to prove this, consider the function g which maps x to f ( x ) − x. it is ≥ 0 on a and ≤ 0 on b. by the intermediate value theorem, g has a zero in ; this zero is a fixed point. brouwer is said to have expressed this as follows : " instead of examining a surface, we will prove the theorem about a piece of string. let us begin with the string in an unfolded state, then refold it. let us flatten the refolded string. again a point of the string has not changed its position with respect to its original position on the unfolded string. "


additionally, the inspiration of colleagues was accounted for to have expanded. along these lines, adopting agile practices in a distributed environment has demonstrated to be valuable for the quality of the project and its execution. thus, these can be seen as some of the advantages achieved by combining agile in distributed development, however, the list is exhaustive. the main benefits can be listed as follows :


turian et al. ( 2003 ) point out that, " any mt evaluation measure is less reliable on shorter translations ", and show that increasing the amount of data improves the reliability of a metric. however, they add that "... reliability on shorter texts, as short as one sentence or even one phrase, is highly desirable because a reliable mt evaluation measure can greatly accelerate exploratory data analysis ". banerjee et al. ( 2005 ) highlight five attributes that a good automatic metric must possess ; correlation, sensitivity, consistency, reliability and generality. any good metric must correlate highly with human judgment, it must be consistent, giving similar results to the same mt system on similar text.


in mathematics, in the field of group theory, a modular subgroup is a subgroup that is a modular element in the lattice of subgroups, where the meet operation is defined by the intersection and the join operation is defined by the subgroup generated by the union of subgroups. by the modular property of groups, every quasinormal subgroup ( that is, a subgroup that permutes with all subgroups ) is modular. in particular, every normal subgroup is modular.


the stanford dash multiprocessor system implements a variation of processor consistency which is incomparable ( neither weaker nor stronger ) to goodman's definitions. all processors need to be consistent in the order in which they see writes by one processor and in the way they see writes by different processors to the same location. however, they do not need to be consistent when the writes are by different processors to different locations.


these theorems provide necessary conditions for planarity that are not sufficient conditions, and therefore can only be used to prove a graph is not planar, not that it is planar. if both theorem 1 and 2 fail, other methods may be used. whitney's planarity criterion gives a characterization based on the existence of an algebraic dual ; mac lane's planarity criterion gives an algebraic characterization of finite planar graphs, via their cycle spaces ; the fraysseix – rosenstiehl planarity criterion gives a characterization based on the existence of a bipartition of the cotree edges of a depth - first search tree. it is central to the left - right planarity testing algorithm ; schnyder's theorem gives a characterization of planarity in terms of partial order dimension ; colin de verdiere's planarity criterion gives a characterization based on the maximum multiplicity of the second eigenvalue of certain schrodinger operators defined by the graph. the hanani – tutte theorem states that a graph is planar if and only if it has a drawing in which each independent pair of edges crosses an even number of times ; it can be used to characterize the planar graphs via a system of equations modulo 2.


the former is supported through some form of object literal, declarations where objects can be defined at runtime through special syntax such as {... } and passed directly to a variable. while most systems support a variety of cloning, ex nihilo object creation is not as prominent. in class - based languages, a new instance is constructed through a class's constructor function, a special function that reserves a block of memory for the object's members ( properties and methods ) and returns a reference to that block. an optional set of constructor arguments can be passed to the function and are usually held in properties.


in mathematics, in particular the study of abstract algebra, a dedekind – hasse norm is a function on an integral domain that generalises the notion of a euclidean function on euclidean domains.


first minimize the maximal value of the load on all of the network routing node links do that by minimizing a load upper bound value that is applied to all links. the full mass of the flow will be split equally across the possible parallel routes. find the bottleneck links of the first layer ( see below ), then set their loading amount at the found minimum.


although the enhancement of the output code was considerable, the resulting increase in complexity of the compiler caused problems with the limited address space. at the time, better optimized code was seen to be an enabler to bootstrapping the code in pascal. in retrospect, the remaining assembly written sections were the problem, and needed to be eliminated, the sooner the better. another way to say this is that the space problems could be transient, but having significant program sections written in assembly are a serious and lasting problem.


expert systems tend to capture the expertise, of individuals in different organizations, on the same topic. by contrast a kbs, produced by logico - linguistic modeling, seeks to capture the expertise of individuals in the same organization on different topics. the emphasis is on the elicitation of organizational or group knowledge rather than individual experts. in logico - linguistic modeling the stakeholders become the experts. the end point of this stage is an ssm style conceptual models such as figure 1.


an alternative and equivalent definition is that a family of sets forms a delta - matroid when the convex hull of its indicator vectors ( the analogue of a matroid polytope ) has the property that every edge length is either one or the square root of two. delta - matroids were defined by andre bouchet in 1987. algorithms for matroid intersection and the matroid parity problem can be extended to some cases of delta - matroids. delta - matroids have also been used to study constraint satisfaction problems.


multiple edges, not allowed under the definition above, are two or more edges that join the same two vertices. in one more general sense of the term allowing multiple edges, a graph is an ordered triple g = ( v, e, ) { \ displaystyle g = ( v, e, \ phi ) } comprising : v { \ displaystyle v }, a set of vertices ( also called nodes or points ) ; e { \ displaystyle e }, a set of edges ( also called links or lines ) ; : e → { { x, y } x, y ∈ v and x = y } { \ displaystyle \ phi : e \ to \ { \ { x, y \ } \ mid x, y \ in v \ ; { \ textrm { and } } \ ; x \ neq y \ } }, an incidence function mapping every edge to an unordered pair of vertices ( that is, an edge is associated with two distinct vertices ). to avoid ambiguity, this type of object may be called precisely an undirected multigraph. a loop is an edge that joins a vertex to itself.


in programming, an edge case typically involves input values that require special handling in an algorithm behind a computer program. as a measure for validating the behavior of computer programs in such cases, unit tests are usually created ; they are testing boundary conditions of an algorithm, function or method. a series of edge cases around each " boundary " can be used to give reasonable coverage and confidence using the assumption that if it behaves correctly at the edges, it should behave everywhere else. for example, a function that divides two numbers might be tested using both very large and very small numbers. this assumes that if it works for both ends of the magnitude spectrum, it should work correctly in between.


3 ).


interest in these primes first arose due to their connection with fermat's last theorem. wolstenholme primes are also related to other special classes of numbers, studied in the hope to be able to generalize a proof for the truth of the theorem to all positive integers greater than two. the only two known wolstenholme primes are 16843 and 2124679 ( sequence a088164 in the oeis ). there are no other wolstenholme primes less than 109.


in mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities. for example, for a set { f i } { \ displaystyle \ { f _ { i } \ } } of polynomials over a ring r { \ displaystyle r }, the solution set is the subset of r { \ displaystyle r } on which the polynomials all vanish ( evaluate to 0 ), formally { x ∈ r : i ∈ i, f i ( x ) = 0 } { \ displaystyle \ { x \ in r : \ forall i \ in i, f _ { i } ( x ) = 0 \ } } the feasible region of a constrained optimization problem is the solution set of the constraints.


in painting, “ brownness ” defines earth tone. at the beginning of a painting, primitive painters used soil, animal fat, minerals, charcoal, and chalk combined to be a color around 40, 000 years ago. therefore, the first group of colors was a natural palette by themselves. and earth tone palette was very handy to mix from scratch.


the principle of integrity furthers this concept into honesty and accuracy throughout all professional psychological endeavors. another area where apa guidelines move beyond the belmont report is in the setting of standards. the apa establishes standards for all reputable members of the psychology community ( particularly those members of the american psychological association ). the association sets a code of conduct for all apa individuals, which, when violated, can result in termination of professional licensure or membership.


every song or recording has a unique identity by which they are licensed and tracked. details of songs or recordings are notified to the pros directly, or through catco, an electronic tracking system. it needs to be clarified that while blanket licenses are commonly issued to music - users, the latter are responsible for " usage returns " – the actual frequency of performances under the license – which then becomes the basis for the pro to apportion royalties to writers, publishers, and record labels.


in concurrency control, path expressions are a mechanism for expressing permitted sequences of execution. for example, a path expression like " { read }, write " might specify that either multiple simultaneous executions of read or a single execution of write but not both are allowed at any point in time. it is important to know that the path expressions are a mechanism for the synchronization of processes at the monitor level in the software.


in mathematics, a bundle map ( or bundle morphism ) is a morphism in the category of fiber bundles. there are two distinct, but closely related, notions of bundle map, depending on whether the fiber bundles in question have a common base space. there are also several variations on the basic theme, depending on precisely which category of fiber bundles is under consideration. in the first three sections, we will consider general fiber bundles in the category of topological spaces. then in the fourth section, some other examples will be given.


