string metrics and edit distances. there are many ways of measuring distances between strings of characters, which may represent sentences in computational linguistics or code words in coding theory. edit distances attempt to measure the number of changes necessary to get from one string to another.


this little program prints three “ 1 ” s to the right, reverses direction and moves left printing 0 ’ s until it hits a blank. we will print all the symbols that our machine uses : here at the end we find that a blank on the left has “ come into play ” so we leave it as part of the total configuration. given that we have done our job correctly, we add the starting conditions and see “ where the theorem goes ”.


in naive set theory, a set is described as a well - defined collection of objects. these objects are called the elements or members of the set. objects can be anything : numbers, people, other sets, etc. for instance, 4 is a member of the set of all even integers. clearly, the set of even numbers is infinitely large ; there is no requirement that a set be finite. the definition of sets goes back to georg cantor. he wrote in his 1915 article beitrage zur begrundung der transfiniten mengenlehre : “ unter einer'menge'verstehen wir jede zusammenfassung m von bestimmten wohlunterschiedenen objekten unserer anschauung oder unseres denkens ( welche die'elemente'von m genannt werden ) zu einem ganzen. ” – georg cantor “ a set is a gathering together into a whole of definite, distinct objects of our perception or of our thought — which are called elements of the set. ” – georg cantor


in mathematics, counterexamples are often used to prove the boundaries of possible theorems. by using counterexamples to show that certain conjectures are false, mathematical researchers can then avoid going down blind alleys and learn to modify conjectures to produce provable theorems. it is sometimes said that mathematical development consists primarily in finding ( and proving ) theorems and counterexamples.


in recent years many other matrix factorization models have been developed to exploit the ever increasing amount and variety of available interaction data and use cases. hybrid matrix factorization algorithms are capable of merging explicit and implicit interactions or both content and collaborative data


excessive use of whitespace, especially trailing whitespace at the end of lines, is considered a nuisance. however correct use of whitespace can make the code easier to read and help group related logic. most languages only recognize ascii characters as whitespace, or in some cases unicode newlines as well, but not most of the characters listed above. the c language defines whitespace characters to be " space, horizontal tab, new - line, vertical tab, and form - feed ". the http network protocol requires different types of whitespace to be used in different parts of the protocol, such as : only the space character in the status line, crlf at the end of a line, and " linear whitespace " in header values.


0 & 0 & 1 & 0 & 0 \ \ 0 & 0 & 0 & 0 & 1 \ \ 0 & 0 & 0 & 1 & 0 \ end { pmatrix } }. }


ranap handles signaling for the iu - ps - rnc and 3g sgsn and iu - cs - rnc and 3g msc. it also provides the signaling channel to transparently pass messages between the user equipment ( ue ) and the cn. in lte, ranap has been replaced by s1ap. in sa ( standalone ) installations of 5g, s1ap will be replaced by ngap.


therefore, a single recursive call locates the desired element in the correct partition, and we build upon this for quickselect : / / returns the k - th smallest element of list within left.. right inclusive / / ( i. e. left < = k < = right ). function select ( list, left, right, k ) is if left = right then / / if the list contains only one element, return list / / return that element pivotindex : =... / / select a pivotindex between left and right, / / e. g., left + floor ( rand ( ) % ( right − left + 1 ) ) pivotindex : = partition ( list, left, right, pivotindex ) / / the pivot is in its final sorted position if k = pivotindex then return list else if k < pivotindex then return select ( list, left, pivotindex − 1, k ) else return select ( list, pivotindex + 1, right, k ) note the resemblance to quicksort : just as the minimum - based selection algorithm is a partial selection sort, this is a partial quicksort, generating and partitioning only o ( log n ) { \ displaystyle o ( \ log n ) } of its o ( n ) { \ displaystyle o ( n ) } partitions. this simple procedure has expected linear performance, and, like quicksort, has quite good performance in practice. it is also an in - place algorithm, requiring only constant memory overhead if tail call optimization is available, or if eliminating the tail recursion with a loop : function select ( list, left, right, k ) is loop if left = right then return list pivotindex : =... / / select pivotindex between left and right pivotindex : = partition ( list, left, right, pivotindex ) if k = pivotindex then return list else if k < pivotindex then right : = pivotindex − 1 else left : = pivotindex + 1


