For instance, consider a study where researchers compare a drug with a placebo. If the patients who are given the drug get better than the patients given the placebo by chance, it may appear that the drug is effective, but in fact the conclusion is incorrect. In reverse, type II errors are errors of omission.


In process improvement efforts, quality costs or cost of quality is a means to quantify the total cost of quality-related efforts and deficiencies. It was first described by Armand V. Feigenbaum in a 1956 Harvard Business Review article.Prior to its introduction, the general perception was that higher quality requires higher costs, either by buying better materials or machines or by hiring more labor. Furthermore, while cost accounting had evolved to categorize financial transactions into revenues, expenses, and changes in shareholder equity, it had not attempted to categorize costs relevant to quality, which is especially important given that most people involved in manufacturing never set hands on the product. By classifying quality-related entries from a company's general ledger, management and quality practitioners can evaluate investments in quality based on cost improvement and profit enhancement.


The number of colors required to color unit distance graphs is also unknown (the Hadwiger–Nelson problem): some unit distance graphs require five colors, and every unit distance graph can be colored with seven colors. For every algebraic number there is a unit distance graph with two vertices that must be that distance apart. According to the Beckman–Quarles theorem, the only plane transformations that preserve all unit distance graphs are the isometries.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 238, 1238, 2348, and 12348 are the patterns related to Braille pattern dots-126, since the two additional dots of kantenji patterns 0126, 1267, and 01267 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Members of the class of Brandt semigroups are required to satisfy not just one condition but a set of additional properties. A large collection of special classes of semigroups have been defined though not all of them have been studied equally intensively.


In order to demonstrate the use of some of the indicative verb tenses in Louisiana French, take the example of manger, meaning "to eat": Some minor simplification of tenses is exhibited in the conjugation of the verb manger, namely of the plural first and second person conjugations which are inflected identically to the third person singular. Not only this, but the inflection of the third person plural verb form has diverged between the form identical to Standard French and the use of -ont in for all verbs. The elision that is common in many aspects of French is accelerated in Louisiana French with the schwa in je often omitted regardless of the presence of a following vowel as well as the regular use of t'es (tu es) and t'as (tu as) as opposed to such avoidance in Standard French. The present progressive tense of Louisiana French initially appears alien as compared to Standard French but après/apé possesses the same function signified by en train de.


It is commonly stated as: In a given instance of the stable-roommates problem (SRP), each of 2n participants ranks the others in strict order of preference. A matching is a set of n disjoint pairs of participants. A matching M in an instance of SRP is stable if there are no two participants x and y, each of whom prefers the other to their partner in M. Such a pair is said to block M, or to be a blocking pair with respect to M.


In the Dart language, used in the Flutter SDK, the conventions are similar to those of Java, except that constants are written in lowerCamelCase. Dart imposes the syntactic rule that non-local identifiers beginning with an underscore (_) are treated as private (since the language does not have explicit keywords for public or private access). Additionally, source file names do not follow Java's "one public class per source file, name must match" rule, instead using snake_case for filenames.


In the BitTorrent file distribution system, a torrent file or meta-info file is a computer file that contains metadata about files and folders to be distributed, and usually also a list of the network locations of trackers, which are computers that help participants in the system find each other and form efficient distribution groups called swarms. A torrent file does not contain the content to be distributed; it only contains information about those files, such as their names, folder structure, sizes, and cryptographic hash values for verifying file integrity. Torrent files are normally named with the extension ".torrent". A torrent file acts like a table of contents (index) that allows computers to find information through the use of a BitTorrent client.


In planar graphs, colorings with k {\displaystyle k} distinct colors are dual to nowhere-zero flows over the ring Z k {\displaystyle \mathbb {Z} _{k}} of integers modulo k {\displaystyle k} . In this duality, the difference between the colors of two adjacent regions is represented by a flow value across the edge separating the regions. In particular, the existence of nowhere-zero 4-flows is equivalent to the four color theorem. The snark theorem generalizes this result to nonplanar graphs. == References ==


In the first half of the 20th century, various formalisms were proposed to capture the informal concept of a computable function, with μ-recursive functions, Turing machines and the lambda calculus possibly being the best-known examples today. The surprising fact that they are essentially equivalent, in the sense that they are all encodable into each other, supports the Church-Turing thesis. Another shared feature is more rarely commented on: they all are most readily understood as models of sequential computation. The subsequent consolidation of computer science required a more subtle formulation of the notion of computation, in particular explicit representations of concurrency and communication.


In the Apple Darwin operating system, and in the macOS and iOS operating systems built on top of it, the path of the dynamic linker that should be used is embedded at link time into one of the Mach-O load commands in the executable image. In those systems, dynamically loaded shared libraries can be identified either by the filename suffix .dylib or by their placement inside the bundle for a framework. The dynamic linker not only links the target executable to the shared libraries but also places machine code functions at specific address points in memory that the target executable knows about at link time. When an executable wishes to interact with the dynamic linker, it simply executes the machine-specific call or jump instruction to one of those well-known address points.


which is equivalent to ∀ F ∃ A ∀ x  ⇒ x ∈ A ] . {\displaystyle \forall {\mathcal {F}}\,\exists A\forall x\Rightarrow x\in A].} Compared to the axiom stated at the top of this section, this variation asserts only one direction of the implication, rather than both directions.


In more advanced mathematics, the partial sums of the harmonic series 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ {\displaystyle 1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+\cdots } grow logarithmically. In the design of computer algorithms, logarithmic growth, and related variants, such as log-linear, or linearithmic, growth are very desirable indications of efficiency, and occur in the time complexity analysis of algorithms such as binary search.Logarithmic growth can lead to apparent paradoxes, as in the martingale roulette system, where the potential winnings before bankruptcy grow as the logarithm of the gambler's bankroll. It also plays a role in the St.


Notationally: ∀ x , x ′ ∈ X , f ( x ) = f ( x ′ ) ⟹ x = x ′ , {\displaystyle \forall x,x'\in X,f(x)=f(x')\implies x=x',} or, equivalently (using logical transposition), ∀ x , x ′ ∈ X , x ≠ x ′ ⟹ f ( x ) ≠ f ( x ′ ) . {\displaystyle \forall x,x'\in X,x\neq x'\implies f(x)\neq f(x').} The function is surjective, or onto, if each element of the codomain is mapped to by at least one element of the domain.


In natural language processing, semantic compression is a process of compacting a lexicon used to build a textual document (or a set of documents) by reducing language heterogeneity, while maintaining text semantics. As a result, the same ideas can be represented using a smaller set of words. In most applications, semantic compression is a lossy compression, that is, increased prolixity does not compensate for the lexical compression, and an original document cannot be reconstructed in a reverse process.


\ matches any single character surrounded by "" since the brackets are escaped, for example: "", "", "", "", "]", and "" (bracket space bracket). s. * matches s followed by zero or more characters, for example: "s", "saw", "seed", "s3w96.7", and "s6#h%(>>>m n mQ".


In population dynamics the growth of human population is sometimes supposed to be double exponential. Varfolomeyev and Gurevich experimentally fit N ( y ) = 375.6 ⋅ 1.00185 1.00737 y − 1000 {\displaystyle N(y)=375.6\cdot 1.00185^{1.00737^{y-1000}}\,} where N(y) is the population in millions in year y.


The GDP Deflator Index, or real GDP, measures the level of prices of all-new, domestically produced, final goods and services in an economy. Market performance indices include the labour market index/job index and proprietary stock market index investment instruments offered by brokerage houses. Some indices display market variations.


In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself.An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.


In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development has been motivated by descriptive complexity theory and their relationship to database query languages, in particular to Datalog.


Other references are given in the References below. The basic definitions in this article are contained within the first few chapters of any of these books. Any monoid can be understood as a special sort of category (with a single object whose self-morphisms are represented by the elements of the monoid), and so can any preorder.


The complement is a determiner phrase (or noun phrase, depending on analytical scheme followed).Determiner Phrase: the head of a determiner phrase (DP) is a determiner. DPs were proposed under generative syntax; not all theories of syntax agree that they exist.Complementizer Phrase: the head of a complementizer phrase (CP) is a complementizer, like that in English. In some cases the C head is covert (not overtly present). The complement of C is generally agreed to be a tense phrase (TP).Tense Phrase: the head of a tense phrase (TP) is tense; these are phrases in which the head is an abstract category representing tense; the complement is a verb phrase.Aspect Phrase: the head of an aspect phrase (AspP) is aspect; these are phrases in which the head is an abstract syntactic category representing aspect. In more traditional analysis the entire phrase (including any elements denoting tense or aspect) is considered to be simply a verb phrase.


In telecommunications, a femtocell is a small, low-power cellular base station, typically designed for use in a home or small business. A broader term which is more widespread in the industry is small cell, with femtocell as a subset. It connects to the service provider's network via broadband (such as DSL or cable); current designs typically support four to eight simultaneously active mobile phones in a residential setting depending on version number and femtocell hardware, and eight to sixteen mobile phones in enterprise settings. A femtocell allows service providers to extend service coverage indoors or at the cell edge, especially where access would otherwise be limited or unavailable.


Marking a causal process modifies it, a mark not transmitted by a pseudo process. Meanwhile, causal forks are "the means by which causal structure is generated and modified". Others have found Salmon's theory of mark transmission to have shortcomings, however, whereby it can fail to discern causal processes from pseudo processes.


The need for information sharing has led to the need to depart from the rigidity of MAC in favor of balancing need to protect with need to share. When the ‘balance’ is decided at the discretion of users, the access control is called discretionary access control (DAC) that is more tolerant of actions that manage risk where MAC requires risk avoidance. Allowing users and systems to manage the risk of sharing information is in some way contrary to the original motivation for MAC.


