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


that is, the image and the codomain of the function are equal. a surjective function is a surjection. notationally : y ∈ y, x ∈ x such that y = f ( x ).


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


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


in the cbd approach, developed by ehtibar dzhafarov, janne kujala, and colleagues, ( non ) contextuality is treated as a property of any system of random variables, defined as a set r = { r q c : q ∈ q, q c, c ∈ c } { \ displaystyle { \ mathcal { r } } = \ left \ { r _ { q } ^ { c } : q \ in q, q \ prec c, c \ in c \ right \ } } in which each random variable r q c { \ displaystyle r _ { q } ^ { c } } is labeled by its content q { \ displaystyle q }, the property it measures, and its context c { \ displaystyle c }, the set of recorded circumstances under which it is recorded ( including but not limited to which other random variables it is recorded together with ) ; q c { \ displaystyle q \ prec c } stands for " q { \ displaystyle q } is measured in c { \ displaystyle c } ". the variables within a context are jointly distributed, but variables from different contexts are stochastically unrelated, defined on different sample spaces. a ( probabilistic ) coupling of the system r { \ displaystyle { \ mathcal { r } } } is defined as a system s { \ displaystyle s } in which all variables are jointly distributed and, in any context c { \ displaystyle c }, r c = { r q c : q ∈ q, q c } { \ displaystyle r ^ { c } = \ left \ { r _ { q } ^ { c } : q \ in q, q \ prec c \ right \ } } and s c = { s q c : q ∈ q, q c } { \ displaystyle s ^ { c } = \ left \ { s _ { q } ^ { c } : q \ in q, q \ prec c \ right \ } } are identically distributed. the system is considered noncontextual if it has a coupling s { \ displaystyle s } such that the probabilities pr { \ displaystyle \ pr \ left } are maximal possible for all contexts c, c ′ { \ displaystyle c, c'} and contents q { \ displaystyle q } such that q c, c ′ { \ displaystyle q \ prec c, c'}


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


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


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


in the early 19th century, carl friedrich gauss observed that non - zero integer solutions to homogeneous polynomial equations with rational coefficients exist if non - zero rational solutions exist. in the 1850s, leopold kronecker formulated the kronecker – weber theorem, introduced the theory of divisors, and made numerous other connections between number theory and algebra. he then conjectured his " liebster jugendtraum " ( " dearest dream of youth " ), a generalization that was later put forward by hilbert in a modified form as his twelfth problem, which outlines a goal to have number theory operate only with rings that are quotients of polynomial rings over the integers.


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


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


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


performing this calculation in any software that used the floating - point coprocessor, such as windows calculator, would allow users to discover whether their pentium chip was affected. the correct value of the calculation is : when converted to the hexadecimal value used by the processor, 4, 195, 835 = 0x4005fb and 3, 145, 727 = 0x2fffff. the'5'in 0x4005fb triggers the access to the'empty'array cells. as a result, the value returned by a flawed pentium processor is incorrect at or beyond four digits : which is actually the value of 4, 195, 579 / 3, 145, 727 = 4, 195, 835 - 256 / 3, 145, 727.


in mathematics, in particular in computational algebra, the berlekamp – zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after elwyn berlekamp and hans zassenhaus. as a consequence of gauss's lemma, this amounts to solving the problem also over the rationals. the algorithm starts by finding factorizations over suitable finite fields using hensel's lemma to lift the solution from modulo a prime p to a convenient power of p. after this the right factors are found as a subset of these. the worst case of this algorithm is exponential in the number of factors. van hoeij ( 2002 ) improved this algorithm by using the lll algorithm, substantially reducing the time needed to choose the right subsets of mod p factors.


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


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


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


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


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


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


in probability theory, slutsky ’ s theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables. the theorem was named after eugen slutsky. slutsky's theorem is also attributed to harald cramer.


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


in mathematics and especially game theory, the airport problem is a type of fair division problem in which it is decided how to distribute the cost of an airport runway among different players who need runways of different lengths. the problem was introduced by s. c. littlechild and g. owen in 1973. their proposed solution is : divide the cost of providing the minimum level of required facility for the smallest type of aircraft equally among the number of landings of all aircraft divide the incremental cost of providing the minimum level of required facility for the second smallest type of aircraft ( above the cost of the smallest type ) equally among the number of landings of all but the smallest type of aircraft. continue thus until finally the incremental cost of the largest type of aircraft is divided equally among the number of landings made by the largest aircraft type. the authors note that the resulting set of landing charges is the shapley value for an appropriately defined game.


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


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


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


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


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


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


the independent variables.


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


although named after joseph - louis lagrange, who published it in 1795, the method was first discovered in 1779 by edward waring. it is also an easy consequence of a formula published in 1783 by leonhard euler. uses of lagrange polynomials include the newton – cotes method of numerical integration, shamir's secret sharing scheme in cryptography, and reed – solomon error correction in coding theory. for equispaced nodes, lagrange interpolation is susceptible to runge's phenomenon of large oscillation.


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


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


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


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


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


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


in phonetics, a tilde is used as a diacritic that is placed above a letter, below it or superimposed onto the middle of it : a tilde above a letter indicates nasalization, e. g.,. a tilde superimposed onto the middle of a letter indicates velarization or pharyngealization, e. g.,. if no precomposed unicode character exists, the unicode character u + 0334 combining tilde overlay can be used to generate one. a tilde below a letter indicates laryngealisation, e. g.. if no precomposed unicode character exists, the unicode character u + 0330 combining tilde below can be used to generate one.


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


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


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


this was demonstrated more formally and in greater detail by xavier defago, et al. a fundamental result in distributed computing is that achieving consensus in asynchronous systems in which even one crash failure can occur is impossible in the most general case. this was shown in 1985 by michael j. fischer, nancy lynch, and mike paterson, and is sometimes called the flp result. since consensus and atomic broadcast are equivalent, flp applies also to atomic broadcast. the flp result does not prohibit the implementation of atomic broadcast in practice, but it does require making less stringent assumptions than flp in some respect, such as about processor and communication timings.


thus, the inventory is grouped into three categories ( a, b, and c ) in order of their estimated importance.'a'items are very important for an organization.


in the case of queries that read data from the database, the sparql language specifies four different query variations for different purposes. select query used to extract raw values from a sparql endpoint, the results are returned in a table format. construct query used to extract information from the sparql endpoint and transform the results into valid rdf.


the commodore 64 used x5c ( ascii : \ ) while the oric used x5f ( ascii : _ ). ibm's ebcdic code page 037 uses xb1 for the £ while its code page 285 uses x5b. icl's 1900 - series mainframes used a six - bit ( 64 - position character set ) encoding for characters, loosely based on bs 4730, with the £ symbol represented as octal 23 ( hex 13, dec 19 ).