, an ) with a0 = 0. then the largest stopping time to exercise the american option in an optimal way is τ max : = { n if a n = 0, min { n ∈ { 0, …, n − 1 } a n + 1 < 0 } if a n < 0. { \ displaystyle \ tau _ { \ text { max } } : = { \ begin { cases } n & { \ text { if } } a _ { n } = 0, \ \ \ min \ { n \ in \ { 0, \ dots, n - 1 \ } \ mid a _ { n + 1 } < 0 \ } & { \ text { if } } a _ { n } < 0. \ end { cases } } } since a is predictable, the event { τmax = n } = { an = 0, an + 1 < 0 } is in fn for every n ∈ { 0, 1,.


in terms of the number of comparisons, the performance of binary search can be analyzed by viewing the run of the procedure on a binary tree. the root node of the tree is the middle element of the array. the middle element of the lower half is the left child node of the root, and the middle element of the upper half is the right child node of the root. the rest of the tree is built in a similar fashion.


{ \ displaystyle \ mathbb { n }. } n { \ displaystyle \ mathbb { n } } is the intersection of all sets satisfying ( 1 ) and ( 2 ). there are many sets that satisfy ( 1 ) and ( 2 ) – for example, the set { 1, 1. 649, 2, 2. 649, 3, 3. 649, … } satisfies the definition. however, condition ( 3 ) specifies the set of natural numbers by removing the sets with extraneous members.


in the early 2000s, some web developers began to question why web authors ever made the leap into authoring in xhtml. others countered that the problems ascribed to the use of xhtml could mostly be attributed to two main sources : the production of invalid xhtml documents by some web authors and the lack of support for xhtml built into internet explorer 6. they went on to describe the benefits of xml - based web documents ( i. e. xhtml ) regarding searching, indexing, and parsing as well as future - proofing the web itself.


it is basically testing how well a system recovers from crashes, hardware failures, or other catastrophic problems examples of recovery testing : while an application is running, suddenly restart the computer, and afterwards check the validness of the application's data integrity. while an application is receiving data from a network, unplug the connecting cable. after some time, plug the cable back in and analyze the application's ability to continue receiving data from the point at which the network connection disappeared.


it is the part of the observed score that would recur across different measurement occasions in the absence of error. errors of measurement are composed of both random error and systematic error. it represents the discrepancies between scores obtained on tests and the corresponding true scores. this conceptual breakdown is typically represented by the simple equation : observed test score = true score + errors of measurement


in probability theory, a stochastic process is said to have stationary increments if its change only depends on the time span of observation, but not on the time when the observation was started. many large families of stochastic processes have stationary increments either by definition ( e. g. levy processes ) or by construction ( e. g. random walks )


in the following, a short introduction to input - output analysis and its environmental extension for the calculation of material footprints or rme indicators is provided. the inter - industry flows within an economy form an n×n matrix z and the total output of each industry forms an n×1 vector x. by dividing each flow into an industry ( i. e., each element of z ) by the total output of that same industry, we obtain an n×n matrix of so - called technical coefficients a. in matrix algebra, this reads as follows : a = z × x ^ − 1 { \ displaystyle a = z \ times { \ hat { x } } ^ { - 1 } } where : x ^ { \ displaystyle { \ hat { x } } } represents the vector x diagonlized into a matrix ( x ^ = i x → { \ displaystyle { \ hat { x } } = i { \ vec { x } } } ) matrix a contains the multipliers for the inter - industry inputs required to supply one unit of industry output. a certain total economic output x is required to satisfy a given level of final demand y. this final demand may be domestic ( for private households as well as the public sector ) or foreign ( exports ) and can be written as an n×1 vector. when this vector of final demand y is multiplied by the leontief inverse ( i−a ) −1, we obtain total output x. i is the identity matrix so that the following matrix equation is the result of equivalence operations in our previous equation : x → = ( i − a ) − 1 × y → { \ displaystyle { \ vec { x } } = \ left ( i - a \ right ) ^ { - 1 } \ times { \ vec { y } } } the leontief inverse contains the multipliers for the direct and indirect inter - industry inputs required to provide 1 unit of output to final demand.


although these examples offer alternate strategies for achieving the same abstraction, they do not fundamentally alter the need to support abstract nouns in code – all programming relies on an ability to abstract verbs as functions, nouns as data structures, and either as processes. consider for example a sample java fragment to represent some common farm " animals " to a level of abstraction suitable to model simple aspects of their hunger and feeding. it defines an animal class to represent both the state of the animal and its functions : with the above definition, one could create objects of type animal and call their methods like this : in the above example, the class animal is an abstraction used in place of an actual animal, livingthing is a further abstraction ( in this case a generalisation ) of animal.


