective is to minimize the expected "risk" I  = E  = ∫ V ( f ( x ) , y ) d p ( x , y ) . {\displaystyle I=\mathbb {E} =\int V(f(x),y)\,dp(x,y)\ .} A common paradigm in this situation is to estimate a function f ^ {\displaystyle {\hat {f}}} through empirical risk minimization or regularized empirical risk minimization (usually Tikhonov regularization).


In order to decrypt, we turn the ciphertext back into a vector, then simply multiply by the inverse matrix of the key matrix (IFK/VIV/VMI in letters). We find that, modulo 26, the inverse of the matrix used in the previous example is: ( 6 24 1 13 16 10 20 17 15 ) − 1 ( mod 26 ) ≡ ( 8 5 10 21 8 21 21 12 8 ) {\displaystyle {\begin{pmatrix}6&24&1\\13&16&10\\20&17&15\end{pmatrix}}^{-1}{\pmod {26}}\equiv {\begin{pmatrix}8&5&10\\21&8&21\\21&12&8\end{pmatrix}}} Taking the previous example ciphertext of 'POH', we get: ( 8 5 10 21 8 21 21 12 8 ) ( 15 14 7 ) = ( 260 574 539 ) ≡ ( 0 2 19 ) ( mod 26 ) {\displaystyle {\begin{pmatrix}8&5&10\\21&8&21\\21&12&8\end{pmatrix}}{\begin{pmatrix}15\\14\\7\end{pmatrix}}={\begin{pmatrix}260\\574\\539\end{pmatrix}}\equiv {\begin{pmatrix}0\\2\\19\end{pmatrix}}{\pmod {26}}} which gets us back to 'ACT', as expected. Two complications exist in picking the encrypting matrix: Not all matrices have an inverse. The matrix will have an inverse if and only if its determinant is not zero.


In statistics, inter-rater reliability (also called by various similar names, such as inter-rater agreement, inter-rater concordance, inter-observer reliability, inter-coder reliability, and so on) is the degree of agreement among independent observers who rate, code, or assess the same phenomenon. Assessment tools that rely on ratings must exhibit good inter-rater reliability, otherwise they are not valid tests. There are a number of statistics that can be used to determine inter-rater reliability. Different statistics are appropriate for different types of measurement. Some options are joint-probability of agreement, such as Cohen's kappa, Scott's pi and Fleiss' kappa; or inter-rater correlation, concordance correlation coefficient, intra-class correlation, and Krippendorff's alpha.


This notion has relevance in pure mathematics, as well as in any other field that uses classical logic. Outside of mathematics, statements which can be characterized informally as vacuously true can be misleading. Such statements make reasonable assertions about qualified objects which do not actually exist.


In telecommunications, transparency can refer to: The property of an entity that allows another entity to pass through it without altering either of the entities. The property that allows a transmission system or channel to accept, at its input, unmodified user information, and deliver corresponding user information at its output, unchanged in form or information content. The user information may be changed internally within the transmission system, but it is restored to its original form prior to the output without the involvement of the user. The quality of a data communications system or device that uses a bit-oriented link protocol that does not depend on the bit sequence structure used by the data source.Some communication systems are not transparent.


For example, if a VLIW device has five execution units, then a VLIW instruction for the device has five operation fields, each field specifying what operation should be done on that corresponding execution unit. To accommodate these operation fields, VLIW instructions are usually at least 64 bits wide, and far wider on some architectures.


Thus, all five inferences involving A and B and any of the five values of C may be replaced by the single descriptive inference "(A and B) implies the particular value of D". To establish that the prime implicants or descriptive inferences derived from the data by the QCA method are causal requires establishing the existence of causal mechanism using another method such as process tracing, formal logic, intervening variables, or established multidisciplinary knowledge. The method is used in social science and is based on the binary logic of Boolean algebra, and attempts to ensure that all possible combinations of variables that can be made across the cases under investigation are considered.


They prepare the next generation for school, work, and decision-making. The way in which a child is nurtured at a young age and through adolescence has both psychological and developmental effects that effect their future.


In mathematics, a hyper-finite field is an uncountable field similar in many ways to finite fields. More precisely a field F is called hyper-finite if it is uncountable and quasi-finite, and for every subfield E, every absolutely entire E-algebra (regular field extension of E) of smaller cardinality than F can be embedded in F. They were introduced by Ax (1968). Every hyper-finite field is a pseudo-finite field, and is in particular a model for the first-order theory of finite fields.


In the case that p = 3 the following three matrices H m {\displaystyle \mathbf {H} _{m}} can be chosen H 1 = ( 0 0 0 0 0 − 1 0 1 0 ) {\displaystyle \mathbf {H} _{1}={\begin{pmatrix}0&0&0\\0&0&-1\\0&1&0\end{pmatrix}}} , H 2 = ( 0 0 1 0 0 0 − 1 0 0 ) {\displaystyle \mathbf {H} _{2}={\begin{pmatrix}0&0&1\\0&0&0\\-1&0&0\end{pmatrix}}} , H 3 = ( 0 − 1 0 1 0 0 0 0 0 ) . {\displaystyle \mathbf {H} _{3}={\begin{pmatrix}0&-1&0\\1&0&0\\0&0&0\end{pmatrix}}.} In this particular case, the homogeneous linear equations can be written as 0 =  × A y k {\displaystyle \mathbf {0} =_{\times }\,\mathbf {A} \,\mathbf {y} _{k}} for k = 1 , … , N {\displaystyle \,k=1,\ldots ,N} where  × {\displaystyle _{\times }} is the matrix representation of the vector cross product.


Because the "dits" are created automatically by the pendulum mechanism, but the "dahs" are keyed the old-fashioned way, the keys are called "semi-automatic". (Modern electronic keyers create both the "dits" and the "dahs" automatically, as long as one of the switches is in contact, and are called "fully-automatic".)


In probability theory, one may describe the distribution of a random variable as belonging to a family of probability distributions, distinguished from each other by the values of a finite number of parameters. For example, one talks about "a Poisson distribution with mean value λ". The function defining the distribution (the probability mass function) is: f ( k ; λ ) = e − λ λ k k ! .


{\displaystyle k!} permutations so P k n = C k n × k ! {\displaystyle P_{k}^{n}=C_{k}^{n}\times k!}


Such mixture problem are often formulated with normalized constraints, so that the nonnegative components sum to one, in which case the feasible region forms a simplex. The quality of the bread mixtures can be estimated using response surface methodology, and then a local maximum can be computed using a nonlinear programming method, such as sequential quadratic programming. In operations research, linear programming problems can be solved by the simplex algorithm of George Dantzig.


In mathematics, a nonempty collection of sets is called a 𝜎-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation.


In mathematics, a chaos machine is a class of algorithms constructed on the base of chaos theory (mainly deterministic chaos) to produce pseudo-random oracle. It represents the idea of creating a universal scheme with modular design and customizable parameters, which can be applied wherever randomness and sensitiveness is needed.Theoretical model was published in early 2015 by Maciej A. Czyzewski. It was designed specifically to combine the benefits of hash function and pseudo-random function. However, it can be used to implement many cryptographic primitives, including cryptographic hashes, message authentication codes and randomness extractors.


In mathematics, a factorisation of a free monoid is a sequence of subsets of words with the property that every word in the free monoid can be written as a concatenation of elements drawn from the subsets. The Chen–Fox–Lyndon theorem states that the Lyndon words furnish a factorisation. The Schützenberger theorem relates the definition in terms of a multiplicative property to an additive property.Let A* be the free monoid on an alphabet A. Let Xi be a sequence of subsets of A* indexed by a totally ordered index set I. A factorisation of a word w in A* is an expression w = x i 1 x i 2 ⋯ x i n {\displaystyle w=x_{i_{1}}x_{i_{2}}\cdots x_{i_{n}}\ } with x i j ∈ X i j {\displaystyle x_{i_{j}}\in X_{i_{j}}} and i 1 ≥ i 2 ≥ … ≥ i n {\displaystyle i_{1}\geq i_{2}\geq \ldots \geq i_{n}} . Some authors reverse the order of the inequalities.


In plane geometry the Kovner–Besicovitch measure is a number defined for any bounded convex set describing how close to being centrally symmetric it is. It is the fraction of the area of the set that can be covered by its largest centrally symmetric subset.


In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimension. Matrices are used in most areas of mathematics and most scientific fields, either directly, or through their use in geometry and numerical analysis. Matrix theory is the branch of mathematics that focuses on the study of matrices. It was initially a sub-branch of linear algebra, but soon grew to include subjects related to graph theory, algebra, combinatorics and statistics.


In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968.


Other allowed signs are 1010 (A) and 1110 (E) for positive and 1011 (B) for negative. IBM System/360 processors will use the 1010 (A) and 1011 (B) signs if the A bit is set in the PSW, for the ASCII-8 standard that never passed. Most implementations also provide unsigned BCD values with a sign nibble of 1111 (F).


For instance, i was coded as "2", but d was coded as "222". Myer's 1866 manual also includes a 3-element fixed length code using four elements, and the 1872 manual has a 3-element fixed length code using three elements. There is little sign that these codes were widely used. The 1872 manual includes a variable length code using four elements which Myer says was used by the Army, but is superseded.


In mathematics, the notion of a divisor originally arose within the context of arithmetic of whole numbers. With the development of abstract rings, of which the integers are the archetype, the original notion of divisor found a natural extension. Divisibility is a useful concept for the analysis of the structure of commutative rings because of its relationship with the ideal structure of such rings.


