however, this conclusion is not a mathematical certainty ; there exist undirected graphs ( such as the graph formed by removing a single edge from a large complete graph ) that are unlikely to arise as social networks but in which most vertices have higher degree than the average of their neighbors'degrees. the friendship paradox may be restated in graph theory terms as " the average degree of a randomly selected node in a network is less than the average degree of neighbors of a randomly selected node ", but this leaves unspecified the exact mechanism of averaging ( i. e., macro vs micro averaging ). let g = ( v, e ) { \ displaystyle g = ( v, e ) } be an undirected graph with | v | = n { \ displaystyle | v | = n } and | e | = m { \ displaystyle | e | = m }, having no isolated nodes.


a natural example is strings with concatenation as the binary operation, and the empty string as the identity element. restricting to non - empty strings gives an example of a semigroup that is not a monoid. positive integers with addition form a commutative semigroup that is not a monoid, whereas the non - negative integers do form a monoid.


in the 1980s ibm researcher harlan mills oversaw the development of the cobol structuring facility, which applied a structuring algorithm to cobol code. mills's transformation involved the following steps for each procedure. identify the basic blocks in the procedure. assign a unique label to each block's entry path, and label each block's exit paths with the labels of the entry paths they connect to.


fine - grained multithreading — such as in a barrel processor — issues instructions for different threads after every cycle, while coarse - grained multithreading only switches to issue instructions from another thread when the current executing thread causes some long latency events ( like page fault etc. ). coarse - grain multithreading is more common for less context switch between threads. for example, intel's montecito processor uses coarse - grained multithreading, while sun's ultrasparc t1 uses fine - grained multithreading.


in number theory, ostrowski's theorem, due to alexander ostrowski ( 1916 ), states that every non - trivial absolute value on the rational numbers q { \ displaystyle \ mathbb { q } } is equivalent to either the usual real absolute value or a p - adic absolute value.


in mathematics, the plus sign " + " almost invariably indicates an operation that satisfies the axioms assigned to addition in the type of algebraic structure that is known as a field. for boolean algebra, this means that the logical operation signified by " + " is not the same as the inclusive disjunction signified by " ∨ " but is actually equivalent to the logical inequality operator signified by " = ", or what amounts to the same thing, the exclusive disjunction signified by " xor " or " ⊕ ". naturally, these variations in usage have caused some failures to communicate between mathematicians and switching engineers over the years. at any rate, one has the following array of corresponding forms for the symbols associated with logical inequality : x + y x ≡ y j x y x x o r y x = y { \ displaystyle { \ begin { aligned } x & + y & x & \ not \ equiv y & jxy \ \ x & \ mathrm { ~ xor ~ } y & x & \ neq y \ end { aligned } } } this explains why " eq " is often called " xnor " in the combinational logic of circuit engineers, since it is the negation of the xor operation ; " nxor " is a less commonly used alternative. another rationalization of the admittedly circuitous name " xnor " is that one begins with the " both false " operator nor and then adds the exception " or both true ".


in the decision version of problems, the problem of producing an integer flow satisfying all demands is np - complete, even for only two commodities and unit capacities ( making the problem strongly np - complete in this case ). if fractional flows are allowed, the problem can be solved in polynomial time through linear programming, or through ( typically much faster ) fully polynomial time approximation schemes.


the notion of counting may be extended to them in the sense of establishing ( the existence of ) a bijection with some well - understood set. for instance, if a set can be brought into bijection with the set of all natural numbers, then it is called " countably infinite. " this kind of counting differs in a fundamental way from counting of finite sets, in that adding new elements to a set does not necessarily increase its size, because the possibility of a bijection with the original set is not excluded.


in mathematical logic and computer science, the calculus of constructions ( coc ) is a type theory created by thierry coquand. it can serve as both a typed programming language and as constructive foundation for mathematics. for this second reason, the coc and its variants have been the basis for coq and other proof assistants. some of its variants include the calculus of inductive constructions ( which adds inductive types ), the calculus of ( co ) inductive constructions ( which adds coinduction ), and the predicative calculus of inductive constructions ( which removes some impredicativity ).


in mathematics graph theory a process graph or p - graph is a directed bipartite graph used in workflow modeling.


an attacker would then be able to run system commands using the application's privileges. texas instruments calculators ( particularly the ti - 85 and ti - 82 ) were originally designed to use only interpreted programs written in dialects of ti - basic ; however, after users discovered bugs that could be exploited to allow native z - 80 code to run on the calculator hardware, ti released programming data to support third - party development. ( this did not carry on to the arm - based ti - nspire, for which jailbreaks using ndless have been found but are still actively fought against by texas instruments. ) some versions of the iphone allow an unauthorised user to access the phone while it is locked.


in physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. the regulator, also known as a " cutoff ", models our lack of knowledge about physics at unobserved scales ( e. g. scales of small size or large energy levels ). it compensates for ( and requires ) the possibility that " new physics " may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an " effective theory " within its intended scale of use.


the main categories for non - iid data can be summarized as follows : covariate shift : local nodes may store examples that have different statistical distributions compared to other nodes. an example occurs in natural language processing datasets where people typically write the same digits / letters with different stroke widths or slants. prior probability shift : local nodes may store labels that have different statistical distributions compared to other nodes.


non - redundant information is most often obtained through contacts in different clusters. when two separate clusters possess non - redundant information, there is said to be a structural hole between them. thus, a network that bridges structural holes will provide network benefits that are in some degree additive, rather than overlapping.


in real analysis, the following result is called young's convolution inequality : suppose f { \ displaystyle f } is in the lebesgue space l p ( r d ) { \ displaystyle l ^ { p } ( \ mathbb { r } ^ { d } ) } and g { \ displaystyle g } is in l q ( r d ) { \ displaystyle l ^ { q } ( \ mathbb { r } ^ { d } ) } and with 1 ≤ p, q, r ≤ ∞. { \ displaystyle 1 \ leq p, q, r \ leq \ infty. } then here the star denotes convolution, l p { \ displaystyle l ^ { p } } is lebesgue space, and denotes the usual l p { \ displaystyle l ^ { p } } norm. equivalently, if p, q, r ≥ 1 { \ displaystyle p, q, r \ geq 1 } and 1 p + 1 q + 1 r = 2 { \ textstyle { \ frac { 1 } { p } } + { \ frac { 1 } { q } } + { \ frac { 1 } { r } } = 2 } then


in mathematics, coxeter matroids are generalization of matroids depending on a choice of a coxeter group w and a parabolic subgroup p. ordinary matroids correspond to the case when p is a maximal parabolic subgroup of a symmetric group w. they were introduced by gelfand and serganova ( 1987, 1987b ), who named them after h. s. m. coxeter. borovik, gelfand & white ( 2003 ) give a detailed account of coxeter matroids.


in the context of telecommunications, a terminal is a device which ends a telecommunications link and is the point at which a signal enters or leaves a network. examples of terminal equipment include telephones, fax machines, computer terminals, printers and workstations. an end instrument is a piece of equipment connected to the wires at the end of a telecommunications link. in telephony, this is usually a telephone connected to a local loop. end instruments that relate to data terminal equipment include printers, computers, barcode readers, automated teller machines ( atms ) and the console ports of routers.


in mathematics, the rank, prufer rank, or torsion - free rank of an abelian group a is the cardinality of a maximal linearly independent subset. the rank of a determines the size of the largest free abelian group contained in a. if a is torsion - free then it embeds into a vector space over the rational numbers of dimension rank a. for finitely generated abelian groups, rank is a strong invariant and every such group is determined up to isomorphism by its rank and torsion subgroup. torsion - free abelian groups of rank 1 have been completely classified. however, the theory of abelian groups of higher rank is more involved. the term rank has a different meaning in the context of elementary abelian groups.


rather than adopting an updated set of primary colors, proponents of split - primary theory explain this lack of chroma by the purported presence of chemical impurities, small amounts of other colors, in the paints, or biases away from the ideal primary toward one or the other of the adjacent colors. every red paint, for example, is said to be tainted with, or biased toward, either blue or yellow, every blue paint toward either red or green, and every yellow toward either green or orange. these biases are said to result in mixtures that contain sets of complementary colors, darkening the resulting color.


languages such as japanese and chinese form possessive constructions with nouns using possessive particles, in the same way as described for pronouns above. an example from japanese is neko no iro ( " the cat's color " ), where neko means " cat ", no is the particle, and iro means " color ".


in the ( n2 − 1 ) - dimensional adjoint representation, the generators are represented by ( n2 − 1 ) × ( n2 − 1 ) matrices, whose elements are defined by the structure constants themselves : ( t a ) j k = − i f a j k. { \ displaystyle \ left ( t _ { a } \ right ) _ { jk } = - if _ { ajk }. }


8. specifying relevant conditions to which the concept applies, as a procedure ( computer programming, formal concept analysis ). 9.


output : prefix sum 0 ≤ j ≤ i m j { \ displaystyle \ bigoplus _ { 0 \ leq j \ leq i } m _ { j } } of processor i { \ displaystyle i }. x : = m i { \ displaystyle x : = m _ { i } } σ : = m i { \ displaystyle \ sigma : = m _ { i } } for 0 ≤ k ≤ d − 1 { \ displaystyle 0 \ leq k \ leq d - 1 } do y : = i xor 2 k { \ displaystyle y : = i { \ text { xor } } 2 ^ { k } } send σ { \ displaystyle \ sigma } to y { \ displaystyle y } receive m { \ displaystyle m } from y { \ displaystyle y } σ : = σ ⊕ m { \ displaystyle \ sigma : = \ sigma \ oplus m } if bit k { \ displaystyle k } in i { \ displaystyle i } is set then x : = x ⊕ m { \ displaystyle x : = x \ oplus m } endfor the algorithm works as follows.


in mathematics a group is a set together with a binary operation on the set called multiplication that obeys the group axioms. the axiom of choice is an axiom of zfc set theory which in one form states that every set can be wellordered. in zf set theory, i. e. zfc without the axiom of choice, the following statements are equivalent : for every nonempty set x there exists a binary operation • such that ( x, • ) is a group. the axiom of choice is true.