{ \ displaystyle f ( x, 0 ) = f ( x ). } the dual problem with respect to the chosen perturbation function is given by sup y ∗ ∈ y ∗ − f ∗ ( 0, y ∗ ) { \ displaystyle \ sup _ { y ^ { * } \ in y ^ { * } } - f ^ { * } \ left ( 0, y ^ { * } \ right ) } where f ∗ { \ displaystyle f ^ { * } } is the convex conjugate in both variables of f. { \ displaystyle f. }


a similar situation exists regarding the korean ks x 1001 character set, in which microsoft maps the euc - kr or uhc code for the wave dash ( 0xa1ad ) to u + 223c tilde operator, while ibm and apple map it to u + 301c. microsoft also uses u + ff5e to map the ks x 1001 raised tilde ( 0xa2a6 ), while apple uses u + 02dc small tilde. the current unicode reference glyph for u + 301c has been corrected to match the jis standard in response to a 2014 proposal, which noted that while the existing unicode reference glyph had been matched by fonts from the discontinued windows xp, all other major platforms including later versions of microsoft windows shipped with fonts matching the jis reference glyph for u + 301c. the jis / shift jis wave dash is still formally mapped to u + 301c as of jis x 0213, whereas the whatwg encoding standard used by html5 follows microsoft in mapping 0x8160 to u + ff5e. these two code points have a similar or identical glyph in several fonts, reducing the confusion and incompatibility.


the set of all possible die rolls is both mutually exclusive and collectively exhaustive ( i. e., " mece " ). the events 1 and 6 are mutually exclusive but not collectively exhaustive. the events " even " ( 2, 4 or 6 ) and " not - 6 " ( 1, 2, 3, 4, or 5 ) are also collectively exhaustive but not mutually exclusive.


extreme storm flood protection levels have been revised based on new federal emergency management agency guidelines for 100 - year and 500 - year design flood elevations. in the new orleans metropolitan area, 35 percent of which sits below sea level, is protected by hundreds of miles of levees and flood gates. this system failed catastrophically, with numerous breaks, during hurricane katrina ( 2005 ) in the city proper and in eastern sections of the metro area, resulting in the inundation of approximately 50 percent of the metropolitan area, ranging from a few inches to twenty feet in coastal communities. the morganza spillway provides a method of diverting water from the mississippi river when a river flood threatens new orleans, baton rouge and other major cities on the lower mississippi.


in some applications, such as substring search, one can compute a hash function h for every k - character substring of a given n - character string by advancing a window of width k characters along the string ; where k is a fixed integer, and n is greater than k. the straightforward solution, which is to extract such a substring at every character position in the text and compute h separately, requires a number of operations proportional to k · n. however, with the proper choice of h, one can use the technique of rolling hash to compute all those hashes with an effort proportional to mk + n where m is the number of occurrences of the substring. the most familiar algorithm of this type is rabin - karp with best and average case performance o ( n + mk ) and worst case o ( n · k ) ( in all fairness, the worst case here is gravely pathological : both the text string and substring are composed of a repeated single character, such as t = " aaaaaaaaaaa ", and s = " aaa " ). the hash function used for the algorithm is usually the rabin fingerprint, designed to avoid collisions in 8 - bit character strings, but other suitable hash functions are also used.


in the field of theoretical computer science the computability and complexity of computational problems are often sought - after. computability theory describes the degree to which problems are computable, whereas complexity theory describes the asymptotic degree of resource consumption. computational problems are therefore confined into complexity classes.


after completing the customer migration, sprint pcs sold the gsm radio interface network equipment to omnipoint communications in january 2000. omnipoint was later purchased by voicestream wireless which subsequently became t - mobile us. in august 2022, t - mobile us announced dead - zone cell phone coverage across the us using " midband " ( 1900 mhz ) pcs spectrum and starlink gen2 satellite cell coverage, to begin testing in 2023. using this satellite and midband spectrum, t - mobile plans to be able to connect by satellite to common mobile devices, unlike previous generations of satellite phones which used specialized earth - bound radios to connect to geosynchronous satellites with characteristic long lag time in communications.


in statistical genetics, felsenstein's tree - pruning algorithm ( or felsenstein's tree - peeling algorithm ), attributed to joseph felsenstein, is an algorithm for computing the likelihood of an evolutionary tree from nucleic acid sequence data. the algorithm is often used as a subroutine in a search for a maximum likelihood estimate for an evolutionary tree. further, it can be used in a hypothesis test for whether evolutionary rates are constant ( by using likelihood ratio tests ). it can also be used to provide error estimates for the parameters describing an evolutionary tree. = = references = =


the following problem is the main open problem in this area of research : find an explicit polynomial of polynomial degree that requires circuits of superpolynomial size. the state of the art is a ω ( n log d ) { \ displaystyle \ omega ( n \ log d ) } lower bound for the size of a circuit computing, e. g., the polynomial x 1 d + + x n d { \ displaystyle x _ { 1 } ^ { d } + \ cdots + x _ { n } ^ { d } } given by strassen and by baur and strassen. more precisely, strassen used bezout's lemma to show that any circuit that simultaneously computes the n { \ displaystyle n } polynomials x 1 d, …, x n d { \ displaystyle x _ { 1 } ^ { d }, \ ldots, x _ { n } ^ { d } } is of size ω ( n log d ), { \ displaystyle \ omega ( n \ log d ), } and later baur and strassen showed the following : given an arithmetic circuit of size s { \ displaystyle s } computing a polynomial f, { \ displaystyle f, } one can construct a new circuit of size at most o ( s ) { \ displaystyle o ( s ) } that computes f { \ displaystyle f } and all the n { \ displaystyle n } partial derivatives of f.


the relative simplicity of the algorithm makes it a popular first choice amongst optimizing algorithms. it is used widely in artificial intelligence, for reaching a goal state from a starting node. different choices for next nodes and starting nodes are used in related algorithms.


in terms of the legendre symbol, the law of quadratic reciprocity states for positive odd primes p, q { \ displaystyle p, q } we have ( p q ) ( q p ) = ( − 1 ) p − 1 2 q − 1 2. { \ displaystyle \ left ( { \ frac { p } { q } } \ right ) \ left ( { \ frac { q } { p } } \ right ) = ( - 1 ) ^ { { \ frac { p - 1 } { 2 } } { \ frac { q - 1 } { 2 } } }. } using the definition of the legendre symbol this is equivalent to a more elementary statement about equations.


because of the high value of these'a'items, frequent value analysis is required. in addition to that, an organization needs to choose an appropriate order pattern ( e. g.'just - in - time') to avoid excess capacity.'b'items are important, but of course less important than'a'items and more important than'c'items. therefore,'b'items are intergroup items.'c'items are marginally important.


such a point, if it exists, is called a global minimum point of the function and its value at this point is called the global minimum ( value ) of the function. if the function takes − ∞ { \ displaystyle - \ infty } as a value then − ∞ { \ displaystyle - \ infty } is necessarily the global minimum value and the minimization problem can be answered ; this is ultimately the reason why the definition of " proper " requires that the function never take − ∞ { \ displaystyle - \ infty } as a value. assuming this, if the function's domain is empty or if the function is identically equal to + ∞ { \ displaystyle + \ infty } then the minimization problem once again has an immediate answer.


the order dimension of a partial order is the minimum number of linear orders whose intersection is the given partial order. if a partial order has bounded order dimension, then an adjacency labeling scheme for the vertices in its comparability graph may be defined by labeling each vertex with its position in each of the defining linear orders, and determining that two vertices are adjacent if each corresponding pair of numbers in their labels has the same order relation as each other pair. in particular, this allows for an adjacency labeling scheme for the chordal comparability graphs, which come from partial orders of dimension at most four.


in telecommunications, a proprietary protocol is a communications protocol owned by a single organization or individual.


in cryptography, modular arithmetic directly underpins public key systems such as rsa and diffie – hellman, and provides finite fields which underlie elliptic curves, and is used in a variety of symmetric key algorithms including advanced encryption standard ( aes ), international data encryption algorithm ( idea ), and rc4. rsa and diffie – hellman use modular exponentiation. in computer algebra, modular arithmetic is commonly used to limit the size of integer coefficients in intermediate calculations and data.


in mathematics, constraint counting is counting the number of constraints in order to compare it with the number of variables, parameters, etc. that are free to be determined, the idea being that in most cases the number of independent choices that can be made is the excess of the latter over the former. for example, in linear algebra if the number of constraints ( independent equations ) in a system of linear equations equals the number of unknowns then precisely one solution exists ; if there are fewer independent equations than unknowns, an infinite number of solutions exist ; and if the number of independent equations exceeds the number of unknowns, then no solutions exist. in the context of partial differential equations, constraint counting is a crude but often useful way of counting the number of free functions needed to specify a solution to a partial differential equation.


in mathematics, the robinson – schensted – knuth correspondence, also referred to as the rsk correspondence or rsk algorithm, is a combinatorial bijection between matrices a with non - negative integer entries and pairs ( p, q ) of semistandard young tableaux of equal shape, whose size equals the sum of the entries of a. more precisely the weight of p is given by the column sums of a, and the weight of q by its row sums. it is a generalization of the robinson – schensted correspondence, in the sense that taking a to be a permutation matrix, the pair ( p, q ) will be the pair of standard tableaux associated to the permutation under the robinson – schensted correspondence. the robinson – schensted – knuth correspondence extends many of the remarkable properties of the robinson – schensted correspondence, notably its symmetry : transposition of the matrix a results in interchange of the tableaux p, q.


in number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to q, the field of rational numbers. cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with fermat's last theorem. it was in the process of his deep investigations of the arithmetic of these fields ( for prime n ) – and more precisely, because of the failure of unique factorization in their rings of integers – that ernst kummer first introduced the concept of an ideal number and proved his celebrated congruences.


in telecommunication, the term access control is defined in u. s. federal standard 1037c with the following meanings : a service feature or technique used to permit or deny use of the components of a communication system. a technique used to define or restrict the rights of individuals or application programs to obtain data from, or place data onto, a storage device. the definition or restriction of the rights of individuals or application programs to obtain data from, or place data into, a storage device. the process of limiting access to the resources of an ais ( automated information system ) to authorized users, programs, processes, or other systems. that function performed by the resource controller that allocates system resources to satisfy user requests. this definition depends on several other technical terms from federal standard 1037c.


in the early 1980s, when simple mail transfer protocol ( smtp ) was designed, it provided for no real verification of sending user or system. this was not a problem while email systems were run by trusted corporations and universities, but since the commercialization of the internet in the early 1990s, spam, phishing, and other crimes have been found to increasingly involve email. email authentication is a necessary first step towards identifying the origin of messages, and thereby making policies and laws more enforceable. hinging on domain ownership is a stance that emerged in the early 2000.