In state space search, a state space is formally represented as a tuple S: ⟨ S , A , A c t i o n ( s ) , R e s u l t ( s , a ) , C o s t ( s , a ) ⟩ {\displaystyle S:\langle S,A,Action(s),Result(s,a),Cost(s,a)\rangle } , in which: S {\displaystyle S} is the set of all possible states; A {\displaystyle A} is the set of possible actions, not related to a particular state but regarding all the state space; A c t i o n ( s ) {\displaystyle Action(s)} is the function that establish which action is possible to perform in a certain state; R e s u l t ( s , a ) {\displaystyle Result(s,a)} is the function that returns the state reached performing action a {\displaystyle a} in state s {\displaystyle s} C o s t ( s , a ) {\displaystyle Cost(s,a)} is the cost of performing an action a {\displaystyle a} in state s {\displaystyle s} . In many state spaces a is a constant, but this is not always true.


In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms.


In the fourth standard, "unification criteria for maintaining compatibility with previous standards" (過去の規格との互換性を維持するための包摂規準, kako no kikaku to no gokansei wo iji suru tame no hōsetsu kijun) is defined. Their application is limited to 29 code points whose glyphs vary greatly between the standards JIS C 6226-1983 on and after and JIS C 6226-1978. For those 29 code points, the glyphs from JIS C 6226-1983 on and after are displayed as "A", and the glyphs from JIS C 6226-1978 as "B". On each of them, both "A" and "B" glyphs may be applied. However, in order to claim compatibility with the standard, whether the "A" or "B" form has been used for each code point must be explicitly noted.


In software engineering and development, a software metric is a standard of measure of a degree to which a software system or process possesses some property. Even if a metric is not a measurement (metrics are functions, while measurements are the numbers obtained by the application of metrics), often the two terms are used as synonyms. Since quantitative measurements are essential in all sciences, there is a continuous effort by computer science practitioners and theoreticians to bring similar approaches to software development. The goal is obtaining objective, reproducible and quantifiable measurements, which may have numerous valuable applications in schedule and budget planning, cost estimation, quality assurance, testing, software debugging, software performance optimization, and optimal personnel task assignments.


In some parts of the world, such as the UK and Commonwealth countries, 999 (pronounced as 9-9-9) is the emergency telephone number. 999 was a London punk band active during the 1970s. 999 is also the short name for the visual novel Nine Hours, Nine Persons, Nine Doors. 999 is the last 3 digit number. == References ==


Hence, "binary data" in computers are actually sequences of bytes. On a higher level, data is accessed in groups of 1 word (4 bytes) for 32-bit systems and 2 words for 64-bit systems. In applied computer science and in the information technology field, the term binary data is often specifically opposed to text-based data, referring to any sort of data that cannot be interpreted as text.


In the notation above, P is the set X, Q is a collection S of subsets of X, R is the binary relation "is contained in" between elements and subsets, and R−1 restricted to Q × P* is the function "contains" from subsets to selected elements. Whereas an exact cover problem involves selecting subsets and the relation "contains" from subsets to elements, an exact hitting set problem involves selecting elements and the relation "is contained in" from elements to subsets. In a sense, an exact hitting set problem is the inverse of the exact cover problem involving the same set and collection of subsets.


Religious vows are of two varieties: simple vows and solemn vows. The highest level of commitment is exemplified by those who have taken their solemn, perpetual vows. There once were significant technical differences between them in canon law; but these differences were suppressed by the current Code of Canon Law in 1983, although the nominal distinction is maintained.


In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of the molecule.


Yet the output is: i=54, a=1.000000 Another example is: Take 2 numbers: 2.56 × 10 0 {\displaystyle 2.56\times 10^{0}} and 2.34 × 10 2 {\displaystyle 2.34\times 10^{2}} we bring the first number to the same power of 10 {\displaystyle 10} as the second one: 0.0256 × 10 2 {\displaystyle 0.0256\times 10^{2}} The addition of the 2 numbers is: 0.0256*10^2 2.3400*10^2 + ____________ 2.3656*10^2 After padding the second number (i.e., 2.34 × 10 2 {\displaystyle 2.34\times 10^{2}} ) with two 0 {\displaystyle 0} s, the bit after 4 {\displaystyle 4} is the guard digit, and the bit after is the round digit. The result after rounding is 2.37 {\displaystyle 2.37} as opposed to 2.36 {\displaystyle 2.36} , without the extra bits (guard and round bits), i.e., by considering only 0.02 + 2.34 = 2.36 {\displaystyle 0.02+2.34=2.36} . The error therefore is 0.01 {\displaystyle 0.01} .


But all nullary constructors, thus all monomorphic types, have the same, simplest kind; namely ∗ {\displaystyle *} . Since higher-order type operators are uncommon in programming languages, in most programming practice, kinds are used to distinguish between data types and the types of constructors which are used to implement parametric polymorphism. Kinds appear, either explicitly or implicitly, in languages whose type systems account for parametric polymorphism in a programmatically accessible way, such as C++, Haskell and Scala.


In the latter case, it may use either a transport layer virtual circuit protocol such as the TCP protocol, allowing data to be delivered in order. Although the lower-layer switching is connectionless, or it may be a data link layer or network layer switching mode, where all data packets belonging to the same traffic stream are delivered over the same path, and traffic flows are identified by some connection identifier reducing the overhead of routing decisions on a packet-by-packet basis for the network. Connection-oriented protocol services are often, but not always, reliable network services that provide acknowledgment after successful delivery and automatic repeat request functions in case of missing or corrupted data.


In natural language processing (NLP), a word embedding is a representation of a word. The embedding is used in text analysis. Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that words that are closer in the vector space are expected to be similar in meaning. Word embeddings can be obtained using language modeling and feature learning techniques, where words or phrases from the vocabulary are mapped to vectors of real numbers. Methods to generate this mapping include neural networks, dimensionality reduction on the word co-occurrence matrix, probabilistic models, explainable knowledge base method, and explicit representation in terms of the context in which words appear.Word and phrase embeddings, when used as the underlying input representation, have been shown to boost the performance in NLP tasks such as syntactic parsing and sentiment analysis.


In psychology, cognitive science, and in neuroscience, there have been two main approaches for describing how humans perceive and classify emotion: continuous or categorical. The continuous approach tends to use dimensions such as negative vs. positive, calm vs. aroused. The categorical approach tends to use discrete classes such as happy, sad, angry, fearful, surprise, disgust. Different kinds of machine learning regression and classification models can be used for having machines produce continuous or discrete labels. Sometimes models are also built that allow combinations across the categories, e.g. a happy-surprised face or a fearful-surprised face.The following sections consider many of the kinds of input data used for the task of emotion recognition.


For example, there are Hands-Free Profile (HFP) 1.5 implementations using both Bluetooth 2.0 and Bluetooth 1.2 core specifications. The way a device uses Bluetooth depends on its profile capabilities. The profiles provide standards that manufacturers follow to allow devices to use Bluetooth in the intended manner.


In practice, it may be necessary to regularize the whitened STA, since whitening amplifies noise along stimulus dimensions that are poorly explored by the stimulus (i.e., axes along which the stimulus has low variance). A common approach to this problem is ridge regression. The regularized STA, computed using ridge regression, can be written S T A r i d g e = T n s p ( X T X + λ I ) − 1 X T y , {\displaystyle \mathrm {STA} _{ridge}={\tfrac {T}{n_{sp}}}\left(X^{T}X+\lambda I\right)^{-1}X^{T}\mathbf {y} ,} where I {\displaystyle I} denotes the identity matrix and λ {\displaystyle \lambda } is the ridge parameter controlling the amount of regularization. This procedure has a simple Bayesian interpretation: ridge regression is equivalent to placing a prior on the STA elements that says they are drawn i.i.d. from a zero-mean Gaussian prior with covariance proportional to the identity matrix. The ridge parameter sets the inverse variance of this prior, and is usually fit by cross-validation or empirical Bayes.


The branch operated for some time. On 1 September 1932, 27-year-old Polish mathematician Marian Rejewski and two fellow Poznań University mathematics graduates, Henryk Zygalski and Jerzy Różycki, joined the Bureau full-time and moved to Warsaw. Their first task was to reconstruct a four-letter German naval cipher.Near the end of 1932 Rejewski was asked to work a couple of hours a day on breaking the Enigma.


The stream nomenclature alludes to a physical setup in which the observers are physically separated and have no control over the emitted events from the subject/stream source. This pattern thus suits any process by which data arrives from some input that is not available to the CPU at startup, but instead arrives seemingly at random (HTTP requests, GPIO data, user input from peripherals, distributed databases and blockchains, etc.). Most modern programming languages comprise built-in event constructs implementing the observer-pattern components. While not mandatory, most observer implementations use background threads listening for subject events and other support mechanisms provided by the kernel.


In the decision-making process, optimisation is almost always intractable in any implementation, whether machine or neural. Because of this, defined parameters or boundaries must be implemented in the process in order to achieve an acceptable outcome. This method is known as applying bounded rationality, where an individual makes a collective and rational choice that considers “the limits of human capability to calculate, the severe deficiencies of human knowledge about the consequences of choice, and the limits of human ability to adjudicate among multiple goals”. They are essentially incorporating a series of criteria, referred to as alternatives for choice. These alternatives are often not initially given to the decision maker, so a theory of search is also incorporated.


In mathematics, the signature defect of a singularity measures the correction that a singularity contributes to the signature theorem. Hirzebruch (1973) introduced the signature defect for the cusp singularities of Hilbert modular surfaces. Michael Francis Atiyah, H. Donnelly, and I. M. Singer (1983) defined the signature defect of the boundary of a manifold as the eta invariant, the value as s = 0 of their eta function, and used this to show that Hirzebruch's signature defect of a cusp of a Hilbert modular surface can be expressed in terms of the value at s = 0 or 1 of a Shimizu L-function.