In query by example, the element used to search is a multimedia content (image, audio, video). In other words, the query is a media. Often, it's used audiovisual indexing. It will be necessary to choose the criteria we are going to use for creating metadata.


In the context of free and open-source software, proprietary software only available as a binary executable is referred to as a blob or binary blob. The term usually refers to a device driver module loaded into the kernel of an open-source operating system, and is sometimes also applied to code running outside the kernel, such as system firmware images, microcode updates, or userland programs. The term blob was first used in database management systems to describe a collection of binary data stored as a single entity. When computer hardware vendors provide complete technical documentation for their products, operating system developers are able to write hardware device drivers to be included in the operating system kernels.


Scheinerman also conjectured that segments with only three directions would be sufficient to represent 3-colorable graphs, and West (1991) conjectured that analogously every planar graph could be represented using four directions. If a graph is represented with segments having only k directions and no two segments belong to the same line, then the graph can be colored using k colors, one color for each direction. Therefore, if every planar graph can be represented in this way with only four directions, then the four color theorem follows.


In the following pseudocode algorithm, dist is an array that contains the current distances from the source to other vertices, i.e. dist is the current distance from the source to the vertex u. The prev array contains pointers to previous-hop nodes on the shortest path from source to the given vertex (equivalently, it is the next-hop on the path from the given vertex to the source). The code u ← vertex in Q with min dist, searches for the vertex u in the vertex set Q that has the least dist value. Graph.Edges(u, v) returns the length of the edge joining (i.e. the distance between) the two neighbor-nodes u and v. The variable alt on line 14 is the length of the path from the root node to the neighbor node v if it were to go through u. If this path is shorter than the current shortest path recorded for v, that current path is replaced with this alt path. 1 function Dijkstra(Graph, source): 2 3 for each vertex v in Graph.Vertices: 4 dist ← INFINITY 5 prev ← UNDEFINED 6 add v to Q 7 dist ← 0 8 9 while Q is not empty: 10 u ← vertex in Q with min dist 11 remove u from Q 12 13 for each neighbor v of u still in Q: 14 alt ← dist + Graph.Edges(u, v) 15 if alt < dist: 16 dist ← alt 17 prev ← u 18 19 return dist, prev If we are only interested in a shortest path between vertices source and target, we can terminate the search after line 10 if u = target.


Prominent intersection type systems include the Coppo–Dezani type assignment system, the Barendregt-Coppo–Dezani type assignment system, and the essential intersection type assignment system. Most strikingly, intersection type systems are closely related to (and often exactly characterize) normalization properties of λ-terms under β-reduction. In programming languages, such as TypeScript and Scala, intersection types are used to express ad hoc polymorphism.


In mathematics, in the field of group theory, a metanilpotent group is a group that is nilpotent by nilpotent. In other words, it has a normal nilpotent subgroup such that the quotient group is also nilpotent. In symbols, G {\displaystyle G} is metanilpotent if there is a normal subgroup N {\displaystyle N} such that both N {\displaystyle N} and G / N {\displaystyle G/N} are nilpotent. The following are clear: Every metanilpotent group is a solvable group. Every subgroup and every quotient of a metanilpotent group is metanilpotent.


In physics, a dynamical system evolving in time may be described in a phase space, that is by the evolution in time of some variables. If this variables are bounded, that is having a minimum and a maximum, for a theorem due to Liouville, a measure can be defined in the space, having a measure space where the lemma applies. As a consequence, given a configuration of the system (a point in the phase space) the average return period close to this configuration (in the neighbourhood of the point) is inversely proportional to the considered size of volume surrounding the configuration. Normalizing the measure space to 1, it becomes a probability space and the measure P ( A ) {\displaystyle P(A)} of its set A {\displaystyle A} represents the probability of finding the system in the states represented by the points of that set. In this case the lemma implies that the smaller is the probability to be in a certain state (or close to it), the longer is the time of return near that state.In formulas, if A {\displaystyle A} is the region close to the starting point and T R {\displaystyle T_{R}} is the return period, its average value is: ⟨ T R ⟩ = τ / P ( A ) {\displaystyle \langle T_{R}\rangle =\tau /P(A)} Where τ {\displaystyle \tau } is a characteristic time of the system in question. Note that since the volume of A {\displaystyle A} , therefore P ( A ) {\displaystyle P(A)} , depends exponentially on the n {\displaystyle n} variables in the system ( A = ϵ n {\displaystyle A=\epsilon ^{n}} , with ϵ {\displaystyle \epsilon } infinitesimal side, therefore less than 1, of the volume in n {\displaystyle n} dimensions), P ( A ) {\displaystyle P(A)} decreases very rapidly as the variables of the system increase and consequently the return period increases exponentially.In practice, as the variables needed to describe the system increase, the return period increases rapidly.


Removing stop words and punctuation Some tokens are less important than others. For instance, common words such as "the" might not be very helpful for revealing the essential characteristics of a text. So usually it is a good idea to eliminate stop words and punctuation marks before doing further analysis.


In mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable-roommate problem (SRP) is the problem of finding a stable matching for an even-sized set. A matching is a separation of the set into disjoint pairs ("roommates"). The matching is stable if there are no two elements which are not roommates and which both prefer each other to their roommate under the matching. This is distinct from the stable-marriage problem in that the stable-roommates problem allows matches between any two elements, not just between classes of "men" and "women".


{\displaystyle c.} Also, recall that a Hermitian (or real symmetric) matrix has real eigenvalues. It can be shown that, for a given matrix, the Rayleigh quotient reaches its minimum value λ min {\displaystyle \lambda _{\min }} (the smallest eigenvalue of M) when x {\displaystyle \mathbf {x} } is v min {\displaystyle \mathbf {v} _{\min }} (the corresponding eigenvector).


In software engineering, code coverage is a percentage measure of the degree to which the source code of a program is executed when a particular test suite is run. A program with high test coverage has more of its source code executed during testing, which suggests it has a lower chance of containing undetected software bugs compared to a program with low test coverage. Many different metrics can be used to calculate test coverage.


In physical geography, a channel is a type of landform consisting of the outline of a path of relatively shallow and narrow body of water or of other fluids (e.g., lava), most commonly the confine of a river, river delta or strait. The word often refers to a natural body of water, while the cognate term canal denotes a similar artificial structure. Channels are important for the functionality of ports and other bodies of water used for navigability for shipping.


Much of the system's core, including the LWKT subsystem, the IPI messaging subsystem and the new kernel memory allocator, are lockless, meaning that they work without using mutexes, with each process operating on a single CPU. Critical sections are used to protect against local interrupts, individually for each CPU, guaranteeing that a thread currently being executed will not be preempted.Serializing tokens are used to prevent concurrent accesses from other CPUs and may be held simultaneously by multiple threads, ensuring that only one of those threads is running at any given time. Blocked or sleeping threads therefore do not prevent other threads from accessing the shared resource unlike a thread that is holding a mutex.


In some languages, the grammatical expression of past tense is combined with the expression of other categories such as grammatical aspect (see tense–aspect). Thus a language may have several types of past tense form, their use depending on what aspectual or other additional information is to be encoded. French, for example, has a compound past (passé composé) for expressing completed events, and imperfect for continuous or repetitive events. Some languages that grammaticalise for past tense do so by inflecting the verb, while others do so periphrastically using auxiliary verbs, also known as "verbal operators" (and some do both, as in the example of French given above).


In mathematics, an addition chain for computing a positive integer n can be given by a sequence of natural numbers starting with 1 and ending with n, such that each number in the sequence is the sum of two previous numbers. The length of an addition chain is the number of sums needed to express all its numbers, which is one less than the cardinality of the sequence of numbers.


In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same number of elements.


In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions. DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling). Directed acyclic graphs are sometimes instead called acyclic directed graphs or acyclic digraphs.


The pps sampling results in a fixed sample size n (as opposed to Poisson sampling which is similar but results in a random sample size with expectancy of n). When selecting items with replacement the selection procedure is to just draw one item at a time (like getting n draws from a multinomial distribution with N elements, each with their own p i {\displaystyle p_{i}} selection probability). If doing a without-replacement sampling, the schema can become more complex. : 93


In programming language theory, flow-sensitive typing (also called flow typing or occurrence typing) is a type system where the type of an expression depends on its position in the control flow. In statically typed languages, a type of an expression is determined by the types of the sub-expressions that compose it. However, in flow-sensitive typing, an expression's type may be updated to a more specific type if it follows an operation that validates its type. Validating operations can include type predicates, imperative updates, and control flow.


This automorphism group permutes the three 8-dimensional irreducible representations of Spin(8); these being the vector representation and two chiral spin representations. These automorphisms do not project to automorphisms of SO(8). The vector representation—the natural action of SO(8) (hence Spin(8)) on F8—consists over the real numbers of Euclidean 8-vectors and is generally known as the "defining module", while the chiral spin representations are also known as "half-spin representations", and all three of these are fundamental representations.


The most common choice is the initial ordinal in that class. This is usually taken as the definition of cardinal number in axiomatic set theory.Assuming the axiom of choice, the cardinalities of the infinite sets are denoted ℵ 0 < ℵ 1 < ℵ 2 < … . {\displaystyle \aleph _{0}<\aleph _{1}<\aleph _{2}<\ldots .}


Consider a segment that begins at n = kL + M, for any integer k, and define: x k  ≜ { x  , 1 ≤ n ≤ L + M − 1 0 , otherwise . {\displaystyle x_{k}\ \triangleq {\begin{cases}x,&1\leq n\leq L+M-1\\0,&{\textrm {otherwise}}.\end{cases}}} y k  ≜ x k  ∗ h  = ∑ m = 1 M h  ⋅ x k  . {\displaystyle y_{k}\ \triangleq \ x_{k}*h=\sum _{m=1}^{M}h\cdot x_{k}.}


The challenge remains to search large indices or popular query lists in under a few milliseconds so that the user sees results pop up while typing. Autocomplete can have an adverse effect on individuals and businesses when negative search terms are suggested when a search takes place. Autocomplete has now become a part of reputation management as companies linked to negative search terms such as scam, complaints and fraud seek to alter the results. Google in particular have listed some of the aspects that affect how their algorithm works, but this is an area that is open to manipulation.


