Instead of sending the caller ID in between the first and second ring, some systems (such as in the UK) use line reversal to announce the caller ID, or caller ID signals are simply sent without any announcement. Instead of Bell 202, the European alternative V.23 is sometimes used (without the 75-baud reverse channel) or the data is sent using DTMF signalling. In general, CID as transmitted from the origin of the call is only the calling party's full phone number (including area code, and including international access code and country code if it's an international call).


If ∑ b ∈ A N n ( x − k − 1 b ) = 0 {\displaystyle \sum _{b\in A}N_{n}(x_{-k}^{-1}b)\,=\,0} , define p ^ n ( a ∣ x − k − 1 ) = 1 / | A | {\displaystyle {\hat {p}}_{n}(a\mid x_{-k}^{-1})\,=\,1/|A|} . To i ≥ 1 {\displaystyle i\geq 1} , define Λ n ( x − i − 1 ) = 2 ∑ y ∈ A ∑ a ∈ A N n ( y x − i − 1 a ) log   {\displaystyle \Lambda _{n}(x_{-i}^{-1})\,=\,2\,\sum _{y\in A}\sum _{a\in A}N_{n}(yx_{-i}^{-1}a)\log \left\,} where y x − i − 1 = ( y , x − i , … , x − 1 ) {\displaystyle yx_{-i}^{-1}=(y,x_{-i},\ldots ,x_{-1})} and p ^ n ( a ∣ x − i − 1 y ) = N n ( y x − i − 1 a ) ∑ b ∈ A N n ( y x − i − 1 b ) . {\displaystyle {\hat {p}}_{n}(a\mid x_{-i}^{-1}y)={\frac {N_{n}(yx_{-i}^{-1}a)}{\sum _{b\in A}N_{n}(yx_{-i}^{-1}b)}}.}


In mathematics, a cocountable subset of a set X is a subset Y whose complement in X is a countable set. In other words, Y contains all but countably many elements of X. Since the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals. If the complement is finite, then one says Y is cofinite.


Secondly, the FIC formulae depend on the specifics of the models used for the observed data and also on how precision is to be measured. The clearest case is where precision is taken to be mean squared error, say r j = b j 2 + τ j 2 {\displaystyle r_{j}=b_{j}^{2}+\tau _{j}^{2}} in terms of squared bias and variance for the estimator associated with model j {\displaystyle j} . FIC formulae are then available in a variety of situations, both for handling parametric, semiparametric and nonparametric situations, involving separate estimation of squared bias and variance, leading to estimated precision r ^ j {\displaystyle {\hat {r}}_{j}} .


In object-oriented programming languages that do not support higher-order functions, objects can be an effective substitute. An object's methods act in essence like functions, and a method may accept objects as parameters and produce objects as return values. Objects often carry added run-time overhead compared to pure functions, however, and added boilerplate code for defining and instantiating an object and its method(s). Languages that permit stack-based (versus heap-based) objects or structs can provide more flexibility with this method. An example of using a simple stack based record in Free Pascal with a function that returns a function: The function a() takes a Txy record as input and returns the integer value of the sum of the record's x and y fields (3 + 7).


In mobile telecommunications technology, the concept of mobile signature roaming means an access point (AP) should be able to get a mobile signature from any end-user, even if the AP and the end-user have not contracted a commercial relationship with the same MSSP. Otherwise, an AP would have to build commercial terms with as many MSSPs as possible, and this might be a cost burden. This means that a mobile signature transaction issued by an application provider should be able to reach the appropriate MSSP, and this should be transparent for the AP.


In more technical terms, let us assume that we have a theory described by a certain function Z {\displaystyle Z} of the state variables { s i } {\displaystyle \{s_{i}\}} and a certain set of coupling constants { J k } {\displaystyle \{J_{k}\}} . This function may be a partition function, an action, a Hamiltonian, etc. It must contain the whole description of the physics of the system. Now we consider a certain blocking transformation of the state variables { s i } → { s ~ i } {\displaystyle \{s_{i}\}\to \{{\tilde {s}}_{i}\}} , the number of s ~ i {\displaystyle {\tilde {s}}_{i}} must be lower than the number of s i {\displaystyle s_{i}} .


In the majority of models, sampling fewer taxon with more sites per taxon demonstrated higher accuracy. Generally, with the alignment of a relatively equal number of total nucleotide sites, sampling more genes per taxon has higher bootstrapping replicability than sampling more taxa. However, unbalanced datasets within genomic databases make increasing the gene comparison per taxon in uncommonly sampled organisms increasingly difficult.


In some cases, tasks depend on each other. These interdependencies can be illustrated by a directed acyclic graph. Intuitively, some tasks cannot begin until others are completed.


In some applications it is useful to be able to compute the Bernoulli numbers B0 through Bp − 3 modulo p, where p is a prime; for example to test whether Vandiver's conjecture holds for p, or even just to determine whether p is an irregular prime. It is not feasible to carry out such a computation using the above recursive formulae, since at least (a constant multiple of) p2 arithmetic operations would be required. Fortunately, faster methods have been developed which require only O(p (log p)2) operations (see big O notation). David Harvey describes an algorithm for computing Bernoulli numbers by computing Bn modulo p for many small primes p, and then reconstructing Bn via the Chinese remainder theorem.


In practice, incorrectly received coded data blocks are often stored at the receiver rather than discarded, and when the re-transmitted block is received, the two blocks are combined. This is called Hybrid ARQ with soft combining (Dahlman et al., p. 120).


"Don't embarrass me with bad pictures" Users may have the ability to control which pictures they post on their own Facebook page, but they do not have the ability to control what others post. Posting and "tagging" unflattering pictures of others may create expectancy violations. "Don't mess up my profile" Several participants expressed annoyance of others who alter their profiles knowing that their alterations could be perceived negatively, though they did not mention changing their passwords or protecting themselves in other ways.


So f0 is still the truth value of ψ, but the Rx value produces a result that is linear in x. Also after any Q i x i {\displaystyle {\mathsf {Q}}_{i}x_{i}} we add R x 1 … R x i {\displaystyle \mathrm {R} _{x_{1}}\dots \mathrm {R} _{x_{i}}} in ψ′ in order to reduce the degree down to 1 after arithmetizing Q i {\displaystyle {\mathsf {Q}}_{i}} . Now let's describe the protocol. If n is the length of ψ, all arithmetic operations in the protocol are over a field of size at least n4 where n is the length of ψ. Phase 0: P → V: P sends f0 to V. V checks that f0= 1 and rejects if not.


In the chart below, the Carian letter for each vowel is followed by the conventional transcription with the Greek equivalent in parentheses. An epenthetic schwa to break up clusters may have been unwritten.


In some programming languages, given a two-argument function f (or a binary operator), the outer product, f, of two one-dimensional arrays, A and B, is a two-dimensional array C such that C = f(A, B). This is syntactically represented in various ways: in APL, as the infix binary operator ∘.f; in J, as the postfix adverb f/; in R, as the function outer(A, B, f) or the special %o%; in Mathematica, as Outer. In MATLAB, the function kron(A, B) is used for this product. These often generalize to multi-dimensional arguments, and more than two arguments.


In tau-square notation from N. Bourbaki's Theory of Sets, the quantifiers are defined as follows: ( ∃ x ) A ( x ) ≡ ( τ x ( A ) | x ) A {\displaystyle (\exists x)A(x)\ \equiv \ (\tau _{x}(A)|x)A} ( ∀ x ) A ( x ) ≡ ¬ ( τ x ( ¬ A ) | x ) ¬ A ≡ ( τ x ( ¬ A ) | x ) A {\displaystyle (\forall x)A(x)\ \equiv \ \neg (\tau _{x}(\neg A)|x)\neg A\ \equiv \ (\tau _{x}(\neg A)|x)A} where A is a relation in L, x is a variable, and τ x ( A ) {\displaystyle \tau _{x}(A)} juxtaposes a τ {\displaystyle \tau } at the front of A, replaces all instances of x with ◻ {\displaystyle \square } , and links them back to τ {\displaystyle \tau } . Then let Y be an assembly, (Y|x)A denotes the replacement of all variables x in A with Y. This notation is equivalent to the Hilbert notation and is read the same. It is used by Bourbaki to define cardinal assignment since they do not use the axiom of replacement. Defining quantifiers in this way leads to great inefficiencies. For instance, the expansion of Bourbaki's original definition of the number one, using this notation, has length approximately 4.5 × 1012, and for a later edition of Bourbaki that combined this notation with the Kuratowski definition of ordered pairs, this number grows to approximately 2.4 × 1054.


In mathematics, the logarithm is the inverse function to exponentiation. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base 10 is called the decimal or common logarithm and is commonly used in science and engineering.


Several models were produced which dispensed with the power transformer, but had circuit features which only allowed operation from AC. Some early models were available in both AC-only and AC/DC versions, with the AC/DC versions sometimes slightly more expensive.Television receivers were first commercially sold in England in 1936 for the new 'Television Service' broadcast by the British Broadcasting Corporation. All pre World War II sets used mains transformers and consequently were AC only.


Negative bases are rarely used. In a system with more than | b | {\displaystyle |b|} unique digits, numbers may have many different possible representations.


In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from X to Y is often denoted with the notation X ↪ Y {\displaystyle X\hookrightarrow Y} . In the more general setting of category theory, a monomorphism (also called a monic morphism or a mono) is a left-cancellative morphism. That is, an arrow f: X → Y such that for all objects Z and all morphisms g1, g2: Z → X, f ∘ g 1 = f ∘ g 2 ⟹ g 1 = g 2 .


These simpler expressions make up the majority of redundant, optimizable expressions in programs written in languages other than concatenative languages. An optimizing compiler can only win on redundancies that the programmer could have avoided in the source code.The second way leaves a computed value on the data stack, duplicating it as needed. This uses operations to copy stack entries.