in the following discussion, the following conventions are adopted. k { \ displaystyle \ mathbb { k } } will denote one of the fields of real or complex numbers, denoted r { \ displaystyle \ mathbb { r } }, c { \ displaystyle \ mathbb { c } }, respectively. the vector space of m × n { \ displaystyle m \ times n } matrices over k { \ displaystyle \ mathbb { k } } is denoted by k m × n { \ displaystyle \ mathbb { k } ^ { m \ times n } }. for a ∈ k m × n { \ displaystyle a \ in \ mathbb { k } ^ { m \ times n } }, a t { \ displaystyle a ^ { \ textsf { t } } } and a ∗ { \ displaystyle a ^ { * } } denote the transpose and hermitian transpose ( also called conjugate transpose ) respectively.


in organisms with a changeable shape, such as amoeboid organisms, most directional terms are meaningless, since the shape of the organism is not constant and no distinct axes are fixed. similarly, in spherically symmetrical organisms, there is nothing to distinguish one line through the centre of the organism from any other. an indefinite number of triads of mutually perpendicular axes could be defined, but any such choice of axes would be useless, as nothing would distinguish a chosen triad from any others. in such organisms, only terms such as superficial and deep, or sometimes proximal and distal, are usefully descriptive.


processes are complex events constituted by a sequence of events. but even simple events can be conceived as complex entities involving an object, a time and the property exemplified by the object at this time. traditionally, metaphysicians tended to emphasize static being over dynamic events. this tendency has been opposed by so - called process philosophy or process ontology, which ascribes ontological primacy to events and processes.


in source code, the null character is often represented as the escape sequence \ 0 in string literals ( for example, " abc \ 0def " ) or in character constants ('\ 0') ; the latter may also be written instead simply as 0 ( without quotes nor slash ). in many languages ( such as c, which introduced this notation ), this is not a separate escape sequence, but an octal escape sequence with a single octal digit 0 ; as a consequence, \ 0 must not be followed by any of the digits 0 through 7 ; otherwise it is interpreted as the start of a longer octal escape sequence. other escape sequences that are found in use in various languages are \ 000, \ x00, \ z, or \ u0000. a null character can be placed in a url with the percent code % 00.


in the 5th century bc, hippocrates of chios showed that the lune of hippocrates and two other lunes could be exactly squared ( converted into a square having the same area ) by straightedge and compass. in 1766 the finnish mathematician daniel wijnquist, quoting daniel bernoulli, listed all five geometrical squareable lunes, adding to those known by hippocrates. in 1771 leonard euler gave a general approach and obtained certain equation to the problem. in 1933 and 1947 it was proven by nikolai chebotaryov and his student anatoly dorodnov that these five are the only squarable lunes.


in this case, to ensure that an application of a rewriting rule is not going to interfere with other resolution steps, a safe solution is to create a copy of the node represented by clause δ { \ displaystyle \ delta }. this solution increases proof size and some caution is needed when doing this. the heuristic for rule selection is important to achieve a good compression performance.


each of the standards has been placed in one of four fundamental categories to promote educational evaluations that are proper, useful, feasible, and accurate. in these sets of standards, validity and reliability considerations are covered under the accuracy topic. the tests are aimed at ensuring that student evaluations will provide sound, accurate, and credible information about student learning and performance, however ; standardized tests offer narrow information on many forms of intelligence and relying on them harms students because they inaccurately measure a student's potential for success.


the problem was not so acute on minicomputers and mainframes where the vendor often specified standards for their libraries, but on microcomputers the programming systems were generally delivered by a variety of 3rd party companies with no interest in standardization. nevertheless, this problem was being addressed in the early 1990s through the introduction of various shared library systems. these were actually intended to ease resource use on smaller platforms, by allowing a number of programs using a common resource, like the gui, to share a single copy of code instead of each loading a separate copy into memory.


scores using this metric have historically been known as " raw " scores. tests taken in october 2004 or later have a score range from 200 to 600. the median score is 400, with a standard deviation of 25 points.


in mathematics and computer science, the binary goppa code is an error - correcting code that belongs to the class of general goppa codes originally described by valerii denisovich goppa, but the binary structure gives it several mathematical advantages over non - binary variants, also providing a better fit for common usage in computers and telecommunication. binary goppa codes have interesting properties suitable for cryptography in mceliece - like cryptosystems and similar setups.


in some systems and in the context of message processing systems ( often real - time systems ), this term also refers to the goal of establishing a single agreed sequence of messages within a database formed by a particular but arbitrary sequencing of records. the key concept is that data combined in a certain sequence is a " truth " which may be analyzed and processed giving particular results, and that although the sequence is arbitrary ( and thus another correct but equally arbitrary sequencing would ultimately provide different results in any analysis ), it is desirable to agree that the sequence enshrined in the " single version of the truth " is the version that will be considered " the truth ", and that any conclusions drawn from analysis of the database are valid and unarguable, and ( in a technical context ) the database may be duplicated to a backup environment to ensure a persistent record is kept of the " single version of the truth ". the key point is when the database is created using an external data source ( such as a sequence of trading messages from a stock exchange ) an arbitrary selection is made of one possibility from two or more equally valid representations of the input data, but henceforth the decision sets " in stone " one and only one version of the truth.


in terms of performance, virtualization imposes a cost in the additional work the cpu has to perform to virtualize the underlying hardware. instructions that perform this extra work, and other activities that require virtualization, tend to lie in operating system calls. in an unmodified operating system, os calls introduce the greatest portion of virtualization " overhead ". paravirtualization or other virtualization techniques may help with these issues. vmware developed the virtual machine interface for this purpose, and selected operating systems currently support this. a comparison between full virtualization and paravirtualization for the esx server shows that in some cases paravirtualization is much faster.


in telecommunication, call setup is the process of establishing a virtual circuit across a telecommunications network. call setup is typically accomplished using a signaling protocol. the term call set - up time has the following meanings : the overall length of time required to establish a circuit - switched call between users. for data communication, the overall length of time required to establish a circuit - switched call between terminals ; i. e., the time from the initiation of a call request to the beginning of the call message. note : call set - up time is the summation of : ( a ) call request time — the time from initiation of a calling signal to the delivery to the caller of a proceed - to - select signal ; ( b ) selection time — the time from the delivery of the proceed - to - select signal until all the selection signals have been transmitted ; and ( c ) post selection time — the time from the end of the transmission of the selection signals until the delivery of the call - connected signal to the originating terminal.


the modulo operation, as implemented in many programming languages and calculators, is an application of modular arithmetic that is often used in this context. the logical operator xor sums 2 bits, modulo 2. in music, arithmetic modulo 12 is used in the consideration of the system of twelve - tone equal temperament, where octave and enharmonic equivalency occurs ( that is, pitches in a 1 : 2 or 2 : 1 ratio are equivalent, and c - sharp is considered the same as d - flat ).


in the ibm system / 360 and its successors, including the current z / architecture machines, the boot process is known as initial program load ( ipl ). ibm coined this term for the 7030 ( stretch ), revived it for the design of the system / 360, and continues to use it in those environments today. in the system / 360 processors, an ipl is initiated by the computer operator by selecting the three hexadecimal digit device address ( cuu ; c = i / o channel address, uu = control unit and device address ) followed by pressing the load button. on the high end system / 360 models, most system / 370 and some later systems, the functions of the switches and the load button are simulated using selectable areas on the screen of a graphics console, often an ibm 2250 - like device or an ibm 3270 - like device.


in some cases, it is required to compute an envy - minimizing allocation in a distributed manner, i. e., each agent should compute his / her own allocation, in a way that guarantees that the resulting allocation is consistent. this problem can be solved by presenting it as an asymmetric distributed constraint optimization problem ( adcop ) as follows. add a binary variable vij for each agent i and item j. the variable value is " 1 " if the agent gets the item, and " 0 " otherwise. the variable is owned by agent i. to express the constraint that each item is given to at most one agent, add binary constraints for each two different variables related to the same item, with an infinite cost if the two variables are simultaneously " 1 ", and a zero cost otherwise.


some have a bell inlet for a faster more effective flush. a problem with the valve type flush mechanism is that it invariably starts to leak after a couple of years use due to wear and tear of the valve, particles, etc. trapped in the valve.


the use of a high level language ( c ) to implement the operating system, and the reliance on standardized interfaces was in contrast to the assembly language oriented approaches of the past. as hardware vendors adapted unix to their systems, new and useful features were added to unix, e. g., fast file systems and tunable process schedulers. however, all the companies that adapted unix made unique changes to it, rather than collaborating on an industry standard to create " unix for supercomputers ".


if all of the residuals are equal, or do not fan out, they exhibit homoscedasticity. however, a terminological difference arises in the expression mean squared error ( mse ). the mean squared error of a regression is a number computed from the sum of squares of the computed residuals, and not of the unobservable errors.


after its cancellation when the work has been finished, the switching schedule then facilitates restoration of the normal running arrangements. switching components can also be tagged to reflect any operational restrictions that are in force. the network component / connectivity model, and associated diagrams, must always be kept absolutely up to date. the switching schedule facility therefore also allows'patches'to the network model to be applied to the live version at the appropriate stage ( s ) of the jobs. the term'patch'is derived from the method previously used to maintain the wallboard diagrams.


am, a computer mathematician that generates new mathematical concepts. it managed to produce by itself the notion of prime number and the goldbach conjecture.


therefore, people are called on to abide by a secret law. at least two things need to be examined : first is that the operation of a more general " chilling effect " that imposing a non disclosed law may have and ; secondly the social effects of discrimination, which take an entirely new light in the context of no longer discriminating against race creed color age or religion, but on the basis of a number, a number which has been assigned to all members of society reflecting information about that person which is unknown. accordingly, there can be no definition at present of what information credit repositories collect or even what the use of that information is or what it reflects.