the distance of products to each other indicate either how different they are. the dimensions must be labelled by the researcher. this requires subjective judgement and is often very challenging. see perceptual mapping.


in telecommunications, a terminal adapter or ta acts as an interface between a terminal device, such as a computer or telephone, and a communications network ( typically an integrated services digital network ).


in some applications it may be acceptable to retrieve a " good guess " of the nearest neighbor. in those cases, we can use an algorithm which doesn't guarantee to return the actual nearest neighbor in every case, in return for improved speed or memory savings. often such an algorithm will find the nearest neighbor in a majority of cases, but this depends strongly on the dataset being queried. algorithms that support the approximate nearest neighbor search include locality - sensitive hashing, best bin first and balanced box - decomposition tree based search.


in mathematics, a rosati involution, named after carlo rosati, is an involution of the rational endomorphism ring of an abelian variety induced by a polarization. let a { \ displaystyle a } be an abelian variety, let a ^ = p i c 0 ( a ) { \ displaystyle { \ hat { a } } = \ mathrm { pic } ^ { 0 } ( a ) } be the dual abelian variety, and for a ∈ a { \ displaystyle a \ in a }, let t a : a → a { \ displaystyle t _ { a } : a \ to a } be the translation - by - a { \ displaystyle a } map, t a ( x ) = x + a { \ displaystyle t _ { a } ( x ) = x + a }. then each divisor d { \ displaystyle d } on a { \ displaystyle a } defines a map d : a → a ^ { \ displaystyle \ phi _ { d } : a \ to { \ hat { a } } } via d ( a ) = { \ displaystyle \ phi _ { d } ( a ) = }. the map d { \ displaystyle \ phi _ { d } } is a polarization if d { \ displaystyle d } is ample.


in software engineering, software system safety optimizes system safety in the design, development, use, and maintenance of software systems and their integration with safety - critical hardware systems in an operational environment.


in mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. edges of the original graph that cross between the groups will produce edges in the partitioned graph. if the number of resulting edges is small compared to the original graph, then the partitioned graph may be better suited for analysis and problem - solving than the original. finding a partition that simplifies graph analysis is a hard problem, but one that has applications to scientific computing, vlsi circuit design, and task scheduling in multiprocessor computers, among others.


as with racter, the question is how much the programmer filtered the output of the program, keeping only the occasional interesting output. also, mathematics being a very specialized domain, it is doubtful whether the techniques used can be abstracted to general cognition. another mathematical program, called geometry, was celebrated for making an insightful discovery of an original proof that an isosceles triangle has equal base angles.


in simple terms, a convex function refers to a function whose graph is shaped like a cup ∪ { \ displaystyle \ cup } ( or a straight line like a linear function ), while a concave function's graph is shaped like a cap ∩ { \ displaystyle \ cap }. convex functions play an important role in many areas of mathematics.


in philately, an invert error occurs when part of a stamp is printed upside - down. inverts are perhaps the most spectacular of postage stamp errors, not only because of their striking visual appearance, but because some are quite rare, and highly valued by stamp collectors.


in mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. these rules are formalized with a ranking of the operators. the rank of an operator is called its precedence, and an operation with a higher precedence is performed before operations with lower precedence. calculators generally perform operations with the same precedence from left to right, but some programming languages and calculators adopt different conventions.


which is succeeded by an account of the fellowship examination, in 1823 ( g. and w. b. whittaker, london, 1823 ) question 1249 in the gentleman's diary ; or mathematical repository for 1829 ( so appearing in late 1828 ) takes up the theme, with solutions appearing in the issue for the following year. one of the solvers, t. s. davies then generalized the result in question 1265 that year, presenting his own solution the following year, drawing on a paper he had already contributed to the philosophical magazine in 1826. there are no cross - references in this material to that described above.


in software engineering, the use of models is an alternative to more common code - based development techniques. a model always conforms to a unique metamodel. one of the currently most active branch of model driven engineering is the approach named model - driven architecture proposed by omg.


in mathematics, a harmonic divisor number, or ore number ( named after øystein ore who defined it in 1948 ), is a positive integer whose divisors have a harmonic mean that is an integer. the first few harmonic divisor numbers are : 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 ( sequence a001599 in the oeis ).


the null hypothesis may be true, whereas we reject h0. on the other hand, the alternative hypothesis h1 may be true, whereas we do not reject h0. two types of error are distinguished : type i error and type ii error.


in numerical analysis, interpolative decomposition ( id ) factors a matrix as the product of two matrices, one of which contains selected columns from the original matrix, and the other of which has a subset of columns consisting of the identity matrix and all its values are no greater than 2 in absolute value.


in music information retrieval, techniques have been developed to determine the key of a piece of classical western music ( recorded in audio data format ) automatically. these methods are often based on a compressed representation of the pitch content in a 12 - dimensional pitch - class profile ( chromagram ) and a subsequent procedure that finds the best match between this representation and one of the prototype vectors of the 24 minor and major keys. for implementation, often the constant - q transform is used, displaying the musical signal on a log frequency scale. although a radical ( over ) simplification of the concept of tonality, such methods can predict the key of classical western music well for most pieces. other methods also take into consideration the sequentiality of music.


then, for k l + m + 1 ≤ n ≤ k l + l + m { \ displaystyle kl + m + 1 \ leq n \ leq kl + l + m }, and equivalently m + 1 ≤ n − k l ≤ l + m { \ displaystyle m + 1 \ leq n - kl \ leq l + m }, we can write : y = m = 1 m h ⋅ x k y k. { \ displaystyle y = \ sum _ { m = 1 } ^ { m } h \ cdot x _ { k } \ \ \ triangleq \ \ y _ { k }. } with the substitution j = n − k l { \ displaystyle j = n - kl }, the task is reduced to computing y k { \ displaystyle y _ { k } } for m + 1 ≤ j ≤ l + m { \ displaystyle m + 1 \ leq j \ leq l + m }.


in statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest. since the forecast error is derived from the same scale of data, comparisons between the forecast errors of different series can only be made when the series are on the same scale. in simple cases, a forecast is compared with an outcome at a single time - point and a summary of forecast errors is constructed over a collection of such time - points. here the forecast may be assessed using the difference or using a proportional error. by convention, the error is defined using the value of the outcome minus the value of the forecast.


in numerical calculation, the days of the week are represented as weekday numbers. if monday is the first day of the week, the days may be coded 1 to 7, for monday through sunday, as is practiced in iso 8601. the day designated with 7 may also be counted as 0, by applying the arithmetic modulo 7, which calculates the remainder of a number after division by 7. thus, the number 7 is treated as 0, the number 8 as 1, the number 9 as 2, the number 18 as 4, and so on.


the court added : " in any case, a computer... is apparatus not mathematics. "


in probability theory and directional statistics, a circular uniform distribution is a probability distribution on the unit circle whose density is uniform for all angles.


in the classic vector space model proposed by salton, wong and yang the term - specific weights in the document vectors are products of local and global parameters. the model is known as term frequency - inverse document frequency model. the weight vector for document d is v d = t { \ displaystyle \ mathbf { v } _ { d } = ^ { t } }, where w t, d = t f t, d ⋅ log | d | | { d ′ ∈ d | t ∈ d ′ } | { \ displaystyle w _ { t, d } = \ mathrm { tf } _ { t, d } \ cdot \ log { \ frac { | d | } { | \ { d'\ in d \, | \, t \ in d'\ } | } } } and t f t, d { \ displaystyle \ mathrm { tf } _ { t, d } } is term frequency of term t in document d ( a local parameter ) log | d | | { d ′ ∈ d | t ∈ d ′ } | { \ displaystyle \ log { \ frac { | d | } { | \ { d'\ in d \, | \, t \ in d'\ } | } } } is inverse document frequency ( a global parameter ). | d | { \ displaystyle | d | } is the total number of documents in the document set ; | { d ′ ∈ d | t ∈ d ′ } | { \ displaystyle | \ { d'\ in d \, | \, t \ in d'\ } | } is the number of documents containing the term t.


in statistics, errors - in - variables models or measurement error models are regression models that account for measurement errors in the independent variables. in contrast, standard regression models assume that those regressors have been measured exactly, or observed without error ; as such, those models account only for errors in the dependent variables, or responses. in the case when some regressors have been measured with errors, estimation based on the standard assumption leads to inconsistent estimates, meaning that the parameter estimates do not tend to the true values even in very large samples. for simple linear regression the effect is an underestimate of the coefficient, known as the attenuation bias. in non - linear models the direction of the bias is likely to be more complicated.


in mathematics, an elementary proof is a mathematical proof that only uses basic techniques. more specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. historically, it was once thought that certain theorems, like the prime number theorem, could only be proved by invoking " higher " mathematical theorems or techniques. however, as time progresses, many of these results have also been subsequently reproven using only elementary techniques.


it is important to compare the class of euclidean domains with the larger class of principal ideal domains ( pids ). an arbitrary pid has much the same " structural properties " of a euclidean domain ( or, indeed, even of the ring of integers ), but when an explicit algorithm for euclidean division is known, one may use the euclidean algorithm and extended euclidean algorithm to compute greatest common divisors and bezout's identity. in particular, the existence of efficient algorithms for euclidean division of integers and of polynomials in one variable over a field is of basic importance in computer algebra.


in the united states, most landlord - tenant law is state - specific.


in the c + + programming language, is a part of the c + + standard library. it is a header file that provides templates and types that enable interoperation between stream buffers and string objects.


in the pingelapese language, transitive verbs are used in one of four of their most common sentence structures. transitive verbs according to this language have two main characteristics. these characteristics are action verbs and the sentence must contain a direct object. to elaborate, an action verb is a verb that has a physical action associated to its meaning.


metaclasses permit concepts to be construed as tokens of other concepts while retaining their ontological status as types. this enables types to be enumerated over, while preserving the ability to inherit from types. for example, metaclasses could allow a machine reasoner to infer from a human - friendly ontology how many elements are in the periodic table, or, given that number of protons is a property of chemical element and isotopes are a subclass of elements, how many protons exist in the isotope hydrogen - 2. metaclasses are sometime organized by levels, in a similar way to the simple theory of types where classes that are not metaclasses are assigned the first level, classes of classes in the first level are in the second level, classes of classes in the second level on the next and so on.


