Similarly, a "300 GB" hard drive can be expected to offer only slightly more than 300×109 = 300000000000, bytes, not 300 × 230 (which would be about 322×109 bytes or "322 GB"). The first terabyte (SI prefix, 1000000000000 bytes) hard disk drive was introduced in 2007. Decimal prefixes were generally used by information processing publications when comparing hard disk capacities.Users must be aware that some programs and operating systems, such as earlier versions of Microsoft Windows and MacOS, may use "MB" and "GB" to denote binary prefixes even when displaying disk drive capacities. Thus, for example, the capacity of a "10 MB" (decimal "M") disk drive could be reported as "9.56 MB", and that of a "300 GB" drive as "279.4 GB". Good software and documentation should specify clearly whether "K", "M", "G" mean binary or decimal multipliers.


In telecommunication, transmit-after-receive time delay is the time interval from removal of RF energy at the local receiver input until the local transmitter is automatically keyed on and the transmitted rf signal amplitude has increased to 90% of its steady-state value. An Exception: High-frequency (HF) transceiver equipment is normally not designed with an interlock between receiver squelch and transmitter on-off key. The transmitter can be keyed on at any time, independent of whether or not a signal is being received at the receiver input.


In the following descriptions, α, β, and γ represent any string of terminals/nonterminals (including the empty string), X and Y represent single nonterminals, and a represents a terminal symbol. Earley's algorithm is a top-down dynamic programming algorithm. In the following, we use Earley's dot notation: given a production X → αβ, the notation X → α • β represents a condition in which α has already been parsed and β is expected.


The player with the most accurate predictions wins the top prize, or a share of it if more than one player has these predictions. In addition, there is a special £3,000,000 prize or share of it for correctly predicting the nine score draws (draws of 1-1 or higher) when these are the only score draws on the coupon. Players can win large cash prizes in a variety of other ways, under a points-based scoring system.


The above procedure is repeated until the solution of constraint equations, σ k ( t + Δ t ) {\displaystyle \sigma _{k}(t+\Delta t)} , converges to a prescribed tolerance of a numerical error. Although there are a number of algorithms to compute the Lagrange multipliers, these difference is rely only on the methods to solve the system of equations. For this methods, quasi-Newton methods are commonly used.


In object-oriented programming, sequential coupling (also known as temporal coupling) is a form of coupling where a class requires its methods to be called in a particular sequence. This may be an anti-pattern, depending on context. Methods whose name starts with Init, Begin, Start, etc. may indicate the existence of sequential coupling.


It provides a user interface, and reads and writes to the post office files directly in order to send, access, and manage email messages. This arrangement is called a "shared-file mail system" (which was also implemented later in competing products such as Microsoft Mail). This is in contrast to a "client/server mail system" which involves a mail client application interacting with a mail server application (the latter then being the focal point of message handling).


In the four color theorem, Kempe was able to prove that all graphs necessarily have a vertex of five or less, or containing a vertex that touches five other vertices, called its neighbors. As such, to prove the four color theorem, it is sufficient to prove that vertices of five or less were all four-colorable. Kempe was able to prove the case of degree four and give a partial proof of degree five using Kempe chains.In this case, Kempe chains are used to prove the idea that no vertex has to be touching four colors different from itself, i.e., having a degree of 4. First, one can create a graph with a vertex v and four vertices as neighbors.


In mathematics, the splitting principle is a technique used to reduce questions about vector bundles to the case of line bundles. In the theory of vector bundles, one often wishes to simplify computations, say of Chern classes. Often computations are well understood for line bundles and for direct sums of line bundles. In this case the splitting principle can be quite useful.


A positive impact of coalescing on inference graph colorability is, for example, when a node interferes with both nodes being coalesced, the degree of the node is reduced by one which leads to improving the overall colorability of the interference graph.There are several coalescing heuristics available: Aggressive coalescing it was first introduced by Chaitin original register allocator. This heuristic aims at coalescing any non-interfering, copy-related nodes.


In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m. In the standard notation of modular arithmetic this congruence is written as a x ≡ 1 ( mod m ) , {\displaystyle ax\equiv 1{\pmod {m}},} which is the shorthand way of writing the statement that m divides (evenly) the quantity ax − 1, or, put another way, the remainder after dividing ax by the integer m is 1. If a does have an inverse modulo m, then there are an infinite number of solutions of this congruence, which form a congruence class with respect to this modulus. Furthermore, any integer that is congruent to a (i.e., in a's congruence class) has any element of x's congruence class as a modular multiplicative inverse. Using the notation of w ¯ {\displaystyle {\overline {w}}} to indicate the congruence class containing w, this can be expressed by saying that the modulo multiplicative inverse of the congruence class a ¯ {\displaystyle {\overline {a}}} is the congruence class x ¯ {\displaystyle {\overline {x}}} such that: a ¯ ⋅ m x ¯ = 1 ¯ , {\displaystyle {\overline {a}}\cdot _{m}{\overline {x}}={\overline {1}},} where the symbol ⋅ m {\displaystyle \cdot _{m}} denotes the multiplication of equivalence classes modulo m. Written in this way, the analogy with the usual concept of a multiplicative inverse in the set of rational or real numbers is clearly represented, replacing the numbers by congruence classes and altering the binary operation appropriately.


In social choice theory, tournaments naturally arise as majority relations of preference profiles. Let A {\displaystyle A} be a finite set of alternatives, and consider a list P = ( ≻ 1 , … , ≻ n ) {\displaystyle P=(\succ _{1},\dots ,\succ _{n})} of linear orders over A {\displaystyle A} . We interpret each order ≻ i {\displaystyle \succ _{i}} as the preference ranking of a voter i {\displaystyle i} . The (strict) majority relation ≻ maj {\displaystyle \succ _{\text{maj}}} of P {\displaystyle P} over A {\displaystyle A} is then defined so that a ≻ maj b {\displaystyle a\succ _{\text{maj}}b} if and only if a majority of the voters prefer a {\displaystyle a} to b {\displaystyle b} , that is | { i ∈ : a ≻ i b } | > | { i ∈ : b ≻ i a } | {\displaystyle |\{i\in :a\succ _{i}b\}|>|\{i\in :b\succ _{i}a\}|} .


In probability theory and statistics, a cross-covariance matrix is a matrix whose element in the i, j position is the covariance between the i-th element of a random vector and j-th element of another random vector. A random vector is a random variable with multiple dimensions. Each element of the vector is a scalar random variable. Each element has either a finite number of observed empirical values or a finite or infinite number of potential values.


δ i k p k M  ( l ) ⟩ ⟩ = ( 2 l + 2 k + 1 ) ! ! ⟨ ⟨ M  ( l − 2 k ) ⟩ ⟩ {\displaystyle {\hat {T}}r_{1}...{\hat {T}}r_{k}\left\langle \left\langle \delta _{i_{1}p_{1}}...\delta _{i_{k}p_{k}}\mathbf {M} _{}^{(l)}\right\rangle \right\rangle =(2l+2k+1)! !\left\langle \left\langle \mathbf {M} _{}^{(l-2k)}\right\rangle \right\rangle } .


The resulting function behaves like a while or a for loop in an imperative language. Used in this way, the Y combinator implements simple recursion. In the lambda calculus, it is not possible to refer to the definition of a function inside its own body by name.


To distinguish this type of vector from those described above, it is common and useful in physics to denote an element ϕ {\displaystyle \phi } of an abstract complex vector space as a ket | ϕ ⟩ {\displaystyle |\phi \rangle } , to refer to it as a "ket" rather than as a vector, and to pronounce it "ket- ϕ {\displaystyle \phi } " or "ket-A" for |A⟩. Symbols, letters, numbers, or even words—whatever serves as a convenient label—can be used as the label inside a ket, with the | ⟩ {\displaystyle |\ \rangle } making clear that the label indicates a vector in vector space.


The most familiar example of a paired difference test occurs when subjects are measured before and after a treatment. Such a "repeated measures" test compares these measurements within subjects, rather than across subjects, and will generally have greater power than an unpaired test. Another example comes from matching cases of a disease with comparable controls.


In pattern recognition, information retrieval, object detection and classification (machine learning), precision and recall are performance metrics that apply to data retrieved from a collection, corpus or sample space. Precision (also called positive predictive value) is the fraction of relevant instances among the retrieved instances. Written as a formula: r e l e v a n t _ r e t r i e v e d _ i n s t a n c e s a l l _ r e t r i e v e d _ i n s t a n c e s {\displaystyle {\frac {relevant\_retrieved\_instances}{all\_{\mathbf {retrieved}}\_instances}}} . Recall (also known as sensitivity) is the fraction of relevant instances that were retrieved.


In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately connected to the uniform spanning tree, a model for a random tree. See also random walk for more general treatment of this topic.


In most models of communication protocol participants communicate through authenticated channels. This means that messages are not anonymous, and receivers know the source of every message they receive. Some models assume a stronger, transferable form of authentication, where each message is signed by the sender, so that a receiver knows not just the immediate source of every message, but the participant that initially created the message. This stronger type of authentication is achieved by digital signatures, and when this stronger form of authentication is available, protocols can tolerate a larger number of faults.The two different authentication models are often called oral communication and written communication models. In an oral communication model, the immediate source of information is known, whereas in stronger, written communication models, every step along the receiver learns not just the immediate source of the message, but the communication history of the message.


They are weakly structured in common use, and become strongly structured in individual-site use. They may be abstract or concrete. They have different meanings in different social worlds but their structure is common enough to more than one world to make them recognizable, a means of translation.


