In number theory and combinatorics, a multipartition of a positive integer n is a way of writing n as a sum, each element of which is in turn a partition. The concept is also found in the theory of Lie algebras.


{\displaystyle H_{D}(x,R)=-\sum _{i\in (1\dots r)}P_{D}(d_{i},x,R)\log P_{D}(d_{i},x,R).} Using this entropy equation we can further calculate H D ( x , R ) {\displaystyle H_{D}(x,R)} for every point x {\displaystyle x} and region shape R {\displaystyle R} . A more complex region, like the eye region, has a more complex distributor and hence higher entropy.


It is essential in assuring that a transmission stays within its channel. An FM radio station, for example, must attenuate everything beyond ±75kHz from the center frequency by a few decibels, and anything beyond ±100 kHz (the channel boundary) by much more. Emissions on further adjacent channels must be reduced to almost zero.


{\displaystyle K_{1}K_{2}\cdots K_{M}.} A conditional probability table can be put into matrix form.


In order to prevent adaptive-chosen-ciphertext attacks, it is necessary to use an encryption or encoding scheme that limits ciphertext malleability and a proof of security of the system. After the theoretical and foundation level development of CCA secure systems, a number of systems have been proposed in the Random Oracle model: the most common standard for RSA encryption is Optimal Asymmetric Encryption Padding (OAEP). Unlike improvised schemes such as the padding used in the early versions of PKCS#1, OAEP has been proven secure in the random oracle model, OAEP was incorporated into PKCS#1 as of version 2.0 published in 1998 as the now-recommended encoding scheme, with the older scheme still supported but not recommended for new applications. However, the golden standard for security is to show the system secure without relying on the Random Oracle idealization.


In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series. It depends on the quantity lim sup n → ∞ | a n | n , {\displaystyle \limsup _{n\rightarrow \infty }{\sqrt{|a_{n}|}},} where a n {\displaystyle a_{n}} are the terms of the series, and states that the series converges absolutely if this quantity is less than one, but diverges if it is greater than one. It is particularly useful in connection with power series.


In music, a reduction is an arrangement or transcription of an existing score or composition in which complexity is lessened to make analysis, performance, or practice easier or clearer; the number of parts may be reduced or rhythm may be simplified, such as through the use of block chords.


In order to avoid regressions being seen by the end-user after release, developers regularly run regression tests after changes are introduced to the software. These tests can include unit tests to catch local regressions as well as integration tests to catch remote regressions. Regression testing techniques often leverage existing test cases to minimize the effort involved in creating them. However, due to the volume of these existing tests, it is often necessary to select a representative subset, using techniques such as test-case prioritization.


In terms of university records, authorities both on the state and federal level have shown an awareness about issues of privacy in education and a distaste for institutions' disclosure of information. The U.S. Department of Education has provided guidance about data discourse and identification, instructing educational institutions to be sensitive to the risk of re-identification of anonymous data by cross-referencing with auxiliary data, to minimize the amount of data in the public domain by decreasing publication of directory information about students and institutional personnel, and to be consistent in the processes of de-identification.


The statement is relative easy to prove by induction on the dimension of Z (even for Y=Z, X=0, c=1) with a K that depends only on N; the point of the theorem is that K is independent of N. In fact, the constant c can be made arbitrarily close to 1, at the expense of the constant K becoming large. The original proof allowed c ( K ) ≈ 1 − const / log  log  K . {\displaystyle c(K)\approx 1-{\text{const}}/\log \log K.}


A porous barrier or ceramic disk may be used to separate the two solutions while allowing the flow of sulfate ions. When the half cells are placed in two entirely different and separate containers, a salt bridge is often used to connect the two cells. The salt bridge typically contains a high concentration of potassium nitrate (a salt that will not interfere chemically with the reaction in either half-cell).


In mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen to be as short as possible. For example, if one chooses to take commutativity for granted, an axiom with six NAND operations and three variables is equivalent to Boolean algebra: ( ( a ∣ b ) ∣ c ) ∣ ( a ∣ ( ( a ∣ c ) ∣ a ) ) = c {\displaystyle ((a\mid b)\mid c)\mid (a\mid ((a\mid c)\mid a))=c} where the vertical bar represents the NAND logical operation (also known as the Sheffer stroke). It is one of 25 candidate axioms for this property identified by Stephen Wolfram, by enumerating the Sheffer identities of length less or equal to 15 elements (excluding mirror images) that have no noncommutative models with four or fewer variables, and was first proven equivalent by William McCune, Branden Fitelson, and Larry Wos. MathWorld, a site associated with Wolfram, has named the axiom the "Wolfram axiom".


In the case of a cache miss, the purpose of using such a structure will be rendered useless and the computer will have to go to the main memory to fetch the required data. However, with a multiple-level cache, if the computer misses the cache closest to the processor (level-one cache or L1) it will then search through the next-closest level(s) of cache and go to main memory only if these methods fail. The general trend is to keep the L1 cache small and at a distance of 1–2 CPU clock cycles from the processor, with the lower levels of caches increasing in size to store more data than L1, hence being more distant but with a lower miss rate. This results in a better AAT. The number of cache levels can be designed by architects according to their requirements after checking for trade-offs between cost, AATs, and size.


In previous work, according to Chi (2000), "researchers have attempted to construct taxonomies of information visualization techniques by examining the data domains that are compatible with these techniques. This is useful because implementers can quickly identify various techniques that can be applied to their domain of interest. However, these taxonomies do not help the implementers understand how to apply and implement these techniques".According to Chi (2000), he and J.T.


In order to treat very large problems, the structure of hierarchical matrices can be improved: H2-matrices replace the general low-rank structure of the blocks by a hierarchical representation closely related to the fast multipole method in order to reduce the storage complexity to O ( n k ) {\displaystyle O(nk)} . In the context of boundary integral operators, replacing the fixed rank k {\displaystyle k} by block-dependent ranks leads to approximations that preserve the rate of convergence of the underlying boundary element method at a complexity of O ( n ) . {\displaystyle O(n).} Arithmetic operations like multiplication, inversion, and Cholesky or LR factorization of H2-matrices can be implemented based on two fundamental operations: the matrix-vector multiplication with submatrices and the low-rank update of submatrices. While the matrix-vector multiplication is straightforward, implementing efficient low-rank updates with adaptively optimized cluster bases poses a significant challenge.


In the Khoisan languages and the International Phonetic Alphabet, the vertical bar is used to write the dental click (ǀ). A double vertical bar is used to write the alveolar lateral click (ǁ). Since these are technically letters, they have their own Unicode code points in the Latin Extended-B range: U+01C0 for the single bar and U+01C1 for the double bar.


In the new memory layout, the ensemble dimension is added to the lowest dimension to reduce possible branch divergence. The impact of the unavoidable branch divergence from data irregularity, caused by the noise, is minimized via a regularization technique using the on-chip memory. Moreover, the cache memory is utilized to amortize unavoidable uncoalesced memory accesses.


In mathematics, division by two or halving has also been called mediation or dimidiation. The treatment of this as a different operation from multiplication and division by other numbers goes back to the ancient Egyptians, whose multiplication algorithm used division by two as one of its fundamental steps. Some mathematicians as late as the sixteenth century continued to view halving as a separate operation, and it often continues to be treated separately in modern computer programming. Performing this operation is simple in decimal arithmetic, in the binary numeral system used in computer programming, and in other even-numbered bases.


{\displaystyle x^{*}(p_{1},p_{2},I)=\left({\frac {Ip_{1}^{\epsilon -1}}{p_{1}^{\epsilon }+p_{2}^{\epsilon }}},{\frac {Ip_{2}^{\epsilon -1}}{p_{1}^{\epsilon }+p_{2}^{\epsilon }}}\right),\quad {\text{with}}\quad \epsilon ={\frac {\delta }{\delta -1}}.} In both cases, the preferences are strictly convex, the demand is unique and the demand function is continuous. 3.


On the probability space we define the space X = { X } {\displaystyle {\mathcal {X}}=\{X\}} of random variables with values in measurable metric space ( U , d u ) {\displaystyle (U,d_{u})} and the space Y = { Y } {\displaystyle {\mathcal {Y}}=\{Y\}} of random variables with values in measurable metric space ( V , d v ) {\displaystyle (V,d_{v})} . By characterizations of probability distributions we understand general problems of description of some set C {\displaystyle {\mathcal {C}}} in the space X {\displaystyle {\mathcal {X}}} by extracting the sets A ⊆ X {\displaystyle {\mathcal {A}}\subseteq {\mathcal {X}}} and B ⊆ Y {\displaystyle {\mathcal {B}}\subseteq {\mathcal {Y}}} which describe the properties of random variables X ∈ A {\displaystyle X\in {\mathcal {A}}} and their images Y = F X ∈ B {\displaystyle Y=\mathbf {F} X\in {\mathcal {B}}} , obtained by means of a specially chosen mapping F: X → Y {\displaystyle \mathbf {F} :{\mathcal {X}}\to {\mathcal {Y}}} . The description of the properties of the random variables X {\displaystyle X} and of their images Y = F X {\displaystyle Y=\mathbf {F} X} is equivalent to the indication of the set A ⊆ X {\displaystyle {\mathcal {A}}\subseteq {\mathcal {X}}} from which X {\displaystyle X} must be taken and of the set B ⊆ Y {\displaystyle {\mathcal {B}}\subseteq {\mathcal {Y}}} into which its image must fall.


Snippets are similar to having static preprocessing included in the editor, and do not require support by a compiler. On the flip side, this means that snippets cannot be invariably modified after the fact, and thus is vulnerable to all of the problems of copy and paste programming. For this reason snippets are primarily used for simple sections of code (with little logic), or for boilerplate, such as copyright notices, function prototypes, common control structures, or standard library imports.