In particular, the convolutional neural network lends itself to eye-tracking, as it is designed for image-centric tasks. With AI, eye-tracking tasks and studies can yield additional information that may not have been detected by human observers. The practice of deep learning also allows for a given neural network to improve at a given task when given enough sample data. This requires a relatively large supply of training data, however.The potential use cases for AI in eye-tracking cover a wide range of topics from medical applications to driver safety to game theory and even education and training applications.


The groups Co2 of order 42,305,421,312,000 = 218 · 36 · 53 · 7 · 11 · 23and Co3 of order 495,766,656,000 = 210 · 37 · 53 · 7 · 11 · 23consist of the automorphisms of Λ fixing a lattice vector of type 2 and type 3, respectively. As the scalar −1 fixes no non-zero vector, these two groups are isomorphic to subgroups of Co1. The inner product on the Leech lattice is defined as 1/8 the sum of the products of respective co-ordinates of the two multiplicand vectors; it is an integer.


In mathematics, a function f is cofunction of a function g if f(A) = g(B) whenever A and B are complementary angles. This definition typically applies to trigonometric functions. The prefix "co-" can be found already in Edmund Gunter's Canon triangulorum (1620).For example, sine (Latin: sinus) and cosine (Latin: cosinus, sinus complementi) are cofunctions of each other (hence the "co" in "cosine"): The same is true of secant (Latin: secans) and cosecant (Latin: cosecans, secans complementi) as well as of tangent (Latin: tangens) and cotangent (Latin: cotangens, tangens complementi): These equations are also known as the cofunction identities.This also holds true for the versine (versed sine, ver) and coversine (coversed sine, cvs), the vercosine (versed cosine, vcs) and covercosine (coversed cosine, cvc), the haversine (half-versed sine, hav) and hacoversine (half-coversed sine, hcv), the havercosine (half-versed cosine, hvc) and hacovercosine (half-coversed cosine, hcc), as well as the exsecant (external secant, exs) and excosecant (external cosecant, exc):


During this time the user may be prevented from closing, resizing, or even minimizing the windows of the affected application (although moving the window is still possible in OS X, as well as previously hidden parts of the window which are usually redrawn, even when the application is otherwise unresponsive). While one application is unresponsive, typically other applications are usable. File system and network delays are another common cause.


{\displaystyle \left.+\lefte^{-ipx}\right\}.} Thus, ∂ E 1 ( x ) / ∂ x 1 + ∂ E 2 ( x ) / ∂ x 2 + ∂ E 3 ( x ) / ∂ x 3 {\displaystyle \partial E_{1}(x)/\partial x_{1}+\partial E_{2}(x)/\partial x_{2}+\partial E_{3}(x)/\partial x_{3}} contains terms of the form p 1 ϵ 1 1 ( p ) + p 2 ϵ 2 1 ( p ) + p 3 ϵ 3 1 ( p ) {\displaystyle p_{1}\epsilon _{1}^{1}(\mathbf {p} )+p_{2}\epsilon _{2}^{1}(\mathbf {p} )+p_{3}\epsilon _{3}^{1}(\mathbf {p} )} which equate to zero by the first of Eq. (4). This gives, ∇ ⋅ E ( x ) = 0 , {\displaystyle \nabla \cdot \mathbf {E} (x)=0,} ∇ ⋅ H ( x ) = 0.


Full-text-searching techniques appeared in the 1960s, for example IBM STAIRS from 1969, and became common in online bibliographic databases in the 1990s. Many websites and application programs (such as word processing software) provide full-text-search capabilities. Some web search engines, such as the former AltaVista, employ full-text-search techniques, while others index only a portion of the web pages examined by their indexing systems.


It has been demonstrated for the first time in 2011 to enable better training of deeper networks, compared to the widely used activation functions prior to 2011, i.e., the logistic sigmoid (which is inspired by probability theory; see logistic regression) and its more practical counterpart, the hyperbolic tangent. A commonly used variant of the ReLU activation function is the Leaky ReLU which allows a small, positive gradient when the unit is not active: f ( x ) = { x if x > 0 , a x otherwise . {\displaystyle f(x)={\begin{cases}x&{\text{if }}x>0,\\ax&{\text{otherwise}}.\end{cases}}} where x is the input to the neuron and a is a small positive constant (in the original paper the value 0.01 was used for a).


In phonology, affricates tend to behave similarly to stops, taking part in phonological patterns that fricatives do not. Kehrein (2002) analyzes phonetic affricates as phonological stops. A sibilant or lateral (and presumably trilled) stop can be realized phonetically only as an affricate and so might be analyzed phonemically as a sibilant or lateral stop. In that analysis, affricates other than sibilants and laterals are a phonetic mechanism for distinguishing stops at similar places of articulation (like more than one labial, coronal, or dorsal place).


In natural language applications, libraries are a way to cope with thousands of details involved in syntax, lexicon, and inflection. The GF Resource Grammar Library is the standard library for Grammatical Framework. It covers the morphology and basic syntax for an increasing number of languages, currently including Afrikaans, Amharic (partial), Arabic (partial), Basque (partial), Bulgarian, Catalan, Chinese, Czech (partial), Danish, Dutch, English, Estonian, Finnish, French, German, Greek ancient (partial), Greek modern, Hebrew (fragments), Hindi, Hungarian (partial), Interlingua, Italian, Japanese, Korean (partial), Latin (partial), Latvian, Maltese, Mongolian, Nepali, Norwegian bokmål, Norwegian nynorsk, Persian, Polish, Punjabi, Romanian, Russian, Sindhi, Slovak (partial), Slovene (partial), Somali (partial), Spanish, Swahili (fragments), Swedish, Thai, Turkish (fragments), and Urdu. In addition, 14 languages have WordNet lexicon and large-scale parsing extensions.A full API documentation of the library can be found at the RGL Synopsis page. The RGL status document gives the languages currently available in the GF Resource Grammar Library, including their maturity.


(The exception to this is when the first digit is negative one and the next two digits are one, like 1111.001=1.001.) This can be converted to the negative of a base-φ representation by negating every digit, standardizing the result, and then marking it as negative. For example, use a minus sign, or some other significance to denote negative numbers.


For k = 1 {\displaystyle k=1} the latter statement can be re-formulated as the # 2 {\displaystyle _{2}} P-completeness of computing, for a given unitary n×n-matrix U {\displaystyle U} over a field of characteristic 2, the n×n-matrix H ( U ) {\displaystyle H(U)} whose i,j-th entry is the Hamiltonian cycle polynomial of a matrix received from U {\displaystyle U} via subjecting its rows and columns to any permutation mapping j to 1 and i to 2 and then removing its 1-st row and 2-nd column (i.e. the sum of the products of the arc weights of the corresponding weighted digraph's Hamiltonian paths from vertex i to vertex j) for i ≠ j and zero for i = j. This matrix satisfies the matrix equation U ( H ( U ) ) T = H ( U ) U T {\displaystyle U(H(U))^{T}=H(U)U^{T}} , while ham  ( U U a a T 1 ) = ( a 1 2 + . .


In public policy, access control to restrict access to systems ("authorization") or to track or monitor behavior within systems ("accountability") is an implementation feature of using trusted systems for security or social control.


In reduced-circumference polar coordinates the spatial metric has the form d Σ 2 = d r 2 1 − k r 2 + r 2 d Ω 2 , where d Ω 2 = d θ 2 + sin 2  θ d ϕ 2 . {\displaystyle \mathrm {d} \mathbf {\Sigma } ^{2}={\frac {\mathrm {d} r^{2}}{1-kr^{2}}}+r^{2}\mathrm {d} \mathbf {\Omega } ^{2},\quad {\text{where }}\mathrm {d} \mathbf {\Omega } ^{2}=\mathrm {d} \theta ^{2}+\sin ^{2}\theta \,\mathrm {d} \phi ^{2}.} k is a constant representing the curvature of the space. There are two common unit conventions: k may be taken to have units of length−2, in which case r has units of length and a(t) is unitless.


In the ER model, the network generated is homogeneous, meaning each node has the same number of links. This is considered to be an exponential network. When comparing the connectivity of the ER model when it undergoes random failures vs directed attacks, we are shown that the exponential network reacts the same way to a random failure as it does to a directed attack. This is due to the homogeneity of the network, making it so that it does not matter whether a random node is selected or one is specifically targeted.


In probability theory, an f {\displaystyle f} -divergence is a function D f ( P ‖ Q ) {\displaystyle D_{f}(P\|Q)} that measures the difference between two probability distributions P {\displaystyle P} and Q {\displaystyle Q} . Many common divergences, such as KL-divergence, Hellinger distance, and total variation distance, are special cases of f {\displaystyle f} -divergence.


Pr ( S ) {\displaystyle \Pr(S)} can again be taken equal to 0.5, to avoid being too suspicious about incoming email. 3 is a good value for s, meaning that the learned corpus must contain more than 3 messages with that word to put more confidence in the spamicity value than in the default value. This formula can be extended to the case where n is equal to zero (and where the spamicity is not defined), and evaluates in this case to P r ( S ) {\displaystyle Pr(S)} .


In most-idle hunting, calls are always delivered to whichever line has been idle the longest. This considers the length of time that the calltaker has been busy versus available. This is typically used in call centers where the calls are being answered by people, to distribute the load evenly.


In statistical inference, the conditional probability is an update of the probability of an event based on new information. The new information can be incorporated as follows: Let A, the event of interest, be in the sample space, say (X,P). The occurrence of the event A knowing that event B has or will have occurred, means the occurrence of A as it is restricted to B, i.e. A ∩ B {\displaystyle A\cap B} . Without the knowledge of the occurrence of B, the information about the occurrence of A would simply be P(A) The probability of A knowing that event B has or will have occurred, will be the probability of A ∩ B {\displaystyle A\cap B} relative to P(B), the probability that B has occurred.