in software development or backward compatibility is a general notion of interoperation between software pieces that will not produce any errors when its functionality is invoked via api. the software is considered stable when its api that is used to invoke functions is stable across different versions. in operating systems upgraded to a newer versions are said to be backward compatible if executable and other files from previous versions will work as usual. in compilers backward compatibility may refer to the ability of a compiler of a newer version of the language to accept source code of programs or data that worked under the previous version. a data format is said to be backward compatible when a newer version of program that can open it opens it without errors just like its predecessor.


the jordan – holder theorem is a more precise way of stating this fact about finite groups. however, a significant difference from integer factorization is that such " building blocks " do not necessarily determine a unique group, since there might be many non - isomorphic groups with the same composition series or, put in another way, the extension problem does not have a unique solution. gorenstein ( d. 1992 ), lyons, and solomon are gradually publishing a simplified and revised version of the proof.


in phylogenetics, informative site is a term used when maximum parsimony is the optimality criterion for construction of a phylogenetic tree. it refers to a characteristic for which the number of character - state evolutionary changes of at this site depends on the topology of the tree. the charactetistics can take on multiple types of data, including morphological ( such as the presence of wings, tentacles, etc. ) or molecular information such as sequences of dna or proteins. the informative site is a position in the relevant set of aligned sequences at which there are at least two different character states and each of those states occurs in at least two of the sequences.


in the encoded format a " 1 " bit indicates a flux transition, while a " 0 " indicates that the magnetic field on the disk does not change for that time interval.


in science and engineering, a system is the part of the universe that is being studied, while the environment is the remainder of the universe that lies outside the boundaries of the system. it is also known as the surroundings or neighborhood, and in thermodynamics, as the reservoir. depending on the type of system, it may interact with the environment by exchanging mass, energy ( including heat and work ), linear momentum, angular momentum, electric charge, or other conserved properties. in some disciplines, such as information theory, information may also be exchanged. the environment is ignored in analysis of the system, except in regard to these interactions.


advantages of this approach include the general increased quality of the data returned in searches and with proper tagging, ontologies finding entries that may not explicitly state the search term but are still relevant. one disadvantage of this approach is that the results that are returned come in the format of the database of their origin and as such, direct comparisons may be difficult. another problem is that the terms used in tagging and searching can sometimes be ambiguous and may cause confusion among the results.


in telecommunications, multiple access schemes are orthogonal when an ideal receiver can completely reject arbitrarily strong unwanted signals from the desired signal using different basis functions. one such scheme is time - division multiple access ( tdma ), where the orthogonal basis functions are nonoverlapping rectangular pulses ( " time slots " ).


it was later argued that it has strong biological motivations and mathematical justifications. in 2011 it was found to enable better training of deeper networks, compared to the widely used activation functions prior to 2011, e. g., the logistic sigmoid ( which is inspired by probability theory ; see logistic regression ) and its more practical counterpart, the hyperbolic tangent. the rectifier is, as of 2017, the most popular activation function for deep neural networks. rectified linear units find applications in computer vision and speech recognition using deep neural nets and computational neuroscience.


in order to understand morphogenetic events, i. e. the growth and shaping of tissues and organs, it is necessary to analyze the packing of cells into tissues. in that context, an analysis of patterning processes can help to identify the underlying mechanisms that drive morphogenesis. = = references = =


in the 1990s, there was a general confusion about the proper character encoding to use to write text in latin croatian on computers. an attempt was made to apply the 7 - bit " yuscii ", later " croscii ", which included the five letters with diacritics at the expense of five non - letter characters (, {, }, @ ), but it was ultimately unsuccessful. because the ascii character @ sorts before a, this led to jokes calling it zabeceda ( zaba = frog, abeceda = alphabet ). other short - lived vendor - specific efforts were also undertaken.


previous work includes the work of d. coppersmith about the dlp in fields of characteristic two. the discrete logarithm problem in a finite field consists of solving the equation a x = b { \ displaystyle a ^ { x } = b } for a, b ∈ f p n { \ displaystyle a, b \ in \ mathbb { f } _ { p ^ { n } } }, p { \ displaystyle p } a prime number and n { \ displaystyle n } an integer. the function f : f p n → f p n, x ↦ a x { \ displaystyle f : \ mathbb { f } _ { p ^ { n } } \ to \ mathbb { f } _ { p ^ { n } }, x \ mapsto a ^ { x } } for a fixed a ∈ f p n { \ displaystyle a \ in \ mathbb { f } _ { p ^ { n } } } is a one - way function used in cryptography. several cryptographic methods are based on the dlp such as the diffie - hellman key exchange, the el gamal cryptosystem and the digital signature algorithm.