A number of dimensional models have been produced, differing in the way in which they are constructed and the way in which they are intended to be interpreted. There are four broad types of dimensional representation, although others also exist: Dimensional representation of the original DSM categories of personality disorders; Dimensional representation based on identification of latent traits with the DSM disorders; Dimensional representation based on the traits from normal personality research; Representation based on integration of dimensional modals, e.g. by using network analysis.The dimensional approach is included in Section III ("Emerging Measures and Models") of the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5), where it is described as an "Alternative DSM-5 Model for Personality Disorders. ": p.761–781 The decision to retain the old DSM-IV categorical model of personality disorders in DSM-5 was controversial, and efforts continue to persuade the American Psychiatric Association to replace it with the dimensional model in DSM 5.1.


In the U.S., the calculation and disclosure of APR is governed by the Truth in Lending Act (which is implemented by the Consumer Financial Protection Bureau (CFPB) in Regulation Z of the Act). In general, APR in the United States is expressed as the periodic (for instance, monthly) interest rate times the number of compounding periods in a year (also known as the nominal interest rate); since the APR must include certain non-interest charges and fees, it requires more detailed calculation. The APR must be disclosed to the borrower within 3 days of applying for a mortgage. This information is typically mailed to the borrower and the APR is found on the truth in lending disclosure statement, which also includes an amortization schedule.


If the content is deemed dangerous or inappropriate, its spread could be curbed immediately.Understandably, methods for countering disinformation that involve algorithmic governance raise ethical concerns. The use of technologies that track and manipulate information raises questions about "who is accountable for their operation, whether they can create injustices and erode civic norms, and how we should resolve their (un)intended consequences".A study from the Pew Research Center reports that public support for restriction of disinformation by both technology companies and government increased among Americans from 2018-2021. However, views on whether government and technology companies should take such steps became increasingly partisan and polarized during the same time period.


In object-oriented programming (OOP), an instance is a concrete occurrence of any object, existing usually during the runtime of a computer program. Formally, "instance" is synonymous with "object" as they are each a particular value (realization), and these may be called an instance object; "instance" emphasizes the distinct identity of the object. The creation of an instance is called instantiation. An object may be varied in a number of ways.


In some hackathons, all work is on a single application, such as an operating system, programming language, or content management system. Such events are often known as "code sprints", and are especially popular for open source software projects, where such events are sometimes the only opportunity for developers to meet face-to-face.Code sprints typically last from one week to three weeks and often take place near conferences at which most of the team attend. Unlike other hackathons, these events rarely include a competitive element. The annual hackathon to work on the operating system OpenBSD, held since 1999, is one such event; it may have originated the word "hackathon".


η . {\displaystyle \eta ^{\prime }S.\eta .} See: distributive law between monads. A generalized distributive law has also been proposed in the area of information theory.


Other methods of defining the correspondence include a nondeterministic algorithm in terms of jeu de taquin. The bijective nature of the correspondence relates it to the enumerative identity ∑ λ ∈ P n ( t λ ) 2 = n ! {\displaystyle \sum _{\lambda \in {\mathcal {P}}_{n}}(t_{\lambda })^{2}=n!} where P n {\displaystyle {\mathcal {P}}_{n}} denotes the set of partitions of n (or of Young diagrams with n squares), and tλ denotes the number of standard Young tableaux of shape λ.


Before virtual memory could be implemented in mainstream operating systems, many problems had to be addressed. Dynamic address translation required expensive and difficult-to-build specialized hardware; initial implementations slowed down access to memory slightly. There were worries that new system-wide algorithms utilizing secondary storage would be less effective than previously used application-specific algorithms.


0 K m , n =  {\displaystyle 0_{K_{m,n}}={\begin{bmatrix}0_{K}&0_{K}&\cdots &0_{K}\\0_{K}&0_{K}&\cdots &0_{K}\\\vdots &\vdots &&\vdots \\0_{K}&0_{K}&\cdots &0_{K}\end{bmatrix}}} The zero matrix is the additive identity in K m , n {\displaystyle K_{m,n}} . That is, for all A ∈ K m , n {\displaystyle A\in K_{m,n}}: 0 K m , n + A = A + 0 K m , n = A {\displaystyle 0_{K_{m,n}}+A=A+0_{K_{m,n}}=A} There is exactly one zero matrix of any given size m × n (with entries from a given ring), so when the context is clear, one often refers to the zero matrix.


The relative point of view is that much of algebraic geometry should be developed for a morphism X → Y of schemes (called a scheme X over Y), rather than for an individual scheme. For example, in studying algebraic surfaces, it can be useful to consider families of algebraic surfaces over any scheme Y. In many cases, the family of all varieties of a given type can itself be viewed as a variety or scheme, known as a moduli space. For some of the detailed definitions in the theory of schemes, see the glossary of scheme theory.


Additionally, MDP allowed the protocol to be optionally configured to send proactive repair packets in the original data transmission block. MDP was a direct predecessor to NORM, with an initial IETF draft published in November 1996. The National Aeronautics and Space Administration (NASA) adopted MDP for reliable file transfers during space missions., and the U.S.


In mathematics, Hall's conjecture is an open question, as of 2015, on the differences between perfect squares and perfect cubes. It asserts that a perfect square y2 and a perfect cube x3 that are not equal must lie a substantial distance apart. This question arose from consideration of the Mordell equation in the theory of integer points on elliptic curves.


In mathematics, a nonempty subset S of a group G is said to be symmetric if it contains the inverses of all of its elements.


In recent years, the term "algebraic statistics" has been used more restrictively, to label the use of algebraic geometry and commutative algebra to study problems related to discrete random variables with finite state spaces. Commutative algebra and algebraic geometry have applications in statistics because many commonly used classes of discrete random variables can be viewed as algebraic varieties.


The load step becomes a separate instruction, and that instruction is statically scheduled much earlier in the code sequence. The compiler puts independent steps in between. Scheduling memory accesses requires explicit, spare registers.


In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"). Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. Some sources use the term existentialization to refer to existential quantification.


A surrogate key may be used as the primary key to avoid giving one candidate key artificial primacy over the others. Since primary keys exist primarily as a convenience to the programmer, surrogate primary keys are often used, in many cases exclusively, in database application design. Due to the popularity of surrogate primary keys, many developers and in some cases even theoreticians have come to regard surrogate primary keys as an inalienable part of the relational data model.


Ammunition and canisters which replenish shields or oxygen can be found while exploring the game's environments, as well as various temporary power-ups. Single-player level objectives can include exterminating all hostile creatures, rescuing civilians, retrieving certain items, or exploring certain locations. Most levels contain platforms, stairs, doors, and liquids which players can control by activating switches.


In probability theory, Cantelli's inequality (also called the Chebyshev-Cantelli inequality and the one-sided Chebyshev inequality) is an improved version of Chebyshev's inequality for one-sided tail bounds. The inequality states that, for λ > 0 , {\displaystyle \lambda >0,} Pr ( X − E  ≥ λ ) ≤ σ 2 σ 2 + λ 2 , {\displaystyle \Pr(X-\mathbb {E} \geq \lambda )\leq {\frac {\sigma ^{2}}{\sigma ^{2}+\lambda ^{2}}},} where X {\displaystyle X} is a real-valued random variable, Pr {\displaystyle \Pr } is the probability measure, E  {\displaystyle \mathbb {E} } is the expected value of X {\displaystyle X} , σ 2 {\displaystyle \sigma ^{2}} is the variance of X {\displaystyle X} .Applying the Cantelli inequality to − X {\displaystyle -X} gives a bound on the lower tail, Pr ( X − E  ≤ − λ ) ≤ σ 2 σ 2 + λ 2 . {\displaystyle \Pr(X-\mathbb {E} \leq -\lambda )\leq {\frac {\sigma ^{2}}{\sigma ^{2}+\lambda ^{2}}}.}


REBOL reifies code as data and vice versa. Many languages, such as Lisp, JavaScript, and Curl, provide an eval or evaluate procedure that effectively reifies the language interpreter. The Logtalk framework for Prolog offers a means to explore reification in the context of logic programming. Smalltalk and Actor languages permit the reification of blocks and messages, which are equivalent of lambda expressions in Lisp, and thisContext in Smallltalk, which is a reification of the current executing block. Homoiconic languages reify the syntax of the language itself in the form of an abstract syntax tree, typically together with eval.


This was still a vast amount of memory at the time, but because of this limitation, architectures since have included various steps away from the original 26-bit design. The ARM architecture version 3 introduced a 32-bit PC and separate PSR, as well as a 32-bit address bus, allowing 4 GiB of memory to be addressed. The change in the PC/PSR layout caused incompatibility with code written for previous architectures, so the processor also included a 26-bit compatibility mode which used the old PC/PSR combination.


In set notation a subset S {\displaystyle S} of a group G {\displaystyle G} is called symmetric if whenever s ∈ S {\displaystyle s\in S} then the inverse of s {\displaystyle s} also belongs to S . {\displaystyle S.} So if G {\displaystyle G} is written multiplicatively then S {\displaystyle S} is symmetric if and only if S = S − 1 {\displaystyle S=S^{-1}} where S − 1 := { s − 1: s ∈ S } . {\displaystyle S^{-1}:=\left\{s^{-1}:s\in S\right\}.}


In mathematics, the concept of an inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers. Given an operation denoted here ∗, and an identity element denoted e, if x ∗ y = e, one says that x is a left inverse of y, and that y is a right inverse of x. (An identity element is an element such that x * e = x and e * y = y for all x and y for which the left-hand sides are defined.) When the operation ∗ is associative, if an element x has both a left inverse and a right inverse, then these two inverses are equal and unique; they are called the inverse element or simply the inverse.


In nature, species do not evolve in isolation but in large networks of interacting species. One of the main goals in evolutionary ecology is to disentangle the evolutionary mechanisms that shape and are shaped by patterns of interaction between species. A particularly important question concerns how coevolution, the reciprocal evolutionary change in local populations of interacting species driven by natural selection, is shaped by the architecture of food webs, plant-animal mutualistic networks, and host-parasite communities. The concept of diffuse coevolution, where adaptation is in response to a suite of biotic interactions, was the first step towards a framework unifying relevant theories in community ecology and coevolution.


