In statistics, Bhattacharyya angle, also called statistical angle, is a measure of distance between two probability measures defined on a finite probability space. It is defined as Δ ( p , q ) = arccos  BC  ( p , q ) {\displaystyle \Delta (p,q)=\arccos \operatorname {BC} (p,q)} where pi, qi are the probabilities assigned to the point i, for i = 1, ..., n, and BC  ( p , q ) = ∑ i = 1 n p i q i {\displaystyle \operatorname {BC} (p,q)=\sum _{i=1}^{n}{\sqrt {p_{i}q_{i}}}} is the Bhattacharya coefficient.The Bhattacharya distance is the geodesic distance in the orthant of the sphere S n − 1 {\displaystyle S^{n-1}} obtained by projecting the probability simplex on the sphere by the transformation p i ↦ p i , i = 1 , … , n {\displaystyle p_{i}\mapsto {\sqrt {p_{i}}},\ i=1,\ldots ,n} . This distance is compatible with Fisher metric. It is also related to Bures distance and fidelity between quantum states as for two diagonal states one has Δ ( ρ , σ ) = arccos  F ( ρ , σ ) . {\displaystyle \Delta (\rho ,\sigma )=\arccos {\sqrt {F(\rho ,\sigma )}}.}


It is a collaborative effort, developed by Sandia National Laboratories, Los Alamos National Laboratories, and the United States Army Research Laboratory, and funded by the Advanced Simulation and Computing Program. It is developed under a BSD license. Pyomo is a python-based optimization Mathematical Programming Language which supports most commercial and open-source solver engines.


{\displaystyle \{1,2,3,\ldots \}.} Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set.


Providers of nomadic VoIP service—those who are unable to determine the location of their users—are exempt from state telecommunications regulation.Another legal issue that the US Congress is debating concerns changes to the Foreign Intelligence Surveillance Act. The issue in question is calls between Americans and foreigners. The NSA is not authorized to tap Americans' conversations without a warrant—but the Internet, and specifically VoIP does not draw as clear a line to the location of a caller or a call's recipient as the traditional phone system does. As VoIP's low cost and flexibility convinces more and more organizations to adopt the technology, surveillance for law enforcement agencies becomes more difficult. VoIP technology has also increased federal security concerns because VoIP and similar technologies have made it more difficult for the government to determine where a target is physically located when communications are being intercepted, and that creates a whole set of new legal challenges.


In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, effective numbers or the computable reals or recursive reals. The concept of a computable real number was introduced by Emile Borel in 1912, using the intuitive notion of computability available at the time.Equivalent definitions can be given using μ-recursive functions, Turing machines, or λ-calculus as the formal representation of algorithms. The computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes.


), and spruces (Picea spp.). In some areas of this biome, the conifers may be a more important canopy species than the broadleaf species. In the Southern Hemisphere, endemic genera such as Nothofagus and Eucalyptus occupy this biome, and most coniferous trees (members of the Araucariaceae and Podocarpaceae) occur in mixtures with broadleaf species, and are classed as broadleaf and mixed forests.


In mathematics, projections onto convex sets (POCS), sometimes known as the alternating projection method, is a method to find a point in the intersection of two closed convex sets. It is a very simple algorithm and has been rediscovered many times. The simplest case, when the sets are affine spaces, was analyzed by John von Neumann. The case when the sets are affine spaces is special, since the iterates not only converge to a point in the intersection (assuming the intersection is non-empty) but to the orthogonal projection of the point onto the intersection.


It is sometimes denoted RSI-value if the SI units are used. An R-value can be given for a material (e.g. for polyethylene foam), or for an assembly of materials (e.g. a wall or a window). In the case of materials, it is often expressed in terms of R-value per metre.


The researchers estimated that a 1024-bit RSA modulus would take about 500 times as long.Not all numbers of a given length are equally hard to factor. The hardest instances of these problems (for currently known techniques) are semiprimes, the product of two prime numbers. When they are both large, for instance more than two thousand bits long, randomly chosen, and about the same size (but not too close, for example, to avoid efficient factorization by Fermat's factorization method), even the fastest prime factorization algorithms on the fastest computers can take enough time to make the search impractical; that is, as the number of digits of the integer being factored increases, the number of operations required to perform the factorization on any computer increases drastically. Many cryptographic protocols are based on the difficulty of factoring large composite integers or a related problem—for example, the RSA problem. An algorithm that efficiently factors an arbitrary integer would render RSA-based public-key cryptography insecure.


In the analysis of algorithms, several authors have studied the computation of the volume of high-dimensional convex bodies, a problem that can also be used to model many other problems in combinatorial enumeration. Often these works use a black box model of computation in which the input is given by a subroutine for testing whether a point is inside or outside of the convex body, rather than by an explicit listing of the vertices or faces of a convex polytope. It is known that, in this model, no deterministic algorithm can achieve an accurate approximation, and even for an explicit listing of faces or vertices the problem is #P-hard. However, a joint work by Martin Dyer, Alan M. Frieze and Ravindran Kannan provided a randomized polynomial time approximation scheme for the problem, providing a sharp contrast between the capabilities of randomized and deterministic algorithms.The main result of the paper is a randomized algorithm for finding an ε {\displaystyle \varepsilon } approximation to the volume of a convex body K {\displaystyle K} in n {\displaystyle n} -dimensional Euclidean space by assuming the existence of a membership oracle.


In network science, preferential attachment means that nodes of a network tend to connect to those nodes which have more links. If the network is growing and new nodes tend to connect to existing ones with linear probability in the degree of the existing nodes then preferential attachment leads to a scale-free network. If this probability is sub-linear then the network’s degree distribution is stretched exponential and hubs are much smaller than in a scale-free network. If this probability is super-linear then almost all nodes are connected to a few hubs.


In mathematics, an open set is a generalization of an open interval in the real line. In a metric space (a set along with a distance defined between any two points), an open set is a set that, along with every point P, contains all points that are sufficiently near to P (that is, all points whose distance to P is less than some value depending on P). More generally, an open set is a member of a given collection of subsets of a given set, a collection that has the property of containing every union of its members, every finite intersection of its members, the empty set, and the whole set itself. A set in which such a collection is given is called a topological space, and the collection is called a topology.


In mathematics and computer science, a balanced boolean function is a boolean function whose output yields as many 0s as 1s over its input set. This means that for a uniformly random input string of bits, the probability of getting a 1 is 1/2. Examples of balanced boolean functions are the function that copies the first bit of its input to the output, and the function that produces the exclusive or of the input bits.


In nature, networks rarely appear in isolation. They are typically elements in larger systems and can have non-trivial effects on one another. For example, infrastructure networks exhibit interdependency to a large degree. The power stations which form the nodes of the power grid require fuel delivered via a network of roads or pipes and are also controlled via the nodes of communications network.


Brasch et al. 2012 show how a generalized Fibonacci sequence also can be connected to the field of economics. In particular, it is shown how a generalized Fibonacci sequence enters the control function of finite-horizon dynamic optimisation problems with one state and one control variable. The procedure is illustrated in an example often referred to as the Brock–Mirman economic growth model.


Relations of this kind are treated in more detail in the Section "Types of spaces". It is not always clear whether a given mathematical object should be considered as a geometric "space", or an algebraic "structure". A general definition of "structure", proposed by Bourbaki, embraces all common types of spaces, provides a general definition of isomorphism, and justifies the transfer of properties between isomorphic structures.


The state set at input position k is called S(k). The parser is seeded with S(0) consisting of only the top-level rule. The parser then repeatedly executes three operations: prediction, scanning, and completion.


Normally, they represent information concerning time ("@past", "@future", etc.), reference ("@def", "@indef", etc.), modality ("@can", "@must", etc.), focus ("@topic", "@focus", etc.), and so on. Within the UNL Program, the process of representing natural language sentences in UNL graphs is called UNLization, and the process of generating natural language sentences out of UNL graphs is called NLization. UNLization, which involves natural language analysis and understanding, is intended to be carried out semi-automatically (i.e., by humans with computer aids); and NLization is intended to be carried out fully automatically.


In network management, fault management is the set of functions that detect, isolate, and correct malfunctions in a telecommunications network, compensate for environmental changes, and include maintaining and examining error logs, accepting and acting on error detection notifications, tracing and identifying faults, carrying out sequences of diagnostics tests, correcting faults, reporting error conditions, and localizing and tracing faults by examining and manipulating database information.When a fault or event occurs, a network component will often send a notification to the network operator using a protocol such as SNMP. An alarm is a persistent indication of a fault that clears only when the triggering condition has been resolved. A current list of problems occurring on the network component is often kept in the form of an active alarm list such as is defined in RFC 3877, the Alarm MIB. A list of cleared faults is also maintained by most network management systems.Fault management systems may use complex filtering systems to assign alarms to severity levels.


The natural logarithm has the number e ≈ 2.718 as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base 2 and is frequently used in computer science.


In operating systems, a task manager is a system monitor program used to provide information about the processes and applications running on a computer, as well as the general status of the computer. Some implementations can also be used to terminate processes and applications, as well as change the processes' scheduling priority. In some environments, users can access a task manager with the Control-Alt-Delete keyboard shortcut. Task managers can display running services (processes) as well as those that were stopped. They can display information about the services, including their process identifier and group identifier.


The maximum among the conductance of clusters provides a bound which can be used, along with inter-cluster edge weight, to define a measure on the quality of clustering. Intuitively, the conductance of a cluster (which can be seen as a set of vertices in a graph) should be low. Apart from this, the conductance of the subgraph induced by a cluster (called "internal conductance") can be used as well.