Note that in the probability inequalities above, the outcome of the protocol is understood to depend only on the random string; both strings x and y remain fixed. In other words, if R(x,y) yields g(x,y,r) when using random string r, then g(x,y,r) = f(x,y) for at least 2/3 of all choices for the string r. The randomized complexity is simply defined as the number of bits exchanged in such a protocol. Note that it is also possible to define a randomized protocol with one-sided error, and the complexity is defined similarly.


Common phonological features that define the natural classes of vowels involved in vowel harmony include vowel backness, vowel height, nasalization, roundedness, and advanced and retracted tongue root. Vowel harmony is found in many agglutinative languages. The given domain of vowel harmony taking effect often spans across morpheme boundaries, and suffixes and prefixes will usually follow vowel harmony rules.


In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's undefinability theorem.


It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction. If "this sentence is false" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.


By 1963–1964 Gödel would disavow Herbrand–Gödel recursion and the λ-calculus in favor of the Turing machine as the definition of "algorithm" or "mechanical procedure" or "formal system".A hypothesis leading to a natural law? : In late 1936 Alan Turing's paper (also proving that the Entscheidungsproblem is unsolvable) was delivered orally, but had not yet appeared in print. On the other hand, Emil Post's 1936 paper had appeared and was certified independent of Turing's work.


It was implemented in ECL running at 25 MHz. Major functional modules were implemented using AMCC ECL ASICs. The project grew beyond its original definition to include a front-end general purpose processor ensemble based on the multiple 68020 processors running Unix System V. The numeric processor ran a small kernel that would allow it to receive job submissions from the Unix system.


In the classification of programming languages, an applicative programming language is built out of functions applied to arguments. Applicative languages are functional, and applicative is often used as a synonym for functional. However, concatenative languages can be functional, while not being applicative.The semantics of applicative languages are based on beta reduction of terms, and side effects such as mutation of state are not permitted.Lisp and ML are applicative programming languages.


In practice, there exist several methods to construct knowledge spaces. The most frequently used method is querying experts. There exist several querying algorithms that allow one or several experts to construct a knowledge space by answering a sequence of simple questions.Another method is to construct the knowledge space by explorative data analysis (for example by item tree analysis) from data. A third method is to derive the knowledge space from an analysis of the problem solving processes in the corresponding domain. == References ==


In telecommunications networks, RANAP (Radio Access Network Application Part) is a protocol specified by 3GPP in TS 25.413 and used in UMTS for signaling between the Core Network, which can be a MSC or SGSN, and the UTRAN. RANAP is carried over Iu-interface. RANAP signalling protocol resides in the control plane of Radio network layer of Iu interface in the UMTS (Universal Mobile Telecommunication System) protocol stack. Iu interface is the interface between RNC (Radio Network Controller) and CN (Core Network).


In probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without replacement in which each sample can be classified into two mutually exclusive categories like Pass/Fail or Employed/Unemployed. As random selections are made from the population, each subsequent draw decreases the population causing the probability of success to change with each draw. Unlike the standard hypergeometric distribution, which describes the number of successes in a fixed sample size, in the negative hypergeometric distribution, samples are drawn until r {\displaystyle r} failures have been found, and the distribution describes the probability of finding k {\displaystyle k} successes in such a sample. In other words, the negative hypergeometric distribution describes the likelihood of k {\displaystyle k} successes in a sample with exactly r {\displaystyle r} failures.


In mathematics, the nth-term test for divergence is a simple test for the divergence of an infinite series:If lim n → ∞ a n ≠ 0 {\displaystyle \lim _{n\to \infty }a_{n}\neq 0} or if the limit does not exist, then ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} diverges.Many authors do not name this test or give it a shorter name.When testing if a series converges or diverges, this test is often checked first due to its ease of use. In the case of p-adic analysis the term test is a necessary and sufficient condition for convergence due to the non-archimedean triangle inequality.


In telecommunication, a two-wire circuit is characterized by supporting transmission in two directions simultaneously, as opposed to four-wire circuits, which have separate pairs for transmit and receive. The subscriber local loop from the telco central office are almost all two wire for analog baseband voice calls (and some digital services like ISDN), and converted to four-wire at the line card back when telephone switching was performed on baseband audio. Today the audio is digitized and processed completely in the digital domain upstream from the local loop. The reason for using two wires rather than four is simple economics—half the materials cost half as much to purchase and install.


In mathematics, the tent map with parameter μ is the real-valued function fμ defined by f μ ( x ) := μ min { x , 1 − x } , {\displaystyle f_{\mu }(x):=\mu \min\{x,\,1-x\},} the name being due to the tent-like shape of the graph of fμ. For the values of the parameter μ within 0 and 2, fμ maps the unit interval  into itself, thus defining a discrete-time dynamical system on it (equivalently, a recurrence relation). In particular, iterating a point x0 in  gives rise to a sequence x n {\displaystyle x_{n}}: x n + 1 = f μ ( x n ) = { μ x n f o r x n < 1 2 μ ( 1 − x n ) f o r 1 2 ≤ x n {\displaystyle x_{n+1}=f_{\mu }(x_{n})={\begin{cases}\mu x_{n}&\mathrm {for} ~~x_{n}<{\frac {1}{2}}\\\mu (1-x_{n})&\mathrm {for} ~~{\frac {1}{2}}\leq x_{n}\end{cases}}} where μ is a positive real constant.


In order to gain access to GSM services, a user needs three things: A billing relationship with a mobile phone operator. This is usually either where services are paid for in advance of them being consumed (prepaid), or where bills are issued and settled after the service has been consumed (postpaid). A mobile phone that is GSM compliant and operates at the same frequency as the operator.


In software development, time-of-check to time-of-use (TOCTOU, TOCTTOU or TOC/TOU) is a class of software bugs caused by a race condition involving the checking of the state of a part of a system (such as a security credential) and the use of the results of that check. TOCTOU race conditions are common in Unix between operations on the file system, but can occur in other contexts, including local sockets and improper use of database transactions. In the early 1990s, the mail utility of BSD 4.3 UNIX had an exploitable race condition for temporary files because it used the mktemp() function.


In modern machines, the time to fetch a variable from the data cache is often several times longer than the time needed for basic ALU operations. A program runs faster without stalls if its memory loads can be started several cycles before the instruction that needs that variable. Complex machines can do this with a deep pipeline and "out-of-order execution" that examines and runs many instructions at once. Register machines can even do this with much simpler "in-order" hardware, a shallow pipeline, and slightly smarter compilers.


A hierarchy consists of an order defined on a set. The term hierarchy is used to stress a hierarchical relation among the elements. The XML specification defines an XML document as a well-formed text if it satisfies a list of syntax rules defined in the specification.


For instance, the three brothers Faloutsos believed that the Internet had a power law degree distribution on the basis of traceroute data; however, it has been suggested that this is a layer 3 illusion created by routers, which appear as high-degree nodes while concealing the internal layer 2 structure of the ASes they interconnect. On a theoretical level, refinements to the abstract definition of scale-free have been proposed.


In most Unix-like systems, all processes of a pipeline are started at the same time, with their streams appropriately connected, and managed by the scheduler together with all other processes running on the machine. An important aspect of this, setting Unix pipes apart from other pipe implementations, is the concept of buffering: for example a sending program may produce 5000 bytes per second, and a receiving program may only be able to accept 100 bytes per second, but no data is lost. Instead, the output of the sending program is held in the buffer. When the receiving program is ready to read data, the next program in the pipeline reads from the buffer.


We should also remember to strike out AAA; this says that since the cube of a is the identity element of G, so is the cube of the inverse of a. Under these conditions the word problem becomes easy. First reduce strings to the empty string, a, aa, A or AA. Then note that we may also multiply by aaa, so we can convert A to aa and convert AA to a. The result is that the word problem, here for the cyclic group of order three, is solvable.


In some cases, simple electromagnetic analysis is not possible or does not provide enough information. Differential electromagnetic analysis (DEMA) attacks are more complex, but are effective against symmetric cryptography implementation, against which SEMA attacks are not. Additionally unlike SEMA, DEMA attacks do not require much knowledge about the device being attacked.


In that case, if it holds a "≈", then X and Y look indistinguishably equal, and if it holds a ">", then X looks clearly more red than Y. The relation ≥ is the disjoint union of the symmetric relation ≈ and the transitive relation >. Using the transitivity of >, the knowledge of both f10 > d30 and d30 > b50 allows one to infer that f10 > b50. However, since ≥ is not transitive, a "paradoxical" inference like "d30 ≥ e20 and e20 ≥ f10, hence d30 ≥ f10" is no longer possible. For the same reason, e.g. "d30 ≈ e20 and e20 ≈ f10, hence d30 ≈ f10" is no longer a valid inference. Similarly, to resolve the original heap variation of the paradox with this approach, the relation "X grains are more a heap than Y grains" could be considered quasitransitive rather than transitive.


In signal processing, the test is often retained in the original form due to Dirichlet: a piecewise monotone bounded periodic function f {\displaystyle f} has a convergent Fourier series whose value at each point is the arithmetic mean of the left and right limits of the function. The condition of piecewise monotonicity is equivalent to having only finitely many local extrema, i.e., that the function changes its variation only finitely many times. (Dirichlet required in addition that the function have only finitely many discontinuities, but this constraint is unnecessarily stringent.) Any signal that can be physically produced in a laboratory satisfies these conditions.As in the pointwise case of the Jordan test, the condition of boundedness can be relaxed if the function is assumed to be absolutely integrable (i.e., L 1 {\displaystyle L^{1}} ) over a period, provided it satisfies the other conditions of the test in a neighborhood of the point x {\displaystyle x} where the limit is taken.