In the following transcriptions, diacritics may be used to distinguish between apical  and laminal . The commonality of  cross-linguistically is 2% in a phonological analysis of 2155 languages


If the paging unit is enabled, addresses in a segment are now virtual addresses, rather than physical addresses as they were on the 80286. That is, the segment starting address, the offset, and the final 32-bit address the segmentation unit derived by adding the two are all virtual (or logical) addresses when the paging unit is enabled. When the segmentation unit generates and validates these 32-bit virtual addresses, the enabled paging unit finally translates these virtual addresses into physical addresses.


The compounding corresponds to a Pólya urn scheme. It is frequently encountered in Bayesian statistics, machine learning, empirical Bayes methods and classical statistics as an overdispersed multinomial distribution. It reduces to the categorical distribution as a special case when n = 1. It also approximates the multinomial distribution arbitrarily well for large α. The Dirichlet-multinomial is a multivariate extension of the beta-binomial distribution, as the multinomial and Dirichlet distributions are multivariate versions of the binomial distribution and beta distributions, respectively.


The feedback vertex set problem has applications in VLSI chip design. Another application is in complexity theory. Some computational problems on graphs are NP-hard in general, but can be solved in polynomial time for graphs with bounded FVS number. Some examples are graph isomorphism and the path reconfiguration problem.


In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive identity the ring is said to have characteristic zero. That is, char(R) is the smallest positive number n such that:(p 198, Thm. 23.14) 1 + ⋯ + 1 ⏟ n summands = 0 {\displaystyle \underbrace {1+\cdots +1} _{n{\text{ summands}}}=0} if such a number n exists, and 0 otherwise.


In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset.


In some languages, morphological features separate verbs based on their transitivity, which suggests this is a salient linguistic feature. For example, in Japanese: However, the definition of transitive verbs as those with one object is not universal, and is not used in grammars of many languages.


Bot accounts on Twitter accelerate true and fake news at the same rate. Misinformation spread by bots has been difficult for social media platforms to address.


An implementation vulnerable to SEMA attacks will perform a different operation depending on whether the bit of the key is 0 or 1, which will use different amounts of power and/or different chip components. This method is prevalent in many different types of side-channel attacks, in particular, power analysis attacks. Thus, the attacker can observe the entire computation of encryption and can deduce the key.


In telecommunication, the term electromagnetic environment (EME) has the following meanings: For a telecommunications system, the spatial distribution of electromagnetic fields surrounding a given site. The electromagnetic environment may be expressed in terms of the spatial and temporal distribution of electric field strength (volts per metre), irradiance (watts per square metre), or energy density (joules per cubic metre). The resulting product of the power and time distribution, in various frequency ranges, of the radiated or conducted electromagnetic emission levels that may be encountered by a military force, system, or platform when performing its assigned mission in its intended operational environment. It is the sum of electromagnetic interference; electromagnetic pulse; hazards of electromagnetic radiation to personnel, ordnance, and volatile materials; and natural phenomena effects of lightning and p-static. All electromagnetic phenomena observable in a given location.


In the fields of chemistry and cheminformatics, the circuit rank of a molecular graph (the number of rings in the smallest set of smallest rings) is sometimes referred to as the Frèrejacque number.


Most mainstream statically-typed languages, such as C++, C#, and Java, are manifestly typed. Complete type inference has traditionally been associated with functional languages such as Haskell and ML. However, many manifestly-typed languages support partial type inference; for example, C++, Java, and C# all infer types in certain limited cases.


In monolithic kernels, a driver can write to any word of memory and thus accidentally corrupt user programs. In Minix 3, when a user expects data from, for example, the file system, it builds a descriptor telling who has access and at what addresses. It then passes an index to this descriptor to the file system, which may pass it to a driver. The file system or driver then asks the kernel to write via the descriptor, making it impossible for them to write to addresses outside the buffer.


In the IT Industry, deployment refers to post-sales process of guiding a client from purchase to use of the software or hardware that was purchased. This includes requirements analysis, scope analysis, customisations, systems integrations, user policies, user training and delivery. These steps are often overseen by a project manager using project management methodologies. Software Deployment involves several professionals that are relatively new to the knowledge based economy such as business analysts, software implementation specialists, solutions architects, and project managers.


In some applications, it is not sufficient to extract only one type of feature to obtain the relevant information from the image data. Instead two or more different features are extracted, resulting in two or more feature descriptors at each image point. A common practice is to organize the information provided by all these descriptors as the elements of one single vector, commonly referred to as a feature vector.


In mathematics, an ordered semigroup is a semigroup (S,•) together with a partial order ≤ that is compatible with the semigroup operation, meaning that x ≤ y implies z•x ≤ z•y and x•z ≤ y•z for all x, y, z in S. An ordered monoid and an ordered group are, respectively, a monoid or a group that are endowed with a partial order that makes them ordered semigroups. The terms posemigroup, pogroup and pomonoid are sometimes used, where "po" is an abbreviation for "partially ordered". The positive integers, the nonnegative integers and the integers form respectively a posemigroup, a pomonoid, and a pogroup under addition and the natural ordering. Every semigroup can be considered as a posemigroup endowed with the trivial (discrete) partial order "=". A morphism or homomorphism of posemigroups is a semigroup homomorphism that preserves the order (equivalently, that is monotonically increasing).


In mathematical optimization, a quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic functions. It has the form minimize 1 2 x T P 0 x + q 0 T x subject to 1 2 x T P i x + q i T x + r i ≤ 0 for i = 1 , … , m , A x = b , {\displaystyle {\begin{aligned}&{\text{minimize}}&&{\tfrac {1}{2}}x^{\mathrm {T} }P_{0}x+q_{0}^{\mathrm {T} }x\\&{\text{subject to}}&&{\tfrac {1}{2}}x^{\mathrm {T} }P_{i}x+q_{i}^{\mathrm {T} }x+r_{i}\leq 0\quad {\text{for }}i=1,\dots ,m,\\&&&Ax=b,\end{aligned}}} where P0, …, Pm are n-by-n matrices and x ∈ Rn is the optimization variable. If P0, …, Pm are all positive semidefinite, then the problem is convex. If these matrices are neither positive nor negative semidefinite, the problem is non-convex. If P1, … ,Pm are all zero, then the constraints are in fact linear and the problem is a quadratic program.


However, with introduction of font formats such as OpenType, those supplemental glyphs were merged into the main fonts, relying on specific software capabilities to access the alternate glyphs. Since Apple's and Microsoft's operating systems supported different character sets in the platform related fonts, some foundries used expert fonts in a different way. These fonts included the characters which were missing on either Macintosh or Windows computers, e.g. fractions, ligatures or some accented glyphs. The goal was to deliver the whole character set to the customer regardless of which operating system was used.


The grounds advanced for the 'hypothesis' are worthless. The authors proposing such opinions might be competent, decent, honest individuals, but the views they present are demonstrably wrong.


In mathematics, computational group theory is the study of groups by means of computers. It is concerned with designing and analysing algorithms and data structures to compute information about groups. The subject has attracted interest because for many interesting groups (including most of the sporadic groups) it is impractical to perform calculations by hand.


In the calculus of variations the Legendre–Clebsch condition is a second-order condition which a solution of the Euler–Lagrange equation must satisfy in order to be a minimum. For the problem of minimizing ∫ a b L ( t , x , x ′ ) d t . {\displaystyle \int _{a}^{b}L(t,x,x')\,dt.\,} the condition is L x ′ x ′ ( t , x ( t ) , x ′ ( t ) ) ≥ 0 , ∀ t ∈  {\displaystyle L_{x'x'}(t,x(t),x'(t))\geq 0,\,\forall t\in }


Performing this operation gives us 2 1 × 0.0001 2 {\displaystyle 2^{1}\times 0.0001_{2}} or 2 − 2 × 0.100 2 {\displaystyle 2^{-2}\times 0.100_{2}} . Without using a guard digit we have 2 1 × 0.100 2 − 2 1 × 0.011 2 {\displaystyle 2^{1}\times 0.100_{2}-2^{1}\times 0.011_{2}} , yielding 2 1 × 0.001 2 = {\displaystyle 2^{1}\times 0.001_{2}=} or 2 − 1 × 0.100 2 {\displaystyle 2^{-1}\times 0.100_{2}} . This gives us a relative error of 1.


In networked systems where competitive decision making takes place, game theory is often used to model system dynamics, and convergence towards equilibria can be considered as a driver of topological evolution. For example, Kasthurirathna and Piraveenan have shown that when individuals in a system display varying levels of rationality, improving the overall system rationality might be an evolutionary reason for the emergence of scale-free networks. They demonstrated this by applying evolutionary pressure on an initially random network which simulates a range of classic games, so that the network converges towards Nash equilibria while being allowed to re-wire. The networks become increasingly scale-free during this process.


In most cases, the annual maintenance costs dwarf the purchase price. For example, when policy servers are used (in both the plugin and proxy-based architectures), high-end hardware is needed in order to handle the workload required to run the web access management infrastructure. Centralized administration is an additional hidden cost, because customers will need to hire and train staff to exclusively manage policy entitlements for the underlying web applications. A final hidden cost relates to regulatory compliance. Since web access management is similar in concept to a firewall (more closely aligned to an application-layer firewall), it must be able to handle major audit requirements, especially for public companies subject to the Sarbanes-Oxley Act (not to mention those that are bound by the Health Insurance Portability and Accountability Act, PCI, or CPNI). Larger companies spend tremendous amounts of time and money auditing these web access management infrastructures since they are the enforcement points for many internal and external applications.


In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set; there are no unpaired elements between the two sets. In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y. The term one-to-one correspondence must not be confused with one-to-one function (an injective function; see figures). A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements.


In statistics and Markov modeling, an ancestral graph is a type of mixed graph to provide a graphical representation for the result of marginalizing one or more vertices in a graphical model that takes the form of a directed acyclic graph.