In the area of mathematical logic and computer science known as type theory, a type constructor is a feature of a typed formal language that builds new types from old ones. Basic types are considered to be built using nullary type constructors. Some type constructors take another type as an argument, e.g., the constructors for product types, function types, power types and list types. New types can be defined by recursively composing type constructors.


One can then also calculate the mean square of the model by dividing the sum of squares of the model minus the degrees of freedom, which is just the number of parameters. Then the F value can be calculated by dividing the mean square of the model by the mean square of the error, and we can then determine significance (which is why you want the mean squares to begin with. ).However, because of the behavior of the process of regression, the distributions of residuals at different data points (of the input variable) may vary even if the errors themselves are identically distributed.


In some countries, declining satisfaction with the urban environment is held to blame for continuing migration to smaller towns and rural areas (so-called urban exodus). Successful urban planning supported Regional planning can bring benefits to a much larger hinterland or city region and help to reduce both congestion along transport routes and the wastage of energy implied by excessive commuting.


It is widely used in a Filipino youth subculture known as Jejemons. kkkk: in Somali and Ethiopian languages spoken in the Horn of Africa, iterations of the letter "k", usually ranging between 2 and 8 k's, are used as a variation of LOL. These iterations are also used by Shona, Ndebele and other Zimbabwean languages speakers, with the longer variant being "kikiki" (emulating a laughing sound).


The number of trailing zeros in a non-zero base-b integer n equals the exponent of the highest power of b that divides n. For example, 14000 has three trailing zeros and is therefore divisible by 1000 = 103, but not by 104. This property is useful when looking for small factors in integer factorization. Some computer architectures have a count trailing zeros operation in their instruction set for efficiently determining the number of trailing zero bits in a machine word.


In matroid theory, an Eulerian matroid is a matroid whose elements can be partitioned into a collection of disjoint circuits.


In mathematics, the geometric topology is a topology one can put on the set H of hyperbolic 3-manifolds of finite volume.


In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson (; French pronunciation: ). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.


In stop/step mode debugging, the core/microcontroller is stopped through the use of breakpoints and then "single-stepped" through the code by executing instructions one at a time. If the other cores/microcontrollers of the SoC have finished synchronously, the overall state of the system can be examined. Stop/step mode debugging includes control/configure techniques, run control of a core/microcontroller, start/stop synchronization with other cores, memory and register access, and additional debug features such as performance counter and run-time memory access.


In the autumn of 1884, Károly Zipernowsky, Ottó Bláthy and Miksa Déri (ZBD), three Hungarian engineers associated with the Ganz Works, had determined that open-core devices were impracticable, as they were incapable of reliably regulating voltage. In their joint 1885 patent applications for novel transformers (later called ZBD transformers), they described two designs with closed magnetic circuits where copper windings were either wound around an iron wire ring core or surrounded by an iron wire core. The two designs were the first application of the two basic transformer constructions in common use to this day, termed "core form" or "shell form" . The Ganz factory had also in the autumn of 1884 made delivery of the world's first five high-efficiency AC transformers, the first of these units having been shipped on September 16, 1884.


Consider for example the random variable of the number of items in a shopper's basket at a supermarket checkout line. Presumably a shopper does not stand in line with nothing to buy (i.e., the minimum purchase is 1 item), so this phenomenon may follow a ZTP distribution.Since the ZTP is a truncated distribution with the truncation stipulated as k > 0, one can derive the probability mass function g(k;λ) from a standard Poisson distribution f(k;λ) as follows: g ( k ; λ ) = P ( X = k ∣ X > 0 ) = f ( k ; λ ) 1 − f ( 0 ; λ ) = λ k e − λ k ! ( 1 − e − λ ) = λ k ( e λ − 1 ) k ! {\displaystyle g(k;\lambda )=P(X=k\mid X>0)={\frac {f(k;\lambda )}{1-f(0;\lambda )}}={\frac {\lambda ^{k}e^{-\lambda }}{k!\left(1-e^{-\lambda }\right)}}={\frac {\lambda ^{k}}{(e^{\lambda }-1)k!}}} The mean is E   = λ 1 − e − λ = λ e λ e λ − 1 {\displaystyle \operatorname {E} ={\frac {\lambda }{1-e^{-\lambda }}}={\frac {\lambda e^{\lambda }}{e^{\lambda }-1}}} and the variance is Var   = λ + λ 2 1 − e − λ − λ 2 ( 1 − e − λ ) 2 = E   ( 1 + λ − E   ) {\displaystyle \operatorname {Var} ={\frac {\lambda +\lambda ^{2}}{1-e^{-\lambda }}}-{\frac {\lambda ^{2}}{(1-e^{-\lambda })^{2}}}=\operatorname {E} (1+\lambda -\operatorname {E} )}


As a bracketing strategy, in each iteration the ITP queries the value of the function on one point and discards the part of the interval between two points where the function value shares the same sign. The queried point is calculated with three steps: it interpolates finding the regula falsi estimate, then it perturbes/truncates the estimate (similar to Regula falsi § Improvements in regula falsi) and then projects the perturbed estimate onto an interval in the neighbourhood of the bisection midpoint. The neighbourhood around the bisection point is calculated in each iteration in order to guarantee minmax optimality (Theorem 2.1 of ). The method depends on three hyper-parameters κ 1 ∈ ( 0 , ∞ ) , κ 2 ∈ [ 1 , 1 + ϕ ) {\displaystyle \kappa _{1}\in (0,\infty ),\kappa _{2}\in \left[1,1+\phi \right)} and n 0 ∈ [ 0 , ∞ ) {\displaystyle n_{0}\in [0,\infty )} where ϕ {\displaystyle \phi } is the golden ratio 1 2 ( 1 + 5 ) {\displaystyle {\tfrac {1}{2}}(1+{\sqrt {5}})}: the first two control the size of the truncation and the third is a slack variable that controls the size of the interval for the projection step.


First, since the self-improvement through learning is more direct and rapid than the evolution process, the social learning algorithm can improve the efficiency of the algorithms mimicking natural evolution. Second, compared with the interaction and learning behaviors in animal groups, the social learning process of human beings exhibits a higher level of intelligence. By emulating human learning behaviors, it is possible to arrive at more effective optimizers than existing swarm intelligence algorithms.


In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word collision refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force.In physics, collisions can be classified by the change in the total kinetic energy of the system before and after the collision: If most or all of the total kinetic energy is lost (dissipated as heat, sound, etc. or absorbed by the objects themselves), the collision is said to be inelastic; such collisions involve objects coming to a full stop. An example of such a collision is a car crash, as cars crumple inward when crashing, rather than bouncing off of each other. This is by design, for the safety of the occupants and bystanders should a crash occur - the frame of the car absorbs the energy of the crash instead.


These relations set strong limitations for the nonexistence of common eigenstates for incompatible observables. The Maccone–Pati uncertainty relations have been experimentally tested for qutrit systems. The new uncertainty relations not only capture the incompatibility of observables but also of quantities that are physically measurable (as variances can be measured in the experiment).


In order to run safely on multiprocessor machines, access to shared resources (like files, data structures) must be serialized so that threads or processes do not attempt to modify the same resource at the same time. In order to prevent multiple threads from accessing or modifying a shared resource simultaneously, DragonFly employs critical sections, and serializing tokens to prevent concurrent access. While both Linux and FreeBSD 5 employ fine-grained mutex models to achieve higher performance on multiprocessor systems, DragonFly does not. Until recently, DragonFly also employed spls, but these were replaced with critical sections.


In the United States, the modern demarcation point is a device defined by FCC rules (47 C.F.R. Part 68) to allow safe connection of third-party telephone customer-premises equipment and wiring to the Public Switched Telephone Network (PSTN). The modern demarcation point is the network interface device (NID) or intelligent network interface device (INID) also known as a "smartjack". The NID is the telco's property.


When information is transferred across time, often to specific points in time, the process is known as forecasting. Forecasting usually requires time series methods, while prediction is often performed on cross-sectional data. Statistical techniques used for prediction include regression and its various sub-categories such as linear regression, generalized linear models (logistic regression, Poisson regression, Probit regression), etc. In case of forecasting, autoregressive moving average models and vector autoregression models can be utilized.


With no differing information to counter the untruths or the general agreement within isolated social clusters, some argue the outcome is an absence of a collective reality. Although social media sites have changed their algorithms to prevent the spread of fake news, the problem still exists. Furthermore, research has shown that while people may know what the scientific community has proved as a fact, they may still refuse to accept it as such.Researchers fear that misinformation in social media is "becoming unstoppable."


In microbiology, genes can move freely even between distantly related bacteria, possibly extending to the whole bacterial domain. As a rule of thumb, microbiologists have assumed that kinds of Bacteria or Archaea with 16S ribosomal RNA gene sequences more similar than 97% to each other need to be checked by DNA-DNA hybridisation to decide if they belong to the same species or not. This concept was narrowed in 2006 to a similarity of 98.7%.DNA-DNA hybridisation is outdated, and results have sometimes led to misleading conclusions about species, as with the pomarine and great skua. Modern approaches compare sequence similarity using computational methods.


In the Microsoft .NET Framework, XML Literal allows a computer program to include XML directly in the code. It is currently only supported in VB.NET 9.0 and VB.NET 10.0. When a Visual Basic expression is embedded in an XML literal, the application creates a LINQ-to-XML object for each literal at run time.