his tests were shorter, but used similar techniques. wundt also measured mental processes and acknowledged the fact that there are individual differences between people.


in telecommunication, bit pairing is the practice of establishing, within a code set, a number of subsets that have an identical bit representation except for the state of a specified bit. note : an example of bit pairing occurs in the international alphabet no. 5 and the american standard code for information interchange ( ascii ), where the upper case letters are related to their respective lower case letters by the state of bit six.


good metric performance, across text types or domains, is important for the reusability of the metric. a metric that only works for text in a specific domain is useful, but less useful than one that works across many domains — because creating a new metric for every new evaluation or domain is undesirable. another important factor in the usefulness of an evaluation metric is to have a good correlation, even when working with small amounts of data, that is candidate sentences and reference translations.


in recent years a number of neural and deep - learning techniques have been proposed. some generalize traditional matrix factorization algorithms via a non - linear neural architecture, or leverage new model types like variational autoencoders. while deep learning has been applied to many different scenarios : context - aware, sequence - aware, social tagging etc. its real effectiveness when used in a simple collaborative recommendation scenario has been put into question.


the adjective which corresponds to squaring is quadratic. the square of an integer may also be called a square number or a perfect square. in algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers.


in probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. it gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. this contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables. marginal variables are those variables in the subset of variables being retained.


in the form stated here, the splitting lemma does not hold in the full category of groups, which is not an abelian category.


in mathematics, set inversion is the problem of characterizing the preimage x of a set y by a function f, i. e., x = f −1 ( y ) = { x ∈ rn | f ( x ) ∈ y }. it can also be viewed as the problem of describing the solution set of the quantified constraint " y ( f ( x ) ) ", where y ( y ) is a constraint, e. g. an inequality, describing the set y. in most applications, f is a function from rn to rp and the set y is a box of rp ( i. e. a cartesian product of p intervals of r ). when f is nonlinear the set inversion problem can be solved using interval analysis combined with a branch - and - bound algorithm. the main idea consists in building a paving of rp made with non - overlapping boxes. for each box, we perform the following tests : if f ( ) ⊂ y we conclude that ⊂ x ; if f ( ) ∩ y = ∅ we conclude that ∩ x = ∅ ; otherwise, the box the box is bisected except if its width is smaller than a given precision. to check the two first tests, we need an interval extension ( or an inclusion function ) for f. classified boxes are stored into subpavings, i. e., union of non - overlapping boxes. the algorithm can be made more efficient by replacing the inclusion tests by contractors.


for example, the permutation ( 1 3 2 4 ) that sends 1 to 3, 3 to 2, 2 to 4 and 4 to 1 is a 4 - cycle, and the permutation ( 1 3 2 ) ( 4 ) that sends 1 to 3, 3 to 2, 2 to 1 and 4 to 4 is considered a 3 - cycle by some authors. on the other hand, the permutation ( 1 3 ) ( 2 4 ) that sends 1 to 3, 3 to 1, 2 to 4 and 4 to 2 is not a cyclic permutation because it separately permutes the pairs { 1, 3 } and { 2, 4 }. the set of elements that are not fixed by a cyclic permutation is called the orbit of the cyclic permutation. every permutation on finitely many elements can be decomposed into cyclic permutations on disjoint orbits. the individual cyclic parts of a permutation are also called cycles, thus the second example is composed of a 3 - cycle and a 1 - cycle ( or fixed point ) and the third is composed of two 2 - cycles.


in mathematical field of combinatorial geometry, the littlewood – offord problem is the problem of determining the number of subsums of a set of vectors that fall in a given convex set. more formally, if v is a vector space of dimension d, the problem is to determine, given a finite subset of vectors s and a convex subset a, the number of subsets of s whose summation is in a. the first upper bound for this problem was proven ( for d = 1 and d = 2 ) in 1938 by john edensor littlewood and a. cyril offord. this littlewood – offord lemma states that if s is a set of n real or complex numbers of absolute value at least one and a is any disc of radius one, then not more than ( c log n / n ) 2 n { \ displaystyle { \ big ( } c \, \ log n / { \ sqrt { n } } { \ big ) } \, 2 ^ { n } } of the 2n possible subsums of s fall into the disc. in 1945 paul erdos improved the upper bound for d = 1 to ( n n / 2 ) ≈ 2 n 1 n { \ displaystyle { n \ choose \ lfloor { n / 2 } \ rfloor } \ approx 2 ^ { n } \, { \ frac { 1 } { \ sqrt { n } } } } using sperner's theorem.


this is because painting is a subtractive color process, for which red and blue are secondary, not primary, colors. although flawed in principle, the split - primary system can be successful in practice, because the recommended blue - biased red and green - biased blue positions are often filled by near approximations of magenta and cyan, respectively, while orange - biased red and violet - biased blue serve as secondary colors, which tend to further widen the mixable gamut. this system is in effect a simplified version of newton's geometrical rule that colors closer together on the hue circle will produce more vibrant mixtures. a mixture, however, produced from two primary colors will be much more highly saturated than one produced from two secondary colors, even though both pairs are the same distance apart on the hue circle, revealing the limitations of the circular model in the prediction of color mixing results.


in the scandinavian languages, adjectives ( both attributive and predicative ) are declined according to the gender, number, and definiteness of the noun they modify. in icelandic and faroese, adjectives are also declined according to grammatical case, unlike the other scandinavian languages. in some cases in swedish, norwegian and danish, adjectives and participles as predicates appear to disagree with their subjects. this phenomenon is referred to as pancake sentences.


in optimization, the line search strategy is one of two basic iterative approaches to find a local minimum x ∗ { \ displaystyle \ mathbf { x } ^ { * } } of an objective function f : r n → r { \ displaystyle f : \ mathbb { r } ^ { n } \ to \ mathbb { r } }. the other approach is trust region. the line search approach first finds a descent direction along which the objective function f { \ displaystyle f } will be reduced and then computes a step size that determines how far x { \ displaystyle \ mathbf { x } } should move along that direction. the descent direction can be computed by various methods, such as gradient descent or quasi - newton method. the step size can be determined either exactly or inexactly.


in mathematics, the quasi - dihedral groups, also called semi - dihedral groups, are certain non - abelian groups of order a power of 2. for every positive integer n greater than or equal to 4, there are exactly four isomorphism classes of non - abelian groups of order 2n which have a cyclic subgroup of index 2. two are well known, the generalized quaternion group and the dihedral group.


in order to de - risk the programme atlas and the mod took an incremental approach to the development and implementation of dii, with a separate contract for each increment. the extended timeline allowed the mod flexibility in defining its requirements. increment 1 : contract awarded march 2005. this covered 70, 000 user access devices ( uads ) and 200, 000 user accounts in the restricted and secret domains in 680 fixed locations.


in the following, let x { \ displaystyle x } be our n { \ displaystyle n } - dimensional input space. let h { \ displaystyle { \ mathcal { h } } } be a class of functions that we wish to use in order to learn a { 0, 1 } { \ displaystyle \ { 0, 1 \ } } - valued target function f { \ displaystyle f } defined over x { \ displaystyle x }. let d { \ displaystyle { \ mathcal { d } } } be the distribution of the inputs over x { \ displaystyle x }. the goal of a learning algorithm a { \ displaystyle { \ mathcal { a } } } is to choose the best function h ∈ h { \ displaystyle h \ in { \ mathcal { h } } } such that it minimizes e r r o r ( h ) = p x d ( h ( x ) = f ( x ) ) { \ displaystyle error ( h ) = p _ { x \ sim { \ mathcal { d } } } ( h ( x ) \ neq f ( x ) ) }.


in the united states and canada, almost all public libraries have computers available for the use of patrons, though some libraries will impose a time limit on users to ensure others will get a turn and keep the library less busy. users are often allowed to print documents that they have created using these computers, though sometimes for a small fee.


information policy is playing a greater role in the economy leading to the production of goods and services, as well as selling them directly to consumers ( ucla, 2009 ). the cost of information varies from a tangible good in that initial costs of the first unit are large and fixed ; however, after that, marginal costs are relatively low ( macinnes, 2011 ). as an increase from the information services, information can be paralleled to that of manufacturing several years ago ( ucla, 2009 ). the digitalization of information allows businesses to make better justified business decisions ( macinnes, 2011 ).


often identical files are installed on multiple computers, for example operating system files. with single - instance storage, only one copy of a file is written to the backup media therefore reducing space. this becomes more important when the storage is offsite and on cloud storage such as amazon s3.


in probability theory, although simple examples illustrate that linear uncorrelatedness of two random variables does not in general imply their independence, it is sometimes mistakenly thought that it does imply that when the two random variables are normally distributed. this article demonstrates that assumption of normal distributions does not have that consequence, although the multivariate normal distribution, including the bivariate normal distribution, does. to say that the pair ( x, y ) { \ displaystyle ( x, y ) } of random variables has a bivariate normal distribution means that every linear combination a x + b y { \ displaystyle ax + by } of x { \ displaystyle x } and y { \ displaystyle y } for constant ( i. e. not random ) coefficients a { \ displaystyle a } and b { \ displaystyle b } ( not both equal to zero ) has a univariate normal distribution. in that case, if x { \ displaystyle x } and y { \ displaystyle y } are uncorrelated then they are independent. however, it is possible for two random variables x { \ displaystyle x } and y { \ displaystyle y } to be so distributed jointly that each one alone is marginally normally distributed, and they are uncorrelated, but they are not independent ; examples are given below.


