As of February 2020, the smallest 23 of the 54 listed numbers have been factored. While the RSA challenge officially ended in 2007, people are still attempting to find the factorizations. According to RSA Laboratories, "Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active."


However, type inference is undecidable. A logic is represented in the LF logical framework by the judgements-as-types representation mechanism. This is inspired by Per Martin-Löf's development of Kant's notion of judgement, in the 1983 Siena Lectures.


A simple algorithm with logarithmic regret is proposed in: UCB-ALP algorithm: The framework of UCB-ALP is shown in the right figure. UCB-ALP is a simple algorithm that combines the UCB method with an Adaptive Linear Programming (ALP) algorithm, and can be easily deployed in practical systems. It is the first work that show how to achieve logarithmic regret in constrained contextual bandits. Although is devoted to a special case with single budget constraint and fixed cost, the results shed light on the design and analysis of algorithms for more general CCB problems.


In metadata, Naming and Design Rules are the formal rules associated with how data elements are structured within a process of creating exchange documents between organizations. Naming and Design Rules are a set of guidelines and naming conventions that go beyond what a single data exchange standard specification will permit. The most common standard that Naming and Design Rules are created on is XML Schema.


.Both these two groups and the dihedral group are semidirect products of a cyclic group of order 2n−1 with a cyclic group of order 2. Such a non-abelian semidirect product is uniquely determined by an element of order 2 in the group of units of the ring Z / 2 n − 1 Z {\displaystyle \mathbb {Z} /2^{n-1}\mathbb {Z} } and there are precisely three such elements, 2 n − 1 − 1 {\displaystyle 2^{n-1}-1} , 2 n − 2 − 1 {\displaystyle 2^{n-2}-1} , and 2 n − 2 + 1 {\displaystyle 2^{n-2}+1} , corresponding to the dihedral group, the quasidihedral, and the modular maximal-cyclic group. The generalized quaternion group, the dihedral group, and the quasidihedral group of order 2n all have nilpotency class n − 1, and are the only isomorphism classes of groups of order 2n with nilpotency class n − 1.


Because of this need for the traditional channel, the speed of teleportation can be no faster than the speed of light (hence the no-communication theorem is not violated). The main advantage with this is that Bell states can be shared using photons from lasers making teleportation achievable through open space having no need to send information through physical cables or optical fibers. Quantum states can be encoded in various degrees of freedom of atoms.


In mathematics, the trace field of a linear group is the field generated by the traces of its elements. It is mostly studied for Kleinian and Fuchsian groups, though related objects are used in the theory of lattices in Lie groups, often under the name field of definition.


For instance, voice and video services that are provided using Internet protocol technology may be classified as “information services” and therefore not subject to traditional voice or video regulation. The distinction in the 1996 Act between telecommunications services and information services was an outgrowth of a series of FCC Orders and decisions dating back to the 1970s that distinguished between “basic” services that were subject to regulation and “enhanced” services that the Commission chose not to regulate in order to foster their development and deployment. The Act places on all telecommunications services providers the duty to interconnect “...directly or indirectly with the facilities and equipment of other telecommunications carriers...” Keeping with this regulatory history, the Commission has chosen to forbear from regulating information services, again seeking to foster their development and deployment.


The resulting instance will inherit all the methods and properties that were defined in the class, which acts as a kind of template from which similarly typed objects can be constructed. Systems that support ex nihilo object creation allow new objects to be created from scratch without cloning from an existing prototype. Such systems provide a special syntax for specifying the properties and behaviors of new objects without referencing existing objects.


In mathematics and social science, a collaboration graph is a graph modeling some social network where the vertices represent participants of that network (usually individual people) and where two distinct participants are joined by an edge whenever there is a collaborative relationship between them of a particular kind. Collaboration graphs are used to measure the closeness of collaborative relationships between the participants of the network.


In probability theory, the Brownian tree, or Aldous tree, or Continuum Random Tree (CRT) is a random real tree that can be defined from a Brownian excursion. The Brownian tree was defined and studied by David Aldous in three articles published in 1991 and 1993. This tree has since then been generalized.


In the computer industry, the inverted text usually displays a selected block of text, the current menu item. Many older people have a slight, comfortable astigmatism. At the high resolution of modern computer screens, they better see black letters on white background rather than vice versa. Therefore, long reversed texts are rare. The reversing is widely used in the various equipment design (from television remotes to dump trucks): a half-erased button or plate remains readable.


In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.


In this regard, some theorists have argued that the additional component would have to ensure that the belief is true. This approach is reflected in the idea that knowledge implies a form of certainty. But it sets the standards of knowledge very high and may require that a belief has to be infallible to amount to knowledge.


In mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other. It is possible to derive an evaluation order or the absence of an evaluation order that respects the given dependencies from the dependency graph.


Job j {\displaystyle j} takes time p j {\displaystyle p_{j}} on any machine it is scheduled to. Q: Uniform-machines scheduling. There are m {\displaystyle m} parallel machines, and they have different given speeds.


Much of our day-to-day lives are significantly influenced by digital data and this would not be possible without Shannon-Fano coding and the ongoing evolution of its methods.In Shannon coding, the symbols are arranged in order from most probable to least probable, and assigned codewords by taking the first l i = ⌈ − log 2  p i ⌉ {\displaystyle l_{i}=\left\lceil -\log _{2}p_{i}\right\rceil } bits from the binary expansions of the cumulative probabilities ∑ k = 1 i − 1 p k . {\displaystyle \sum \limits _{k=1}^{i-1}p_{k}.} Here ⌈ x ⌉ {\displaystyle \lceil x\rceil } denotes the ceiling function (which rounds x {\displaystyle x} up to the next integer value).


In the context of fluorescence microscopy, the probability of measuring a set of number of photons (or digitalization counts proportional to detected light) m =  {\displaystyle \mathbf {m} =} for expected values E =  {\displaystyle \mathbf {E} =} for a detector with K + 1 {\displaystyle K+1} pixels is given by P ( m | E ) = ∏ i K P o i s s o n ( E i ) = ∏ i K E i m i e − E i m i ! {\displaystyle P(\mathbf {m} \vert \mathbf {E} )=\prod _{i}^{K}\mathrm {Poisson} (E_{i})=\prod _{i}^{K}{\frac {{E_{i}}^{m_{i}}e^{-E_{i}}}{m_{i}!}}} it is convenient to work with ln  ( P ) {\displaystyle \ln(P)} since in the context of maximum likelihood estimation we want to find the position of the maximum of the likelihood function and we are not interested in its absolute value. ln  ( P ( m | E ) ) = ∑ i K  {\displaystyle \ln(P(m\vert E))=\sum _{i}^{K}\left} Again since ln  ( m i ! )


In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. The history monoid provides a set of synchronization primitives (such as locks, mutexes or thread joins) for providing rendezvous points between a set of independently executing processes or threads. History monoids occur in the theory of concurrent computation, and provide a low-level mathematical foundation for process calculi, such as CSP the language of communicating sequential processes, or CCS, the calculus of communicating systems.


It may give detailed instructions to each participant about how to test, and how to record bugs found. In some organizations, a bug-bashing session is followed by a party and a prize to the person who finds the worst bug, and/or the person who finds the greatest total of bugs. Bug Bash is a collaboration event, the step-by-step procedure has been given in the article 'Bug Bash—A Collaboration Episode'.


Superscalar CPUs use hardware to decide which operations can run in parallel at runtime, while VLIW CPUs use software (the compiler) to decide which operations can run in parallel in advance. Because the complexity of instruction scheduling is moved into the compiler, complexity of hardware can be reduced substantially.A similar problem occurs when the result of a parallelizable instruction is used as input for a branch. Most modern CPUs guess which branch will be taken even before the calculation is complete, so that they can load the instructions for the branch, or (in some architectures) even start to compute them speculatively.


This final form is unique; in other words, it is independent of the sequence of row operations used. For example, in the following sequence of row operations (where two elementary operations on different rows are done at the first and third steps), the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form. →  →  →  {\displaystyle {\begin{bmatrix}1&3&1&9\\1&1&-1&1\\3&11&5&35\end{bmatrix}}\to {\begin{bmatrix}1&3&1&9\\0&-2&-2&-8\\0&2&2&8\end{bmatrix}}\to {\begin{bmatrix}1&3&1&9\\0&-2&-2&-8\\0&0&0&0\end{bmatrix}}\to {\begin{bmatrix}1&0&-2&-3\\0&1&1&4\\0&0&0&0\end{bmatrix}}} Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss–Jordan elimination. In this case, the term Gaussian elimination refers to the process until it has reached its upper triangular, or (unreduced) row echelon form. For computational reasons, when solving systems of linear equations, it is sometimes preferable to stop row operations before the matrix is completely reduced.


Main memory was also moved to an ECL implementation and the machine was equipped with a whopping-for-the-times 256k-words (2 megabytes) standard. The design spread the memory across 64 banks for fast access at about 8 ns/word, even though the cycle time of any one bank was about 250 ns. A high-speed core memory with a 20 ns access (overall) was also designed as a backup to the semiconductor memory.


By reversing the steps or using the extended Euclidean algorithm, the GCD can be expressed as a linear combination of the two original numbers, that is the sum of the two numbers, each multiplied by an integer (for example, 21 = 5 × 105 + (−2) × 252). The fact that the GCD can always be expressed in this way is known as Bézout's identity. The version of the Euclidean algorithm described above (and by Euclid) can take many subtraction steps to find the GCD when one of the given numbers is much bigger than the other.