In mathematics, the scalar projection of a vector a {\displaystyle \mathbf {a} } on (or onto) a vector b , {\displaystyle \mathbf {b} ,} also known as the scalar resolute of a {\displaystyle \mathbf {a} } in the direction of b , {\displaystyle \mathbf {b} ,} is given by: s = ‖ a ‖ cos  θ = a ⋅ b ^ , {\displaystyle s=\left\|\mathbf {a} \right\|\cos \theta =\mathbf {a} \cdot \mathbf {\hat {b}} ,} where the operator ⋅ {\displaystyle \cdot } denotes a dot product, b ^ {\displaystyle {\hat {\mathbf {b} }}} is the unit vector in the direction of b , {\displaystyle \mathbf {b} ,} ‖ a ‖ {\displaystyle \left\|\mathbf {a} \right\|} is the length of a , {\displaystyle \mathbf {a} ,} and θ {\displaystyle \theta } is the angle between a {\displaystyle \mathbf {a} } and b {\displaystyle \mathbf {b} } . The term scalar component refers sometimes to scalar projection, as, in Cartesian coordinates, the components of a vector are the scalar projections in the directions of the coordinate axes. The scalar projection is a scalar, equal to the length of the orthogonal projection of a {\displaystyle \mathbf {a} } on b {\displaystyle \mathbf {b} } , with a negative sign if the projection has an opposite direction with respect to b {\displaystyle \mathbf {b} } . Multiplying the scalar projection of a {\displaystyle \mathbf {a} } on b {\displaystyle \mathbf {b} } by b ^ {\displaystyle \mathbf {\hat {b}} } converts it into the above-mentioned orthogonal projection, also called vector projection of a {\displaystyle \mathbf {a} } on b {\displaystyle \mathbf {b} } .


If K = R {\displaystyle \mathbb {K} =\mathbb {R} } , then A ∗ = A T {\displaystyle A^{*}=A^{\textsf {T}}} . For A ∈ K m × n {\displaystyle A\in \mathbb {K} ^{m\times n}} , ran  ( A ) {\displaystyle \operatorname {ran} (A)} (standing for "range") denotes the column space (image) of A {\displaystyle A} (the space spanned by the column vectors of A {\displaystyle A} ) and ker  ( A ) {\displaystyle \ker(A)} denotes the kernel (null space) of A {\displaystyle A} . Finally, for any positive integer n {\displaystyle n} , I n ∈ K n × n {\displaystyle I_{n}\in \mathbb {K} ^{n\times n}} denotes the n × n {\displaystyle n\times n} identity matrix.


In some software originating on big-endian machines such as Silicon Graphics, colors were stored in 32 bits similar to ARGB32, but with the alpha in the bottom 8 bits rather than the top. For example, 808000FF would be Red and Green:50.2%, Blue:0% and Alpha:100%, a brown. This is what you would get if RGBA8888 data was read as words on these machines. It is used in Portable Arbitrary Map and in FLTK, but in general it is rare. The bytes are stored in memory on a little-endian machine in the order ABGR.


The requirements for the United States are covered in Title 47 of the Code of Federal Regulations, part 97.119. Land mobile two-way (including public safety and business mobile) require station identifications by call sign. In the case of the GMRS service, this is to be done by each station in a similar manner to the amateur practice, though the time limit is fifteen minutes.


Numerical semigroups are commutative monoids and are also known as numerical monoids.The definition of numerical semigroup is intimately related to the problem of determining nonnegative integers that can be expressed in the form x1n1 + x2 n2 + ... + xr nr for a given set {n1, n2, ..., nr} of positive integers and for arbitrary nonnegative integers x1, x2, ..., xr. This problem had been considered by several mathematicians like Frobenius (1849–1917) and Sylvester (1814–1897) at the end of the 19th century. During the second half of the twentieth century, interest in the study of numerical semigroups resurfaced because of their applications in algebraic geometry.


Schedule 1 drugs have little or no medical benefit, hence their limitations on prescribing. District nurses and health visitors have had limited prescribing rights since the mid-1990s; until then, prescriptions for dressings and simple medicines had to be signed by a doctor. Once issued, a prescription is taken by the patient to a pharmacy, which dispenses the medicine.


With thirty diverse bidders unable to communicate about strategy except through their bids, forming such unanimous agreement is difficult at best." Nevertheless, Federal Communications Commission (FCC) experimented with precautions for spectrum auctions like restricting visibility of bids, limiting the number of bids and anonymous bidding.


To have a lack-of-fit sum of squares that differs from the residual sum of squares, one must observe more than one y-value for each of one or more of the x-values. One then partitions the "sum of squares due to error", i.e., the sum of squares of residuals, into two components: sum of squares due to error = (sum of squares due to "pure" error) + (sum of squares due to lack of fit).The sum of squares due to "pure" error is the sum of squares of the differences between each observed y-value and the average of all y-values corresponding to the same x-value. The sum of squares due to lack of fit is the weighted sum of squares of differences between each average of y-values corresponding to the same x-value and the corresponding fitted y-value, the weight in each case being simply the number of observed y-values for that x-value. Because it is a property of least squares regression that the vector whose components are "pure errors" and the vector of lack-of-fit components are orthogonal to each other, the following equality holds: ∑ ( observed value − fitted value ) 2 (error) = ∑ ( observed value − local average ) 2 (pure error) + ∑ weight × ( local average − fitted value ) 2 (lack of fit) {\displaystyle {\begin{aligned}&\sum ({\text{observed value}}-{\text{fitted value}})^{2}&&{\text{(error)}}\\&\qquad =\sum ({\text{observed value}}-{\text{local average}})^{2}&&{\text{(pure error)}}\\&\qquad \qquad {}+\sum {\text{weight}}\times ({\text{local average}}-{\text{fitted value}})^{2}&&{\text{(lack of fit)}}\end{aligned}}} Hence the residual sum of squares has been completely decomposed into two components.


In practice, testing measures are never perfectly consistent. Theories of test reliability have been developed to estimate the effects of inconsistency on the accuracy of measurement. The basic starting point for almost all theories of test reliability is the idea that test scores reflect the influence of two sorts of factors:1. Consistency factors: stable characteristics of the individual or the attribute that one is trying to measure.


In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. It assumes that the expected returns are known and is optimal for a bettor who values their wealth logarithmically. J. L. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956.


This technique was developed by C E Wynn-Williams at The Cavendish Laboratory and first published in 1932. The original counters used a cascade of "Eccles-Jordan" divide-by-two circuits, today known as flip flops. Early count readings were therefore binary numbers and had to be manually re-calculated into decimal values. Later, with the development of electronic indicators, which started with the introduction of the Dekatron readout tube in the 1950s, and culminating in the modern digital indicator, totalised readings came to be directly indicated in decimal notation.


In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1 cosh  t = 2 e t + e − t = ∑ n = 0 ∞ E n n ! ⋅ t n {\displaystyle {\frac {1}{\cosh t}}={\frac {2}{e^{t}+e^{-t}}}=\sum _{n=0}^{\infty }{\frac {E_{n}}{n! }}\cdot t^{n}} ,where cosh  ( t ) {\displaystyle \cosh(t)} is the hyperbolic cosine function.


In the finding of a pathognomonic sign or symptom it is almost certain that the target condition is present, and in the absence of finding a sine qua non sign or symptom it is almost certain that the target condition is absent. In reality, however, the subjective probability of the presence of a condition is never exactly 100% or 0%, so tests are rather aimed at estimating a post-test probability of a condition or other entity. Most diagnostic tests basically use a reference group to establish performance data such as predictive values, likelihood ratios and relative risks, which are then used to interpret the post-test probability for an individual. In monitoring tests of an individual, the test results from previous tests on that individual may be used as a reference to interpret subsequent tests.


In number theory, the positive remainder is always chosen, but in computing, programming languages choose depending on the language and the signs of a or n. Standard Pascal and ALGOL 68, for example, give a positive remainder (or 0) even for negative divisors, and some programming languages, such as C90, leave it to the implementation when either of n or a is negative (see the table under § In programming languages for details). a modulo 0 is undefined in most systems, although some do define it as a. As described by Leijen, Boute argues that Euclidean division is superior to the other ones in terms of regularity and useful mathematical properties, although floored division, promoted by Knuth, is also a good definition. Despite its widespread use, truncated division is shown to be inferior to the other definitions. However, truncated division satisfies the identity ( − a ) / b = − ( a / b ) = a / ( − b ) {\displaystyle ({-a})/b={-(a/b)}=a/({-b})} .


In scholarly writing, an important objective of classifying sources is to determine their independence and reliability. In contexts such as historical writing, it is almost always advisable to use primary sources and that "if none are available, it is only with great caution that  may proceed to make use of secondary sources." Sreedharan believes that primary sources have the most direct connection to the past and that they "speak for themselves" in ways that cannot be captured through the filter of secondary sources.


In this sense the solution represents the unbounded μ operator that can, if necessary, hunt ad infinitum along the unbounded string of registers until it finds what it is looking for. The pointer register is exactly like any other register with one exception: under the circumstances called "indirect addressing" it provides its contents, rather than the address-operand in the state machine's TABLE, to be the address of the target register (including possibly itself! ).


Most programming languages, even those with no explicit Boolean type, have support for Boolean algebraic operations such as conjunction (AND, &, *), disjunction (OR, |, +), equivalence (EQV, =, ==), exclusive or/non-equivalence (XOR, NEQV, ^, !=, ¬), and negation (NOT, ~, !, ¬). In some languages, like Ruby, Smalltalk, and Alice the true and false values belong to separate classes, e.g., True and False, respectively, so there is no one Boolean type. In SQL, which uses a three-valued logic for explicit comparisons because of its special treatment of Nulls, the Boolean data type (introduced in SQL:1999) is also defined to include more than two truth values, so that SQL Booleans can store all logical values resulting from the evaluation of predicates in SQL. A column of Boolean type can be restricted to just TRUE and FALSE though.


In marketing research, the most frequently used types of observational techniques are: Personal observation observing products in use to detect usage patterns and problems observing license plates in store parking lots determining the socio-economic status of shoppers determining the level of package scrutiny determining the time it takes to make a purchase decision Mechanical observationeye-tracking analysis while subjects watch advertisements oculometers – what the subject is looking at pupilometers – how interested is the viewer electronic checkout scanners – records purchase behaviour on-site cameras in stores people meters (as in monitoring television viewing) e.g.Nielsen box voice pitch meters – measures emotional reactions psychogalvanometer – measures galvanic skin response Auditsretail audits to determine the quality of service in stores inventory audits to determine product acceptance shelf space audits scanner based audits Trace Analysiscredit card records computer cookie records garbology – looking for traces of purchase patterns in garbage detecting store traffic patterns by observing the wear in the floor (long term) or the dirt on the floor (short term) exposure to advertisements Content analysisobserve the content of magazines, television broadcasts, radio broadcasts, or newspapers, either articles, programs, or advertisements


In mathematics, a covering set for a sequence of integers refers to a set of prime numbers such that every term in the sequence is divisible by at least one member of the set. The term "covering set" is used only in conjunction with sequences possessing exponential growth.