another common choice of equivalent martingale measure is the minimal martingale measure, which minimises the variance of the equivalent martingale. for certain situations, the resultant measure q { \ displaystyle q } will not be equivalent to p { \ displaystyle p }. in a finite probability model, for objective probabilities p i { \ displaystyle p _ { i } } and risk - neutral probabilities q i { \ displaystyle q _ { i } } then one must minimise the kullback – leibler divergence d k l ( q ‖ p ) = i = 1 n q i ln ( q i p i ) { \ displaystyle d _ { kl } ( q \ | p ) = \ sum _ { i = 1 } ^ { n } q _ { i } \ ln \ left ( { \ frac { q _ { i } } { p _ { i } } } \ right ) } subject to the requirement that the expected return is r { \ displaystyle r }, where r { \ displaystyle r } is the risk - free rate.


examples of words with these sounds in english are shin, chin, gin and vision ( in the middle of the word ). like most other coronal consonants, palato - alveolar consonants can be articulated either with the tip or blade of the tongue, and are correspondingly called apical or laminal. speakers of english use both variants, and it does not appear to significantly affect the sound of the consonants.


in the context of cybersecurity, new threats are emerging that target these smart systems. the timeline of cyber - kinetic attacks attests incidents from as early as 1982. such attacks on information systems that can have physical world impacts are a complete shift in paradigms within the cyber security community, though not unheard of.


in taxonomy the basis of any particular type of classification is the way in which objects in the domain resemble each other. a resemblance of a type that seems appropriate to the classification that we propose, we may call an affinity, and when we decide how to classify say, a specimen of rock or butterfly, we justify our decision according to the affinities that we observe. other resemblances we dismiss as being out of context or at least non - cogent ; for example, in deciding whether to classify a lizard as having closer affinities to a snake than to a table, biologists rely on affinities such as the scales, blood, physiology, vertebral anatomy, and reproductive system as being more relevant than the possession of four " feet ".


grassmann had published his results in 1844, but saint - venant claimed that he had first developed these ideas in 1832. one of the first mathematicians to appreciate grassmann's ideas during his lifetime was hermann hankel, whose 1867 theorie der complexen zahlensysteme., he developed some of hermann grassmann's algebras and w. r.


it employed the most powerful coding techniques available at the time, including channel encoding and shape encoding. from the mere four bits per symbol ( 9. 6 kbit / s ), the new standards used the functional equivalent of 6 to 10 bits per symbol, plus increasing baud rates from 2, 400 to 3, 429, to create 14. 4, 28. 8, and 33. 6 kbit / s modems. this rate is near the theoretical shannon limit of a phone line.


in the c # programming language, pointers are supported by either marking blocks of code that include pointers with the unsafe keyword, or by using the system. runtime. compilerservices assembly provisions for pointer access. the syntax is essentially the same as in c + +, and the address pointed can be either managed or unmanaged memory. however, pointers to managed memory ( any pointer to a managed object ) must be declared using the fixed keyword, which prevents the garbage collector from moving the pointed object as part of memory management while the pointer is in scope, thus keeping the pointer address valid.


in telephony, the demarcation point is the point at which the public switched telephone network ends and connects with the customer's on - premises wiring. it is the dividing line which determines who is responsible for installation and maintenance of wiring and equipment — customer / subscriber, or telephone company / provider. the demarcation point varies between countries and has changed over time.


in category theory, morphism is a broadly similar idea : the mathematical objects involved need not be sets, and the relationships between them may be something other than maps, although the morphisms between the objects of a given category have to behave similarly to maps in that they have to admit an associative operation similar to function composition. a morphism in category theory is an abstraction of a homomorphism. the study of morphisms and of the structures ( called " objects " ) over which they are defined is central to category theory. much of the terminology of morphisms, as well as the intuition underlying them, comes from concrete categories, where the objects are simply sets with some additional structure, and morphisms are structure - preserving functions. in category theory, morphisms are sometimes also called arrows.


in probability theory, slepian's lemma ( 1962 ), named after david slepian, is a gaussian comparison inequality. it states that for gaussian random variables x = ( x 1, …, x n ) { \ displaystyle x = ( x _ { 1 }, \ dots, x _ { n } ) } and y = ( y 1, …, y n ) { \ displaystyle y = ( y _ { 1 }, \ dots, y _ { n } ) } in r n { \ displaystyle \ mathbb { r } ^ { n } } satisfying e = e = 0 { \ displaystyle \ operatorname { e } = \ operatorname { e } = 0 }, e = e, i = 1, …, n, and e ≤ e for i = j. { \ displaystyle \ operatorname { e } = \ operatorname { e }, \ quad i = 1, \ dots, n, { \ text { and } } \ operatorname { e } \ leq \ operatorname { e } { \ text { for } } i \ neq j. } the following inequality holds for all real numbers u 1, …, u n { \ displaystyle u _ { 1 }, \ ldots, u _ { n } } : pr ≤ pr, { \ displaystyle \ pr \ left \ leq \ pr \ left, } or equivalently, pr ≥ pr.


this method is easiest to use for ip assets with positive cash flows, for those whose cash flows can be estimated with some degree of reliability for future periods, and where a proxy for risk can be used to obtain discount rates. cost approach : the cost approach is based on the economic principle of substitution. this principle states that an investor will pay no more for an asset than the cost to obtain, by purchasing or constructing, a substitute asset of equal utility.


in text data, any unicode character not available in the encoding declared in the header can be represented using a nnn ; numerical character reference. but the text within a cdata section is strictly limited to the characters available in the encoding. because of this, using a cdata section programmatically to quote data that could potentially contain'&'or'<'characters can cause problems when the data happens to contain characters that cannot be represented in the encoding. depending on the implementation of the encoder, these characters can get lost, can get converted to the characters of the nnn ; character reference, or can cause the encoding to fail.


in molecular biology, the btk - type zinc finger or btk motif ( bm ) is a conserved zinc - binding motif containing conserved cysteines and a histidine that is present in certain eukaryotic signalling proteins. the motif is named after bruton's tyrosine kinase ( btk ), an enzyme which is essential for b cell maturation in humans and mice. btk is a member of the tec family of protein tyrosine kinases ( ptk ). these kinases contain a conserved tec homology ( th ) domain between the n - terminal pleckstrin homology ( ph ) domain and the src homology 3 ( sh3 ) domain.


in the configuration random graph, the size distribution of connected components can be expressed via the convolution power of the excess degree distribution ( kryven ( 2017 ) ) : w ( n ) = { μ 1 n − 1 u 1 ∗ n ( n − 2 ), n > 1, u ( 0 ) n = 1. { \ displaystyle w ( n ) = { \ begin { cases } { \ frac { \ mu _ { 1 } } { n - 1 } } u _ { 1 } ^ { * n } ( n - 2 ), & n > 1, \ \ u ( 0 ) & n = 1. \ end { cases } } } here, w ( n ) { \ displaystyle w ( n ) } is the size distribution for connected components, u 1 ( k ) = k + 1 μ 1 u ( k + 1 ), { \ displaystyle u _ { 1 } ( k ) = { \ frac { k + 1 } { \ mu _ { 1 } } } u ( k + 1 ), } is the excess degree distribution, and u ( k ) { \ displaystyle u ( k ) } denotes the degree distribution. as convolution algebras are special cases of hopf algebras, the convolution power is a special case of the ( ordinary ) power in a hopf algebra.


the pointwise information is contained in the distortion tensor g ( x, f ) = { | j ( x, f ) | − 2 / n d t f ( x ) d f ( x ) if j ( x, f ) = 0 i if j ( x, f ) = 0. { \ displaystyle g ( x, f ) = { \ begin { cases } | j ( x, f ) | ^ { - 2 / n } d ^ { t } f ( x ) df ( x ) & { \ text { if } } j ( x, f ) \ not = 0 \ \ i & { \ text { if } } j ( x, f ) = 0. \ end { cases } } } the outer distortion ko and inner distortion ki are defined via the rayleigh quotients k o ( x ) = sup ξ = 0 ⟨ g ( x ) ξ, ξ ⟩ n / 2 | ξ | n, k o ( x ) = sup ξ = 0 ⟨ g − 1 ( x ) ξ, ξ ⟩ n / 2 | ξ | n. { \ displaystyle k _ { o } ( x ) = \ sup _ { \ xi \ not = 0 } { \ frac { \ langle g ( x ) \ xi, \ xi \ rangle ^ { n / 2 } } { | \ xi | ^ { n } } }, \ quad k _ { o } ( x ) = \ sup _ { \ xi \ not = 0 } { \ frac { \ langle g ^ { - 1 } ( x ) \ xi, \ xi \ rangle ^ { n / 2 } } { | \ xi | ^ { n } } }. } the outer distortion can also be characterized by means of an inequality similar to that given in the two - dimensional case. if ω is an open set in rn, then a function ƒ ∈ w1, 1loc ( ω, rn ) has finite distortion if its jacobian is locally integrable and does not change sign, and there is a measurable function ko ( the outer distortion ) such that | d f ( x ) | n ≤ k o ( x ) | j ( x, f ) | { \ displaystyle | df ( x ) | ^ { n } \ leq k _ { o } ( x ) | j ( x, f ) | } almost everywhere.


by construction, such functions respect equality in the sense that x = y → f ( x ) = f ( y ) { \ displaystyle x = y \ to f ( x ) = f ( y ) }, for any inputs from a { \ displaystyle a }. this is worth mentioning since also more broader concepts of " operations " exist in the literature, which may not respect this. and as noted, care must be taken with nomenclature " function ", a word which sees use in most mathematical frameworks.


in terms of proving lower bounds, our knowledge is very limited. since we study the computation of formal polynomials, we know that polynomials of very large degree require large circuits, for example, a polynomial of degree 2 2 n { \ displaystyle 2 ^ { 2 ^ { n } } } require a circuit of size roughly 2 n. { \ displaystyle 2 ^ { n }. } so, the main goal is to prove lower bound for polynomials of small degree, say, polynomial in n.