In programming languages, a delimited continuation, composable continuation or partial continuation, is a "slice" of a continuation frame that has been reified into a function. Unlike regular continuations, delimited continuations return a value, and thus may be reused and composed. Control delimiters, the basis of delimited continuations, were introduced by Matthias Felleisen in 1988 though early allusions to composable and delimited continuations can be found in Carolyn Talcott's Stanford 1984 dissertation, Felleisen et al., Felleisen's 1987 dissertation, and algorithms for functional backtracking, e.g., for pattern matching, for parsing, in the Algebraic Logic Functional programming language, and in the functional implementations of Prolog where the failure continuation is often kept implicit and the reason of being for the success continuation is that it is composable.


Due to the subtyping relation, a term may belong to more than one type. Subtyping is therefore a form of type polymorphism. In object-oriented programming the term 'polymorphism' is commonly used to refer solely to this subtype polymorphism, while the techniques of parametric polymorphism would be considered generic programming.


In probability theory and statistics, a mixture is a probabilistic combination of two or more probability distributions. The concept arises mostly in two contexts: A mixture defining a new probability distribution from some existing ones, as in a mixture distribution or a compound distribution. Here a major problem often is to derive the properties of the resulting distribution. A mixture used as a statistical model such as is often used for statistical classification. The model may represent the population from which observations arise as a mixture of several components, and the problem is that of a mixture model, in which the task is to infer from which of a discrete set of sub-populations each observation originated.


In number theory, Mills' constant is defined as the smallest positive real number A such that the floor function of the double exponential function ⌊ A 3 n ⌋ {\displaystyle \lfloor A^{3^{n}}\rfloor } is a prime number for all positive natural numbers n. This constant is named after William Harold Mills who proved in 1947 the existence of A based on results of Guido Hoheisel and Albert Ingham on the prime gaps. Its value is unproven, but if the Riemann hypothesis is true, it is approximately 1.3063778838630806904686144926... (sequence A051021 in the OEIS).


In mathematics, an evasive Boolean function ƒ (of n variables) is a Boolean function for which every decision tree algorithm has running time of exactly n. Consequently, every decision tree algorithm that represents the function has, at worst case, a running time of n.


In military cryptography, a codress message is an encrypted message whose address is also encrypted. This is usually done to prevent traffic analysis. == References ==


Forward chaining starts with the known facts and asserts new facts. Backward chaining starts with goals, and works backward to determine what facts must be asserted so that the goals can be achieved.Additionally, the concept of 'inference' has expanded to include the process through which trained neural networks generate predictions or decisions.


With the development of formal logic, Hilbert asked whether it would be possible to prove that an axiom system is consistent by analyzing the structure of possible proofs in the system, and showing through this analysis that it is impossible to prove a contradiction. This idea led to the study of proof theory. Moreover, Hilbert proposed that the analysis should be entirely concrete, using the term finitary to refer to the methods he would allow but not precisely defining them.


Engaging in a structured dialogue or repeated discussion, to exchange ideas about how to get specific about what it means and how to clear it up (scrum method). 13. Allocating different applications of the concept to different but related sets (Boolean logic).


In the data warehousing strategy, the data from different sources are extracted and integrated in a single database. For example, various 'omics' datasets may be integrated to provide biological insights into biological systems. Examples include data from genomics, transcriptomics, proteomics, interactomics, metabolomics. Ideally, changes in these sources are regularly synchronized to the integrated database.


In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property (see definition below). This guarantees a low number of collisions in expectation, even if the data is chosen by an adversary. Many universal families are known (for hashing integers, vectors, strings), and their evaluation is often very efficient. Universal hashing has numerous uses in computer science, for example in implementations of hash tables, randomized algorithms, and cryptography.


In mathematics, a random minimum spanning tree may be formed by assigning random weights from some distribution to the edges of an undirected graph, and then constructing the minimum spanning tree of the graph. When the given graph is a complete graph on n vertices, and the edge weights have a continuous distribution function whose derivative at zero is D > 0, then the expected weight of its random minimum spanning trees is bounded by a constant, rather than growing as a function of n. More precisely, this constant tends in the limit (as n goes to infinity) to ζ(3)/D, where ζ is the Riemann zeta function and ζ(3) is Apéry's constant. For instance, for edge weights that are uniformly distributed on the unit interval, the derivative is D = 1, and the limit is just ζ(3).In contrast to uniformly random spanning trees of complete graphs, for which the typical diameter is proportional to the square root of the number of vertices, random minimum spanning trees of complete graphs have typical diameter proportional to the cube root.Random minimum spanning trees of grid graphs may be used for invasion percolation models of liquid flow through a porous medium, and for maze generation. == References ==


While avoiding the problems of depending on delayed recordings, this method was not without its own inherent pitfalls. As the originating station was usually somewhat—as far as 50–100 miles (80–160 km) or more—the signal could frequently be degraded or interfered with by other stations on the same channel during periods of ionospheric or tropospheric disturbance. For that matter, if the originating station experienced technical difficulties and had to leave the air, the receiving station would be left without network programming during the outage as well.


The statement, 'If X exists, then X has most of the φ's' expresses a necessary truth (in the idiolect of the speaker). (C) For any successful theory, the account must not be circular. The properties which are used in the vote must not themselves involve the notion of reference in such a way that it is ultimately impossible to eliminate.


When the active array contains no more processes, the scheduler swaps the active and expired arrays, hence the name O(1) scheduler. In UNIX or Linux, the sar command is used to check the run queue. The vmstat UNIX or Linux command can also be used to determine the number of processes that are queued to run or waiting to run. These appear in the 'r' column. Example: $ vmstat procs -----------memory---------- ---swap-- -----io---- -system-- ------cpu----- r b swpd free buff cache si so bi bo in cs us sy id wa st 2 0 0 4579152 324416 4619528 0 0 402 236 3357 15 20 2 78 0 0 There are two models for Run queues: one that assigns a Run Queue to each physical processor, and the other has only one Run Queue in the system


By analysing the retained data, governments can identify the locations of individuals, an individual's associates and the members of a group such as political opponents. These activities may or may not be lawful, depending on the constitutions and laws of each country. In many jurisdictions, access to these databases may be made by a government with little or no judicial oversight.In the case of commercial data retention, the data retained will usually be on transactions and web sites visited. Data retention also covers data collected by other means (e.g., by Automatic number-plate recognition systems) and held by government and commercial organisations.


In number theory, a balanced prime is a prime number with equal-sized prime gaps above and below it, so that it is equal to the arithmetic mean of the nearest primes above and below. Or to put it algebraically, given a prime number p n {\displaystyle p_{n}} , where n is its index in the ordered set of prime numbers, p n = p n − 1 + p n + 1 2 . {\displaystyle p_{n}={{p_{n-1}+p_{n+1}} \over 2}.} For example, 53 is the sixteenth prime; the fifteenth and seventeenth primes, 47 and 59, add up to 106, and half of that is 53; thus 53 is a balanced prime.


The substitutions may be applied in any order we like, as the result will be the same. Below, the substitutions applied to the number on the previous line are on the right, the resulting number on the left. 211.0 1 _ 0 ϕ = 211 .


In one instance, Trojan horses were used as a targeted threat so that Israeli companies could conduct corporate espionage on each other. The Hotword Trojan, the Ginwui and the PPDropper Trojans are additional examples of Trojans used for corporate espionage. Targeted destination attacks use harvested IP addresses to send messages directly to recipients without an MX record lookup. It aims for specific sites and users by defeating hosted protection services and internal gateways to deliver e-mail with malicious payloads.


In multilevel security mode of operation (also called Controlled Security Mode), all users must have: Signed NDA for ALL information on the system. Proper clearance for SOME information on the system. Formal access approval for SOME information on the system. A valid need to know for SOME information on the system.All users can access SOME data, based on their need to know, clearance and formal access approval


At injection, the compressed air would then press the fuel through the disc-type atomisers into the combustion chamber. Manufacturing engines featuring the open nozzle design was considerably cheaper and easier than making them with a closed nozzle design. It also allows for using tar as fuel.


In social network analysis, betweenness centrality can have different implications. From a macroscopic perspective, bridging positions or "structural holes" (indicated by high betweenness centrality) reflect power, because they allow the person on the bridging position to exercise control (e.g., decide whether to share information or not) over the persons it connects between. From the microscopic perspective of ego networks (i.e., only considering first-degree connections), in online social networks a high betweenness centrality coincides with nominations of closest friends (i.e., strong interpersonal ties), because it reflects social capital investments into the relationship when distant social circles (e.g., family and university) are bridged (often resulting from an introduction by ego).


A proper treatment of this complication calls for the conception of something slightly more general than a sign relation proper, namely, a sign relational complex. In effect, expressed in the roughest practical terms, this allows for missing data in the columns of the relational database table for the sign relation in question. Typically one operates on the default assumption that all of the roles of elementary sign relations are filled, but remains wary enough of the possible exceptions to deal with them on an ad hoc basis.


Analyses differ in how much they rely on morphology to explain them. Some have questioned their linguistic status, as well as the very use of the term "classifier". Not much is known yet about their syntax or phonology.


In the construction of database applications, it can be useful to introduce an additional layer of data dictionary software, i.e. middleware, which communicates with the underlying DBMS data dictionary. Such a "high-level" data dictionary may offer additional features and a degree of flexibility that goes beyond the limitations of the native "low-level" data dictionary, whose primary purpose is to support the basic functions of the DBMS, not the requirements of a typical application. For example, a high-level data dictionary can provide alternative entity-relationship models tailored to suit different applications that share a common database. Extensions to the data dictionary also can assist in query optimization against distributed databases.


One exception to the single-entry-point paradigm is Android. Android applications do not have a single entry point – there is no special main function. Instead, they have essential components (activities and services) which the system can load and run as needed.An occasionally used technique is the fat binary, which consists of several executables for different targets packaged in a single file. Most commonly, this is implemented by a single overall entry point, which is compatible with all targets and branches to the target-specific entry point. Alternative techniques include storing separate executables in separate forks, each with its own entry point, which is then selected by the operating system.


The nine lemma can be proved by direct diagram chasing, or by applying the snake lemma (to the two bottom rows in the first case, and to the two top rows in the second case). Linderholm (p.