In systems engineering, information systems and software engineering, the systems development life cycle (SDLC), also referred to as the application development life cycle, is a process for planning, creating, testing, and deploying an information system. The SDLC concept applies to a range of hardware and software configurations, as a system can be composed of hardware only, software only, or a combination of both. There are usually six stages in this cycle: requirement analysis, design, development and testing, implementation, documentation, and evaluation.


Another Unix breakthrough was to automatically associate input and output to terminal keyboard and terminal display, respectively, by default — the program (and programmer) did absolutely nothing to establish input and output for a typical input-process-output program (unless it chose a different paradigm). In contrast, previous operating systems usually required some—often complex—job control language to establish connections, or the equivalent burden had to be orchestrated by the program.Since Unix provided standard streams, the Unix C runtime environment was obliged to support it as well. As a result, most C runtime environments (and C's descendants), regardless of the operating system, provide equivalent functionality.


In mathematical analysis, the Foias constant is a real number named after Ciprian Foias. It is defined in the following way: for every real number x1 > 0, there is a sequence defined by the recurrence relation x n + 1 = ( 1 + 1 x n ) n {\displaystyle x_{n+1}=\left(1+{\frac {1}{x_{n}}}\right)^{n}} for n = 1, 2, 3, .... The Foias constant is the unique choice α such that if x1 = α then the sequence diverges to infinity. For all other values of x1, the sequence is divergent as well, but it has two accumulation points: 1 and infinity. Numerically, it is α = 1.187452351126501 … {\displaystyle \alpha =1.187452351126501\ldots } .No closed form for the constant is known. When x1 = α then the growth rate of the sequence (xn) is given by the limit lim n → ∞ x n log  n n = 1 , {\displaystyle \lim _{n\to \infty }x_{n}{\frac {\log n}{n}}=1,} where "log" denotes the natural logarithm.The same methods used in the proof of the uniqueness of the Foias constant may also be applied to other similar recursive sequences.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 3678, 13678, 34678, and 134678 are the patterns related to Braille pattern dots-2356, since the two additional dots of kantenji patterns 02356, 23567, and 023567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


The M690T was followed by the M690E specifically for embedded applications which removed the TV output, which required Macrovision licensing for OEMs, and enabled native support for dual TMDS outputs, enabling dual independent DVI interfaces.In January 2011, AMD announced the AMD Embedded G-Series Accelerated Processing Unit. This was the first APU for embedded applications. These were followed by updates in 2013 and 2016.In May 2012, AMD Announced the AMD Embedded R-Series Accelerated Processing Unit. This family of products incorporates the Bulldozer CPU architecture, and Discrete-class Radeon HD 7000G Series graphics. This was followed by a system on a chip (SoC) version in 2015 which offered a faster CPU and faster graphics, with support for DDR4 SDRAM memory.


In residential telephony, an extension telephone is an additional telephone wired to the same telephone line as another. In middle 20th century telephone jargon, the first telephone on a line was a "Main Station" and subsequent ones "Extensions" or even called as intercom. Such extension phones allow making or receiving calls in different rooms, for example in a home, but any incoming call would ring all extensions and any one extension being in use would cause the line to be busy for all users. Some telephones intended for use as extensions have built in intercom features; a key telephone system for a small business may offer two to five lines, lamps indicating lines already in use, the ability to place calls on 'hold' and an intercom on each of the multiple extensions.


Define a matrix P {\displaystyle P} of dimension | I | × | J | {\displaystyle |I|\times |J|} with entries in G 0 = G ∪ { 0 } . {\displaystyle G^{0}=G\cup \{0\}.} Then, it can be shown that every 0-simple semigroup is of the form S = ( I × G 0 × J ) {\displaystyle S=(I\times G^{0}\times J)} with the operation ( i , a , j ) ∗ ( k , b , n ) = ( i , a p j k b , n ) {\displaystyle (i,a,j)*(k,b,n)=(i,ap_{jk}b,n)} .


In public-key cryptography, the Station-to-Station (STS) protocol is a cryptographic key agreement scheme. The protocol is based on classic Diffie–Hellman, and provides mutual key and entity authentication. Unlike the classic Diffie–Hellman, which is not secure against a man-in-the-middle attack, this protocol assumes that the parties have signature keys, which are used to sign messages, thereby providing security against man-in-the-middle attacks. In addition to protecting the established key from an attacker, the STS protocol uses no timestamps and provides perfect forward secrecy.


Most of the tracks have been previously released on singles, extended plays, and via the Linkin Park Underground fan club, while other tracks are being released for the first time on this compilation. Various editions of the release were offered, including on CDs and vinyl. It was released on October 9, 2020.


In statistics, a polykay, or generalised k-statistic, (denoted k r , s {\displaystyle k_{r,s}} ) is a statistic defined as a linear combination of sample moments.


In order to represent code points, column/line numbers are used for one-byte codes and kuten numbers are used for two-byte codes. For a way to identify a character without depending on a code, character names are used.


In score voting, strategic voters who expect all other voters to be strategic will exaggerate their true preferences and use the same quasi-compromising strategy as in approval voting, above. That is, they will give all candidates either the highest possible or the lowest possible rating. This presents an additional problem as compared to the approval method if some voters give honest "weak" votes with middle rankings and other voters give strategic approval votes.


In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted gcd ( x , y ) {\displaystyle \gcd(x,y)} . For example, the GCD of 8 and 12 is 4, that is, gcd ( 8 , 12 ) = 4 {\displaystyle \gcd(8,12)=4} .In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include highest common factor (hcf), etc. Historically, other names for the same concept have included greatest common measure.This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see § In commutative rings below).


It can build self-confidence and self-esteem while enhancing skills and extending networks and social ties. Online volunteering also allows participants to adapt their program of volunteer work to their unique skills and passions.People engaged in virtual volunteering undertake a variety of activities from locations remote to the organization or people they are assisting, via a computer or other Internet-connected device, such as: researching subjects (e.g. for Wikia projects) writing software (see open-source software which is often made by volunteers) fixing software (e.g. Community patches) creating web pages editing or writing proposals, press releases, newsletter articles, etc. translating documents (e.g. Fan translations) developing material for a curriculum designing a database designing graphics scanning documents providing legal, business, medical, agricultural or any other expertise counseling people tutoring or mentoring students moderating online discussion groups writing songs creating a podcast editing a video monitoring the news internet pastoral care answering questions tagging photos and files distributed computing managing other online volunteersIn the developing world, innovative synergies between volunteerism and technology typically focus on mobile communication technologies rather than the Internet. Around 26 per cent of people worldwide had Internet access in 2009.


Note that property equivalence is not the same as property equality. Equivalent properties have the same "values" (i.e., the same property extension), but may have different intensional meaning (i.e., denote different concepts). Property equality should be expressed with the owl:sameAs construct. As this requires that properties are treated as individuals, such axioms are only allowed in OWL Full.


In order to guarantee safety, Gbcast defines three safety properties and ensures they hold, regardless of the pattern of failures:


Example #1 There are 5 pink marbles, 2 blue marbles, and 8 purple marbles. What are the odds in favor of picking a blue marble?Answer: The odds in favour of a blue marble are 2:13. One can equivalently say that the odds are 13:2 against.


Some languages drop the copula in poetic or aphorismic contexts. Examples in English include The more, the better. Out of many, one.


In parametric hypothesis testing problems, a simple or point hypothesis refers to a hypothesis where the parameter's value is assumed to be a single number. In contrast, in a composite hypothesis the parameter's value is given by a set of numbers. For example, when testing the null hypothesis that a distribution is normal with a mean less than or equal to zero against the alternative that the mean is greater than zero (variance known), the null hypothesis does not specify the probability distribution of the appropriate test statistic. In the just mentioned example that would be the Z-statistic belonging to the one-sided one-sample Z-test.


In natural language processing, it is often necessary to compare tree structures (e.g. parse trees) for similarity. Such comparisons can be performed by computing dot products of vectors of features of the trees, but these vectors tend to be very large: NLP techniques have come to a point where a simple dependency relation over two words is encoded with a vector of several millions of features. It can be impractical to represent complex structures such as trees with features vectors. Well-designed kernels allow computing similarity over trees without explicitly computing the feature vectors of these trees. Moreover, kernel methods have been widely used in machine learning tasks ( e.g. SVM ), and thus plenty of algorithms are working natively with kernels, or have an extension that handles kernelization. An example application is classification of sentences, such as different types of questions.


In quantum information theory, the Wehrl entropy, named after Alfred Wehrl, is a classical entropy of a quantum-mechanical density matrix. It is a type of quasi-entropy defined for the Husimi Q representation of the phase-space quasiprobability distribution. See for a comprehensive review of basic properties of classical, quantum and Wehrl entropies, and their implications in statistical mechanics.


In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance, statistical difference or variational distance.


In other imperative programming languages, it is possible to achieve some of the same algorithmic results as are obtained via higher-order functions by dynamically executing code (sometimes called Eval or Execute operations) in the scope of evaluation. There can be significant drawbacks to this approach: The argument code to be executed is usually not statically typed; these languages generally rely on dynamic typing to determine the well-formedness and safety of the code to be executed. The argument is usually provided as a string, the value of which may not be known until run-time. This string must either be compiled during program execution (using just-in-time compilation) or evaluated by interpretation, causing some added overhead at run-time, and usually generating less efficient code.


In nonparametric statistics, a kernel is a weighting function used in non-parametric estimation techniques. Kernels are used in kernel density estimation to estimate random variables' density functions, or in kernel regression to estimate the conditional expectation of a random variable. Kernels are also used in time-series, in the use of the periodogram to estimate the spectral density where they are known as window functions. An additional use is in the estimation of a time-varying intensity for a point process where window functions (kernels) are convolved with time-series data. Commonly, kernel widths must also be specified when running a non-parametric estimation.