In the C99 version of the C programming language and the C++11 version of C++, a long long type is supported that has double the minimum capacity of the standard long. This type is not supported by compilers that require C code to be compliant with the previous C++ standard, C++03, because the long long type did not exist in C++03. For an ANSI/ISO compliant compiler, the minimum requirements for the specified ranges, that is, −(263−1) to 263−1 for signed and 0 to 264−1 for unsigned, must be fulfilled; however, extending this range is permitted.


In practice, the above algorithm is typically iterated to produce a sequence x n {\displaystyle \mathbf {x} _{n}} , n = 1 , 2 , . . .


In probability theory, The Poisson scatter theorem describes a probability model of random scattering. It implies that the number of points in a fixed region will follow a Poisson distribution.


In mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks. A major theme in the mathematical and computational analysis of GDSs is to relate their structural properties (e.g. the network connectivity) and the global dynamics that result. The work on GDSs considers finite graphs and finite state spaces.


In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i.e., if there exists a Turing machine which will enumerate all valid strings of the language. Recursively enumerable languages are known as type-0 languages in the Chomsky hierarchy of formal languages. All regular, context-free, context-sensitive and recursive languages are recursively enumerable. The class of all recursively enumerable languages is called RE.


These terms in biology contain no judgement about the sophistication, superiority, value or adaptiveness of the named trait. "Primitive" in biology means only that the character appeared first in the common ancestor of a clade group and has been passed on largely intact to more recent members of the clade.


That is, the image and the codomain of the function are equal. A surjective function is a surjection. Notationally: ∀ y ∈ Y , ∃ x ∈ X such that y = f ( x ) .


Sets and possibles alike make for a crowded ontology. Sets and possibles alike raise questions we have no way to answer. I propose to be equally undisturbed by these equally mysterious mysteries.


In mathematical logic, a logical system has the soundness property if every formula that can be proved in the system is logically valid with respect to the semantics of the system. In most cases, this comes down to its rules having the property of preserving truth. The converse of soundness is known as completeness. A logical system with syntactic entailment ⊢ {\displaystyle \vdash } and semantic entailment ⊨ {\displaystyle \models } is sound if for any sequence A 1 , A 2 , .


In the CbD approach, developed by Ehtibar Dzhafarov, Janne Kujala, and colleagues, (non)contextuality is treated as a property of any system of random variables, defined as a set R = { R q c: q ∈ Q , q ≺ c , c ∈ C } {\displaystyle {\mathcal {R}}=\left\{R_{q}^{c}:q\in Q,q\prec c,c\in C\right\}} in which each random variable R q c {\displaystyle R_{q}^{c}} is labeled by its content q {\displaystyle q} , the property it measures, and its context c {\displaystyle c} , the set of recorded circumstances under which it is recorded (including but not limited to which other random variables it is recorded together with); q ≺ c {\displaystyle q\prec c} stands for " q {\displaystyle q} is measured in c {\displaystyle c} ". The variables within a context are jointly distributed, but variables from different contexts are stochastically unrelated, defined on different sample spaces. A (probabilistic) coupling of the system R {\displaystyle {\mathcal {R}}} is defined as a system S {\displaystyle S} in which all variables are jointly distributed and, in any context c {\displaystyle c} , R c = { R q c: q ∈ Q , q ≺ c } {\displaystyle R^{c}=\left\{R_{q}^{c}:q\in Q,q\prec c\right\}} and S c = { S q c: q ∈ Q , q ≺ c } {\displaystyle S^{c}=\left\{S_{q}^{c}:q\in Q,q\prec c\right\}} are identically distributed. The system is considered noncontextual if it has a coupling S {\displaystyle S} such that the probabilities Pr  {\displaystyle \Pr \left} are maximal possible for all contexts c , c ′ {\displaystyle c,c'} and contents q {\displaystyle q} such that q ≺ c , c ′ {\displaystyle q\prec c,c'} .


In pseudocode, the algorithm may be expressed as: function CountingSort(input, k) count ← array of k + 1 zeros output ← array of same length as input for i = 0 to length(input) - 1 do j = key(input) count = count + 1 for i = 1 to k do count = count + count for i = length(input) - 1 down to 0 do j = key(input) count = count - 1 output] = input return output Here input is the input array to be sorted, key returns the numeric key of each item in the input array, count is an auxiliary array used first to store the numbers of items with each key, and then (after the second loop) to store the positions where items with each key should be placed, k is the maximum value of the non-negative key values and output is the sorted output array. In summary, the algorithm loops over the items in the first loop, computing a histogram of the number of times each key occurs within the input collection. After that in the second loop, it performs a prefix sum computation on count in order to determine, for each key, the position range where the items having that key should be placed; i.e. items of key i {\displaystyle i} should be placed starting in position count. Finally, in the third loop, it loops over the items of input again, but in reverse order, moving each item into its sorted position in the output array.The relative order of items with equal keys is preserved here; i.e., this is a stable sort.


In the Berkeley RISC design, only eight registers out of a total of 64 are visible to the programs. The complete set of registers are known as the register file, and any particular set of eight as a window. The file allows up to eight procedure calls to have their own register sets. As long as the program does not call down chains longer than eight calls deep, the registers never have to be spilled, i.e. saved out to main memory or cache which is a slow process compared to register access.


In the configuration model, a giant component (GC) exists if ⟨ k 2 ⟩ − 2 ⟨ k ⟩ > 0 , {\displaystyle \langle k^{2}\rangle -2\langle k\rangle >0,} where ⟨ k ⟩ {\displaystyle \langle k\rangle } and ⟨ k 2 ⟩ {\displaystyle \langle k^{2}\rangle } are the first and second moments of the degree distribution. That means that, the critical threshold solely depends on quantities which are uniquely determined by the degree distribution p k {\displaystyle p_{k}} . Configuration model generates locally tree-like networks, meaning that any local neighborhood in such a network takes the form of a tree.


In the early 19th century, Carl Friedrich Gauss observed that non-zero integer solutions to homogeneous polynomial equations with rational coefficients exist if non-zero rational solutions exist.In the 1850s, Leopold Kronecker formulated the Kronecker–Weber theorem, introduced the theory of divisors, and made numerous other connections between number theory and algebra. He then conjectured his "liebster Jugendtraum" ("dearest dream of youth"), a generalization that was later put forward by Hilbert in a modified form as his twelfth problem, which outlines a goal to have number theory operate only with rings that are quotients of polynomial rings over the integers.


In the field of computer science, a pre-topological order or pre-topological ordering of a directed graph is a linear ordering of its vertices such that if there is a directed path from vertex u to vertex v and v comes before u in the ordering, then there is also a directed path from vertex v to vertex u.If the graph is a directed acyclic graph (DAG), topological orderings are pre-topological orderings and vice versa. In other cases, any pre-topological ordering gives a partial order. == References ==


However, this case is easy to detect and correct. With the modulus out of the way, the asymptotic complexity of the algorithm only depends on the multiplication algorithm used to square s at each step. The simple "grade-school" algorithm for multiplication requires O(p2) bit-level or word-level operations to square a p-bit number.


In the early days of telegraphy and radiotelegraphy, individual countries, and sometimes individual states, sometimes set their own regulations. For example, in the period around 1909, California required that "messages must, if practicable, be transmitted immediately on and in order of receipt; if not practicable, then in the following order:" Messages from public agents of the State or of the United States on public business. Messages for immediate publication in newspapers, and not for any secret use. Message relating to sickness or death. Other messages in the order of filing.


Performing this calculation in any software that used the floating-point coprocessor, such as Windows Calculator, would allow users to discover whether their Pentium chip was affected.The correct value of the calculation is: When converted to the hexadecimal value used by the processor, 4,195,835 = 0x4005FB and 3,145,727 = 0x2FFFFF. The '5' in 0x4005FB triggers the access to the 'empty' array cells. As a result, the value returned by a flawed Pentium processor is incorrect at or beyond four digits: which is actually the value of 4,195,579/3,145,727 =4,195,835 - 256/3,145,727.


In mathematics, in particular in computational algebra, the Berlekamp–Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus. As a consequence of Gauss's lemma, this amounts to solving the problem also over the rationals. The algorithm starts by finding factorizations over suitable finite fields using Hensel's lemma to lift the solution from modulo a prime p to a convenient power of p. After this the right factors are found as a subset of these. The worst case of this algorithm is exponential in the number of factors. Van Hoeij (2002) improved this algorithm by using the LLL algorithm, substantially reducing the time needed to choose the right subsets of mod p factors.


Every (conditional) line has zero or more asserted propositions on the right.In other words, natural deduction and sequent calculus systems are particular distinct kinds of Gentzen-style systems. Hilbert-style systems typically have a very small number of inference rules, relying more on sets of axioms. Gentzen-style systems typically have very few axioms, if any, relying more on sets of rules.


That is, the mapping information exists as set and it has a pair for each element in the domain. Of course for any set from some class, there is always the unique element of the singleton 1 {\displaystyle 1} , and so merely a chosen range being a set does not suffice to be granted a function set. In summary, in the set theory context the focus is on capturing particular total relations that are functional.


In the 1980s, Plantronics created a line of cordless products using infrared technology. Though the technology utilized was the same one being used by television remote controls, the link did not require a Federal Communications Commission (FCC) telecommunications approval. One of the first products used the infrared beam to create a communications link between a small transmitter and a base unit which was connected to the telephone network. This product was the first "echo-free" speakerphone for use in conference rooms. The small transmitter could be handheld or clipped to clothing to ensure a good pickup of the speaker's voice.


In mathematics and statistics, random projection is a technique used to reduce the dimensionality of a set of points which lie in Euclidean space. Random projection methods are known for their power, simplicity, and low error rates when compared to other methods. According to experimental results, random projection preserves distances well, but empirical results are sparse. They have been applied to many natural language tasks under the name random indexing.