in later work by vila casado et al., alternative update techniques were studied, in which variable nodes are updated with the newest available check - node information. the intuition behind these algorithms is that variable nodes whose values vary the most are the ones that need to be updated first. highly reliable nodes, whose log - likelihood ratio ( llr ) magnitude is large and does not change significantly from one update to the next, do not require updates with the same frequency as other nodes, whose sign and magnitude fluctuate more widely. these scheduling algorithms show greater speed of convergence and lower error floors than those that use flooding. these lower error floors are achieved by the ability of the informed dynamic scheduling ( ids ) algorithm to overcome trapping sets of near codewords. when nonflooding scheduling algorithms are used, an alternative definition of iteration is used. for an ( n, k ) ldpc code of rate k / n, a full iteration occurs when n variable and n − k constraint nodes have been updated, no matter the order in which they were updated.


the native thread remains attached to the vm until it calls detachcurrentthread ( ) to detach itself. the jni framework does not provide any automatic garbage collection for non - jvm memory resources allocated by code executing on the native side. consequently, native side code ( such as assembly language ) assumes the responsibility for explicitly releasing any such memory resources that the native code acquires. on linux and solaris platforms, if the native code registers itself as a signal handler, it could intercept signals intended for the jvm.


in music, a monad is a single note or pitch. the western chromatic scale, for example, is composed of twelve monads. monads are contrasted to dyads, groups of two notes, triads, groups of three, and so on. = = references = =


the mutant should be the specification that the engineer guesses the programmer has implemented. then, the engineer has to calculate the subset of the vis that yields different results in both specifications. the predicate of this set is used to derive a new test class. some other testing tactics that may also be used are the following : in set extension ( ise ).


an occasional darkly discolored or corroded nickel, dime, quarter, or half dollar can fool the collector by its edge, giving off the appearance of a silver coin. often coin roll hunters also collect special proof coins, tokens and other exonumia, and foreign coins. others attempt to find and complete a set of coins, like the america the beautiful quarters, 50 state quarters, presidential dollars, or even every year and mint of regular designs.


it can be used to reduce fractions to their simplest form, and is a part of many other number - theoretic and cryptographic calculations. euclid poses the problem thus : " given two numbers not prime to one another, to find their greatest common measure ". he defines " a number a multitude composed of units " : a counting number, a positive integer not including zero.


in the area of modern algebra known as group theory, the thompson group th is a sporadic simple group of order 215 · 310 · 53 · 72 · 13 · 19 · 31 = 90745943887872000 ≈ 9×1016.


{ \ displaystyle \ delta \ left ( c ^ { * } ( m _ { 1 } ), c ^ { * } ( m _ { 2 } ) \ right ) \ geqslant h _ { q } ^ { - 1 } \ left ( { \ tfrac { 1 } { 2 } } - \ varepsilon \ right ) \ cdot 2k \ cdot t. } so now the final task is to find a lower bound for t { \ displaystyle t }.


in the following theorems a, p, q ∈ r n × n { \ displaystyle a, p, q \ in \ mathbb { r } ^ { n \ times n } }, and p { \ displaystyle p } and q { \ displaystyle q } are symmetric. the notation p > 0 { \ displaystyle p > 0 } means that the matrix p { \ displaystyle p } is positive definite. theorem ( continuous time version ). given any q > 0 { \ displaystyle q > 0 }, there exists a unique p > 0 { \ displaystyle p > 0 } satisfying a t p + p a + q = 0 { \ displaystyle a ^ { t } p + pa + q = 0 } if and only if the linear system x = a x { \ displaystyle { \ dot { x } } = ax } is globally asymptotically stable.


in semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. the principle is also called frege's principle, because gottlob frege is widely credited for the first modern formulation of it. however, the principle has never been explicitly stated by frege, and arguably it was already assumed by george boole decades before frege's work. the principle of compositionality is highly debated in linguistics. among its most challenging problems there are the issues of contextuality, the non - compositionality of idiomatic expressions, and the non - compositionality of quotations.


in queueing theory, a discipline within the mathematical theory of probability, a polling system or polling model is a system where a single server visits a set of queues in some order. the model has applications in computer networks and telecommunications, manufacturing and road traffic management. the term polling system was coined at least as early as 1968 and the earliest study of such a system in 1957 where a single repairman servicing machines in the british cotton industry was modelled. typically it is assumed that the server visits the different queues in a cyclic manner. exact results exist for waiting times, marginal queue lengths and joint queue lengths at polling epochs in certain models. mean value analysis techniques can be applied to compute average quantities. in a fluid limit, where a very large number of small jobs arrive the individual nodes can be viewed to behave similarly to fluid queues ( with a two state process ).


the first factor corresponds to how likely it is that the chosen edge contains the vertex, which increases when the vertex has more friends. the halving factor simply comes from the fact that each edge has two vertices. so the expected value of the number of friends of a ( randomly chosen ) friend is v ( d ( v ) | e | 1 2 ) d ( v ) = v d ( v ) 2 2 | e |.


enabling pae ( by setting bit 5, pae, of the system register cr4 ) causes major changes to this scheme. by default, the size of each page remains as 4 kb. each entry in the page table and page directory becomes 64 bits long ( 8 bytes ), instead of 32 bits, to allow for additional address bits.


note that in these cases the handle must be something other than a systemwide - unique small integer, otherwise it is forgeable. such an integer may nevertheless be used to identify a capability inside a process ; e. g., file descriptor in linux is unforgeable because its numerical value alone is meaningless, and only in the process context may refer to anything. transferring such a handle requires special care though, as its value often has to be different in the sending and receiving processes. in non - capability - based systems, on the other hand, each process must acquire its own separate handle, by specifying the identity of the resource and the desired access rights ( e. g., each process must open a file itself, by giving the filename and access mode ). such usage is more common even in modern systems that do support passing handles, but it is subject to vulnerabilities like the confused deputy problem.


each user will be associated to a row of the first matrix and each item with a column of the second matrix. the row or column associated to a specific user or item is called latent factors. when a new item is added it has no associated latent factors and the lack of interactions does not allow to learn them, as it was done with other items.


in mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements. for example, the sequence ⟨ a, b, d ⟩ { \ displaystyle \ langle a, b, d \ rangle } is a subsequence of ⟨ a, b, c, d, e, f ⟩ { \ displaystyle \ langle a, b, c, d, e, f \ rangle } obtained after removal of elements c, { \ displaystyle c, } e, { \ displaystyle e, } and f. { \ displaystyle f. } the relation of one sequence being the subsequence of another is a preorder.


in object - oriented programming languages, and other related fields, encapsulation refers to one of two related but distinct notions, and sometimes to the combination thereof : a language mechanism for restricting direct access to some of the object's components. a language construct that facilitates the bundling of data with the methods ( or other functions ) operating on those data. some programming language researchers and academics use the first meaning alone or in combination with the second as a distinguishing feature of object - oriented programming, while some programming languages that provide lexical closures view encapsulation as a feature of the language orthogonal to object orientation. the second definition is motivated by the fact that in many object - oriented languages, and other related fields, the components are not hidden automatically and this can be overridden ; thus, information hiding is defined as a separate notion by those who prefer the second definition. the features of encapsulation are supported using classes in most object - oriented languages, although other alternatives also exist.


in terms of clients and services. each service comprises one or more servers and exports operations that clients invoke by making requests. although using a single, centralized server is the simplest way to implement a service, the resulting service can only be as fault tolerant as the processor executing that server. if this level of fault tolerance is unacceptable, then multiple servers that fail independently can be used. usually, replicas of a single server are executed on separate processors of a distributed system, and protocols are used to coordinate client interactions with these replicas.


in terms of the legendre symbol, the law of quadratic reciprocity for positive odd primes states ( p q ) ( q p ) = ( − 1 ) p − 1 2 q − 1 2. { \ displaystyle \ left ( { \ frac { p } { q } } \ right ) \ left ( { \ frac { q } { p } } \ right ) = ( - 1 ) ^ { { \ frac { p - 1 } { 2 } } { \ frac { q - 1 } { 2 } } }. } a reciprocity law is a generalization of the law of quadratic reciprocity.


the ei condition implies that the total cake - price should be 2, so q + 2 p = 1 { \ displaystyle q + 2p = 1 }. the ei condition again implies that, in any connected ceei division, the cake is cut in the middle. both alice and george receive two peripheral slices and one central slice.


in statistics, econometrics and related fields, multidimensional analysis ( mda ) is a data analysis process that groups data into two categories : data dimensions and measurements. for example, a data set consisting of the number of wins for a single football team at each of several years is a single - dimensional ( in this case, longitudinal ) data set. a data set consisting of the number of wins for several football teams in a single year is also a single - dimensional ( in this case, cross - sectional ) data set. a data set consisting of the number of wins for several football teams over several years is a two - dimensional data set.


in some applications, the observations within each pair can only take the values 0 or 1. for example, 0 may indicate failure and 1 may indicate success. there are 4 possible pairs : { 0, 0 }, { 0, 1 }, { 1, 0 }, and { 1, 1 }. in these cases, the same procedure as the sign test is used, but is known as mcnemar's test.


put in simple technical terms, cochran's q test requires that there only be a binary response ( e. g. success / failure or 1 / 0 ) and that there be more than 2 groups of the same size. the test assesses whether the proportion of successes is the same between groups. often it is used to assess if different observers of the same phenomenon have consistent results ( interobserver variability ).


there are three major kinds of qualities or characteristics : types or kinds ( e. g. mammal ), properties ( e. g. short, strong ), and relations ( e. g. father of, next to ). these are all different types of universals. paradigmatically, universals are abstract ( e. g. humanity ), whereas particulars are concrete ( e. g. the personhood of socrates ).