They needed to know a network of people so that when the time comes for marriage, they were able to seek the services of the match-makers. Finally, when someone came to the match-maker, she must be able to pick out a matching suitors according to her knowledge of the local residents. Normally a perfect couple must have similar social status, economic status, and age.


In the 1970s, Michael D. Plummer and László Lovász conjectured that every bridgeless cubic graph has an exponential number of perfect matchings, strengthening Petersen's theorem that at least one perfect matching exists. In a pair of papers with different sets of co-authors, Kráľ was able to show that this conjecture is true.


Alice determines which operation to perform accordingly to the pair of bits she wants to transmit. She then sends Bob the qubit state evolved through the chosen gate. Said qubit thus encodes information about the two bits Alice used to select the operation, and this information can be retrieved by Bob thanks to pre-shared entanglement between them.


In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter.


In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some matrix decompositions.Tensors are generalizations of matrices to higher dimensions (or rather to higher orders, i.e. the higher number of dimensions) and can consequently be treated as multidimensional fields. The main tensor decompositions are: Tensor rank decomposition; Higher-order singular value decomposition; Tucker decomposition; matrix product states, and operators or tensor trains; Online Tensor Decompositions hierarchical Tucker decomposition; block term decomposition


The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. The Chinese remainder theorem (expressed in terms of congruences) is true over every principal ideal domain. It has been generalized to any ring, with a formulation involving two-sided ideals.


In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤ n. Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube). The strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non-mathematicians and mathematicians. Classically, a regular polytope in n dimensions may be defined as having regular facets (-faces) and regular vertex figures.


In the application of the section 3 of the 1952 Act to Scotland it means any of the following offences: theft, housebreaking with intent to steal, opening lockfast places with intent to steal, reset, plagium, breach of trust and embezzlement, falsehood, fraud and wilful imposition, threats to extort money or with intent to extort money, and malicious mischief any offence under section 28 of the Road Traffic Act 1930 any of the following offences in connection with such an attack as is mentioned in section 1(1)(b) of the Internationally Protected Persons Act 1978: an offence of wilful fireraising an offence under section 2 of the Explosive Substances Act 1883 of causing an explosion likely to cause serious injury to property an offence under section 2 of the Nuclear Material (Offences) Act 1983, where the circumstances are that either, in the case of a contravention of subsection (2), the act falling within paragraph (a) or (b) of that subsection would, had it been done, have constituted an offence falling within sub-paragraph (a) or (b) of this paragraph, or, in the case of a contravention of subsection (3) or (4), the act threatened would, had it been done, have constituted such an offence any of the following offences in connection with such an attack as is mentioned in section 2(1) of the United Nations Personnel Act 1997 an offence of wilful fireraising an offence under section 2 of the Explosive Substances Act 1883 of causing an explosion likely to cause serious injury to property


The unintended consequences of sharing can be complex to analyze and should not necessarily be left to the discretion of users who may have a narrow focus on their own critical need. These documents provide standards guidance on risk management: "Recommended Security Controls for Federal Information Systems & Organizations".


Another notation for the sign of a permutation is given by the more general Levi-Civita symbol (εσ), which is defined for all maps from X to X, and has value zero for non-bijective maps. The sign of a permutation can be explicitly expressed as sgn(σ) = (−1)N(σ)where N(σ) is the number of inversions in σ. Alternatively, the sign of a permutation σ can be defined from its decomposition into the product of transpositions as sgn(σ) = (−1)mwhere m is the number of transpositions in the decomposition. Although such a decomposition is not unique, the parity of the number of transpositions in all decompositions is the same, implying that the sign of a permutation is well-defined.


In the "Twitter revolution", the relationship between the new media and social movement has three distinct characteristics: 1) The Twitter streams represent the interaction mechanism of ecological network 2) The Twitter streams embedding or be embedded into different types of control process; 3) The Twitter streams reflect the change of social movement ecology.


{\displaystyle A-(B\cap C)=(A-B)\cup (A-C).} Applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. De Morgan's laws are an example of a more general concept of mathematical duality.


In mathematics, the Fekete problem is, given a natural number N and a real s ≥ 0, to find the points x1,...,xN on the 2-sphere for which the s-energy, defined by ∑ 1 ≤ i < j ≤ N ‖ x i − x j ‖ − s {\displaystyle \sum _{1\leq i 0 and by ∑ 1 ≤ i < j ≤ N log  ‖ x i − x j ‖ − 1 {\displaystyle \sum _{1\leq i 0, such points are called s-Fekete points, and for s = 0, logarithmic Fekete points (see Saff & Kuijlaars (1997)). More generally, one can consider the same problem on the d-dimensional sphere, or on a Riemannian manifold (in which case ||xi −xj|| is replaced with the Riemannian distance between xi and xj). The problem originated in the paper by Michael Fekete (1923) who considered the one-dimensional, s = 0 case, answering a question of Issai Schur. An algorithmic version of the Fekete problem is number 7 on the list of problems discussed by Smale (1998).


In mathematical analysis, Ekeland's variational principle, discovered by Ivar Ekeland, is a theorem that asserts that there exist nearly optimal solutions to some optimization problems. Ekeland's principle can be used when the lower level set of a minimization problems is not compact, so that the Bolzano–Weierstrass theorem cannot be applied. The principle relies on the completeness of the metric space.The principle has been shown to be equivalent to completeness of metric spaces. In proof theory, it is equivalent to Π11CA0 over RCA0, i.e. relatively strong. It also leads to a quick proof of the Caristi fixed point theorem.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 237, 1237, 2347, and 12347 are the patterns related to Braille pattern dots-123, since the two additional dots of kantenji patterns 0123, 1237, and 01237 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general, type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation, a common one is Thierry Coquand's Calculus of Inductive Constructions.


Once an agreement is reached, the partnership is typically enforceable by civil law, especially if well documented. Partners who wish to make their agreement affirmatively explicit and enforceable typically draw up Articles of Partnership. Trust and pragmatism are also essential as it cannot be expected that everything can be written in the initial partnership agreement, therefore quality governance and clear communication are critical success factors in the long run. It is common for information about formally partnered entities to be made public, such as through a press release, a newspaper ad, or public records laws.


In the area of mathematics known as Ramsey theory, a Ramsey class is one which satisfies a generalization of Ramsey's theorem. Suppose A {\displaystyle A} , B {\displaystyle B} and C {\displaystyle C} are structures and k {\displaystyle k} is a positive integer. We denote by ( B A ) {\displaystyle {\binom {B}{A}}} the set of all subobjects A ′ {\displaystyle A'} of B {\displaystyle B} which are isomorphic to A {\displaystyle A} . We further denote by C → ( B ) k A {\displaystyle C\rightarrow (B)_{k}^{A}} the property that for all partitions X 1 ∪ X 2 ∪ ⋯ ∪ X k {\displaystyle X_{1}\cup X_{2}\cup \dots \cup X_{k}} of ( C A ) {\displaystyle {\binom {C}{A}}} there exists a B ′ ∈ ( C B ) {\displaystyle B'\in {\binom {C}{B}}} and an 1 ≤ i ≤ k {\displaystyle 1\leq i\leq k} such that ( B ′ A ) ⊆ X i {\displaystyle {\binom {B'}{A}}\subseteq X_{i}} .


The principle of the number field sieve (both special and general) can be understood as an improvement to the simpler rational sieve or quadratic sieve. When using such algorithms to factor a large number n, it is necessary to search for smooth numbers (i.e. numbers with small prime factors) of order n1/2. The size of these values is exponential in the size of n (see below).


In network theory, multidimensional networks, a special type of multilayer network, are networks with multiple kinds of relations. Increasingly sophisticated attempts to model real-world systems as multidimensional networks have yielded valuable insight in the fields of social network analysis, economics, urban and international transport, ecology, psychology, medicine, biology, commerce, climatology, physics, computational neuroscience, operations management, and finance.


A simple application of functional dependencies is Heath's theorem; it says that a relation R over an attribute set U and satisfying a functional dependency X → Y can be safely split in two relations having the lossless-join decomposition property, namely into Π X Y ( R ) ⋈ Π X Z ( R ) = R {\displaystyle \Pi _{XY}(R)\bowtie \Pi _{XZ}(R)=R} where Z = U − XY are the rest of the attributes. (Unions of attribute sets are customarily denoted by there juxtapositions in database theory.) An important notion in this context is a candidate key, defined as a minimal set of attributes that functionally determine all of the attributes in a relation.


If the set has n elements, the number of k-combinations, denoted by C ( n , k ) {\displaystyle C(n,k)} or C k n {\displaystyle C_{k}^{n}} , is equal to the binomial coefficient which can be written using factorials as n ! k ! ( n − k ) !


In mathematics, a matrix is a rectangular array of numbers or other data. In physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way. A matrix model describes the behavior of a set of matrices within the framework of quantum mechanics.One important example of a matrix model is the BFSS matrix model proposed by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind in 1997. This theory describes the behavior of a set of nine large matrices.


However, in a few limited instances, a healthcare worker can share personal information without consent if it is in the public interest. These instances are set out in guidance from the General Medical Council, which is the regulatory body for doctors. Sometimes the healthcare worker has to provide the information – if required by law or in response to a court order. The National AIDS Trust has written a guide for people living with HIV to confidentiality in the NHS.