When the system is described by a matrix rather than a vector, this problem can be written as min X ‖ A X − Y ‖ 2 + λ ‖ X ‖ 2 , {\displaystyle \min _{X}\|AX-Y\|^{2}+\lambda \|X\|^{2},} where the vector norm enforcing a regularization penalty on x {\displaystyle x} has been extended to a matrix norm on X {\displaystyle X} . Matrix regularization has applications in matrix completion, multivariate regression, and multi-task learning. Ideas of feature and group selection can also be extended to matrices, and these can be generalized to the nonparametric case of multiple kernel learning.


In mathematics, the Gauss–Kuzmin distribution is a discrete probability distribution that arises as the limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1). The distribution is named after Carl Friedrich Gauss, who derived it around 1800, and Rodion Kuzmin, who gave a bound on the rate of convergence in 1929. It is given by the probability mass function p ( k ) = − log 2  ( 1 − 1 ( 1 + k ) 2 ) . {\displaystyle p(k)=-\log _{2}\left(1-{\frac {1}{(1+k)^{2}}}\right)~.}


In probability theory, Slutsky’s theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables.The theorem was named after Eugen Slutsky. Slutsky's theorem is also attributed to Harald Cramér.


{\displaystyle e\cdot e=e.} The similarly defined trivial monoid is also a group since its only element is its own inverse, and is hence the same as the trivial group. The trivial group is distinct from the empty set, which has no elements, hence lacks an identity element, and so cannot be a group.


In mathematics and especially game theory, the airport problem is a type of fair division problem in which it is decided how to distribute the cost of an airport runway among different players who need runways of different lengths. The problem was introduced by S. C. Littlechild and G. Owen in 1973. Their proposed solution is: Divide the cost of providing the minimum level of required facility for the smallest type of aircraft equally among the number of landings of all aircraft Divide the incremental cost of providing the minimum level of required facility for the second smallest type of aircraft (above the cost of the smallest type) equally among the number of landings of all but the smallest type of aircraft. Continue thus until finally the incremental cost of the largest type of aircraft is divided equally among the number of landings made by the largest aircraft type.The authors note that the resulting set of landing charges is the Shapley value for an appropriately defined game.


In the fields of computational linguistics and natural language processing (NLP), esp. corpus linguistics and machine-learned NLP, it is common to disregard hapax legomena (and sometimes other infrequent words), as they are likely to have little value for computational techniques. This disregard has the added benefit of significantly reducing the memory use of an application, since, by Zipf's law, many words are hapax legomena.


In mobile telecommunications, inter-cell interference coordination (ICIC) techniques apply restrictions to the radio resource management (RRM) block, improving favorable channel conditions across subsets of users that are severely impacted by the interference, and thus attaining high spectral efficiency. This coordinated resource management can be achieved through fixed, adaptive or real-time coordination with the help of additional inter-cell signaling in which the signaling rate can vary accordingly. In general, inter-cell signaling refers to the communication interface among neighboring cells and the received measurement message reports from user equipments (UEs).


In some cases, a file system may not make use of a storage device but can be used to organize and represent access to any data, whether it is stored or dynamically generated (e.g. procfs).


In the first step, messages are passed inwards: starting at the leaves, each node passes a message along the (unique) edge towards the root node. The tree structure guarantees that it is possible to obtain messages from all other adjoining nodes before passing the message on. This continues until the root has obtained messages from all of its adjoining nodes. The second step involves passing the messages back out: starting at the root, messages are passed in the reverse direction. The algorithm is completed when all leaves have received their messages.


This can also be seen as a methodology for writing and structuring large theories: start with a theory, T 0 {\displaystyle T_{0}} , that is known (or assumed) to be consistent, and successively build conservative extensions T 1 {\displaystyle T_{1}} , T 2 {\displaystyle T_{2}} , ... of it. Recently, conservative extensions have been used for defining a notion of module for ontologies: if an ontology is formalized as a logical theory, a subtheory is a module if the whole ontology is a conservative extension of the subtheory. An extension which is not conservative may be called a proper extension.


In some models (standard linear regression, in particular), the equations for each of the data points i = 1, ..., n are stacked together and written in vector form as y = X β + ε , {\displaystyle \mathbf {y} =\mathbf {X} {\boldsymbol {\beta }}+{\boldsymbol {\varepsilon }},\,} where y = ( y 1 y 2 ⋮ y n ) , X = ( x 1 ′ x 2 ′ ⋮ x n ′ ) = ( x 11 ⋯ x 1 p x 21 ⋯ x 2 p ⋮ ⋱ ⋮ x n 1 ⋯ x n p ) , β = ( β 1 ⋮ β p ) , ε = ( ε 1 ε 2 ⋮ ε n ) . {\displaystyle \mathbf {y} ={\begin{pmatrix}y_{1}\\y_{2}\\\vdots \\y_{n}\end{pmatrix}},\quad \mathbf {X} ={\begin{pmatrix}\mathbf {x} '_{1}\\\mathbf {x} '_{2}\\\vdots \\\mathbf {x} '_{n}\end{pmatrix}}={\begin{pmatrix}x_{11}&\cdots &x_{1p}\\x_{21}&\cdots &x_{2p}\\\vdots &\ddots &\vdots \\x_{n1}&\cdots &x_{np}\end{pmatrix}},\quad {\boldsymbol {\beta }}={\begin{pmatrix}\beta _{1}\\\vdots \\\beta _{p}\end{pmatrix}},\quad {\boldsymbol {\varepsilon }}={\begin{pmatrix}\varepsilon _{1}\\\varepsilon _{2}\\\vdots \\\varepsilon _{n}\end{pmatrix}}.} The matrix X is known as the design matrix and encodes all known information about the independent variables.


In multi-exponential fitting, the time-resolved curves are fitted with an exponential decay model to determine the decay constants. While this method is straightforward, it has low accuracy.


Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler.Uses of Lagrange polynomials include the Newton–Cotes method of numerical integration, Shamir's secret sharing scheme in cryptography, and Reed–Solomon error correction in coding theory. For equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation.


In signal processing, multidimensional signal processing covers all signal processing done using multidimensional signals and systems. While multidimensional signal processing is a subset of signal processing, it is unique in the sense that it deals specifically with data that can only be adequately detailed using more than one dimension. In m-D digital signal processing, useful data is sampled in more than one dimension. Examples of this are image processing and multi-sensor radar detection.


In statistics and natural language processing, a topic model is a type of statistical model for discovering the abstract "topics" that occur in a collection of documents. Topic modeling is a frequently used text-mining tool for discovery of hidden semantic structures in a text body. Intuitively, given that a document is about a particular topic, one would expect particular words to appear in the document more or less frequently: "dog" and "bone" will appear more often in documents about dogs, "cat" and "meow" will appear in documents about cats, and "the" and "is" will appear approximately equally in both. A document typically concerns multiple topics in different proportions; thus, in a document that is 10% about cats and 90% about dogs, there would probably be about 9 times more dog words than cat words.


In mathematics, the Hamiltonian cycle polynomial of an n×n-matrix is a polynomial in its entries, defined as ham  ( A ) = ∑ σ ∈ H n ∏ i = 1 n a i , σ ( i ) {\displaystyle \operatorname {ham} (A)=\sum _{\sigma \in H_{n}}\prod _{i=1}^{n}a_{i,\sigma (i)}} where H n {\displaystyle H_{n}} is the set of n-permutations having exactly one cycle. This is an algebraic option useful, in a number of cases, for determining the existence of a Hamiltonian cycle in a directed graph. It is a generalization of the number of Hamiltonian cycles of a digraph as the sum of the products of its Hamiltonian cycles' arc weights (all of which equal unity) for weighted digraphs with arc weights taken from a given commutative ring. In the meantime, for an undirected weighted graph the sum of the products of the edge weights of its Hamiltonian cycles containing any fixed edge (i,j) can be expressed as the product of the weight of (i,j) and the Hamiltonian cycle polynomial of a matrix received from its weighted adjacency matrix via subjecting its rows and columns to any permutation mapping i to 1 and j to 2 and then removing its 1-st row and 2-nd column.


In statistics, a k-th percentile, also known as percentile score or centile, is a score below which a given percentage k of scores in its frequency distribution falls ("exclusive" definition) or a score at or below which a given percentage falls ("inclusive" definition). Percentiles are expressed in the same unit of measurement as the input scores, not in percent; for example, if the scores refer to human weight, the corresponding percentiles will be expressed in kilograms or pounds. In the limit of an infinite sample size, the percentile approximates the percentile function, the inverse of the cumulative distribution function. Percentiles are a type of quantiles, obtained adopting a subdivision into 100 groups.


The improvements included magnetic (non-mercury) core memory of 2000 to 10000 words, UNISERVO II tape drives, which could use either the old UNIVAC I metal tapes or the new PET film tapes, and some circuits that were transistorized (although it was still a vacuum-tube computer). It was fully compatible with existing UNIVAC I programs for both code and data. The UNIVAC II also added some instructions to the UNIVAC I's instruction set.


x {\displaystyle \exists !x} means "there exists exactly one x".In any case (for any function), the following holds: ∀ x ∈ X , ∃ ! y ∈ Y such that y = f ( x ) . {\displaystyle \forall x\in X,\exists !y\in Y{\text{ such that }}y=f(x).} An injective function need not be surjective (not all elements of the codomain may be associated with arguments), and a surjective function need not be injective (some images may be associated with more than one argument). The four possible combinations of injective and surjective features are illustrated in the adjacent diagrams.


In phonetics, a tilde is used as a diacritic that is placed above a letter, below it or superimposed onto the middle of it: A tilde above a letter indicates nasalization, e.g. , . A tilde superimposed onto the middle of a letter indicates velarization or pharyngealization, e.g. , . If no precomposed Unicode character exists, the Unicode character U+0334 ◌̴ COMBINING TILDE OVERLAY can be used to generate one. A tilde below a letter indicates laryngealisation, e.g. . If no precomposed Unicode character exists, the Unicode character U+0330 ◌̰ COMBINING TILDE BELOW can be used to generate one.