other dutch digraphs are never treated as single letters. in hungarian, the digraphs ⟨ cs ⟩, ⟨ dz ⟩, ⟨ gy ⟩, ⟨ ly ⟩, ⟨ ny ⟩, ⟨ sz ⟩, ⟨ ty ⟩, ⟨ zs ⟩, and the trigraph ⟨ dzs ⟩, have their own places in the alphabet ( where ⟨ cs ⟩ follows ⟨ c ⟩, ⟨ dz ⟩ and ⟨ dzs ⟩ follow ⟨ d ⟩, etc. ) in spanish, the digraphs ⟨ ch ⟩ and ⟨ ll ⟩ were formerly treated as distinct letters, but are now split into their constituent letters. in welsh, the alphabet includes the digraphs ⟨ ch ⟩, ⟨ dd ⟩, ⟨ ff ⟩, ⟨ ll ⟩, ⟨ ng ⟩, ⟨ ph ⟩, ⟨ rh ⟩, ⟨ th ⟩.


in the field of reinforcement learning, a softmax function can be used to convert values into action probabilities. the function commonly used is : where the action value q t ( a ) { \ displaystyle q _ { t } ( a ) } corresponds to the expected reward of following action a and τ { \ displaystyle \ tau } is called a temperature parameter ( in allusion to statistical mechanics ). for high temperatures ( τ → ∞ { \ displaystyle \ tau \ to \ infty } ), all actions have nearly the same probability and the lower the temperature, the more expected rewards affect the probability. for a low temperature ( τ → 0 + { \ displaystyle \ tau \ to 0 ^ { + } } ), the probability of the action with the highest expected reward tends to 1.


simone et al. use the following order of preference for the rules ( if applicable to the given context ) : b2 > b3 > { b2 ', b1 } > a1'> a2 ( x > y means that x is preferred over y ). experiments have shown that reduceandreconstruct alone has a worse compression / time ratio than the algorithm recyclepivots. however, while recyclepivots can be applied only once to a proof, reduceandreconstruct may be applied multiple times to produce a better compression. an attempt to combine reduceandreconstruct and recyclepivots algorithms has led to good results. = = notes = =


in meteorology, an inversion is a deviation from the normal change of an atmospheric property with altitude. it almost always refers to an inversion of the air temperature lapse rate, in which case it is called a temperature inversion. normally, air temperature decreases with an increase in altitude, but during an inversion warmer air is held above cooler air. an inversion traps air pollution, such as smog, close to the ground.


in some languages, palatalization is a distinctive feature that distinguishes two consonant phonemes. this feature occurs in russian, irish, and scottish gaelic, among others. phonemic palatalization may be contrasted with either plain or velarized articulation. in many of the slavic languages, and some of the baltic and finnic languages, palatalized consonants contrast with plain consonants, but in irish they contrast with velarized consonants.


in the coindexing stage, each noun phrase is given a unique index, called a " referential index ". in the contraindexing stage, each non - anaphoric noun phrase ( i. e. each noun phrase that is not a reflexive pronoun like " herself " or a reciprocal pronoun like " each other " ) is given a set of " anaphoric indices ". this set consists of the referential indices of all elements that c - command it.


in proof theory, an area of mathematical logic, resolution proof reduction via local context rewriting is a technique for resolution proof reduction via local context rewriting. this proof compression method was presented as an algorithm named reduceandreconstruct, that operates as a post - processing of resolution proofs. reduceandreconstruct is based on a set of local proof rewriting rules that transform a subproof into an equivalent or stronger one.


in some countries such as france, such schemes may be initiated by the central government : schema directeur d'amenagement et de gestion des eaux


in mathematics the let expression is described as the conjunction of expressions. in functional languages the let expression is also used to limit scope. in mathematics scope is described by quantifiers.


cutting - plane methods for general convex continuous optimization and variants are known under various names : kelley's method, kelley – cheney – goldstein method, and bundle methods. they are popularly used for non - differentiable convex minimization, where a convex objective function and its subgradient can be evaluated efficiently but usual gradient methods for differentiable optimization can not be used. this situation is most typical for the concave maximization of lagrangian dual functions. another common situation is the application of the dantzig – wolfe decomposition to a structured optimization problem in which formulations with an exponential number of variables are obtained. generating these variables on demand by means of delayed column generation is identical to performing a cutting plane on the respective dual problem.


similarly, the action of a general reflection will be to switch the entries at positions j − kn and i + kn for each k, fixing all inputs at positions not congruent to i or j modulo n. in the geometric action of s ~ n { \ displaystyle { \ widetilde { s } } _ { n } }, the generator s i { \ displaystyle s _ { i } } acts on an alcove a by reflecting it across one of the bounding planes of the fundamental alcove a0. in the inverse action, it instead reflects a across one of its own bounding planes. from this perspective, a reduced word corresponds to an alcove walk on the tessellated space v.


in relational algebra, a selection ( sometimes called a restriction to avoid confusion with sql's use of select ) is a unary operation written as σ a θ b ( r ) { \ displaystyle \ sigma _ { a \ theta b } ( r ) } or σ a θ v ( r ) { \ displaystyle \ sigma _ { a \ theta v } ( r ) } where : a { \ displaystyle a } and b { \ displaystyle b } are attribute names, θ { \ displaystyle \ theta } is a binary operation in the set { <, ≤, =, =, ≥, > }, { \ displaystyle \ { <, \ leq, =, \ neq, \ geq, > \ }, } v { \ displaystyle v } is a value constant, r { \ displaystyle r } is a relation. the selection σ a θ b ( r ) { \ displaystyle \ sigma _ { a \ theta b } ( r ) } selects all those tuples in r { \ displaystyle r } for which θ { \ displaystyle \ theta } holds between the a { \ displaystyle a } and the b { \ displaystyle b } attribute. the selection σ a θ v ( r ) { \ displaystyle \ sigma _ { a \ theta v } ( r ) } selects all those tuples in r { \ displaystyle r } for which θ { \ displaystyle \ theta } holds between the a { \ displaystyle a } attribute and the value v. { \ displaystyle v. } thus, the selection operator restricts to a subset of the entire database.


in response to various compliance pressures, organizations can introduce unique identifiers for its entire user base to validate that each user belongs in each specific system or application in which he / she has login capabilities. to effectuate such a policy, various individuals familiar with the organization's entire user base and each system - specific user base must be responsible for validating that certain identities should be linked together and other identities should be disassociated from each other. once the validation process is complete, a unique identifier can be assigned to that individual and his or her associated system - specific account login ids.


in mathematics, birch's theorem, named for bryan john birch, is a statement about the representability of zero by odd degree forms.


the result was presented at the conference 100 years in seattle : the mathematics of klee and grunbaum and appeared in annals of mathematics. specifically, the paper presented a 43 - dimensional polytope of 86 facets with a diameter of more than 43. the counterexample has no direct consequences for the analysis of the simplex method, as it does not rule out the possibility of a larger but still linear or polynomial number of steps. various equivalent formulations of the problem had been given, such as the d - step conjecture, which states that the diameter of any 2d - facet polytope in d - dimensional euclidean space is no more than d ; santos leal's counterexample also disproves this conjecture.


in the data stream model, the frequent elements problem is to output a set of elements that constitute more than some fixed fraction of the stream. a special case is the majority problem, which is to determine whether or not any value constitutes a majority of the stream. more formally, fix some positive constant c > 1, let the length of the stream be m, and let fi denote the frequency of value i in the stream. the frequent elements problem is to output the set { i | fi > m / c }. some notable algorithms are : boyer – moore majority vote algorithm count - min sketch lossy counting multi - stage bloom filters misra – gries heavy hitters algorithm misra – gries summary


for let the first terms, of the combination of which all others consist, be designated by signs ; these signs will be a kind of alphabet. it will be convenient for the signs to be as natural as possible — e. g., for one, a point ; for numbers, points ; for the relations of one entity with another, lines ; for the variation of angles and of extremities in lines, kinds of relations. if these are correctly and ingeniously established, this universal writing will be as easy as it is common, and will be capable of being read without any dictionary ; at the same time, a fundamental knowledge of all things will be obtained.


in the keynesian beauty contest, participants are asked to choose a number that will be as close as possible to some fraction of the average of all participants'guesses. suppose there are many players, each attempting to guess ½ of the average from the range 1 - 100. a level zero player will select a number non - strategically. that number might be selected at random, or may have special significance to the player ( in which case it is indistinguishable from a random number by other players ).


in mathematical physics, noncommutative quantum field theory ( or quantum field theory on noncommutative spacetime ) is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions are noncommutative. one commonly studied version of such theories has the " canonical " commutation relation : = i θ μ ν { \ displaystyle = i \ theta ^ { \ mu \ nu } \, \! } which means that ( with any given set of axes ), it is impossible to accurately measure the position of a particle with respect to more than one axis. in fact, this leads to an uncertainty relation for the coordinates analogous to the heisenberg uncertainty principle.


in signal processing, sampling is the reduction of a continuous - time signal to a discrete - time signal. a common example is the conversion of a sound wave to a sequence of " samples ". a sample is a value of the signal at a point in time and / or space ; this definition differs from the term's usage in statistics, which refers to a set of such values. a sampler is a subsystem or operation that extracts samples from a continuous signal. a theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points. the original signal can be reconstructed from a sequence of samples, up to the nyquist limit, by passing the sequence of samples through a type of low - pass filter called a reconstruction filter.


in software development, the specified hardware and software environment can be set up as a testbed for the application under test. in this context, a testbed is also known as the test environment made of : testing hardware equipment ( test bench, optical table, custom testing rig, dummy equipment as simulates an actual product or its counterpart, external environment means, like showers, heaters, fans, vacuum chamber, anechoic chamber ). computing equipment ( processing units, data centers, in - line fpga, environment simulation equipment ).