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


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


in the celtic languages there is a distinction between the so - called substantive verb, used when the predicate is an adjective phrase or prepositional phrase, and the so - called copula, used when the predicate is a noun. the conjugation of the old irish and middle welsh verbs is as follows : the forms of the old irish present tense of the substantive verb, as well as welsh taw, come from the pie root * sta -. the other forms are from the roots * es - and * bhu -. welsh mae originally meant " here is " ( cf. yma'here').


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


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


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


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


in mathematical statistics, the fisher information ( sometimes simply called information ) is a way of measuring the amount of information that an observable random variable x carries about an unknown parameter θ of a distribution that models x. formally, it is the variance of the score, or the expected value of the observed information. the role of the fisher information in the asymptotic theory of maximum - likelihood estimation was emphasized by the statistician ronald fisher ( following some initial results by francis ysidro edgeworth ). the fisher information matrix is used to calculate the covariance matrices associated with maximum - likelihood estimates.


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


in terms of sieve theory the turan sieve is of combinatorial type : deriving from a rudimentary form of the inclusion – exclusion principle. the result gives an upper bound for the size of the sifted set. let a be a set of positive integers ≤ x and let p be a set of primes. for each p in p, let ap denote the set of elements of a divisible by p and extend this to let ad be the intersection of the ap for p dividing d, when d is a product of distinct primes from p. further let a1 denote a itself.


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


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


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


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


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


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


although the pigeonhole principle appears as early as 1624 in a book attributed to jean leurechon, it is commonly called dirichlet's box principle or dirichlet's drawer principle after an 1834 treatment of the principle by peter gustav lejeune dirichlet under the name schubfachprinzip ( " drawer principle " or " shelf principle " ). the principle has several generalizations and can be stated in various ways. in a more quantified version : for natural numbers k and m, if n = km + 1 objects are distributed among m sets, then the pigeonhole principle asserts that at least one of the sets will contain at least k + 1 objects. for arbitrary n and m, this generalizes to k + 1 = ( n − 1 ) / m + 1 = n / m, { \ displaystyle k + 1 = \ lfloor ( n - 1 ) / m \ rfloor + 1 = \ lceil n / m \ rceil, } where { \ displaystyle \ lfloor \ cdots \ rfloor } and { \ displaystyle \ lceil \ cdots \ rceil } denote the floor and ceiling functions, respectively.


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


in some theories of formal semantics, including david dowty's, stative verbs have a logical form that is the lambda expression λ ( x ) : { \ displaystyle \ lambda ( x ) : \ } apart from dowty, z. vendler and c. s. smith have also written influential work on aspectual classification of verbs.


in telecommunications, bit inversion means the changing of the state of a bit to the opposite state, i. e. the changing of a 0 bit to 1 or of a 1 bit to 0. it also refers to the changing of a state representing a given bit to the opposite state. source : federal standard 1037c and mil - std - 188


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


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


in order to ensure that cdss are of high quality, multiple quality assurance ( qa ) tests are performed ( table 1 ). all tests are performed following the annotation comparison step of each ccds build and are independent of individual annotation group qa tests performed prior to the annotation comparison. annotations that fail qa tests undergo a round of manual checking that may improve results or reach a decision to reject annotation matches based on qa failure.


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


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


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


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


" having arisen from the fields of knowledge representation, description logic and formal ontology, semantic web languages have a closer relationship to philosophical ontology than do conventional programming languages such as java or python. accordingly, the nature of metaclasses is informed by philosophical notions such as abstract objects, the abstract and concrete, and type - token distinction.


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


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


in mathematics, 0. 999... ( also written as 0. 9 or 0.. 9 ) denotes the repeating decimal consisting of an unending sequence of 9s after the decimal point. this repeating decimal represents the smallest number no less than every decimal number in the sequence ( 0. 9, 0. 99, 0. 999,... ) ; that is, the supremum of this sequence. this number is equal to 1. in other words, " 0. 999... " is not " almost exactly " or " very, very nearly but not quite " 1 – rather, " 0. 999... " and " 1 " represent exactly the same number.


in mathematics, property b is a certain set theoretic property. formally, given a finite set x, a collection c of subsets of x has property b if we can partition x into two disjoint subsets y and z such that every set in c meets both y and z. the property gets its name from mathematician felix bernstein, who first introduced the property in 1908. property b is equivalent to 2 - coloring the hypergraph described by the collection c. a hypergraph with property b is also called 2 - colorable. : 468 sometimes it is also called bipartite, by analogy to the bipartite graphs. property b is often studied for uniform hypergraphs ( set systems in which all subsets of the system have the same cardinality ) but it has also been considered in the non - uniform case. the problem of checking whether a collection c has property b is called the set splitting problem.


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


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


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


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


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


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


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


in the diagrams, p is used for n ’ s parent, g for the grandparent, and u will denote n ’ s uncle. the diagrams show the parent node p as the left child of its parent g even though it is possible for p to be on either side. the sample code covers both possibilities by means of the side variable dir. n is the insertion node, but as the operation proceeds also other nodes may become current ( see case i2 ).


this made it harder to interface other processors. upgrading to a more powerful processor would subtly change the timings, and timing restraints were not always tightly specified. nor were electrical parameters and physical dimensions.


in reality, initial exponential growth is often not sustained forever. after some period, it will be slowed by external or environmental factors. for example, population growth may reach an upper limit due to resource limitations. in 1845, the belgian mathematician pierre francois verhulst first proposed a mathematical model of growth like this, called the " logistic growth ".


the total time for his algorithm is o ( m log m ). for planar graphs with maximum degree δ ≥ 7, the optimal number of colors is again exactly δ. with the stronger assumption that δ ≥ 9, it is possible to find an optimal edge coloring in linear time ( cole & kowalik 2008 ). for d - regular graphs which are pseudo - random in the sense that their adjacency matrix has second largest eigenvalue ( in absolute value ) at most d1−ε, d is the optimal number of colors ( ferber & jain 2020 ).


the first rsa numbers generated, from rsa - 100 to rsa - 500, were labeled according to their number of decimal digits. later, beginning with rsa - 576, binary digits are counted instead. an exception to this is rsa - 617, which was created before the change in the numbering scheme. the numbers are listed in increasing order below.


in most cases, elm is used as a single hidden layer feedforward network ( slfn ) including but not limited to sigmoid networks, rbf networks, threshold networks, fuzzy inference networks, complex neural networks, wavelet networks, fourier transform, laplacian transform, etc. due to its different learning algorithm implementations for regression, classification, sparse coding, compression, feature learning and clustering, multi elms have been used to form multi hidden layer networks, deep learning or hierarchical networks. a hidden node in elm is a computational element, which need not be considered as classical neuron. a hidden node in elm can be classical artificial neurons, basis functions, or a subnetwork formed by some hidden nodes.


ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. godel's incompleteness theorems, published in 1931, showed that hilbert's program was unattainable for key areas of mathematics. in his first theorem, godel showed that any consistent system with a computable set of axioms which is capable of expressing arithmetic can never be complete : it is possible to construct a statement that can be shown to be true, but that cannot be derived from the formal rules of the system. in his second theorem, he showed that such a system could not prove its own consistency, so it certainly cannot be used to prove the consistency of anything stronger with certainty. this refuted hilbert's assumption that a finitistic system could be used to prove the consistency of itself, and therefore could not prove everything else.


factorization may also refer to more general decompositions of a mathematical object into the product of smaller or simpler objects. for example, every function may be factored into the composition of a surjective function with an injective function. matrices possess many kinds of matrix factorizations. for example, every matrix has a unique lup factorization as a product of a lower triangular matrix l with all diagonal entries equal to one, an upper triangular matrix u, and a permutation matrix p ; this is a matrix formulation of gaussian elimination.


in mathematics, if a { \ displaystyle a } is a subset of b, { \ displaystyle b, } then the inclusion map ( also inclusion function, insertion, or canonical injection ) is the function ι { \ displaystyle \ iota } that sends each element x { \ displaystyle x } of a { \ displaystyle a } to x, { \ displaystyle x, } treated as an element of b : { \ displaystyle b : } a " hooked arrow " ( u + 21aa rightwards arrow with hook ) is sometimes used in place of the function arrow above to denote an inclusion map ; thus : ( however, some authors use this hooked arrow for any embedding. ) this and other analogous injective functions from substructures are sometimes called natural injections. given any morphism f { \ displaystyle f } between objects x { \ displaystyle x } and y { \ displaystyle y }, if there is an inclusion map into the domain ι : a → x, { \ displaystyle \ iota : a \ to x, } then one can form the restriction f ι { \ displaystyle f \, \ iota } of f. { \ displaystyle f. } in many instances, one can also construct a canonical inclusion into the codomain r → y { \ displaystyle r \ to y } known as the range of f. { \ displaystyle f. }


in the 2005 star trek : enterprise episode " the aenar ", it was used in the aenar city.


one downside to the risc design was that the programs that run on them tend to be larger. this is because compilers must generate longer sequences of the simpler instructions to perform the same results. since these instructions must be loaded from memory anyway, the larger code offsets some of the risc design's fast memory handling.


in psycholinguistics, semantic processing is the stage of language processing that occurs after one hears a word and encodes its meaning : the mind relates the word to other words with similar meanings. once a word is perceived, it is placed in a context mentally that allows for a deeper processing. therefore, semantic processing produces memory traces that last longer than those produced by shallow processing, since shallow processing produces fragile memory traces that decay rapidly. semantic processing is the deepest level of processing and it requires the listener to think about the meaning of the cue.


2 ( 2 ). in computer science terms, programming in the large can refer to programming code that represents the high - level state transition logic of a system. this logic encodes information such as when to wait for messages, when to send messages, when to compensate for failed non - acid transactions, etc. a language that was designed to explicitly support programming in the large is bpel.


conversely, a group of participants can atomically broadcast messages by achieving consensus regarding the first message to be received, followed by achieving consensus on the next message, and so forth until all the messages have been received. thus, atomic broadcast reduces to consensus.


in the northeast caucasian languages, such as tsez, the dative also takes the functions of the lative case in marking the direction of an action. by some linguists, they are still regarded as two separate cases in those languages, although the suffixes are exactly the same for both cases. other linguists list them separately only for the purpose of separating syntactic cases from locative cases. an example with the ditransitive verb " show " ( literally : " make see " ) is given below : the dative / lative is also used to indicate possession, as in the example below, because there is no such verb as " to have ".


in the early days of computing, cpu time was expensive, and peripherals were very slow. when the computer ran a program that needed access to a peripheral, the central processing unit ( cpu ) would have to stop executing program instructions while the peripheral processed the data. this was usually very inefficient. the first computer using a multiprogramming system was the british leo iii owned by j. lyons and co.


these scores, based on a normal curve, are known as " scaled " scores. because of their grounding in this model, scaled mat scores of 500 - 600 are extremely rare, as they would be more than four standard deviations above the norm of 400.


the order of a hypergraph ( x, e ) { \ displaystyle ( x, e ) } is the number of vertices in x { \ displaystyle x }. the size of the hypergraph is the number of edges in e { \ displaystyle e }. the order of an edge e = ( d, c ) { \ displaystyle e = ( d, c ) } in a directed hypergraph is | e | = ( | d |, | c | ) { \ displaystyle | e | = ( | d |, | c | ) } : that is, the number of vertices in its tail followed by the number of vertices in its head.


the new networks have higher download speeds, with a peak speed of 10 gigabits per second ( gbit / s ) when there is only one user in the network. 5g has higher bandwidth to deliver faster speeds than 4g and can thus connect more different devices, improving the quality of internet services in crowded areas. due to the increased bandwidth, it is expected the 5g networks will increasingly be used as general internet service providers ( isps ), competing with existing isps such as cable internet, and also will make possible new applications in internet - of - things ( iot ) and machine - to - machine areas. cellphones with 4g capability alone are not able to use the 5g networks.


then, the distances between consecutive occurrences of the strings are likely to be multiples of the length of the keyword. thus finding more repeated strings narrows down the possible lengths of the keyword, since we can take the greatest common divisor of all the distances. the reason this test works is that if a repeated string occurs in the plaintext, and the distance between corresponding characters is a multiple of the keyword length, the keyword letters will line up in the same way with both occurrences of the string.


every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily a surjection. the composition of surjective functions is always surjective. any function can be decomposed into a surjection and an injection.


read before write, read after read and write before write ordering is still preserved in this model. the processor consistency model is similar to the pram consistency model with a stronger condition that defines all writes to the same memory location must be seen in the same sequential order by all other processes. processor consistency is weaker than sequential consistency but stronger than the pram consistency model.