in mathematics, the power set ( or powerset ) of a set s is the set of all subsets of s, including the empty set and s itself. in axiomatic set theory ( as developed, for example, in the zfc axioms ), the existence of the power set of any set is postulated by the axiom of power set. the powerset of s is variously denoted as p ( s ), ( s ), p ( s ), p ( s ) { \ displaystyle \ mathbb { p } ( s ) }, ( s ) { \ displaystyle \ wp ( s ) }, or 2s. the notation 2s, meaning the set of all functions from s to a given set of two elements ( e. g., { 0, 1 } ), is used because the powerset of s can be identified with, equivalent to, or bijective to the set of all the functions from s to the given two elements set. any subset of p ( s ) is called a family of sets over s.


in mathematics, the euclidean algorithm, or euclid's algorithm, is an efficient method for computing the greatest common divisor ( gcd ) of two integers ( numbers ), the largest number that divides them both without a remainder. it is named after the ancient greek mathematician euclid, who first described it in his elements ( c. 300 bc ).


in the computer science fields of knowledge engineering and ontology, the sigma knowledge engineering environment is an open source computer program for the development of formal ontologies. it is designed for use with the suggested upper merged ontology. it originally included only the vampire theorem prover as its core deductive inference engine, but now allows use of many other provers that have participated in the casc / cade competitions.


in numerical analysis, hill climbing is a mathematical optimization technique which belongs to the family of local search. it is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by making an incremental change to the solution. if the change produces a better solution, another incremental change is made to the new solution, and so on until no further improvements can be found. for example, hill climbing can be applied to the travelling salesman problem.


thus, the solution x 0 = a − 1 b { \ displaystyle x _ { 0 } = a ^ { - 1 } \ mathbf { b } } only exists where an actual corner exists in the window n { \ displaystyle n }. a methodology for performing automatic scale selection for this corner localization method has been presented by lindeberg by minimizing the normalized residual d ~ min = c − b t a − 1 b trace a { \ displaystyle { \ tilde { d } } _ { \ min } = { \ frac { c - b ^ { t } a ^ { - 1 } b } { \ operatorname { trace } a } } } over scales.


p ) ⋅ β q ( σ ∘ ι p, p + 1,...


it is guaranteed to be a vertex of the convex hull of the polygon. alternatively, the vertex with the smallest y - coordinate among the ones with the largest x - coordinates or the vertex with the smallest x - coordinate among the ones with the largest y - coordinates ( or any other of 8 " smallest, largest " x / y combinations ) will do as well. once a vertex of the convex hull is chosen, one can then apply the formula using the previous and next vertices, even if those are not on the convex hull, as there can be no local concavity on this vertex.


in the case of broadcast packets over a switching loop, the situation may develop into a broadcast storm. in a very simple example, a switch with three ports a, b, and c has a normal node connected to port a while ports b and c are connected to each other in a loop. all ports have the same link speed and run in full duplex mode. now, when a broadcast frame enters the switch through port a, this frame is forwarded to all ports but the source port, i. e. ports b and c. both frames exiting ports b and c traverse the loop in opposite directions and reenter the switch through their counterpart port.


in most current use cases, the letters a – f or a – f represent the values 10 – 15, while the numerals 0 – 9 are used to represent their decimal values. there is no universal convention to use lowercase or uppercase, so each is prevalent or preferred in particular environments by community standards or convention ; even mixed case is used. seven - segment displays use mixed - case abcdef to make digits that can be distinguished from each other. there is some standardization of using spaces ( rather than commas or another punctuation mark ) to separate hex values in a long list. for instance, in the following hex dump, each 8 - bit byte is a 2 - digit hex number, with spaces between them, while the 32 - bit offset at the start is an 8 - digit hex number.


these algorithms are called auction algorithms, push - relabel algorithms, or preflow - push algorithms. some of these algorithms were shown to be equivalent. some of the local methods assume that the graph admits a perfect matching ; if this is not the case, then some of these methods might run forever. : 3 a simple technical way to solve this problem is to extend the input graph to a complete bipartite graph, by adding artificial edges with very large weights.


the algebra is named for logicians adolf lindenbaum and alfred tarski. starting in the academic year 1926 - 1927, lindenbaum pioneered his method in jan łukasiewicz's mathematical logic seminar, and the method was popularized and generalized in subsequent decades through work by tarski. the lindenbaum – tarski algebra is considered the origin of the modern algebraic logic.


this statistic is named after major percy alexander macmahon who showed in 1913 that the distribution of the major index on all permutations of a fixed length is the same as the distribution of inversions. that is, the number of permutations of length n with k inversions is the same as the number of permutations of length n with major index equal to k. ( these numbers are known as mahonian numbers, also in honor of macmahon. )


in probability theory, the van den berg – kesten ( bk ) inequality or van den berg – kesten – reimer ( bkr ) inequality states that the probability for two random events to both happen, and at the same time one can find " disjoint certificates " to show that they both happen, is at most the product of their individual probabilities. the special case for two monotone events ( the notion as used in the fkg inequality ) was first proved by van den berg and kesten in 1985, who also conjectured that the inequality holds in general, not requiring monotonicity. reimer later proved this conjecture. : 159 : 44 the inequality is applied to probability spaces with a product structure, such as in percolation problems. : 829


in the case of constituency tree, a subtree is defined as a node and all its children ( e. g., ] ] ] is a subtree of the two trees ). terminals are not considered subtree ( e. g. is not a subtree ). the subtree kernel count the number of common subtrees between two given trees. in this example, there are seven common subtrees : ] ] ], ] ] ], ], ], ], ] ( counted twice as it appears twice ).


in mathematics, power iteration ( also known as the power method ) is an eigenvalue algorithm : given a diagonalizable matrix a { \ displaystyle a }, the algorithm will produce a number λ { \ displaystyle \ lambda }, which is the greatest ( in absolute value ) eigenvalue of a { \ displaystyle a }, and a nonzero vector v { \ displaystyle v }, which is a corresponding eigenvector of λ { \ displaystyle \ lambda }, that is, a v = λ v { \ displaystyle av = \ lambda v }. the algorithm is also known as the von mises iteration. power iteration is a very simple algorithm, but it may converge slowly. the most time - consuming operation of the algorithm is the multiplication of matrix a { \ displaystyle a } by a vector, so it is effective for a very large sparse matrix with appropriate implementation.


in the japanese kantenji braille, the standard 8 - dot braille patterns 267, 1267, 2467, and 12467 are the patterns related to braille pattern dots - 135, since the two additional dots of kantenji patterns 0135, 1357, and 01357 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


from the definition of the square root, we have that b × b = b { \ displaystyle { \ sqrt { b } } \ times { \ sqrt { b } } = b }. therefore, the exponent r { \ displaystyle r } must be such that b r × b r = b { \ displaystyle b ^ { r } \ times b ^ { r } = b }. using the fact that multiplying makes exponents add gives b r + r = b { \ displaystyle b ^ { r + r } = b }.


in mathematics, anticommutativity is a specific property of some non - commutative mathematical operations. swapping the position of two arguments of an antisymmetric operation yields a result which is the inverse of the result with unswapped arguments. the notion inverse refers to a group structure on the operation's codomain, possibly with another operation. subtraction is an anticommutative operation because commuting the operands of a − b gives b − a = − ( a − b ) ; for example, 2 − 10 = − ( 10 − 2 ) = −8. another prominent example of an anticommutative operation is the lie bracket. in mathematical physics, where symmetry is of central importance, these operations are mostly called antisymmetric operations, and are extended in an associative setting to cover more than two arguments.


we conclude that supp ( δ p ) { \ displaystyle \ operatorname { supp } ( \ delta _ { p } ) } is the closure of the singleton set { p }, { \ displaystyle \ { p \ }, } which is { p } { \ displaystyle \ { p \ } } itself. in fact, a measure μ { \ displaystyle \ mu } on the real line is a dirac measure δ p { \ displaystyle \ delta _ { p } } for some point p { \ displaystyle p } if and only if the support of μ { \ displaystyle \ mu } is the singleton set { p }. { \ displaystyle \ { p \ }. } consequently, dirac measure on the real line is the unique measure with zero variance ( provided that the measure has variance at all ).


in some cases, a polygon has to be covered not with arbitrary rectangles but with rectangles from a finite family.


in mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. the binary operation of a semigroup is most often denoted multiplicatively ( just notation, not necessarily the elementary arithmetic multiplication ) : x · y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair ( x, y ). associativity is formally expressed as that ( x · y ) · z = x · ( y · z ) for all x, y and z in the semigroup. semigroups may be considered a special case of magmas, where the operation is associative, or as a generalization of groups, without requiring the existence of an identity element or inverses.


in telephony, a special information tone ( sit ) is an in - band international standard call progress tone consisting of three rising tones indicating a call has failed. it usually precedes a recorded announcement describing the problem. because the sit is well known in many countries, callers can understand that their call has failed, even though they do not understand the language of the recorded announcement ( e. g., when calling internationally ) instead of assuming the recording is voicemail or some other intended function. like a dial tone or busy signal, the sit is an in - band signal intended both to be heard by the caller, and to be detected by automated dialing equipment to determine a call has failed. in north america, the at & t / bellcore sit standard allows the frequency and duration of the tones to vary slightly - making eight distinct messages specifically for automated equipment ; indicating not only a failed call, but also the specific reason for the failure ( e. g., disconnected number, busy circuits, dialing error, etc. ).


there exists a dedicated group of enthusiasts who use tvro ( tv receive - only ) gear such as satellite dishes to peek in on backhaul signals that are available on any of the dozens of broadcast satellites that are visible from almost any point on earth. in its early days, their hobby was strengthened by the fact that most backhaul was analog and in the clear ( unscrambled or unencrypted ) which made for a vast smorgasbord of free television available for the technically inclined amateur. in recent years, full - time content and cable channels have added encryption and conditional access, and occasional signals are steadily becoming digital, which has had a deleterious effect on the hobby.