In processing the recall, a Health Hazard Assessment will be conducted by the FDA to determine the recall class (defined above). Level, notification, instructions, mechanics, impacts on economy, and individual consumer must all be considered in determining recall strategy. Level of recall refers to which part of the distribution chain to which the recall is extended (wholesale, retail, pharmacy, medical user, etc.). Notification is the way consumers are alerted to the recall.


In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. These matrices generalize permutation matrices and arise naturally when using Dodgson condensation to compute a determinant. They are also closely related to the six-vertex model with domain wall boundary conditions from statistical mechanics. They were first defined by William Mills, David Robbins, and Howard Rumsey in the former context.


Control surfaces with motorized faders can read and write mix automation. The control surface connects to the host computer via many different interfaces. MIDI was the first major interface created for this purpose, although many devices now use USB, FireWire, or Ethernet.


In statistics, naive Bayes classifiers are a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features (see Bayes classifier). They are among the simplest Bayesian network models, but coupled with kernel density estimation, they can achieve high accuracy levels.Naive Bayes classifiers are highly scalable, requiring a number of parameters linear in the number of variables (features/predictors) in a learning problem. Maximum-likelihood training can be done by evaluating a closed-form expression,: 718 which takes linear time, rather than by expensive iterative approximation as used for many other types of classifiers. In the statistics literature, naive Bayes models are known under a variety of names, including simple Bayes and independence Bayes. All these names reference the use of Bayes' theorem in the classifier's decision rule, but naive Bayes is not (necessarily) a Bayesian method.


In the 20th century, many generalizations of sets were invented, e.g., fuzzy sets (Zadeh, 1965), or rediscovered, e.g., multisets (Knuth, 1997). As a result, these generalizations created a unification problem in the foundation of mathematics. The concept of a named set was created as a solution to this problem. Its generalization of mathematical structures allowed for the unification of all known generalizations of sets.


In order to deal with high data-rates, several architectural paradigms are commonly used: Pipeline of processors - each stage of the pipeline consisting of a processor performing one of the functions listed above. Parallel processing with multiple processors, often including multithreading. Specialized microcoded engines to more efficiently accomplish the tasks at hand.


In particular, if two random variables X {\displaystyle X} and Y {\displaystyle Y} (in L 2 ( Ω , P ) {\displaystyle L^{2}(\Omega ,P)} ) are independent, then the centered random variables X − E ( X ) {\displaystyle X-E(X)} and Y − E ( Y ) {\displaystyle Y-E(Y)} are orthogonal. (This means that the two variables have zero covariance: they are uncorrelated.) In that case, the Pythagorean theorem in the kernel of the expectation operator implies that the variances of X {\displaystyle X} and Y {\displaystyle Y} satisfy the identity: sometimes called the Pythagorean theorem of statistics, and is of importance in linear regression.


With dataflow path widths of 8 bits to 64 bits and beyond, they nevertheless present a common architecture at the machine language level across the entire line. Using microcode to implement an emulator enables the computer to present the architecture of an entirely different computer. The System/360 line used this to allow porting programs from earlier IBM machines to the new family of computers, e.g. an IBM 1401/1440/1460 emulator on the IBM S/360 model 40.


In telecommunication, coded mark inversion (CMI) is a non-return-to-zero (NRZ) line code. It encodes zero bits as a half bit time of zero followed by a half bit time of one, and while one bits are encoded as a full bit time of a constant level. The level used for one bits alternates each time one is coded. This is vaguely reminiscent of, but quite different from, Miller encoding, which also uses half-bit and full-bit pulses, but additionally uses the half-one/half-zero combination and arranges them so that the signal always spends at least a full bit time at a particular level before transitioning again. CMI doubles the bitstream frequency, when compared to its simple NRZ equivalent, but allows easy and reliable clock recovery.


In the direct scheme, the destination decodes the data using the signal received from the source node on the first phase where the second phase transmission is omitted so that the relay node is not involved in transmission. The decoding signal received from the source node is written as: r d , s = h d , s x s + n d , s {\displaystyle r_{d,s}=h_{d,s}x_{s}+n_{d,s}\quad } While the advantage of the direct scheme is its simplicity in terms of the decoding processing, the received signal power can be severely low if the distance between the source node and the destination node is large. Thus, in the following we consider non-cooperative scheme which exploits signal relaying to improve the signal quality.


In the X.509 trust model, a certificate authority (CA) is responsible for signing certificates. These certificates act as an introduction between two parties, which means that a CA acts as a trusted third party. A CA processes requests from people or organizations requesting certificates (called subscribers), verifies the information, and potentially signs an end-entity certificate based on that information. To perform this role effectively, a CA needs to have one or more broadly trusted root certificates or intermediate certificates and the corresponding private keys.


In statistical mechanics, one sometimes uses negative temperatures to describe systems with population inversion, which can be considered to have a temperature greater than positive infinity, because the coefficient of energy in the population distribution function is −1/Temperature. In this context, a temperature of −0 is a (theoretical) temperature larger than any other negative temperature, corresponding to the (theoretical) maximum conceivable extent of population inversion, the opposite extreme to +0.


In the (currently used) Gregorian calendar, alongside Tuesday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Thursday. The 28-year sub-cycle only spans across century years divisible by 400, e.g. 1600, 2000, and 2400. 400 year cycle century 1: 9, 15, 26, 37, 43, 54, 65, 71, 82, 93, 99 century 2: 105, 111, 122, 133, 139, 150, 161, 167, 178, 189, 195 century 3: 201, 207, 218, 229, 235, 246, 257, 263, 274, 285, 291 century 4: 303, 314, 325, 331, 342, 353, 359, 370, 381, 387, 398


In some cases, often where the changes are the most striking, Unicode has encoded variant characters, making it unnecessary to switch between fonts or lang attributes. However, some variants with arguably minimal differences get distinct codepoints, and not every variant with arguably substantial changes gets a unique codepoint. As an example, take a character such as 入 (U+5165), for which the only way to display the variants is to change font (or lang attribute) as described in the previous table. On the other hand, for 內 (U+5167), the variant of 内 (U+5185) gets a unique codepoint.


Algorithm Delete(r): D1. Find the host leaf: Perform an exact match search to find the leaf node L that contains r.D2. Delete r: Remove r from node L.D3.


In 1975 IBM started a project to develop a telephone switch that required performance about three times that of their fastest contemporary computers. To reach this goal, the development team began to study the massive amount of performance data IBM had collected over the last decade. This study demonstrated that the complex ISA was in fact a significant problem; because only the most basic instructions were guaranteed to be implemented in hardware, compilers ignored the more complex ones that only ran in hardware on certain machines.


MAIN - This is the normal setting when the engine is running. Sometimes this position is labeled "ON" or "RUN". RESERVE - In this position, a known but small volume of fuel is available to allow the rider to be able to reach a petrol station.


Most used simple caching to provide extremely fast RISC machines, with very compact code. Another benefit was that the interrupt latencies were very small, smaller than most CISC machines (a rare trait in RISC machines). The Burroughs large systems architecture used this approach.


In mathematics, the Mersenne conjectures concern the characterization of a kind of prime numbers called Mersenne primes, meaning prime numbers that are a power of two minus one.


Because its location in parent’s node is the only thing of importance, it is symbolised by (meaning: the current node N is a NIL node and left child) in the left column of the delete diagrams. As the operation proceeds also proper nodes (of black height ≥ 1) may become current (see e. g. case D2). By counting the black bullets ( and ) in a delete diagram it can be observed that the paths through N have one bullet less than the other paths.


The closer the approximation is to zero or one, the more helpful the approximation is in linear cryptanalysis. However, in practice, the binary variables are not independent, as is assumed in the derivation of the piling-up lemma. This consideration has to be kept in mind when applying the lemma; it is not an automatic cryptanalysis formula.


The specification includes signal names and functions, timing, and electrical constraints. The last MIPI board-adopted version of Specification for Parallel Trace Interface is version 2.0 (October 2011).The MIPI High-Speed Trace Interface (MIPI HTI) specifies how to stream trace data over the physical layer of standard interfaces, such as PCI Express, DisplayPort, HDMI, or USB. The current version of the specification allows for one to six lanes.


In mathematics, more specifically in computational algebra, a straight-line program (SLP) for a finite group G = ⟨S⟩ is a finite sequence L of elements of G such that every element of L either belongs to S, is the inverse of a preceding element, or the product of two preceding elements. An SLP L is said to compute a group element g ∈ G if g ∈ L, where g is encoded by a word in S and its inverses. Intuitively, an SLP computing some g ∈ G is an efficient way of storing g as a group word over S; observe that if g is constructed in i steps, the word length of g may be exponential in i, but the length of the corresponding SLP is linear in i. This has important applications in computational group theory, by using SLPs to efficiently encode group elements as words over a given generating set. Straight-line programs were introduced by Babai and Szemerédi in 1984 as a tool for studying the computational complexity of certain matrix group properties.


In order to explore more complex relationships, axes must be reordered. By arranging the axes in 3-dimensional space (however, still in parallel, like nails in a nail bed), an axis can have more than two neighbors in a circle around the central attribute, and the arrangement problem gets easier (for example by using a minimum spanning tree). A prototype of this visualization is available as extension to the data mining software ELKI. However, the visualization is harder to interpret and interact with than a linear order.


In mathematics, and in particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function x ↦ f(x) to its translation x ↦ f(x + a). In time series analysis, the shift operator is called the lag operator. Shift operators are examples of linear operators, important for their simplicity and natural occurrence.