Sometimes only constraints on distribution are known; one can then use the principle of maximum entropy to determine a single distribution, the one with the greatest entropy given the constraints. (Analogously, in the specific context of a dynamic Bayesian network, the conditional distribution for the hidden state's temporal evolution is commonly specified to maximize the entropy rate of the implied stochastic process.) Often these conditional distributions include parameters that are unknown and must be estimated from data, e.g., via the maximum likelihood approach.


Euler's totient function is a multiplicative function, meaning that if two numbers m and n are relatively prime, then φ(mn) = φ(m)φ(n). This function gives the order of the multiplicative group of integers modulo n (the group of units of the ring Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } ). It is also used for defining the RSA encryption system.


In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally, a PIT algorithm is given an arithmetic circuit that computes a polynomial p in a field, and decides whether p is the zero polynomial. Determining the computational complexity required for polynomial identity testing is one of the most important open problems in algebraic computing complexity.


In software engineering, a monolithic application is a single unified software application which is self-contained and independent from other applications, but typically lacks flexibility. There are advantages and disadvantages of building applications in a monolithic style of software architecture, depending on requirements. Alternative styles to monolithic applications include multitier architectures, distributed computing and microservices. The design philosophy is that the application is responsible not just for a particular task, but can perform every step needed to complete a particular function.


In its simplest and most naïve form, this way of analyzing word forms, called "item-and-arrangement", treats words as if they were made of morphemes put after each other ("concatenated") like beads on a string. More recent and sophisticated approaches, such as distributed morphology, seek to maintain the idea of the morpheme while accommodating non-concatenated, analogical, and other processes that have proven problematic for item-and-arrangement theories and similar approaches. Morpheme-based morphology presumes three basic axioms: Baudouin's "single morpheme" hypothesis: Roots and affixes have the same status as morphemes.


In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", or "for any". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable.


. . , m i n d − 1 , m i n d − 1 } {\displaystyle k_{min}=\{min_{0},min_{0},min_{1},min_{1},...,min_{d-1},min_{d-1}\}} k m a x = { m a x 0 , m a x 0 , m a x 1 , m a x 1 , .


The doubly extreme case ' ⊢ ', where both the antecedent and consequent lists of formulas are empty is "not satisfiable". In this case, the meaning of the sequent is effectively ' ⊤ ⊢ ⊥ '. This is equivalent to the sequent ' ⊢ ⊥ ', which clearly cannot be valid.


In mathematics, a semigroupoid (also called semicategory, naked category or precategory) is a partial algebra that satisfies the axioms for a small category, except possibly for the requirement that there be an identity at each object. Semigroupoids generalise semigroups in the same way that small categories generalise monoids and groupoids generalise groups. Semigroupoids have applications in the structural theory of semigroups. Formally, a semigroupoid consists of: a set of things called objects.


These curves are defined to satisfy conformal invariance and a domain Markov property. It was discovered by Oded Schramm (2000) as a conjectured scaling limit of the planar uniform spanning tree (UST) and the planar loop-erased random walk (LERW) probabilistic processes, and developed by him together with Greg Lawler and Wendelin Werner in a series of joint papers. Besides UST and LERW, the Schramm–Loewner evolution is conjectured or proven to describe the scaling limit of various stochastic processes in the plane, such as critical percolation, the critical Ising model, the double-dimer model, self-avoiding walks, and other critical statistical mechanics models that exhibit conformal invariance.


In more formal probability theory, a random variable is a function X defined from a sample space Ω to a measurable space called the state space. If an element in Ω is mapped to an element in state space by X, then that element in state space is a realization. Elements of the sample space can be thought of as all the different possibilities that could happen; while a realization (an element of the state space) can be thought of as the value X attains when one of the possibilities did happen. Probability is a mapping that assigns numbers between zero and one to certain subsets of the sample space, namely the measurable subsets, known here as events. Subsets of the sample space that contain only one element are called elementary events. The value of the random variable (that is, the function) X at a point ω ∈ Ω, x = X ( ω ) {\displaystyle x=X(\omega )} is called a realization of X.


In the article A Universal Data Compression System, Rissanen introduced a consistent algorithm to estimate the probabilistic context tree that generates the data. This algorithm's function can be summarized in two steps: Given the sample produced by a chain with memory of variable length, we start with the maximum tree whose branches are all the candidates to contexts to the sample; The branches in this tree are then cut until you obtain the smallest tree that's well adapted to the data. Deciding whether or not shortening the context is done through a given gain function, such as the ratio of the log-likelihood.Be X 0 , … , X n − 1 {\displaystyle X_{0},\ldots ,X_{n-1}} a sample of a finite probabilistic tree ( τ , p ) {\displaystyle (\tau ,p)} . For any sequence x − j − 1 {\displaystyle x_{-j}^{-1}} with j ≤ n {\displaystyle j\leq n} , it is possible to denote by N n ( x − j − 1 ) {\displaystyle N_{n}(x_{-j}^{-1})} the number of occurrences of the sequence in the sample, i.e., N n ( x − j − 1 ) = ∑ t = 0 n − j 1 { X t t + j − 1 = x − j − 1 } {\displaystyle N_{n}(x_{-j}^{-1})=\sum _{t=0}^{n-j}\mathbf {1} \left\{X_{t}^{t+j-1}=x_{-j}^{-1}\right\}} Rissanen first built a context maximum candidate, given by X n − K ( n ) n − 1 {\displaystyle X_{n-K(n)}^{n-1}} , where K ( n ) = C log  n {\displaystyle K(n)=C\log {n}} and C {\displaystyle C} is an arbitrary positive constant.


In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the same base. In the case of numbers that are not square-free, the factorization is written without exponents, writing the repeated factor as many times as needed. Smith numbers were named by Albert Wilansky of Lehigh University, as he noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith: 4937775 = 3 · 5 · 5 · 65837while 4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + (6 + 5 + 8 + 3 + 7)in base 10.


In technical communication, topic-based authoring is a modular approach to content creation where content is structured around topics that can be mixed and reused in different contexts. It is defined in contrast with book-oriented or narrative content, written in the linear structure of written books.Topic-based authoring is popular in the technical publications and documentation arenas, as it is especially suitable for technical documentation. Tools supporting this approach typically store content in XHTML or other XML formats and support content reuse, management, and the dynamic assembly of personalized information.


In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms.


Sepp Hochreiter analyzed the vanishing gradient problem in 1991 and attributed to it the reason why deep learning did not work well. To overcome this problem, Long Short-Term Memory (LSTM) recurrent neural networks had skip connections or residual connections with a weight of 1.0 in every LSTM cell (called the constant error carrousel) to compute y t + 1 = F ( x t ) + x t {\textstyle y_{t+1}=F(x_{t})+x_{t}} . During backpropagation through time, this becomes the above-mentioned residual formula y = F ( x ) + x {\textstyle y=F(x)+x} for feedforward neural networks.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 25, 125, 245, and 1245 are the patterns related to Braille pattern dots-14, since the two additional dots of kantenji patterns 014, 147, and 0147 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In mathematics, Hua's lemma, named for Hua Loo-keng, is an estimate for exponential sums. It states that if P is an integral-valued polynomial of degree k, ε {\displaystyle \varepsilon } is a positive real number, and f a real function defined by f ( α ) = ∑ x = 1 N exp  ( 2 π i P ( x ) α ) , {\displaystyle f(\alpha )=\sum _{x=1}^{N}\exp(2\pi iP(x)\alpha ),} then ∫ 0 1 | f ( α ) | λ d α ≪ P , ε N μ ( λ ) {\displaystyle \int _{0}^{1}|f(\alpha )|^{\lambda }d\alpha \ll _{P,\varepsilon }N^{\mu (\lambda )}} ,where ( λ , μ ( λ ) ) {\displaystyle (\lambda ,\mu (\lambda ))} lies on a polygonal line with vertices ( 2 ν , 2 ν − ν + ε ) , ν = 1 , … , k . {\displaystyle (2^{\nu },2^{\nu }-\nu +\varepsilon ),\quad \nu =1,\ldots ,k.} == References ==


The multinomial distribution models the outcome of n experiments, where the outcome of each trial has a categorical distribution, such as rolling a k-sided die n times. Let k be a fixed finite number. Mathematically, we have k possible mutually exclusive outcomes, with corresponding probabilities p1, ..., pk, and n independent trials.


Third, find all covers of cardinality k {\displaystyle k} that do not violate the budget. Using these covers of cardinality k {\displaystyle k} as starting points, apply the modified greedy algorithm, maintaining the best cover found so far. Call this cover H 2 {\displaystyle H_{2}} .


Consequently, a random integer with at most 2n digits (for large enough n) is about half as likely to be prime as a random integer with at most n digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime (log(101000) ≈ 2302.6), whereas among positive integers of at most 2000 digits, about one in 4600 is prime (log(102000) ≈ 4605.2). In other words, the average gap between consecutive prime numbers among the first N integers is roughly log(N).


In technology, agile development involves teams self-managing to a large extent (though agile development is commonly still practiced within a hierarchical organization, which means that certain types of decisions such as hiring, firing, and pay raises remain the prerogative of managers). In scrum, an agile framework, team members assign work to be done among themselves, either by free choice or by consensus. The scrum master role in scrum is not a management role as such, but is a role that involves helping remove obstacles to progress and ensuring that the basic scrum framework is adhered to by all parties, inside and outside the team - both aspects of the role being more akin to facilitation than to top-down micromanagement. Agile frameworks such as scrum have also begun being used in non-technology companies and organizations.


In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on n {\displaystyle n} -dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} by the Euclidean metric.


For example, to indicate the product of binomials, parentheses are usually used, thus: ( 2 x + 3 ) ( 3 x + 4 ) {\displaystyle (2x+3)(3x+4)} . But if one of the binomials itself contains parentheses, as in ( 2 ( a + b ) + 3 ) {\displaystyle (2(a+b)+3)} one or more pairs of parentheses may be replaced by brackets, thus:   {\displaystyle } . Beyond elementary mathematics, brackets are mostly used for other purposes, e.g. to denote a closed interval, or an equivalence class, so they appear rarely for grouping.