by bezout's identity, there are r and s such that r n + s a = 1. { \ displaystyle rn + sa = 1. } multiply both sides by b : r n b + s a b = b. { \ displaystyle rnb + sab = b. } the first term on the left is divisible by n, and the second term is divisible by ab, which by hypothesis is divisible by n. therefore their sum, b, is also divisible by n.


in quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. cluster states are generated in lattices of qubits with ising type interactions. a cluster c is a connected subset of a d - dimensional lattice, and a cluster state is a pure state of the qubits located on c. they are different from other types of entangled states such as ghz states or w states in that it is more difficult to eliminate quantum entanglement ( via projective measurements ) in the case of cluster states.


concurrent schedules often induce rapid alternation between the keys. to prevent this, a " changeover delay " is commonly introduced : each schedule is inactivated for a brief period after the subject switches to it.


ng5 f5 11. g3 nh6 12. bd3 nf7 13. bxf5?


in mathematics, the n - dimensional integer lattice ( or cubic lattice ), denoted z n { \ displaystyle \ mathbb { z } ^ { n } }, is the lattice in the euclidean space r n { \ displaystyle \ mathbb { r } ^ { n } } whose lattice points are n - tuples of integers. the two - dimensional integer lattice is also called the square lattice, or grid lattice. z n { \ displaystyle \ mathbb { z } ^ { n } } is the simplest example of a root lattice. the integer lattice is an odd unimodular lattice.


stack machines can work around the memory delay by either having a deep out - of - order execution pipeline covering many instructions at once, or more likely, they can permute the stack such that they can work on other workloads while the load completes, or they can interlace the execution of different program threads, as in the unisys a9 system. today's increasingly parallel computational loads suggests, however, this might not be the disadvantage it's been made out to be in the past. stack machines can omit the operand fetching stage of a register machine. for example, in the java optimized processor ( jop ) microprocessor the top 2 operands of stack directly enter a data forwarding circuit that is faster than the register file.


in order to build the classification models, the samples belonging to each class need to be analysed using principal component analysis ( pca ) ; only the significant components are retained. for a given class, the resulting model then describes either a line ( for one principal component or pc ), plane ( for two pcs ) or hyper - plane ( for more than two pcs ). for each modelled class, the mean orthogonal distance of training data samples from the line, plane, or hyper - plane ( calculated as the residual standard deviation ) is used to determine a critical distance for classification. this critical distance is based on the f - distribution and is usually calculated using 95 % or 99 % confidence intervals.


the contraction generated by the cooling supposedly produced the high pressure required to transform graphite into diamond. moissan published his work in a series of articles in the 1890s. many other scientists tried to replicate his experiments. sir william crookes claimed success in 1909.


in attributive sentences ( see below ), as well as agreement in person and number between the subject and the verb, there is also agreement of gender and number between the subject and the head of the attribute when it is a noun or an adjective. in catalan there are four main types of sentence : predicative sentences, consisting of a subject, a verb and some complements. en jordi va collir tres roses per a la nuria ( jordi picked three roses for nuria ).


it is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. in other words, the center of mass is the particle equivalent of a given object for application of newton's laws of motion. in the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid.


a variant of this problem gives the total number of travelers available, and asks for the maximum distance that can be reached. in the cars across the desert problem, the starting base has unlimited units of fuel. each car can carry at most 1 unit of supplies at any time, and can travel 1 unit of distance on 1 unit of fuel.


sometimes schools do half - day in - service days in which students are dismissed early, rather than full - day holidays. unplanned interruptions in schooling ( such as weather events like heavy snow ) can extend the school year on occasion. such calendar extensions, as well as the initial cancellations, are decided by each local administration and announced to the parents in as timely manner as possible.


to show that a system s is required to prove a theorem t, two proofs are required. the first proof shows t is provable from s ; this is an ordinary mathematical proof along with a justification that it can be carried out in the system s. the second proof, known as a reversal, shows that t itself implies s ; this proof is carried out in the base system. the reversal establishes that no axiom system s ′ that extends the base system can be weaker than s while still proving t.


in order to say something about the security properties of the above explained xtr encryption scheme, first it is important to check the security of the xtr group, which means how hard it is to solve the discrete logarithm problem there. the next part will then state the equivalency between the discrete logarithm problem in the xtr group and the xtr version of the discrete logarithm problem, using only the traces of elements.


in mathematics, an integer sequence is a sequence ( i. e., an ordered list ) of integers. an integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms. for example, the sequence 0, 1, 1, 2, 3, 5, 8, 13,... ( the fibonacci sequence ) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one : an implicit description.


in practice this becomes computationally onerous as k { \ displaystyle ~ k ~ } and n { \ displaystyle ~ n ~ } increase so it is probably only worth using exact tests for small samples. for larger samples, asymptotic approximations are accurate enough and easier to calculate. one of these approximations is the likelihood ratio.


in the case of server consolidation, many small physical servers can be replaced by one larger physical server to decrease the need for more ( costly ) hardware resources such as cpus, and hard drives. although hardware is consolidated in virtual environments, typically oss are not. instead, each os running on a physical server is converted to a distinct os running inside a virtual machine.


in mathematics, the thue – morse sequence or prouhet – thue – morse sequence or parity sequence is the binary sequence ( an infinite sequence of 0s and 1s ) obtained by starting with 0 and successively appending the boolean complement of the sequence obtained thus far. the first few steps of this procedure yield the strings 0 then 01, 0110, 01101001, 0110100110010110, and so on, which are prefixes of the thue – morse sequence. the full sequence begins : 01101001100101101001011001101001.... the sequence is named after axel thue and marston morse.


in statistics, qualitative comparative analysis ( qca ) is a data analysis based on set theory to examine the relationship of conditions to outcome. qca describes the relationship in terms of necessary conditions and sufficient conditions. the technique was originally developed by charles ragin in 1987 to study data sets that are too small for linear regression analysis but large for cross - case analysis.