In scalar setting, McDiarmid's inequality provides one common way of bounding the differences by applying Azuma's inequality to a Doob martingale. A version of the bounded differences inequality holds in the matrix setting. Let { Z k: k = 1 , 2 , … , n } {\displaystyle \{Z_{k}:k=1,2,\ldots ,n\}} be an independent, family of random variables, and let H {\displaystyle \mathbf {H} } be a function that maps n {\displaystyle n} variables to a self-adjoint matrix of dimension d {\displaystyle d} .


In mathematics, and particularly in number theory, N is a primary pseudoperfect number if it satisfies the Egyptian fraction equation 1 N + ∑ p | N 1 p = 1 , {\displaystyle {\frac {1}{N}}+\sum _{p\,|\;\!N}{\frac {1}{p}}=1,} where the sum is over only the prime divisors of N.


In mathematics the division polynomials provide a way to calculate multiples of points on elliptic curves and to study the fields generated by torsion points. They play a central role in the study of counting points on elliptic curves in Schoof's algorithm.


In science and engineering, the terms data processing and information systems are considered too broad, and the term data processing is typically used for the initial stage followed by a data analysis in the second stage of the overall data handling. Data analysis uses specialized algorithms and statistical calculations that are less often observed in a typical general business environment. For data analysis, software suites like SPSS or SAS, or their free counterparts such as DAP, gretl or PSPP are often used.


In number theory, a congruence of squares is a congruence commonly used in integer factorization algorithms.


In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called disturbances.


In the following the majority judgment winner for the first group of voters is determined. The sorted ratings would be as follows: Result: With the votes of the first group of voters, A has the median rating of "Excellent" and B has the median rating of "Fair". Thus, A is elected majority judgment winner by the first group of voters.


Similarly, Berger codes can detect any number of zero-to-one bit-flip errors, as long as no one-to-zero bit-flip errors occur in the same code word. Berger codes cannot correct any error. Like all unidirectional error detecting codes, Berger codes can also be used in delay-insensitive circuits.


In statistics, every conjecture concerning the unknown probability distribution of a collection of random variables representing the observed data X {\displaystyle X} in some study is called a statistical hypothesis. If we state one hypothesis only and the aim of the statistical test is to see whether this hypothesis is tenable, but not to investigate other specific hypotheses, then such a test is called a null hypothesis test. As our statistical hypothesis will, by definition, state some property of the distribution, the null hypothesis is the default hypothesis under which that property does not exist. The null hypothesis is typically that some parameter (such as a correlation or a difference between means) in the populations of interest is zero.


The technique is also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov. The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes.


In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector α {\displaystyle {\boldsymbol {\alpha }}} , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The Dirichlet parameter vector captures the prior belief about the situation and can be seen as a pseudocount: observations of each outcome that occur before the actual data is collected.


In telecommunication, a cryptochannel is a complete system of crypto-communications between two or more holders or parties. It includes: (a) the cryptographic aids prescribed; (b) the holders thereof; (c) the indicators or other means of identification; (d) the area or areas in which effective; (e) the special purpose, if any, for which provided; and (f) pertinent notes as to distribution, usage, etc. A cryptochannel is analogous to a radio circuit.


Similarly, in 1998, Tijn Borghuis introduced modal pure type systems (MPTS). Roorda has discussed the application of pure type systems to functional programming; and Roorda and Jeuring have proposed a programming language based on pure type systems.The systems from the lambda cube are all known to be strongly normalizing. Pure type systems in general need not be, for example System U from Girard's paradox is not.


In music theory, a parameter denotes an element which may be manipulated (composed), separately from the other elements. The term is used particularly for pitch, loudness, duration, and timbre, though theorists or composers have sometimes considered other musical aspects as parameters. The term is particularly used in serial music, where each parameter may follow some specified series. Paul Lansky and George Perle criticized the extension of the word "parameter" to this sense, since it is not closely related to its mathematical sense, but it remains common. The term is also common in music production, as the functions of audio processing units (such as the attack, release, ratio, threshold, and other variables on a compressor) are defined by parameters specific to the type of unit (compressor, equalizer, delay, etc.).


Let lower case letters n , x . . .


In statistical theory, the Pitman closeness criterion, named after E. J. G. Pitman, is a way of comparing two candidate estimators for the same parameter. Under this criterion, estimator A is preferred to estimator B if the probability that estimator A is closer to the true value than estimator B is greater than one half. Here the meaning of closer is determined by the absolute difference in the case of a scalar parameter, or by the Mahalanobis distance for a vector parameter.


In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity of the additive group of m × n {\displaystyle m\times n} matrices, and is denoted by the symbol O {\displaystyle O} or 0 {\displaystyle 0} followed by subscripts corresponding to the dimension of the matrix as the context sees fit. Some examples of zero matrices are 0 1 , 1 =  , 0 2 , 2 =  , 0 2 , 3 =  . {\displaystyle 0_{1,1}={\begin{bmatrix}0\end{bmatrix}},\ 0_{2,2}={\begin{bmatrix}0&0\\0&0\end{bmatrix}},\ 0_{2,3}={\begin{bmatrix}0&0&0\\0&0&0\end{bmatrix}}.\ }


Firstly, the page table walker, which uses physical addresses to access the page table and directory, can now access physical addresses greater than the 32-bit physical addresses (no PAE system). From the CR3, the page table walker can access page directories and tables that are beyond the 32-bit range. Secondly, the physical address for the data that is being accessed (stored in the page table) can be represented as a physical address that is greater than the 32-bit address (no PAE system).


In model checking, a transition system is sometimes defined to include an additional labeling function for the states as well, resulting in a notion that encompasses that of Kripke structure.Action languages are extensions of transition systems, adding a set of fluents F, a set of values V, and a function that maps F × S to V.


In the "Fall Revolution" series of science-fiction books, author Ken Macleod riffs and puns on the expression by writing about entities composed of information actually "wanting", as in desiring, freedom and the machinations of several human characters with differing political and ideological agendas, to facilitate or disrupt these entities' quest for freedom. In the cyberpunk world of post-singularity transhuman culture described by Charles Stross in his books like Accelerando and Singularity Sky, the wish of information to be free is a law of nature.


Continued fractions have a number of remarkable properties related to the Euclidean algorithm for integers or real numbers. Every rational number p {\displaystyle p} / q {\displaystyle q} has two closely related expressions as a finite continued fraction, whose coefficients ai can be determined by applying the Euclidean algorithm to ( p , q ) {\displaystyle (p,q)} . The numerical value of an infinite continued fraction is irrational; it is defined from its infinite sequence of integers as the limit of a sequence of values for finite continued fractions.


It can also be the natural minor scale or Aeolian mode with raised third and lowered fifth intervals. It may also be derived from the Phrygian Dominant scale, but this time, the second is major, while the fifth is diminished.


In situations where software must not crash for any reason, error swallowing is a practice that a programmer can easily fall into. For example, a plugin that is running inside another application is expected to handle all errors and exceptions in such a way as to not crash the application in which it is embedded. Blanket catching of errors and exceptions is a pattern that is easy to fall into when attempting to prevent crashes at all costs, and when you combine that with poor logging tools, error swallowing can happen.


In the above execution scheme, the tasks which correspond to increasing job size are placed in a queue, with the tasks belonging to the largest gang scheduled first, but this method of execution tends to lead to the starvation of resources of smaller jobs and is therefore unfit to be executed in systems where the number of processors is comparatively low.The AFCFS and LGFS also have to deal with possible processor failure. In such a case, tasks executing on that processor are submitted to other processors for execution. The tasks wait in the head of the queue on these processors while the current processor is being repaired. There are two scenarios which emerge from the above issue: Blocking case: The processors assigned to the interrupted jobs are blocked and cannot execute other jobs in their queue until the jobs from the damaged processors are cleared. Non-blocking case: This case is incurred when the jobs already executing in the processors are processed early instead of waiting for the blocked jobs to resume execution.


This is done by treating each count within the size variable as a single sampling unit. Samples are then identified by selecting at even intervals among these counts within the size variable.


Another example, coming from formal language theory, is the free semigroup generated by a nonempty set (an alphabet), with string concatenation as the binary operation, and the involution being the map which reverses the linear order of the letters in a string. A third example, from basic set theory, is the set of all binary relations between a set and itself, with the involution being the converse relation, and the multiplication given by the usual composition of relations. Semigroups with involution appeared explicitly named in a 1953 paper of Viktor Wagner (in Russian) as result of his attempt to bridge the theory of semigroups with that of semiheaps.


In recent decades, the SKI combinator calculus, with only two primitive combinators, K and S, has become the canonical approach to combinatory logic. B, C, and W can be expressed in terms of S and K as follows: B = S (K S) K C = S (S (K (S (K S) K)) S) (K K) K = K W = S S (S K)Another way is, having defined B as above, to further define C = S(BBS)(KK) and W = CSI. Going the other direction, SKI can be defined in terms of B,C,K,W as: I = W K K = K S = B (B (B W) C) (B B) = B (B W) (B B C).Also of note, Y combinator has a short expression in this system, as Y = BU(CBU), where U = WI = SII is the self-application combinator. Then we have Yg = U(BgU) = BgU(BgU) = g(U(BgU)) = g(Yg).