In organization development, the initial phase within the Cognitive work analysis (CWA) framework is Work Domain Analysis. It provides a description of the constraints that govern the purpose and the function of the systems under analysis.


In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindström in 1966. They were later studied for their applications in logic in computer science and database query languages.


In software engineering, CI/CD or CICD is the combined practices of continuous integration (CI) and continuous delivery (CD) or, less often, continuous deployment. They are sometimes referred to collectively as continuous development or continuous software development.


In number theory, the Elkies trinomial curves are certain hyperelliptic curves constructed by Noam Elkies which have the property that rational points on them correspond to trinomial polynomials giving an extension of Q with particular Galois groups. One curve, C168, gives Galois group PSL(2,7) from a polynomial of degree seven, and the other, C1344, gives Galois group AL(8), the semidirect product of a 2-elementary group of order eight acted on by PSL(2, 7), giving a transitive permutation subgroup of the symmetric group on eight roots of order 1344. The equation of the curve C168 is: y 2 = x ( 81 x 5 + 396 x 4 + 738 x 3 + 660 x 2 + 269 x + 48 ) {\displaystyle y^{2}=x(81x^{5}+396x^{4}+738x^{3}+660x^{2}+269x+48)} The curve is a plane algebraic curve model for a Galois resolvent for the trinomial polynomial equation x7 + bx + c = 0. If there exists a point (x, y) on the (projectivized) curve, there is a corresponding pair (b, c) of rational numbers, such that the trinomial polynomial either factors or has Galois group PSL(2,7), the finite simple group of order 168.


In parallel computing, the fork–join model is a way of setting up and executing parallel programs, such that execution branches off in parallel at designated points in the program, to "join" (merge) at a subsequent point and resume sequential execution. Parallel sections may fork recursively until a certain task granularity is reached. Fork–join can be considered a parallel design pattern. : 209 ff. It was formulated as early as 1963.By nesting fork–join computations recursively, one obtains a parallel version of the divide and conquer paradigm, expressed by the following generic pseudocode: solve(problem): if problem is small enough: solve problem directly (sequential algorithm) else: for part in subdivide(problem) fork subtask to solve(part) join all subtasks spawned in previous loop return combined results


{\displaystyle \|B\|=\sup\{|B(x_{1},x_{2})|:\|x_{i}\|_{\infty }\leq 1\}.} The exponent 4/3 is optimal, i.e., cannot be improved by a smaller exponent. It is also known that for real scalars the aforementioned constant is sharp.


As of April 2011 O2 will unlock any of their pay-monthly phones for free, even if they're still in contract, with the exception of handsets made exclusively for them, such as their Palm devices.Carphone Warehouse, one of the largest UK phone retailers, offers unlocked phones with most PAYG deals. As of January 1, 2014, all phones sold by 3 UK are unlocked. Phones bought before this date will be unlocked for free.On 17 December 2019, Ofcom announced that it would explore a mandate banning SIM locking. On 27 October 2020, The UK's mobile networks are to be forbidden from selling phones locked to their services from December 2021.


In number theory, a totative of a given positive integer n is an integer k such that 0 < k ≤ n and k is coprime to n. Euler's totient function φ(n) counts the number of totatives of n. The totatives under multiplication modulo n form the multiplicative group of integers modulo n.


In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension.


In programming languages, ad hoc polymorphism is a kind of polymorphism in which polymorphic functions can be applied to arguments of different types, because a polymorphic function can denote a number of distinct and potentially heterogeneous implementations depending on the type of argument(s) to which it is applied. When applied to object-oriented or procedural concepts, it is also known as function overloading or operator overloading. The term ad hoc in this context is not intended to be pejorative; it refers simply to the fact that this type of polymorphism is not a fundamental feature of the type system. This is in contrast to parametric polymorphism, in which polymorphic functions are written without mention of any specific type, and can thus apply a single abstract implementation to any number of types in a transparent way. This classification was introduced by Christopher Strachey in 1967.


In probability and statistics, the generalized integer gamma distribution (GIG) is the distribution of the sum of independent gamma distributed random variables, all with integer shape parameters and different rate parameters. This is a special case of the generalized chi-squared distribution. A related concept is the generalized near-integer gamma distribution (GNIG).


But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented. Other categorizations have been proposed. For example, Mosteller and Tukey (1977) distinguished grades, ranks, counted fractions, counts, amounts, and balances.


In computer-assisted translation, a technique called fuzzy matching is used to find the most likely translation of a piece of text, using previous translated texts as a basis. In hypnotherapy, fuzzy language is deliberately used for the purpose of trance induction. Hypnotic suggestions are often couched in a somewhat vague, general or ambiguous language requiring interpretation by the subject.


By dividing a high-rate data stream into numerous low-rate data streams, OFDM enables longer duration symbols. A cyclic prefix (CP) may be inserted to create a (time) guard interval that prevents ISI entirely.


In the distributed memory model, each processing entity has its own memory. Because of this, processing entities must send and receive messages to each other to share its local data or get access to remote data.


In the first stage logico-linguistic modeling uses SSM for systems analysis. This stage seeks to structure the problem in the client organization by identifying stakeholders, modelling organizational objectives and discussing possible solutions. At this stage it not assumed that a KBS will be a solution and logico-linguistic modeling often produces solutions that do not require a computerized KBS.


In RLNC, it will randomly choose two coding coefficients, d 1 {\displaystyle d_{1}} and d 2 {\displaystyle d_{2}} in the example. The node will multiply each symbol of packet f {\displaystyle f} by d 1 {\displaystyle d_{1}} , and each symbol of packet e {\displaystyle e} by d 2 {\displaystyle d_{2}} . Then, it will add the results symbol-wise to produce the new coded data. It will perform the same operations of multiplication and addition to the coding coefficients of the coded packets.


In order for the whole system to work, one has to postulate that: ∀ m ∈ M , I D ∈ { 0 , 1 } ∗: D e c r y p t ( E x t r a c t ( P , K m , I D ) , P , E n c r y p t ( P , m , I D ) ) = m {\displaystyle \forall m\in {\mathcal {M}},ID\in \left\{0,1\right\}^{*}:\mathrm {Decrypt} \left(\mathrm {Extract} \left({\mathcal {P}},K_{m},ID\right),{\mathcal {P}},\mathrm {Encrypt} \left({\mathcal {P}},m,ID\right)\right)=m}


The constrained optimization leads to the Marshallian demand function: x ∗ ( p 1 , p 2 , I ) = ( α I ( α + β ) p 1 , β I ( α + β ) p 2 ) . {\displaystyle x^{*}(p_{1},p_{2},I)=\left({\frac {\alpha I}{(\alpha +\beta )p_{1}}},{\frac {\beta I}{(\alpha +\beta )p_{2}}}\right).} 2.


High-performance FFT implementations make many modifications to the implementation of such an algorithm compared to this simple pseudocode. For example, one can use a larger base case than N=1 to amortize the overhead of recursion, the twiddle factors exp   {\displaystyle \exp} can be precomputed, and larger radices are often used for cache reasons; these and other optimizations together can improve the performance by an order of magnitude or more. (In many textbook implementations the depth-first recursion is eliminated in favor of a nonrecursive breadth-first approach, although depth-first recursion has been argued to have better memory locality.) Several of these ideas are described in further detail below.


In proof theory, proof nets are a geometrical method of representing proofs that eliminates two forms of bureaucracy that differentiate proofs: (A) irrelevant syntactical features of regular proof calculi, and (B) the order of rules applied in a derivation. In this way, the formal properties of proof identity correspond more closely to the intuitively desirable properties. Proof nets were introduced by Jean-Yves Girard. This distinguishes proof nets from regular proof calculi such as the natural deduction calculus and the sequent calculus, where these phenomena are present. For instance, these two linear logic proofs are identical: And their corresponding nets will be the same.


In mobile telephony GSM 03.38 or 3GPP 23.038 is a character encoding used in GSM networks for SMS (Short Message Service), CB (Cell Broadcast) and USSD (Unstructured Supplementary Service Data). The 3GPP TS 23.038 standard (originally GSM recommendation 03.38) defines GSM 7-bit default alphabet which is mandatory for GSM handsets and network elements, but the character set is suitable only for English and a number of Western-European languages. Languages such as Chinese, Korean or Japanese must be transferred using the 16-bit UCS-2 character encoding. A limited number of languages, like Portuguese, Spanish, Turkish and a number of languages used in India written with a Brahmic scripts may use 7-bit encoding with national language shift table defined in 3GPP 23.038. For binary messages, 8-bit encoding is used.


In recent times, cache control instructions have become less popular as increasingly advanced application processor designs from Intel and ARM devote more transistors to accelerating code written in traditional languages, e.g., performing automatic prefetch, with hardware to detect linear access patterns on the fly. However the techniques may remain valid for throughput-oriented processors, which have a different throughput vs latency tradeoff, and may prefer to devote more area to execution units.


As regards English, there are many verb forms and constructions which combine time reference with continuous and/or perfect aspect, and with indicative, subjunctive or conditional mood. Particularly in some English language teaching materials, some or all of these forms can be referred to simply as tenses (see below).


In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a sketch can be used to speed up explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numerical linear algebra algorithms.