In the second sentence, "is" can however be interpreted as an ordinary copula and the past participle as an adjective. Sentences of the second type are called false passives by some linguists, who feel that such sentences are simply confused with the passive voice due to their outward similarity. Other linguists consider the second type to be a different kind of passive – a stative passive (rarely called statal, static, or resultative passive), in contrast to the dynamic or eventive passive illustrated by the first sentence.


In terms of the quartic residue symbol, the law of quartic reciprocity for Gaussian integers states that if π and θ are primary (congruent to 1 mod (1+i)3) Gaussian primes then   − 1 = ( − 1 ) N π − 1 4 N θ − 1 4 . {\displaystyle {\Bigg }\left^{-1}=(-1)^{{\frac {N\pi -1}{4}}{\frac {N\theta -1}{4}}}.}


Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer. For a comprehensible introduction to the topic see.Formally, cluster states | ϕ { κ } ⟩ C {\displaystyle |\phi _{\{\kappa \}}\rangle _{C}} are states which obey the set eigenvalue equations: K ( a ) | ϕ { κ } ⟩ C = ( − 1 ) κ a | ϕ { κ } ⟩ C {\displaystyle K^{(a)}{\left|\phi _{\{\kappa \}}\right\rangle _{C}}=(-1)^{\kappa _{a}}{\left|\phi _{\{\kappa \}}\right\rangle _{C}}} where K ( a ) {\displaystyle K^{(a)}} are the correlation operators K ( a ) = σ x ( a ) ⨂ b ∈ N ( a ) σ z ( b ) {\displaystyle K^{(a)}=\sigma _{x}^{(a)}\bigotimes _{b\in \mathrm {N} (a)}\sigma _{z}^{(b)}} with σ x {\displaystyle \sigma _{x}} and σ z {\displaystyle \sigma _{z}} being Pauli matrices, N ( a ) {\displaystyle N(a)} denoting the neighbourhood of a {\displaystyle a} and { κ a ∈ { 0 , 1 } | a ∈ C } {\displaystyle \{\kappa _{a}\in \{0,1\}|a\in C\}} being a set of binary parameters specifying the particular instance of a cluster state.


In the context of searching for information, researchers have identified two forms of information overload: outcome overload where there are too many sources of information and textual overload where the individual sources are too long. This form of information overload may cause searchers to be less systematic. Disillusionment when a search is more challenging than expected may result in an individual being less able to search effectively. Information overload when searching can result in a satisficing strategy. : 7


In the Russian peasant method, the powers of two in the decomposition of the multiplicand are found by writing it on the left and progressively halving the left column, discarding any remainder, until the value is 1 (or −1, in which case the eventual sum is negated), while doubling the right column as before. Lines with even numbers on the left column are struck out, and the remaining numbers on the right are added together.


Suppose we have a preparation procedure for a system in a physics lab: For example, the procedure might involve a physical apparatus and some protocols for manipulating the apparatus. As a result of this preparation procedure, some system is produced and maintained in isolation for some small period of time. By repeating this laboratory preparation procedure we obtain a sequence of systems X1, X2, ....,Xk, which in our mathematical idealization, we assume is an infinite sequence of systems.


In mathematical physics, especially quantum mechanics, it is common to write the inner product between elements as ⟨a|b⟩, as a short version of ⟨a|·|b⟩, or ⟨a|Ô|b⟩, where Ô is an operator. This is known as Dirac notation or bra–ket notation, to note vectors from the dual spaces of the Bra ⟨A| and the Ket |B⟩. But there are other notations used. In continuum mechanics, chevrons may be used as Macaulay brackets.


The process of search can be divided in three parts: Generate descriptors for the media which we are going to use as query and the descriptors for the media in our database. Compare descriptors of the query and our database’s media. List the media sorted by maximum coincidence.


In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behavior can be characterized: two readily understood behaviors are that the sequence eventually takes a constant value, and that values in the sequence continue to change but can be described by an unchanging probability distribution.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 38, 138, 348, and 1348 are the patterns related to Braille pattern dots-26, since the two additional dots of kantenji patterns 026, 267, and 0267 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 23, 123, 234, and 1234 are the 8-dot braille patterns related to Braille pattern dots-12, since the two additional dots of kantenji patterns 012, 127, and 0127 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Further, Giles and Pulleyblank showed that if P {\displaystyle P} is a polytope whose vertices are all integer valued, then P {\displaystyle P} is the solution set of some TDI system A x ≤ b {\displaystyle Ax\leq b} , where b {\displaystyle b} is integer valued. Note that TDI is a weaker sufficient condition for integrality than total unimodularity. == References ==


In philosophy of science, confirmation holism, also called epistemological holism, is the view that no individual statement can be confirmed or disconfirmed by an empirical test, but rather that only a set of statements (a whole theory) can be so. It is attributed to Willard Van Orman Quine who motivated his holism through extending Pierre Duhem's problem of underdetermination in physical theory to all knowledge claims.Duhem's idea was, roughly, that no theory of any type can be tested in isolation but only when embedded in a background of other hypotheses, e.g. hypotheses about initial conditions. Quine thought that this background involved not only such hypotheses but also our whole web of belief, which, among other things, includes our mathematical and logical theories and our scientific theories. This last claim is sometimes known as the Duhem–Quine thesis.A related claim made by Quine, though contested by some (see Adolf Grünbaum 1962), is that one can always protect one's theory against refutation by attributing failure to some other part of our web of belief. In his own words, "Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system."


In natural language processing, multinomial LR classifiers are commonly used as an alternative to naive Bayes classifiers because they do not assume statistical independence of the random variables (commonly known as features) that serve as predictors. However, learning in such a model is slower than for a naive Bayes classifier, and thus may not be appropriate given a very large number of classes to learn. In particular, learning in a Naive Bayes classifier is a simple matter of counting up the number of co-occurrences of features and classes, while in a maximum entropy classifier the weights, which are typically maximized using maximum a posteriori (MAP) estimation, must be learned using an iterative procedure; see #Estimating the coefficients.


In natural language processing, dependency-based parsing can be formulated as an ASP problem. The following code parses the Latin sentence "Puella pulchra in villa linguam latinam discit", "the pretty girl is learning Latin in the villa". The syntax tree is expressed by the arc predicates which represent the dependencies between the words of the sentence. The computed structure is a linearly ordered rooted tree.


One of the motivations of establishing a distinct, higher level of linguistic analysis is, then, to explain the structural ambiguity due to the constructional homonymities at a lower level. On the other hand, each linguistic level also captures some structural similarities within the level that are not explained in lower levels. Chomsky uses this argument as well to motivate the establishment of distinct levels of linguistic analysis.Chomsky then shows that a grammar which analyzes sentences up to the phrase structure level contains many constructional homonymities at the phrase structure level where the resulting ambiguities need to be explained at a higher level. Then he shows how his newly invented “transformational level” can naturally and successfully function as that higher level. He further claims that any phrase structure grammar which cannot explain these ambiguities as successfully as transformational grammar does must be considered "inadequate".


In mathematics, given a non-empty set of objects of finite extension in d {\displaystyle d} -dimensional space, for example a set of points, a bounding sphere, enclosing sphere or enclosing ball for that set is an d {\displaystyle d} -dimensional solid sphere containing all of these objects. Used in computer graphics and computational geometry, a bounding sphere is a special type of bounding volume. There are several fast and simple bounding sphere construction algorithms with a high practical value in real-time computer graphics applications.In statistics and operations research, the objects are typically points, and generally the sphere of interest is the minimal bounding sphere, that is, the sphere with minimal radius among all bounding spheres.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 368, 1368, 3468, and 13468 are the patterns related to Braille pattern dots-256, since the two additional dots of kantenji patterns 0256, 2567, and 02567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In early versions of the problem, the gambler begins with no initial knowledge about the machines. Herbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward.


It arose in connection with James Watt's pioneering work on the steam engine. The equation of the curve can be given in polar coordinates as r 2 = b 2 −  2 . {\displaystyle r^{2}=b^{2}-\left^{2}.}


Which is why it is important to consider encryption, hashing, and other security mechanisms in your design to ensure that information collected from a potential attacker won't allow access. Another key feature to client-server security design is good coding practices.


In the Shrikhande graph, any two vertices I and J have two distinct neighbors in common (excluding the two vertices I and J themselves), which holds true whether or not I is adjacent to J. In other words, it is strongly regular and its parameters are: {16,6,2,2}, i.e., λ = μ = 2 {\displaystyle \lambda =\mu =2} . This equality implies that the graph is associated with a symmetric BIBD. The Shrikhande graph shares these parameters with exactly one other graph, the 4×4 rook's graph, i.e., the line graph L(K4,4) of the complete bipartite graph K4,4. The latter graph is the only line graph L(Kn,n) for which the strong regularity parameters do not determine that graph uniquely but are shared with a different graph, namely the Shrikhande graph (which is not a rook's graph).The Shrikhande graph is locally hexagonal; that is, the neighbors of each vertex form a cycle of six vertices.


In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.


This was partly because differences in their architectures required these changes to optimize Unix to each architecture.Thus as general purpose operating systems became stable, supercomputers began to borrow and adapt the critical system code from them and relied on the rich set of secondary functions that came with them, not having to reinvent the wheel. However, at the same time the size of the code for general purpose operating systems was growing rapidly. By the time Unix-based code had reached 500,000 lines long, its maintenance and use was a challenge.


In practice, the functions f {\displaystyle f} and F {\displaystyle F} are often not known or assumed. However, they can be estimated from an observed frequency distribution. In this section, we give an example. Consider the following table, representing a sample of 3,800 (discrete-valued) observations: Because the observations are discrete-valued, constructing the exact distribution of the median is not an immediate translation of the above expression for Pr ( Median = v ) {\displaystyle \Pr(\operatorname {Median} =v)} ; one may (and typically does) have multiple instances of the median in one's sample.