In proof theory, a branch of mathematical logic, proof mining (or proof unwinding) is a research program that studies or analyzes formalized proofs, especially in analysis, to obtain explicit bounds, ranges or rates of convergence from proofs that, when expressed in natural language, appear to be nonconstructive. This research has led to improved results in analysis obtained from the analysis of classical proofs.


In 2015, the IETF upgraded its weak "informational" recommendation of 1998, that datagram switching nodes perform active queue management (AQM), to make it a stronger and more detailed "best current practice" recommendation. While the initial datagram queueing model was simple to implement and needed no more tuning than queue lengths, support of more sophisticated and parametrized mechanisms were found necessary "to improve and preserve Internet performance" (RED, ECN etc.). Further research on the subject was also called for, with a list of identified items.


That is, for any property P ( k ) {\displaystyle P(k)} of the integer k {\displaystyle k} , one can rewrite the restricted sum ∑ k: P ( k ) f ( k ) {\displaystyle \sum _{k:P(k)}f(k)} in the unrestricted form ∑ k f ( k ) ⋅  {\displaystyle \sum _{k}f(k)\cdot } . With this convention, f ( k ) {\displaystyle f(k)} does not need to be defined for the values of k for which the Iverson bracket equals 0; that is, a summand f ( k )  {\displaystyle f(k)} must evaluate to 0 regardless of whether f ( k ) {\displaystyle f(k)} is defined. The notation was originally introduced by Kenneth E. Iverson in his programming language APL, though restricted to single relational operators enclosed in parentheses, while the generalisation to arbitrary statements, notational restriction to square brackets, and applications to summation, was advocated by Donald Knuth to avoid ambiguity in parenthesized logical expressions.


This was demonstrated more formally and in greater detail by Xavier Défago, et al.A fundamental result in distributed computing is that achieving consensus in asynchronous systems in which even one crash failure can occur is impossible in the most general case. This was shown in 1985 by Michael J. Fischer, Nancy Lynch, and Mike Paterson, and is sometimes called the FLP result. Since consensus and atomic broadcast are equivalent, FLP applies also to atomic broadcast. The FLP result does not prohibit the implementation of atomic broadcast in practice, but it does require making less stringent assumptions than FLP in some respect, such as about processor and communication timings.


Thus, the inventory is grouped into three categories (A, B, and C) in order of their estimated importance. 'A' items are very important for an organization.


In the case of queries that read data from the database, the SPARQL language specifies four different query variations for different purposes. SELECT query Used to extract raw values from a SPARQL endpoint, the results are returned in a table format. CONSTRUCT query Used to extract information from the SPARQL endpoint and transform the results into valid RDF.


The Commodore 64 used x5C (ASCII: \) while the Oric used x5F (ASCII: _). IBM's EBCDIC code page 037 uses xB1 for the £ while its code page 285 uses x5B. ICL's 1900-series mainframes used a six-bit (64-position character set) encoding for characters, loosely based on BS 4730, with the £ symbol represented as octal 23 (hex 13, dec 19).


r is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface). ℓ is the length of the object to or over which the torque is being applied. φ (phi) is the angle of twist in radians. G is the shear modulus, also called the modulus of rigidity, and is usually given in gigapascals (GPa), lbf/in2 (psi), or lbf/ft2 or in ISO units N/mm2. The product JTG is called the torsional rigidity wT.


In mathematics, the Jessen–Wintner theorem, introduced by Jessen and Wintner (1935), asserts that a random variable of Jessen–Wintner type, meaning the sum of an almost surely convergent series of independent discrete random variables, is of pure type.


In the Celtic languages there is a distinction between the so-called substantive verb, used when the predicate is an adjective phrase or prepositional phrase, and the so-called copula, used when the predicate is a noun. The conjugation of the Old Irish and Middle Welsh verbs is as follows: The forms of the Old Irish present tense of the substantive verb, as well as Welsh taw, come from the PIE root *stā-. The other forms are from the roots *es- and *bhū-. Welsh mae originally meant "here is" (cf. yma 'here').


In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the perfect fifth with ratio 3/2 (equivalent to 31/ 21) and the perfect fourth with ratio 4/3 (equivalent to 22/ 31) are Pythagorean intervals. All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system. However, some Pythagorean intervals are also used in other tuning systems. For instance, the above-mentioned Pythagorean perfect fifth and fourth are also used in just intonation.


In probability theory, a normalizing constant is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e.g., to make it a probability density function or a probability mass function.


In statistics and machine learning, double descent is the phenomenon where a statistical model with a small number of parameters and a model with an extremely large number of parameters have a small error, but a model whose number of parameters is about the same as the number of data points used to train the model will have a large error. It was discovered around 2018 when researchers were trying to reconcile the bias-variance tradeoff in classical statistics, which states that having too many parameters will yield an extremely large error, with the 2010s empirical observation of machine learning practitioners that the larger models are, the better they work. The scaling behavior of double descent has been found to follow a broken neural scaling law functional form.


19. Specifying a series of logical operators or inferential system which captures all or most cases to which the concept applies (algorithm). 20.


In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized by the statistician Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates.


A sticking knife scores points. The thrower must be standing at least a set distance away from the target, with higher distances for more challenging events. IKTHOF keeps a ranking of its members based on their performance during these sponsored competitions. EuroThrowers maintains a register of the world records, and for each championship publishes the full scores together with the meetings' reports.


In terms of sieve theory the Turán sieve is of combinatorial type: deriving from a rudimentary form of the inclusion–exclusion principle. The result gives an upper bound for the size of the sifted set. Let A be a set of positive integers ≤ x and let P be a set of primes. For each p in P, let Ap denote the set of elements of A divisible by p and extend this to let Ad be the intersection of the Ap for p dividing d, when d is a product of distinct primes from P. Further let A1 denote A itself.


In telecommunication, the term means a record of both completed and attempted accesses and service, or data forming a logical path linking a sequence of events, used to trace the transactions that have affected the contents of a record. In information or communications security, information audit means a chronological record of system activities to enable the reconstruction and examination of the sequence of events and/or changes in an event. Information put away or transmitted in paired structure that might be depended upon in court. An audit trail is a progression of records of computer data about a working framework, an application, or client exercises.


This choice is motivated by their status as the driving force behind the development of algebraic number theory. Since the late nineteenth century, binary quadratic forms have given up their preeminence in algebraic number theory to quadratic and more general number fields, but advances specific to binary quadratic forms still occur on occasion. Pierre Fermat stated that if p is an odd prime then the equation p = x 2 + y 2 {\displaystyle p=x^{2}+y^{2}} has a solution iff p ≡ 1 ( mod 4 ) {\displaystyle p\equiv 1{\pmod {4}}} , and he made similar statement about the equations p = x 2 + 2 y 2 {\displaystyle p=x^{2}+2y^{2}} , p = x 2 + 3 y 2 {\displaystyle p=x^{2}+3y^{2}} , p = x 2 − 2 y 2 {\displaystyle p=x^{2}-2y^{2}} and p = x 2 − 3 y 2 {\displaystyle p=x^{2}-3y^{2}} .


In nonstandard analysis, a hyperinteger n is a hyperreal number that is equal to its own integer part. A hyperinteger may be either finite or infinite. A finite hyperinteger is an ordinary integer. An example of an infinite hyperinteger is given by the class of the sequence (1, 2, 3, ...) in the ultrapower construction of the hyperreals.


Scarf's fixed-point method was a break-through in the mathematics of computation generally, and specifically in optimization and computational economics. Later researchers continued to develop iterative methods for computing fixed-points, both for topological models like Scarf's and for models described by functions with continuous second derivatives or convexity or both. Of course, "global Newton methods" for essentially convex and smooth functions and path-following methods for diffeomorphisms converged faster than did robust algorithms for continuous functions, when the smooth methods are applicable.


In the early days of computational discourse, the study of discourse relations was closely entangled with the study of discourse structure, so that theories such as RST and SDRT effectively postulate tree structures. (SDRT permits relations between independent nodes in a tree, but the tree still defines accessibility domains.) For practical annotation, however, this was felt to be a disadvantage because discourse relations could only be annotated after the global coherence of a particular text has been understood, and annotators disagreed widely (as already observed by Mann and Thompson 1987). For theoretical reasons, the tree model was criticized because at least some types of discourse relations (especially what Hobbs referred to as elaboration) was apparently not constrained by tree structures but could connect elements disconnected in the tree (Knott et al. 2001).This has been the motivation to perform the annotation of discourse relations independently from discourse structure, and this "shallow" model of discourse coherence could be annotated from local context alone.


In systems design, a fail-fast system is one which immediately reports at its interface any condition that is likely to indicate a failure. Fail-fast systems are usually designed to stop normal operation rather than attempt to continue a possibly flawed process. Such designs often check the system's state at several points in an operation, so any failures can be detected early. The responsibility of a fail-fast module is detecting errors, then letting the next-highest level of the system handle them.


Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the name Schubfachprinzip ("drawer principle" or "shelf principle").The principle has several generalizations and can be stated in various ways. In a more quantified version: for natural numbers k and m, if n = km + 1 objects are distributed among m sets, then the pigeonhole principle asserts that at least one of the sets will contain at least k + 1 objects. For arbitrary n and m, this generalizes to k + 1 = ⌊ ( n − 1 ) / m ⌋ + 1 = ⌈ n / m ⌉ , {\displaystyle k+1=\lfloor (n-1)/m\rfloor +1=\lceil n/m\rceil ,} where ⌊ ⋯ ⌋ {\displaystyle \lfloor \cdots \rfloor } and ⌈ ⋯ ⌉ {\displaystyle \lceil \cdots \rceil } denote the floor and ceiling functions, respectively.


In some covering problems, the covering should satisfy some additional requirements. In particular, in the rainbow covering problem, each of the original objects has a "color", and it is required that the covering contains exactly one (or at most one) object of each color. Rainbow covering was studied e.g. for covering points by intervals: There is a set J of n colored intervals on the real line, and a set P of points on the real line. A subset Q of J is called a rainbow set if it contains at most a single interval of each color.