In mathematics, the Kleene–Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Haskell Curry's combinatory logic introduced in 1930, and Alonzo Church's original lambda calculus, introduced in 1932–1933, both originally intended as systems of formal logic. The paradox was exhibited by Stephen Kleene and J. B. Rosser in 1935.


As such, the child object can continue to be modified and amended over time without rearranging the structure of its associated prototype as in class-based systems. It is also important to note that not only data, but also methods can be added or changed. For this reason, some prototype-based languages refer to both data and methods as "slots" or "members".


To prove this, consider the function g which maps x to f(x) − x. It is ≥ 0 on a and ≤ 0 on b. By the intermediate value theorem, g has a zero in ; this zero is a fixed point. Brouwer is said to have expressed this as follows: "Instead of examining a surface, we will prove the theorem about a piece of string. Let us begin with the string in an unfolded state, then refold it. Let us flatten the refolded string. Again a point of the string has not changed its position with respect to its original position on the unfolded string."


Additionally, the inspiration of colleagues was accounted for to have expanded. Along these lines, adopting agile practices in a distributed environment has demonstrated to be valuable for the quality of the project and its execution. Thus, these can be seen as some of the advantages achieved by combining agile in distributed development, however, the list is exhaustive. The main benefits can be listed as follows:


Turian et al. (2003) point out that, "Any MT evaluation measure is less reliable on shorter translations", and show that increasing the amount of data improves the reliability of a metric. However, they add that "... reliability on shorter texts, as short as one sentence or even one phrase, is highly desirable because a reliable MT evaluation measure can greatly accelerate exploratory data analysis".Banerjee et al. (2005) highlight five attributes that a good automatic metric must possess; correlation, sensitivity, consistency, reliability and generality. Any good metric must correlate highly with human judgment, it must be consistent, giving similar results to the same MT system on similar text.


In mathematics, in the field of group theory, a modular subgroup is a subgroup that is a modular element in the lattice of subgroups, where the meet operation is defined by the intersection and the join operation is defined by the subgroup generated by the union of subgroups. By the modular property of groups, every quasinormal subgroup (that is, a subgroup that permutes with all subgroups) is modular. In particular, every normal subgroup is modular.


The Stanford DASH multiprocessor system implements a variation of processor consistency which is incomparable (neither weaker nor stronger) to Goodman's definitions. All processors need to be consistent in the order in which they see writes by one processor and in the way they see writes by different processors to the same location. However, they do not need to be consistent when the writes are by different processors to different locations.


These theorems provide necessary conditions for planarity that are not sufficient conditions, and therefore can only be used to prove a graph is not planar, not that it is planar. If both theorem 1 and 2 fail, other methods may be used. Whitney's planarity criterion gives a characterization based on the existence of an algebraic dual; Mac Lane's planarity criterion gives an algebraic characterization of finite planar graphs, via their cycle spaces; The Fraysseix–Rosenstiehl planarity criterion gives a characterization based on the existence of a bipartition of the cotree edges of a depth-first search tree. It is central to the left-right planarity testing algorithm; Schnyder's theorem gives a characterization of planarity in terms of partial order dimension; Colin de Verdière's planarity criterion gives a characterization based on the maximum multiplicity of the second eigenvalue of certain Schrödinger operators defined by the graph. The Hanani–Tutte theorem states that a graph is planar if and only if it has a drawing in which each independent pair of edges crosses an even number of times; it can be used to characterize the planar graphs via a system of equations modulo 2.


The former is supported through some form of object literal, declarations where objects can be defined at runtime through special syntax such as {...} and passed directly to a variable. While most systems support a variety of cloning, ex nihilo object creation is not as prominent.In class-based languages, a new instance is constructed through a class's constructor function, a special function that reserves a block of memory for the object's members (properties and methods) and returns a reference to that block. An optional set of constructor arguments can be passed to the function and are usually held in properties.


In mathematics, in particular the study of abstract algebra, a Dedekind–Hasse norm is a function on an integral domain that generalises the notion of a Euclidean function on Euclidean domains.


First minimize the maximal value of the load on all of the network routing node links Do that by minimizing a load upper bound value that is applied to all links. The full mass of the flow will be split equally across the possible parallel routes. Find the bottleneck links of the first layer (see below), then set their loading amount at the found minimum.


Although the enhancement of the output code was considerable, the resulting increase in complexity of the compiler caused problems with the limited address space. At the time, better optimized code was seen to be an enabler to bootstrapping the code in Pascal. In retrospect, the remaining assembly written sections WERE the problem, and needed to be eliminated, the sooner the better. Another way to say this is that the space problems could be transient, but having significant program sections written in assembly are a serious and lasting problem.


Expert systems tend to capture the expertise, of individuals in different organizations, on the same topic. By contrast a KBS, produced by logico-linguistic modeling, seeks to capture the expertise of individuals in the same organization on different topics. The emphasis is on the elicitation of organizational or group knowledge rather than individual experts. In logico-linguistic modeling the stakeholders become the experts. The end point of this stage is an SSM style conceptual models such as figure 1.


An alternative and equivalent definition is that a family of sets forms a delta-matroid when the convex hull of its indicator vectors (the analogue of a matroid polytope) has the property that every edge length is either one or the square root of two. Delta-matroids were defined by André Bouchet in 1987. Algorithms for matroid intersection and the matroid parity problem can be extended to some cases of delta-matroids.Delta-matroids have also been used to study constraint satisfaction problems.


Multiple edges, not allowed under the definition above, are two or more edges that join the same two vertices. In one more general sense of the term allowing multiple edges, a graph is an ordered triple G = ( V , E , ϕ ) {\displaystyle G=(V,E,\phi )} comprising: V {\displaystyle V} , a set of vertices (also called nodes or points); E {\displaystyle E} , a set of edges (also called links or lines); ϕ: E → { { x , y } ∣ x , y ∈ V and x ≠ y } {\displaystyle \phi :E\to \{\{x,y\}\mid x,y\in V\;{\textrm {and}}\;x\neq y\}} , an incidence function mapping every edge to an unordered pair of vertices (that is, an edge is associated with two distinct vertices).To avoid ambiguity, this type of object may be called precisely an undirected multigraph. A loop is an edge that joins a vertex to itself.


In programming, an edge case typically involves input values that require special handling in an algorithm behind a computer program. As a measure for validating the behavior of computer programs in such cases, unit tests are usually created; they are testing boundary conditions of an algorithm, function or method. A series of edge cases around each "boundary" can be used to give reasonable coverage and confidence using the assumption that if it behaves correctly at the edges, it should behave everywhere else.For example, a function that divides two numbers might be tested using both very large and very small numbers. This assumes that if it works for both ends of the magnitude spectrum, it should work correctly in between.


Interest in these primes first arose due to their connection with Fermat's Last Theorem. Wolstenholme primes are also related to other special classes of numbers, studied in the hope to be able to generalize a proof for the truth of the theorem to all positive integers greater than two. The only two known Wolstenholme primes are 16843 and 2124679 (sequence A088164 in the OEIS). There are no other Wolstenholme primes less than 109.


In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities. For example, for a set { f i } {\displaystyle \{f_{i}\}} of polynomials over a ring R {\displaystyle R} , the solution set is the subset of R {\displaystyle R} on which the polynomials all vanish (evaluate to 0), formally { x ∈ R: ∀ i ∈ I , f i ( x ) = 0 } {\displaystyle \{x\in R:\forall i\in I,f_{i}(x)=0\}} The feasible region of a constrained optimization problem is the solution set of the constraints.


In painting, “brownness” defines earth tone. At the beginning of a painting, primitive painters used soil, animal fat, minerals, charcoal, and chalk combined to be a color around 40,000 years ago. Therefore, the first group of colors was a natural palette by themselves. And earth tone palette was very handy to mix from scratch.


The principle of integrity furthers this concept into honesty and accuracy throughout all professional psychological endeavors.Another area where APA guidelines move beyond the Belmont report is in the setting of standards. The APA establishes standards for all reputable members of the psychology community (particularly those members of the American Psychological Association). The association sets a code of conduct for all APA individuals, which, when violated, can result in termination of professional licensure or membership.


Every song or recording has a unique identity by which they are licensed and tracked. Details of songs or recordings are notified to the PROs directly, or through Catco, an electronic tracking system. It needs to be clarified that while blanket licenses are commonly issued to music-users, the latter are responsible for "usage returns" – the actual frequency of performances under the license – which then becomes the basis for the PRO to apportion royalties to writers, publishers, and record labels.


In concurrency control, path expressions are a mechanism for expressing permitted sequences of execution. For example, a path expression like " {read}, write" might specify that either multiple simultaneous executions of read or a single execution of write but not both are allowed at any point in time. It is important to know that the path expressions are a mechanism for the synchronization of processes at the monitor level in the software.


In mathematics, a bundle map (or bundle morphism) is a morphism in the category of fiber bundles. There are two distinct, but closely related, notions of bundle map, depending on whether the fiber bundles in question have a common base space. There are also several variations on the basic theme, depending on precisely which category of fiber bundles is under consideration. In the first three sections, we will consider general fiber bundles in the category of topological spaces. Then in the fourth section, some other examples will be given.