in telecommunication, bilateral synchronization ( or bilateral control ) is a synchronization control system between exchanges a and b in which the clock at telephone exchange a controls the data received at exchange b and the clock at exchange b controls the data received at exchange a. bilateral synchronization is usually implemented by deriving the timing from the incoming bitstream. source : from federal standard 1037c in support of mil - std - 188


from the perspective of copy elimination, this heuristic has the best results. on the other hand, aggressive coalescing could impact the colorability of the inference graph. conservative coalescing it mainly uses the same heuristic as aggressive coalescing but it merges moves if, and only if, it does not compromise the colorability of the interference graph. iterated coalescing it removes one particular move at the time, while keeping the colorability of the graph. optimistic coalescing it is based on aggressive coalescing, but if the inference graph colorability is compromised, then it gives up as few moves as possible.


in graphs that have negative cycles, the set of shortest simple paths from v to all other vertices do not necessarily form a tree. for simple connected graphs, shortest - path trees can be used to suggest a non - linear relationship between two network centrality measures, closeness and degree. by assuming that the branches of the shortest - path trees are statistically similar for any root node in one network, one may show that the size of the branches depend only on the number of branches connected to the root vertex, i. e. to the degree of the root node. from this one deduces that the inverse of closeness, a length scale associated with each vertex, varies approximately linearly with the logarithm of degree. the relationship is not exact but it captures a correlation between closeness and degree in large number of networks constructed from real data and this success suggests that shortest - path trees can be a useful approximation in network analysis.


it iteratively does hill - climbing, each time with a random initial condition x 0 { \ displaystyle x _ { 0 } }. the best x m { \ displaystyle x _ { m } } is kept : if a new run of hill climbing produces a better x m { \ displaystyle x _ { m } } than the stored state, it replaces the stored state. random - restart hill climbing is a surprisingly effective algorithm in many cases. it turns out that it is often better to spend cpu time exploring the space, than carefully optimizing from an initial condition.


in mathematics, the energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. this quantity is studied in the context of spectral graph theory. more precisely, let g be a graph with n vertices.


in the following discussion, let k ( s ) be the complexity of the string s. it is not hard to see that the minimal description of a string cannot be too much larger than the string itself — the program generatestring2 above that outputs s is a fixed amount larger than s. theorem : there is a constant c such that. k ( s ) ≤ | s | + c.


in order to find information on the web, most users make use of search engines, which crawl the web, index it and show a list of results ordered by relevance. the use of search engines to access information through the web has become a key factor for online businesses, which depend on the flow of users visiting their pages. one of these companies is foundem. foundem provides a " vertical search " service to compare products available on online markets for the u. k.


understanding how individual interactions within networks influence coevolution, and conversely how coevolution influences the overall structure of networks, requires an appreciation for how pair - wise interactions change due to their broader community contexts as well as how this community context shapes selective pressures. accordingly, research is now focusing on how reciprocal selection influences and is embedded within the structure of multispecies interactive webs, not only on particular species in isolation. coevolution in a community context can be addressed theoretically via mathematical modeling and simulation, by looking at ancient footprints of evolutionary history via ecological patterns that persist and are observable today, and by performing laboratory experiments with microorganisms.


in plant morphology, a cataphyll ( sometimes also called a cataphyllum or cataphyll leaf ) is a reduced, small leaf. many plants have both " true leaves " ( euphylls ), which perform most of the photosynthesis, and cataphylls, which are modified to perform other functions. cataphylls include bracts, bracteoles and bud scales, as well as any small leaves that resemble scales, known as scale leaves. the functions of cataphylls, such as bud scales, may be short - lived, and they are often shed after their function is fulfilled.


in text processing, a proximity search looks for documents where two or more separately matching term occurrences are within a specified distance, where distance is the number of intermediate words or characters. in addition to proximity, some implementations may also impose a constraint on the word order, in that the order in the searched text must be identical to the order of the search query. proximity searching goes beyond the simple matching of words by adding the constraint of proximity and is generally regarded as a form of advanced search. for example, a search could be used to find " red brick house ", and match phrases such as " red house of brick " or " house made of red brick ". by limiting the proximity, these phrases can be matched while avoiding documents where the words are scattered or spread across a page or in unrelated articles in an anthology.


standing or kneeling targets must be no more than 45 yards ( 41 m ) from the firing line. points are scored with 1 for a hit ( resulting in the faceplate falling ), and 0 for a miss ( whether it strikes the surrounding faceplate, misses it, or " splits " on the edge of the kill but fails to down the target ). the highest score of a competition forms the benchmark for all the other scores – they are calculated as a percentage of this score rather than the total number of targets.


due to its difficulty, it is fairly scarcely done. lag the effect experienced when the game runs slower than its normal speed due to an excess of instructions for the cpu to calculate in the time of one frame. thus, the cpu will spread the calculations over multiple frames.


in surveying, the repetition method is used to improve precision and accuracy of measurements of horizontal angles. the same angle is measured multiple times, with the survey instrument rotated so that systematic errors tend to cancel. the arithmetic mean of these observations gives true value of an angle.


in such case three possibilities exists : continue with both processors : this is based on the assumption that the fault is transient and may not appear again. take out the active processor and continue with the other. continue with active processor but remove other processor from service. when a processor is taken out, it is subjected to extensive testing to identify a marginal failure.


in mathematics, the category fdhilb has all finite - dimensional hilbert spaces for objects and the linear transformations between them as morphisms.


station identification in that case usually consists of the station's name, frequency, and a slogan ; unlicensed stations are not allowed to use formal call signs. international shortwave broadcasters usually do not use callsigns, instead giving the name of the service and the location of the home office, and occasionally the frequencies that the current broadcast is being transmitted on. there are a few exceptions, particularly in the united states, the time station wwv being a prime example.


which 3d point xest is the best estimate of x given y 1 ′ { \ displaystyle \ mathbf { y }'_ { 1 } } and y 2 ′ { \ displaystyle \ mathbf { y }'_ { 2 } } and the geometry of the cameras? the answer is often found by defining an error measure which depends on xest and then minimizing this error. in the following sections, some of the various methods for computing xest presented in the literature are briefly described. all triangulation methods produce xest = x in the case that y 1 = y 1 ′ { \ displaystyle \ mathbf { y } _ { 1 } = \ mathbf { y }'_ { 1 } } and y 2 = y 2 ′ { \ displaystyle \ mathbf { y } _ { 2 } = \ mathbf { y }'_ { 2 } }, that is, when the epipolar constraint is satisfied ( except for singular points, see below ). it is what happens when the constraint is not satisfied which differs between the methods.


4. computing term frequencies or tf - idf after pre - processing the text data, we can then proceed to generate features. for document clustering, one of the most common ways to generate features for a document is to calculate the term frequencies of all its tokens.


in mathematics, the four - spiral semigroup is a special semigroup generated by four idempotent elements. this special semigroup was first studied by karl byleen in a doctoral dissertation submitted to the university of nebraska in 1977. it has several interesting properties : it is one of the most important examples of bi - simple but not completely - simple semigroups ; it is also an important example of a fundamental regular semigroup ; it is an indispensable building block of bisimple, idempotent - generated regular semigroups. a certain semigroup, called double four - spiral semigroup, generated by five idempotent elements has also been studied along with the four - spiral semigroup.


the complexities of creating such a secure system come from the fact that the behaviour of humans is not always rational or predictable. even in a very - well secured computer system, a malicious individual can telephone a worker and pretend to be a private investigator working for the software company, and ask for the individual's password, a dishonest process called " phishing ". as well, even with a well - secured system, if a worker decides to put the company's electronic files on a usb drive to take them home to work on them over the weekend ( against many companies'policies ), and then loses this usb drive, the company's data may be compromised.


using human characteristics as descriptors of machines in metaphorical ways was already practiced by alan turing with terms such as " memory ", " search " and " stimulus ". in contrast, a heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well - defined correct or optimal result. as an effective method, an algorithm can be expressed within a finite amount of space and time, and in a well - defined formal language for calculating a function. starting from an initial state and initial input ( perhaps empty ), the instructions describe a computation that, when executed, proceeds through a finite number of well - defined successive states, eventually producing " output " and terminating at a final ending state. the transition from one state to the next is not necessarily deterministic ; some algorithms, known as randomized algorithms, incorporate random input.


in mathematics, the symbolic method in invariant theory is an algorithm developed by arthur cayley, siegfried heinrich aronhold, alfred clebsch, and paul gordan in the 19th century for computing invariants of algebraic forms. it is based on treating the form as if it were a power of a degree one form, which corresponds to embedding a symmetric power of a vector space into the symmetric elements of a tensor product of copies of it.


in the tsvd setting, given the eigen - decomposition k = q σ q t { \ displaystyle k = q \ sigma q ^ { t } } and using a prescribed threshold λ n { \ displaystyle \ lambda n }, a regularized inverse can be formed for the kernel matrix by discarding all the eigenvalues that are smaller than this threshold. thus, the filter function for tsvd can be defined as g λ ( σ ) = { 1 / σ, if σ ≥ λ n 0, otherwise. { \ displaystyle g _ { \ lambda } ( \ sigma ) = \ left \ { { \ begin { array } { lcll } 1 / \ sigma &, & { \ text { if } } \ sigma \ geq \ lambda n \ \ 0 &, & { \ text { otherwise } } \ \ \ end { array } } \ right.. } it can be shown that tsvd is equivalent to the ( unsupervised ) projection of the data using ( kernel ) principal component analysis ( pca ), and that it is also equivalent to minimizing the empirical risk on the projected data ( without regularization ). note that the number of components kept for the projection is the only free parameter here. = = references = =


in reverse polish notation, the operators follow their operands. for example, to add 3 and 4 together, the expression is 3 4 + rather than 3 + 4. the expression 3 − 4 + 5 in conventional notation is 3 4 − 5 + in reverse polish notation : 4 is first subtracted from 3, then 5 is added to it. the concept of a stack, a last - in / first - out construct, is integral to the left - to - right evaluation of rpn.


in number theory, the calkin – wilf tree is a tree in which the vertices correspond one - to - one to the positive rational numbers. the tree is rooted at the number 1, and any rational number expressed in simplest terms as the fraction a / b has as its two children the numbers a / a + b and a + b / b. every positive rational number appears exactly once in the tree.


this possibly induces a reassignment of the other nodes p, c, s, d also. if something has been changed by the case, this is shown in the column group after. an arrow → in column next signifies that the rebalancing is complete with this step.


in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints — primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.