in signal processing this process is known as discrete convolution.


in particular, the value of the coefficient of determination will shrink relative to the original data. to lessen the chance or amount of overfitting, several techniques are available ( e. g., model comparison, cross - validation, regularization, early stopping, pruning, bayesian priors, or dropout ). the basis of some techniques is either ( 1 ) to explicitly penalize overly complex models or ( 2 ) to test the model's ability to generalize by evaluating its performance on a set of data not used for training, which is assumed to approximate the typical unseen data that a model will encounter.


in mathematics, a q - matrix is a square matrix whose associated linear complementarity problem lcp ( m, q ) has a solution for every vector q.


some consider it to be an anti - pattern. there are valid forms of the pattern, including the use of the volatile keyword in java and explicit memory barriers in c + +. the pattern is typically used to reduce locking overhead when implementing " lazy initialization " in a multi - threaded environment, especially as part of the singleton pattern. lazy initialization avoids initializing a value until the first time it is accessed.


in the context of a jump process that takes states in a state space s { \ displaystyle \ mathrm { s } }, consider the set of random variables ( x n, t n ) { \ displaystyle ( x _ { n }, t _ { n } ) }, where t n { \ displaystyle t _ { n } } represents the jump times and x n { \ displaystyle x _ { n } } represents the associated states in the sequence of states ( see figure ). let the sequence of inter - arrival times τ n = t n − t n − 1 { \ displaystyle \ tau _ { n } = t _ { n } - t _ { n - 1 } }. in order for the sequence ( x n, t n ) { \ displaystyle ( x _ { n }, t _ { n } ) } to be considered a markov renewal process the following condition should hold : pr ( τ n + 1 ≤ t, x n + 1 = j ( x 0, t 0 ), ( x 1, t 1 ), …, ( x n = i, t n ) ) = pr ( τ n + 1 ≤ t, x n + 1 = j x n = i ) n ≥ 1, t ≥ 0, i, j ∈ s { \ displaystyle { \ begin { aligned } & \ pr ( \ tau _ { n + 1 } \ leq t, x _ { n + 1 } = j \ mid ( x _ { 0 }, t _ { 0 } ), ( x _ { 1 }, t _ { 1 } ), \ ldots, ( x _ { n } = i, t _ { n } ) ) \ \ = { } & \ pr ( \ tau _ { n + 1 } \ leq t, x _ { n + 1 } = j \ mid x _ { n } = i ) \, \ forall n \ geq 1, t \ geq 0, i, j \ in \ mathrm { s } \ end { aligned } } }


in the fields of machine learning, the theory of computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position if its covariance matrix is equal to the identity matrix.


there are two running instances of each role. in this example, the cache is distributed across all instances of the dedicated cache1 role. a dedicated topology has the advantage of scaling the caching tier independently of any other role in the cloud service. for the best caching performance, a dedicated topology is recommended because the role instances do not share their resources with other application code and services.


however, the values are frequently represented as 1 or 0, which corresponds to counting the number of successes in a single trial : 1 ( success ) or 0 ( failure ) ; see § counting. often, binary data is used to represent one of two conceptually opposed values, e. g. : the outcome of an experiment ( " success " or " failure " ) the response to a yes – no question ( " yes " or " no " ) presence or absence of some feature ( " is present " or " is not present " ) the truth or falsehood of a proposition ( " true " or " false ", " correct " or " incorrect " ) however, it can also be used for data that is assumed to have only two possible values, even if they are not conceptually opposed or conceptually represent all possible values in the space. for example, binary data is often used to represent the party choices of voters in elections in the united states, i. e. republican or democratic.


in order to explain column - level encryption it is important to outline basic database structure. a typical relational database is divided into tables that are divided into columns that each have rows of data. whilst tde usually encrypts an entire database, column - level encryption allows for individual columns within a database to be encrypted. it is important to establish that the granularity of column - level encryption causes specific strengths and weaknesses to arise when compared to encrypting an entire database.