below is the example that compares sparql and sql queries for medications that treats " tb of vertebra ". select? medication where {? diagnosis a example : diagnosis.? diagnosis example : name “ tb of vertebra ”.? medication example : cantreat? diagnosis. } select drug. medid from diagnosis, drug, drug _ diagnosis where diagnosis. diagnosisid = drug _ diagnosis. diagnosisid and drug. medid = drug _ diagnosis. medid and diagnosis. name = ” tb of vertebra ”


the reason is that if v { \ displaystyle v } is an f { \ displaystyle f } - vector space and q : v → f { \ displaystyle q : v \ to f } is a quadratic form and v { \ displaystyle v } is an element of v { \ displaystyle v } such that q ( v ) = a ∈ f × { \ displaystyle q ( v ) = a \ in f ^ { \ times } }, then for all u ∈ f × { \ displaystyle u \ in f ^ { \ times } }, q ( u v ) = a u 2 { \ displaystyle q ( uv ) = au ^ { 2 } } and thus it is sometimes more convenient to talk about the square classes which the quadratic form represents. every element of the square class group is an involution. it follows that, if the number of square classes of a field is finite, it must be a power of two. = = references = =


in greek, for example, the imperfective sometimes adds the notion of " try to do something " ( the so - called conative imperfect ) ; hence, the same verb, in the imperfective ( present or imperfect ) and aorist, respectively, is used to convey look and see, search and find, listen and hear. ( for example, ηκουομεν ( ekouomen, " we listened " ) vs. ηκουσαμεν ( ekousamen, " we heard " ). ) spanish has similar pairs for certain verbs, such as ( imperfect and preterite, respectively ) sabia ( " i knew " ) vs. supe ( " i found out " ), podia ( " i was able to " ) vs. pude ( " i succeeded ( in doing something ) " ), queria ( " i wanted to " ) vs. quise ( " i tried to " ), and no queria ( " i did not want to " ) vs. no quise ( " i refused ( to do something ) " ). such differences are often highly language - specific.


in some communication systems, a receiver can achieve character synchronization from an undifferentiated bit stream, or start - of - header synchronization from a byte stream, without the overhead of an explicit syncword. for example, the fsk441 protocol achieves character synchronization by synchronizing on any " space " characters in the message — in effect, every " space " character in the message does double duty as a syncword. for example, crc - based framing achieves character and start - of - header synchronization. in a self - synchronizing code, every character is, in effect, a syncword, and can be used to achieve character synchronization in an undifferentiated bit stream.


in the age of advanced mobile devices, there is some disadvantage in using phonewords. devices with physical keyboards such as blackberry and some other smartphones do not have the apportioned letters on the keys used for dialing, so one is unable to do alphabetic dialing without some other cross - reference to the actual phone number. this can be overcome by phonewords also being accompanied by the actual numeric phone number, allowing users of such smartphones to dial using the numeric phone number. however, devices which have virtual keyboards, including ios and android devices, will translate phoneword phone numbers in webpages and sms messages to their proper digits within a hyperlink leading to that device's phone app, and their keypads show the appropriate local mapping of letters within their virtual dialpad.


in probability theory and statistics, the chi distribution is a continuous probability distribution over the non - negative real line. it is the distribution of the positive square root of a sum of squared independent gaussian random variables. equivalently, it is the distribution of the euclidean distance between a multivariate gaussian random variable and the origin. it is thus related to the chi - squared distribution by describing the distribution of the positive square roots of a variable obeying a chi - squared distribution.


in queueing theory, a discipline within the mathematical theory of probability, a fluid limit, fluid approximation or fluid analysis of a stochastic model is a deterministic real - valued process which approximates the evolution of a given stochastic process, usually subject to some scaling or limiting criteria. fluid limits were first introduced by thomas g. kurtz publishing a law of large numbers and central limit theorem for markov chains. it is known that a queueing network can be stable, but have an unstable fluid limit. = = references = =


in the context of machine learning, the exploration - exploitation tradeoff is often encountered in reinforcement learning, a type of machine learning that involves training agents to make decisions based on feedback from the environment. the agent must decide whether to exploit the current best - known policy or explore new policies to improve its performance. various algorithms have been developed to address this challenge, such as epsilon - greedy, thompson sampling, and the upper confidence bound. = = references = =


in practice, the main application of the peano kernel theorem is to bound the error of an approximation that is exact for all f ∈ p ν { \ displaystyle f \ in \ mathbb { p } _ { \ nu } }. the theorem above follows from the taylor polynomial for f { \ displaystyle f } with integral remainder : f ( x ) = f ( a ) + ( x − a ) f ′ ( a ) + ( x − a ) 2 2 f ″ ( a ) + + ( x − a ) ν ν! f ( ν ) ( a ) + 1 ν! a x ( x − θ ) ν f ( ν + 1 ) ( θ ) d θ, { \ displaystyle { \ begin { aligned } f ( x ) = f ( a ) + { } & ( x - a ) f'( a ) + { \ frac { ( x - a ) ^ { 2 } } { 2 } } f'' ( a ) + \ cdots \ \ & \ cdots + { \ frac { ( x - a ) ^ { \ nu } } { \ nu! } } f ^ { ( \ nu ) } ( a ) + { \ frac { 1 } { \ nu! } } \ int _ { a } ^ { x } ( x - \ theta ) ^ { \ nu } f ^ { ( \ nu + 1 ) } ( \ theta ) \, d \ theta, \ end { aligned } } } defining l ( f ) { \ displaystyle l ( f ) } as the error of the approximation, using the linearity of l { \ displaystyle l } together with exactness for f ∈ p ν { \ displaystyle f \ in \ mathbb { p } _ { \ nu } } to annihilate all but the final term on the right - hand side, and using the ( ⋅ ) + { \ displaystyle ( \ cdot ) _ { + } } notation to remove the x { \ displaystyle x } - dependence from the integral limits.


in the context of group theory, a sequence g 0 → f 1 g 1 → f 2 g 2 → f 3 → f n g n { \ displaystyle g _ { 0 } \ ; { \ xrightarrow { f _ { 1 } } } \ ; g _ { 1 } \ ; { \ xrightarrow { f _ { 2 } } } \ ; g _ { 2 } \ ; { \ xrightarrow { f _ { 3 } } } \ ; \ cdots \ ; { \ xrightarrow { f _ { n } } } \ ; g _ { n } } of groups and group homomorphisms is called exact if the image of each homomorphism is equal to the kernel of the next : i m ( f k ) = k e r ( f k + 1 ). { \ displaystyle \ mathrm { im } ( f _ { k } ) = \ mathrm { ker } ( f _ { k + 1 } ). \! } note that the sequence of groups and homomorphisms may be either finite or infinite.


in the field of topology, a circle is not limited to the geometric concept, but to all of its homeomorphisms. two topological circles are equivalent if one can be transformed into the other via a deformation of r3 upon itself ( known as an ambient isotopy ).