here k { \ displaystyle k } is the ratio of magnification or dilation factor or scale factor or similitude ratio. such a transformation can be called an enlargement if the scale factor exceeds 1. the above - mentioned fixed point s is called homothetic center or center of similarity or center of similitude.


in the configuration model, the degree of each vertex is pre - defined, rather than having a probability distribution from which the given degree is chosen. as opposed to the erdos – renyi model, the degree sequence of the configuration model is not restricted to have a poisson distribution, the model allows the user to give the network any desired degree distribution.


in some applications of elliptic curve cryptography and the elliptic curve method of factorization ( ecm ) it is necessary to consider the scalar multiplication p. one way to do this is to compute successively : p, p = p + p, p = p + p, …, p = p + p { \ displaystyle p, \ quad p = p + p, \ quad p = p + p, \ dots, p = p + p } but it is faster to use double - and - add method, e. g. p = ( p ) + p. in general to compute p, write k = i ≤ l k i 2 i { \ displaystyle k = \ sum _ { i \ leq l } k _ { i } 2 ^ { i } } with ki in { 0, 1 } and l = { \ displaystyle l = }, kl = 1, then : (...


in its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation ; it is a simple corollary that the opposite is true of concave transformations. jensen's inequality generalizes the statement that the secant line of a convex function lies above the graph of the function, which is jensen's inequality for two points : the secant line consists of weighted means of the convex function ( for t ∈ ), t f ( x 1 ) + ( 1 − t ) f ( x 2 ), { \ displaystyle tf ( x _ { 1 } ) + ( 1 - t ) f ( x _ { 2 } ), } while the graph of the function is the convex function of the weighted means, f ( t x 1 + ( 1 − t ) x 2 ). { \ displaystyle f ( tx _ { 1 } + ( 1 - t ) x _ { 2 } ). } thus, jensen's inequality is f ( t x 1 + ( 1 − t ) x 2 ) ≤ t f ( x 1 ) + ( 1 − t ) f ( x 2 ).


{ \ displaystyle \ | f \ | _ { \ mathcal { d } } ^ { 2 } = \ sum _ { n \ geq 0 } ( n + 1 ) | a _ { n } | ^ { 2 }. } clearly, d { \ displaystyle { \ mathcal { d } } } contains all the polynomials and, more generally, all functions f { \ displaystyle f }, holomorphic on d { \ displaystyle \ mathbb { d } } such that f ′ { \ displaystyle f'} is bounded on d { \ displaystyle \ mathbb { d } }. the reproducing kernel of d { \ displaystyle { \ mathcal { d } } } at w ∈ c { 0 } { \ displaystyle w \ in \ mathbb { c } \ setminus \ { 0 \ } } is given by k w ( z ) = 1 z w log ( 1 1 − z w ) ( z ∈ c { 0 } ). { \ displaystyle k _ { w } ( z ) = { \ frac { 1 } { z { \ overline { w } } } } \ log \ left ( { \ frac { 1 } { 1 - z { \ overline { w } } } } \ right ) \ ; \ ; \ ; \ ; \ ; ( z \ in \ mathbb { c } \ setminus \ { 0 \ } ). }


the dirichlet distribution is the conjugate prior of the multinomial in bayesian statistics. dirichlet - multinomial distribution. beta - binomial distribution. negative multinomial distribution hardy – weinberg principle ( it is a trinomial distribution with probabilities ( θ 2, 2 θ ( 1 − θ ), ( 1 − θ ) 2 ) { \ displaystyle ( \ theta ^ { 2 }, 2 \ theta ( 1 - \ theta ), ( 1 - \ theta ) ^ { 2 } ) } )


considering there are no short term incentives to reward this front load effort required from companies engaging in collaboration, the motivation to do so is weak. to combat these high initial upfront costs, some organizations with complementary interests collaborate with each other to form " clusters ". with a common goal driving the group, there is noticeably increased efficiency in providing services which is why there is a faster return on investments working like this. unfortunately, the success of agencies with similar missions clustering together discourages more comprehensive collaborations.


in probability theory and statistics, the normal - exponential - gamma distribution ( sometimes called the neg distribution ) is a three - parameter family of continuous probability distributions. it has a location parameter μ { \ displaystyle \ mu }, scale parameter θ { \ displaystyle \ theta } and a shape parameter k { \ displaystyle k }.


in the chemical and process industries, a process has inherent safety if it has a low level of danger even if things go wrong. inherent safety contrasts with other processes where a high degree of hazard is controlled by protective systems. as perfect safety cannot be achieved, common practice is to talk about inherently safer design. “ an inherently safer design is one that avoids hazards instead of controlling them, particularly by reducing the amount of hazardous material and the number of hazardous operations in the plant. ”


definition let l { \ displaystyle l } be a partial differential operator in the plane ; define and be ordinary differential operators with respect to x { \ displaystyle x } or y { \ displaystyle y } ; a i, b i ∈ q ( x, y ) { \ displaystyle a _ { i }, b _ { i } \ in \ mathbb { q } ( x, y ) } for all i ; m { \ displaystyle m } and n { \ displaystyle n } are natural numbers not less than 2. assume the coefficients a i { \ displaystyle a _ { i } }, i = 0, …, m − 1 { \ displaystyle i = 0, \ ldots, m - 1 } are such that l { \ displaystyle l } and l m { \ displaystyle { \ mathfrak { l } } _ { m } } form a janet basis. if m { \ displaystyle m } is the smallest integer with this property then l x m ( l ) ≡ ⟨ ⟨ l, l m ⟩ ⟩ { \ displaystyle \ mathbb { l } _ { x ^ { m } } ( l ) \ equiv { \ langle \ langle } l, { \ mathfrak { l } } _ { m } { \ rangle \ rangle } } is called a laplace divisor of l { \ displaystyle l }.


a bios interrupt handler would then translate the program's request to match the hardware that was actually present. the smm in the 386sl is a better way to do this. some 8 - bit home computers used the nmi line to permit a " warm start " if the system had locked up.


the loser of each game puts one unit into the pot. play continues in like fashion through all the players until one of the players has beaten all the others in succession. the original problem, stated in a letter dated 10 april 1711, from montmort to nicholas bernoulli is for n = 2 and is attributed to m. de waldegrave. the problem, according to montmort, is to find the expectation of each player and the probability that the pool will be won within a specified number of games.


in the early stages of product development, it is common to use development boards with dedicated and readily accessible debug interfaces for connecting the debug tools. socs employed in the mobile market rely on two debug technologies : stop - mode debugging via a scan chain and stop - mode debugging via memory - mapped debug registers. the following non - mipi debug standards are well established in the embedded market : ieee 1149. 1 jtag ( 5 - pin ) and arm serial wire debug ( 2 - pin ), both using single - ended pins. thus, there was no need for the mipi debug working group to specify a stop - mode debug protocol or to specify a debug interface.


in the context of fair item allocation, the following results are known. unanimous approximate maximin - share fairness : when there are two groups, a positive multiplicative approximation to mms - fairness can be guaranteed if - and - only - if the numbers of agents in the groups are ( 1, n - 1 ) or ( 2, 2 ) or ( 2, 3 ). the positive results are attainable by polynomial - time algorithms. in all other cases, there are instances in which at least one agent with a positive mms gets a zero value in all allocations.


another useful application for gis regards flood risk assessment. using digital elevation models combined with peak discharge data can predict which areas of a floodplain will be submerged depending on the amount of rainfall. in a study of the illinois river watershed, rabie ( 2014 ) found that a decently accurate flood risk map could be generated using only dems and stream gauge data. analysis based on these two parameters alone does not account for manmade developments including levees or drainage systems, and therefore should not be considered a comprehensive result.


in statistics, the rv coefficient is a multivariate generalization of the squared pearson correlation coefficient ( because the rv coefficient takes values between 0 and 1 ). it measures the closeness of two set of points that may each be represented in a matrix. the major approaches within statistical multivariate data analysis can all be brought into a common framework in which the rv coefficient is maximised subject to relevant constraints. specifically, these statistical methodologies include : principal component analysis canonical correlation analysis multivariate regression statistical classification ( linear discrimination ). one application of the rv coefficient is in functional neuroimaging where it can measure the similarity between two subjects'series of brain scans or between different scans of a same subject.


primer - blast is widely used, and freely accessible from the national center for biotechnology information ( ncbi ) website. on the other hand, fastpcr, a commercial application, allows simultaneous testing of a single primer or a set of primers designed for multiplex target sequences.


this sequence differs from ( a, r, m, y ). also, the sequence ( 1, 1, 2, 3, 5, 8 ), which contains the number 1 at two different positions, is a valid sequence. sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers ( 2, 4, 6,... ).


in mathematical analysis, the whitney covering lemma, or whitney decomposition, asserts the existence of a certain type of partition of an open set in a euclidean space. originally it was employed in the proof of hassler whitney's extension theorem. the lemma was subsequently applied to prove generalizations of the calderon – zygmund decomposition. roughly speaking, the lemma states that it is possible to decompose an open set by cubes each of whose diameters is proportional, within certain bounds, to its distance from the boundary of the open set.


the more sophisticated record - oriented file systems have more in common with simple databases than with other file systems. cms file system – the native file system of the conversational monitor system component of vm / 370 files - 11 – early versions were record - oriented ; support for " streams " was added later michigan terminal system ( mts ) – provides " line files " where record lengths and line numbers are associated as metadata with each record in the file, lines can be added, replaced, updated with the same or different length records, and deleted anywhere in the file without the need to read and rewrite the entire file. os4000 for gec's os4000 operating system, on the gec 4000 series minicomputers a fat12 and fat16 ( and fat32 ) extension to support database - like file types random file, direct file, keyed file and sequential file in digital research flexos, ibm 4680 os and toshiba 4690 os.


in probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. it is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events ( subsets of the sample space ). for instance, if x is used to denote the outcome of a coin toss ( " the experiment " ), then the probability distribution of x would take the value 0. 5 ( 1 in 2 or 1 / 2 ) for x = heads, and 0. 5 for x = tails ( assuming that the coin is fair ). more commonly, probability distributions are used to compare the relative occurrence of many different random values. probability distributions can be defined in different ways and for discrete or for continuous variables. distributions with special properties or for especially important applications are given specific names..