In the area of Wireless Communications one main application is to facilitate wireless access, such as 5G and WiFi simultaneously from the same antenna. In other words, radio signals are carried over fiber-optic cable. Thus, a single antenna can receive any and all radio signals (5G, Wifi, cell, etc..) carried over a single-fiber cable to a central location where equipment then converts the signals; this is opposed to the traditional way where each protocol type (5G, WiFi, cell) requires separate equipment at the location of the antenna.Although radio transmission over fiber is used for multiple purposes, such as in cable television (CATV) networks and in satellite base stations, the term RoF is usually applied when this is done for wireless access. In RoF systems, wireless signals are transported in optical form between a central station and a set of base stations before being radiated through the air.


c_cc is zero and c_cc is non-zero In this case, the data in the buffer are "available for reading" after the specified number of characters have been received in the buffer. In other words, read() waits for a minimum amount of data (which may be larger than what the caller is prepared to read in the system call), will not return zero data, and may wait indefinitely. c_cc and c_cc are both non-zero In this case, the data in the buffer are "available for reading" after the specified number of characters have been received in the buffer or the timeout has expired since the last character was entered. There is no timeout for the very first character. In other words, read() waits for a minimum amount of data (which may be larger than what the caller is prepared to read in the system call), will not return zero data, may wait indefinitely, but won't wait longer than the specified timeout if at least one character is in the buffer to be read.


Also, having chosen such e {\displaystyle e} , it is simpler to test whether gcd ( e , p − 1 ) = 1 {\displaystyle \gcd(e,p-1)=1} and gcd ( e , q − 1 ) = 1 {\displaystyle \gcd(e,q-1)=1} while generating and testing the primes in step 1 of the key generation. Values of p {\displaystyle p} or q {\displaystyle q} that fail this test can be rejected there and then. (Even better: if e is prime and greater than 2, then the test p mod e ≠ 1 {\displaystyle p{\bmod {e}}\neq 1} can replace the more expensive test gcd ( p − 1 , e ) = 1 {\displaystyle \gcd(p-1,e)=1} .)


Similarly, the Boolean is the type with two values. The unit type is implemented in most functional programming languages. The void type that is used in some imperative programming languages serves some of its functions, but because its carrier set is empty, it has some limitations (as detailed below).


In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain (PID) can be uniquely decomposed in much the same way that integers have a prime factorization. The result provides a simple framework to understand various canonical form results for square matrices over fields.


Oltra-Massuet and Arregi (2005) argue that the metrical structure, as well, makes reference to hierarchical syntactic structure in Spanish. The extent of the interaction between the syntax and phonology at the interface is a matter of current debate. == Notes ==


In pseudocode: if error is True then set x to 0 In guarded command language: if error → x := 0 □ ¬ {\displaystyle \neg } error → skip fi If the second guard is omitted and error is False, the result is abort.


The earliest uses of the method of infinite descent appear in Euclid's Elements. A typical example is Proposition 31 of Book 7, in which Euclid proves that every composite integer is divided (in Euclid's terminology "measured") by some prime number.The method was much later developed by Fermat, who coined the term and often used it for Diophantine equations. Two typical examples are showing the non-solvability of the Diophantine equation r 2 + s 4 = t 4 {\displaystyle r^{2}+s^{4}=t^{4}} and proving Fermat's theorem on sums of two squares, which states that an odd prime p can be expressed as a sum of two squares when p ≡ 1 ( mod 4 ) {\displaystyle p\equiv 1{\pmod {4}}} (see Modular arithmetic and proof by infinite descent).


In short, a network is in system optimum (SO) when the total system cost is the minimum among all possible assignments. System Optimum is based on the assumption that routes of all vehicles would be controlled by the system, and that rerouting would be based on maximum utilization of resources and minimum total system cost. (Cost can be interpreted as travel time.) Hence, in a System Optimum routing algorithm, all routes between a given OD pair have the same marginal cost.


In the worst case, merge sort uses approximately 39% fewer comparisons than quicksort does in its average case, and in terms of moves, merge sort's worst case complexity is O(n log n) - the same complexity as quicksort's best case.Merge sort is more efficient than quicksort for some types of lists if the data to be sorted can only be efficiently accessed sequentially, and is thus popular in languages such as Lisp, where sequentially accessed data structures are very common. Unlike some (efficient) implementations of quicksort, merge sort is a stable sort. Merge sort's most common implementation does not sort in place; therefore, the memory size of the input must be allocated for the sorted output to be stored in (see below for variations that need only n/2 extra spaces).


Notably, the addition operation, logadd (for multiple terms, LogSumExp) can be viewed as a deformation of maximum or minimum. The log semiring has applications in mathematical optimization, since it replaces the non-smooth maximum and minimum by a smooth operation. The log semiring also arises when working with numbers that are logarithms (measured on a logarithmic scale), such as decibels (see Decibel § Addition), log probability, or log-likelihoods.


In such systems, a central complexity measure is the number of synchronous communication rounds required to complete the task.This complexity measure is closely related to the diameter of the network. Let D be the diameter of the network. On the one hand, any computable problem can be solved trivially in a synchronous distributed system in approximately 2D communication rounds: simply gather all information in one location (D rounds), solve the problem, and inform each node about the solution (D rounds).


This results in P ( A ∣ B ) = P ( A ∩ B ) / P ( B ) {\textstyle P(A\mid B)=P(A\cap B)/P(B)} whenever P(B) > 0 and 0 otherwise.This approach results in a probability measure that is consistent with the original probability measure and satisfies all the Kolmogorov axioms. This conditional probability measure also could have resulted by assuming that the relative magnitude of the probability of A with respect to X will be preserved with respect to B (cf. a Formal Derivation below). The wording "evidence" or "information" is generally used in the Bayesian interpretation of probability.


In the binary case, the correlation function between the variables X n {\displaystyle X_{n}} and X k {\displaystyle X_{k}} of the chain depends on the distance n − k {\displaystyle n-k} only. It is defined as follows: K ( r ) = ⟨ ( X n − X ¯ ) ( X n + r − X ¯ ) ⟩ = ⟨ X n X n + r ⟩ − X ¯ 2 , {\displaystyle K(r)=\langle (X_{n}-{\bar {X}})(X_{n+r}-{\bar {X}})\rangle =\langle X_{n}X_{n+r}\rangle -{\bar {X}}^{2},} where the symbol ⟨ ⋯ ⟩ {\displaystyle \langle \cdots \rangle } denotes averaging over all n. By definition, K ( − r ) = K ( r ) , K ( 0 ) = X ¯ ( 1 − X ¯ ) . {\displaystyle K(-r)=K(r),K(0)={\bar {X}}(1-{\bar {X}}).} There is a relation between the memory function and the correlation function of the binary additive Markov chain: K ( r ) = ∑ s = 1 m K ( r − s ) F ( s ) , r = 1 , 2 , … . {\displaystyle K(r)=\sum _{s=1}^{m}K(r-s)F(s),\,\,\,\,r=1,2,\dots \,.}


The first three examples possess simple parametric representations, which is not true for the fourth and fifth examples. The fifth example shows the possibly complicated geometric structure of an implicit curve. The implicit function theorem describes conditions under which an equation F ( x , y ) = 0 {\displaystyle F(x,y)=0} can be solved implicitly for x and/or y – that is, under which one can validly write x = g ( y ) {\displaystyle x=g(y)} or y = f ( x ) {\displaystyle y=f(x)} .


In order to create specialized packet processing platforms, a variety of technologies have been developed and deployed. These technologies, which span the breadth of hardware and software, have all been designed with the aim of maximizing speed and throughput while minimizing latency.


In the first round P {\displaystyle P} processors combine their blocks into P / 2 {\displaystyle P/2} blocks. Then P / 2 {\displaystyle P/2} processors combine the P / 2 {\displaystyle P/2} blocks into P / 4 {\displaystyle P/4} . This procedure is continued until all the data is combined in one block.


In telecommunication, data compaction is the reduction of the number of data elements, bandwidth, cost, and time for the generation, transmission, and storage of data without loss of information by eliminating unnecessary redundancy, removing irrelevancy, or using special coding. Examples of data compaction methods are the use of fixed-tolerance bands, variable-tolerance bands, slope-keypoints, sample changes, curve patterns, curve fitting, variable-precision coding, frequency analysis, and probability analysis. Simply squeezing noncompacted data into a smaller space, for example by increasing packing density by transferring images from newsprint to microfilm or by transferring data on punched cards onto magnetic tape, is not data compaction.


In the context of continuous optimization, individual learning exists in the form of local heuristics or conventional exact enumerative methods. Examples of individual learning strategies include the hill climbing, Simplex method, Newton/Quasi-Newton method, interior point methods, conjugate gradient method, line search, and other local heuristics. Note that most of the common individual learning methods are deterministic. In combinatorial optimization, on the other hand, individual learning methods commonly exist in the form of heuristics (which can be deterministic or stochastic) that are tailored to a specific problem of interest. Typical heuristic procedures and schemes include the k-gene exchange, edge exchange, first-improvement, and many others.


By symmetry, for only successes, the 95% confidence interval is . The rule is useful in the interpretation of clinical trials generally, particularly in phase II and phase III where often there are limitations in duration or statistical power. The rule of three applies well beyond medical research, to any trial done n times. If 300 parachutes are randomly tested and all open successfully, then it is concluded with 95% confidence that fewer than 1 in 100 parachutes with the same characteristics (3/300) will fail.


Primality testing is a field that has been around since the time of Fermat, in whose time most algorithms were based on factoring, which become unwieldy with large input; modern algorithms treat the problems of determining whether a number is prime and what its factors are separately. It became of practical importance with the advent of modern cryptography. Although many current tests result in a probabilistic output (N is either shown composite, or probably prime, such as with the Baillie–PSW primality test or the Miller–Rabin test), the elliptic curve test proves primality (or compositeness) with a quickly verifiable certificate.Previously-known prime-proving methods such as the Pocklington primality test required at least partial factorization of N ± 1 {\displaystyle N\pm 1} in order to prove that N {\displaystyle N} is prime. As a result, these methods required some luck and are generally slow in practice.