in several fields, especially computing, deprecation is the discouragement of use of some terminology, feature, design, or practice, typically because it has been superseded or is no longer considered efficient or safe, without completely removing it or prohibiting its use. typically, deprecated materials are not completely removed to ensure legacy compatibility or back up practice in case new methods are not functional in an odd scenario. it can also imply that a feature, design, or practice will be removed or discontinued entirely in the future.


the most computationally expensive component of the best predictor formula is inverting the covariance matrix σ { \ displaystyle \ mathbf { \ sigma } }, which has cubic complexity o ( n 3 ) { \ displaystyle { \ mathcal { o } } ( n ^ { 3 } ) }. similarly, evaluating likelihood involves both calculating σ − 1 { \ displaystyle \ mathbf { \ sigma } ^ { - 1 } } and the determinant det ( σ ) { \ displaystyle \ det ( \ mathbf { \ sigma } ) } which has the same cubic complexity. gaussian process approximations can often be expressed in terms of assumptions on y { \ displaystyle y } under which log ℓ ( y ) { \ displaystyle \ log \ ell ( \ mathbf { y } ) } and μ y ∗ { \ displaystyle \ mathbf { \ mu } _ { \ mathbf { y } } ^ { * } } can be calculated with much lower complexity. since these assumptions are generally not believed to reflect reality, the likelihood and the best predictor obtained in this way are not exact, but they are meant to be close to their original values.


in non - smooth method, unilateral interactions between bodies are fundamentally modelled by the signorini condition for non - penetration, and impact laws are used to define the impact process. the signorini condition can be expressed as the complementarity problem : g ≥ 0, λ ≥ 0, λ g { \ displaystyle g \ geq 0, \ quad \ lambda \ geq 0, \ quad \ lambda \ perp g }, where g { \ displaystyle g } denotes the distance between two bodies and λ { \ displaystyle \ lambda } denotes the contact force generated by the unilateral constraints, as shown in the figure below. moreover, in terms of the concept of proximal point of convex theory, the signorini condition can be equivalently expressed as : λ = p r o j r + ( λ − ρ g ) { \ displaystyle \ lambda = { \ rm { proj } } _ { \ mathbb { r } ^ { + } } ( \ lambda - \ rho g ) }, where ρ > 0 { \ displaystyle \ rho > 0 } denotes an auxiliary parameter, and p r o j c ( x ) { \ displaystyle { \ rm { proj } } _ { \ bf { c } } ( x ) } represents the proximal point in the set c { \ displaystyle c } to the variable x { \ displaystyle x }, defined as : p r o j c ( x ) = a r g m i n y ∈ c ‖ y − x ‖ { \ displaystyle { \ rm { proj } } _ { \ bf { c } } ( x ) = { \ rm { argmin } } _ { y \ in c } \ | y - x \ | }. both the expressions above represent the dynamic behaviour of unilateral constraints : on the one hand, when the normal distance g n { \ displaystyle g _ { \ rm { n } } } is above zero, the contact is open, which means that there is no contact force between bodies, λ = 0 { \ displaystyle \ lambda = 0 } ; on the other hand, when the normal distance g n { \ displaystyle g _ { \ rm { n } } } is equal to zero, the contact is closed, resulting in λ ≥ 0 { \ displaystyle \ lambda \ geq 0 }.


if the participant makes a mistake, the experimenter prompts them to start again. the threat of negative evaluation is the social stressor.


the choice of loss function here gives rise to several well - known learning algorithms such as regularized least squares and support vector machines. a purely online model in this category would learn based on just the new input ( x t + 1, y t + 1 ) { \ displaystyle ( x _ { t + 1 }, y _ { t + 1 } ) }, the current best predictor f t { \ displaystyle f _ { t } } and some extra stored information ( which is usually expected to have storage requirements independent of training data size ). for many formulations, for example nonlinear kernel methods, true online learning is not possible, though a form of hybrid online learning with recursive algorithms can be used where f t + 1 { \ displaystyle f _ { t + 1 } } is permitted to depend on f t { \ displaystyle f _ { t } } and all previous data points ( x 1, y 1 ), …, ( x t, y t ) { \ displaystyle ( x _ { 1 }, y _ { 1 } ), \ ldots, ( x _ { t }, y _ { t } ) }.


designed by plp architecture, the development has 546 rooms with most units grouped into " twodios " – two en - suite bedrooms that share a small kitchenette. there are also some private suites. the units sizes range from 9. 2 square metres ( 99 sq ft ) for an ensuite rooms with a 5. 8 square metres ( 62 sq ft ) shared kitchenette, to 12 square metres ( 130 sq ft ) for a shared ensuite and 16. 5 square metres ( 178 sq ft ) shared ensuite with kitchenette. each floor features one larger kitchen with a dining table, which is shared between 30 and 70 residents, and themed communal living spaces such as a games room, a cinema, a'disco - launderette ', a hidden garden and a spa. a restaurant, gym and co - working spaces are located in the lower floors of the building.


in mathematics, the generalized taxicab number taxicab ( k, j, n ) is the smallest number — if it exists — that can be expressed as the sum of j kth positive powers in n different ways. for k = 3 and j = 2, they coincide with taxicab number. t a x i c a b ( 1, 2, 2 ) = 4 = 1 + 3 = 2 + 2. { \ displaystyle \ mathrm { taxicab } ( 1, 2, 2 ) = 4 = 1 + 3 = 2 + 2. }


the univac 1232 was a military version of the 490. the univac 492 is similar to the univac 490, but with extended memory to 64k 30 - bit words. the univac 494 was a 30 - bit word machine and successor to the univac 490 / 492 with faster cpu and 131k ( later 262k ) core memory.


in support vector machines ( svms ), the formulating the primal problem of svms as the dual problem can be used to implement kernel trick, but the latter has higher time complexity in the historical cases.


in mathematics, specifically additive number theory, romanov's theorem is a mathematical theorem proved by nikolai pavlovich romanov. it states that given a fixed base b, the set of numbers that are the sum of a prime and a positive integer power of b has a positive lower asymptotic density.


in remote sensing, " ground truth " refers to information collected at the imaged location. ground truth allows image data to be related to real features and materials on the ground. the collection of ground truth data enables calibration of remote - sensing data, and aids in the interpretation and analysis of what is being sensed. examples include cartography, meteorology, analysis of aerial photographs, satellite imagery and other techniques in which data are gathered at a distance.


in mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. that is, the group operation is commutative. with addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. abelian groups are named after early 19th century mathematician niels henrik abel. the concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. the theory of abelian groups is generally simpler than that of their non - abelian counterparts, and finite abelian groups are very well understood and fully classified.


in the context of business process integration ( see figure ), data modeling complements business process modeling, and ultimately results in database generation. the process of designing a database involves producing the previously described three types of schemas - conceptual, logical, and physical. the database design documented in these schemas are converted through a data definition language, which can then be used to generate a database. a fully attributed data model contains detailed attributes ( descriptions ) for every entity within it. the term " database design " can describe many different parts of the design of an overall database system.


simon tatham's contribution, based on duff's device, is a notable example of the genre, and is the basis for protothreads and similar implementations. in addition to duff's objections, tatham's own comments provide a frank evaluation of the limitations of this approach : " as far as i know, this is the worst piece of c hackery ever seen in serious production code. " the main shortcomings of this approximation are that, in not maintaining a separate stack frame for each coroutine, local variables are not preserved across yields from the function, it is not possible to have multiple entries to the function, and control can only be yielded from the top - level routine.


in mathematics, one can define a product of group subsets in a natural way. if s and t are subsets of a group g, then their product is the subset of g defined by s t = { s t : s ∈ s and t ∈ t }. { \ displaystyle st = \ { st : s \ in s { \ text { and } } t \ in t \ }. } the subsets s and t need not be subgroups for this product to be well defined.


in optimization, a self - concordant function is a function f : r → r { \ displaystyle f : \ mathbb { r } \ rightarrow \ mathbb { r } } for which | f ( x ) | ≤ 2 f ″ ( x ) 3 / 2 { \ displaystyle | f'''( x ) | \ leq 2f'' ( x ) ^ { 3 / 2 } } or, equivalently, a function f : r → r { \ displaystyle f : \ mathbb { r } \ rightarrow \ mathbb { r } } that, wherever f ″ ( x ) > 0 { \ displaystyle f'' ( x ) > 0 }, satisfies | d d x 1 f ″ ( x ) | ≤ 1 { \ displaystyle \ left | { \ frac { d } { dx } } { \ frac { 1 } { \ sqrt { f'' ( x ) } } } \ right | \ leq 1 } and which satisfies f ( x ) = 0 { \ displaystyle f'''( x ) = 0 } elsewhere. more generally, a multivariate function f ( x ) : r n → r { \ displaystyle f ( x ) : \ mathbb { r } ^ { n } \ rightarrow \ mathbb { r } } is self - concordant if d d α ∇ 2 f ( x + α y ) | α = 0 2 y t ∇ 2 f ( x ) y ∇ 2 f ( x ) { \ displaystyle \ left. { \ frac { d } { d \ alpha } } \ nabla ^ { 2 } f ( x + \ alpha y ) \ right | _ { \ alpha = 0 } \ preceq 2 { \ sqrt { y ^ { t } \ nabla ^ { 2 } f ( x ) \, y } } \, \ nabla ^ { 2 } f ( x ) } or, equivalently, if its restriction to any arbitrary line is self - concordant.


in statistics, multiple correspondence analysis ( mca ) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. it does this by representing data as points in a low - dimensional euclidean space. the procedure thus appears to be the counterpart of principal component analysis for categorical data. mca can be viewed as an extension of simple correspondence analysis ( ca ) in that it is applicable to a large set of categorical variables.


while we cannot do this by simply rearranging the quantifiers, we show that it is yet enough to prove the theorem for sentences of that form. finally we prove the theorem for sentences of that form. this is done by first noting that a sentence such as b =...... φ ( x1... xk, y1... ym ) is either refutable ( its negation is always true ) or satisfiable, i. e. there is some model in which it holds ( it might even be always true, i. e. a tautology ) ; this model is simply assigning truth values to the subpropositions from which b is built.


in the ibm system / 370 models with virtual storage ( dat ) and 24 - bit addresses, control register 0 specifies a segment size of either 64 kib or 1 mib and a page size of either 2 kib or 4 kib ; control register 1 contains a segment table designator ( std ), which specifies the length and real address of the segment table. each segment table entry contains a page table location, a page table length and an invalid bit. ibm later expanded the address size to 31 bits and added two bits to the segment table entries : segment - protection bit segment is read - only common - segment bit the segment is shared between address spaces ; this bit is set to optimize tlb useeach of ibm's dat implementations includes a translation cache, which ibm called a translation lookaside buffer ( tlb ).


in the 19th century new developments such as the discovery of photography, rowland's invention of the concave diffraction grating, and schumann's works on discovery of vacuum ultraviolet ( fluorite for prisms and lenses, low - gelatin photographic plates and absorption of uv in air below 185 nm ) made advance to shorter wavelengths very fast. at the same time dewar observed series in alkali spectra, hartley found constant wave - number differences, balmer discovered a relation connecting wavelengths in the visible hydrogen spectrum, and finally rydberg derived a formula for wave - numbers of spectral series. meanwhile, the substantial summary of past experiments performed by maxwell ( 1873 ), resulted in his equations of electromagnetic waves.


one says also a is prime to b or a is coprime with b. the numbers 8 and 9 are coprime, despite the fact that neither considered individually is a prime number, since 1 is their only common divisor. on the other hand, 6 and 9 are not coprime, because they are both divisible by 3. the numerator and denominator of a reduced fraction are coprime, by definition.


in the early 1970s, diffie worked with martin hellman to develop the fundamental ideas of dual - key, or public key, cryptography. they published their results in 1976 — solving one of the fundamental problems of cryptography, key distribution — and essentially broke the monopoly that had previously existed where government entities controlled cryptographic technology and the terms on which other individuals could have access to it. " from the moment diffie and hellman published their findings..., the national security agency's crypto monopoly was effectively terminated.... every company, every citizen now had routine access to the sorts of cryptographic technology that not many years ago ranked alongside the atom bomb as a source of power. " the solution has become known as diffie – hellman key exchange.


this bias is especially prevalent in group settings where one thinks the collective opinion of their own group matches that of the larger population. since the members of a group reach a consensus and rarely encounter those who dispute it, they tend to believe that everybody thinks the same way. the false - consensus effect is not restricted to cases where people believe that their values are shared by the majority, but it still manifests as an overestimate of the extent of their belief. additionally, when confronted with evidence that a consensus does not exist, people often assume that those who do not agree with them are defective in some way.