{\displaystyle \Pr \left\geq \Pr \left.} While this intuitive-seeming result is true for Gaussian processes, it is not in general true for other random variables—not even those with expectation 0. As a corollary, if ( X t ) t ≥ 0 {\displaystyle (X_{t})_{t\geq 0}} is a centered stationary Gaussian process such that E   ≥ 0 {\displaystyle \operatorname {E} \geq 0} for all t {\displaystyle t} , it holds for any real number c {\displaystyle c} that Pr  X t ≤ c ] ≥ Pr  X t ≤ c ] Pr  X t ≤ c ] , T , S > 0. {\displaystyle \Pr \left}X_{t}\leq c\right]\geq \Pr \left}X_{t}\leq c\right]\Pr \left}X_{t}\leq c\right],\quad T,S>0.}


Another term, used to denote call attempts that fail during the call setup procedure, is blocked calls. The call setup success rate in conventional (so-called land-line) networks is extremely high and is significantly above 99.9%. In mobile communication systems using radio channels the call setup success rate is lower and may range for commercial networks between 90% and 98% or higher.


In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p. That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of pn copies of g, and not fewer, is equal to the identity element. The orders of different elements may be different powers of p. Abelian p-groups are also called p-primary or simply primary. A finite group is a p-group if and only if its order (the number of its elements) is a power of p. Given a finite group G, the Sylow theorems guarantee the existence of a subgroup of G of order pn for every prime power pn that divides the order of G. Every finite p-group is nilpotent. The remainder of this article deals with finite p-groups. For an example of an infinite abelian p-group, see Prüfer group, and for an example of an infinite simple p-group, see Tarski monster group.


In programming and software development, fuzzing or fuzz testing is an automated software testing technique that involves providing invalid, unexpected, or random data as inputs to a computer program. The program is then monitored for exceptions such as crashes, failing built-in code assertions, or potential memory leaks. Typically, fuzzers are used to test programs that take structured inputs.


In the context of telephony, a telephone line (the system) typically offers a set of features that include call forwarding and call waiting. Call waiting allows one call to be suspended while a second call is answered, while call forwarding enables a customer to specify a secondary phone number to which additional calls will be forwarded in the event that the customer is already using the phone. To illustrate the example, we consider a telephone line provided to a customer, and we assume that both call forwarding and call waiting are enabled on the line. When a first call arrives on the line, the phone rings and is answered.


In phylogenetics, maximum parsimony is an optimality criterion under which the phylogenetic tree that minimizes the total number of character-state changes (or minimizes the cost of differentially weighted character-state changes). Under the maximum-parsimony criterion, the optimal tree will minimize the amount of homoplasy (i.e., convergent evolution, parallel evolution, and evolutionary reversals). In other words, under this criterion, the shortest possible tree that explains the data is considered best. Some of the basic ideas behind maximum parsimony were presented by James S. Farris in 1970 and Walter M. Fitch in 1971.Maximum parsimony is an intuitive and simple criterion, and it is popular for this reason.


In pattern recognition and machine learning, a feature vector is an n-dimensional vector of numerical features that represent some object. Many algorithms in machine learning require a numerical representation of objects, since such representations facilitate processing and statistical analysis. When representing images, the feature values might correspond to the pixels of an image, while when representing texts the features might be the frequencies of occurrence of textual terms. Feature vectors are equivalent to the vectors of explanatory variables used in statistical procedures such as linear regression.


In spoken language Yes/no questions will oftentimes differ in their word order from the statement form. For example, in English: English Statement: HE WILL BUY THE SHIRT.English Yes/no Q:WILL HE BUY THE SHIRT?In ASL, yes/no questions are marked by the non-manual grammatical markings (as discussed in section 4.4.1). This eyebrow raise, slight tilt of the head and lean forward are what indicate that a yes/no question is being asked, without any change in word order from the statement form. There is speculation amongst linguists that these non-manual grammatical markings that indicate a yes/no questions are similar to the question intonation of spoken languages.Yes/no questions differ from wh-questions as they do not differ in word order from the original statement form of the sentence, whereas wh-questions do.


The examples we choose should stress simple dutifulness. The first of these methods, argues Kant, is destined to fail because students will not come to understand the unconditional nature of duty. The examples will also not be very inspiring.


Both of these examples use multiple sensors to sample signals and form images based on the manipulation of these multiple signals. Processing in multi-dimension (m-D) requires more complex algorithms, compared to the 1-D case, to handle calculations such as the fast Fourier transform due to more degrees of freedom. In some cases, m-D signals and systems can be simplified into single dimension signal processing methods, if the considered systems are separable.


The order of a group G is denoted by ord(G) or |G|, and the order of an element a is denoted by ord(a) or |a|, instead of ord  ( ⟨ a ⟩ ) , {\displaystyle \operatorname {ord} (\langle a\rangle ),} where the brackets denote the generated group. Lagrange's theorem states that for any subgroup H of a finite group G, the order of the subgroup divides the order of the group; that is, |H| is a divisor of |G|. In particular, the order |a| of any element is a divisor of |G|.


In order to assess the performance of machine learning models, TensorFlow gives API access to commonly used metrics. Examples include various accuracy metrics (binary, categorical, sparse categorical) along with other metrics such as Precision, Recall, and Intersection-over-Union (IoU).


In mathematical programming and polyhedral combinatorics, the Hirsch conjecture is the statement that the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n − d. That is, any two vertices of the polytope must be connected to each other by a path of length at most n − d. The conjecture was first put forth in a letter by Warren M. Hirsch to George B. Dantzig in 1957 and was motivated by the analysis of the simplex method in linear programming, as the diameter of a polytope provides a lower bound on the number of steps needed by the simplex method. The conjecture is now known to be false in general. The Hirsch conjecture was proven for d < 4 and for various special cases, while the best known upper bounds on the diameter are only sub-exponential in n and d. After more than fifty years, a counter-example was announced in May 2010 by Francisco Santos Leal, from the University of Cantabria.


The row is then interpreted as a relvar composed of a set of tuples, with each tuple consisting of the two items: the name of the relevant column and the value this row provides for that column. Each column expects a data value of a particular type. For example, one column might require a unique identifier, another might require text representing a person's name, another might require an integer representing hourly pay in dollars.


In the Catalan language, sentences consist of a collection of noun phrases grouped around a verb. One of these noun phrases has the syntactic function of subject while the others function as complements (direct, indirect, prepositional or verbal), or adverbials (of time, place, manner, etc.). The sentence can be introduced by a 'frame' (for example 'as far as X is concerned', or an adverbial of time or place). The main features of the sentence are the agreement in person and number between the subject and the verb - which marks the relation between the speaker, on the one hand, and his or her interlocutors and any other people, on the other - and time, which situates the action in relation to the present of the speaker or in relation to the time of the other sentences of the text or discourse.


Thus, recipes for the production of hydrochloric acid only appear in the late sixteenth century, the earliest being found in Giovanni Battista Della Porta's (1535–1615) Magiae naturalis ("Natural Magic") and in the works of other contemporary chemists like Andreas Libavius (c. 1550–1616), Jean Beguin (1550–1620), and Oswald Croll (c. 1563– 1609). The knowledge of mineral acids such as hydrochloric acid would be of key importance to seventeenth-century chemists like Daniel Sennert (1572–1637) and Robert Boyle (1627–1691), who used their capability to rapidly dissolve metals in their demonstrations of the composite nature of bodies.


- four years study (4 B.Eng. or B.ASc. )Names are traditionally prefixed with the ir.


In mathematics, in particular linear algebra, the Bunch–Nielsen–Sorensen formula, named after James R. Bunch, Christopher P. Nielsen and Danny C. Sorensen, expresses the eigenvectors of the sum of a symmetric matrix A {\displaystyle A} and the outer product, v v T {\displaystyle vv^{T}} , of vector v {\displaystyle v} with itself.


In functional programming, property-based testing has allowed the mathematical specification and testing (if not exhaustive testing) of the expected behaviour of individual functions. The Object Constraint Language (and specializations such as Java Modeling Language) has allowed object-oriented systems to be formally specified, if not necessarily formally verified.


In the United States, the Health Insurance Portability and Accountability Act and Health Information Technology for Economic and Clinical Health Act require companies to report data breaches to affected individuals and the federal government. Health Information Privacy Health Insurance Portability and Accountability Act of 1996 (HIPAA). - 45 CFR Parts 160 and 164, Standards for Privacy of Individually Identifiable Health Information and Security Standards for the Protection of Electronic Protected Health Information. HIPAA includes provisions designed to save health care businesses money by encouraging electronic transactions, as well as regulations to protect the security and confidentiality of patient information.


For example, many early email systems were not 8-bit clean; they seemed to transfer typical short text messages properly, but converted "unusual" characters (the control characters, the "high ASCII" characters) in an irreversible way into some other "usual" character. Many of these systems also changed user data in other irreversible ways – such as inserting linefeeds to make sure each line is less than some maximum length, and inserting a ">" at the beginning of every line that begins with "From ". Until 8BITMIME, a variety of binary-to-text encoding techniques have been overlaid on top of such systems to restore transparency – to make sure that any possible file can be transferred so that the final output "user data" is actually identical to the original user data.