These are also sometimes called canonical maps. A canonical isomorphism is a canonical map that is also an isomorphism (i.e., invertible). In some contexts, it might be necessary to address an issue of choices of canonical maps or canonical isomorphisms; for a typical example, see prestack. For a discussion of the problem of defining a canonical map see Kevin Buzzard's talk at the 2022 Grothendieck conference.


A researcher may request outputs which breach the 'rules of thumb' as long as (1) they are non-disclosive (2) they are important and (3) this is an exceptional request. It is up to the researcher to prove that any 'unsafe' outputs are non-disclosive, but the checker has the final say. Since there are no hard rules, this requires knowledge on disclosure risks and judgment from both the researcher and the checker. It requires training and an understanding of statistics and data analysis, although it has been argued that this can be used to make the process more efficient than a rules-based model. The UK Data Service employs a principles-based approach to statistical disclosure control from its Secure Data Service.


This method was proposed in Shannon's "A Mathematical Theory of Communication" (1948), his article introducing the field of information theory. Fano's method divides the source symbols into two sets ("0" and "1") with probabilities as close to 1/2 as possible. Then those sets are themselves divided in two, and so on, until each set contains only one symbol.


In model theory, an atomic formula is satisfiable if there is a collection of elements of a structure that render the formula true. If A is a structure, φ is a formula, and a is a collection of elements, taken from the structure, that satisfy φ, then it is commonly written that A ⊧ φ If φ has no free variables, that is, if φ is an atomic sentence, and it is satisfied by A, then one writes A ⊧ φIn this case, one may also say that A is a model for φ, or that φ is true in A. If T is a collection of atomic sentences (a theory) satisfied by A, one writes A ⊧ T


In the following table, each row shows undisputed Greek cognates sharing the three ablaut grades of a root. The four sonorants and the two semivowels are represented as individual letters, other consonants as C and the vowel or its absence as (V). The reconstructed PIE e grade and zero grade of the above roots may be arranged as follows: An extension of the table to PIE roots ending in presumed laryngeals allows many Greek cognates to follow a regular ablaut pattern.


In most parliamentary democracies, members of a parliament can propose a motion of confidence or of no confidence in the government or executive. The results of such motions show how much support the government currently has in parliament. Should a motion of confidence fail, or a motion of no confidence pass, the government will usually either resign and allow other politicians to form a new government, or call an election.


In order to generate a Janet basis, a ranking of derivatives must be defined. It is a total ordering such that for any derivatives δ {\displaystyle \delta } , δ 1 {\displaystyle \delta _{1}} and δ 2 {\displaystyle \delta _{2}} , and any derivation operator θ {\displaystyle \theta } the relations δ ⪯ θ δ {\displaystyle \delta \preceq \theta \delta } , and δ 1 ⪯ δ 2 → δ δ 1 ⪯ δ δ 2 {\displaystyle \delta _{1}\preceq \delta _{2}\rightarrow \delta \delta _{1}\preceq \delta \delta _{2}} are valid. Here graded lexicographic term orderings g r l e x {\displaystyle grlex} are applied.


These were not merely binary-coded decimal (BCD). Most machines had ten vacuum tubes per digit in each processor register.


In the following example green edges are being evaluated by the algorithm and red edges have been deleted.


In mathematical logic, a formal calculation, or formal operation, is a calculation that is systematic but without a rigorous justification. It involves manipulating symbols in an expression using a generic substitution without proving that the necessary conditions hold. Essentially, it involves the form of an expression without considering its underlying meaning. This reasoning can either serve as positive evidence that some statement is true when it is difficult or unnecessary to provide proof or as an inspiration for the creation of new (completely rigorous) definitions. However, this interpretation of the term formal is not universally accepted, and some consider it to mean quite the opposite: a completely rigorous argument, as in formal mathematical logic.


In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that, at first glance, suggest the possibility of communication faster-than-light. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics, such as the EPR paradox, or violations of local realism obtained in tests of Bell's theorem. In these experiments, the no-communication theorem shows that failure of local realism does not lead to what could be referred to as "spooky communication at a distance" (in analogy with Einstein's labeling of quantum entanglement as requiring "spooky action at a distance" on the assumption of QM's completeness).


In telecommunications, net gain is the overall gain of a transmission circuit. Net gain is measured by applying a test signal at an appropriate power level at the input port of a circuit and measuring the power delivered at the output port. The net gain in dB is calculated by taking 10 times the common logarithm of the ratio of the output power to the input power. The net gain expressed in dB may be positive or negative.


Execute test suites of test cases. Generate associated test reports.These individual objectives may be fulfilled by unit test framework tools, stubs or drivers.A test harness may provide some of the following benefits: Increased productivity due to automation of the testing process. Increased probability that regression testing will occur.


In computer science, they are used for analyzing sorting algorithms; in quantum physics, for describing states of particles; and in biology, for describing RNA sequences. The number of permutations of n distinct objects is n factorial, usually written as n!, which means the product of all positive integers less than or equal to n. Technically, a permutation of a set S is defined as a bijection from S to itself. That is, it is a function from S to S for which every element occurs exactly once as an image value.


In the fantasy role-playing game Dungeons & Dragons, an Outer Plane is one of a number of general types of planes of existence. They can also be referred to as godly planes, spiritual planes or divine planes. The Outer Planes are home to beings such as deities and their servants such as demons, celestials and devils. Each Outer Plane is usually the physical manifestation of a particular moral and ethical alignment and the entities that dwell there often embody the traits related to that alignment.


In prior iterations of Visual Basic, all statements in a condition would have been evaluated even if the outcome of the condition could be determined before evaluating a condition. For example: This was not only inefficient, but could lead to unexpected results for any person used to another language. In Visual Basic .NET, the new AndAlso and OrElse operators have been added to provide short-circuit evaluation like many other languages.


The logistic regression model itself simply models probability of output in terms of input and does not perform statistical classification (it is not a classifier), though it can be used to make a classifier, for instance by choosing a cutoff value and classifying inputs with probability greater than the cutoff as one class, below the cutoff as the other; this is a common way to make a binary classifier. Analogous linear models for binary variables with a different sigmoid function instead of the logistic function (to convert the linear combination to a probability) can also be used, most notably the probit model; see § Alternatives. The defining characteristic of the logistic model is that increasing one of the independent variables multiplicatively scales the odds of the given outcome at a constant rate, with each independent variable having its own parameter; for a binary dependent variable this generalizes the odds ratio.


In the United States only, the two largest carriers are instead implementing 4G LTE in the 700 MHz band, which was reallocated from TV broadcasting during the DTV transition. TV stations were forced to move to lower UHF and even far worse VHF frequencies with poorer mobile TV and even regular terrestrial TV performance, because the 700 MHz band has better radio propagation characteristics that allow mobile phone signal to penetrate deeper into buildings with less attenuation than the 1700 MHz or 2100 MHz bands.AT&T Mobility devices use former TV channel 53 and 54 nationwide and has purchased spectrum from former TV channel 55 nationwide (purchased from Qualcomm's defunct MediaFLO pay TV service), and also channel 56 in densely populated areas such as California and the Northeast Corridor. Verizon Wireless formerly held frequencies just above TV channel 51, which is still in use, causing adjacent-channel interference that is preventing the carrier from using them until the planned top-down spectrum repacking occurs. The channel 52 spectrum was later purchased by T-Mobile US who now uses this spectrum for their network. Verizon now uses higher blocks within the former TV band (channels 60 and 61).


In mathematics, a minimal counterexample is the smallest example which falsifies a claim, and a proof by minimal counterexample is a method of proof which combines the use of a minimal counterexample with the ideas of proof by induction and proof by contradiction. More specifically, in trying to prove a proposition P, one first assumes by contradiction that it is false, and that therefore there must be at least one counterexample. With respect to some idea of size (which may need to be chosen carefully), one then concludes that there is such a counterexample C that is minimal. In regard to the argument, C is generally something quite hypothetical (since the truth of P excludes the possibility of C), but it may be possible to argue that if C existed, then it would have some definite properties which, after applying some reasoning similar to that in an inductive proof, would lead to a contradiction, thereby showing that the proposition P is indeed true.If the form of the contradiction is that we can derive a further counterexample D, that is smaller than C in the sense of the working hypothesis of minimality, then this technique is traditionally called proof by infinite descent.


COBOL-74 added subprograms, giving programmers the ability to control the data each part of the program could access. COBOL-85 then added nested subprograms, allowing programmers to hide subprograms.


In the Northern hemisphere, characteristic dominant broadleaf trees in this biome include oaks (Quercus spp. ), beeches (Fagus spp. ), maples (Acer spp. ), or birches (Betula spp.).


In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The most common such robust statistics are the interquartile range (IQR) and the median absolute deviation (MAD). These are contrasted with conventional or non-robust measures of scale, such as sample standard deviation, which are greatly influenced by outliers. These robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency on contaminated data, at the cost of inferior efficiency on clean data from distributions such as the normal distribution. To illustrate robustness, the standard deviation can be made arbitrarily large by increasing exactly one observation (it has a breakdown point of 0, as it can be contaminated by a single point), a defect that is not shared by robust statistics.


In relational algebra, a projection is a unary operation written as Π a 1 , . . .