{\displaystyle F(x,0)=f(x).} The dual problem with respect to the chosen perturbation function is given by sup y ∗ ∈ Y ∗ − F ∗ ( 0 , y ∗ ) {\displaystyle \sup _{y^{*}\in Y^{*}}-F^{*}\left(0,y^{*}\right)} where F ∗ {\displaystyle F^{*}} is the convex conjugate in both variables of F . {\displaystyle F.}


A similar situation exists regarding the Korean KS X 1001 character set, in which Microsoft maps the EUC-KR or UHC code for the wave dash (0xA1AD) to U+223C ∼ TILDE OPERATOR, while IBM and Apple map it to U+301C. Microsoft also uses U+FF5E to map the KS X 1001 raised tilde (0xA2A6), while Apple uses U+02DC ˜ SMALL TILDE.The current Unicode reference glyph for U+301C has been corrected to match the JIS standard in response to a 2014 proposal, which noted that while the existing Unicode reference glyph had been matched by fonts from the discontinued Windows XP, all other major platforms including later versions of Microsoft Windows shipped with fonts matching the JIS reference glyph for U+301C.The JIS / Shift JIS wave dash is still formally mapped to U+301C as of JIS X 0213, whereas the WHATWG Encoding Standard used by HTML5 follows Microsoft in mapping 0x8160 to U+FF5E. These two code points have a similar or identical glyph in several fonts, reducing the confusion and incompatibility.


The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., "MECE"). The events 1 and 6 are mutually exclusive but not collectively exhaustive. The events "even" (2,4 or 6) and "not-6" (1,2,3,4, or 5) are also collectively exhaustive but not mutually exclusive.


Extreme storm flood protection levels have been revised based on new Federal Emergency Management Agency guidelines for 100-year and 500-year design flood elevations.In the New Orleans Metropolitan Area, 35 percent of which sits below sea level, is protected by hundreds of miles of levees and flood gates. This system failed catastrophically, with numerous breaks, during Hurricane Katrina (2005) in the city proper and in eastern sections of the Metro Area, resulting in the inundation of approximately 50 percent of the metropolitan area, ranging from a few inches to twenty feet in coastal communities. The Morganza Spillway provides a method of diverting water from the Mississippi River when a river flood threatens New Orleans, Baton Rouge and other major cities on the lower Mississippi.


In some applications, such as substring search, one can compute a hash function h for every k-character substring of a given n-character string by advancing a window of width k characters along the string; where k is a fixed integer, and n is greater than k. The straightforward solution, which is to extract such a substring at every character position in the text and compute h separately, requires a number of operations proportional to k·n. However, with the proper choice of h, one can use the technique of rolling hash to compute all those hashes with an effort proportional to mk + n where m is the number of occurrences of the substring.The most familiar algorithm of this type is Rabin-Karp with best and average case performance O(n+mk) and worst case O(n·k) (in all fairness, the worst case here is gravely pathological: both the text string and substring are composed of a repeated single character, such as t="AAAAAAAAAAA", and s="AAA"). The hash function used for the algorithm is usually the Rabin fingerprint, designed to avoid collisions in 8-bit character strings, but other suitable hash functions are also used.


In the field of theoretical computer science the computability and complexity of computational problems are often sought-after. Computability theory describes the degree to which problems are computable, whereas complexity theory describes the asymptotic degree of resource consumption. Computational problems are therefore confined into complexity classes.


After completing the customer migration, Sprint PCS sold the GSM radio interface network equipment to Omnipoint Communications in January 2000. Omnipoint was later purchased by VoiceStream Wireless which subsequently became T-Mobile US. In August 2022, T-Mobile US announced dead-zone cell phone coverage across the US using "midband" (1900 MHz) PCS spectrum and Starlink Gen2 satellite cell coverage, to begin testing in 2023. Using this satellite and midband spectrum, T-Mobile plans to be able to connect by satellite to common mobile devices, unlike previous generations of satellite phones which used specialized Earth-bound radios to connect to geosynchronous satellites with characteristic long lag time in communications.


In statistical genetics, Felsenstein's tree-pruning algorithm (or Felsenstein's tree-peeling algorithm), attributed to Joseph Felsenstein, is an algorithm for computing the likelihood of an evolutionary tree from nucleic acid sequence data. The algorithm is often used as a subroutine in a search for a maximum likelihood estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using likelihood ratio tests). It can also be used to provide error estimates for the parameters describing an evolutionary tree. == References ==


The following problem is the main open problem in this area of research: find an explicit polynomial of polynomial degree that requires circuits of superpolynomial size. The state of the art is a Ω ( n log  d ) {\displaystyle \Omega (n\log d)} lower bound for the size of a circuit computing, e.g., the polynomial x 1 d + ⋯ + x n d {\displaystyle x_{1}^{d}+\cdots +x_{n}^{d}} given by Strassen and by Baur and Strassen. More precisely, Strassen used Bézout's lemma to show that any circuit that simultaneously computes the n {\displaystyle n} polynomials x 1 d , … , x n d {\displaystyle x_{1}^{d},\ldots ,x_{n}^{d}} is of size Ω ( n log  d ) , {\displaystyle \Omega (n\log d),} and later Baur and Strassen showed the following: given an arithmetic circuit of size s {\displaystyle s} computing a polynomial f , {\displaystyle f,} one can construct a new circuit of size at most O ( s ) {\displaystyle O(s)} that computes f {\displaystyle f} and all the n {\displaystyle n} partial derivatives of f .


The relative simplicity of the algorithm makes it a popular first choice amongst optimizing algorithms. It is used widely in artificial intelligence, for reaching a goal state from a starting node. Different choices for next nodes and starting nodes are used in related algorithms.


In terms of the Legendre symbol, the law of quadratic reciprocity states for positive odd primes p , q {\displaystyle p,q} we have ( p q ) ( q p ) = ( − 1 ) p − 1 2 q − 1 2 . {\displaystyle \left({\frac {p}{q}}\right)\left({\frac {q}{p}}\right)=(-1)^{{\frac {p-1}{2}}{\frac {q-1}{2}}}.} Using the definition of the Legendre symbol this is equivalent to a more elementary statement about equations.


Because of the high value of these 'A' items, frequent value analysis is required. In addition to that, an organization needs to choose an appropriate order pattern (e.g. 'just-in-time') to avoid excess capacity. 'B' items are important, but of course less important than 'A' items and more important than 'C' items. Therefore, 'B' items are intergroup items. 'C' items are marginally important.


Such a point, if it exists, is called a global minimum point of the function and its value at this point is called the global minimum (value) of the function. If the function takes − ∞ {\displaystyle -\infty } as a value then − ∞ {\displaystyle -\infty } is necessarily the global minimum value and the minimization problem can be answered; this is ultimately the reason why the definition of "proper" requires that the function never take − ∞ {\displaystyle -\infty } as a value. Assuming this, if the function's domain is empty or if the function is identically equal to + ∞ {\displaystyle +\infty } then the minimization problem once again has an immediate answer.


The order dimension of a partial order is the minimum number of linear orders whose intersection is the given partial order. If a partial order has bounded order dimension, then an adjacency labeling scheme for the vertices in its comparability graph may be defined by labeling each vertex with its position in each of the defining linear orders, and determining that two vertices are adjacent if each corresponding pair of numbers in their labels has the same order relation as each other pair. In particular, this allows for an adjacency labeling scheme for the chordal comparability graphs, which come from partial orders of dimension at most four.


In telecommunications, a proprietary protocol is a communications protocol owned by a single organization or individual.


In cryptography, modular arithmetic directly underpins public key systems such as RSA and Diffie–Hellman, and provides finite fields which underlie elliptic curves, and is used in a variety of symmetric key algorithms including Advanced Encryption Standard (AES), International Data Encryption Algorithm (IDEA), and RC4. RSA and Diffie–Hellman use modular exponentiation. In computer algebra, modular arithmetic is commonly used to limit the size of integer coefficients in intermediate calculations and data.


In mathematics, constraint counting is counting the number of constraints in order to compare it with the number of variables, parameters, etc. that are free to be determined, the idea being that in most cases the number of independent choices that can be made is the excess of the latter over the former. For example, in linear algebra if the number of constraints (independent equations) in a system of linear equations equals the number of unknowns then precisely one solution exists; if there are fewer independent equations than unknowns, an infinite number of solutions exist; and if the number of independent equations exceeds the number of unknowns, then no solutions exist. In the context of partial differential equations, constraint counting is a crude but often useful way of counting the number of free functions needed to specify a solution to a partial differential equation.


In mathematics, the Robinson–Schensted–Knuth correspondence, also referred to as the RSK correspondence or RSK algorithm, is a combinatorial bijection between matrices A with non-negative integer entries and pairs (P,Q) of semistandard Young tableaux of equal shape, whose size equals the sum of the entries of A. More precisely the weight of P is given by the column sums of A, and the weight of Q by its row sums. It is a generalization of the Robinson–Schensted correspondence, in the sense that taking A to be a permutation matrix, the pair (P,Q) will be the pair of standard tableaux associated to the permutation under the Robinson–Schensted correspondence. The Robinson–Schensted–Knuth correspondence extends many of the remarkable properties of the Robinson–Schensted correspondence, notably its symmetry: transposition of the matrix A results in interchange of the tableaux P,Q.


In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to Q, the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem. It was in the process of his deep investigations of the arithmetic of these fields (for prime n) – and more precisely, because of the failure of unique factorization in their rings of integers – that Ernst Kummer first introduced the concept of an ideal number and proved his celebrated congruences.