in the early days of mobile telephony, the operators ( carriers ) charged for all air time consumed by the mobile phone user, which included both outbound and inbound telephone calls. as mobile phone adoption rates increased, competition between operators meant that some decided not to charge for incoming calls in some markets ( also called " calling party pays " ). the european market adopted a calling party pays model throughout the gsm environment and soon various other gsm markets also started to emulate this model. in hong kong, singapore, canada, and the united states, it is common for the party receiving the call to be charged per minute, although a few carriers are beginning to offer unlimited received phone calls.


in mathematics and statistics, in the context of markov processes, the kolmogorov equations, including kolmogorov forward equations and kolmogorov backward equations, are a pair of systems of differential equations that describe the time evolution of the process's distribution. this article, as opposed to the article titled kolmogorov equations, focuses on the scenario where we have a continuous - time markov chain ( so the state space ω { \ displaystyle \ omega } is countable ). in this case, we can treat the kolmogorov equations as a way to describe the probability p ( x, s ; y, t ) { \ displaystyle p ( x, s ; y, t ) }, where x, y ∈ ω { \ displaystyle x, y \ in \ omega } ( the state space ) and t > s, t, s ∈ r ≥ 0 { \ displaystyle t > s, t, s \ in \ mathbb { r } _ { \ geq 0 } } are the final and initial times, respectively.


in most of the approaches listed here, a well - understood block cipher ( such as aes ) is used as a primitive to take the place of an ideal random function. this has the advantage that incorporation of a secret key into the algorithm is easy. where aes is mentioned in the following discussion, any other good block cipher would work as well.


in the following figure, the graph c is a covering graph of the graph h. the covering map f from c to h is indicated with the colours. for example, both blue vertices of c are mapped to the blue vertex of h. the map f is a surjection : each vertex of h has a preimage in c. furthermore, f maps bijectively each neighbourhood of a vertex v in c onto the neighbourhood of the vertex f ( v ) in h. for example, let v be one of the purple vertices in c ; it has two neighbours in c, a green vertex u and a blue vertex t. similarly, let v ′ be the purple vertex in h ; it has two neighbours in h, the green vertex u ′ and the blue vertex t ′. the mapping f restricted to { t, u, v } is a bijection onto { t ′, u ′, v ′ }. this is illustrated in the following figure : similarly, we can check that the neighbourhood of a blue vertex in c is mapped one - to - one onto the neighbourhood of the blue vertex in h :


a profinite identity is a pair u and v of profinite words. a semigroup s is said to satisfy the profinite identity u = v if, for each semigroup morphism : a + → s { \ displaystyle \ phi : a ^ { + } \ to s }, the equality ^ ( u ) = ^ ( v ) { \ displaystyle { \ hat { \ phi } } ( u ) = { \ hat { \ phi } } ( v ) } holds. a variety of finite semigroups is the class of finite semigroups satisfying a set of profinite identities p. a variety of finite monoids is defined like a variety of finite semigroups, with the difference that one should consider monoid morphisms : a ∗ → m { \ displaystyle \ phi : a ^ { * } \ to m } instead of semigroup morphisms : a + → m { \ displaystyle \ phi : a ^ { + } \ to m }. a variety of finite ordered semigroups / monoids is also given by a similar definition, with the difference that one should consider morphisms of ordered semigroups / monoids.


most countries have legal requirements that mandate electromagnetic compatibility : electronic and electrical hardware must still work correctly when subjected to certain amounts of emi, and should not emit emi, which could interfere with other equipment ( such as radios ). radio frequency signal quality has declined throughout the 21st century by roughly one decibel per year as the spectrum becomes increasingly crowded. this has inflicted a red queen's race on the mobile phone industry as companies have been forced to put up more cellular towers ( at new frequencies ) that then cause more interference thereby requiring more investment by the providers and frequent upgrades of mobile phones to match.


this pattern of alternation ensures the resulting sums are all positive integers. changing the rule so that either the odd - or even - indexed summands are given negative signs ( regardless of the parity of n ) changes the signs of the resulting sums but not their absolute values. miodrag zivkovic proved in 1999 that there are only a finite number of alternating factorials that are also prime numbers, since 3612703 divides af ( 3612702 ) and therefore divides af ( n ) for all n ≥ 3612702. as of 2006, the known primes and probable primes are af ( n ) for ( sequence a001272 in the oeis ) n = 3, 4, 5, 6, 7, 8, 10, 15, 19, 41, 59, 61, 105, 160, 661, 2653, 3069, 3943, 4053, 4998, 8275, 9158, 11164only the values up to n = 661 have been proved prime in 2006. af ( 661 ) is approximately 7. 818097272875 × 101578.


in probability and statistics, a natural exponential family ( nef ) is a class of probability distributions that is a special case of an exponential family ( ef ).


in shape analysis, skeleton ( or topological skeleton ) of a shape is a thin version of that shape that is equidistant to its boundaries. the skeleton usually emphasizes geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width. together with the distance of its points to the shape boundary, the skeleton can also serve as a representation of the shape ( they contain all the information necessary to reconstruct the shape ). skeletons have several different mathematical definitions in the technical literature, and there are many different algorithms for computing them.


in probability theory, the coupon collector's problem describes " collect all coupons and win " contests. it asks the following question : if each box of a brand of cereals contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought to collect all n coupons? an alternative statement is : given n coupons, how many coupons do you expect you need to draw with replacement before having drawn each coupon at least once? the mathematical analysis of the problem reveals that the expected number of trials needed grows as θ ( n log ( n ) ) { \ displaystyle \ theta ( n \ log ( n ) ) }. for example, when n = 50 it takes about 225 trials on average to collect all 50 coupons.


for example, every vector v in three - dimensional space can be written uniquely as v x e x + v y e y + v z e z, { \ displaystyle v _ { x } \, \ mathbf { e } _ { x } + v _ { y } \, \ mathbf { e } _ { y } + v _ { z } \, \ mathbf { e } _ { z }, } the scalars v x { \ displaystyle v _ { x } }, v y { \ displaystyle v _ { y } }, v z { \ displaystyle v _ { z } } being the scalar components of the vector v. in the n - dimensional euclidean space r n { \ displaystyle \ mathbb { r } ^ { n } }, the standard basis consists of n distinct vectors { e i : 1 ≤ i ≤ n }, { \ displaystyle \ { \ mathbf { e } _ { i } : 1 \ leq i \ leq n \ }, } where ei denotes the vector with a 1 in the ith coordinate and 0's elsewhere. standard bases can be defined for other vector spaces, whose definition involves coefficients, such as polynomials and matrices. in both cases, the standard basis consists of the elements of the space such that all coefficients but one are 0 and the non - zero one is 1.


in number theory, a symbol is any of many different generalizations of the legendre symbol. this article describes the relations between these various generalizations. the symbols below are arranged roughly in order of the date they were introduced, which is usually ( but not always ) in order of increasing generality. legendre symbol ( a p ) { \ displaystyle \ left ( { \ frac { a } { p } } \ right ) } defined for p a prime, a an integer, and takes values 0, 1, or −1.


in statistics, aggregate data are data combined from several measurements. when data is aggregated, groups of observations are replaced with summary statistics based on those observations. in a data warehouse, the use of aggregate data dramatically reduces the time to query large sets of data. developers pre - summarise queries that are regularly used, such as weekly sales across several dimensions for example by item hierarchy or geographical hierarchy. in economics, aggregate data or data aggregates are high - level data that are composed from a multitude or combination of other more individual data, such as : in macroeconomics, data such as the overall price level or overall inflation rate ; and in microeconomics, data of an entire sector of an economy composed of many firms, or of all households in a city or region.


in order to provide performance guarantees to traffic flows it is necessary to specify some minimal performance of the server ( depending on reservations in the network, or scheduling policy, etc. ). service curves provide a means of expressing resource availability. several kinds of service curves exists, like weakly strict, variable capacity node, etc. see for an overview.


as an example, a bag of 100 real - world dice is a random probability mass function ( random pmf ) — to sample this random pmf you put your hand in the bag and draw out a die, that is, you draw a pmf. a bag of dice manufactured using a crude process 100 years ago will likely have probabilities that deviate wildly from the uniform pmf, whereas a bag of state - of - the - art dice used by las vegas casinos may have barely perceptible imperfections. we can model the randomness of pmfs with the dirichlet distribution. the dirichlet process is specified by a base distribution h { \ displaystyle h } and a positive real number α { \ displaystyle \ alpha } called the concentration parameter ( also known as scaling parameter ).


even if testing is automated and tests effectively measure the level of business risk, teams without a coordinated end - to - end quality process tend to have trouble satisfying the business expectations within today's compressed delivery cycles. trying to remove risks at the end of each iteration has been shown to be significantly slower and more resource - intensive than building quality into the product through defect prevention strategies such as development testing. organizations adopt continuous testing because they recognize that these problems are preventing them from delivering quality software at the desired speed. they recognize the growing importance of software as well as the rising cost of software failure, and they are no longer willing to make a tradeoff between time, scope, and quality.


a positive integer that has no square divisors except 1 is called square - free. for a non - negative integer n, the nth square number is n2, with 02 = 0 being the zeroth one.


in particular, if s and t intersect only in the identity, then every element of st has a unique expression as a product st with s in s and t in t. if s and t also commute, then st is a group, and is called a zappa – szep product. even further, if s or t is normal in st, then st coincides with the semidirect product of s and t. finally, if both s and t are normal in st, then st coincides with the direct product of s and t. if s and t are subgroups whose intersection is the trivial subgroup ( identity element ) and additionally st = g, then s is called a complement of t and vice versa. by a ( locally unambiguous ) abuse of terminology, two subgroups that intersect only on the ( otherwise obligatory ) identity are sometimes called disjoint.