For positive odd primes p , q {\displaystyle p,q} the solubility of n 2 − p ≡ 0 mod q {\displaystyle n^{2}-p\equiv 0{\bmod {q}}} for n {\displaystyle n} determines the solubility of m 2 − q ≡ 0 mod p {\displaystyle m^{2}-q\equiv 0{\bmod {p}}} for m {\displaystyle m} and vice versa by the comparatively simple criterion whether ( − 1 ) p − 1 2 q − 1 2 {\displaystyle (-1)^{{\frac {p-1}{2}}{\frac {q-1}{2}}}} is 1 {\displaystyle 1} or − 1 {\displaystyle -1} . By the factor theorem and the behavior of degrees in factorizations the solubility of such quadratic congruence equations is equivalent to the splitting of associated quadratic polynomials over a residue ring into linear factors. In this terminology the law of quadratic reciprocity is stated as follows. For positive odd primes p , q {\displaystyle p,q} the splitting of the polynomial x 2 − p {\displaystyle x^{2}-p} in mod q {\displaystyle {\bmod {q}}} -residues determines the splitting of the polynomial x 2 − q {\displaystyle x^{2}-q} in mod p {\displaystyle {\bmod {p}}} -residues and vice versa through the quantity ( − 1 ) p − 1 2 q − 1 2 ∈ { ± 1 } {\displaystyle (-1)^{{\frac {p-1}{2}}{\frac {q-1}{2}}}\in \{\pm 1\}} . This establishes the bridge from the name giving reciprocating behavior of primes introduced by Legendre to the splitting behavior of polynomials used in the generalizations.


In natural language processing and information retrieval, explicit semantic analysis (ESA) is a vectoral representation of text (individual words or entire documents) that uses a document corpus as a knowledge base. Specifically, in ESA, a word is represented as a column vector in the tf–idf matrix of the text corpus and a document (string of words) is represented as the centroid of the vectors representing its words. Typically, the text corpus is English Wikipedia, though other corpora including the Open Directory Project have been used.ESA was designed by Evgeniy Gabrilovich and Shaul Markovitch as a means of improving text categorization and has been used by this pair of researchers to compute what they refer to as "semantic relatedness" by means of cosine similarity between the aforementioned vectors, collectively interpreted as a space of "concepts explicitly defined and described by humans", where Wikipedia articles (or ODP entries, or otherwise titles of documents in the knowledge base corpus) are equated with concepts. The name "explicit semantic analysis" contrasts with latent semantic analysis (LSA), because the use of a knowledge base makes it possible to assign human-readable labels to the concepts that make up the vector space.


In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for proving classical propositional tautologies.


In probability theory the hypoexponential distribution or the generalized Erlang distribution is a continuous distribution, that has found use in the same fields as the Erlang distribution, such as queueing theory, teletraffic engineering and more generally in stochastic processes. It is called the hypoexponetial distribution as it has a coefficient of variation less than one, compared to the hyper-exponential distribution which has coefficient of variation greater than one and the exponential distribution which has coefficient of variation of one.


For functions of a single real variable whose graphs have a bounded number of intersection points, the complexity of the lower or upper envelope can be bounded using Davenport–Schinzel sequences, and these envelopes can be computed efficiently by a divide-and-conquer algorithm that computes and then merges the envelopes of subsets of the functions.For convex functions or quasiconvex functions, the upper envelope is again convex or quasiconvex. The lower envelope is not, but can be replaced by the lower convex envelope to obtain an operation analogous to the lower envelope that maintains convexity.


In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number a/b is a "good" approximation of a real number α if the absolute value of the difference between a/b and α may not decrease if a/b is replaced by another rational number with a smaller denominator.


From the 1980s onwards, critics increasingly refused to ask questions about diegetic elements of the text, instead acknowledging that many elements simply cannot be known definitively.Focus shifted away from whether the ghosts were real and onto how James generated and then sustained the text's ambiguity. A study into revisions James made to two paragraphs in the novella concluded that James was not striving for clarity, but to create a text which could not be interpreted definitively in either direction.This is still a position held by many critics, such as Giovanni Bottiroli, who argues that evidence for the intended ambiguity of the text can be found at the beginning of the novella, where Douglas tells his fictional audience that the governess had never told anyone but himself about the events that happened at Bly, and that they "would easily judge" why. Bottiroli believes that this address to Douglas' fictional audience is also meant as an address to the reader, telling them that they will "easily judge" whether or not the ghosts are real.


A major result of complexity theory is that NP can be characterized as the problems solvable by probabilistically checkable proofs where the verifier uses O(log n) random bits and examines only a constant number of bits of the proof string (the class PCP(log n, 1)). More informally, this means that the NP verifier described above can be replaced with one that just "spot-checks" a few places in the proof string, and using a limited number of coin flips can determine the correct answer with high probability. This allows several results about the hardness of approximation algorithms to be proven.


In radio networks, the n nodes may in every round choose to either transmit or receive a message. If no collision detection is available, then a node cannot distinguish between silence or receiving more than one message at a time. Should collision detection be available, then a node may detect more than one incoming message at the same time, even though the messages itself cannot be decoded in that case. In the beeping model, nodes can only distinguish between silence or at least one message via carrier sensing. Known runtimes for single-hop networks range from a constant (expected with collision detection) to O(n log n) rounds (deterministic and no collision detection). In multi-hop networks, known runtimes differ from roughly O((D+ log n)(log2 log n)) rounds (with high probability in the beeping model), O(D log n) (deterministic in the beeping model), O(n) (deterministic with collision detection) to O(n log3/2 n (log log n)0.5) rounds (deterministic and no collision detection).


Search engines rank web pages by their expected relevance to a user's query using a combination of query-dependent and query-independent methods. Query-independent methods attempt to measure the estimated importance of a page, independent of any consideration of how well it matches the specific query. Query-independent ranking is usually based on link analysis; examples include the HITS algorithm, PageRank and TrustRank.


In microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting. It involves determining the best approach to use when looking for a specific item or person in a sizable, uncharted environment. The goal of the theory is to determine the best search strategy, one that maximises the chance of finding the target while minimising search-related expenses. Search theory clarifies how buyers and sellers choose when to acknowledge a coordinating offer for a transaction.


In numerical linear algebra, the Rayleigh–Ritz method is commonly applied to approximate an eigenvalue problem for the matrix A ∈ C N × N {\displaystyle A\in \mathbb {C} ^{N\times N}} of size N {\displaystyle N} using a projected matrix of a smaller size m < N {\displaystyle m


It may be used in both wired or wireless communications, so that adjacent frequency bands on the same media can avoid interference. The spectrum can also be licensed for low-power devices such as a private mobile phone network. == References ==


In the branches of mathematical logic known as proof theory and type theory, a pure type system (PTS), previously known as a generalized type system (GTS), is a form of typed lambda calculus that allows an arbitrary number of sorts and dependencies between any of these. The framework can be seen as a generalisation of Barendregt's lambda cube, in the sense that all corners of the cube can be represented as instances of a PTS with just two sorts. In fact, Barendregt (1991) framed his cube in this setting.


If we consider the thesis and its converse as definition, then the hypothesis is an hypothesis about the application of the mathematical theory developed from the definition. For the acceptance of the hypothesis, there are, as we have suggested, quite compelling grounds. The Church–Turing Thesis: Stephen Kleene, in Introduction To Metamathematics, finally goes on to formally name "Church's Thesis" and "Turing's Thesis", using his theory of recursive realizability.


For each qubit sent, Alice chooses one computational basis state and one Hadamard basis state such that the state of the qubit is one of these two states. Alice then announces those two states. Alice will note whether the state is the computational basis state or the Hadamard basis state; that piece of information makes up the secret bit that Alice wishes to communicate to Bob.


In some languages, the tilde is a diacritic mark placed over a letter to indicate a change in its pronunciation:


In statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of L p {\displaystyle L^{p}} metrics, and measures of central tendency can be characterized as solutions to variational problems. In penalized regression, "L1 penalty" and "L2 penalty" refer to penalizing either the L 1 {\displaystyle L^{1}} norm of a solution's vector of parameter values (i.e. the sum of its absolute values), or its L 2 {\displaystyle L^{2}} norm (its Euclidean length). Techniques which use an L1 penalty, like LASSO, encourage solutions where many parameters are zero. Techniques which use an L2 penalty, like ridge regression, encourage solutions where most parameter values are small. Elastic net regularization uses a penalty term that is a combination of the L 1 {\displaystyle L^{1}} norm and the L 2 {\displaystyle L^{2}} norm of the parameter vector.


In the field of database design, a multi-model database is a database management system designed to support multiple data models against a single, integrated backend. In contrast, most database management systems are organized around a single data model that determines how data can be organized, stored, and manipulated. Document, graph, relational, and key–value models are examples of data models that may be supported by a multi-model database.


In some models, all operations to different locations are relaxed. A read or write may be reordered with respect to a different read or write in a different location. The weak ordering may be classified under this category and two types of release consistency models (RCsc and RCpc) also come under this model. Three commercial architectures are also proposed under this category of relaxation: the Digital Alpha, SPARC V9 relaxed memory order (RMO), and IBM PowerPC models.


In the United States, the Environmental Protection Agency (EPA) sets performance standards for marine sanitation devices, and the U.S. Coast Guard (USCG) issues regulations governing the design, construction, certification, installation and operation of MSDs.USCG has certified three kinds of marine sanitation devices.


In number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions. A weaker condition is also important, respecting only products of coprime numbers, and such functions are called multiplicative functions. Outside of number theory, the term "multiplicative function" is often taken to be synonymous with "completely multiplicative function" as defined in this article.


PGP uses key IDs to refer to public keys for a variety of purposes. These are not, properly speaking, fingerprints, since their short length prevents them from being able to securely authenticate a public key. 32bit key ids should not be used as current hardware can generate a colliding 32bit key id in just 4 seconds.


Just as in the 2-component cat code, one needs to stabilize the code in order to prevent bit-flips. The same strategies can be used but are challenging to implement experimentally because higher order non-linearities are required. == References ==


In order to generate the next sequence, first take the previous pattern, add the next letter from the alphabet, and then repeat the previous pattern. The first few steps are listed here. A generator can be found here ABACABA is a "quickly growing word", often described as chiastic or "symmetrically organized around a central axis" (see: Chiastic structure and Χ). The number of members in each iteration is a(n) = 2n − 1, the Mersenne numbers (OEIS: A000225).