In nouns, the thematic vowel is almost always *o, and only becomes *e when there is no ending or when followed by *h₂ in the neuter nominative/accusative plural. Here is an example paradigm for *h₂ŕ̥tḱos 'bear', a thematic animate noun, supplemented by the neuter *h₂érh₃trom 'plough' for the nominative/accusative: Again, athematic nouns show ablaut and accent shifts, mainly between the "strong" cases (nominative and vocative in all numbers, and accusative singular/dual) and the "weak" cases (all others). A few endings are also different from the thematic paradigm; for example, the nominative/accusative neuter has *-∅ instead of *-m. See Athematic accent/ablaut classes of PIE nouns for examples.


In the early 21st century a rapid development of ICT services and electronical devices took place, in which the internet servers multiplied by a factor of 1000 to 395 million and its still increasing. This increase can be explained by moores law, which states, that the development of ICT increases every year by 16-20%, so it will double in numbers every four to five years. Alongside this development and the high investments in increasing demand for ICT capable products, a high environmental impact came with it. Software and Hardware development as well as production causing already in 2008 the same amount of CO2-emissions as global air travels.There are two sides of ICT, the positive environmental possibilities and the shadow side.


Similar forced disclosure laws in Australia, Finland, France, and India compel individual suspects under investigation to hand over encryption keys or passwords during a criminal investigation. In the United States, the federal criminal case of United States v. Fricosu addressed whether a search warrant can compel a person to reveal an encryption passphrase or password. The Electronic Frontier Foundation (EFF) argued that this is a violation of the protection from self-incrimination given by the Fifth Amendment.


These conflicts can indicate an HGT event or may be the result of uncertainty in gene tree inference. To reduce uncertainty, bipartition analyses typically focus on strongly supported bipartitions such as those associated with branches with bootstrap values or posterior probabilities above certain thresholds. Any gene family found to have one or several conflicting, but strongly supported, bipartitions is considered as an HGT candidate.Quartet decomposition Quartets are trees consisting of four leaves.


Assuming that the statistical correlation function is Gaussian of the form G ( x , y ) = δ 2 exp  ( − r 2 σ 2 ) {\displaystyle G(x,y)=\delta ^{2}\exp \left(-{\frac {r^{2}}{\sigma ^{2}}}\right)} where δ {\displaystyle \delta } is the root mean square height, r {\displaystyle r} is the distance from the point ( x , y ) {\displaystyle (x,y)} , and σ {\displaystyle \sigma } is the correlation length, then the Fourier transform of the correlation function is | s ( k surf ) | 2 = 1 4 π σ 2 δ 2 exp  ( − σ 2 k surf 2 4 ) {\displaystyle |s(k_{\text{surf}})|^{2}={\frac {1}{4\pi }}\sigma ^{2}\delta ^{2}\exp \left(-{\frac {\sigma ^{2}k_{\text{surf}}^{2}}{4}}\right)} where s {\displaystyle s} is a measure of the amount of each spatial frequency k surf {\displaystyle k_{\text{surf}}} which help couple photons into a surface plasmon. If the surface only has one Fourier component of roughness (i.e. the surface profile is sinusoidal), then the s {\displaystyle s} is discrete and exists only at k = 2 π a {\displaystyle k={\frac {2\pi }{a}}} , resulting in a single narrow set of angles for coupling. If the surface contains many Fourier components, then coupling becomes possible at multiple angles.


In probability theory, concentration inequalities provide bounds on how a random variable deviates from some value (typically, its expected value). The law of large numbers of classical probability theory states that sums of independent random variables are, under very mild conditions, close to their expectation with a large probability. Such sums are the most basic examples of random variables concentrated around their mean. Recent results show that such behavior is shared by other functions of independent random variables. Concentration inequalities can be sorted according to how much information about the random variable is needed in order to use them.


In the case of classical propositional logic, satisfiability is decidable for propositional formulae. In particular, satisfiability is an NP-complete problem, and is one of the most intensively studied problems in computational complexity theory.


In telecommunication, a distributed-queue dual-bus network (DQDB) is a distributed multi-access network that (a) supports integrated communications using a dual bus and distributed queuing, (b) provides access to local or metropolitan area networks, and (c) supports connectionless data transfer, connection-oriented data transfer, and isochronous communications, such as voice communications. IEEE 802.6 is an example of a network providing DQDB access methods.


The computer designs based on this theory were called reduced instruction set computing (RISC). RISCs usually had larger numbers of registers, accessed by simpler instructions, with a few instructions specifically to load and store data to memory. The result was a very simple core CPU running at very high speed, supporting the sorts of operations the compilers were using anyway.


. . , 2 n } {\displaystyle =\{1,2,...,2n\}} .Equivalently, haf  ( A ) = ∑ M ∈ M ∏ ( u , v ) ∈ M A u , v {\displaystyle \operatorname {haf} (A)=\sum _{M\in {\mathcal {M}}}\prod _{\scriptscriptstyle (u,v)\in M}A_{u,v}} where M {\displaystyle {\mathcal {M}}} is the set of all 1-factors (perfect matchings) on the complete graph K 2 n {\displaystyle K_{2n}} , namely the set of all ( 2 n ) !


In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs. For example, the factorial function n!


In fact, there exist instances of theoretical non-quantum correlations which, a priori, do not seem physically implausible. The aim of device-independent reconstructions is to show that all such supra-quantum examples are precluded by a reasonable physical principle. The physical principles proposed so far include no-signalling, Non-Trivial Communication Complexity, No-Advantage for Nonlocal computation, Information Causality, Macroscopic Locality, and Local Orthogonality.


In the case of d = 2 {\displaystyle d=2} the rectangle is represented by ( ( x m i n , y m i n ) , ( x m a x , y m a x ) ) {\displaystyle \,((x_{min},y_{min}),(x_{max},y_{max}))} and the MBR thus four corners ( x m i n , y m i n , x m a x , y m a x ) {\displaystyle \,(x_{min},y_{min},x_{max},y_{max})} .


As well, in yes/no questions, the non-manual marking must be used over the whole utterance in order for it to be judged as a statement opposed to a question. The yes/no question is the same word order as the statement form of the sentence, with the addition of non-manual grammatical markings. This can be seen in the examples below. ASL Statement:JUAN WILL BUY SHOES TODAY "Juan will buy shoes today"ASL Yes/no Question:_____________________brow raise JUAN WILL BUY SHOES TODAY "Will Juan buy shoes today?"


In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schrödinger operators, and five concern operators that incorporate the Coulomb potential.In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems. Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was in fact the Cantor set, a challenge known as the "Ten Martini Problem" after the reward that Mark Kac offered for solving it.The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984.


In telecommunications, 6G is the sixth generation mobile system standard currently under development for wireless communications technologies supporting cellular data networks. It is the planned successor to 5G and will likely be significantly faster. Like its predecessors, 6G networks will probably be broadband cellular networks, in which the service area is divided into small geographical areas called cells. Several companies (Airtel, Anritsu, Apple, Ericsson, Fly, Huawei, Jio, Keysight, LG, Nokia, NTT Docomo, Samsung, Vi, Xiaomi), research institutes (Technology Innovation Institute, the Interuniversity Microelectronics Centre) and countries (United States, countries in the European Union, Russia, China, India, Japan, South Korea, Singapore and United Arab Emirates) have shown interest in 6G networks.6G networks are expected to be even more diverse than their predecessors and are likely to support applications beyond current mobile use scenarios, such as ubiquitous instant communications, pervasive intelligence and the Internet of Things (IoT). It is expected that mobile network operators will adopt flexible decentralized business models for 6G, with local spectrum licensing, spectrum sharing, infrastructure sharing, and intelligent automated management underpinned by mobile edge computing, artificial intelligence (AI), short-packet communication and blockchain technologies.The Next G Alliance, released its report on 6G in February 2022, outlining the development roadmap of 6G. As of 2023, there is no universally-accepted government or non-government standard for what qualifies as 6G technology and it is still in the early stage of development, but expect to be deployed in 2028 as scheduled.


In mathematics, a composition ring, introduced in (Adler 1962), is a commutative ring (R, 0, +, −, ·), possibly without an identity 1 (see non-unital ring), together with an operation ∘: R × R → R {\displaystyle \circ :R\times R\rightarrow R} such that, for any three elements f , g , h ∈ R {\displaystyle f,g,h\in R} one has ( f + g ) ∘ h = ( f ∘ h ) + ( g ∘ h ) {\displaystyle (f+g)\circ h=(f\circ h)+(g\circ h)} ( f ⋅ g ) ∘ h = ( f ∘ h ) ⋅ ( g ∘ h ) {\displaystyle (f\cdot g)\circ h=(f\circ h)\cdot (g\circ h)} ( f ∘ g ) ∘ h = f ∘ ( g ∘ h ) . {\displaystyle (f\circ g)\circ h=f\circ (g\circ h).} It is not generally the case that f ∘ g = g ∘ f {\displaystyle f\circ g=g\circ f} , nor is it generally the case that f ∘ ( g + h ) {\displaystyle f\circ (g+h)} (or f ∘ ( g ⋅ h ) {\displaystyle f\circ (g\cdot h)} ) has any algebraic relationship to f ∘ g {\displaystyle f\circ g} and f ∘ h {\displaystyle f\circ h} .


When the transfer function method is used, attention is focused on the locations in the s-plane where the transfer function is undefined (the poles) or zero (the zeroes; see Zeroes and poles). Two different transfer functions are of interest to the designer. If the feedback loops in the system are opened (that is prevented from operating) one speaks of the open-loop transfer function, while if the feedback loops are operating normally one speaks of the closed-loop transfer function. For more on the relationship between the two, see root-locus.


Conversely, the OS may deny access, and thus neither open the file nor return a handle. In a capability-based system, handles can be passed between processes, with associated access rights.