in mathematics, a balanced matrix is a 0 - 1 matrix ( a matrix where every entry is either zero or one ) that does not contain any square submatrix of odd order having all row sums and all column sums equal to 2. balanced matrices are studied in linear programming. the importance of balanced matrices comes from the fact that the solution to a linear programming problem is integral if its matrix of coefficients is balanced and its right hand side or its objective vector is an all - one vector. in particular, if one searches for an integral solution to a linear program of this kind, it is not necessary to explicitly solve an integer linear program, but it suffices to find an optimal vertex solution of the linear program itself. as an example, the following matrix is a balanced matrix : { \ displaystyle { \ begin { bmatrix } 1 & 1 & 1 & 1 \ \ 1 & 1 & 0 & 0 \ \ 1 & 0 & 1 & 0 \ \ 1 & 0 & 0 & 1 \ \ \ end { bmatrix } } }


it was described as a " stunning advance " in the citation for wiles's abel prize award in 2016. it also proved much of the taniyama – shimura conjecture, subsequently known as the modularity theorem, and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques. the unsolved problem stimulated the development of algebraic number theory in the 19th and 20th centuries. it is among the most notable theorems in the history of mathematics and prior to its proof was in the guinness book of world records as the " most difficult mathematical problem ", in part because the theorem has the largest number of unsuccessful proofs.


in qualification rounds, teams are ranked by their ranking score, or their average number of ranking points ( rp ) per match. to ensure high placement, it is not only important to win matches, but to complete the secondary objectives as well, to amass as many ranking points as possible.


a recursive ordinal notation must satisfy the following two additional properties : the subset of natural numbers is a recursive set the induced well - ordering on the subset of natural numbers is a recursive relationthere are many such schemes of ordinal notations, including schemes by wilhelm ackermann, heinz bachmann, wilfried buchholz, georg cantor, solomon feferman, gerhard jager, isles, pfeiffer, wolfram pohlers, kurt schutte, gaisi takeuti ( called ordinal diagrams ), oswald veblen. stephen cole kleene has a system of notations, called kleene's o, which includes ordinal notations but it is not as well behaved as the other systems described here. usually one proceeds by defining several functions from ordinals to ordinals and representing each such function by a symbol.


a typical assessment includes identifying the extent of the project area, evaluating existing uses, documenting amenities and characteristics such as habitats, species, public access, development, and considering impact of future desired use. if the team decides the site is fit to implement soft engineering, a complex process is designed in order to achieve the predetermined goals of the development and complete with objectives. standards and targets must then be created to measure project development and progress.


that is, if vertex v has d ( v ) edges touching it ( representing a person who has d ( v ) friends ), then the average number μ of friends of a random person in the graph is μ = v ∈ v d ( v ) | v | = 2 | e | | v |. { \ displaystyle \ mu = { \ frac { \ sum _ { v \ in v } d ( v ) } { | v | } } = { \ frac { 2 | e | } { | v | } }. } the average number of friends that a typical friend has can be modeled by choosing a random person ( who has at least one friend ), and then calculating how many friends their friends have on average.


in probability theory and statistics, smoothness of a density function is a measure which determines how many times the density function can be differentiated, or equivalently the limiting behavior of distribution ’ s characteristic function. formally, we call the distribution of a random variable x ordinary smooth of order β if its characteristic function satisfies d 0 | t | − β ≤ | φ x ( t ) | ≤ d 1 | t | − β as t → ∞ { \ displaystyle d _ { 0 } | t | ^ { - \ beta } \ leq | \ varphi _ { x } ( t ) | \ leq d _ { 1 } | t | ^ { - \ beta } \ quad { \ text { as } } t \ to \ infty } for some positive constants d0, d1, β. the examples of such distributions are gamma, exponential, uniform, etc. the distribution is called supersmooth of order β if its characteristic function satisfies d 0 | t | β 0 exp ( − | t | β / γ ) ≤ | φ x ( t ) | ≤ d 1 | t | β 1 exp ( − | t | β / γ ) as t → ∞ { \ displaystyle d _ { 0 } | t | ^ { \ beta _ { 0 } } \ exp { \ big ( } - | t | ^ { \ beta } / \ gamma { \ big ) } \ leq | \ varphi _ { x } ( t ) | \ leq d _ { 1 } | t | ^ { \ beta _ { 1 } } \ exp { \ big ( } - | t | ^ { \ beta } / \ gamma { \ big ) } \ quad { \ text { as } } t \ to \ infty } for some positive constants d0, d1, β, γ and constants β0, β1. such supersmooth distributions have derivatives of all orders. examples : normal, cauchy, mixture normal.


in multitasking operating systems, processes ( running programs ) need a way to create new processes, e. g. to run other programs. fork and its variants are typically the only way of doing so in unix - like systems. for a process to start the execution of a different program, it first forks to create a copy of itself. then, the copy, called the " child process ", calls the exec system call to overlay itself with the other program : it ceases execution of its former program in favor of the other.


in mathematics, the hilbert metric, also known as the hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n - dimensional euclidean space rn. it was introduced by david hilbert ( 1895 ) as a generalization of cayley's formula for the distance in the cayley – klein model of hyperbolic geometry, where the convex set is the n - dimensional open unit ball. hilbert's metric has been applied to perron – frobenius theory and to constructing gromov hyperbolic spaces.


most cryptographic protocols rely on finite fields, i. e., fields with finitely many elements. the relation of two fields is expressed by the notion of a field extension. galois theory, initiated by evariste galois in the 1830s, is devoted to understanding the symmetries of field extensions.


in recent years, due to growing computational power, which allows for training in large ensemble learning in a reasonable time frame, the number of ensemble learning applications has grown increasingly. some of the applications of ensemble classifiers include :


in mathematics and computer science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. primality certificates allow the primality of a number to be rapidly checked without having to run an expensive or unreliable primality test. " succinct " usually means that the proof should be at most polynomially larger than the number of digits in the number itself ( for example, if the number has b bits, the proof might contain roughly b2 bits ). primality certificates lead directly to proofs that problems such as primality testing and the complement of integer factorization lie in np, the class of problems verifiable in polynomial time given a solution.


using these preliminaries, it is possible to investigate the effect of sample size on the standard errors of the mean and median. the observed mean is 3. 16, the observed raw median is 3 and the observed interpolated median is 3. 174. the following table gives some comparison statistics. the expected value of the median falls slightly as sample size increases while, as would be expected, the standard errors of both the median and the mean are proportionate to the inverse square root of the sample size. the asymptotic approximation errs on the side of caution by overestimating the standard error.


they describe precisely all recursively enumerable languages, which makes parsing impossible in general : it is an undecidable problem to decide whether a given string can be generated by a given w - grammar. hence, their use must be seriously constrained when used for automatic parsing or translation. restricted and modified variants of w - grammars were developed to address this, e. g. extended affix grammars ( eags ), applied to describe the grammars of natural language such as english and spanish ) ; q - systems, also applied to natural language processing ; the cdl series of languages, applied as compiler construction languages for programming languages. after the 1970s, interest in the approach waned ; occasionally, new studies are published.


in radiology and nuclear medicine applications, the practice of dictating and transcribing ( or using speech recognition ) is well entrenched and the output of these is typically unstructured or minimally structured prose, encoded as plain text and distributed by fax or hl7 version 2 messages or some equally primitive mechanism. the persistent form of these " documents " is not well - standardized, but many customers expect a vna to be able to accept them in whatever local format is preferred. the same principles apply as for the storage of any non - dicom content, including the use of hl7 version 2 messages or xds to provide metadata in lieu of a structured " header ", such as in the case of reports rendered as pdf, when they have not been encapsulated in dicom or cda objects. now that hl7 has promised to relax its previously closed ip policy, including offering cda free for use, it is possible that cda will become the preferred form of encoding, but vnas will still need to accept ( and possibly transcode ) reports in a plethora of form from the installed base. dicom defines templates for the encoding of human - generated reports as dicom structured report ( sr ) objects, and ihe specifies these in the simple image and numeric report ( sinr ) profile.


in some languages, predicative adjectives and copular complements receive a form of person agreement that is distinct from that used on ordinary predicative verbs. although that is a form of conjugation in that it refers back to the person of the subject, it is not " verbal " because it always derives from pronouns that have become clitic to the nouns to which they refer. an example of nonverbal person agreement, along with contrasting verbal conjugation, can be found from beja ( person agreement affixes in bold ) : wun. tu. wi, “ you ( fem. ) are big ” hada. b. wa, “ you ( masc. )


it is still used in some areas. the second egyptian multiplication and division technique was known from the hieratic moscow and rhind mathematical papyri written in the seventeenth century b. c. by the scribe ahmes. although in ancient egypt the concept of base 2 did not exist, the algorithm is essentially the same algorithm as long multiplication after the multiplier and multiplicand are converted to binary. the method as interpreted by conversion to binary is therefore still in wide use today as implemented by binary multiplier circuits in modern computer processors.


load balancing the servers that host the desktops. managing desktop images. redirecting multimedia processing to the client. = = references = =


the uk national variant of iso 646 was standardised as bs 4730 in 1985. this code was identical to ascii except for two characters : x23 encoded £ instead of #, while x7e encoded ( overline ) instead of ~ ( tilde ). ms - dos on the ibm pc originally used a proprietary 8 - bit character set code page 437 in which the £ symbol was encoded as x9c ; adoption of the iso / iec 8859 - 1 ( " iso latin - 1 " ) standard code xa3 only came later with microsoft windows.


in number theory, cramer's conjecture, formulated by the swedish mathematician harald cramer in 1936, is an estimate for the size of gaps between consecutive prime numbers : intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be. it states that p n + 1 − p n = o ( ( log p n ) 2 ), { \ displaystyle p _ { n + 1 } - p _ { n } = o ( ( \ log p _ { n } ) ^ { 2 } ), \ } where pn denotes the nth prime number, o is big o notation, and " log " is the natural logarithm. while this is the statement explicitly conjectured by cramer, his heuristic actually supports the stronger statement lim sup n → ∞ p n + 1 − p n ( log p n ) 2 = 1, { \ displaystyle \ limsup _ { n \ rightarrow \ infty } { \ frac { p _ { n + 1 } - p _ { n } } { ( \ log p _ { n } ) ^ { 2 } } } = 1, } and sometimes this formulation is called cramer's conjecture. however, this stronger version is not supported by more accurate heuristic models, which nevertheless support the first version of cramer's conjecture. neither form has yet been proven or disproven.