Let A d {\displaystyle A_{d}} denote the set of elements of A {\displaystyle A} divisible by d {\displaystyle d} when d {\displaystyle d} is a product of distinct primes from P {\displaystyle P} . Further let A 1 {\displaystyle A_{1}} denote A {\displaystyle A} itself. Let z {\displaystyle z} be a positive real number and P ( z ) {\displaystyle P(z)} denote the product of the primes in P {\displaystyle P} which are ≤ z {\displaystyle \leq z} .


The initial object in the category of bounded lattices is a Boolean domain. In computer science, a Boolean variable is a variable that takes values in some Boolean domain. Some programming languages feature reserved words or symbols for the elements of the Boolean domain, for example false and true. However, many programming languages do not have a Boolean datatype in the strict sense. In C or BASIC, for example, falsity is represented by the number 0 and truth is represented by the number 1 or −1, and all variables that can take these values can also take any other numerical values.


Here, a conceptual problem arises. The basic reason is that the income of one institutional unit is the expenditure of another, and the input of one institutional unit is the output of another. If therefore we want to measure the total value-added by all institutional units, we need to devise a consistent procedure for grossing and netting the incomes and outlays of all units, within a system of transactors. Lacking such a system, we would end up double counting incomes and expenditures of interacting units, exaggerating the quantity of value-added or investments.To estimate the annual net output of a country, for example, the cost of goods and services used up is deducted from gross revenue, all flows are valued uniformly, and flows which fall outside the production boundary are excluded.


In modern mathematical language, the problem posed on the tablet is the following: a rectangle has area A = 0.75 and diagonal c = 1.25. What are the lengths a and b of the sides of the rectangle? The solution can be understood as proceeding in two stages: in stage 1, the quantity c 2 − 2 A {\displaystyle {\sqrt {c^{2}-2A}}} is computed to be 0.25. In stage 2, the well-attested Old Babylonian method of completing the square is used to solve what is effectively the system of equations b − a = 0.25, ab = 0.75.


In the Internet Protocol Suite (TCP/IP), OSI's data link layer functionality is contained within its lowest layer, the link layer. The TCP/IP link layer has the operating scope of the link a host is connected to, and only concerns itself with hardware issues to the point of obtaining hardware (MAC) addresses for locating hosts on the link and transmitting data frames onto the link. The link-layer functionality was described in RFC 1122 and is defined differently than the data link layer of OSI, and encompasses all methods that affect the local link. The TCP/IP model is not a top-down comprehensive design reference for networks.


For instance, this is true of the order polytope of any partially ordered set, a polytope defined by pairwise inequalities between coordinates corresponding to comparable elements in the set. Another well-known polytope in combinatorial optimization is the matching polytope. Clearly, one seeks for finding matchings algorithmically and one technique is linear programming.


For example, in the word 寿司 (sushi), the two characters are respectively read as su and shi, but the character 寿 means "one's natural life span" and 司 means "to administer", neither of which has anything to do with the food – this is ateji. Conversely, in the word 煙草 (tabako) for "tobacco", the individual kanji respectively mean "smoke" and "herb", which corresponds to the meaning, while none of their possible readings have a phonetic relationship to the word tabako – this is jukujikun. In some cases, however, the kanji were chosen for both their semantic and phonetic values, a form of phono-semantic matching.


In probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing probabilities on a logarithmic scale ( − inf , 0 ] {\displaystyle (-\inf ,0]} , instead of the standard  {\displaystyle } unit interval. Since the probabilities of independent events multiply, and logarithms convert multiplication to addition, log probabilities of independent events add. Log probabilities are thus practical for computations, and have an intuitive interpretation in terms of information theory: the negative of the average log probability is the information entropy of an event. Similarly, likelihoods are often transformed to the log scale, and the corresponding log-likelihood can be interpreted as the degree to which an event supports a statistical model. The log probability is widely used in implementations of computations with probability, and is studied as a concept in its own right in some applications of information theory, such as natural language processing.


The Born rule associates a probability with each unit vector in the Hilbert space, in such a way that these probabilities sum to 1 for any set of unit vectors comprising an orthonormal basis. Moreover, the probability associated with a unit vector is a function of the density operator and the unit vector, and not of additional information like a choice of basis for that vector to be embedded in. Gleason's theorem establishes the converse: all assignments of probabilities to unit vectors (or, equivalently, to the operators that project onto them) that satisfy these conditions take the form of applying the Born rule to some density operator. Gleason's theorem holds if the dimension of the Hilbert space is 3 or greater; counterexamples exist for dimension 2.


Because of this, it is less affected by the curse of dimensionality than e.g. a p-dimensional smoother. Furthermore, the AM is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with AM, like many other machine learning methods, include model selection, overfitting, and multicollinearity.


In multi-programming or in a multi-user environment, many users may execute the same program, written so that its code and data are in separate pages. To minimize RAM use, all users share a single copy of the program. Each process's page table is set up so that the pages that address code point to the single shared copy, while the pages that address data point to different physical pages for each process. Different programs might also use the same libraries.


In numerical analysis, the Kahan summation algorithm, also known as compensated summation, significantly reduces the numerical error in the total obtained by adding a sequence of finite-precision floating-point numbers, compared to the obvious approach. This is done by keeping a separate running compensation (a variable to accumulate small errors), in effect extending the precision of the sum by the precision of the compensation variable. In particular, simply summing n {\displaystyle n} numbers in sequence has a worst-case error that grows proportional to n {\displaystyle n} , and a root mean square error that grows as n {\displaystyle {\sqrt {n}}} for random inputs (the roundoff errors form a random walk). With compensated summation, using a compensation variable with sufficiently high precision the worst-case error bound is effectively independent of n {\displaystyle n} , so a large number of values can be summed with an error that only depends on the floating-point precision of the result.The algorithm is attributed to William Kahan; Ivo Babuška seems to have come up with a similar algorithm independently (hence Kahan–Babuška summation). Similar, earlier techniques are, for example, Bresenham's line algorithm, keeping track of the accumulated error in integer operations (although first documented around the same time) and the delta-sigma modulation.


In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.


In particle physics, a hyperon is any baryon containing one or more strange quarks, but no charm, bottom, or top quark. This form of matter may exist in a stable form within the core of some neutron stars. Hyperons are sometimes generically represented by the symbol Y.


In some cases the two methods may yield essentially the same results. The basis functions are typically found by computing the eigenvectors of the covariance matrix of the data set. A more advanced technique is to form a kernel out of the data, using a fixed kernel. The basis functions from the eigenvectors of the kernel matrix are thus non-linear in the location of the data (see Mercer's theorem and the kernel trick for more information).


In molecular biology and genetics, DNA annotation or genome annotation is the process of describing the structure and function of the components of a genome, by analyzing and interpreting them in order to extract their biological significance and understand the biological processes in which they participate. Among other things, it identifies the locations of genes and all the coding regions in a genome and determines what those genes do.Annotation is performed after a genome is sequenced and assembled, and is a necessary step in genome analysis before the sequence is deposited in a database and described in a published article. Although describing individual genes and their products or functions is sufficient to consider this description as an annotation, the depth of analysis reported in literature for different genomes vary widely, with some reports including additional information that goes beyond a simple annotation.


In the Java Collections Framework, the class List represents an ordered collection of objects of type MyClass. Upper bounds are specified using extends: A List extends MyClass> is a list of objects of some subclass of MyClass, i.e. any object in the list is guaranteed to be of type MyClass, so one can iterate over it using a variable of type MyClass However, it is not guaranteed that one can add any object of type MyClass to that list: The converse is true for lower bounds, which are specified using super: A List super MyClass> is a list of objects of some superclass of MyClass, i.e. the list is guaranteed to be able to contain any object of type MyClass, so one can add any object of type MyClass: However, it is not guaranteed that one can iterate over that list using a variable of type MyClass: In order to be able to do both add objects of type MyClass to the list and iterate over it using a variable of type MyClass, a List is needed, which is the only type of List that is both List extends MyClass> and List super MyClass>.The mnemonics PECS (Producer Extends, Consumer Super) from the book Effective Java by Joshua Bloch gives an easy way to remember when to use wildcards (corresponding to Covariance and Contravariance) in Java.


In the field of nonparametric optimization, Voronoi manifolds serve as valuable tools for reducing the sample size and selecting promising points. They help identify regions of interest where experiments or evaluations should be focused, leading to efficient optimization algorithms and improved convergence rates.


The reason is that, in any minimum-length partition, every maximal line-segment can be "pushed" until it hits one of the vertices of the boundary, without changing the total length. Therefore, there are only O ( n 2 ) {\displaystyle O(n^{2})} candidates for a line segment in an optimal partition, and they can be checked efficiently using dynamic programming. : 166–167 If the raw polygon might have holes, even if they are degenerate holes (i.e., single points), the problem is NP-hard.


Binary logarithms are included in the standard C mathematical functions and other mathematical software packages. The integer part of a binary logarithm can be found using the find first set operation on an integer value, or by looking up the exponent of a floating point value. The fractional part of the logarithm can be calculated efficiently.