Then for any observable f {\displaystyle f} in the domain of L {\displaystyle L} , one has L f ( η ) = ∑ Λ ∫ ξ: ξ Λ c = η Λ c c Λ ( η , d ξ )  {\displaystyle Lf(\eta )=\sum _{\Lambda }\int _{\xi :\xi _{\Lambda ^{c}}=\eta _{\Lambda ^{c}}}c_{\Lambda }(\eta ,d\xi )} . For example, for the stochastic Ising model we have G = Z d {\displaystyle G=\mathbb {Z} ^{d}} , S = { − 1 , + 1 } {\displaystyle S=\{-1,+1\}} , c Λ = 0 {\displaystyle c_{\Lambda }=0} if Λ ≠ { i } {\displaystyle \Lambda \neq \{i\}} for some i ∈ G {\displaystyle i\in G} and c i ( η , η i ) = exp   {\displaystyle c_{i}(\eta ,\eta ^{i})=\exp} where η i {\displaystyle \eta ^{i}} is the configuration equal to η {\displaystyle \eta } except it is flipped at site i {\displaystyle i} . β {\displaystyle \beta } is a new parameter modeling the inverse temperature.


The target can be identified by an URI (e.g., fragment identifiers) and/or a selector that defines a domain-, resource- or application-specific access protocol, e.g., offset-based, XPath-based, etc. Web Annotation was standardized on February 23, 2017 with the release of three official Recommendations by the W3C Web Annotation Working Group: Web Annotation Data Model Web Annotation Vocabulary Web Annotation ProtocolThese recommendations were accompanied by additional working group notes that describe their application: Embedding Web Annotations in HTML Selectors and StatesThe Web Annotation data model is also provided in machine-readable form as the Web Annotation ontology. Note that this ontology defines the Web Annotation namespace (https://www.w3.org/ns/oa#), and that this namespace is conventionally abbreviated as oa. This is the abbreviation for Open Annotation, a W3C Community Group whose specifications formed the basis for the Web Annotation standard.Web Annotation supersedes other standardization initiatives for annotations on the web within the W3C.


Electromagnetism has been studied since ancient times. Many ancient civilizations, including the Greeks and the Mayans created wide-ranging theories to explain lightning, static electricity, and the attraction between magnetized pieces of iron ore. However, it wasn't until the late 18th century that scientists began to develop a mathematical basis for understanding the nature of electromagnetic interactions.


This derived directly from the hardware design of the Intel 8086 (and, subsequently, the closely related 8088), which had exactly 20 address pins. (Both were packaged in 40-pin DIP packages; even with only 20 address lines, the address and data buses were multiplexed to fit all the address and data lines within the limited pin count.) Each segment begins at a multiple of 16 bytes, called a paragraph, from the beginning of the linear (flat) address space.


In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values μ a {\displaystyle \mu _{a}} and μ b {\displaystyle \mu _{b}} and standard deviation σ a {\displaystyle \sigma _{a}} and σ b {\displaystyle \sigma _{b}} respectively is: D s n = ( μ a − μ b ) ( σ a + σ b ) {\displaystyle D_{sn}={(\mu _{a}-\mu _{b}) \over (\sigma _{a}+\sigma _{b})}} In the case of Gaussian-distributed data and unbiased class distributions, this statistic can be related to classification accuracy given an ideal linear discrimination, and a decision boundary can be derived.This distance is frequently used to identify vectors that have significant difference. One usage is in bioinformatics to locate genes that are differential expressed on microarray experiments.


In mathematics, the Moore determinant is a determinant defined for Hermitian matrices over a quaternion algebra, introduced by Moore (1922).


In the U.S., New York is the only state that does not allow peer-to-peer car rental because the owner cannot exclude him or herself from liability to a renter.


In the first two stages of the algorithm, the time complexity is O(N2L + NL2), the space complexity is O(N2 + NL + L2). The refinement stage adds to the time complexity another term, O(N3L). MUSCLE is often used as a replacement for Clustal, since it usually (but not always) gives better sequence alignments, depending on the chosen options. is significantly faster than Clustal, more so for larger alignments.


By failing to check the length of the string, it also overwrites the value of B: B's value has now been inadvertently replaced by a number formed from part of the character string. In this example "e" followed by a zero byte would become 25856. Writing data past the end of allocated memory can sometimes be detected by the operating system to generate a segmentation fault error that terminates the process. To prevent the buffer overflow from happening in this example, the call to strcpy could be replaced with strlcpy, which takes the maximum capacity of A (including a null-termination character) as an additional parameter and ensures that no more than this amount of data is written to A: When available, the strlcpy library function is preferred over strncpy which does not null-terminate the destination buffer if the source string's length is greater than or equal to the size of the buffer (the third argument passed to the function), therefore A may not be null-terminated and cannot be treated as a valid C-style string.


15; 2009, c. 13; 2010, c. 15.


These applications are elaborated below. But an illustrative note bears adding here. It is sometimes claimed that what is at issue in these problems is the supervenience claim itself.


For a concrete example, take the universal and existential quantifiers ∀ and ∃, respectively. Their truth conditions can be specified as A ⊨ ∀ x ϕ  ⟺ ϕ A , x , a ¯ ∈ ∀ A {\displaystyle A\models \forall x\phi \iff \phi ^{A,x,{\bar {a}}}\in \forall _{A}} A ⊨ ∃ x ϕ  ⟺ ϕ A , x , a ¯ ∈ ∃ A , {\displaystyle A\models \exists x\phi \iff \phi ^{A,x,{\bar {a}}}\in \exists _{A},} where ∀ A {\displaystyle \forall _{A}} is the singleton whose sole member is dom(A), and ∃ A {\displaystyle \exists _{A}} is the set of all non-empty subsets of dom(A) (i.e. the power set of dom(A) minus the empty set).


In most physical and biological sciences, the use of either quantitative or qualitative methods is uncontroversial, and each is used when appropriate. In the social sciences, particularly in sociology, social anthropology and psychology, the use of one or other type of method can be a matter of controversy and even ideology, with particular schools of thought within each discipline favouring one type of method and pouring scorn on to the other. The majority tendency throughout the history of social science, however, is to use eclectic approaches-by combining both methods.


In probability theory, Ville's inequality provides an upper bound on the probability that a supermartingale exceeds a certain value. The inequality is named after Jean Ville, who proved it in 1939. The inequality has applications in statistical testing.


In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices, with predicates for equality and adjacency testing.


In some computer programming languages, the size in bits of certain data types 64-bit computing A 64-bit integer can represent up to 18,446,744,073,709,551,616 values. Base 64 is used in with Base64 encoding and other data compression formats. In 8-bit home computers, a common shorthand for the Commodore 64 The ASCII code 64 is for the @ symbol The Nintendo 64 video game console and (historically) the Commodore 64. Since 1996, the number 64 has been an abbreviation or slang for Nintendo 64 (though N64 is more common) along with the games Super Mario 64, Mario Kart 64 and more.


For the rest of the time, the mobile can carry out measurements on the network, detecting surrounding transmitters on different frequencies. This allows safe inter frequency handovers, something which is difficult in CDMA systems, not supported at all in IS-95 and supported through complex system additions in Universal Mobile Telecommunications System (UMTS). This in turn allows for co-existence of microcell layers with macrocell layers.


α → ( α r e f ) ! : ∀ α . ( α r e f ) → α :=: ∀ α .


In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times. An infinite word is recurrent if and only if it is a sesquipower.A uniformly recurrent word is a recurrent word in which for any given factor X in the sequence, there is some length nX (often much longer than the length of X) such that X appears in every block of length nX. The terms minimal sequence and almost periodic sequence (Muchnik, Semenov, Ushakov 2003) are also used.


In some nonlinear systems, parameters are explicit. In others they are implicit, and the system of nonlinear equations is written F ( u ) = 0 {\displaystyle F(\mathbf {u} )=0} where u {\displaystyle \mathbf {u} } is an n-vector, and its image F ( u ) {\displaystyle F(\mathbf {u} )} is an n-1 vector. This formulation, without an explicit parameter space is not usually suitable for the formulations in the following sections, because they refer to parameterized autonomous nonlinear dynamical systems of the form: u ′ = F ( u , λ ) . {\displaystyle \mathbf {u} '=F(\mathbf {u} ,\lambda ).} However, in an algebraic system there is no distinction between unknowns u {\displaystyle \mathbf {u} } and the parameters.


An advantage of these methods is that in the favorable cases it can find the exact value of the joint spectral radius and provide a certificate that this is the exact value. The second family of methods approximate the extremal norm with modern optimization techniques, such as ellipsoid norm approximation, semidefinite programming, Sum Of Squares, and conic programming. The advantage of these methods is that they are easy to implement, and in practice, they provide in general the best bounds on the joint spectral radius.


Different theorists have different categorizations and conceptualizations of defence mechanisms. Large reviews of theories of defence mechanisms are available from Paulhus, Fridhandler and Hayes (1997) and Cramer (1991). The Journal of Personality published a special issue on defence mechanisms (1998).


In the early decades of telegraphy, many efficiency improvements were incorporated into operations. The Morse code itself was one of these: it roughly coded more commonly used symbols into shorter keying sequences, and the rare ones into longer, thus leading to data compression online. The introduction of Morse symbols called procedural signs or prosigns was then just a logical progression. They were not defined by the inventors of Morse code, but were gradually introduced to improve the speed and accuracy of high-volume message handling, especially between professional telegraph operators operating over the time's long distance contacts, such as short wave radio and transatlantic cable. Improvements to the legibility of formal written telegraph messages (telegrams) using white space formatting were thus supported by the creation of procedure symbols. Mastery of these Morse code prosigns was important in becoming an efficient telegraph operator, as was the command of many other forms of abbreviation.