In telecommunication, the term access control is defined in U.S. Federal Standard 1037C with the following meanings: A service feature or technique used to permit or deny use of the components of a communication system. A technique used to define or restrict the rights of individuals or application programs to obtain data from, or place data onto, a storage device. The definition or restriction of the rights of individuals or application programs to obtain data from, or place data into, a storage device. The process of limiting access to the resources of an AIS (Automated Information System) to authorized users, programs, processes, or other systems. That function performed by the resource controller that allocates system resources to satisfy user requests.This definition depends on several other technical terms from Federal Standard 1037C.


In the early 1980s, when Simple Mail Transfer Protocol (SMTP) was designed, it provided for no real verification of sending user or system. This was not a problem while email systems were run by trusted corporations and universities, but since the commercialization of the Internet in the early 1990s, spam, phishing, and other crimes have been found to increasingly involve email. Email authentication is a necessary first step towards identifying the origin of messages, and thereby making policies and laws more enforceable. Hinging on domain ownership is a stance that emerged in the early 2000.


In the following discussion, the following conventions are adopted. K {\displaystyle \mathbb {K} } will denote one of the fields of real or complex numbers, denoted R {\displaystyle \mathbb {R} } , C {\displaystyle \mathbb {C} } , respectively. The vector space of m × n {\displaystyle m\times n} matrices over K {\displaystyle \mathbb {K} } is denoted by K m × n {\displaystyle \mathbb {K} ^{m\times n}} . For A ∈ K m × n {\displaystyle A\in \mathbb {K} ^{m\times n}} , A T {\displaystyle A^{\textsf {T}}} and A ∗ {\displaystyle A^{*}} denote the transpose and Hermitian transpose (also called conjugate transpose) respectively.


In organisms with a changeable shape, such as amoeboid organisms, most directional terms are meaningless, since the shape of the organism is not constant and no distinct axes are fixed. Similarly, in spherically symmetrical organisms, there is nothing to distinguish one line through the centre of the organism from any other. An indefinite number of triads of mutually perpendicular axes could be defined, but any such choice of axes would be useless, as nothing would distinguish a chosen triad from any others. In such organisms, only terms such as superficial and deep, or sometimes proximal and distal, are usefully descriptive.


Processes are complex events constituted by a sequence of events. But even simple events can be conceived as complex entities involving an object, a time and the property exemplified by the object at this time. Traditionally, metaphysicians tended to emphasize static being over dynamic events. This tendency has been opposed by so-called process philosophy or process ontology, which ascribes ontological primacy to events and processes.


In source code, the null character is often represented as the escape sequence \0 in string literals (for example, "abc\0def") or in character constants ('\0'); the latter may also be written instead simply as 0 (without quotes nor slash). In many languages (such as C, which introduced this notation), this is not a separate escape sequence, but an octal escape sequence with a single octal digit 0; as a consequence, \0 must not be followed by any of the digits 0 through 7; otherwise it is interpreted as the start of a longer octal escape sequence. Other escape sequences that are found in use in various languages are \000, \x00, \z, or \u0000. A null character can be placed in a URL with the percent code %00.


In the 5th century BC, Hippocrates of Chios showed that the Lune of Hippocrates and two other lunes could be exactly squared (converted into a square having the same area) by straightedge and compass. In 1766 the Finnish mathematician Daniel Wijnquist, quoting Daniel Bernoulli, listed all five geometrical squareable lunes, adding to those known by Hippocrates. In 1771 Leonard Euler gave a general approach and obtained certain equation to the problem. In 1933 and 1947 it was proven by Nikolai Chebotaryov and his student Anatoly Dorodnov that these five are the only squarable lunes.


In this case, to ensure that an application of a rewriting rule is not going to interfere with other resolution steps, a safe solution is to create a copy of the node represented by clause δ {\displaystyle \delta } . This solution increases proof size and some caution is needed when doing this. The heuristic for rule selection is important to achieve a good compression performance.


Each of the standards has been placed in one of four fundamental categories to promote educational evaluations that are proper, useful, feasible, and accurate. In these sets of standards, validity and reliability considerations are covered under the accuracy topic. The tests are aimed at ensuring that student evaluations will provide sound, accurate, and credible information about student learning and performance, however; standardized tests offer narrow information on many forms of intelligence and relying on them harms students because they inaccurately measure a student's potential for success.


The problem was not so acute on minicomputers and mainframes where the vendor often specified standards for their libraries, but on microcomputers the programming systems were generally delivered by a variety of 3rd party companies with no interest in standardization. Nevertheless, this problem was being addressed in the early 1990s through the introduction of various shared library systems. These were actually intended to ease resource use on smaller platforms, by allowing a number of programs using a common resource, like the GUI, to share a single copy of code instead of each loading a separate copy into memory.


Scores using this metric have historically been known as "raw" scores. Tests taken in October 2004 or later have a score range from 200 to 600. The median score is 400, with a standard deviation of 25 points.


In mathematics and computer science, the binary Goppa code is an error-correcting code that belongs to the class of general Goppa codes originally described by Valerii Denisovich Goppa, but the binary structure gives it several mathematical advantages over non-binary variants, also providing a better fit for common usage in computers and telecommunication. Binary Goppa codes have interesting properties suitable for cryptography in McEliece-like cryptosystems and similar setups.


In some systems and in the context of message processing systems (often real-time systems), this term also refers to the goal of establishing a single agreed sequence of messages within a database formed by a particular but arbitrary sequencing of records. The key concept is that data combined in a certain sequence is a "truth" which may be analyzed and processed giving particular results, and that although the sequence is arbitrary (and thus another correct but equally arbitrary sequencing would ultimately provide different results in any analysis), it is desirable to agree that the sequence enshrined in the "single version of the truth" is the version that will be considered "the truth", and that any conclusions drawn from analysis of the database are valid and unarguable, and (in a technical context) the database may be duplicated to a backup environment to ensure a persistent record is kept of the "single version of the truth". The key point is when the database is created using an external data source (such as a sequence of trading messages from a stock exchange) an arbitrary selection is made of one possibility from two or more equally valid representations of the input data, but henceforth the decision sets "in stone" one and only one version of the truth.


In terms of performance, virtualization imposes a cost in the additional work the CPU has to perform to virtualize the underlying hardware. Instructions that perform this extra work, and other activities that require virtualization, tend to lie in operating system calls. In an unmodified operating system, OS calls introduce the greatest portion of virtualization "overhead".Paravirtualization or other virtualization techniques may help with these issues. VMware developed the Virtual Machine Interface for this purpose, and selected operating systems currently support this. A comparison between full virtualization and paravirtualization for the ESX Server shows that in some cases paravirtualization is much faster.


In telecommunication, call setup is the process of establishing a virtual circuit across a telecommunications network. Call setup is typically accomplished using a signaling protocol. The term call set-up time has the following meanings: The overall length of time required to establish a circuit-switched call between users. For data communication, the overall length of time required to establish a circuit-switched call between terminals; i.e., the time from the initiation of a call request to the beginning of the call message.Note: Call set-up time is the summation of: (a) call request time—the time from initiation of a calling signal to the delivery to the caller of a proceed-to-select signal; (b) selection time—the time from the delivery of the proceed-to-select signal until all the selection signals have been transmitted; and (c) post selection time—the time from the end of the transmission of the selection signals until the delivery of the call-connected signal to the originating terminal.


The modulo operation, as implemented in many programming languages and calculators, is an application of modular arithmetic that is often used in this context. The logical operator XOR sums 2 bits, modulo 2. In music, arithmetic modulo 12 is used in the consideration of the system of twelve-tone equal temperament, where octave and enharmonic equivalency occurs (that is, pitches in a 1:2 or 2:1 ratio are equivalent, and C-sharp is considered the same as D-flat).


In the IBM System/360 and its successors, including the current z/Architecture machines, the boot process is known as Initial Program Load (IPL). IBM coined this term for the 7030 (Stretch), revived it for the design of the System/360, and continues to use it in those environments today. In the System/360 processors, an IPL is initiated by the computer operator by selecting the three hexadecimal digit device address (CUU; C=I/O Channel address, UU=Control unit and Device address) followed by pressing the LOAD button. On the high end System/360 models, most System/370 and some later systems, the functions of the switches and the LOAD button are simulated using selectable areas on the screen of a graphics console, often an IBM 2250-like device or an IBM 3270-like device.


In some cases, it is required to compute an envy-minimizing allocation in a distributed manner, i.e., each agent should compute his/her own allocation, in a way that guarantees that the resulting allocation is consistent. This problem can be solved by presenting it as an Asymmetric distributed constraint optimization problem (ADCOP) as follows. Add a binary variable vij for each agent i and item j. The variable value is "1" if the agent gets the item, and "0" otherwise. The variable is owned by agent i. To express the constraint that each item is given to at most one agent, add binary constraints for each two different variables related to the same item, with an infinite cost if the two variables are simultaneously "1", and a zero cost otherwise.


Some have a bell inlet for a faster more effective flush. A problem with the valve type flush mechanism is that it invariably starts to leak after a couple of years use due to wear and tear of the valve, particles, etc. trapped in the valve.


The use of a high level language (C) to implement the operating system, and the reliance on standardized interfaces was in contrast to the assembly language oriented approaches of the past. As hardware vendors adapted Unix to their systems, new and useful features were added to Unix, e.g., fast file systems and tunable process schedulers. However, all the companies that adapted Unix made unique changes to it, rather than collaborating on an industry standard to create "Unix for supercomputers".


If all of the residuals are equal, or do not fan out, they exhibit homoscedasticity. However, a terminological difference arises in the expression mean squared error (MSE). The mean squared error of a regression is a number computed from the sum of squares of the computed residuals, and not of the unobservable errors.