formally, a sequence of numbers s 0, s 1, s 2, s 3, … { \ displaystyle s _ { 0 }, s _ { 1 }, s _ { 2 }, s _ { 3 }, \ ldots } is constant - recursive if it satisfies a recurrence relation where c i { \ displaystyle c _ { i } } are constants. for example, the fibonacci sequence satisfies the recurrence relation f n = f n − 1 + f n − 2, { \ displaystyle f _ { n } = f _ { n - 1 } + f _ { n - 2 }, } where f n { \ displaystyle f _ { n } } is the n { \ displaystyle n } th fibonacci number. constant - recursive sequences are studied in combinatorics and the theory of finite differences.


in his formal published treatises, archimedes solved the same problem using the method of exhaustion. the 15th century saw the work of nicholas of cusa, further developed in the 17th century by johannes kepler, in particular, the calculation of the area of a circle by representing the latter as an infinite - sided polygon. simon stevin's work on the decimal representation of all numbers in the 16th century prepared the ground for the real continuum.


in order to evaluate the outcomes of a program, the evaluator first needs to monitor the process in order to assess the implementation of the intervention. the reason for this is that many program failures are due to failures in the implementation of the program. therefore, in order to determine whether or not the planned outcomes have been reached, the evaluator needs to assess how the intervention was implemented.


computer manufacturers who had a significant business in the defense, aerospace, or related industries, also offered ada compilers and tools on their platforms ; these included concurrent computer corporation, cray research, inc., digital equipment corporation, harris computer systems, and siemens nixdorf informationssysteme ag. in 1991, the us department of defense began to require the use of ada ( the ada mandate ) for all software, though exceptions to this rule were often granted. the department of defense ada mandate was effectively removed in 1997, as the dod began to embrace commercial off - the - shelf ( cots ) technology. similar requirements existed in other nato countries : ada was required for nato systems involving command and control and other functions, and ada was the mandated or preferred language for defense - related applications in countries such as sweden, germany, and canada. by the late 1980s and early 1990s, ada compilers had improved in performance, but there were still barriers to fully exploiting ada's abilities, including a tasking model that was different from what most real - time programmers were used to. because of ada's safety - critical support features, it is now used not only for military applications, but also in commercial projects where a software bug can have severe consequences, e. g., avionics and air traffic control, commercial rockets such as the ariane 4 and 5, satellites and other space systems, railway transport and banking.


in the following examples, computed values are in bold, while register numbers are not. for example, to write the value 3 to register 1, ( which already contains a 6 ), and then add 7 to register 1 and store the result in register 2, i. e. : i0 : r1 = 6 i1 : r1 = 3 i2 : r2 = r1 + 7 = 10 following execution, register 2 should contain the value 10. however, if i1 ( write 3 to register 1 ) does not fully exit the pipeline before i2 starts executing, it means that r1 does not contain the value 3 when i2 performs its addition. in such an event, i2 adds 7 to the old value of register 1 ( 6 ), and so register 2 contains 13 instead, i. e. : i0 : r1 = 6 i2 : r2 = r1 + 7 = 13 i1 : r1 = 3 this error occurs because i2 reads register 1 before i1 has committed / stored the result of its write operation to register 1. so when i2 is reading the contents of register 1, register 1 still contains 6, not 3.


by taking the determiner, a function word, to be head over the noun, a structure is established that is analogous to the structure of the finite clause, with a complementizer. apart from the minimalist program, however, the dp hypothesis is rejected by most other modern theories of syntax and grammar, in part because these theories lack the relevant functional categories. dependency grammars, for instance, almost all assume the traditional np analysis of noun phrases. for illustrations of different analyses of noun phrases depending on whether the dp hypothesis is rejected or accepted, see the next section.


in mathematics, a residuated boolean algebra is a residuated lattice whose lattice structure is that of a boolean algebra. examples include boolean algebras with the monoid taken to be conjunction, the set of all formal languages over a given alphabet σ under concatenation, the set of all binary relations on a given set x under relational composition, and more generally the power set of any equivalence relation, again under relational composition. the original application was to relation algebras as a finitely axiomatized generalization of the binary relation example, but there exist interesting examples of residuated boolean algebras that are not relation algebras, such as the language example.