in summer, the so - called “ fast ” search robot was launched, working in parallel with the actual pages intended for indexing. the base of the " fast robot " is updated every 1. 5 – 2 hours. the ranking algorithm has been improved to increase search accuracy. search capabilities have been expanded with the help of yandex. dictionaries ” and “ yandex.


kellerer and woeginger study a variant in which there are at most 3 * m jobs, and each machine must contain at most 3 jobs ( this can be seen as a generalization of 3 - partition problem ). they show that mlpt attains at most ( 4 m − 1 ) / ( 3 m ) { \ displaystyle ( 4m - 1 ) / ( 3m ) } of the minimum largest sum, which the same approximation ratio that lpt attains for the unconstrained problem. the bound is tight for mlpt.


a field with a single derivation operator is called an ordinary differential field ; if there is a finite set containing several commuting derivation operators the field is called a partial differential field. here differential operators with derivatives ∂ x = ∂ ∂ x { \ textstyle \ partial _ { x } = { \ frac { \ partial } { \ partial x } } } and ∂ y = ∂ ∂ y { \ textstyle \ partial _ { y } = { \ frac { \ partial } { \ partial y } } } with coefficients from some differential field are considered. its elements have the form i, j r i, j ( x, y ) ∂ x i ∂ y j { \ textstyle \ sum _ { i, j } r _ { i, j } ( x, y ) \ partial _ { x } ^ { i } \ partial _ { y } ^ { j } } ; almost all coefficients r i, j { \ displaystyle r _ { i, j } } are zero.


in mathematical logic, rosser's trick is a method for proving godel's incompleteness theorems without the assumption that the theory being considered is ω - consistent ( smorynski 1977, p. 840 ; mendelson 1977, p. 160 ). this method was introduced by j. barkley rosser in 1936, as an improvement of godel's original proof of the incompleteness theorems that was published in 1931. while godel's original proof uses a sentence that says ( informally ) " this sentence is not provable ", rosser's trick uses a formula that says " if this sentence is provable, there is a shorter proof of its negation ".


in phonetics, a continuant is a speech sound produced without a complete closure in the oral cavity. by one defintion, continuant is a distinctive feature that refers to any sound produced with an incomplete closure of the vocal tract, thus encompassing all sounds ( including vowels ) except stops, affricates and nasals. by another definition, it refers exclusively to consonantal sounds produced with an incomplete closure of the oral cavity, prototypically approximants and fricatives, but sometimes also trills. compare sonorants ( resonants ), a class of speech sounds which includes vowels, approximants and nasals ( but not fricatives ), and contrasts with obstruents.


joan clarke was also one such woman who made immense contributions to computing during world war ii. she was a british mathematician and codebreaker who worked at bletchley park on breaking codes generated by enigma machines, eventually developing alan turing's bombe technology to aid in deciphering complex nazi messages.


in probability theory and information theory, adjusted mutual information, a variation of mutual information may be used for comparing clusterings. it corrects the effect of agreement solely due to chance between clusterings, similar to the way the adjusted rand index corrects the rand index. it is closely related to variation of information : when a similar adjustment is made to the vi index, it becomes equivalent to the ami. the adjusted measure however is no longer metrical.


in the external memory model, the number of memory transfers it needs to perform a sort of n { \ displaystyle n } items on a machine with cache of size z { \ displaystyle z } and cache lines of length l { \ displaystyle l } is o ( n l log z n ) { \ displaystyle o \ left ( { \ tfrac { n } { l } } \ log _ { z } n \ right ) }, under the tall cache assumption that z = ω ( l 2 ) { \ displaystyle z = \ omega ( l ^ { 2 } ) }. this number of memory transfers has been shown to be asymptotically optimal for comparison sorts. funnelsort also achieves the asymptotically optimal runtime complexity of θ ( n log n ) { \ displaystyle \ theta ( n \ log n ) }.


later authors such as diana l. paxson and freya aswynn follow blum ( 1989 ) in drawing a direct correlation between runic divination and tarot divination. they may discuss runes in the context of " spreads " and advocate the usage of " rune cards ". modern authors like ralph blum sometimes include a " blank rune " in their sets. some were to replace a lost rune, but according to ralph blum this was the god odin's rune, the rune of the beginning and the end, representing " the divine in all human transactions ".


in probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a poisson point process, i. e., a process in which events occur continuously and independently at a constant average rate. it is a particular case of the gamma distribution. it is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. in addition to being used for the analysis of poisson point processes it is found in various other contexts. the exponential distribution is not the same as the class of exponential families of distributions. this is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and poisson distributions.


in order to mount a brute - force or dictionary based wpa password cracking attack on a wifi user with wpa or wpa2 enabled, a hacker must first sniff the wpa 4 - way handshake. the user can be elicited to provide this sequence by first forcing them offline with the deauthentication attack. in a similar phishing style attack without password cracking, wifiphisher starts with a deauthentication attack to disconnect the user from their legitimate base station, then mounts a man - in - the - middle attack to collect passwords supplied by an unwitting user.


fuzzy logic is increasingly employed in diagnostic and medical equipment capable of measuring gradations of a condition. in information services, fuzzy concepts are frequently encountered because a customer or client asks a question about something which could be interpreted in different ways, or, a document is transmitted of a type or meaning which cannot be easily allocated to a known type or category, or to a known procedure. it might take considerable inquiry to " place " the information, or establish in what framework it should be understood.


these weights should exceed the weights of all existing matchings, to prevent appearance of artificial edges in the possible solution. as shown by mulmuley, vazirani and vazirani, the problem of minimum weight perfect matching is converted to finding minors in the adjacency matrix of a graph. using the isolation lemma, a minimum weight perfect matching in a graph can be found with probability at least 1⁄2. for a graph with n vertices, it requires o ( log 2 ( n ) ) { \ displaystyle o ( \ log ^ { 2 } ( n ) ) } time.


in terms of structure, a triglyph may be carved from a single block with a metope, or the triglyph block may have slots cut into it to allow a separately cut metope ( in stone or wood ) to be slid into place, as at the temple of aphaea. of the two groups of 6th - century metopes from foce del sele, now in the museum at paestum, the earlier uses the first method, the later the second. there may be some variation in design within a single structure to allow for corner contraction, an adjustment of the column spacing and arrangement of the doric frieze in a temple to make the design appear more harmonious. in the evolution of the doric order, the placing of the triglyphs evolved somewhat, especially at corners.


in mathematics, an alternating group is the group of even permutations of a finite set. the alternating group on a set of n elements is called the alternating group of degree n, or the alternating group on n letters and denoted by an or alt ( n ).


in telecommunication, signaling is the use of signals for controlling communications. this may constitute an information exchange concerning the establishment and control of a telecommunication circuit and the management of the network.


the technique is known as a " trivial hash function " or, when used specifically for branch tables, " double dispatch ". for this to be feasible, the range of all possible values of the data needs to be small ( e. g. an ascii or ebcdic character value which have a range of hexadecimal'00'–'ff '. if the actual range is guaranteed to be smaller than this, the array can be truncated to less than 256 bytes ).


there are several algorithms for subband tree structuring that find a set of optimal bases that provide the most desirable representation of the data relative to a particular cost function ( entropy, energy compaction, etc. ). there were relevant studies in signal processing and communications fields to address the selection of subband trees ( orthogonal basis ) of various kinds, e. g. regular, dyadic, irregular, with respect to performance metrics of interest including energy compaction ( entropy ), subband correlations and others. discrete wavelet transform theory ( continuous in the time variable ) offers an approximation to transform discrete ( sampled ) signals. in contrast, the discrete - time subband transform theory enables a perfect representation of already sampled signals.


in mathematics, legendre's three - square theorem states that a natural number can be represented as the sum of three squares of integers n = x 2 + y 2 + z 2 { \ displaystyle n = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } if and only if n is not of the form n = 4 a ( 8 b + 7 ) { \ displaystyle n = 4 ^ { a } ( 8b + 7 ) } for nonnegative integers a and b. the first numbers that cannot be expressed as the sum of three squares ( i. e. numbers that can be expressed as n = 4 a ( 8 b + 7 ) { \ displaystyle n = 4 ^ { a } ( 8b + 7 ) } ) are 7, 15, 23, 28, 31, 39, 47, 55, 60, 63, 71... ( sequence a004215 in the oeis ).


in the unified modeling language ( uml ), an object diagram focuses on some particular set of objects and attributes, and the links between these instances. a correlated set of object diagrams provides insight into how an arbitrary view of a system is expected to evolve over time. early uml specifications described object diagrams as such : " an object diagram is a graph of instances, including objects and data values. a static object diagram is an instance of a class diagram ; it shows a snapshot of the detailed state of a system at a point in time.


in mathematics, a uniform matroid is a matroid in which the independent sets are exactly the sets containing at most r elements, for some fixed integer r. an alternative definition is that every permutation of the elements is a symmetry.


then, every process — including the x server — should be able to command the kernel to perform mode - setting operations, and the kernel would ensure that concurrent operations don't result in an inconsistent state. the new kernel api and code added to the drm module to perform these mode - setting operations was called kernel mode - setting ( kms ). kernel mode - setting provides several benefits. the most immediate is of course the removal of duplicate mode - setting code, from both the kernel ( linux console, fbdev ) and user space ( x server ddx drivers ).