for example, following a known software design structure, such as client and broker, can help in designing a well - built structure with a solid foundation. furthermore, if the software is to be modified in the future, it is even more important that it follows a logical foundation of separation between the client and server. this is because if a programmer comes in and cannot clearly understand the dynamics of the program, they may end up adding or changing something that can add a security flaw. even with the best design, this is always a possibility, but the better the standardization of the design, the less chance there is of this occurring.


thus, print carries the individuating power of the phonetic alphabet much further than manuscript culture could ever do. print is the technology of individualism.


if the affected program is running with special privileges, or accepts data from untrusted network hosts ( e. g. a webserver ) then the bug is a potential security vulnerability. if the stack buffer is filled with data supplied from an untrusted user then that user can corrupt the stack in such a way as to inject executable code into the running program and take control of the process. this is one of the oldest and more reliable methods for attackers to gain unauthorized access to a computer.


in mathematics, rational reconstruction is a method that allows one to recover a rational number from its value modulo a sufficiently large integer.


a continuum of complex morphology of language may be adopted. the three models of morphology stem from attempts to analyze languages that more or less match different categories in this typology. the item - and - arrangement approach fits very naturally with agglutinative languages.


in mathematics, a free boolean algebra is a boolean algebra with a distinguished set of elements, called generators, such that : each element of the boolean algebra can be expressed as a finite combination of generators, using the boolean operations, and the generators are as independent as possible, in the sense that there are no relationships among them ( again in terms of finite expressions using the boolean operations ) that do not hold in every boolean algebra no matter which elements are chosen.


for the bluetooth low energy stack, according to bluetooth 4. 0 a special set of profiles applies. a host operating system can expose a basic set of profiles ( namely obex, hid and audio sink ) and manufacturers can add additional profiles to its driver and stack to enhance what their bluetooth device can do. devices such as mobile phones can expose additional profiles by installing appropriate apps.


in the japanese kantenji braille, the standard 8 - dot braille patterns 57, 157, 457, and 1457 are the patterns related to braille pattern dots - 34, since the two additional dots of kantenji patterns 034, 347, and 0347 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in software development and product management, a user story is an informal, natural language description of features of a software system. they are written from the perspective of an end user or user of a system, and may be recorded on index cards, post - it notes, or digitally in project management software. depending on the project, user stories may be written by different stakeholders like client, user, manager, or development team. user stories are a type of boundary object. they facilitate sensemaking and communication ; and may help software teams document their understanding of the system and its context.


in signal processing, the above definition is often used without the normalization, that is, without subtracting the mean and dividing by the variance. when the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the autocorrelation coefficient or autocovariance function.


in mathematics, the greedy algorithm for egyptian fractions is a greedy algorithm, first described by fibonacci, for transforming rational numbers into egyptian fractions. an egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as 5 / 6 = 1 / 2 + 1 / 3. as the name indicates, these representations have been used as long ago as ancient egypt, but the first published systematic method for constructing such expansions was described in 1202 in the liber abaci of leonardo of pisa ( fibonacci ). it is called a greedy algorithm because at each step the algorithm chooses greedily the largest possible unit fraction that can be used in any representation of the remaining fraction.


in these scenarios, modularity is an abstraction of the 2nd isomorphism theorem. for example, the subspaces of a vector space ( and more generally the submodules of a module over a ring ) form a modular lattice. in a not necessarily modular lattice, there may still be elements b for which the modular law holds in connection with arbitrary elements x and a ( for a ≤ b ).


{ \ displaystyle \ operatorname { disc } ( { \ mathcal { h } } ) : = \ min _ { \ chi : v \ rightarrow \ { - 1, + 1 \ } } \ operatorname { disc } ( { \ mathcal { h } }, \ chi ). } these notions as well as the term'discrepancy'seem to have appeared for the first time in a paper of beck.


in the counter - electronic codebook mode, the cascaded cipher uses full strength aes - 128 in counter mode to generate a secure key stream and supplies this key - stream to a reduced round serpent in electronic codebook mode to encrypt each plaintext block. to increase performance, each inner key stream block is reused several times to encrypt multiple blocks.


and here, kant says, we are liable to error in two ways. the first type of error consists in trying to attract students into being moral by providing them examples in which morality and self - love coincide. the second type of error consists in trying to emotionally arouse the students about morality by providing examples of extraordinary moral heroism, above what morality normally requires.


in probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.


in mathematics, the babenko – beckner inequality ( after k. ivan babenko and william e. beckner ) is a sharpened form of the hausdorff – young inequality having applications to uncertainty principles in the fourier analysis of lp spaces. the ( q, p ) - norm of the n - dimensional fourier transform is defined to be ‖ f ‖ q, p = sup f ∈ l p ( r n ) ‖ f f ‖ q ‖ f ‖ p, where 1 < p ≤ 2, and 1 p + 1 q = 1. { \ displaystyle \ | { \ mathcal { f } } \ | _ { q, p } = \ sup _ { f \ in l ^ { p } ( \ mathbb { r } ^ { n } ) } { \ frac { \ | { \ mathcal { f } } f \ | _ { q } } { \ | f \ | _ { p } } }, { \ text { where } } 1


in stage two, testers will recruit test subjects across a broad spectrum of abilities. for example, in one study, experienced users showed no problem using any design, from the first to the last, while naive users and self - identified power users both failed repeatedly. later on, as the design smooths out, users should be recruited from the target population.


petersburg paradox. in microbiology, the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth. during this bacterial growth phase, the number of new cells appearing is proportional to the population. this terminological confusion between logarithmic growth and exponential growth may be explained by the fact that exponential growth curves may be straightened by plotting them using a logarithmic scale for the growth axis.


the command will be applied to all unit codes sent. it is also possible to send a message with no unit codes, just a house code and a command code. this will apply to the command to the last group of units codes previously sent.


in the category of graphs, the product is the tensor product of graphs. in the category of relations, the product is given by the disjoint union. ( this may come as a bit of a surprise given that the category of sets is a subcategory of the category of relations. )


in probability theory and statistics, the conway – maxwell – poisson ( cmp or com – poisson ) distribution is a discrete probability distribution named after richard w. conway, william l. maxwell, and simeon denis poisson that generalizes the poisson distribution by adding a parameter to model overdispersion and underdispersion. it is a member of the exponential family, has the poisson distribution and geometric distribution as special cases and the bernoulli distribution as a limiting case.


this raises the question of how to implement this randomized allocation in practice? one cannot just randomize for each object separately, since this may result in allocations in which some people get many objects while other people get no objects.