in mathematics, a signature matrix is a diagonal matrix whose diagonal elements are plus or minus 1, that is, any matrix of the form : a = ( ± 1 0 0 0 0 ± 1 0 0 0 0 ± 1 0 0 0 0 ± 1 ) { \ displaystyle a = { \ begin { pmatrix } \ pm 1 & 0 & \ cdots & 0 & 0 \ \ 0 & \ pm 1 & \ cdots & 0 & 0 \ \ \ vdots & \ vdots & \ ddots & \ vdots & \ vdots \ \ 0 & 0 & \ cdots & \ pm 1 & 0 \ \ 0 & 0 & \ cdots & 0 & \ pm 1 \ end { pmatrix } } } any such matrix is its own inverse, hence is an involutory matrix. it is consequently a square root of the identity matrix. note however that not all square roots of the identity are signature matrices.


the distinction between data and derived value is illustrated by the information ladder. however, data has staged a comeback with the popularisation of the term big data, which refers to the collection and analyses of massive sets of data. several organisations have established data management centers ( dmc ) for their operations.


one start code, one house code, and one function code is known as an x10 frame and represent the minimum components of a valid x10 data packet. each frame is sent twice in succession to make sure the receivers understand it over any power line noise for purposes of redundancy, reliability, and to accommodate line repeaters. after allowing for retransmission, line control, etc., data rates are around 20 bit / s, making x10 data transmission so slow that the technology is confined to turning devices on and off or other very simple operations.


we also add a team node for each team and connect each game node { i, j } with i < j to v, and connects each of them from s by an edge with capacity rij – which represents the number of plays between these two teams. we also add a team node for each team and connect each game node { i, j } with two team nodes i and j to ensure one of them wins. one does not need to restrict the flow value on these edges. finally, edges are made from team node i to the sink node t and the capacity of wk + rk – wi is set to prevent team i from winning more than wk + rk. let s be the set of all teams participating in the league and let r ( s − { k } ) = i, j ∈ { s − { k } } i < j r i j { \ displaystyle r ( s - \ { k \ } ) = \ sum _ { i, j \ in \ { s - \ { k \ } \ } \ atop i


in probability theory, a branch of mathematics poisson - dirichlet distributions are probability distributions on the set of nonnegative, non - decreasing sequences with sum 1, depending on two parameters α ∈ [ 0, 1 ) { \ displaystyle \ alpha \ in [ 0, 1 ) } and θ ∈ ( − α, ∞ ) { \ displaystyle \ theta \ in ( - \ alpha, \ infty ) }. it can be defined as follows. one considers independent random variables ( y n ) n ≥ 1 { \ displaystyle ( y _ { n } ) _ { n \ geq 1 } } such that y n { \ displaystyle y _ { n } } follows the beta distribution of parameters 1 − α { \ displaystyle 1 - \ alpha } and θ + n α { \ displaystyle \ theta + n \ alpha }. then, the poisson - dirichlet distribution p d ( α, θ ) { \ displaystyle pd ( \ alpha, \ theta ) } of parameters α { \ displaystyle \ alpha } and θ { \ displaystyle \ theta } is the law of the random decreasing sequence containing y 1 { \ displaystyle y _ { 1 } } and the products y n k = 1 n − 1 ( 1 − y k ) { \ displaystyle y _ { n } \ prod _ { k = 1 } ^ { n - 1 } ( 1 - y _ { k } ) }. this definition is due to jim pitman and marc yor. it generalizes kingman's law, which corresponds to the particular case α = 0 { \ displaystyle \ alpha = 0 }.


( why do we have all these abbreviations anyway? saving bandwidth?


in mathematics, a kleene algebra ( klay - nee ; named after stephen cole kleene ) is an idempotent ( and thus partially ordered ) semiring endowed with a closure operator. it generalizes the operations known from regular expressions.


( 1 ) this is a bank. this bank accepted my identification. ( 2 ) she is a bank teller.


created in 1978, it is still used today for applications involving digital signatures. using number theory, the rsa algorithm selects two prime numbers, which help generate both the encryption and decryption keys. a publicly available public - key encryption application called pretty good privacy ( pgp ) was written in 1991 by phil zimmermann, and distributed free of charge with source code. pgp was purchased by symantec in 2010 and is regularly updated.


in number theory, lucas's theorem expresses the remainder of division of the binomial coefficient ( m n ) { \ displaystyle { \ tbinom { m } { n } } } by a prime number p in terms of the base p expansions of the integers m and n. lucas's theorem first appeared in 1878 in papers by edouard lucas.