Between the two extremes the realizations are discrete distributions with less and less concentration as α {\displaystyle \alpha } increases. The Dirichlet process can also be seen as the infinite-dimensional generalization of the Dirichlet distribution. In the same way as the Dirichlet distribution is the conjugate prior for the categorical distribution, the Dirichlet process is the conjugate prior for infinite, nonparametric discrete distributions.


They are distinct because they possess a variety of desirable properties, most importantly the existence of a sufficient statistic. The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935–1936. Exponential families of distributions provides a general framework for selecting a possible alternative parameterisation of a parametric family of distributions, in terms of natural parameters, and for defining useful sample statistics, called the natural sufficient statistics of the family.


However, only the receiving party has access to the decryption key that enables messages to be read. Public-key encryption was first described in a secret document in 1973; beforehand, all encryption schemes were symmetric-key (also called private-key). : 478 Although published subsequently, the work of Diffie and Hellman was published in a journal with a large readership, and the value of the methodology was explicitly described.


"Depending upon how appropriate the upgrades are considered by other owners of the same model, this may reduce or enhance the value of the car. If the car is in regular use, non-original upgrades are likely to be more acceptable; if the car is a stored collector's piece, originality would be more important. It is important as a restorer or owner to know what is acceptable to the potential market for the finished car, in order not to de-value it.


In mathematics, Veblen's theorem, introduced by Oswald Veblen (1912), states that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree. Thus, it is closely related to the theorem of Euler (1736) that a finite graph has an Euler tour (a single non-simple cycle that covers the edges of the graph) if and only if it is connected and every vertex has even degree. Indeed, a representation of a graph as a union of simple cycles may be obtained from an Euler tour by repeatedly splitting the tour into smaller cycles whenever there is a repeated vertex.


Therefore, φ(9) = 6. As another example, φ(1) = 1 since for n = 1 the only integer in the range from 1 to n is 1 itself, and gcd(1, 1) = 1.


The list of revisions from the start to HEAD (in graph theory terms, the unique path in the tree, which forms a linear graph as before) is the trunk or mainline. Conversely, when a revision can be based on more than one previous revision (when a node can have more than one parent), the resulting process is called a merge, and is one of the most complex aspects of revision control. This most often occurs when changes occur in multiple branches (most often two, but more are possible), which are then merged into a single branch incorporating both changes.


( z ∈ w ↔ ( z ∈ x ∨ z = y ) ) . {\displaystyle \forall x.\forall y.\exists w.\forall z. {\big (}z\in w\leftrightarrow (z\in x\lor z=y){\big )}.}


In statistics, some Monte Carlo methods require independent observations in a sample to be drawn from a one-dimensional distribution in sorted order. In other words, all n order statistics are needed from the n observations in a sample. The naive method performs a sort and takes O(n log n) time. There are also O(n) algorithms which are better suited for large n. The special case of drawing n sorted observations from the uniform distribution on  is equivalent to drawing from the uniform distribution on an n-dimensional simplex; this task is a part of sequential importance resampling.


In order to represent any network, it is necessary to characterize the properties of the corresponding graph of nodes and links. Studies on the collaboration network of movie actors have been described in literature such as the work done by (Watts and Strogatz, 1998), and Barabási and Albert in (1999) and (2000). The general characteristics are described below. According to Watts and Strogatz (1998), the movie/actor network indicated the following characteristics showing a small-world property of the underlying network:Size: 225 226 Average degree: 61 Average path length: 3.65 Clustering coefficient: 0.79Compared to a random graph of the same size and average degree, the average path length is close in value.


In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default. The motivation is twofold: first, maximizing entropy minimizes the amount of prior information built into the distribution; second, many physical systems tend to move towards maximal entropy configurations over time.


In program analysis, shape analysis is a static code analysis technique that discovers and verifies properties of linked, dynamically allocated data structures in (usually imperative) computer programs. It is typically used at compile time to find software bugs or to verify high-level correctness properties of programs. In Java programs, it can be used to ensure that a sort method correctly sorts a list. For C programs, it might look for places where a block of memory is not properly freed.


From an a-priori point of view, the main criticism is that taking s → 0 {\displaystyle s\rightarrow 0} is far from leading to a noninformative prior. Moreover, a-posteriori, it assigns zero probability to any set that does not include the observations.The imprecise Dirichlet process has been proposed to overcome these issues. The basic idea is to fix s > 0 {\displaystyle s>0} but do not choose any precise base measure G 0 {\displaystyle G_{0}} . More precisely, the imprecise Dirichlet process (IDP) is defined as follows: I D P: { D P ( s , G 0 ): G 0 ∈ P } {\displaystyle ~~\mathrm {IDP} :~\left\{\mathrm {DP} \left(s,G_{0}\right):~~G_{0}\in \mathbb {P} \right\}} where P {\displaystyle \mathbb {P} } is the set of all probability measures. In other words, the IDP is the set of all Dirichlet processes (with a fixed s > 0 {\displaystyle s>0} ) obtained by letting the base measure G 0 {\displaystyle G_{0}} to span the set of all probability measures.


Consider a computer program for recognizing dogs (the relevant element) in a digital photograph. Upon processing a picture which contains ten cats and twelve dogs, the program identifies eight dogs. Of the eight elements identified as dogs, only five actually are dogs (true positives), while the other three are cats (false positives).


Each bit completes a small task, which then builds up to the final bigger task. Like writing code on a computer, it is easier to write the basic smaller parts and make them work first, and then put them together to finish the larger more complicated code, instead of tackling the entire code from the very beginning. The first solution is less risky because if something goes wrong with the code, it is easier to look for the problem in the smaller bits, since the segment with the problem will be the one that does not work, while in the latter solution, the programmer may have to look through the entire code to search for a single error, which proves time-consuming.


In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number n such that the sum of all divisors of n (the sum-of-divisors function σ(n)) is equal to 2n − 1, the sum of all proper divisors of n, s(n) = σ(n) − n, then being equal to n − 1. The only known almost perfect numbers are powers of 2 with non-negative exponents (sequence A000079 in the OEIS). Therefore the only known odd almost perfect number is 20 = 1, and the only known even almost perfect numbers are those of the form 2k for some positive integer k; however, it has not been shown that all almost perfect numbers are of this form. It is known that an odd almost perfect number greater than 1 would have at least six prime factors.If m is an odd almost perfect number then m(2m − 1) is a Descartes number. Moreover if a and b are positive odd integers such that b + 3 < a < m / 2 {\displaystyle b+3


In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic, stating that if a univariate polynomial has a simple root modulo a prime number p, then this root can be lifted to a unique root modulo any higher power of p. More generally, if a polynomial factors modulo p into two coprime polynomials, this factorization can be lifted to a factorization modulo any higher power of p (the case of roots corresponds to the case of degree 1 for one of the factors). By passing to the "limit" (in fact this is an inverse limit) when the power of p tends to infinity, it follows that a root or a factorization modulo p can be lifted to a root or a factorization over the p-adic integers. These results have been widely generalized, under the same name, to the case of polynomials over an arbitrary commutative ring, where p is replaced by an ideal, and "coprime polynomials" means "polynomials that generate an ideal containing 1". Hensel's lemma is fundamental in p-adic analysis, a branch of analytic number theory. The proof of Hensel's lemma is constructive, and leads to an efficient algorithm for Hensel lifting, which is fundamental for factoring polynomials, and gives the most efficient known algorithm for exact linear algebra over the rational numbers.


In statistics, the bootstrap is a method for inferring the variability of data that has an unknown distribution using pseudoreplications of the original data. For example, given a set of 100 data points, a pseudoreplicate is a data set of the same size (100 points) randomly sampled from the original data, with replacement. That is, each original data point may be represented more than once in the pseudoreplicate, or not at all. Statistical support involves evaluation of whether the original data has similar properties to a large set of pseudoreplicates.


Participants were asked to watch a 20-minute news video (half of the participants saw the negative images and the other half did not) and an additional ten-minute video. They were instructed to pay attention because they would be tested afterwards. A follow up survey was sent 6 to 7 weeks later to measure memory and recall from the news video.


In queueing theory, a discipline within the mathematical theory of probability, the decomposition method is an approximate method for the analysis of queueing networks where the network is broken into subsystems which are independently analyzed.The individual queueing nodes are considered to be independent G/G/1 queues where arrivals are governed by a renewal process and both service time and arrival distributions are parametrised to match the first two moments of data. == References ==


The sample code for the Banked XIOS implementation published in the MP/M II System Implementors Guide was written by Altos (and carries a disclaimer that it only works as-is with their Sun Series 8000).The "8000" contained in the name of Altos' first series of computer did cause some confusion in the marketplace because its name may have suggested the inclusion of the 16-bit Zilog Z8000 processor, which had just been released in 1979, although Altos' ACS-8000 did not use this processor, but the older 8-bit Z80. A 1981 review in Computerworld, comparing the ACS 8000 with other multi-user systems, found that Altos' Z80 processor was underpowered, especially for CPU-intensive tasks (most other multi-user systems used 16-bit processors by then), but the ACS-8000 was found adequate for multi-user order entry systems. A configuration with a 10-MB hard-drive plus a 1-MB 8" floppy drive, bundled with a printer and one terminal was priced at $12,340 (the same machine but with four terminals was $15,625), which was considerably less than most other multi-user systems, which were typically priced in the $25,000–$50,000 range.


. . , N } {\displaystyle q_{i}\in \{0,1,...,k\},\forall i\in \{1,2,...,N\}} and that at least one component q i = k {\displaystyle q_{i}=k} Let S N d {\displaystyle S_{N}^{d}} represent a N-dimensional hypersphere with radius of d = ‖ q → ‖ {\displaystyle d=\left\Vert {\vec {q}}\right\Vert } .


In some cases a KBS could not be built because the organization did not have all the knowledge needed to support all their activities. In these cases logico-linguistic modeling showed shortcomings in the supply of information and where more was needed. For example, a planning department in a telecoms company


In mathematics, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it's defined by a ratio between the number of divisors an integer has and that integer raised to some positive power. For any possible exponent, whichever integer has the highest ratio is a superior highly composite number. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer.