more generally, recall is simply the complement of the type ii error rate ( i. e., one minus the type ii error rate ). precision is related to the type i error rate, but in a slightly more complicated way, as it also depends upon the prior distribution of seeing a relevant vs. an irrelevant item. the above cat and dog example contained 8 − 5 = 3 type i errors ( false positives ) out of 10 total cats ( true negatives ), for a type i error rate of 3 / 10, and 12 − 5 = 7 type ii errors, for a type ii error rate of 7 / 12. precision can be seen as a measure of quality, and recall as a measure of quantity. higher precision means that an algorithm returns more relevant results than irrelevant ones, and high recall means that an algorithm returns most of the relevant results ( whether or not irrelevant ones are also returned ).


the presence of an increasing amount of on - line data will necessitate greater use of automatic data processing in decision - making. saving data on multiple memory locations will guarantee the safekeeping of the acts. statistical data will be available in real time and under multiple profiles, with great benefits for top level decision - making.


in order to increase traffic capacity and safety, a route may have two or more separate roads for each direction of traffic. alternatively, a given road might be declared one - way.


in probability and statistics, the class of exponential dispersion models ( edm ) is a set of probability distributions that represents a generalisation of the natural exponential family. exponential dispersion models play an important role in statistical theory, in particular in generalized linear models because they have a special structure which enables deductions to be made about appropriate statistical inference.


implicit regularization is essentially ubiquitous in modern machine learning approaches, including stochastic gradient descent for training deep neural networks, and ensemble methods ( such as random forests and gradient boosted trees ). in explicit regularization, independent of the problem or model, there is always a data term, that corresponds to a likelihood of the measurement and a regularization term that corresponds to a prior. by combining both using bayesian statistics, one can compute a posterior, that includes both information sources and therefore stabilizes the estimation process. by trading off both objectives, one chooses to be more addictive to the data or to enforce generalization ( to prevent overfitting ).


the manuscripts available are of variable quality, and invariably incomplete. by careful analysis of the translations and originals, hypotheses have been made about the contents of the original text ( copies of which are no longer available ). ancient texts which refer to the elements itself, and to other mathematical theories that were current at the time it was written, are also important in this process.


such procedures are often implemented in various convenience routines such as daemon ( 3 ) in unix. systems often start daemons at boot time that will respond to network requests, hardware activity, or other programs by performing some task. daemons such as cron may also perform defined tasks at scheduled times.


in natural languages, the meaning of a complex spoken sentence can be understood by decomposing it into smaller lexical segments ( roughly, the words of the language ), associating a meaning to each segment, and combining those meanings according to the grammar rules of the language. though lexical recognition is not thought to be used by infants in their first year, due to their highly limited vocabularies, it is one of the major processes involved in speech segmentation for adults. three main models of lexical recognition exist in current research : first, whole - word access, which argues that words have a whole - word representation in the lexicon ; second, decomposition, which argues that morphologically complex words are broken down into their morphemes ( roots, stems, inflections, etc. ) and then interpreted and ; third, the view that whole - word and decomposition models are both used, but that the whole - word model provides some computational advantages and is therefore dominant in lexical recognition. to give an example, in a whole - word model, the word " cats " might be stored and searched for by letter, first " c ", then " ca ", " cat ", and finally " cats ". the same word, in a decompositional model, would likely be stored under the root word " cat " and could be searched for after removing the " s " suffix.


in software engineering, continuous integration ( ci ) is the practice of merging all developers'working copies to a shared mainline several times a day. nowadays it is typically implemented in such a way that it triggers an automated build with testing. grady booch first proposed the term ci in his 1991 method, although he did not advocate integrating several times a day. extreme programming ( xp ) adopted the concept of ci and did advocate integrating more than once per day – perhaps as many as tens of times per day.


in mathematical optimization, fractional programming is a generalization of linear - fractional programming. the objective function in a fractional program is a ratio of two functions that are in general nonlinear. the ratio to be optimized often describes some kind of efficiency of a system.


in order to find and communicate with clients in proximity of a device, the protocol makes use of both the server and client modes of bluetooth le, switching between the two frequently. in server mode the device advertises its ephid to be read by clients, with clients scanning for servers. when a client and server meet, the client reads the ephid and subsequently writes its own ephid to the server. the two devices then store the encounter in their respective contact logs in addition to a coarse timestamp and signal strength. the signal strength is later used as part of the infection reporting process to estimate the distance between an infected patient and the user.


note that the polynomial is a q - analogue of the hook length formula. furthermore, let λ be a rectangular partition of size n, and let x be the set of semi - standard young tableaux of shape λ. let c = z / kz act on x via k - promotion. then ( x, c, q − κ ( λ ) s λ ( 1, q, q 2, …, q k − 1 ) ) { \ displaystyle ( x, c, q ^ { - \ kappa ( \ lambda ) } s _ { \ lambda } ( 1, q, q ^ { 2 }, \ dotsc, q ^ { k - 1 } ) ) } exhibit the cyclic sieving phenomenon.


in modern protocol design, protocols are layered to form a protocol stack. layering is a design principle that divides the protocol design task into smaller steps, each of which accomplishes a specific part, interacting with the other parts of the protocol only in a small number of well - defined ways. layering allows the parts of a protocol to be designed and tested without a combinatorial explosion of cases, keeping each design relatively simple. the communication protocols in use on the internet are designed to function in diverse and complex settings.


in mathematics, especially in the area of abstract algebra dealing with ordered structures on abelian groups, the hahn embedding theorem gives a simple description of all linearly ordered abelian groups. it is named after hans hahn.


in number theory, buchi's problem, also known as the n squares'problem, is an open problem named after the swiss mathematician julius richard buchi. it asks whether there is a positive integer m such that every sequence of m or more integer squares, whose second difference is constant and equal to 2, is necessarily a sequence of squares of the form ( x + i ) 2, i = 1, 2,..., m,... for some integer x. in 1983, douglas hensley observed that buchi's problem is equivalent to the following : does there exist a positive integer m such that, for all integers x and a, the quantity ( x + n ) 2 + a cannot be a square for more than m consecutive values of n, unless a = 0?


in practical applications, one would have several bdks on record, possibly for different customers, or to contain the scope of key compromise. when processing transactions, it is important for the receiver to know which bdk was used to initialize the originating device. to achieve this, the 80 - bit ksn is structured into three parts : as key set id, a trsm id, and the transaction counter. the algorithm specifies that the transaction counter is 21 - bits, but treats the remaining 59 bits opaquely ( the algorithm only specifies that unused bits be 0 - padded to a nibble boundary, and then'f'padded to the 80 - bit boundary ).


in the above experiment, participants were presented with a list of 100 familiar words and were asked to read them aloud while simultaneously trying to remember each one. subsequent to this, participants were asked to make a recognition decision based on the number of " yes " responses that were accompanied by some recollective experience. the results demonstrate the differing relationships between the " yes " and " no " conditions and " remember " and " know " memory performance. the outcome confirms that although familiarity and recollection may involve different processes, the remember / know exemplar does not probe them directly.


( this step is the same as in factor analysis ). estimate the discriminant function coefficients and determine the statistical significance and validity — choose the appropriate discriminant analysis method. the direct method involves estimating the discriminant function so that all the predictors are assessed simultaneously.


first, they define a set of items that are called small. let t be the total size of all small items. then, they construct a matrix a representing all configurations with sum < 2.


in mathematics, a regular matroid is a matroid that can be represented over all fields.


in studies of the networks of citations between scientific papers, derek de solla price showed in 1965 that the number of links to papers — i. e., the number of citations they receive — had a heavy - tailed distribution following a pareto distribution or power law, and thus that the citation network is scale - free. he did not however use the term " scale - free network ", which was not coined until some decades later. in a later paper in 1976, price also proposed a mechanism to explain the occurrence of power laws in citation networks, which he called " cumulative advantage " but which is today more commonly known under the name preferential attachment. recent interest in scale - free networks started in 1999 with work by albert - laszlo barabasi and reka albert at the university of notre dame who mapped the topology of a portion of the world wide web, finding that some nodes, which they called " hubs ", had many more connections than others and that the network as a whole had a power - law distribution of the number of links connecting to a node.


in the early 1980s, nlp was advertised as an important advance in psychotherapy and counseling, and attracted some interest in counseling research and clinical psychology. however, as controlled trials failed to show any benefit from nlp and its advocates made increasingly dubious claims, scientific interest in nlp faded. numerous literature reviews and meta - analyses have failed to show evidence for nlp's assumptions or effectiveness as a therapeutic method. while some nlp practitioners have argued that the lack of empirical support is due to insufficient research which tests nlp, the consensus scientific opinion is that nlp is pseudoscience and that attempts to dismiss the research findings based on these arguments " s an admission that nlp does not have an evidence base and that nlp practitioners are seeking a post - hoc credibility.


the equation a 2 = c + d 2 { \ displaystyle a ^ { 2 } = c + d ^ { 2 } } shows that | a | > √c. thus, if the nested radical is real, and if denesting is possible, then a > 0. then the solution is


in mathematics, the chevalley – shephard – todd theorem in invariant theory of finite groups states that the ring of invariants of a finite group acting on a complex vector space is a polynomial ring if and only if the group is generated by pseudoreflections. in the case of subgroups of the complex general linear group the theorem was first proved by g. c. shephard and j. a. todd ( 1954 ) who gave a case - by - case proof. claude chevalley ( 1955 ) soon afterwards gave a uniform proof. it has been extended to finite linear groups over an arbitrary field in the non - modular case by jean - pierre serre.


different kinds of kolmogorov complexity are studied : the uniform complexity, prefix complexity, monotone complexity, time - bounded kolmogorov complexity, and space - bounded kolmogorov complexity. an axiomatic approach to kolmogorov complexity based on blum axioms ( blum 1967 ) was introduced by mark burgin in the paper presented for publication by andrey kolmogorov. the axiomatic approach encompasses other approaches to kolmogorov complexity.