Most CB operators prefer to use self-assigned handles reflecting some aspect of their personality; it is generally considered a breach of CB etiquette to use real names, even that of the user. Family Radio Service and Multi-Use Radio Service have no station identification requirement, though groups of individual users have their own procedures, such as using license plates or informal callsigns (some groups within the Boy Scouts of America, for example, use the troop number followed by the scout's initials as a callsign). Wi-Fi access points are not required by law to identify (they are unlicensed transmitters) but the Wi-Fi standards include provision for an identifier called an SSID, which is transmitted as a routine part of Wi-Fi network traffic. However, since a number of standard Wi-Fi channels are shared with the amateur radio spectrum, amateur radio-operated High Speed Multimedia (HSMM), or "hinternet", access points usually use the call sign of the control operator as the SSID, this suffices as proper station identification for the access point being operated as an amateur radio transceiver.


In modern management usage, the term data is increasingly replaced by information or even knowledge in a non-technical context. Thus data management has become information management or knowledge management. This trend obscures the raw data processing and renders interpretation implicit.


In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution, negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution, but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat.


The need to convert a and b into Montgomery form and their product out of Montgomery form means that computing a single product by Montgomery multiplication is slower than the conventional or Barrett reduction algorithms. However, when performing many multiplications in a row, as in modular exponentiation, intermediate results can be left in Montgomery form. Then the initial and final conversions become a negligible fraction of the overall computation. Many important cryptosystems such as RSA and Diffie–Hellman key exchange are based on arithmetic operations modulo a large odd number, and for these cryptosystems, computations using Montgomery multiplication with R a power of two are faster than the available alternatives.


In software deployment, an environment or tier is a computer system or set of systems in which a computer program or software component is deployed and executed. In simple cases, such as developing and immediately executing a program on the same machine, there may be a single environment, but in industrial use, the development environment (where changes are originally made) and production environment (what end users use) are separated, often with several stages in between. This structured release management process allows phased deployment (rollout), testing, and rollback in case of problems. Environments may vary significantly in size: the development environment is typically an individual developer's workstation, while the production environment may be a network of many geographically distributed machines in data centers, or virtual machines in cloud computing. Code, data, and configuration may be deployed in parallel, and need not connect to the corresponding tier—for example, pre-production code might connect to a production database.


In some languages, affricates contrast phonemically with stop–fricative sequences: Polish affricate /ʈ͡ʂ/ in czysta 'clean (f.)' versus stop–fricative /tʂ/ in trzysta 'three hundred'. Klallam affricate /t͡s/ in k'ʷə́nc 'look at me' versus stop–fricative /ts/ in k'ʷə́nts 'he looks at it'.The exact phonetic difference varies between languages. In stop–fricative sequences, the stop has a release burst before the fricative starts; but in affricates, the fricative element is the release.


In tensor notation, the triple product is expressed using the Levi-Civita symbol: and referring to the i {\displaystyle i} -th component of the resulting vector. This can be simplified by performing a contraction on the Levi-Civita symbols, ε i j k ε k ℓ m = δ i j ℓ m = δ i ℓ δ j m − δ i m δ j ℓ , {\displaystyle \varepsilon _{ijk}\varepsilon ^{k\ell m}=\delta _{ij}^{\ell m}=\delta _{i}^{\ell }\delta _{j}^{m}-\delta _{i}^{m}\delta _{j}^{\ell }\,,} where δ j i {\displaystyle \delta _{j}^{i}} is the Kronecker delta function ( δ j i = 0 {\displaystyle \delta _{j}^{i}=0} when i ≠ j {\displaystyle i\neq j} and δ j i = 1 {\displaystyle \delta _{j}^{i}=1} when i = j {\displaystyle i=j} ) and δ i j ℓ m {\displaystyle \delta _{ij}^{\ell m}} is the generalized Kronecker delta function. We can reason out this identity by recognizing that the index k {\displaystyle k} will be summed out leaving only i {\displaystyle i} and j {\displaystyle j} .


In the problem, each machine provides a random reward from a probability distribution specific to that machine, that is not known a-priori. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between "exploitation" of the machine that has the highest expected payoff and "exploration" to get more information about the expected payoffs of the other machines.


In most illustrations of the gambler's fallacy and the reverse gambler's fallacy, the trial (e.g. flipping a coin) is assumed to be fair. In practice, this assumption may not hold. For example, if a coin is flipped 21 times, the probability of 21 heads with a fair coin is 1 in 2,097,152. Since this probability is so small, if it happens, it may well be that the coin is somehow biased towards landing on heads, or that it is being controlled by hidden magnets, or similar.


In proto-writing, used for inventories and the like, physical objects are represented by stylized or conventionalized pictures, or pictograms. For example, the pictorial Dongba symbols without Geba annotation cannot represent the Naxi language, but are used as a mnemonic for reciting oral literature. Some systems also use ideograms, symbols denoting abstract concepts.


The problem is these samples may be biased in a way that is difficult to quantify or adjust for. For example, if interviewers decide to question the first person they see, they may oversample tall respondents (who are more easily visible from a distance), which could lead to an overestimate of average income. This non-random element is a source of uncertainty about the nature of the actual sample.


Analysis focuses not only on linguistic forms such as words, sentences, grammar, phonology, etc. but also on subtle cues such as prosody and register that signal contextual presupposition. Linguistic based analysis is not the only component that is useful for establishing instances of Interactional sociolinguistics. Culture also plays a large role in understanding this phenomenon.


In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution, nearest-neighbor distribution function or nearest neighbor distribution is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. More specifically, nearest neighbor functions are defined with respect to some point in the point process as being the probability distribution of the distance from this point to its nearest neighboring point in the same point process, hence they are used to describe the probability of another point existing within some distance of a point. A nearest neighbor function can be contrasted with a spherical contact distribution function, which is not defined in reference to some initial point but rather as the probability distribution of the radius of a sphere when it first encounters or makes contact with a point of a point process. Nearest neighbor function are used in the study of point processes as well as the related fields of stochastic geometry and spatial statistics, which are applied in various scientific and engineering disciplines such as biology, geology, physics, and telecommunications.


In probability theory and directional statistics, a wrapped exponential distribution is a wrapped probability distribution that results from the "wrapping" of the exponential distribution around the unit circle.


Both Alice and Bob announce these bits publicly and run a check to see if more than a certain number of them agree. If this check passes, Alice and Bob proceed to use privacy amplification and information reconciliation techniques to create some number of shared secret keys.


random variables. That is, there are underlying, generally unobservable, quantities that are i.i.d. – exchangeable sequences are mixtures of i.i.d. sequences.


The fact that particles can be identical has important consequences in statistical mechanics, where calculations rely on probabilistic arguments, which are sensitive to whether or not the objects being studied are identical. As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox.


The graph referred to is the graph with n vertices, with vertices i and j connected by an edge when a i j ≠ 0 {\displaystyle a_{ij}\neq 0} , and the degree is the degree of the vertices. A crucial aspect of such algorithms is a tie breaking strategy when there is a choice of renumbering resulting in the same degree. A version of the minimum degree algorithm was implemented in the MATLAB function symmmd (where MMD stands for multiple minimum degree), but has now been superseded by a symmetric approximate multiple minimum degree function symamd, which is faster. This is confirmed by theoretical analysis, which shows that for graphs with n vertices and m edges, MMD has a tight upper bound of O ( n 2 m ) {\displaystyle O(n^{2}m)} on its running time, whereas for AMD a tight bound of O ( n m ) {\displaystyle O(nm)} holds. Cummings, Fahrbach, and Fatehpuria designed an exact minimum degree algorithm with O ( n m ) {\displaystyle O(nm)} running time, and showed that no such algorithm can exist that runs in time O ( n m 1 − ε ) {\displaystyle O(nm^{1-\varepsilon })} , for any ε > 0 {\displaystyle \varepsilon >0} , assuming the strong exponential time hypothesis.


In mathematics — specifically, in ergodic theory — a maximising measure is a particular kind of probability measure. Informally, a probability measure μ is a maximising measure for some function f if the integral of f with respect to μ is "as big as it can be". The theory of maximising measures is relatively young and quite little is known about their general structure and properties.


In mathematics, a skeleton of a category is a subcategory that, roughly speaking, does not contain any extraneous isomorphisms. In a certain sense, the skeleton of a category is the "smallest" equivalent category, which captures all "categorical properties" of the original. In fact, two categories are equivalent if and only if they have isomorphic skeletons. A category is called skeletal if isomorphic objects are necessarily identical.


In selective attention experiments, the participants may be asked to repeat aloud the content of the message they are listening to. This task is known as shadowing. As Colin Cherry (1953) found, people do not recall the shadowed message well, suggesting that most of the processing necessary to shadow the attended to message occurs in working memory and is not preserved in the long-term store. Performance on the unattended message is worse.


In mass spectrometry, a matrix is a compound that promotes the formation of ions. Matrix compounds are used in matrix-assisted laser desorption/ionization (MALDI), matrix-assisted ionization (MAI), and fast atom bombardment (FAB).


In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion. The coefficient of determination can be more (intuitively) informative than MAE, MAPE, MSE, and RMSE in regression analysis evaluation, as the former can be expressed as a percentage, whereas the latter measures have arbitrary ranges. It also proved more robust for poor fits compared to SMAPE on the test datasets in the article.When evaluating the goodness-of-fit of simulated (Ypred) vs. measured (Yobs) values, it is not appropriate to base this on the R2 of the linear regression (i.e., Yobs= m·Ypred + b). The R2 quantifies the degree of any linear correlation between Yobs and Ypred, while for the goodness-of-fit evaluation only one specific linear correlation should be taken into consideration: Yobs = 1·Ypred + 0 (i.e., the 1:1 line).


In mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on the notion of a limit, which is in general impossible to define for a ring. Many of the properties of the derivative are true of the formal derivative, but some, especially those that make numerical statements, are not. Formal differentiation is used in algebra to test for multiple roots of a polynomial.


In the United Kingdom, Ofcom directs fixed-line telephone network providers, mobile phone providers and broadband service providers to provide number portability under the Porting Authorisation Code rules and Migration Authorisation Code code of practice respectively. As the UK was an EU member country, the Ofcom direction was intended to reflect the requirements of EU Directive 2002/22/EU.


The General Data Protection Regulation (GDPR) is an example of this. In other places, like in the United States, privacy law is argued by some to be less developed in this regard. By example, some legislation, or lack thereof, allow companies to self-regulate their collection and dissemination practices of consumer information.


For example, ( b 1 ) 3 = b 1 × b 1 × b 1 = b 1 + 1 + 1 = b 3 {\displaystyle (b^{1})^{3}=b^{1}\times b^{1}\times b^{1}=b^{1+1+1}=b^{3}} . Taking the cube root of both sides gives b 1 = b {\displaystyle b^{1}=b} . The rule that multiplying makes exponents add can also be used to derive the properties of negative integer exponents.


In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was proven by Wassily Hoeffding in 1963.Hoeffding's inequality is a special case of the Azuma–Hoeffding inequality and McDiarmid's inequality. It is similar to the Chernoff bound, but tends to be less sharp, in particular when the variance of the random variables is small. It is similar to, but incomparable with, one of Bernstein's inequalities.


In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn. Equivalently, g(n) is the largest least common multiple (lcm) of any partition of n, or the maximum number of times a permutation of n elements can be recursively applied to itself before it returns to its starting sequence. For instance, 5 = 2 + 3 and lcm(2,3) = 6. No other partition of 5 yields a bigger lcm, so g(5) = 6.


If all numerators are 1 in a fraction written in this form, and all denominators are different from each other, the result is an Egyptian fraction representation of the number. This notation was also sometimes combined with the composite fraction notation: two composite fractions written next to each other would represent the sum of the fractions.The complexity of this notation allows numbers to be written in many different ways, and Fibonacci described several methods for converting from one style of representation to another. In particular, chapter II.7 contains a list of methods for converting an improper fraction to an Egyptian fraction, including the greedy algorithm for Egyptian fractions, also known as the Fibonacci–Sylvester expansion.


In statistics, compositional data are quantitative descriptions of the parts of some whole, conveying relative information. Mathematically, compositional data is represented by points on a simplex. Measurements involving probabilities, proportions, percentages, and ppm can all be thought of as compositional data.


The exclusive constraint states that at most one of the causes 1 and 2 can be true, i.e. both cannot be true simultaneously. The Inclusive (at least one) constraint states that at least one of the causes 1, 2 or 3 must be true, i.e. all cannot be false simultaneously. The one and only one (OaOO or simply O) constraint states that only one of the causes 1, 2 or 3 must be true.


In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f: A → B and g: B → A between the sets A and B, then there exists a bijective function h: A → B. In terms of the cardinality of the two sets, this classically implies that if |A| ≤ |B| and |B| ≤ |A|, then |A| = |B|; that is, A and B are equipotent. This is a useful feature in the ordering of cardinal numbers. The theorem is named after Felix Bernstein and Ernst Schröder. It is also known as the Cantor–Bernstein theorem or Cantor–Schröder–Bernstein theorem, after Georg Cantor, who first published it (albeit without proof).


A tolerable idea may be given of the danger of too great a multiplicity of vulgar names, by imagining what geography would be, or, for instance, the Post-office administration, supposing every town had a totally different name in every language. Various bodies and the authors of many technical and semi-technical books do not simply adapt existing common names for various organisms; they try to coin (and put into common use) comprehensive, useful, authoritative, and standardised lists of new names. The purpose typically is: to create names from scratch where no common names exist to impose a particular choice of name where there is more than one common name to improve existing common names to replace them with names that conform more to the relatedness of the organismsOther attempts to reconcile differences between widely separated regions, traditions, and languages, by arbitrarily imposing nomenclature, often reflect narrow perspectives and have unfortunate outcomes.


For example, a microphone converts an acoustic signal to a voltage waveform, and a speaker does the reverse.Another important property of a signal is its entropy or information content. Information theory serves as the formal study of signals and their content. The information of a signal is often accompanied by noise, which primarily refers to unwanted modifications of signals, but is often extended to include unwanted signals conflicting with desired signals (crosstalk).


In most of the alphabets of India and Southeast Asia, vowels are indicated through diacritics or modification of the shape of the consonant. These are called abugidas. Some abugidas, such as Ethiopic and Cree, are learned by children as syllabaries, and so are often called "syllabics". However, unlike true syllabaries, there is not an independent glyph for each syllable.


In the Linux operating system, JFS is supported with the kernel module (since the kernel version 2.4.18pre9-ac4) and the complementary userspace utilities packaged under the name JFSutils. Most Linux distributions support JFS unless it is specifically removed due to space restrictions, such as on live CDs.According to benchmarks of the available filesystems for Linux, JFS is fast and reliable, with consistently good performance under different kinds of load.Actual usage of JFS in Linux is uncommon, as ext4 typically offers better performance. JFS does have a niche role in Linux: it offers a case-insensitive mount option, unlike most other Linux file systems.There are also potential problems with JFS, such as its implementation of journal writes. They can be postponed until there is another trigger—potentially indefinitely, which can cause data loss over a theoretically infinite timeframe.


In the 1950s and 1960s, travel on an "air ferry" was possible—airplanes, often ex-military, specially equipped to take a small number of cars in addition to foot passengers. These operated various routes including between the United Kingdom and Continental Europe. Companies operating such services included Channel Air Bridge, Silver City Airways, and Corsair. The term is also applied to any "ferrying" by air, and is commonly used when referring to airborne military operations.


In mathematics, a Catalan pseudoprime is an odd composite number n satisfying the congruence ( − 1 ) n − 1 2 ⋅ C n − 1 2 ≡ 2 ( mod n ) , {\displaystyle (-1)^{\frac {n-1}{2}}\cdot C_{\frac {n-1}{2}}\equiv 2{\pmod {n}},} where Cm denotes the m-th Catalan number. The congruence also holds for every odd prime number n that justifies the name pseudoprimes for composite numbers n satisfying it.


In some important economic applications, the relevant change in the constraint set cannot be easily understood as an increase with respect to the strong set order and so Theorem 3 cannot be easily applied. For example, consider a consumer who maximizes a utility function u: X → R {\displaystyle u:X\to \mathbb {R} } subject to a budget constraint. At price p {\displaystyle p} in R + + n {\displaystyle \mathbb {R} _{++}^{n}} and wealth w > 0 {\displaystyle w>0} , his budget set is B ( p , w ) = { x ∈ X | p ⋅ x ≤ w } {\displaystyle B(p,w)=\{x\in X\ |\ p\cdot x\leq w\}} and his demand set at ( p , w ) {\displaystyle (p,w)} is (by definition) D ( p , w ) = arg  max x ∈ B ( p , w ) u ( x ) {\displaystyle D(p,w)=\arg \max _{x\in B(p,w)}u(x)} .


Doug Laney, vice president and analyst at Gartner, conducted research on Wall Street valued companies, which found that companies that had become information-centric, treating data as an asset, often had market-to-book values two to three times higher than the norm. On the topic, Laney commented: "Even as we are in the midst of the Information Age, information simply is not valued by those in the valuation business. However, we believe that, over the next several years, those in the business of valuing corporate investments, including equity analysts, will be compelled to consider a company's wealth of information in properly valuing the company itself." In the latter part of the 2010s, the list of most valuable firms in the world (a list traditionally dominated by oil and energy companies) was dominated by data firms – Microsoft, Alphabet, Apple, Amazon and Facebook.


In recreational mathematics, arithmetic billiards provide a geometrical method to determine the least common multiple and the greatest common divisor of two natural numbers by making use of reflections inside a rectangle whose sides are the two given numbers. This is an easy example of trajectory analysis of dynamical billiards. Arithmetic billiards have been discussed as mathematical puzzles by Hugo Steinhaus and Martin Gardner, and are known to mathematics teachers under the name 'Paper Pool'. They have been used as a source of questions in mathematical circles.


The term relates to the notion that the improved estimate is made closer to the value supplied by the 'other information' than the raw estimate. In this sense, shrinkage is used to regularize ill-posed inference problems. Shrinkage is implicit in Bayesian inference and penalized likelihood inference, and explicit in James–Stein-type inference. In contrast, simple types of maximum-likelihood and least-squares estimation procedures do not include shrinkage effects, although they can be used within shrinkage estimation schemes.


This process is known as dead reckoning. The accuracy and precision of the different PRSs is not the same.


In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which gk ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n. So g is a primitive root modulo n if and only if g is a generator of the multiplicative group of integers modulo n. Gauss defined primitive roots in Article 57 of the Disquisitiones Arithmeticae (1801), where he credited Euler with coining the term. In Article 56 he stated that Lambert and Euler knew of them, but he was the first to rigorously demonstrate that primitive roots exist for a prime n. In fact, the Disquisitiones contains two proofs: The one in Article 54 is a nonconstructive existence proof, while the proof in Article 55 is constructive.