This objective is a quadratic form in b {\displaystyle \mathbf {b} } . Taking the gradient of this quadratic form with respect to b {\displaystyle \mathbf {b} } and equating it to zero (when b = β ^ {\displaystyle \mathbf {b} ={\hat {\beta }}} ) gives 2 X T Ω − 1 X β ^ − 2 X T Ω − 1 y = 0 {\displaystyle 2\mathbf {X} ^{\mathsf {T}}\mathbf {\Omega } ^{-1}\mathbf {X} {\hat {\beta }}-2\mathbf {X} ^{\mathsf {T}}\mathbf {\Omega } ^{-1}\mathbf {y} =0} Therefore, the minimum of the objective function can be computed yielding the explicit formula: β ^ = ( X T Ω − 1 X ) − 1 X T Ω − 1 y . {\displaystyle \mathbf {\hat {\beta }} =\left(\mathbf {X} ^{\mathsf {T}}\mathbf {\Omega } ^{-1}\mathbf {X} \right)^{-1}\mathbf {X} ^{\mathsf {T}}\mathbf {\Omega } ^{-1}\mathbf {y} .} The quantity Ω − 1 {\displaystyle \mathbf {\Omega } ^{-1}} is known as the precision matrix (or dispersion matrix), a generalization of the diagonal weight matrix.


In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship between one or more independent variables and a dependent variable. Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise (i.e. are not robust to assumption violations). Robust regression methods are designed to limit the effect that violations of assumptions by the underlying data-generating process have on regression estimates. For example, least squares estimates for regression models are highly sensitive to outliers: an outlier with twice the error magnitude of a typical observation contributes four (two squared) times as much to the squared error loss, and therefore has more leverage over the regression estimates. The Huber loss function is a robust alternative to standard square error loss that reduces outliers' contributions to the squared error loss, thereby limiting their impact on regression estimates.


The number of iterations is then decoupled to the number of points (each point can be considered more than once). The incremental gradient method can be shown to provide a minimizer to the empirical risk. Incremental techniques can be advantageous when considering objective functions made up of a sum of many terms e.g. an empirical error corresponding to a very large dataset.


There is an additive definition of the psi function as well. Quoting from Dickson, R. Dedekind proved that, if n {\displaystyle n} is decomposed in every way into a product a b {\displaystyle ab} and if e {\displaystyle e} is the g.c.d. of a , b {\displaystyle a,b} then ∑ a ( a / e ) φ ( e ) = n ∏ p | n ( 1 + 1 p ) {\displaystyle \sum _{a}(a/e)\varphi (e)=n\prod _{p|n}\left(1+{\frac {1}{p}}\right)} where a {\displaystyle a} ranges over all divisors of n {\displaystyle n} and p {\displaystyle p} over the prime divisors of n {\displaystyle n} and φ {\displaystyle \varphi } is the totient function.


In the field of networking, the Government Secure Intranet (GSi) puts in place a secure link between central government departments. It is an IP-based virtual private network based on broadband technology introduced in April 1998 and further upgraded in February 2004. Among other things, it offers a variety of advanced services including file transfer and search facilities, directory services, email exchange facilities (both between network members and over the Internet) as well as voice and video services. An additional network is currently also under development: the Public Sector Network (PSN) will be the network to interconnect public authorities (including departments and agencies in England; devolved administrations and local governments) and facilitate in particular sharing of information and services among each other.


Which one(s) are appropriate depend on a variety of factors, such as: Which assumptions (if any) may be made a priori about the distributions from which the data have been sampled? For example, in many situations it may be assumed that the underlying distributions are normal distributions. In other cases the data are categorical, coming from a discrete distribution over a nominal scale, such as which entry was selected from a menu. Does the hypothesis being tested apply to the distributions as a whole, or just some population parameter, for example the mean or the variance? Is the hypothesis being tested merely that there is a difference in the relevant population characteristics (in which case a two-sided test may be indicated), or does it involve a specific bias ("A is better than B"), so that a one-sided test can be used?


Many scientists such as Maxwell, Heaviside and Hertz unsuccessfully attempted to solve these problems by incorporating either Fresnel or Stokes' theories into Maxwell's new electromagnetic laws. Hendrik Lorentz spent considerable effort along these lines. After working on this problem for a decade, the issues with Stokes' theory caused him to abandon it and to follow Fresnel's suggestion of a (mostly) stationary aether (1892, 1895).


In order to encrypt or decrypt data, use the standard block cipher mode of operation on all but the last two blocks of data. The following steps describe how to handle the last two blocks of the plaintext, called Pn−1 and Pn, where the length of Pn−1 equals the block size of the cipher in bits, B; the length of the last block, Pn, is M bits; and K is the key that is in use. M can range from 1 to B, inclusive, so Pn could possibly be a complete block. The CBC mode description also makes use of the ciphertext block just previous to the blocks concerned, Cn−2, which may in fact be the IV if the plaintext fits within two blocks.


Well before any significant investments are made, the uncertainty is reduced to a level where the risk can be carried comfortably. In this kind of environment the uncertainty level decreases rapidly in the beginning and the cone shape is less obvious. The software business however is very volatile and there is an external pressure to decrease the uncertainty level over time.


In mathematics, a prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2p + 2 therefore satisfies Chen's theorem. The Chen primes are named after Chen Jingrun, who proved in 1966 that there are infinitely many such primes. This result would also follow from the truth of the twin prime conjecture as the lower member of a pair of twin primes is by definition a Chen prime.


In such a scenario, the second smallest eigenvalue ( λ 2 {\displaystyle \lambda _{2}} ) of L {\displaystyle L} , yields a lower bound on the optimal cost ( c {\displaystyle c} ) of ratio-cut partition with c ≥ λ 2 n {\displaystyle c\geq {\frac {\lambda _{2}}{n}}} . The eigenvector ( V 2 {\displaystyle V_{2}} ) corresponding to λ 2 {\displaystyle \lambda _{2}} , called the Fiedler vector, bisects the graph into only two communities based on the sign of the corresponding vector entry. Division into a larger number of communities can be achieved by repeated bisection or by using multiple eigenvectors corresponding to the smallest eigenvalues. The examples in Figures 1,2 illustrate the spectral bisection approach.


In the Bayesian (or epistemological) interpretation, probability measures a "degree of belief". Bayes' theorem links the degree of belief in a proposition before and after accounting for evidence. For example, suppose it is believed with 50% certainty that a coin is twice as likely to land heads than tails. If the coin is flipped a number of times and the outcomes observed, that degree of belief will probably rise or fall, but might even remain the same, depending on the results. For proposition A and evidence B, P (A), the prior, is the initial degree of belief in A. P (A | B), the posterior, is the degree of belief after incorporating news that B is true. the quotient P(B | A)/P(B) represents the support B provides for A.For more on the application of Bayes' theorem under the Bayesian interpretation of probability, see Bayesian inference.


In policy iteration (Howard 1960), step one is performed once, and then step two is performed once, then both are repeated until policy converges. Then step one is again performed once and so on. (Policy iteration was invented by Howard to optimize Sears catalogue mailing, which he had been optimizing using value iteration.)


The type of co-ownership does not affect the right of co-owners to sell their fractional interest in the property to others during their lifetimes, but it does affect their power to will the property upon death to their devisees in the case of joint tenants. However, any joint tenant can change this by severing the joint tenancy. This occurs whenever a joint tenant transfers his or her fractional interest in the property. Laws can vary from place to place, and the following general discussion will not be applicable in its entirety to all jurisdictions.


In the United Kingdom the Data Protection Act 1998 (c 29) (Information Commissioner) implemented the EU Directive on the protection of personal data . It replaced the Data Protection Act 1984 (c 35). The 2016 General Data Protection Regulation supersedes previous Protection Acts. The Data Protection Act 2018 (c 12) updates data protection laws in the UK. It is a national law which complements the European Union's General Data Protection Regulation (GDPR).


With the definition given, ⟨ ρ ∗ ( g ) φ , ρ ( g ) v ⟩ = ⟨ ρ ( g − 1 ) T φ , ρ ( g ) v ⟩ = ( ρ ( g − 1 ) T φ ) T ρ ( g ) v = φ T ρ ( g − 1 ) ρ ( g ) v = φ T v = ⟨ φ , v ⟩ . {\displaystyle \langle {\rho }^{*}(g)\varphi ,\rho (g)v\rangle =\langle \rho (g^{-1})^{T}\varphi ,\rho (g)v\rangle =(\rho (g^{-1})^{T}\varphi )^{T}\rho (g)v=\varphi ^{T}\rho (g^{-1})\rho (g)v=\varphi ^{T}v=\langle \varphi ,v\rangle .}


In the 1970s through the early 1980s, paper tape was commonly used to transfer binary data for incorporation in either mask-programmable read-only memory (ROM) chips or their erasable counterparts EPROMs. A significant variety of encoding formats were developed for use in computer and ROM/EPROM data transfer. Encoding formats commonly used were primarily driven by those formats that EPROM programming devices supported and included various ASCII hex variants as well as a number of proprietary formats. A much more primitive as well as a much longer high-level encoding scheme was also used, BNPF (Begin-Negative-Positive-Finish), also written as BPNF.


In some cases, random necklaces can be split equally using fewer cuts. Mathematicians Noga Alon, Dor Elboim, Gábor Tardos and János Pach studied the typical number of cuts required to split a random necklace between two thieves. In the model they considered, a necklace is chosen uniformly at random from the set of necklaces with t colors and m beads of each color. As m tends to infinity, the probability that the necklace can be split using ⌊(t + 1)/2⌋ cuts or less tends to zero while the probability that it's possible to split with ⌊(t + 1)/2⌋ + 1 cuts is bounded away from zero.


{\displaystyle ~{\frac {a-{\sqrt {a^{2}-c}}}{2}}~.} Thus x and y are rational if and only if d = a 2 − c {\displaystyle d={\sqrt {a^{2}-c}}~} is a rational number. For explicitly choosing the various signs, one must consider only positive real square roots, and thus assuming c > 0.