&& for short-circuit logical AND. (4 && 2) is true.In C, C++, and Go, a prefix & is a unary operator denoting the address in memory of the argument, e.g. &x, &func, &a. In C++ and PHP, unary prefix & before a formal parameter of a function denotes pass-by-reference.In Pascal, the & as the first character of an identifier prevents the compiler from treating it as a keyword, thus escaping it. In Fortran, the ampersand forces the compiler to treat two lines as one.


Some of the most basic are the percentage of program subroutines and the percentage of program statements called during execution of the test suite. Test coverage was among the first methods invented for systematic software testing. The first published reference was by Miller and Maloney in Communications of the ACM, in 1963.


Similar definitions exist for digraphs, in terms of directed cycles. Finding a vertex-disjoint cycle cover of a directed graph can also be performed in polynomial time by a similar reduction to perfect matching. However, adding the condition that each cycle should have length at least 3 makes the problem NP-hard.


Later Macs could also read and write 1.44 MB HD disks in PC format with fixed rotation speed. Higher capacities were similarly achieved by Acorn's RISC OS (800 KB for DD, 1,600 KB for HD) and AmigaOS (880 KB for DD, 1,760 KB for HD). All 3½-inch disks have a rectangular hole in one corner which, if obstructed, write-enables the disk.


They >completely< forgot me! I had _nothing_ to do with it. (Commonly interpreted as underlining, which is an alternative to italics.)


"The theorem appears in a 1922 publication of Ernst Steinitz, after whom it is named. It can be proven by mathematical induction (as Steinitz did), by finding the minimum-energy state of a two-dimensional spring system and lifting the result into three dimensions, or by using the circle packing theorem. Several extensions of the theorem are known, in which the polyhedron that realizes a given graph has additional constraints; for instance, every polyhedral graph is the graph of a convex polyhedron with integer coordinates, or the graph of a convex polyhedron all of whose edges are tangent to a common midsphere.


In machine learning, specifically empirical risk minimization, MSE may refer to the empirical risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The MSE is a measure of the quality of an estimator. As it is derived from the square of Euclidean distance, it is always a positive value that decreases as the error approaches zero.


The algorithm takes its name from the fact that, when this rewriting is done and the resulting proof is displayed as a DAG (directed acyclic graph), the unit node η {\displaystyle \eta } appears lower (i.e., closer to the root) than it used to appear in the original proof. A naive implementation exploiting theorem would require the proof to be traversed and fixed after each unit node is lowered. It is possible, however, to do better by first collecting and removing all the unit nodes in a single traversal, and afterwards fixing the whole proof in a single second traversal.


Brief instructional blocks can be recorded for review by students — they will see the exact presentation that occurred in the classroom with the teacher's audio input. This can help transform learning and instruction. Many companies and projects now focus on creating supplemental instructional materials specifically designed for interactive whiteboards. One recent use of the IWB is in shared reading lessons. Mimic books, for instance, allow teachers to project children's books onto the interactive whiteboard with book-like interactivity.


In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by Dickson (1904) that for a finite set of linear forms a1 + b1n, a2 + b2n, ..., ak + bkn with bi ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this (Ribenboim 1996, 6.I). The case k = 1 is Dirichlet's theorem. Two other special cases are well-known conjectures: there are infinitely many twin primes (n and 2 + n are primes), and there are infinitely many Sophie Germain primes (n and 1 + 2n are primes). Dickson's conjecture is further extended by Schinzel's hypothesis H.


In several studies, participants read a list of high or low frequency words along with nonwords (or pseudowords). They were tasked with pronouncing the words or nonwords as fast as possible. High frequency words were read aloud faster than low frequency words. Participants read the nonwords the slowest. More errors were made when pronouncing the low frequency words than the high frequency words.


In fact, all square roots of natural numbers, other than of perfect squares, are irrational.Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence. For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat.


For general closed convex sets, the limit point need not be the projection. Classical work on the case of two closed convex sets shows that the rate of convergence of the iterates is linear. There are now extensions that consider cases when there are more than two sets, or when the sets are not convex, or that give faster convergence rates.


This chain of extensions canonically embeds the natural numbers in the other number systems. Properties of the natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics.


The term Cone of Uncertainty is used in software development where the technical and business environments change very rapidly. However, the concept, under different names, is a well-established basic principle of cost engineering. Most environments change so slowly that they can be considered static for the duration of a typical project, and traditional project management methods therefore focus on achieving a full understanding of the environment through careful analysis and planning.


In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring (described below) of a triangulation of an n {\displaystyle n} -dimensional simplex contains a cell whose vertices all have different colors. The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain. Sperner colorings have been used for effective computation of fixed points and in root-finding algorithms, and are applied in fair division (cake cutting) algorithms.


Therefore, the dyadic product is linear in both of its operands. In general, two dyadics can be added to get another dyadic, and multiplied by numbers to scale the dyadic. However, the product is not commutative; changing the order of the vectors results in a different dyadic.


The HID descriptor is a hard coded array of bytes that describes the device's data packets. This includes: how many packets the device supports, the size of the packets, and the purpose of each byte and bit in the packet. For example, a keyboard with a calculator program button can tell the host that the button's pressed/released state is stored as the 2nd bit in the 6th byte in data packet number 4 (note: these locations are only illustrative and are device-specific).


In mathematics, the plethystic exponential is a certain operator defined on (formal) power series which, like the usual exponential function, translates addition into multiplication. This exponential operator appears naturally in the theory of symmetric functions, as a concise relation between the generating series for elementary, complete and power sums homogeneous symmetric polynomials in many variables. Its name comes from the operation called plethysm, defined in the context of so-called lambda rings. In combinatorics, the plethystic exponential is a generating function for many well studied sequences of integers, polynomials or power series, such as the number of integer partitions. It is also an important technique in the enumerative combinatorics of unlabelled graphs, and many other combinatorial objects.In geometry and topology, the plethystic exponential of a certain geometric/topologic invariant of a space, determines the corresponding invariant of its symmetric products.


In mathematical logic, the Paris–Harrington theorem states that a certain combinatorial principle in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in Peano arithmetic, is not provable in this system. The combinatorial principle is however provable in slightly stronger systems. This result has been described by some (such as the editor of the Handbook of Mathematical Logic in the references below) as the first "natural" example of a true statement about the integers that could be stated in the language of arithmetic, but not proved in Peano arithmetic; it was already known that such statements existed by Gödel's first incompleteness theorem.


If the CPU guesses wrong, all of these instructions and their context need to be flushed and the correct ones loaded, which takes time. This has led to increasingly complex instruction-dispatch logic that attempts to guess correctly, and the simplicity of the original reduced instruction set computing (RISC) designs has been eroded. VLIW lacks this logic, and thus lacks its energy use, possible design defects, and other negative aspects.


In the case where the compact set K {\displaystyle K} is also convex, the above theorem has as a corollary the first part of the next theorem, which is also often called the Krein–Milman theorem. The convex hull of the extreme points of K {\displaystyle K} forms a convex subset of K {\displaystyle K} so the main burden of the proof is to show that there are enough extreme points so that their convex hull covers all of K . {\displaystyle K.} For this reason, the following corollary to the above theorem is also often called the Krein–Milman theorem.


In the International Phonetic Alphabet (IPA), aspirated consonants are written using the symbols for voiceless consonants followed by the aspiration modifier letter ⟨◌ʰ⟩, a superscript form of the symbol for the voiceless glottal fricative ⟨h⟩. For instance, ⟨p⟩ represents the voiceless bilabial stop, and ⟨pʰ⟩ represents the aspirated bilabial stop. Voiced consonants are seldom actually aspirated. Symbols for voiced consonants followed by ⟨◌ʰ⟩, such as ⟨bʰ⟩, typically represent consonants with murmured voiced release (see below).


On the other hand, genuine quantifiers (e.g., 'every professor') bear scope. An 'every-NP' triggers the introduction of a complex condition of the form K1 → K2, where K1 and K2 are sub-DRSs representing the restriction and the scope of the quantification respectively. Unlike true quantifiers, indefinite noun phrases just contribute a new DR (together with some descriptive material in terms of conditions on the DR), which is placed in a larger structure. This larger structure can be the top-level DRS or some sub-DRS according to the sentence-internal environment of the analyzed noun phrase—in other words, a level that is accessible to an anaphor that comes later.


In some machine translation and natural language processing systems, written texts in human languages are parsed by computer programs. Human sentences are not easily parsed by programs, as there is substantial ambiguity in the structure of human language, whose usage is to convey meaning (or semantics) amongst a potentially unlimited range of possibilities but only some of which are germane to the particular case. So an utterance "Man bites dog" versus "Dog bites man" is definite on one detail but in another language might appear as "Man dog bites" with a reliance on the larger context to distinguish between those two possibilities, if indeed that difference was of concern. It is difficult to prepare formal rules to describe informal behaviour even though it is clear that some rules are being followed.In order to parse natural language data, researchers must first agree on the grammar to be used.


Some explosives, e.g. ANFO, show reduced sensitivity under pressure. A transient pressure wave from a nearby detonation may compress the explosive sufficiently to make its initiation fail. This can be prevented by introducing sufficient delays into the firing sequence.A sympathetic detonation during mine blasting may influence the seismic signature of the blast, by boosting the P-wave amplitude without significantly amplifying the surface wave.