After its cancellation when the work has been finished, the switching schedule then facilitates restoration of the normal running arrangements. Switching components can also be tagged to reflect any Operational Restrictions that are in force. The network component/connectivity model, and associated diagrams, must always be kept absolutely up to date. The switching schedule facility therefore also allows 'patches' to the network model to be applied to the live version at the appropriate stage(s) of the jobs. The term 'patch' is derived from the method previously used to maintain the wallboard diagrams.


AM, a computer mathematician that generates new mathematical concepts. It managed to produce by itself the notion of prime number and the Goldbach conjecture.


Therefore, people are called on to abide by a secret law. At least two things need to be examined: First is that the operation of a more general "chilling effect" that imposing a non disclosed law may have and; Secondly the social effects of discrimination, which take an entirely new light in the context of no longer discriminating against race creed color age or religion, but on the basis of a number, a number which has been assigned to all members of society reflecting information about that person which is unknown. Accordingly, there can be no definition at present of what information credit repositories collect or even what the use of that information is or what it reflects.


His tests were shorter, but used similar techniques. Wundt also measured mental processes and acknowledged the fact that there are individual differences between people.


In telecommunication, bit pairing is the practice of establishing, within a code set, a number of subsets that have an identical bit representation except for the state of a specified bit. Note: An example of bit pairing occurs in the International Alphabet No. 5 and the American Standard Code for Information Interchange (ASCII), where the upper case letters are related to their respective lower case letters by the state of bit six.


Good metric performance, across text types or domains, is important for the reusability of the metric. A metric that only works for text in a specific domain is useful, but less useful than one that works across many domains—because creating a new metric for every new evaluation or domain is undesirable. Another important factor in the usefulness of an evaluation metric is to have a good correlation, even when working with small amounts of data, that is candidate sentences and reference translations.


In recent years a number of neural and deep-learning techniques have been proposed. Some generalize traditional Matrix factorization algorithms via a non-linear neural architecture, or leverage new model types like Variational Autoencoders. While deep learning has been applied to many different scenarios: context-aware, sequence-aware, social tagging etc. its real effectiveness when used in a simple collaborative recommendation scenario has been put into question.


The adjective which corresponds to squaring is quadratic. The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers.


In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables. Marginal variables are those variables in the subset of variables being retained.


In the form stated here, the splitting lemma does not hold in the full category of groups, which is not an abelian category.


In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f −1(Y ) = {x ∈ Rn | f(x) ∈ Y }. It can also be viewed as the problem of describing the solution set of the quantified constraint "Y(f (x))", where Y( y) is a constraint, e.g. an inequality, describing the set Y. In most applications, f is a function from Rn to Rp and the set Y is a box of Rp (i.e. a Cartesian product of p intervals of R). When f is nonlinear the set inversion problem can be solved using interval analysis combined with a branch-and-bound algorithm.The main idea consists in building a paving of Rp made with non-overlapping boxes. For each box , we perform the following tests: if f () ⊂ Y we conclude that  ⊂ X; if f () ∩ Y = ∅ we conclude that  ∩ X = ∅; Otherwise, the box  the box is bisected except if its width is smaller than a given precision.To check the two first tests, we need an interval extension (or an inclusion function)  for f. Classified boxes are stored into subpavings, i.e., union of non-overlapping boxes. The algorithm can be made more efficient by replacing the inclusion tests by contractors.


For example, the permutation (1 3 2 4) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 is a 4-cycle, and the permutation (1 3 2)(4) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 is considered a 3-cycle by some authors. On the other hand, the permutation (1 3)(2 4) that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs {1, 3} and {2, 4}. The set of elements that are not fixed by a cyclic permutation is called the orbit of the cyclic permutation. Every permutation on finitely many elements can be decomposed into cyclic permutations on disjoint orbits. The individual cyclic parts of a permutation are also called cycles, thus the second example is composed of a 3-cycle and a 1-cycle (or fixed point) and the third is composed of two 2-cycles.


In mathematical field of combinatorial geometry, the Littlewood–Offord problem is the problem of determining the number of subsums of a set of vectors that fall in a given convex set. More formally, if V is a vector space of dimension d, the problem is to determine, given a finite subset of vectors S and a convex subset A, the number of subsets of S whose summation is in A. The first upper bound for this problem was proven (for d = 1 and d = 2) in 1938 by John Edensor Littlewood and A. Cyril Offord. This Littlewood–Offord lemma states that if S is a set of n real or complex numbers of absolute value at least one and A is any disc of radius one, then not more than ( c log  n / n ) 2 n {\displaystyle {\Big (}c\,\log n/{\sqrt {n}}{\Big )}\,2^{n}} of the 2n possible subsums of S fall into the disc. In 1945 Paul Erdős improved the upper bound for d = 1 to ( n ⌊ n / 2 ⌋ ) ≈ 2 n 1 n {\displaystyle {n \choose \lfloor {n/2}\rfloor }\approx 2^{n}\,{\frac {1}{\sqrt {n}}}} using Sperner's theorem.


This is because painting is a subtractive color process, for which red and blue are secondary, not primary, colors. Although flawed in principle, the split-primary system can be successful in practice, because the recommended blue-biased red and green-biased blue positions are often filled by near approximations of magenta and cyan, respectively, while orange-biased red and violet-biased blue serve as secondary colors, which tend to further widen the mixable gamut. This system is in effect a simplified version of Newton's geometrical rule that colors closer together on the hue circle will produce more vibrant mixtures. A mixture, however, produced from two primary colors will be much more highly saturated than one produced from two secondary colors, even though both pairs are the same distance apart on the hue circle, revealing the limitations of the circular model in the prediction of color mixing results.


In the Scandinavian languages, adjectives (both attributive and predicative) are declined according to the gender, number, and definiteness of the noun they modify. In Icelandic and Faroese, adjectives are also declined according to grammatical case, unlike the other Scandinavian languages. In some cases in Swedish, Norwegian and Danish, adjectives and participles as predicates appear to disagree with their subjects. This phenomenon is referred to as pancake sentences.


In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum x ∗ {\displaystyle \mathbf {x} ^{*}} of an objective function f: R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } . The other approach is trust region. The line search approach first finds a descent direction along which the objective function f {\displaystyle f} will be reduced and then computes a step size that determines how far x {\displaystyle \mathbf {x} } should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either exactly or inexactly.


In mathematics, the quasi-dihedral groups, also called semi-dihedral groups, are certain non-abelian groups of order a power of 2. For every positive integer n greater than or equal to 4, there are exactly four isomorphism classes of non-abelian groups of order 2n which have a cyclic subgroup of index 2. Two are well known, the generalized quaternion group and the dihedral group.


In order to de-risk the programme Atlas and the MOD took an incremental approach to the development and implementation of DII, with a separate contract for each increment. The extended timeline allowed the MOD flexibility in defining its requirements. Increment 1: Contract awarded March 2005. This covered 70,000 user access devices (UADs) and 200,000 user accounts in the Restricted and Secret domains in 680 fixed locations.


In the following, let X {\displaystyle X} be our n {\displaystyle n} -dimensional input space. Let H {\displaystyle {\mathcal {H}}} be a class of functions that we wish to use in order to learn a { 0 , 1 } {\displaystyle \{0,1\}} -valued target function f {\displaystyle f} defined over X {\displaystyle X} . Let D {\displaystyle {\mathcal {D}}} be the distribution of the inputs over X {\displaystyle X} . The goal of a learning algorithm A {\displaystyle {\mathcal {A}}} is to choose the best function h ∈ H {\displaystyle h\in {\mathcal {H}}} such that it minimizes e r r o r ( h ) = P x ∼ D ( h ( x ) ≠ f ( x ) ) {\displaystyle error(h)=P_{x\sim {\mathcal {D}}}(h(x)\neq f(x))} .


In the United States and Canada, almost all public libraries have computers available for the use of patrons, though some libraries will impose a time limit on users to ensure others will get a turn and keep the library less busy. Users are often allowed to print documents that they have created using these computers, though sometimes for a small fee.


Information policy is playing a greater role in the economy leading to the production of goods and services, as well as selling them directly to consumers (UCLA, 2009). The cost of information varies from a tangible good in that initial costs of the first unit are large and fixed; however, after that, marginal costs are relatively low (MacInnes, 2011). As an increase from the information services, information can be paralleled to that of manufacturing several years ago (UCLA, 2009). The digitalization of information allows businesses to make better justified business decisions (MacInnes, 2011).


Often identical files are installed on multiple computers, for example operating system files. With single-instance storage, only one copy of a file is written to the backup media therefore reducing space. This becomes more important when the storage is offsite and on cloud storage such as Amazon S3.


In probability theory, although simple examples illustrate that linear uncorrelatedness of two random variables does not in general imply their independence, it is sometimes mistakenly thought that it does imply that when the two random variables are normally distributed. This article demonstrates that assumption of normal distributions does not have that consequence, although the multivariate normal distribution, including the bivariate normal distribution, does. To say that the pair ( X , Y ) {\displaystyle (X,Y)} of random variables has a bivariate normal distribution means that every linear combination a X + b Y {\displaystyle aX+bY} of X {\displaystyle X} and Y {\displaystyle Y} for constant (i.e. not random) coefficients a {\displaystyle a} and b {\displaystyle b} (not both equal to zero) has a univariate normal distribution. In that case, if X {\displaystyle X} and Y {\displaystyle Y} are uncorrelated then they are independent. However, it is possible for two random variables X {\displaystyle X} and Y {\displaystyle Y} to be so distributed jointly that each one alone is marginally normally distributed, and they are uncorrelated, but they are not independent; examples are given below.