In some domains, a few dozen different source and target schema (proprietary data formats) may exist. An "exchange" or "interchange format" is often developed for a single domain, and then necessary routines (mappings) are written to (indirectly) transform/translate each and every source schema to each and every target schema by using the interchange format as an intermediate step. That requires a lot less work than writing and debugging the hundreds of different routines that would be required to directly translate each and every source schema directly to each and every target schema. Examples of these transformative interchange formats include: Standard Interchange Format for geospatial data; Data Interchange Format for spreadsheet data; Open Document Format for spreadsheets, charts, presentations and word processing documents; GPS eXchange Format or Keyhole Markup Language for describing GPS data; and GDSII for integrated circuit layout.


An important example of normal variance-mean mixtures is the generalised hyperbolic distribution in which the mixing distribution is the generalized inverse Gaussian distribution. The probability density function of a normal variance-mean mixture with mixing probability density g {\displaystyle g} is f ( x ) = ∫ 0 ∞ 1 2 π σ 2 v exp  ( − ( x − α − β v ) 2 2 σ 2 v ) g ( v ) d v {\displaystyle f(x)=\int _{0}^{\infty }{\frac {1}{\sqrt {2\pi \sigma ^{2}v}}}\exp \left({\frac {-(x-\alpha -\beta v)^{2}}{2\sigma ^{2}v}}\right)g(v)\,dv} and its moment generating function is M ( s ) = exp  ( α s ) M g ( β s + 1 2 σ 2 s 2 ) , {\displaystyle M(s)=\exp(\alpha s)\,M_{g}\left(\beta s+{\frac {1}{2}}\sigma ^{2}s^{2}\right),} where M g {\displaystyle M_{g}} is the moment generating function of the probability distribution with density function g {\displaystyle g} , i.e. M g ( s ) = E ( exp  ( s V ) ) = ∫ 0 ∞ exp  ( s v ) g ( v ) d v . {\displaystyle M_{g}(s)=E\left(\exp(sV)\right)=\int _{0}^{\infty }\exp(sv)g(v)\,dv.}


In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.


In mathematics, two objects, especially systems of axioms or semantics for them, are called cryptomorphic if they are equivalent but not obviously equivalent. In particular, two definitions or axiomatizations of the same object are "cryptomorphic" if it is not obvious that they define the same object. Examples of cryptomorphic definitions abound in matroid theory and others can be found elsewhere, e.g., in group theory the definition of a group by a single operation of division, which is not obviously equivalent to the usual three "operations" of identity element, inverse, and multiplication. This word is a play on the many morphisms in mathematics, but "cryptomorphism" is only very distantly related to "isomorphism", "homomorphism", or "morphisms". The equivalence may in a cryptomorphism, if it is not actual identity, be informal, or may be formalized in terms of a bijection or equivalence of categories between the mathematical objects defined by the two cryptomorphic axiom systems.


One disk is allowed to spin freely, and the other is driven by a motor. Mode locking occurs when the freely-spinning disk turns at a frequency that is a rational multiple of that of the driven rotator. The simplest mathematical model that exhibits mode-locking is the circle map, which attempts to capture the motion of the spinning disks at discrete time intervals.


Historically, there have been several formalizations of rewriting in an abstract setting, each with its idiosyncrasies. This is due in part to the fact that some notions are equivalent, see below in this article. The formalization that is most commonly encountered in monographs and textbooks, and which is generally followed here, is due to Gérard Huet (1980).


The nimber addition and multiplication operations are associative and commutative. Each nimber is its own negative. In particular for some pairs of ordinals, their nimber sum is smaller than either addend. The minimum excludant operation is applied to sets of nimbers.


In probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formula states that if X, Y, and Z are random variables on the same probability space, and the covariance of X and Y is finite, then cov  ( X , Y ) = E  ( cov  ( X , Y ∣ Z ) ) + cov  ( E  ( X ∣ Z ) , E  ( Y ∣ Z ) ) . {\displaystyle \operatorname {cov} (X,Y)=\operatorname {E} (\operatorname {cov} (X,Y\mid Z))+\operatorname {cov} (\operatorname {E} (X\mid Z),\operatorname {E} (Y\mid Z)).} The nomenclature in this article's title parallels the phrase law of total variance.


In some applications (e.g., building data models from only partially observed data) one wants to find the "nearest" correlation matrix to an "approximate" correlation matrix (e.g., a matrix which typically lacks semi-definite positiveness due to the way it has been computed). In 2002, Higham formalized the notion of nearness using the Frobenius norm and provided a method for computing the nearest correlation matrix using the Dykstra's projection algorithm, of which an implementation is available as an online Web API.This sparked interest in the subject, with new theoretical (e.g., computing the nearest correlation matrix with factor structure) and numerical (e.g. usage the Newton's method for computing the nearest correlation matrix) results obtained in the subsequent years.


In statistics, the analogous process is usually dividing a difference (a distance) by a scale factor (a measure of statistical dispersion), which yields a dimensionless number, which is called normalization. Most often, this is dividing errors or residuals by the standard deviation or sample standard deviation, respectively, yielding standard scores and studentized residuals.


However, it remains unproven as of 2022. The number of primes between prime squares is 2, 5, 6, 15, 9, 22, 11, 27, ... OEIS: A050216. Legendre's conjecture that there is a prime between consecutive integer squares directly implies that there are at least two primes between prime squares for pn ≥ 3 since pn+1 − pn ≥ 2.


In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions. When specialized to solving feasible linear optimization problems with rational data, the ellipsoid method is an algorithm which finds an optimal solution in a number of steps that is polynomial in the input size. The ellipsoid method generates a sequence of ellipsoids whose volume uniformly decreases at every step, thus enclosing a minimizer of a convex function.


The sequence of output subcommands required to accomplish the input command is generated by situations (i.e., branching conditions) that cause the FSA to transition from one output subcommand to the next. In step 4, each of the situations that are defined in step 3 are analyzed to reveal their dependencies on world and task states. This step identifies the detailed relationships between entities, events, and states of the world that cause a particular situation to be true.


In the balanced number partitioning problem, there are constraints on the number of items that can be allocated to each subset (these are called cardinality constraints). Another variant is the multidimensional number partitioning.


The term is also used for other devices which can both transmit and receive through a communications channel, such as optical transceivers which transmit and receive light in optical fiber systems, and bus transceivers which transmit and receive digital data in computer data buses. Radio transceivers are widely used in wireless devices. One large use is in two-way radios, which are audio transceivers used for bidirectional person-to-person voice communication.


In some texts, a trivial proof refers to a statement involving a material implication P→Q, where the consequent Q, is always true. Here, the proof follows immediately by virtue of the definition of material implication in which as the implication is true regardless of the truth value of the antecedent P if the consequent is fixed as true.A related concept is a vacuous truth, where the antecedent P in a material implication P→Q is false. In this case, the implication is always true regardless of the truth value of the consequent Q – again by virtue of the definition of material implication.


In public transportation, schedule adherence or on-time performance refers to the level of success of the service (such as a bus or train) remaining on the published schedule. On time performance, sometimes referred to as on time running, is normally expressed as a percentage, with a higher percentage meaning more vehicles are on time. The level of on time performance for many transport systems is a very important measure of the effectiveness of the system.


For this reason, security and access control became a major focus of the Multics project in 1965. Another ongoing issue was properly handling computing resources: users spent most of their time staring at the terminal and thinking about what to input instead of actually using the resources of the computer, and a time-sharing system should give the CPU time to an active user during these periods. Finally, the systems typically offered a memory hierarchy several layers deep, and partitioning this expensive resource led to major developments in virtual memory systems.


In networking jargon, a computer, phone, or internet of things device connected to a computer network is sometimes referred to as an end system or end station, because it sits at the edge of the network. The end user directly interacts with an end system that provides information or services.End systems that are connected to the Internet are also referred to as internet hosts; this is because they host (run) internet applications such as a web browser or an email retrieval program. The Internet's end systems include some computers with which the end user does not directly interact. These include mail servers, web servers, or database servers.


In print, summation and product are represented by special symbols; but other iterated operators often are denoted by larger variants of the symbol for the ordinary binary operator. Thus, the iterations of the four operations mentioned above are denoted ∑ , ∏ , ⋃ , {\displaystyle \sum ,\ \prod ,\ \bigcup ,} and ⋂ {\displaystyle \bigcap } , respectively.More generally, iteration of a binary function is generally denoted by a slash: iteration of f {\displaystyle f} over the sequence ( a 1 , a 2 … , a n ) {\displaystyle (a_{1},a_{2}\ldots ,a_{n})} is denoted by f / ( a 1 , a 2 … , a n ) {\displaystyle f/(a_{1},a_{2}\ldots ,a_{n})} , following the notation for reduce in Bird–Meertens formalism. In general, there is more than one way to extend a binary operation to operate on finite sequences, depending on whether the operator is associative, and whether the operator has identity elements.


Hence the degree of ψ ℓ {\displaystyle \psi _{\ell }} is equal to either 1 2 ( l 2 − 1 ) {\displaystyle {\frac {1}{2}}(l^{2}-1)} , 1 2 ( l − 1 ) {\displaystyle {\frac {1}{2}}(l-1)} , or 0. René Schoof observed that working modulo the ℓ {\displaystyle \ell } th division polynomial allows one to work with all ℓ {\displaystyle \ell } -torsion points simultaneously. This is heavily used in Schoof's algorithm for counting points on elliptic curves.