Under a Montagovian approach, the indefinite a donkey, which is assumed to be inherently an existential quantifier, ends up becoming a universal quantifier, an unwelcome result because the change in quantificational force cannot be accounted for in any principled way. DRT avoids this problem by assuming that indefinites introduce discourse referents (DRs), which are stored in the mental representation and are accessible (or not, depending on the conditions) to expressions like pronouns and other anaphoric elements. Furthermore, they are inherently non-quantificational, and pick up quantificational force depending upon the context.


Minnan also has words consisting of a consonant followed by a syllabic nasal, such as pn̄g "cooked rice". So far, all of these syllabic consonants, at least in the lexical words, have been sonorants, such as , , , and , which have a voiced quality similar to vowels. (They can carry tone, for example.)


P(A|B) (the conditional probability of A given B) typically differs from P(B|A). For example, if a person has dengue fever, the person might have a 90% chance of being tested as positive for the disease. In this case, what is being measured is that if event B (having dengue) has occurred, the probability of A (tested as positive) given that B occurred is 90%, simply writing P(A|B) = 90%.


In operations on numerical values, problems can arise that result in unexpected output, slowing of a process, or crashing. These can be from a lack of awareness of the qualities of the data storage such as a loss of precision due to rounding, numerically unstable algorithms, arithmetic overflow and underflow, or from lack of awareness of how calculations are handled by different software coding languages such as division by zero which in some languages may throw an exception, and in others may return a special value such as NaN or infinity.


Some consider "inter-city" service to be that which operates as an express service between two main city stations, bypassing intermediate stations. However, this term is used in Australia (Sydney for example) to describe the regional trains operating beyond the boundaries of the suburban services, even though some of these "inter-city" services stop all stations similar to German regional services. In this regard, the German service delineations and naming conventions are clearer and better used for academic purposes.


In the concept discovery step, terms are grouped to meaning bearing units, which correspond to an abstraction of the world and therefore to concepts. The grouped terms are these domain-specific terms and their synonyms, which were identified in the domain terminology extraction step.


In the following the Majority Judgment winner for the normal ballots is determined. The sorted ratings would be as follows: Result: The median of A is between "Good" and "Poor" and thus is rounded down to "Poor". The median of B is "Fair". Thus, B is elected Majority Judgment winner.


This phenomenon is closely related to the coupon collector's problem: in order to be connected, a random graph needs enough edges for each vertex to be incident to at least one edge. More precisely, if random edges are added one by one to a graph, then with high probability the first edge whose addition connects the whole graph touches the last isolated vertex.For different models including the random subgraphs of grid graphs, the connected components are described by percolation theory. A key question in this theory is the existence of a percolation threshold, a critical probability above which a giant component (or infinite component) exists and below which it does not.


In recursion theory, the Kleene–Brouwer order may be applied to the computation trees of implementations of total recursive functionals. A computation tree is well-founded if and only if the computation performed by it is total recursive. Each state x {\displaystyle x} in a computation tree may be assigned an ordinal number | | x | | {\displaystyle ||x||} , the supremum of the ordinal numbers 1 + | | y | | {\displaystyle 1+||y||} where y {\displaystyle y} ranges over the children of x {\displaystyle x} in the tree. In this way, the total recursive functionals themselves can be classified into a hierarchy, according to the minimum value of the ordinal at the root of a computation tree, minimized over all computation trees that implement the functional. The Kleene–Brouwer order of a well-founded computation tree is itself a recursive well-ordering, and at least as large as the ordinal assigned to the tree, from which it follows that the levels of this hierarchy are indexed by recursive ordinals.


There is no penalty for incorrect answers. The final song of each round is designated as the "Fast Track" and is played at double value. During the season finale, this song is played as a "Fast Track Challenge," in which the teams must respond within the time needed for Shazam to identify it. No multiple-choice answers are offered, and only the first team to buzz in is given a chance to name the song and win the money for it.


When compared to shipping boxes and printing user manuals, the pace and efficiency provided by the App Store is profound and has changed software distribution forever. During the early development of the Electronic AppWrapper, it became the first commercial software distribution catalog to allow digital data encryption and provide digital rights management for apps, music and data. This was a tremendous advance for the independent developers who could not possibly access the financial resources to publish software boxes across the country and the world, in order to reach their audience.


In the U.S. and Canada, dissemination of flood warnings is covered by Specific Area Message Encoding (SAME) code FLW, which is used by the U.S. Emergency Alert System and NOAA Weather Radio network and in Canada's Weatheradio Canada network. "Flood statements" are issued by the National Weather Service to inform the public of flooding along major streams in which there is not a serious threat to life or property. They may also follow a flood warning to give later information.


For our example key matrix: | 6 24 1 13 16 10 20 17 15 | = 6 ( 16 ⋅ 15 − 10 ⋅ 17 ) − 24 ( 13 ⋅ 15 − 10 ⋅ 20 ) + 1 ( 13 ⋅ 17 − 16 ⋅ 20 ) = 441 ≡ 25 ( mod 26 ) {\displaystyle {\begin{vmatrix}6&24&1\\13&16&10\\20&17&15\end{vmatrix}}=6(16\cdot 15-10\cdot 17)-24(13\cdot 15-10\cdot 20)+1(13\cdot 17-16\cdot 20)=441\equiv 25{\pmod {26}}} So, modulo 26, the determinant is 25. Since 25 = 5 2 {\displaystyle 25=5^{2}} and 26 = 2 × 13 {\displaystyle 26=2\times 13} , 25 has no common factors with 26, and this matrix can be used for the Hill cipher. The risk of the determinant having common factors with the modulus can be eliminated by making the modulus prime. Consequently, a useful variant of the Hill cipher adds 3 extra symbols (such as a space, a period and a question mark) to increase the modulus to 29.


In standard truth-functional propositional logic, association, or associativity are two valid rules of replacement. The rules allow one to move parentheses in logical expressions in logical proofs. The rules (using logical connectives notation) are: and where " ⇔ {\displaystyle \Leftrightarrow } " is a metalogical symbol representing "can be replaced in a proof with".


The time it takes to organise teams and have them cooperate can be time-consuming. Additionally, there is a potential risk of having a free-rider problem, where individuals within a team can get away with no contribution to the work and still be compensated the same amount as their peers.However, free-riding can be eliminated by organising set protocols. This allows for easier communication and decision-making, giving each member of the team responsibilities and requirements that are agreed upon.


In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject used in most modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated by a linear system (see linearization), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.


In register machines, a common subexpression (a subexpression which is used multiple times with the same result value) can be evaluated just once and its result saved in a fast register. The subsequent reuses have no time or code cost, just a register reference. This optimization speeds simple expressions (for example, loading variable X or pointer P) as well as less-common complex expressions.


By isolating the kernel from concurrency, many parts of the kernel no longer need to be modified to support SMP. However, as in giant-lock SMP systems only one processor can run the kernel code at a time, performance for applications spending significant amounts of time in the kernel is not much improved. Accordingly, the giant-lock approach is commonly seen as a preliminary means of bringing SMP support to an operating system, yielding benefits only in user space. Most modern operating systems use a fine-grained locking approach.


Every job j {\displaystyle j} consists of m {\displaystyle m} operations O i j {\displaystyle O_{ij}} for i = 1 , … , m {\displaystyle i=1,\ldots ,m} , to be scheduled in the given order. Operation O i j {\displaystyle O_{ij}} must be processed for p i j {\displaystyle p_{ij}} units on machine i {\displaystyle i} . J: Job-shop problem. Every job j {\displaystyle j} consists of n j {\displaystyle n_{j}} operations O k j {\displaystyle O_{kj}} for k = 1 , … , n j {\displaystyle k=1,\ldots ,n_{j}} , to be scheduled in that order. Operation O k j {\displaystyle O_{kj}} must be processed for p k j {\displaystyle p_{kj}} units on a dedicated machine μ k j {\displaystyle \mu _{kj}} with μ k j ≠ μ k ′ j {\displaystyle \mu _{kj}\neq \mu _{k'j}} for k ≠ k ′ {\displaystyle k\neq k'} .


In strongly typed programming languages, each parameter's type must be specified in the procedure declaration. Languages using type inference attempt to discover the types automatically from the function's body and usage. Dynamically typed programming languages defer type resolution until run-time. Weakly typed languages perform little to no type resolution, relying instead on the programmer for correctness. Some languages use a special keyword (e.g. void) to indicate that the subroutine has no parameters; in formal type theory, such functions take an empty parameter list (whose type is not void, but rather unit).


In mathematics, low-rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix (the data) and an approximating matrix (the optimization variable), subject to a constraint that the approximating matrix has reduced rank. The problem is used for mathematical modeling and data compression. The rank constraint is related to a constraint on the complexity of a model that fits the data. In applications, often there are other constraints on the approximating matrix apart from the rank constraint, e.g., non-negativity and Hankel structure. Low-rank approximation is closely related to numerous other techniques, including principal component analysis, factor analysis, total least squares, latent semantic analysis, orthogonal regression, and dynamic mode decomposition.


In terms of machine learning and pattern classification, the labels of a set of random observations can be divided into 2 or more classes. Each observation is called an instance and the class it belongs to is the label. The Bayes error rate of the data distribution is the probability an instance is misclassified by a classifier that knows the true class probabilities given the predictors. For a multiclass classifier, the expected prediction error may be calculated as follows: E P E = E x  {\displaystyle EPE=E_{x}} where x is the instance, E  {\displaystyle E} the expectation value, Ck is a class into which an instance is classified, P(Ck|x) is the conditional probability of label k for instance x, and L() is the 0–1 loss function: L ( x , y ) = 1 − δ x , y = { 0 if x = y 1 if x ≠ y , {\displaystyle L(x,y)=1-\delta _{x,y}={\begin{cases}0&{\text{if }}x=y\\1&{\text{if }}x\neq y\end{cases}},} where δ x , y {\displaystyle \delta _{x,y}} is the Kronecker delta.