In telecommunication, a tactical communications system is a communications system that (a) is used within, or in direct support of, tactical forces, (b) is designed to meet the requirements of changing tactical situations and varying environmental conditions, (c) provides securable communications, such as voice, data, and video, among mobile users to facilitate command and control within, and in support of, tactical forces, and (d) usually requires extremely short installation times, usually on the order of hours, in order to meet the requirements of frequent relocation.


In portfolio theory in finance, an objective often is to choose a portfolio of risky assets such that the distribution of the random portfolio return has desirable properties. For example, one might want to choose the portfolio return having the lowest variance for a given expected value. Here the random vector is the vector r {\displaystyle \mathbf {r} } of random returns on the individual assets, and the portfolio return p (a random scalar) is the inner product of the vector of random returns with a vector w of portfolio weights — the fractions of the portfolio placed in the respective assets. Since p = wT r {\displaystyle \mathbf {r} } , the expected value of the portfolio return is wTE( r {\displaystyle \mathbf {r} } ) and the variance of the portfolio return can be shown to be wTCw, where C is the covariance matrix of r {\displaystyle \mathbf {r} } .


Loosely speaking, rejection of the null hypothesis implies that there is sufficient evidence against it. As a particular example, if a null hypothesis states that a certain summary statistic T {\displaystyle T} follows the standard normal distribution N(0,1), then the rejection of this null hypothesis could mean that (i) the mean of T {\displaystyle T} is not 0, or (ii) the variance of T {\displaystyle T} is not 1, or (iii) T {\displaystyle T} is not normally distributed. Different tests of the same null hypothesis would be more or less sensitive to different alternatives. However, even if we do manage to reject the null hypothesis for all 3 alternatives, and even if we know the distribution is normal and variance is 1, the null hypothesis test does not tell us which non-zero values of the mean are now most plausible. The more independent observations from the same probability distribution one has, the more accurate the test will be, and the higher the precision with which one will be able to determine the mean value and show that it is not equal to zero; but this will also increase the importance of evaluating the real-world or scientific relevance of this deviation.


+ t 2 ∑ ⟨ ⟨ i , j ⟩ ⟩ ( c i σ † c j σ + h . c . ) + J ∑ ⟨ i , j ⟩ ( S i ⋅ S j − n i n j 4 ) − μ ∑ i n i , {\displaystyle {\mathcal {\hat {H}}}=t_{1}\sum \limits _{\langle i,j\rangle }\left(c_{i\sigma }^{\dagger }c_{j\sigma }+\mathrm {h.c.} \right)\ +\ t_{2}\sum \limits _{\langle \langle i,j\rangle \rangle }\left(c_{i\sigma }^{\dagger }c_{j\sigma }+\mathrm {h.c.} \right)\ +\ J\sum \limits _{\langle i,j\rangle }\left(\mathbf {S} _{i}\cdot \mathbf {S} _{j}-{\frac {n_{i}n_{j}}{4}}\right)-\ \mu \sum \limits _{i}n_{i},} where ⟨...⟩ and ⟨⟨...⟩⟩ denote the nearest and next-nearest neighbors, respectively, with two different values for the hopping integral (t1 and t2) and μ is the chemical potential.


Ground truth also helps with atmospheric correction. Since images from satellites have to pass through the atmosphere, they can get distorted because of absorption in the atmosphere. So ground truth can help fully identify objects in satellite photos.


Permissible station content is defined by the FCC as: "...only noncommercial voice information pertaining to traffic and road conditions, traffic hazard and travel advisories, directions, availability of lodging, rest stops and service stations, and descriptions of local points of interest. It is not permissible to identify the commercial name of any business whose service may be available within or outside the coverage area of a Travelers' Information Station. However, to facilitate announcements concerning departures/arrivals and parking areas at air, train, and bus terminals, the trade name identification of carriers is permitted.


In the fields of predictive modelling and probabilistic forecasting, the Markov property is considered desirable since it may enable the reasoning and resolution of the problem that otherwise would not be possible to be resolved because of its intractability. Such a model is known as a Markov model.


In polyhedral combinatorics, the hypersimplex Δ d , k {\displaystyle \Delta _{d,k}} is a convex polytope that generalizes the simplex. It is determined by two integers d {\displaystyle d} and k {\displaystyle k} , and is defined as the convex hull of the d {\displaystyle d} -dimensional vectors whose coefficients consist of k {\displaystyle k} ones and d − k {\displaystyle d-k} zeros. Equivalently, Δ d , k {\displaystyle \Delta _{d,k}} can be obtained by slicing the d {\displaystyle d} -dimensional unit hypercube  d {\displaystyle ^{d}} with the hyperplane of equation x 1 + ⋯ + x d = k {\displaystyle x_{1}+\cdots +x_{d}=k} and, for this reason, it is a ( d − 1 ) {\displaystyle (d-1)} -dimensional polytope when 0 < k < d {\displaystyle 0


must be nowhere near as talented as the devoted and serious method actors that aren't so popular like . "In general, the reversal usually goes: Most people believe A and B are both true. B is false.


Evaluating the loop condition can have side effects, so an additional evaluation by the if construct should be compensated by replacing the while loop with a do {} while. If the code used do {} while in the first place, the whole guarding process is not needed, as the loop body is guaranteed to execute at least once. This code can be optimized further. For example, strength reduction could remove the two multiplications inside the loop (6*i and a), and induction variable elimination could then elide i completely. Since 6 * i must be in lock step with i itself, there is no need to have both.


For example, the cake may be the 1-dimensional interval  and each piece is an interval; or, the cake may be a rectangle cut along its longer side so that each piece is a rectangle. Every cut-set can be represented by n numbers xi, i = 1, ..., n, where xi is the length of the ith piece. We assume that the total length of the cake is 1, so x1 + ... + xn = 1.


Exact tests that are based on discrete test statistics may be conservative, indicating that the actual rejection rate lies below the nominal significance level α {\displaystyle \alpha } . As an example, this is the case for Fisher's exact test and its more powerful alternative, Boschloo's test. If the test statistic is continuous, it will reach the significance level exactly.Parametric tests, such as those used in exact statistics, are exact tests when the parametric assumptions are fully met, but in practice, the use of the term exact (significance) test is reserved for non-parametric tests, i.e., tests that do not rest on parametric assumptions.


In number theory, an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied to the product ab is the sum of the values of the function applied to a and b:


In the Sprague–Grundy theory the minimum excluded ordinal is used to determine the nimber of a normal-play impartial game. In such a game, either player has the same moves in each position and the last player to move wins. The nimber is equal to 0 for a game that is lost immediately by the first player, and is equal to the mex of the nimbers of all possible next positions for any other game. For example, in a one-pile version of Nim, the game starts with a pile of n stones, and the player to move may take any positive number of stones.


Memory controllers such as the Intel 945 Chipset list the configurations they support: "256-Mib, 512-Mib, and 1-Gib DDR2 technologies for ×8 and ×16 devices", "four ranks for all DDR2 devices up to 512-Mibit density", "eight ranks for 1-Gibit DDR2 devices". As an example, take an i945 memory controller with four Kingston KHX6400D2/1G memory modules, where each module has a capacity of 1 GiB. Kingston describes each module as composed of 16 "64M×8-bit" chips with each chip having an 8-bit-wide data bus.


Equivalent to bitwise addition without use of a carry bit. ||: Concatenation operator. Combine the strings on either side of the operator. 0a: a string of a 0 bits.


From the 1920s through the 1970s, typing speed (along with shorthand speed) was an important secretarial qualification and typing contests were popular and often publicized by typewriter companies as promotional tools. A less common measure of the speed of a typist, CPM is used to identify the number of characters typed per minute. This is a common measurement for typing programs, or typing tutors, as it can give a more accurate measure of a person's typing speed without having to type for a prolonged period of time.


The numbers less than ( n k ) {\displaystyle {\tbinom {n}{k}}} correspond to all k-combinations of {0, 1, ..., n − 1}. The correspondence does not depend on the size n of the set that the k-combinations are taken from, so it can be interpreted as a map from N to the k-combinations taken from N; in this view the correspondence is a bijection. The number N corresponding to (ck, ..., c2, c1) is given by N = ( c k k ) + ⋯ + ( c 2 2 ) + ( c 1 1 ) {\displaystyle N={\binom {c_{k}}{k}}+\cdots +{\binom {c_{2}}{2}}+{\binom {c_{1}}{1}}} .The fact that a unique sequence corresponds to any non-negative number N was first observed by D. H. Lehmer.


In number theory, Bertrand's postulate is a theorem stating that for any integer n > 1 {\displaystyle n>1} , there always exists at least one prime number such that n < p < 2 n . {\displaystyle n


Atari's 8-bit line used a SYSTEM RESET button for this same purpose. Debugging NMIs have appeared in a number of forms, including the Apple Macintosh's "programmers' button", and certain key combinations on Sun workstations. With the introduction of Windows 2000, Microsoft allowed the use of an NMI to cause a system to either break into a debugger, or dump the contents of memory to disk and reboot.Debugging NMIs have also been used by devices that allow leisure users and gamers to manipulate running programs.


In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same vector space (for example, a bilinear form or a multilinear form) that is zero whenever any pair of arguments is equal. More generally, the vector space may be a module over a commutative ring. The notion of alternatization (or alternatisation) is used to derive an alternating multilinear map from any multilinear map with all arguments belonging to the same space.


In military operations, high-value targets such as command centers are frequently protected by layers of defense systems, which may in turn be protected by other systems. In order to reach a target, all of its defenses must be taken down, making it into a secondary target. Each target needs a certain amount of resources to be allocated to it in order to perform a successful attack. The optimal set of targets to attack, to obtain the most value for the resources expended, can be modeled as a closure problem.