In later work by Vila Casado et al., alternative update techniques were studied, in which variable nodes are updated with the newest available check-node information.The intuition behind these algorithms is that variable nodes whose values vary the most are the ones that need to be updated first. Highly reliable nodes, whose log-likelihood ratio (LLR) magnitude is large and does not change significantly from one update to the next, do not require updates with the same frequency as other nodes, whose sign and magnitude fluctuate more widely. These scheduling algorithms show greater speed of convergence and lower error floors than those that use flooding. These lower error floors are achieved by the ability of the Informed Dynamic Scheduling (IDS) algorithm to overcome trapping sets of near codewords.When nonflooding scheduling algorithms are used, an alternative definition of iteration is used. For an (n, k) LDPC code of rate k/n, a full iteration occurs when n variable and n − k constraint nodes have been updated, no matter the order in which they were updated.


The native thread remains attached to the VM until it calls DetachCurrentThread() to detach itself.The JNI framework does not provide any automatic garbage collection for non-JVM memory resources allocated by code executing on the native side. Consequently, native side code (such as assembly language) assumes the responsibility for explicitly releasing any such memory resources that the native code acquires. On Linux and Solaris platforms, if the native code registers itself as a signal handler, it could intercept signals intended for the JVM.


In music, a monad is a single note or pitch. The Western chromatic scale, for example, is composed of twelve monads. Monads are contrasted to dyads, groups of two notes, triads, groups of three, and so on. == References ==


The mutant should be the specification that the engineer guesses the programmer has implemented. Then, the engineer has to calculate the subset of the VIS that yields different results in both specifications. The predicate of this set is used to derive a new test class.Some other testing tactics that may also be used are the following: In Set Extension (ISE).


An occasional darkly discolored or corroded nickel, dime, quarter, or half dollar can fool the collector by its edge, giving off the appearance of a silver coin. Often coin roll hunters also collect special proof coins, tokens and other exonumia, and foreign coins. Others attempt to find and complete a set of coins, like the America the Beautiful Quarters, 50 State Quarters, Presidential Dollars, or even every year and mint of regular designs.


It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. Euclid poses the problem thus: "Given two numbers not prime to one another, to find their greatest common measure". He defines "A number  a multitude composed of units": a counting number, a positive integer not including zero.


In the area of modern algebra known as group theory, the Thompson group Th is a sporadic simple group of order 215 · 310 · 53 · 72 · 13 · 19 · 31 = 90745943887872000 ≈ 9×1016.


{\displaystyle \Delta \left(C^{*}(m_{1}),C^{*}(m_{2})\right)\geqslant H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k\cdot T.} So now the final task is to find a lower bound for T {\displaystyle T} .


In the following theorems A , P , Q ∈ R n × n {\displaystyle A,P,Q\in \mathbb {R} ^{n\times n}} , and P {\displaystyle P} and Q {\displaystyle Q} are symmetric. The notation P > 0 {\displaystyle P>0} means that the matrix P {\displaystyle P} is positive definite. Theorem (continuous time version). Given any Q > 0 {\displaystyle Q>0} , there exists a unique P > 0 {\displaystyle P>0} satisfying A T P + P A + Q = 0 {\displaystyle A^{T}P+PA+Q=0} if and only if the linear system x ˙ = A x {\displaystyle {\dot {x}}=Ax} is globally asymptotically stable.


In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. The principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. However, the principle has never been explicitly stated by Frege, and arguably it was already assumed by George Boole decades before Frege's work. The principle of compositionality is highly debated in linguistics. Among its most challenging problems there are the issues of contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations.


In queueing theory, a discipline within the mathematical theory of probability, a polling system or polling model is a system where a single server visits a set of queues in some order. The model has applications in computer networks and telecommunications, manufacturing and road traffic management. The term polling system was coined at least as early as 1968 and the earliest study of such a system in 1957 where a single repairman servicing machines in the British cotton industry was modelled.Typically it is assumed that the server visits the different queues in a cyclic manner. Exact results exist for waiting times, marginal queue lengths and joint queue lengths at polling epochs in certain models. Mean value analysis techniques can be applied to compute average quantities.In a fluid limit, where a very large number of small jobs arrive the individual nodes can be viewed to behave similarly to fluid queues (with a two state process).


The first factor corresponds to how likely it is that the chosen edge contains the vertex, which increases when the vertex has more friends. The halving factor simply comes from the fact that each edge has two vertices. So the expected value of the number of friends of a (randomly chosen) friend is ∑ v ( d ( v ) | E | 1 2 ) d ( v ) = ∑ v d ( v ) 2 2 | E | .


Enabling PAE (by setting bit 5, PAE, of the system register CR4) causes major changes to this scheme. By default, the size of each page remains as 4 KB. Each entry in the page table and page directory becomes 64 bits long (8 bytes), instead of 32 bits, to allow for additional address bits.


Note that in these cases the handle must be something other than a systemwide-unique small integer, otherwise it is forgeable. Such an integer may nevertheless be used to identify a capability inside a process; e.g., file descriptor in Linux is unforgeable because its numerical value alone is meaningless, and only in the process context may refer to anything. Transferring such a handle requires special care though, as its value often has to be different in the sending and receiving processes. In non-capability-based systems, on the other hand, each process must acquire its own separate handle, by specifying the identity of the resource and the desired access rights (e.g., each process must open a file itself, by giving the filename and access mode). Such usage is more common even in modern systems that do support passing handles, but it is subject to vulnerabilities like the confused deputy problem.


Each user will be associated to a row of the first matrix and each item with a column of the second matrix. The row or column associated to a specific user or item is called latent factors. When a new item is added it has no associated latent factors and the lack of interactions does not allow to learn them, as it was done with other items.


In mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements. For example, the sequence ⟨ A , B , D ⟩ {\displaystyle \langle A,B,D\rangle } is a subsequence of ⟨ A , B , C , D , E , F ⟩ {\displaystyle \langle A,B,C,D,E,F\rangle } obtained after removal of elements C , {\displaystyle C,} E , {\displaystyle E,} and F . {\displaystyle F.} The relation of one sequence being the subsequence of another is a preorder.


In object-oriented programming languages, and other related fields, encapsulation refers to one of two related but distinct notions, and sometimes to the combination thereof: A language mechanism for restricting direct access to some of the object's components. A language construct that facilitates the bundling of data with the methods (or other functions) operating on those data.Some programming language researchers and academics use the first meaning alone or in combination with the second as a distinguishing feature of object-oriented programming, while some programming languages that provide lexical closures view encapsulation as a feature of the language orthogonal to object orientation. The second definition is motivated by the fact that in many object-oriented languages, and other related fields, the components are not hidden automatically and this can be overridden; thus, information hiding is defined as a separate notion by those who prefer the second definition. The features of encapsulation are supported using classes in most object-oriented languages, although other alternatives also exist.


In terms of clients and services. Each service comprises one or more servers and exports operations that clients invoke by making requests. Although using a single, centralized server is the simplest way to implement a service, the resulting service can only be as fault tolerant as the processor executing that server. If this level of fault tolerance is unacceptable, then multiple servers that fail independently can be used. Usually, replicas of a single server are executed on separate processors of a distributed system, and protocols are used to coordinate client interactions with these replicas.


In terms of the Legendre symbol, the law of quadratic reciprocity for positive odd primes states ( p q ) ( q p ) = ( − 1 ) p − 1 2 q − 1 2 . {\displaystyle \left({\frac {p}{q}}\right)\left({\frac {q}{p}}\right)=(-1)^{{\frac {p-1}{2}}{\frac {q-1}{2}}}.} A reciprocity law is a generalization of the law of quadratic reciprocity.


The EI condition implies that the total cake-price should be 2, so q + 2 p = 1 {\displaystyle q+2p=1} . The EI condition again implies that, in any connected CEEI division, the cake is cut in the middle. Both Alice and George receive two peripheral slices and one central slice.


In statistics, econometrics and related fields, multidimensional analysis (MDA) is a data analysis process that groups data into two categories: data dimensions and measurements. For example, a data set consisting of the number of wins for a single football team at each of several years is a single-dimensional (in this case, longitudinal) data set. A data set consisting of the number of wins for several football teams in a single year is also a single-dimensional (in this case, cross-sectional) data set. A data set consisting of the number of wins for several football teams over several years is a two-dimensional data set.


In some applications, the observations within each pair can only take the values 0 or 1. For example, 0 may indicate failure and 1 may indicate success. There are 4 possible pairs: {0,0}, {0,1}, {1,0}, and {1,1}. In these cases, the same procedure as the sign test is used, but is known as McNemar's test.


Put in simple technical terms, Cochran's Q test requires that there only be a binary response (e.g. success/failure or 1/0) and that there be more than 2 groups of the same size. The test assesses whether the proportion of successes is the same between groups. Often it is used to assess if different observers of the same phenomenon have consistent results (interobserver variability).


There are three major kinds of qualities or characteristics: types or kinds (e.g. mammal), properties (e.g. short, strong), and relations (e.g. father of, next to). These are all different types of universals.Paradigmatically, universals are abstract (e.g. humanity), whereas particulars are concrete (e.g. the personhood of Socrates).