The set  as a subspace of R {\displaystyle \mathbb {R} } is both open and closed, whereas as a subset of R {\displaystyle \mathbb {R} } it is only closed. As a subspace of R {\displaystyle \mathbb {R} } ,  ∪  is composed of two disjoint open subsets (which happen also to be closed), and is therefore a disconnected space. Let S = [0, 1) be a subspace of the real line R {\displaystyle \mathbb {R} } .


In software engineering, secure coding aims to guard against the accidental introduction of security vulnerabilities. It is also possible to create software designed from the ground up to be secure. Such systems are secure by design. Beyond this, formal verification aims to prove the correctness of the algorithms underlying a system; important for cryptographic protocols for example.


In the domain of logical frameworks, the term higher-order abstract syntax is usually used to refer to a specific representation that uses the binders of the meta-language to encode the binding structure of the object language. For instance, the logical framework LF has a λ-construct, which has arrow (→) type. As an example, consider we wanted to formalize a very primitive language with untyped expressions, a built-in set of variables, and a let construct (let = in ), which allows to bind variables var with definition exp in expressions exp'. In Twelf syntax, we could do as follows: Here, exp is the type of all expressions and var the type of all built-in variables (implemented perhaps as natural numbers, which is not shown).


Boxes present the advantage of being very easily manipulated by computers, as they form the heart of interval analysis. Many interval algorithms naturally provide solutions that are regular subpavings.In computation, a well-known application of subpaving in R² is the Quadtree data structure. In image tracing context and other applications is important to see X⁻ as topological interior, as illustrated.


In the 2010s, as social media gained prominence, Russia then began to use platforms such as Facebook, Twitter, and YouTube to spread disinformation. Russian web brigades and bots, typically operated by Russia's Internet Research Agency (IRA), were commonly used to disseminate disinformation throughout these social media channels. As of late 2017, Facebook believed that as many as 126 million of its users had seen content from Russian disinformation campaigns on its platform. Twitter stated that it had found 36,000 Russian bots spreading tweets related to the 2016 U.S.


All ten rotors were interchangeable in any part of either maze. Using rotors to control the stepping of other rotors was a feature of an earlier cipher machine, the US ECM Mark II. Mercury also used double-wired rotors, consisting of "Inside and Outside Scrambled Wheels", the Outer wheels being settable in a number of positions with respect to the Inner wheels.


In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} in k-dimensional space ℝk, the elements of their Euclidean distance matrix A are given by squares of distances between them. That is A = ( a i j ) ; a i j = d i j 2 = ‖ x i − x j ‖ 2 {\displaystyle {\begin{aligned}A&=(a_{ij});\\a_{ij}&=d_{ij}^{2}\;=\;\lVert x_{i}-x_{j}\rVert ^{2}\end{aligned}}} where ‖ ⋅ ‖ {\displaystyle \|\cdot \|} denotes the Euclidean norm on ℝk. A =  {\displaystyle A={\begin{bmatrix}0&d_{12}^{2}&d_{13}^{2}&\dots &d_{1n}^{2}\\d_{21}^{2}&0&d_{23}^{2}&\dots &d_{2n}^{2}\\d_{31}^{2}&d_{32}^{2}&0&\dots &d_{3n}^{2}\\\vdots &\vdots &\vdots &\ddots &\vdots &\\d_{n1}^{2}&d_{n2}^{2}&d_{n3}^{2}&\dots &0\\\end{bmatrix}}} In the context of (not necessarily Euclidean) distance matrices, the entries are usually defined directly as distances, not their squares.


In network theory, a giant component is a connected component of a given random graph that contains a significant fraction of the entire graph's vertices. More precisely, in graphs drawn randomly from a probability distribution over arbitrarily large graphs, a giant component is a connected component whose fraction of the overall number of vertices is bounded away from zero. In sufficiently dense graphs distributed according to the Erdős–Rényi model, a giant component exists with high probability.


However, it demonstrates a general technique that has since been used in a wide range of proofs, including the first of Gödel's incompleteness theorems and Turing's answer to the Entscheidungsproblem. Diagonalization arguments are often also the source of contradictions like Russell's paradox and Richard's paradox. : 27


Sekiro: Shadows Die Twice as the sword wielded by the Divine Dragon. Elden Ring as a spear greatly resembling the Seven-Branced Sword called the Death Ritual Spear. Monster Hunter series as a Greatsword crafted from electric monster Kirin, King Thundersword.


The conjecture was significant, because if true, it would have implied the four color theorem: as Tait described, the four-color problem is equivalent to the problem of finding 3-edge-colorings of bridgeless cubic planar graphs. In a Hamiltonian cubic planar graph, such an edge coloring is easy to find: use two colors alternately on the cycle, and a third color for all remaining edges. Alternatively, a 4-coloring of the faces of a Hamiltonian cubic planar graph may be constructed directly, using two colors for the faces inside the cycle and two more colors for the faces outside.


In the buffer layer, between 5 wall units and 30 wall units, neither law holds, such that: For 5 < y + < 30 {\displaystyle 5


In telecommunications, in-band signaling is the sending of control information within the same band or channel used for data such as voice or video. This is in contrast to out-of-band signaling which is sent over a different channel, or even over a separate network. In-band signals may often be heard by telephony participants, while out-of-band signals are inaccessible to the user. The term is also used more generally, for example of computer data files that include both literal data, and metadata and/or instructions for how to process the literal data.


This is most conspicuous in uppercase and lowercase characters: uppercase characters are in columns 4 (100) and 5 (101), while the corresponding lowercase characters are in columns 6 (110) and 7 (111), requiring only toggling the 6th bit (2nd high bit) to switch case; as there are only 26 letters, the remaining 6 points in each column were occupied by symbols or, in one case, a control character (DEL, in 127). This is also present, but less precisely, in the organization of digits and symbols in columns 2 (010) and 3 (011) – this discrepancy is the source of bit-paired layouts. Ideally the characters would have been ordered so that unshifted and shifted values of a typewriter key were in adjacent columns, allowing shifting to be implemented by toggling the 5th bit (1st high bit).


In statistical mechanics, the Gibbs algorithm, introduced by J. Willard Gibbs in 1902, is a criterion for choosing a probability distribution for the statistical ensemble of microstates of a thermodynamic system by minimizing the average log probability ⟨ ln  p i ⟩ = ∑ i p i ln  p i {\displaystyle \langle \ln p_{i}\rangle =\sum _{i}p_{i}\ln p_{i}\,} subject to the probability distribution pi satisfying a set of constraints (usually expectation values) corresponding to the known macroscopic quantities. in 1948, Claude Shannon interpreted the negative of this quantity, which he called information entropy, as a measure of the uncertainty in a probability distribution. In 1957, E.T. Jaynes realized that this quantity could be interpreted as missing information about anything, and generalized the Gibbs algorithm to non-equilibrium systems with the principle of maximum entropy and maximum entropy thermodynamics.Physicists call the result of applying the Gibbs algorithm the Gibbs distribution for the given constraints, most notably Gibbs's grand canonical ensemble for open systems when the average energy and the average number of particles are given.


The other constraints are that the measurements of the function are given constants up to order n {\displaystyle n} . The entropy attains an extremum when the functional derivative is equal to zero: δ J δ p ( p ) = ln  p ( x ) + 1 − η 0 − ∑ j = 1 n λ j f j ( x ) = 0 {\displaystyle {\frac {\delta J}{\delta p}}\left(p\right)=\ln {p(x)}+1-\eta _{0}-\sum _{j=1}^{n}\lambda _{j}f_{j}(x)=0} Therefore, the extremal entropy probability distribution in this case must be of the form ( λ 0 := η 0 − 1 {\displaystyle \lambda _{0}:=\eta _{0}-1} ), p ( x ) = e − 1 + η 0 ⋅ e ∑ j = 1 n λ j f j ( x ) = exp  ( ∑ j = 0 n λ j f j ( x ) ) , {\displaystyle p(x)=e^{-1+\eta _{0}}\cdot e^{\sum _{j=1}^{n}\lambda _{j}f_{j}(x)}=\exp \left(\sum _{j=0}^{n}\lambda _{j}f_{j}(x)\right)\;,} remembering that f 0 ( x ) = 1 {\displaystyle f_{0}(x)=1} . It can be verified that this is the maximal solution by checking that the variation around this solution is always negative.


In natural time domain each event is characterized by two terms, the "natural time" χ, and the energy Qk. χ is defined as k/N, where k is a natural number (the k-th event) and N is the total number of events in the time sequence of data. A related term, pk, is the ratio Qk / Qtotal, which describes the fractional energy released. The term κ1 is the variance in natural time: κ 1 = ∑ k = 1 N p k ( χ k ) 2 − ( ∑ k = 1 N p k χ k ) 2 {\displaystyle \kappa _{1}=\sum _{k=1}^{N}p_{k}(\chi _{k})^{2}-{\bigl (}\sum _{k=1}^{N}p_{k}\chi _{k}{\bigr )}^{2}} where χ k = k / N {\displaystyle \textstyle \chi _{k}=k/N} and p k = Q k ∑ n = 1 N Q n {\displaystyle \textstyle \ p_{k}={\frac {Q_{k}}{\sum _{n=1}^{N}Q_{n}}}}


In numerical analysis, the minimum degree algorithm is an algorithm used to permute the rows and columns of a symmetric sparse matrix before applying the Cholesky decomposition, to reduce the number of non-zeros in the Cholesky factor. This results in reduced storage requirements and means that the Cholesky factor can be applied with fewer arithmetic operations. (Sometimes it may also pertain to an incomplete Cholesky factor used as a preconditioner—for example, in the preconditioned conjugate gradient algorithm.) Minimum degree algorithms are often used in the finite element method where the reordering of nodes can be carried out depending only on the topology of the mesh, rather than on the coefficients in the partial differential equation, resulting in efficiency savings when the same mesh is used for a variety of coefficient values.