In renewal-anomalous files, a random period is taken independently from a waiting time probability density function (WT-PDF; see Continuous-time Markov process for more information) of the form: ψ α ( t ) ∼ k ( k t ) − 1 − α , 0 < α ≤ 1 {\displaystyle \psi _{\alpha }(t)\sim k(kt)^{-1-\alpha },0<\alpha \leq 1} , where k is a parameter. Then, all the particles in the file stand still for this random period, where afterwards, all the particles attempt jumping in accordance with the rules of the file. This procedure is carried on over and over again. The equation of motion for the particles’ PDF in a renewal-anomalous file is obtained when convoluting the equation of motion for a Brownian file with a kernel k α ( t ) {\displaystyle k_{\alpha }(t)}: Here, the kernel k α ( t ) {\displaystyle k_{\alpha }(t)} and the WT-PDF ψ α ( t ) {\displaystyle \psi _{\alpha }(t)} are related in Laplace space, k ¯ α ( s ) = s ψ ¯ α ( s ) 1 − ψ ¯ α ( s ) {\displaystyle {\bar {k}}_{\alpha }(s)={\frac {s{\bar {\psi }}_{\alpha }(s)}{1-{\bar {\psi }}_{\alpha }(s)}}} . (The Laplace transform of a function f ( t ) {\displaystyle f(t)} reads, f ¯ ( s ) = ∫ 0 ∞ f ( t ) e − s t d t {\displaystyle {\bar {f}}(s)=\int _{0}^{\infty }f(t)e^{-st}\,dt} .) The reflecting boundary conditions accompanied Eq. (8) are obtained when convoluting the boundary conditions of a Brownian file with the kernel k α ( t ) {\displaystyle k_{\alpha }(t)} , where here and in a Brownian file the initial conditions are identical.


In systems such as CGA or SFS and most cryptographic peer-to-peer networks, fingerprints are embedded into pre-existing address and name formats (such as IPv6 addresses, file names or other identification strings). If addresses and names are already being exchanged through trusted channels, this approach allows fingerprints to piggyback on them.In PGP, most keys are created in such a way that what is called the "key ID" is equal to the lower 32 or 64 bits respectively of a key fingerprint.


Character sets that may be available in one system may not be so in others. In other cases, one or more of the following transformation types may be required to meet the business and technical needs of the server or data warehouse: Selecting only certain columns to load: (or selecting null columns not to load). For example, if the source data has three columns (aka "attributes"), roll_no, age, and salary, then the selection may take only roll_no and salary. Or, the selection mechanism may ignore all those records where salary is not present (salary = null). Translating coded values: (e.g., if the source system codes male as "1" and female as "2", but the warehouse codes male as "M" and female as "F") Encoding free-form values: (e.g., mapping "Male" to "M") Deriving a new calculated value: (e.g., sale_amount = qty * unit_price) Sorting or ordering the data based on a list of columns to improve search performance Joining data from multiple sources (e.g., lookup, merge) and deduplicating the data Aggregating (for example, rollup — summarizing multiple rows of data — total sales for each store, and for each region, etc.) Generating surrogate-key values Transposing or pivoting (turning multiple columns into multiple rows or vice versa) Splitting a column into multiple columns (e.g., converting a comma-separated list, specified as a string in one column, into individual values in different columns) Disaggregating repeating columns Looking up and validating the relevant data from tables or referential files Applying any form of data validation; failed validation may result in a full rejection of the data, partial rejection, or no rejection at all, and thus none, some, or all of the data is handed over to the next step depending on the rule design and exception handling; many of the above transformations may result in exceptions, e.g., when a code translation parses an unknown code in the extracted data


In mathematical finite group theory, an N-group is a group all of whose local subgroups (that is, the normalizers of nontrivial p-subgroups) are solvable groups. The non-solvable ones were classified by Thompson during his work on finding all the minimal finite simple groups.


In programming languages, an abstract type is a type in a nominative type system that cannot be instantiated directly; a type that is not abstract – which can be instantiated – is called a concrete type. Every instance of an abstract type is an instance of some concrete subtype. Abstract types are also known as existential types.An abstract type may provide no implementation, or an incomplete implementation. In some languages, abstract types with no implementation (rather than an incomplete implementation) are known as protocols, interfaces, signatures, or class types.


In the 8-bit versions, while running, the CP/M operating system loaded into memory had three components: Basic Input/Output System (BIOS), Basic Disk Operating System (BDOS), Console Command Processor (CCP).The BIOS and BDOS were memory-resident, while the CCP was memory-resident unless overwritten by an application, in which case it was automatically reloaded after the application finished running. A number of transient commands for standard utilities were also provided. The transient commands resided in files with the extension .COM on disk. The BIOS directly controlled hardware components other than the CPU and main memory.


In telephony, call control refers to the software within a telephone switch that supplies its central function. Call control decodes addressing information and routes telephone calls from one end point to another. It also creates the features that can be used to adapt standard switch operation to the needs of users.


In order to strengthen parity protection for the sound samples, the parity bit is calculated on only the top six bits of each NICAM sample. Early BBC NICAM research showed that uncorrected errors in the least significant four bits were preferable to the reduced overall protection offered by parity-protecting all ten bits.


In the System/360, other than the 360/67, and System/370 architectures, the general-purpose registers were 32 bits wide, the machine did 32-bit arithmetic operations, and addresses were always stored in 32-bit words, so the architecture was considered 32-bit, but the machines ignored the top 8 bits of the address resulting in 24-bit addressing. Much of System/360's and System/370's large installed code base relied on a 24-bit logical address; In particular, a heavily used machine instruction, LA, Load Address, explicitly cleared the top eight bits of the address being placed in a register. If the 24-bit limit were to be removed, this would create migration problems for existing software. This was addressed by adding an addressing mode bit to the Program Status Word controlling whether the program runs in 24-bit mode, in which the top eight bits of virtual addresses are ignored, or 31-bit mode, in which only the uppermost bit of virtual addresses are ignored.


The 8-bit ISO 8859-2 (Latin-2) standard was developed by ISO. MS-DOS introduced 8-bit encoding CP852 for Central European languages, disregarding the ISO standard. Microsoft Windows spread yet another 8-bit encoding called CP1250, which had a few letters mapped one-to-one with ISO 8859-2, but also had some mapped elsewhere.


The fork operation creates a separate address space for the child. The child process has an exact copy of all the memory segments of the parent process. In modern UNIX variants that follow the virtual memory model from SunOS-4.0, copy-on-write semantics are implemented and the physical memory need not be actually copied.


In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers. It is an instance of a scheme for numbering permutations and is an example of an inversion table. The Lehmer code is named in reference to Derrick Henry Lehmer, but the code had been known since 1888 at least.


In order to apply backtracking to a specific class of problems, one must provide the data P for the particular instance of the problem that is to be solved, and six procedural parameters, root, reject, accept, first, next, and output. These procedures should take the instance data P as a parameter and should do the following: root(P): return the partial candidate at the root of the search tree. reject(P,c): return true only if the partial candidate c is not worth completing. accept(P,c): return true if c is a solution of P, and false otherwise. first(P,c): generate the first extension of candidate c. next(P,s): generate the next alternative extension of a candidate, after the extension s. output(P,c): use the solution c of P, as appropriate to the application.The backtracking algorithm reduces the problem to the call backtrack(root(P)), where backtrack is the following recursive procedure: procedure backtrack(P, c) is if reject(P, c) then return if accept(P, c) then output(P, c) s ← first(P, c) while s ≠ NULL do backtrack(P, s) s ← next(P, s)


In the case of a pepper which is unique to each user, the tradeoff is gaining extra security at the cost of storing more information securely. Compromising one password hash and revealing its secret pepper will have no effect on other password hashes and their secret pepper, so each pepper must be individually discovered, which greatly increases the time taken to attack the password hashes.


In the aforementioned interview, Vass also described their plans for the company's first multi-user computer, based on a CP/M-derived executive that they called AMEX (Altos Multiuser Executive). Their new design planned to support up to four users, by providing each user with its own 48 KB of dedicated program memory (addressable by the 8-bit Z80 processor through bank switching), while the 16 KB of memory for the operating system's image could be shared by all users. An advertisement for the "Sun-Series ACS8000-6" sold under Altos' own brand appeared in the November 1979 issue of Byte, and indeed promised to support up to four users by means of its AMEX kernel, and supporting a maximum system memory of 208 KB. The ACS 8000 could run at least three multi-user operating systems: Altos' own AMEX, Oasis, or MP/M.


In number theory, a rational reciprocity law is a reciprocity law involving residue symbols that are related by a factor of +1 or –1 rather than a general root of unity. As an example, there are rational biquadratic and octic reciprocity laws. Define the symbol (x|p)k to be +1 if x is a k-th power modulo the prime p and -1 otherwise. Let p and q be distinct primes congruent to 1 modulo 4, such that (p|q)2 = (q|p)2 = +1.


In this case, positive numbers always have a most significant digit between 0 and 4 (inclusive), while negative numbers are represented by the 10's complement of the corresponding positive number. As a result, this system allows for 32-bit packed BCD numbers to range from −50,000,000 to +49,999,999, and −1 is represented as 99999999. (As with two's complement binary numbers, the range is not symmetric about zero.)


In statistics, scale analysis is a set of methods to analyze survey data, in which responses to questions are combined to measure a latent variable. These items can be dichotomous (e.g. yes/no, agree/disagree, correct/incorrect) or polytomous (e.g. disagree strongly/disagree/neutral/agree/agree strongly). Any measurement for such data is required to be reliable, valid, and homogeneous with comparable results over different studies.


Outliers, being the most extreme observations, may include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum are not always outliers because they may not be unusually far from other observations. Naive interpretation of statistics derived from data sets that include outliers may be misleading.


In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is x, and the most common symbol for the output is y; the function itself is commonly written y = f(x).It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and y are independent variables. Functions with multiple outputs are often referred to as vector-valued functions.


Take for example the following exchange: A (to passerby): I am out of gas. B: There is a gas station 'round the corner.Here, B does not say, but conversationally implicates, that the gas station is open, because otherwise his utterance would not be relevant in the context. Conversational implicatures are classically seen as contrasting with entailments: They are not necessary or logical consequences of what is said, but are defeasible (cancellable). So, B could continue without contradiction: B: But unfortunately it's closed today.An example of a conventional implicature is "Donovan is poor but happy", where the word "but" implicates a sense of contrast between being poor and being happy.Later linguists introduced refined and different definitions of the term, leading to somewhat different ideas about which parts of the information conveyed by an utterance are actually implicatures and which are not.