= λ e − λ t − e − λ t ∑ u = 1 x − 1 ( λ u t u − 1 ( u − 1 ) ! − λ u + 1 t u u ! ) {\displaystyle {\begin{aligned}f(t)&{}={\frac {d}{dt}}\Pr(T_{x}\leq t)={\frac {d}{dt}}\Pr(X_{t}\geq x)={\frac {d}{dt}}(1-\Pr(X_{t}\leq x-1))\\\\&{}={\frac {d}{dt}}\left(1-\sum _{u=0}^{x-1}\Pr(X_{t}=u)\right)={\frac {d}{dt}}\left(1-\sum _{u=0}^{x-1}{\frac {(\lambda t)^{u}e^{-\lambda t}}{u!


In the example that follows, there are exactly two complete lead-reductions that produce two very different results. The fact that the results are irreducible (not only lead-irreducible) is specific to the example, although this is rather common with such small examples. In this two variable example, the monomial ordering that is used is the lexicographic order with x > y , {\displaystyle x>y,} and we consider the reduction of by G = { g 1 , g 2 } , {\displaystyle G=\{g_{1},g_{2}\},} with For the first reduction step, either the first or the second term of f may be reduced. However, the reduction of a term amounts to removing this term at the cost of adding new lower terms; if it is not the first reducible term that is reduced, it may occur that a further reduction adds a similar term, which must be reduced again.


In the United States, the U.S. Food and Drug Administration (FDA) controls antimicrobial handsoaps and sanitizers as over-the-counter drugs (OTC) because they are intended for topical anti-microbial use to prevent disease in humans.The FDA requires strict labeling which informs consumers on proper use of this OTC drug and dangers to avoid, including warning adults not to ingest, not to use in the eyes, to keep out of the reach of children, and to allow use by children only under adult supervision. According to the American Association of Poison Control Centers, there were nearly 12,000 cases of hand sanitizer ingestion in 2006. If ingested, alcohol-based hand sanitizers can cause alcohol poisoning in small children.


They may be running traditionally in-house software or general purpose software such as DOS. Many of the newer ones have touch screens. They may be connected to computerized point of sale networks using any type of protocol. Such systems may be accessed remotely for the purpose of obtaining records or troubleshooting. Many businesses also use tablet computers as cash registers, utilizing the sale system as downloadable app-software.


In designing an artificial intelligence agent, it was soon realized that representing common-sense knowledge, knowledge that humans simply take for granted, was essential to make an AI that could interact with humans using natural language. Cyc was meant to address this problem.


In statistics, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will include the true value (parameter) of interest. It can be defined as the proportion of instances where the interval surrounds the true value as assessed by long-run frequency.


The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample to another) and its bias (how far off the average estimated value is from the true value). For an unbiased estimator, the MSE is the variance of the estimator. Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard error.


This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form.In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see Toroidal cores below). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs. The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1,400 to 2,000 V) than the voltage of utilization loads (100 V initially preferred).


In nonstandard analysis, a monad or also a halo is the set of points infinitesimally close to a given point.Given a hyperreal number x in R∗, the monad of x is the set monad ( x ) = { y ∈ R ∗ ∣ x − y is infinitesimal } . {\displaystyle {\text{monad}}(x)=\{y\in \mathbb {R} ^{*}\mid x-y{\text{ is infinitesimal}}\}.} If x is finite (limited), the unique real number in the monad of x is called the standard part of x. == References ==


The first recall device in the United States was adopted in Los Angeles in 1903. Typically, the process involves the collection of citizen petitions for the recall of an elected official; if a sufficient number of valid signatures are collected and verified, a recall election is triggered. There have been four gubernatorial recall elections in U.S.


The linkage criterion determines the distance between sets of observations as a function of the pairwise distances between observations. Some commonly used linkage criteria between two sets of observations A and B and a distance d are: Some of these can only be recomputed recursively (WPGMA, WPGMC), for many a recursive computation with Lance-Williams-equations is more efficient, while for other (Mini-Max, Hausdorff, Medoid) the distances have to be computed with the slower full formula. Other linkage criteria include: The probability that candidate clusters spawn from the same distribution function (V-linkage). The product of in-degree and out-degree on a k-nearest-neighbour graph (graph degree linkage). The increment of some cluster descriptor (i.e., a quantity defined for measuring the quality of a cluster) after merging two clusters.


The following Algorithm B doesn't have this disadvantage, but it also doesn't have the fast arithmetic modulo p {\displaystyle p} Algorithm A has in that case. Algorithm B Select a Q {\displaystyle Q} -bit prime q {\displaystyle q} so that q ≡ 7 mod 12 {\displaystyle q\equiv 7\ {\text{mod}}\ 12} . Find the roots r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} of X 2 − X + 1 mod q {\displaystyle X^{2}-X+1\ {\text{mod}}\ q} .


In mathematics, an interleave sequence is obtained by merging two sequences via an in shuffle. Let S {\displaystyle S} be a set, and let ( x i ) {\displaystyle (x_{i})} and ( y i ) {\displaystyle (y_{i})} , i = 0 , 1 , 2 , … , {\displaystyle i=0,1,2,\ldots ,} be two sequences in S . {\displaystyle S.} The interleave sequence is defined to be the sequence x 0 , y 0 , x 1 , y 1 , … {\displaystyle x_{0},y_{0},x_{1},y_{1},\dots } .


Clustered lasso is a generalization of fused lasso that identifies and groups relevant covariates based on their effects (coefficients). The basic idea is to penalize the differences between the coefficients so that nonzero ones cluster. This can be modeled using the following regularization: ∑ i < j p | β i − β j | ≤ t 2 . {\displaystyle \sum _{i


Query-dependent methods attempt to measure the degree to which a page matches a specific query, independent of the importance of the page. Query-dependent ranking is usually based on heuristics that consider the number and locations of matches of the various query words on the page itself, in the URL or in any anchor text referring to the page. In webometrics, it is possible to rank institutions according to their presence in the web (number of webpages) and the impact of these contents, such as the Webometrics Ranking of World Universities.


In the first loop, the original (parent) process forks 10 copies of itself. Each of these child processes (detected by the fact that fork() returned zero) prints a message, sleeps, and exits. All of the children are created at essentially the same time (since the parent is doing very little in the loop), so it is somewhat random when each of them gets scheduled for the first time - thus the scrambled order of their messages. During the loop, an array of child process IDs is built.


In medicine, sampling is gathering of matter from the body to aid in the process of a medical diagnosis and/or evaluation of an indication for treatment, further medical tests or other procedures. In this sense, the sample is the gathered matter, and the sampling tool or sampler is the person or material to collect the sample. Sampling is a prerequisite for many medical tests, but generally not for medical history, physical examination and radiologic tests.


Bentley also proposed using range trees, which improved query time to O ( log d  n + k ) {\displaystyle O(\log ^{d}n+k)} but increased space to O ( n log d − 1  n ) {\displaystyle O(n\log ^{d-1}n)} . Dan Willard used downpointers, a special case of fractional cascading to reduce the query time further to O ( log d − 1  n + k ) {\displaystyle O(\log ^{d-1}n+k)} . While the above results were achieved in the pointer machine model, further improvements have been made in the word RAM model of computation in low dimensions (2D, 3D, 4D).


In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p-adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the ring of adeles. The metaplectic group has a particularly significant infinite-dimensional linear representation, the Weil representation. It was used by André Weil to give a representation-theoretic interpretation of theta functions, and is important in the theory of modular forms of half-integral weight and the theta correspondence.


In mathematics, a completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. The class of completely regular semigroups forms an important subclass of the class of regular semigroups, the class of inverse semigroups being another such subclass. Alfred H. Clifford was the first to publish a major paper on completely regular semigroups though he used the terminology "semigroups admitting relative inverses" to refer to such semigroups. The name "completely regular semigroup" stems from Lyapin's book on semigroups.


In the context of Regulation (EU) No 910/2014 (eIDAS), a qualified digital certificate is a public key certificate issued by a trust service provider which has government-issued qualifications. The certificate is designed to ensure the authenticity and data integrity of an electronic signature and its accompanying message and/or attached data.


Since relabels and saturating pushes increase Φ, the total number of nonsaturating pushes must make up the difference of (2| V | − 1)(| V | − 2) + (2| V | − 1)(2| V || E |) ≤ 4| V |2| E |. This results in a time bound of O(V 2E) for the nonsaturating push operations. In sum, the algorithm executes O(V 2) relabels, O(VE) saturating pushes and O(V 2E) nonsaturating pushes. Data structures can be designed to pick and execute an applicable operation in O(1) time. Therefore, the time complexity of the algorithm is O(V 2E).


In statistical inference based on regression coefficients, yes; in predictive modelling applications, correction is neither necessary nor appropriate. To understand this, consider the measurement error as follows. Let y be the outcome variable, x be the true predictor variable, and w be an approximate observation of x. Frost and Thompson suggest, for example, that x may be the true, long-term blood pressure of a patient, and w may be the blood pressure observed on one particular clinic visit. Regression dilution arises if we are interested in the relationship between y and x, but estimate the relationship between y and w. Because w is measured with variability, the slope of a regression line of y on w is less than the regression line of y on x. Does this matter?


In 2012, the court ruled that under the All Writs Act, the defendant was required to produce an unencrypted hard drive for the court.In many jurisdictions, the legal status of forced disclosure remains unclear. The 2016 FBI–Apple encryption dispute concerns the ability of courts in the United States to compel manufacturers' assistance in unlocking cell phones whose contents are cryptographically protected. As a potential counter-measure to forced disclosure some cryptographic software supports plausible deniability, where the encrypted data is indistinguishable from unused random data (for example such as that of a drive which has been securely wiped).


In the Zeroth Part, Chapter 0, Conway introduces a specialized form of set notation, having the form {L|R}, where L and R are again of this form, built recursively, terminating in {|}, which is to be read as an analog of the empty set. Given this object, axiomatic definitions for addition, subtraction, multiplication, division and inequality may be given. As long as one insists that L


Codes such as MARLOWE operate with this approach. The binary collision approximation can also be extended to simulate dynamic composition changes of a material due to prolonged ion irradiation, i.e. due to ion implantation and sputtering.At low ion energies, the approximation of independent collisions between atoms starts to break down.