In syntactic ambiguity, the same sequence of words is interpreted as having different syntactic structures. In contrast, in semantic ambiguity the structure remains the same, but the individual words are interpreted differently. Controlled natural languages are often designed to be unambiguous so that they can be parsed into a logical form.


In terms of composition of the differential operator Di which takes the partial derivative with respect to xi: D i ∘ D j = D j ∘ D i {\displaystyle D_{i}\circ D_{j}=D_{j}\circ D_{i}} .From this relation it follows that the ring of differential operators with constant coefficients, generated by the Di, is commutative; but this is only true as operators over a domain of sufficiently differentiable functions. It is easy to check the symmetry as applied to monomials, so that one can take polynomials in the xi as a domain. In fact smooth functions are another valid domain.


Category theory deals with abstract objects and morphisms between those objects. In category theory, an automorphism is an endomorphism (i.e., a morphism from an object to itself) which is also an isomorphism (in the categorical sense of the word, meaning there exists a right and left inverse endomorphism). This is a very abstract definition since, in category theory, morphisms are not necessarily functions and objects are not necessarily sets. In most concrete settings, however, the objects will be sets with some additional structure and the morphisms will be functions preserving that structure.


In mathematics, especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose. Specifically, the commutation matrix K(m,n) is the nm × mn matrix which, for any m × n matrix A, transforms vec(A) into vec(AT): K(m,n) vec(A) = vec(AT) .Here vec(A) is the mn × 1 column vector obtain by stacking the columns of A on top of one another: vec  ( A ) =  T {\displaystyle \operatorname {vec} (\mathbf {A} )=^{\mathrm {T} }} where A = . In other words, vec(A) is the vector obtained by vectorizing A in column-major order. Similarly, vec(AT) is the vector obtaining by vectorizing A in row-major order. In the context of quantum information theory, the commutation matrix is sometimes referred to as the swap matrix or swap operator


The maximum entropy principle is also needed to guarantee the uniqueness and consistency of probability assignments obtained by different methods, statistical mechanics and logical inference in particular. The maximum entropy principle makes explicit our freedom in using different forms of prior data. As a special case, a uniform prior probability density (Laplace's principle of indifference, sometimes called the principle of insufficient reason), may be adopted.


Active Format Description is occasionally incorrectly referred to as "Active Format Descriptor". There is no "descriptor" (descriptor has a specific meaning in ISO/IEC 13818-1, MPEG syntax). The AFD data is carried in the Video Layer of MPEG, ISO/IEC 13818-2.


In the book The Humane Interface, Jef Raskin championed what he termed quasimodes, which are modes that are kept in place only through some constant action on the part of the user; such modes are also called spring-loaded modes. The term quasimode is a composite of the Latin prefix quasi- (which means almost, to some degree) and the English word "mode". Modifier keys on the keyboard, such as the Shift key, the Alt key and the Control key, are all examples of a quasimodal interface. The application enters into that mode as long as the user is performing a conscious action, like pressing a key and keeping it pressed while invoking a command.


For example, if one wishes to prove that every girl in the United States (A) has brown hair (B), one can either try to directly prove A → B {\displaystyle A\to B} by checking that all girls in the United States do indeed have brown hair, or try to prove ¬ B → ¬ A {\displaystyle \neg B\to \neg A} by checking that all girls without brown hair are indeed all outside the US. In particular, if one were to find at least one girl without brown hair within the US, then one would have disproved ¬ B → ¬ A {\displaystyle \neg B\to \neg A} , and equivalently A → B {\displaystyle A\to B} . In general, for any statement where A implies B, not B always implies not A. As a result, proving or disproving either one of these statements automatically proves or disproves the other, as they are logically equivalent to each other.


In the era of the electrical telegraph, its principal users were post offices, railway stations, the more important governmental centers (ministries), stock exchanges, very few nationally distributed newspapers, the largest internationally important corporations, and wealthy individuals. Despite the fact that telephone devices existed before the invention of the telephone exchange, their success and economical operation would have been impossible on the same schema and structure of the contemporary telegraph, as prior to the invention of the telephone exchange switchboard, early telephones were hardwired to and communicated with only a single other telephone (such as from an individual's home to the person's business). A telephone exchange is a telephone system for a small geographic area that provides the switching (interconnection) of subscriber lines for calls made between them. Telephone exchanges replaced small telephone systems that connected its users with direct lines between each and every subscriber station.


While such sources are still at a developmental stage QKD has been carried out successfully with them. However, as current sources operate at a low efficiency and frequency key rates and transmission distances are limited. Another solution is to modify the BB84 protocol, as is done for example in the SARG04 protocol, in which the secure key rate scales as t 3 / 2 {\displaystyle t^{3/2}} .


It also entails two-way explicit key confirmation, making it an authenticated key agreement with key confirmation (AKC) protocol. STS was originally presented in 1987 in the context of ISDN security (O'Higgins et al. 1987), finalized in 1989 and generally presented by Whitfield Diffie, Paul C. van Oorschot and Michael J. Wiener in 1992. The historical context for the protocol is also discussed in Diffie (1988).


The APEX API provides services to manage partitions, processes and timing, as well as partition/process communication and error handling. The partitioning environment can be implemented by using a hypervisor to map partitions to virtual machines, but this is not required. The standard is overseen by the AEEC APEX Subcommittee.


In software development, agile practices (sometimes written "Agile") include requirements discovery and solutions improvement through the collaborative effort of self-organizing and cross-functional teams with their customer(s)/end user(s), Popularized in the 2001 Manifesto for Agile Software Development, these values and principles were derived from and underpin a broad range of software development frameworks, including Scrum and Kanban.While there is much anecdotal evidence that adopting agile practices and values improves the effectiveness of software professionals, teams and organizations, the empirical evidence is mixed and hard to find.


In set theory, an element of a subset inherits all the attributes contained in the superset. For example, a student is a person. Therefore, the set of students is a subset of the set of persons.


It is assumed that G is simple, that is, it does not contain loops or parallel edges. Let A be the adjacency matrix of G and let λ i {\displaystyle \lambda _{i}} , i = 1 , … , n {\displaystyle i=1,\ldots ,n} , be the eigenvalues of A. Then the energy of the graph is defined as: E ( G ) = ∑ i = 1 n | λ i | . {\displaystyle E(G)=\sum _{i=1}^{n}|\lambda _{i}|.}


This necessary distributivity of • over ∨ does not in general entail distributivity of ∧ over ∨, that is, a residuated lattice need not be a distributive lattice. However distributivity of ∧ over ∨ is entailed when • and ∧ are the same operation, a special case of residuated lattices called a Heyting algebra. Alternative notations for x•y include x◦y, x;y (relation algebra), and x⊗y (linear logic).


In mathematics, addition and multiplication of real numbers is associative. By contrast, in computer science, the addition and multiplication of floating point numbers is not associative, as rounding errors are introduced when dissimilar-sized values are joined together.To illustrate this, consider a floating point representation with a 4-bit mantissa: Even though most computers compute with 24 or 53 bits of mantissa, this is an important source of rounding error, and approaches such as the Kahan summation algorithm are ways to minimise the errors. It can be especially problematic in parallel computing.


In the case of bipartite graphs or multigraphs with maximum degree Δ, the optimal number of colors is exactly Δ. Cole, Ost & Schirra (2001) showed that an optimal edge coloring of these graphs can be found in the near-linear time bound O(m log Δ), where m is the number of edges in the graph; simpler, but somewhat slower, algorithms are described by Cole & Hopcroft (1982) and Alon (2003). The algorithm of Alon (2003) begins by making the input graph regular, without increasing its degree or significantly increasing its size, by merging pairs of vertices that belong to the same side of the bipartition and then adding a small number of additional vertices and edges. Then, if the degree is odd, Alon finds a single perfect matching in near-linear time, assigns it a color, and removes it from the graph, causing the degree to become even. Finally, Alon applies an observation of Gabow (1976), that selecting alternating subsets of edges in an Euler tour of the graph partitions it into two regular subgraphs, to split the edge coloring problem into two smaller subproblems, and his algorithm solves the two subproblems recursively.


In mathematics, the layer cake representation of a non-negative, real-valued measurable function f {\displaystyle f} defined on a measure space ( Ω , A , μ ) {\displaystyle (\Omega ,{\mathcal {A}},\mu )} is the formula f ( x ) = ∫ 0 ∞ 1 L ( f , t ) ( x ) d t , {\displaystyle f(x)=\int _{0}^{\infty }1_{L(f,t)}(x)\,\mathrm {d} t,} for all x ∈ Ω {\displaystyle x\in \Omega } , where 1 E {\displaystyle 1_{E}} denotes the indicator function of a subset E ⊆ Ω {\displaystyle E\subseteq \Omega } and L ( f , t ) {\displaystyle L(f,t)} denotes the super-level set L ( f , t ) = { y ∈ Ω ∣ f ( y ) ≥ t } . {\displaystyle L(f,t)=\{y\in \Omega \mid f(y)\geq t\}.} The layer cake representation follows easily from observing that 1 L ( f , t ) ( x ) = 1  ( t ) {\displaystyle 1_{L(f,t)}(x)=1_{}(t)} and then using the formula f ( x ) = ∫ 0 f ( x ) d t . {\displaystyle f(x)=\int _{0}^{f(x)}\,\mathrm {d} t.}


In marketing, customers can be grouped into fuzzy clusters based on their needs, brand choices, psycho-graphic profiles, or other marketing related partitions.


Other examples include the functions sin  ( x ) x {\displaystyle {\frac {\sin(x)}{x}}} and x x . {\displaystyle x^{x}.} Liouville's theorem states that elementary antiderivatives, if they exist, are in the same differential field as the function, plus possibly a finite number of applications of the logarithm function.


Initially, every element in the matrix is zeros. Then for each “edge” point in the original space, we can formulate a circle in the parameter space and increase the voting number of the grid cell which the circle passes through. This process is called “voting”. After voting, we can find local maxima in the accumulator matrix. The positions of the local maxima are corresponding to the circle centers in the original space.