Out-of-order delivery When a collection of related packets is routed through a network, different packets may take different routes, each resulting in a different delay. The result is that the packets arrive in a different order than they were sent. This problem requires special additional protocols for rearranging out-of-order packets. The reordering process requires additional buffering at the receiver, and, as with packet delay variation, increases the overall latency for the stream.


In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree. The Stern–Brocot tree was introduced independently by Moritz Stern (1858) and Achille Brocot (1861). Stern was a German number theorist; Brocot was a French clockmaker who used the Stern–Brocot tree to design systems of gears with a gear ratio close to some desired value by finding a ratio of smooth numbers near that value. The root of the Stern–Brocot tree corresponds to the number 1. The parent-child relation between numbers in the Stern–Brocot tree may be defined in terms of continued fractions or mediants, and a path in the tree from the root to any other number q provides a sequence of approximations to q with smaller denominators than q. Because the tree contains each positive rational number exactly once, a breadth first search of the tree provides a method of listing all positive rationals that is closely related to Farey sequences. The left subtree of the Stern–Brocot tree, containing the rational numbers in the range (0,1), is called the Farey tree.


In practice many channels have memory. Namely, at time i {\displaystyle i} the channel is given by the conditional probability P ( y i | x i , x i − 1 , x i − 2 , . . .


In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.


When this group has order 16, Dummit and Foote refer to this group as the "modular group of order 16", as its lattice of subgroups is modular. In this article this group will be called the modular maximal-cyclic group of order 2 n {\displaystyle 2^{n}} . Its presentation is: ⟨ r , s ∣ r 2 n − 1 = s 2 = 1 , s r s = r 2 n − 2 + 1 ⟩ {\displaystyle \langle r,s\mid r^{2^{n-1}}=s^{2}=1,\ srs=r^{2^{n-2}+1}\rangle \,\!}


In order to achieve optimal place and routing for partitioned designs, the engineer must focus on FPGA pin count and inter-FPGA signals. After partitioning the design into separate FPGAs, the number of inter-FPGA signals must not to exceed the pin count on the FPGA. This is very difficult to avoid when circuit designs are immense, thus signals must utilize strategies such as time-division multiplexing (TDM) which multiple signals can be transferred over a single line. These multiple signals, called sub-channels, take turns being transferred over the line over a time slot. When the TDM ratio is high, the bus clock frequency has to be reduced to accommodate time slots for each sub-channel. By reducing the clock frequency the throughput of the system is hindered.


However, neither instrument used electricity as a sound-source. The first electric synthesizer was invented in 1876 by Elisha Gray. The "Musical Telegraph" was a chance by-product of his telephone technology when Gray discovered that he could control sound from a self-vibrating electromagnetic circuit and so invented a basic oscillator.


When personal confidential information is shared between healthcare workers, consent is taken as implied. If a patient doesn't want a healthcare worker to share confidential health information, they need to make this clear and discuss the matter with healthcare staff. Patients have the right, in most situations, to refuse permission for a health care professional to share their information with another healthcare professional, even one giving them care—but are advised, where appropriate, about the dangers of this course of action, due to possible drug interactions.


In some languages multi-level breaks are also possible. For handling exceptional situations, specialized exception handling constructs were added, such as try/catch/finally in Java. The throw-catch exception handling mechanisms can also be easily abused to create non-transparent control structures, just like goto can be abused.


In order to prove a lower bound for the distance of a code C ∗ {\displaystyle C^{*}} we prove that the Hamming distance of an arbitrary but distinct pair of codewords has a lower bound. So let Δ ( c 1 , c 2 ) {\displaystyle \Delta (c^{1},c^{2})} be the Hamming distance of two codewords c 1 {\displaystyle c^{1}} and c 2 {\displaystyle c^{2}} . For any given m 1 ≠ m 2 ∈ ( F q k ) K , {\displaystyle m_{1}\neq m_{2}\in \left(\mathbb {F} _{q^{k}}\right)^{K},} we want a lower bound for Δ ( C ∗ ( m 1 ) , C ∗ ( m 2 ) ) . {\displaystyle \Delta (C^{*}(m_{1}),C^{*}(m_{2})).}


(also shortest addition chain, 5 multiplications).On the other hand, the determination of a shortest addition chain is hard: no efficient optimal methods are currently known for arbitrary exponents, and the related problem of finding a shortest addition chain for a given set of exponents has been proven NP-complete. Even given a shortest chain, addition-chain exponentiation requires more memory than the binary method, because it must potentially store many previous exponents from the chain. So in practice, shortest addition-chain exponentiation is primarily used for small fixed exponents for which a shortest chain can be pre-computed and is not too large.


In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way). The concept of a group was elaborated for handling, in a unified way, many mathematical structures such as numbers, geometric shapes and polynomial roots.


The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1). Years 6, 12 and 23 of the cycle are common years beginning on Monday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Monday.


In software engineering, version control (also known as revision control, source control, or source code management) is a class of systems responsible for managing changes to computer programs, documents, large web sites, or other collections of information. Version control is a component of software configuration management.Changes are usually identified by a number or letter code, termed the "revision number", "revision level", or simply "revision". For example, an initial set of files is "revision 1". When the first change is made, the resulting set is "revision 2", and so on.


In mathematics, Arf semigroups are certain subsets of the non-negative integers closed under addition, that were studied by Cahit Arf (1948). They appeared as the semigroups of values of Arf rings. A subset of the integers forms a monoid if it includes zero, and if every two elements in the subset have a sum that also belongs to the subset. In this case, it is called a "numerical semigroup". A numerical semigroup is called an Arf semigroup if, for every three elements x, y, and z with z = min(x, y, and z), the semigroup also contains the element x + y − z. For instance, the set containing zero and all even numbers greater than 10 is an Arf semigroup.


Overfilling a buffer on the stack is more likely to derail program execution than overfilling a buffer on the heap because the stack contains the return addresses for all active function calls. A stack buffer overflow can be caused deliberately as part of an attack known as stack smashing.


There is a copy of the pids array in all 11 processes, but only in the parent is it complete - the copy in each child will be missing the lower-numbered child PIDs, and have zero for its own PID. (Not that this really matters, as only the parent process actually uses this array.) The second loop executes only in the parent process (because all of the children have exited before this point), and waits for each child to exit.


Two competing notational conventions split the field of matrix calculus into two separate groups. The two groups can be distinguished by whether they write the derivative of a scalar with respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be treated as column vectors when combined with matrices (rather than row vectors).


Policy formulation – Involves exploring a variation of options or alternative courses of action available for addressing the problem. (appraisal, dialogue, formulation, and consolidation) Decision-making – Government decides on an ultimate course of action, whether to perpetuate the policy status quo or alter it. (Decision could be 'positive', 'negative', or 'no-action') Implementation – The ultimate decision made earlier will be put into practice.


This tactic applies only to VIS' variables of type Z {\displaystyle \mathbb {Z} } (or its "subtype" N {\displaystyle \mathbb {N} } ). It consists in associating a range to a variable and deriving test classes by comparing the variable with the limits of the range in some ways. More formally, let n be a variable of type Z {\displaystyle \mathbb {Z} } and let  {\displaystyle } be the associated range.


In the 1880s, German scientist Herman Von Helmholtz derived the equation for the maximum work which can be reversibly obtained from a closed system.


In probability theory, the support of a probability distribution can be loosely thought of as the closure of the set of possible values of a random variable having that distribution. There are, however, some subtleties to consider when dealing with general distributions defined on a sigma algebra, rather than on a topological space. More formally, if X: Ω → R {\displaystyle X:\Omega \to \mathbb {R} } is a random variable on ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} then the support of X {\displaystyle X} is the smallest closed set R X ⊆ R {\displaystyle R_{X}\subseteq \mathbb {R} } such that P ( X ∈ R X ) = 1. {\displaystyle P\left(X\in R_{X}\right)=1.} In practice however, the support of a discrete random variable X {\displaystyle X} is often defined as the set R X = { x ∈ R: P ( X = x ) > 0 } {\displaystyle R_{X}=\{x\in \mathbb {R} :P(X=x)>0\}} and the support of a continuous random variable X {\displaystyle X} is defined as the set R X = { x ∈ R: f X ( x ) > 0 } {\displaystyle R_{X}=\{x\in \mathbb {R} :f_{X}(x)>0\}} where f X ( x ) {\displaystyle f_{X}(x)} is a probability density function of X {\displaystyle X} (the set-theoretic support).Note that the word support can refer to the logarithm of the likelihood of a probability density function.


In number theory, a Fermi–Dirac prime is a prime power whose exponent is a power of two. These numbers are named from an analogy to Fermi–Dirac statistics in physics based on the fact that each integer has a unique representation as a product of Fermi–Dirac primes without repetition. Each element of the sequence of Fermi–Dirac primes is the smallest number that does not divide the product of all previous elements. Srinivasa Ramanujan used the Fermi–Dirac primes to find the smallest number whose number of divisors is a given power of two.


Then T {\displaystyle T} is the number of linear codes C i n i , i ∈ S {\displaystyle C_{in}^{i},i\in S} having the distance H q − 1 ( 1 2 − ε ) ⋅ 2 k . {\displaystyle H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k.} Now we want to estimate | S | .


In statistical modeling (especially process modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.


In the following example, graph H is a minor of graph G: H. G. The following diagram illustrates this. First construct a subgraph of G by deleting the dashed edges (and the resulting isolated vertex), and then contract the gray edge (merging the two vertices it connects):