In simple conditions, F can be easily computed in terms of population size or of genealogical information. F is often denoted using lowercase (f), but should not be confused with the coancestry coefficient. However, the above prediction for the fitness decline rarely applies, since it was derived assuming no selection, and fitness is precisely the target trait of natural selection.


In mathematics, the Lévy–Prokhorov metric (sometimes known just as the Prokhorov metric) is a metric (i.e., a definition of distance) on the collection of probability measures on a given metric space. It is named after the French mathematician Paul Lévy and the Soviet mathematician Yuri Vasilyevich Prokhorov; Prokhorov introduced it in 1956 as a generalization of the earlier Lévy metric.


In the calculation of low energy states the term proportional to n 2 U {\displaystyle n^{2}U} means that large occupation of a single site is improbable, allowing for truncation of local Hilbert space to states containing at most d < ∞ {\displaystyle d<\infty } particles. Then the local Hilbert space dimension is d + 1. {\displaystyle d+1.}


In mathematical logic, the De Bruijn notation is a syntax for terms in the λ calculus invented by the Dutch mathematician Nicolaas Govert de Bruijn. It can be seen as a reversal of the usual syntax for the λ calculus where the argument in an application is placed next to its corresponding binder in the function instead of after the latter's body.


In 1970, electronic parts were introduced, and the current black-coloured plates were changed to blue. The range of sets was reduced by one with the deletion of the old No. 9 set and the renumbering of the old No. 0 to 8 sets to No. 1 to 9. The No. 10 set remained unchanged.


However, not every total recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other equivalent classes of functions are the functions of lambda calculus and the functions that can be computed by Markov algorithms. The subset of all total recursive functions with values in {0,1} is known in computational complexity theory as the complexity class R.


So how does a state machine move an arbitrarily large constant directly into a register, e.g. MOVE (k, r) (Move constant k to register r)? If huge constants are necessary they must either start out in the registers themselves or be created by the state machine using a finite number of instructions e.g. multiply and add subroutines using INC and DEC (but not a quasi-infinite number of these! ).Sometimes the constant k will be created by use of CLR ( r ) followed by INC ( r ) repeated k times – e.g. to put the constant k=3 into register r, i.e. 3 → r, so at the end of the instruction =3: CLR (r), INC (r), INC (r), INC (r).


In the United States, the 100-year flood provides the risk basis for flood insurance rates. Complete information on the National Flood Insurance Program (NFIP) is available here. A regulatory flood or base flood is routinely established for river reaches through a science-based rule-making process targeted to a 100-year flood at the historical average recurrence interval. In addition to historical flood data, the process accounts for previously established regulatory values, the effects of flood-control reservoirs, and changes in land use in the watershed.


The difference of two Moser–de Bruijn numbers, multiplied by two, is never square. Every natural number can be formed in a unique way as the sum of a Moser–de Bruijn number and twice a Moser–de Bruijn number. This representation as a sum defines a one-to-one correspondence between integers and pairs of integers, listed in order of their positions on a Z-order curve. The Moser–de Bruijn sequence can be used to construct pairs of transcendental numbers that are multiplicative inverses of each other and both have simple decimal representations. A simple recurrence relation allows values of the Moser–de Bruijn sequence to be calculated from earlier values, and can be used to prove that the Moser–de Bruijn sequence is a 2-regular sequence.


The set of k-almost primes is usually denoted by Pk. The smallest k-almost prime is 2k. The first few k-almost primes are: The number πk(n) of positive integers less than or equal to n with exactly k prime divisors (not necessarily distinct) is asymptotic to: π k ( n ) ∼ ( n log  n ) ( log  log  n ) k − 1 ( k − 1 ) !


Let Kp be a boolean variable which indicates whether p is a corner, then the entropy of Kp is used to measure the information of p being a corner. For a set of pixels Q, the total entropy of KQ (not normalized) is: H(Q) = ( c + n ) log2( c + n ) - clog2c - nlog2n where c = |{ i ∈ Q: Ki is true}| (number of corners) where n = |{ i ∈ Q: Ki is false}| (number of non-corners)The information gain can then be represented as: Hg= H(P) - H(Pb) - H(Ps) - H(Pd)A recursive process is applied to each subsets in order to select each x that could maximize the information gain. For example, at first an x is selected to partition P into Pd, Ps, Pb with the most information; then for each subset Pd, Ps, Pb, another y is selected to yield the most information gain (notice that the y could be the same as x ).


In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime. For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem.


The frame received on port B is then forwarded to ports A and C, the frame received on port C to ports A and B. So, the node on port A receives two copies of its own broadcast frame while the other two copies produced by the loop continue to cycle. Likewise, each broadcast frame entering the system continues to cycle through the loop in both directions, rebroadcasting back to the network in each loop, and broadcasts accumulate. Eventually, the accumulated broadcasts exhaust the egress capacity of the links, the switch begins dropping frames, and communication across the switch becomes unreliable or even impossible.


In number theory, a strong prime is a prime number that is greater than the arithmetic mean of the nearest prime above and below (in other words, it's closer to the following than to the preceding prime). Or to put it algebraically, writing the sequence of prime numbers as (p1, p2, p3, ...) = (2, 3, 5, ...), pn is a strong prime if pn > pn − 1 + pn + 1/2. For example, 17 is the seventh prime: the sixth and eighth primes, 13 and 19, add up to 32, and half that is 16; 17 is greater than 16, so 17 is a strong prime. The first few strong primes are 11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499 (sequence A051634 in the OEIS).In a twin prime pair (p, p + 2) with p > 5, p is always a strong prime, since 3 must divide p − 2, which cannot be prime.


In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data. SID does not require that the user parametrizes the system matrices before solving a parametric optimization problem and, as a consequence, SID methods do not suffer from problems related to local minima that often lead to unsatisfactory identification results.


In the R5RS standard and also in later reports, the syntax of Scheme can easily be extended via the macro system. The R5RS standard introduced a powerful hygienic macro system that allows the programmer to add new syntactic constructs to the language using a simple pattern matching sublanguage (R5RS sec 4.3). Prior to this, the hygienic macro system had been relegated to an appendix of the R4RS standard, as a "high level" system alongside a "low level" macro system, both of which were treated as extensions to Scheme rather than an essential part of the language.Implementations of the hygienic macro system, also called syntax-rules, are required to respect the lexical scoping of the rest of the language. This is assured by special naming and scoping rules for macro expansion and avoids common programming errors that can occur in the macro systems of other programming languages.


In the context of computer science, semantics refers to the meaning behind programming language constructs, distinguishing it from their mere syntax, which is the arrangement of symbols and keywords. This concept is crucial for ensuring that code is not only correctly written in terms of syntax but also logically meaningful and functional. According to Euzenat, semantics "provides the rules for interpreting the syntax which do not provide the meaning directly but constrains the possible interpretations of what is declared".


In server/client architectures, the program at the other side may not be an authorised client and the client's server may not be an authorised server. Even when they are, a man-in-the-middle attack could compromise communications. Often the easiest way to break the security of a client/server system is not to go head on to the security mechanisms, but instead to go around them. A man in the middle attack is a simple example of this, because you can use it to collect details to impersonate a user.


In the context of information science, an ontology is a formal representation of knowledge within a domain, using hierarchies of terms including their definitions, attributes, and relations. Ontologies provide a common terminology in a machine-readable framework that facilitates sharing and discovery of data. Having an established ontology for nanoparticles is important for cancer nanomedicine due to the need of researchers to search, access, and analyze large amounts of data.The NanoParticle Ontology is an ontology for the preparation, chemical composition, and characterization of nanomaterials involved in cancer research.


In public-key cryptography and computer security, a root key ceremony is a procedure during which a unique pair of public and private root keys gets generated. Depending on the certificate policy, the generation of the root keys may require notarization, legal representation, witnesses, and "key holders" to be present, as the information on the system is the responsibility of the parties. A commonly recognized practice is to follow the SAS 70 standard for root key ceremonies.At the heart of every certificate authority (CA) is at least one root key or root certificate and usually at least one intermediate root certificate. "Root key" is the term for a unique passcode that must be generated for secure server interaction with a protective network, usually called the root zone.


In the 1967 Black Power, Stokely Carmichael introduces black nationalism. He illustrates the prosperity of the black race in the United States as being dependent on the implementation of black sovereignty. Under his theory, black nationalism in the United States would allow Blacks to socially, economically and politically be empowered in a manner that has never been plausible in American history. A Black nation would work to reverse the exploitation of the Black race in America, as Blacks would intrinsically work to benefit their own state of affairs.


This is the class of functions from A {\displaystyle A} to C {\displaystyle C} in a pure set theory. Below the notation x → y {\displaystyle x\to y} is also used for y x {\displaystyle y^{x}} , for the sake of distinguishing it from ordinal exponentiation. When functions are understood as just function graphs as above, the membership proposition f ∈ C A {\displaystyle f\in C^{A}} is also written f: A → C {\displaystyle f\colon A\to C} . The boolean-valued χ B: A → { 0 , 1 } {\displaystyle \chi _{B}\colon A\to \{0,1\}} are among the classes discussed next.