In some theories of formal semantics, including David Dowty's, stative verbs have a logical form that is the lambda expression λ ( x ):  {\displaystyle \lambda (x):\ } Apart from Dowty, Z. Vendler and C. S. Smith have also written influential work on aspectual classification of verbs.


In telecommunications, bit inversion means the changing of the state of a bit to the opposite state, i.e. the changing of a 0 bit to 1 or of a 1 bit to 0. It also refers to the changing of a state representing a given bit to the opposite state. Source: Federal Standard 1037C and MIL-STD-188


If they have the representation I ≡ ⟨ f 1 , … , f p ⟩ {\displaystyle I\equiv \langle f_{1},\ldots ,f_{p}\rangle } and J ≡ ⟨ g 1 , … , g q ⟩ , {\displaystyle J\equiv \langle g_{1},\ldots ,g_{q}\rangle ,} f i {\displaystyle f_{i}} , g j ∈ D {\displaystyle g_{j}\in {\mathcal {D}}} for all i {\displaystyle i} and j {\displaystyle j} , the sum is generated by the union of the generators of I {\displaystyle I} and J {\displaystyle J} . The solution space of the equations corresponding to Gcrd  ( I , J ) {\displaystyle \operatorname {Gcrd} (I,J)} is the intersection of the solution spaces of its arguments. The least common left multiple (Lclm) or left intersection of two ideals I {\displaystyle I} and J {\displaystyle J} is the largest ideal with the property that it is contained both in I {\displaystyle I} and J {\displaystyle J} .


In mathematics, a logical matrix may be described as d-disjunct and/or d-separable. These concepts play a pivotal role in the mathematical area of non-adaptive group testing. In the mathematical literature, d-disjunct matrices may also be called super-imposed codes or d-cover-free families.According to Chen and Hwang (2006), A matrix is said to be d-separable if no two sets of d columns have the same boolean sum. A matrix is said to be d ¯ {\displaystyle {\overline {d}}} -separable (that's d with an overline) if no two sets of d-or-fewer columns have the same boolean sum.


In order to ensure that CDSs are of high quality, multiple quality assurance (QA) tests are performed (Table 1). All tests are performed following the annotation comparison step of each CCDS build and are independent of individual annotation group QA tests performed prior to the annotation comparison. Annotations that fail QA tests undergo a round of manual checking that may improve results or reach a decision to reject annotation matches based on QA failure.


The statement has a short proof in a more powerful system: in fact the proof given in the previous paragraph is a proof in the system of Peano arithmetic plus the statement "Peano arithmetic is consistent" (which, per the incompleteness theorem, cannot be proved in Peano arithmetic). In this argument, Peano arithmetic can be replaced by any more powerful consistent system, and a googolplex can be replaced by any number that can be described concisely in the system. Harvey Friedman found some explicit natural examples of this phenomenon, giving some explicit statements in Peano arithmetic and other formal systems whose shortest proofs are ridiculously long (Smoryński 1982).


The simulation presumed a complete graph with random relations having a random unbalanced triad selected for transformation. The evolution of the signed graph with N nodes under this process is studied and simulated to describe the stationary density of friendly links. Balance theory has been severely challenged, especially in its application to large systems, on the theoretical ground that friendly relations tie a society together, while a society divided into two camps of enemies would be highly unstable. Experimental studies have also provided only weak confirmation of the predictions of structural balance theory.


In mathematics, a twisted polynomial is a polynomial over a field of characteristic p {\displaystyle p} in the variable τ {\displaystyle \tau } representing the Frobenius map x ↦ x p {\displaystyle x\mapsto x^{p}} . In contrast to normal polynomials, multiplication of these polynomials is not commutative, but satisfies the commutation rule τ x = x p τ {\displaystyle \tau x=x^{p}\tau } for all x {\displaystyle x} in the base field. Over an infinite field, the twisted polynomial ring is isomorphic to the ring of additive polynomials, but where multiplication on the latter is given by composition rather than usual multiplication. However, it is often easier to compute in the twisted polynomial ring — this can be applied especially in the theory of Drinfeld modules.


This is famous as the Molloy-Reed criterion. The intuition behind this criterion is that if the giant component (GC) exists, then the average degree of a randomly chosen vertex i {\displaystyle i} in a connected component should be at least 2. Molloy-Reed criterion can also be expressed as: ∑ i k i ( k i − 2 ) > 0 , {\displaystyle \sum _{i}k_{i}(k_{i}-2)>0,} which implies that, although the size of the GC may depend on p 0 {\displaystyle p_{0}} and p 2 {\displaystyle p_{2}} , the number of nodes of degree 0 and 2 have no contribution in the existence of the giant component.


"Having arisen from the fields of knowledge representation, description logic and formal ontology, Semantic Web languages have a closer relationship to philosophical ontology than do conventional programming languages such as Java or Python. Accordingly, the nature of metaclasses is informed by philosophical notions such as abstract objects, the abstract and concrete, and type-token distinction.


In metadata, a vocabulary-based transformation (VBT) is a transformation aided by the use of a semantic equivalence statements within a controlled vocabulary. Many organizations today require communication between two or more computers. Although many standards exist to exchange data between computers such as HTML or email, there is still much structured information that needs to be exchanged between computers that is not standardized. The process of mapping one source of data into another is often a slow and labor-intensive process. VBT is a possible way to avoid much of the time and cost of manual data mapping using traditional extract, transform, load technologies.


In order to sterilize items effectively, it is important to use optimal parameters when running an autoclave cycle. A 2017 study performed by the Johns Hopkins Hospital biocontainment unit tested the ability of pass-through autoclaves to decontaminate loads of simulated biomedical waste when run on the factory default setting. The study found that 18 of 18 (100%) mock patient loads (6 PPE, 6 linen, and 6 liquid loads) passed sterilization tests with the optimized parameters compared to only 3 of 19 (16%) mock loads that passed with use of the factory default settings.There are physical, chemical, and biological indicators that can be used to ensure that an autoclave reaches the correct temperature for the correct amount of time. If a non-treated or improperly treated item can be confused for a treated item, then there is the risk that they will become mixed up, which, in some areas such as surgery, is critical.


In mathematics, 0.999... (also written as 0.9 or 0..9) denotes the repeating decimal consisting of an unending sequence of 9s after the decimal point. This repeating decimal represents the smallest number no less than every decimal number in the sequence (0.9, 0.99, 0.999, ...); that is, the supremum of this sequence. This number is equal to 1. In other words, "0.999..." is not "almost exactly" or "very, very nearly but not quite" 1 – rather, "0.999..." and "1" represent exactly the same number.


In mathematics, Property B is a certain set theoretic property. Formally, given a finite set X, a collection C of subsets of X has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z. The property gets its name from mathematician Felix Bernstein, who first introduced the property in 1908.Property B is equivalent to 2-coloring the hypergraph described by the collection C. A hypergraph with property B is also called 2-colorable. : 468 Sometimes it is also called bipartite, by analogy to the bipartite graphs. Property B is often studied for uniform hypergraphs (set systems in which all subsets of the system have the same cardinality) but it has also been considered in the non-uniform case.The problem of checking whether a collection C has Property B is called the set splitting problem.


Otherwise, the jurisdiction must vote to update its code and bring its inspectors up to date on the changes being made to the code. Most jurisdictions update their codes regularly to avoid backlash from architects and building contractors who respond to outdated codes by seeking variances to permit the use of more efficient design solutions and technologies accepted in areas using more modern codes. The model codes may either be adopted outright as the building codes for a jurisdiction, or they may be adopted with amendments or additional rules.


In terrestrial radio and television broadcasting, centralcasting refers to the use of systems automation by which customised signals for broadcast by multiple individual stations may be created at one central facility.


Hartmanis' model – quite similar to Melzak's (1961) model – uses two and three-register adds and subtracts and two parameter copies; Cook and Reckhow's model reduce the number of parameters (registers called out in the program instructions) to one call-out by use of an accumulator "AC". The solution in a nutshell: Design our machine/model with unbounded indirection – provide an unbounded "address" register that can potentially name (call out) any register no matter how many there are. For this to work, in general, the unbounded register requires an ability to be cleared and then incremented (and, possibly, decremented) by a potentially infinite loop.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 3578, 13578, 34578, and 134578 are the patterns related to Braille pattern dots-2346, since the two additional dots of kantenji patterns 02346, 23467, and 023467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Femtocells are an alternative way to deliver the benefits of fixed–mobile convergence (FMC). The distinction is that most FMC architectures require a new dual-mode handset which works with existing unlicensed spectrum home/enterprise wireless access points, while a femtocell-based deployment will work with existing handsets but requires the installation of a new access point that uses licensed spectrum.


In mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator T: X → Y {\displaystyle T:X\rightarrow Y} acting between Hilbert spaces X {\displaystyle X} and Y {\displaystyle Y} , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator T ∗ T {\displaystyle T^{*}T} (where T ∗ {\displaystyle T^{*}} denotes the adjoint of T {\displaystyle T} ). The singular values are non-negative real numbers, usually listed in decreasing order (σ1(T), σ2(T), …). The largest singular value σ1(T) is equal to the operator norm of T (see Min-max theorem). If T acts on Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , there is a simple geometric interpretation for the singular values: Consider the image by T {\displaystyle T} of the unit sphere; this is an ellipsoid, and the lengths of its semi-axes are the singular values of T {\displaystyle T} (the figure provides an example in R 2 {\displaystyle \mathbb {R} ^{2}} ).


In the course of time many network queueing disciplines have been developed. Each of these provides specific reordering or dropping of network packets inside various transmit or receive buffers. Queuing disciplines are commonly used as attempts to compensate for various networking conditions, like reducing the latency for certain classes of network packets, and are generally used as part of QoS measures.Examples of algorithms suitable for managing network traffic include: Several of the above have been implemented as Linux kernel modules and are freely available.