in the classical setting, rg can be viewed as the following problem. alice, bob, and the referee is given some statement. alice is trying to convince the referee that the statement is true while bob is trying to convince the referee that the statement is false. the referee, who has limited computing power, will look at the proofs provided by alice and bob, ask them questions, and at the end of the day decide which player is correct ( wins ).


in set theory and order theory, the cantor – bernstein theorem states that the cardinality of the second type class, the class of countable order types, equals the cardinality of the continuum. it was used by felix hausdorff and named by him after georg cantor and felix bernstein. cantor constructed a family of countable order types with the cardinality of the continuum, and in his 1901 inaugural dissertation bernstein proved that such a family can have no higher cardinality. = = references = =


in partition calculus, part of combinatorial set theory, a branch of mathematics, the erdos – rado theorem is a basic result extending ramsey's theorem to uncountable sets. it is named after paul erdos and richard rado. it is sometimes also attributed to đuro kurepa who proved it under the additional assumption of the generalised continuum hypothesis, and hence the result is sometimes also referred to as the erdos – rado – kurepa theorem.


one picks a set ι to be the type of individuals. for example, ι might be the set of natural numbers, or the set of atoms ( in a set theory with atoms ) or any other set one is interested in. then if τ1,..., τm are types, the type ( τ1,..., τm ) is the power set of the product τ1×... ×τm, which can also be thought of informally as the set of ( propositional predicative ) functions from this product to a 2 - element set { true, false }. the ramified type ( τ1,..., τm | σ1,..., σn ) can be modeled as the product of the type ( τ1,..., τm, σ1,..., σn ) with the set of sequences of n quantifiers ( or ) indicating which quantifier should be applied to each variable σi. ( one can vary this slightly by allowing the σs to be quantified in any order, or allowing them to occur before some of the τs, but this makes little difference except to the bookkeeping. )


in summary, each perspective focuses attention on the same fundamental questions, then answers those questions from that viewpoint, creating different descriptive representations ( i. e., models ), which translate from higher to lower perspectives. the basic model for the focus ( or product abstraction ) remains constant. the basic model of each column is uniquely defined, yet related across and down the matrix. in addition, the six categories of enterprise architecture components, and the underlying interrogatives that they answer, form the columns of the zachman framework and these are : inventory sets — what process flows — how distribution networks — where responsibility assignments — who timing cycles — when motivation intentions — whyin zachman's opinion, the single factor that makes his framework unique is that each element on either axis of the matrix is explicitly distinguishable from all the other elements on that axis. the representations in each cell of the matrix are not merely successive levels of increasing detail, but actually are different representations — different in context, meaning, motivation, and use. because each of the elements on either axis is explicitly different from the others, it is possible to define precisely what belongs in each cell.


stack overflow may be difficult to avoid when using recursive procedures since many compilers assume that the recursion stack is a contiguous area of memory, and some allocate a fixed amount of space for it. compilers may also save more information in the recursion stack than is strictly necessary, such as return address, unchanging parameters, and the internal variables of the procedure. thus, the risk of stack overflow can be reduced by minimizing the parameters and internal variables of the recursive procedure or by using an explicit stack structure.


in telecommunications, a block check character ( bcc ) is a character added to a transmission block to facilitate error detection. in longitudinal redundancy checking and cyclic redundancy checking, block check characters are computed for, and added to, each message block transmitted. this block check character is compared with a second block check character computed by the receiver to determine whether the transmission is error free.


in the above uml class diagram, the client class refers to the common abstractexpression interface for interpreting an expression interpret ( context ). the terminalexpression class has no children and interprets an expression directly. the nonterminalexpression class maintains a container of child expressions ( expressions ) and forwards interpret requests to these expressions. the object collaboration diagram shows the run - time interactions : the client object sends an interpret request to the abstract syntax tree.


however, if all voter factions have the same proportion of strategic and honest voters, simulations show that any significant proportion of honest voters will lead to results which tend to be more satisfying to voters than approval voting, and indeed, more satisfying than any other method with the same unbiased proportion of strategic voters. strategic voters are faced with the initial tactic as to how highly to score their second - choice candidate. the voter may want to retain expression of a high preference of their favorite candidate over their second choice. but that does not allow the same voter to express a high preference of their second choice over any others. in a simulation study using polling data collected under a majority judgment method, that method's designers found that score voting was more vulnerable to strategy than any other method they studied, including plurality.