The trace 1 condition means ∑ j a j ∗ a j = 1. {\displaystyle \sum _{j}a_{j}^{*}a_{j}=1.} Let p i = a i ∗ a i , {\displaystyle p_{i}=a_{i}^{*}a_{i},} and vi be the normalized ai. We see that { p i , v i } {\displaystyle \left\{p_{i},v_{i}\right\}} gives the mixed state ρ.


In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. It is a method which relies on the well-ordering principle, and is often used to show that a given equation, such as a Diophantine equation, has no solutions.Typically, one shows that if a solution to a problem existed, which in some sense was related to one or more natural numbers, it would necessarily imply that a second solution existed, which was related to one or more 'smaller' natural numbers. This in turn would imply a third solution related to smaller natural numbers, implying a fourth solution, therefore a fifth solution, and so on. However, there cannot be an infinity of ever-smaller natural numbers, and therefore by mathematical induction, the original premise—that any solution exists—is incorrect: its correctness produces a contradiction.


In telecommunication networks, the transmission time is the amount of time from the beginning until the end of a message transmission. In the case of a digital message, it is the time from the first bit until the last bit of a message has left the transmitting node. The packet transmission time in seconds can be obtained from the packet size in bit and the bit rate in bit/s as: Packet transmission time = Packet size / Bit rateExample: Assuming 100 Mbit/s Ethernet, and the maximum packet size of 1526 bytes, results in Maximum packet transmission time = 1526×8 bit / (100 × 106 bit/s) ≈ 122 μs


In single-ended signalling, the transmitter generates a single voltage that the receiver compares with a fixed reference voltage, both relative to a common ground connection shared by both ends. In many instances, single-ended designs are not feasible. Another difficulty is the electromagnetic interference that can be generated by a single-ended signalling system that attempts to operate at high speed.


In object-oriented programming, there is also the concept of a static member variable, which is a "class variable" of a statically defined class, i.e., a member variable of a given class which is shared across all instances (objects), and is accessible as a member variable of these objects. A class variable of a dynamically defined class, in languages where classes can be defined at run time, is allocated when the class is defined and is not static. Object constants known at compile-time, such as string literals, are usually allocated statically. In object-oriented programming, the virtual method tables of classes are usually allocated statically. A statically defined value can also be global in its scope ensuring the same immutable value is used throughout a run for consistency.


In mathematical logic, a proof calculus or a proof system is built to prove statements.


In the third quarter of 2006, at least 12 billion text messages were sent on AT&T's network, up almost 15% from the preceding quarter. In the U.S., while texting is mainly popular among people from 13–22 years old, it is also increasing among adults and business users. The age that a child receives his/her first cell phone has also decreased, making text messaging a popular way of communicating.


The largest component has logarithmic size. The graph is a pseudoforest. Most of its components are trees: the number of vertices in components that have cycles grows more slowly than any unbounded function of the number of vertices.


Traversing this Eulerian trail generates an orientation D of G such that every point has indegree and outdegree = k. Next, replace every vertex v ϵ V(D) by two vertices v’ and v”, and replace every directed edge uv of the oriented graph by an undirected edge from u’ to v”. Since D has in- and outdegrees equal to k the resulting bipartite graph G’ is k-regular. The edges of G’ can be partitioned into k perfect matchings by a theorem of Kőnig. Now merging v’ with v” for every v recovers the graph G, and maps the k perfect matchings of G’ onto k 2-factors of G which partition its edges.


In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has a particularly deep and interesting connection to the theory of finite sporadic groups in mathematics. These codes are named in honor of Marcel J. E. Golay whose 1949 paper introducing them has been called, by E. R. Berlekamp, the "best single published page" in coding theory.There are two closely related binary Golay codes. The extended binary Golay code, G24 (sometimes just called the "Golay code" in finite group theory) encodes 12 bits of data in a 24-bit word in such a way that any 3-bit errors can be corrected or any 7-bit errors can be detected. The other, the perfect binary Golay code, G23, has codewords of length 23 and is obtained from the extended binary Golay code by deleting one coordinate position (conversely, the extended binary Golay code is obtained from the perfect binary Golay code by adding a parity bit). In standard coding notation, the codes have parameters  and , corresponding to the length of the codewords, the dimension of the code, and the minimum Hamming distance between two codewords, respectively.


The model makes the assumption that customers have some idea of what they want and what the standard of the good or service should be. Models of sequential search have been used in many disciplines, including finance and labour economics. Sequential search models are used in labour economics to examine how employees look for work and how employers hire new employees.


The symbol ( n k ) {\displaystyle {\tbinom {n}{k}}} is usually read as "n choose k" because there are ( n k ) {\displaystyle {\tbinom {n}{k}}} ways to choose an (unordered) subset of k elements from a fixed set of n elements. For example, there are ( 4 2 ) = 6 {\displaystyle {\tbinom {4}{2}}=6} ways to choose 2 elements from { 1 , 2 , 3 , 4 } , {\displaystyle \{1,2,3,4\},} namely { 1 , 2 } , { 1 , 3 } , { 1 , 4 } , { 2 , 3 } , { 2 , 4 } , {\displaystyle \{1,2\},\,\{1,3\},\,\{1,4\},\,\{2,3\},\,\{2,4\},} and { 3 , 4 } . {\displaystyle \{3,4\}.} The binomial coefficients can be generalized to ( z k ) {\displaystyle {\tbinom {z}{k}}} for any complex number z and integer k ≥ 0, and many of their properties continue to hold in this more general form.


Flat addressing is possible by applying multiple instructions, which however leads to slower programs. The memory model concept derives from the setup of the segment registers. For example, in the tiny model CS=DS=SS, that is the program's code, data, and stack are all contained within a single 64 KB segment. In the small memory model DS=SS, so both data and stack reside in the same segment; CS points to a different code segment of up to 64 KB.


It will also not be perfectly aligned with the directions of the document, causing aliasing. Features smaller than the resolution will also not be reproduced. In addition, human vision is sensitive to luminance contrast ratio.


...  point is that one or two degrees is about the experience that we have had in the last 10,000 years, the era of human civilization. There haven't been—globally averaged, we're talking—fluctuations of more than a degree or so. So we're actually getting into uncharted territory from the point of view of the relatively benign climate of the last 10,000 years, if we warm up more than a degree or two.


In simple electromagnetic analysis (SEMA) attacks, the attacker deduces the key directly by observing the trace. It is very effective against asymmetric cryptography implementations. Typically, only a few traces are needed, though the attacker needs to have a strong understanding of the cryptographic device and of the implementation of the cryptographic algorithm.


Then for any function f: A → B {\displaystyle f:A\to B} , the restriction f | S: S → B {\displaystyle f|_{S}:S\to B} of a function f {\displaystyle f} onto S {\displaystyle S} can be defined as the composition f | S = f ∘ i S {\displaystyle f|_{S}=f\circ i_{S}} . Analogously, for an inclusion i T: T ↪ B {\displaystyle i_{T}:T\hookrightarrow B} the corestriction f | T: A → T {\displaystyle f|^{T}:A\to T} of f {\displaystyle f} onto T {\displaystyle T} is the unique function f | T {\displaystyle f|^{T}} such that there is a decomposition f = i T ∘ f | T {\displaystyle f=i_{T}\circ f|^{T}} . The corestriction exists if and only if T {\displaystyle T} contains the image of f {\displaystyle f} .


In order to apply control theory tools to the analysis of behavior trees, they can be defined as three-tuple. T i = { f i , r i , Δ t } , {\displaystyle T_{i}=\{f_{i},r_{i},\Delta t\},} where i ∈ N {\displaystyle i\in \mathbb {N} } is the index of the tree, f i: R n → R n {\displaystyle f_{i}:\mathbb {R} ^{n}\rightarrow \mathbb {R} ^{n}} is a vector field representing the right hand side of an ordinary difference equation, Δ t {\displaystyle \Delta t} is a time step and r i: R n → { R i , S i , F i } {\displaystyle r_{i}:\mathbb {R} ^{n}\rightarrow \{R_{i},S_{i},F_{i}\}} is the return status, that can be equal to either Running R i {\displaystyle R_{i}} , Success S i {\displaystyle S_{i}} , or Failure F i {\displaystyle F_{i}} . Note: A task is a degenerate behavior tree with no parent and no child.


Variants of the functional predicate definition using apartness relations on setoids have been defined as well. It is a metatheorem for theories containing B C S T {\displaystyle {\mathsf {BCST}}} that adding a function symbol for a provenly total class function is a conservative extension, despite this changing the scope of bounded Separation. Some notational conveniences involving function application will only work when a set has indeed been established to be a function.


In mathematics, economics, and computer science, the stable matching polytope or stable marriage polytope is a convex polytope derived from the solutions to an instance of the stable matching problem.


In mathematics, a divisor of an integer n {\displaystyle n} , also called a factor of n {\displaystyle n} , is an integer m {\displaystyle m} that may be multiplied by some integer to produce n {\displaystyle n} . In this case, one also says that n {\displaystyle n} is a multiple of m . {\displaystyle m.} An integer n {\displaystyle n} is divisible or evenly divisible by another integer m {\displaystyle m} if m {\displaystyle m} is a divisor of n {\displaystyle n} ; this implies dividing n {\displaystyle n} by m {\displaystyle m} leaves no remainder.


We can further define a programming language in which we can ensure that even more sophisticated functions always halt. For example, the Ackermann function, which is not primitive recursive, nevertheless is a total computable function computable by a term rewriting system with a reduction ordering on its arguments (Ohlebusch, 2002, pp. 67). Despite the above examples of programming languages which guarantee termination of the programs, there exists no programming language which captures exactly the total recursive functions, i.e. the functions which can be computed by a Turing machine that always halts. This is because existence of such a programming language would be a contradiction to the non-semi-decidability of the problem whether a Turing machine halts on every input.