In mathematical group theory, a C-group is a group such that the centralizer of any involution has a normal Sylow 2-subgroup. They include as special cases CIT-groups where the centralizer of any involution is a 2-group, and TI-groups where any Sylow 2-subgroups have trivial intersection. The simple C-groups were determined by Suzuki (1965), and his classification is summarized by Gorenstein (1980, 16.4). The classification of C-groups was used in Thompson's classification of N-groups. The simple C-groups are the projective special linear groups PSL2(p) for p a Fermat or Mersenne prime the projective special linear groups PSL2(9) the projective special linear groups PSL2(2n) for n≥2 the projective special linear groups PSL3(q) for q a prime power the Suzuki groups Sz(22n+1) for n≥1 the projective unitary groups PU3(q) for q a prime power


Uncertainties can also be defined by the relative error (Δx)/x, which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, σ, which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval x ± u. However, the most general way of characterizing uncertainty is by specifying its probability distribution.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 235, 1235, 2345, and 12345 are the patterns related to Braille pattern dots-124, since the two additional dots of kantenji patterns 0124, 1247, and 01247 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


So the parser should also use the rule A → w if ε is in Fi(w) and it sees on the input stream a symbol that could follow A. Therefore, we also need the Follow-set of A, written as Fo(A) here, which is defined as the set of terminals a such that there is a string of symbols αAaβ that can be derived from the start symbol. We use $ as a special terminal indicating end of input stream, and S as start symbol. Computing the Follow-sets for the nonterminals in a grammar can be done as follows: initialize Fo(S) with { $ } and every other Fo(Ai) with the empty set if there is a rule of the form Aj → wAiw' , then if the terminal a is in Fi(w' ), then add a to Fo(Ai) if ε is in Fi(w' ), then add Fo(Aj) to Fo(Ai) if w' has length 0, then add Fo(Aj) to Fo(Ai) repeat step 2 until all Fo sets stay the same.This provides the least fixed point solution to the following system: Fo(S) ⊇ {$} Fo(A) ⊇ Fi(w)·Fo(B) for each rule of the form B → ... A wNow we can define exactly which rules will appear where in the parsing table.


Thus measuring leakage, or Iddq testing, is a quick, inexpensive method for finding defective chips. Increased leakage is a common failure mode resulting from non-catastrophic overstress of a semiconductor device, when the junction or the gate oxide suffers permanent damage not sufficient to cause a catastrophic failure. Overstressing the gate oxide can lead to stress-induced leakage current.


Altmetrics did not originally cover citation counts, but calculate scholar impact based on diverse online research output, such as social media, online news media, online reference managers and so on. It demonstrates both the impact and the detailed composition of the impact. Altmetrics could be applied to research filter, promotion and tenure dossiers, grant applications and for ranking newly-published articles in academic search engines.


Infiltrating organizations is an important tool because these institutions are already seen as legitimate in the eyes of the people and provide a platform to express their ideas. When infiltrating, the dissident identifies needs of the organization and then links those needs to solutions that his ideology can provide. This was a technique that the Communist Party USA employed.


{\displaystyle X_{0},X_{1},X_{2},...} then X 0 {\displaystyle X_{0}} is the state which the machine starts in and X 10 {\displaystyle X_{10}} is the random variable describing its state after 10 transitions. The process continues forever, indexed by the natural numbers. An example of a stochastic process which is not a Markov chain is the model of a machine which has states A and E and moves to A from either state with 50% chance if it has ever visited A before, and 20% chance if it has never visited A before (leaving a 50% or 80% chance that the machine moves to E).


In the United States House of Representatives, a motion to recommit can be made with or without instructions. If the motion is made without instructions, the bill or resolution is simply sent back to the committee. If the motion is made with instructions and the motion is agreed to, the chairman of the committee in question will immediately report the bill or resolution back to the whole House with the new language. In this sense, a motion to recommit with instructions is effectively an amendment.


In telecommunication, a mobile VPN is a solution that provides data user mobility and ensures secure network access with predictable performance. Data user mobility is defined as uninterrupted connectivity or the ability to stay connected and communicate to a possibly remote data network while changing the network access medium or points of attachment.In 2001, Huawei launched a product named "MVPN". In this case "MVPN" had a different meaning from the way that later industry sources would use the term. The Huawei product was focused on delivering a seamless corporate phone system to users whether they were on desktop phones or mobile devices. Although the web page is no longer available, the company advertised that their MVPN had the following advantages over a standard phone system: Direct connectivity – the corporate network becomes part of mobile operator's network through direct connection Private numbering plan – the communication is tailored to company organization Corporate Business Group – all offices and employees are part of one common group, that includes all mobile and desk phones Short dialing – a short number to access each employee, no meter on his mobile or desk phone Smart Divert – easy divert within company group Groups and subgroups – Several sub-groups could be defined within the group with different changing as well as with separate numbering plan Calls control – certain destinations could be allowed or barred both on mobile and desk phones.


The internal language of closed symmetric monoidal categories is linear logic and the type system is the linear type system. Many examples of closed monoidal categories are symmetric. However, this need not always be the case, as non-symmetric monoidal categories can be encountered in category-theoretic formulations of linguistics; roughly speaking, this is because word-order in natural language matters.


In such games, however, it is often found that creativity is lowered and the words stray towards having obvious associations again. This game is sometimes known as "Word for Word". Sometimes, repeated words are forbidden or otherwise noted on a separate list for interest. A variant with an arbitrary name (sometimes called Ultra Word Association) involves associating words in a grid, where the first word is placed in the top-left, and where each word must be placed adjacent to another one and must associate with all those words adjacent to it.


In the 1990s, Noam Elkies, followed by A. O. L. Atkin devised improvements to Schoof's basic algorithm by making a distinction among the primes ℓ 1 , … , ℓ s {\displaystyle \ell _{1},\ldots ,\ell _{s}} that are used. A prime ℓ {\displaystyle \ell } is called an Elkies prime if the characteristic equation of the Frobenius endomorphism, ϕ 2 − t ϕ + q = 0 {\displaystyle \phi ^{2}-t\phi +q=0} , splits over F ℓ {\displaystyle \mathbb {F} _{\ell }} . Otherwise ℓ {\displaystyle \ell } is called an Atkin prime. Elkies primes are the key to improving the asymptotic complexity of Schoof's algorithm.


An example would be to trade the electric charge, Q, (related to the abelian group U(1) of electromagnetism), for the new quantum number exp(2iπ Q). Then this becomes a multiplicative quantum number by virtue of the charge being an additive quantum number. However, this route is usually followed only for discrete subgroups of U(1), of which Z2 finds the widest possible use.


Digitally modulated signals (e.g. QAM or PSK) are basically made of two CW carriers (the I and Q components, which are out-of-phase carriers). In fact, the information (bits or symbols) is carried by given combinations of phase and/or amplitude of the I and Q components.


Available in several varieties; analog, analog spread spectrum (100 kHz bandwidth), digital, and digital spread spectrum, most being sold today are low-cost analog models, which are still susceptible to eavesdropping. Digital variants can still be scanned, but are received as a digital hiss and therefore are difficult to eavesdrop upon. Digital transmission is immune to static interference but can experience signal fade (brief silence) as the phone goes out of range of the base.


In the NMOS 6502 and derivatives (e.g., 6510), the simultaneous assertion of a hardware interrupt line and execution of BRK was not accounted for in the design—the BRK instruction will be ignored in such a case. Also, the status of the decimal mode flag in the processor status register is unchanged following an interrupt of any kind. This behavior can potentially result in a difficult to locate bug in the interrupt handler if decimal mode happens to be enabled at the time of an interrupt. These anomalies were corrected in all CMOS versions of the processor.


There is no standard method for applying the task. The most commonly used one is a letter rating task, which involves having participants judge all the letters of the alphabet.


It has also been observed that misinformation and disinformation reappear on social media sites. A research study watched the process of thirteen rumors appearing on Twitter and noticed that eleven of those same stories resurfaced multiple times, after time had passed.A social media app called Parler has caused much chaos as well. Right winged Twitter users who were banned on the app moved to Parler after the Capitol Hill riots, and the app was being used to plan and facilitate more illegal and dangerous activities.


In the contemporary literature, there are two primary (and non-equivalent) formulations of supervenience (for both definitions let A and B be sets of properties). (1) A-properties supervene on B-properties if and only if all things that are B-indiscernible are A-indiscernible. Formally: ∀ x ∀ y ( ∀ X ∈ B ( X x ↔ X y ) → ∀ Y ∈ A ( Y x ↔ Y y ) ) {\displaystyle \forall x\forall y(\forall X_{\in B}(Xx\leftrightarrow Xy)\rightarrow \forall Y_{\in A}(Yx\leftrightarrow Yy))} (2) A-properties supervene on B-properties if and only if anything that has an A-property has some B-property such that anything that has that B-property also has that A-property. Formally: ∀ x ∀ X ∈ A ( X x → ∃ Y ∈ B ( Y x ∧ ∀ y ( Y y → X y ) ) ) {\displaystyle \forall x\forall X_{\in A}(Xx\rightarrow \exists Y_{\in B}(Yx\land \forall y(Yy\rightarrow Xy)))} For example, if one lets A be a set of mental properties, lets B be a set of physical properties, and chooses a domain of discourse consisting of persons, then (1) says that any two persons who are physically indiscernible are mentally indiscernible, and (2) says that any person who has a mental property has some physical property such that any person with that physical property has that mental property.


The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company.