}{\prod _{j=0}^{k}n_{j}!}}} If any q i = 0 {\displaystyle q_{i}=0} , then the vector q → {\displaystyle {\vec {q}}} is shared in common between orthants. Because of this, the multiplying factor on the permutation must be adjusted from 2 N {\displaystyle 2^{N}} to be 2 N − n 0 {\displaystyle 2^{N-n_{0}}} Multiplying the number of amount of permutations by the adjusted amount of orthants yields, E = N !


n 2 ! ⋅ ( N − n 1 − n 2 ) ! ( N − n 1 − n 2 − n 3 ) !


If a = b, then b = a (symmetric). If a = b and b = c, then a = c (transitive). Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.


The original Highway Network paper not only introduced the basic principle for very deep feedforward networks, but also included experimental results with 20, 50, and 100 layers networks, and mentioned ongoing experiments with up to 900 layers. Networks with 50 or 100 layers had lower training error than their plain network counterparts, but no lower training error than their 20 layers counterpart (on the MNIST dataset, Figure 1 in ). No improvement on test accuracy was reported with networks deeper than 19 layers (on the CIFAR-10 dataset; Table 1 in ).


In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. A Gödel numbering is a precomplete numbering on the set of computable functions so the generalized theorem yields the Kleene recursion theorem as a special case.Given a precomplete numbering ν {\displaystyle \nu } , then for any partial computable function f {\displaystyle f} with two parameters there exists a total computable function t {\displaystyle t} with one parameter such that ∀ n ∈ N: ν ∘ f ( n , t ( n ) ) = ν ∘ t ( n ) . {\displaystyle \forall n\in \mathbb {N} :\nu \circ f(n,t(n))=\nu \circ t(n).}


Apple's Garage Band even purveys digital music lessons using the very same iTunes account as used for the iOS App Store, they are all part of the same App Store. Electronic bookstores such as Kindle, Barnes and Noble or Kobo are further examples of successful electronic distribution using the App Store concept. For the Electronic AppWrapper distribution, encryption and the digital rights of the software were universally managed for all participating developers much like stores participating in a shopping mall.


In order for consistency in data to be maintained and to attain scalable processor systems where every processor has its own memory, the processor consistency model was derived. All processors need to be consistent in the order in which they see writes done by one processor and in the way they see writes by different processors to the same location (coherence is maintained). However, they do not need to be consistent when the writes are by different processors to different locations. Every write operation can be divided into several sub-writes to all memories.


Under the assumption of stationary statistics, at a given position, the normalized correlation function is g ( 2 ) = ⟨ E ^ − ( 0 ) E ^ − ( τ ) E ^ + ( τ ) E ^ + ( 0 ) ⟩ ⟨ E ^ − ( 0 ) E ^ + ( 0 ) ⟩ ⟨ E ^ − ( τ ) E ^ + ( τ ) ⟩ {\displaystyle g^{(2)}={\frac {\langle {\hat {E}}^{-}(0){\hat {E}}^{-}(\tau ){\hat {E}}^{+}(\tau ){\hat {E}}^{+}(0)\rangle }{\langle {\hat {E}}^{-}(0){\hat {E}}^{+}(0)\rangle \langle {\hat {E}}^{-}(\tau ){\hat {E}}^{+}(\tau )\rangle }}} g ( 2 ) {\displaystyle g^{(2)}} here measures the probability of coincidence of two photons being detected with a time difference τ {\displaystyle \tau } .For all varieties of chaotic light, the following relationship between the first order and second-order coherences holds: g ( 2 ) ( τ ) = 1 + | g ( 1 ) ( τ ) | 2 {\displaystyle g^{(2)}(\tau )=1+|g^{(1)}(\tau )|^{2}} . This relationship is true for both the classical and quantum correlation functions.


332, 149 S.E. 541 (1929). "In assessing statutory language, unless words have acquired a peculiar meaning, by virtue of statutory definition or judicial construction, they are to be construed in accordance with their common usage."


, {\displaystyle I(r,\lambda )=\sum _{y=r}^{\infty }{\frac {e^{-\lambda }\lambda ^{y}}{y! }},} where s is the integral part of r. The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution (that is P ( X = n ) / P ( X = n − 1 ) {\displaystyle P(X=n)/P(X=n-1)} ) is given by λ / n {\displaystyle \lambda /n} for n > 0 {\displaystyle n>0} and the displaced Poisson generalizes this ratio to λ / ( n + r ) {\displaystyle \lambda /\left(n+r\right)} . == References ==


This evolution has resulted in more complex and more flexible ICs being created. The newer circuits are programmable and thus allow a single hardware IC design to undertake a number of different functions, where the appropriate software is installed. Network processors are used in the manufacture of many different types of network equipment such as: Routers, software routers and switches (Inter-network processors) Firewalls Session border controllers Intrusion detection devices Intrusion prevention devices Network monitoring systems Network security (secure cryptoprocessors)


Note that the mask constraint relates to the effects and not the causes like the other constraints. The graph's direction is as follows: Causes --> intermediate nodes --> Effects The graph can always be rearranged so there is only one node between any input and any output. See conjunctive normal form and disjunctive normal form. A cause–effect graph is useful for generating a reduced decision table.


In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as a AB = pI, where A and B are square matrices and I is the identity matrix. Given the polynomial p, the matrices A and B can be found by elementary methods. Example:The polynomial x2 + y2 is irreducible over R, but can be written as   = ( x 2 + y 2 )  {\displaystyle \left\left=(x^{2}+y^{2})\left}


In regression, mean response (or expected response) and predicted response, also known as mean outcome (or expected outcome) and predicted outcome, are values of the dependent variable calculated from the regression parameters and a given value of the independent variable. The values of these two responses are the same, but their calculated variances are different. The concept is a generalization of the distinction between the standard error of the mean and the sample standard deviation.


In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions.


In mathematics, a nowhere commutative semigroup is a semigroup S such that, for all a and b in S, if ab = ba then a = b. A semigroup S is nowhere commutative if and only if any two elements of S are inverses of each other.


Some writers on probability call this the "conditional covariance formula" or use other names. Note: The conditional expected values E( X | Z ) and E( Y | Z ) are random variables whose values depend on the value of Z. Note that the conditional expected value of X given the event Z = z is a function of z. If we write E( X | Z = z) = g(z) then the random variable E( X | Z ) is g(Z). Similar comments apply to the conditional covariance.


In mathematical analysis, in particular the subfields of convex analysis and optimization, a proper convex function is an extended real-valued convex function with a non-empty domain, that never takes on the value − ∞ {\displaystyle -\infty } and also is not identically equal to + ∞ . {\displaystyle +\infty .} In convex analysis and variational analysis, a point (in the domain) at which some given function f {\displaystyle f} is minimized is typically sought, where f {\displaystyle f} is valued in the extended real number line  = R ∪ { ± ∞ } . {\displaystyle =\mathbb {R} \cup \{\pm \infty \}.}


In mathematics, a subset R of the integers is called a reduced residue system modulo n if: gcd(r, n) = 1 for each r in R, R contains φ(n) elements, no two elements of R are congruent modulo n.Here φ denotes Euler's totient function. A reduced residue system modulo n can be formed from a complete residue system modulo n by removing all integers not relatively prime to n. For example, a complete residue system modulo 12 is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. The so-called totatives 1, 5, 7 and 11 are the only integers in this set which are relatively prime to 12, and so the corresponding reduced residue system modulo 12 is {1, 5, 7, 11}. The cardinality of this set can be calculated with the totient function: φ(12) = 4. Some other reduced residue systems modulo 12 are: {13,17,19,23} {−11,−7,−5,−1} {−7,−13,13,31} {35,43,53,61}


However, when the code is inserted into a compiler, the compiler may ignore the Bidi char and process the characters in a different order than visually displayed. When the compiler is finished, it could potentially execute code that visually appeared to be non-executable. Formatting marks can be combined multiple times to create complex attacks.


The ordinal series are based on ordinal numbers such as the English first, second, third (for numbers higher than 2, the ordinal forms are also used for fractions; only the fraction 1⁄2 has special forms). For the hundreds, there are competing forms: those in -gent-, from the original Latin, and those in -cent-, derived from centi-, etc. plus the prefixes for 1–9. Many of the items in the following tables are not in general use, but may rather be regarded as coinages by individuals. In scientific contexts, either scientific notation or SI prefixes are used to express very large or very small numbers, and not unwieldy prefixes. The same suffix may be used with more than one series: Examples


In memory errors, the faulting program accesses memory that it should not access. Examples include: Attempting to write to a read-only portion of memory Attempting to execute bytes in memory which are not designated as instructions Attempting to read as data bytes in memory which are designated as instructions Other miscellaneous conflicts between the designation of a part of memory and its useHowever, many modern operating systems implement their memory access-control schemes via paging instead of segmentation, so it is often the case that invalid memory references in operating systems such as Windows are reported via page faults instead of general protection faults. Operating systems typically provide an abstraction layer (such as exception handling or signals) that hides whatever internal processor mechanism was used to raise a memory access error from a program, for the purposes of providing a standard interface for handling many different types of processor-generated error conditions. In terms of the x86 architecture, general protection faults are specific to segmentation-based protection when it comes to memory accesses. However, general protection faults are still used to report other protection violations (aside from memory access violations) when paging is used, such as the use of instructions not accessible from the current privilege level (CPL). While it is theoretically possible for an operating system to utilize both paging and segmentation, for the most part, common operating systems typically rely on paging for the bulk of their memory access control needs.