in reverse accumulation ad, the dependent variable to be differentiated is fixed and the derivative is computed with respect to each sub - expression recursively. in a pen - and - paper calculation, the derivative of the outer functions is repeatedly substituted in the chain rule : in reverse accumulation, the quantity of interest is the adjoint, denoted with a bar w i { \ displaystyle { \ bar { w } } _ { i } } ; it is a derivative of a chosen dependent variable with respect to a subexpression w i { \ displaystyle w _ { i } } : using the chain rule, if w i { \ displaystyle w _ { i } } has successors in the computational graph : w i = j ∈ { successors of i } w j ∂ w j ∂ w i { \ displaystyle { \ bar { w } } _ { i } = \ sum _ { j \ in \ { { \ text { successors of i } } \ } } { \ bar { w } } _ { j } { \ frac { \ partial w _ { j } } { \ partial w _ { i } } } } reverse accumulation traverses the chain rule from outside to inside, or in the case of the computational graph in figure 3, from top to bottom. the example function is scalar - valued, and thus there is only one seed for the derivative computation, and only one sweep of the computational graph is needed to calculate the ( two - component ) gradient. this is only half the work when compared to forward accumulation, but reverse accumulation requires the storage of the intermediate variables wi as well as the instructions that produced them in a data structure known as a " tape " or a wengert list ( however, wengert published forward accumulation, not reverse accumulation ), which may consume significant memory if the computational graph is large.


see linearization § transformation, below, for more details. in general, there is no closed - form expression for the best - fitting parameters, as there is in linear regression. usually numerical optimization algorithms are applied to determine the best - fitting parameters.


eliminating the systematic error improves accuracy but does not change precision. a measurement system is considered valid if it is both accurate and precise. related terms include bias ( non - random or directed effects caused by a factor or factors unrelated to the independent variable ) and error ( random variability ).


for instance, two - dimensional convex hulls can be computed using predicates that test the sign of quadratic polynomials, and therefore may require twice as many bits of precision within these calculations as the input numbers. when integer arithmetic cannot be used ( for instance, when the result of a calculation is an algebraic number rather than an integer or rational number ), a second method is to use symbolic algebra to perform all computations with exactly represented algebraic numbers rather than numerical approximations to them. a third method, sometimes called a " floating point filter ", is to compute numerical predicates first using an inexact method based on floating - point arithmetic, but to maintain bounds on how accurate the result is, and repeat the calculation using slower symbolic algebra methods or numerically with additional precision when these bounds do not separate the calculated value from zero.


in pseudocode, the pairwise summation algorithm for an array x of length n ≥ 0 can be written : s = pairwise ( x ) if n ≤ n base case : naive summation for a sufficiently small array s = 0 for i = 1 to n s = s + x else divide and conquer : recursively sum two halves of the array m = floor ( n / 2 ) s = pairwise ( x ) + pairwise ( x ) end if for some sufficiently small n, this algorithm switches to a naive loop - based summation as a base case, whose error bound is o ( nε ). the entire sum has a worst - case error that grows asymptotically as o ( ε log n ) for large n, for a given condition number ( see below ). in an algorithm of this sort ( as for divide and conquer algorithms in general ), it is desirable to use a larger base case in order to amortize the overhead of the recursion.


if all weights are integers, then the run - time can be improved to o ( m n + n 2 log log n ) { \ displaystyle o ( mn + n ^ { 2 } \ log \ log n ) }, but the resulting algorithm is only weakly - polynomial. if the weights are integers, and all weights are at most c ( where c > 1 is some integer ), then the problem can be solved in o ( m n log ( n ⋅ c ) ) { \ displaystyle o ( m { \ sqrt { n } } \ log ( n \ cdot c ) ) } weakly - polynomial time in a method called weight scaling. in addition to the global methods, there are local methods which are based on finding local updates ( rather than full augmenting paths ). these methods have worse asymptotic runtime guarantees, but they often work better in practice.


if we compute the cross products, we have m = | e x e y e z x a − x 0 0 0 − f 0 | + | e x e y e z − x 0 0 0 r 0 0 | = f ( x − x a ) e z − r 0 x e z = − f x a l ( l − x ) e z. { \ displaystyle \ mathbf { m } = \ left | { \ begin { matrix } \ mathbf { e } _ { x } & \ mathbf { e } _ { y } & \ mathbf { e } _ { z } \ \ x _ { a } - x & 0 & 0 \ \ 0 & - f & 0 \ end { matrix } } \ right | + \ left | { \ begin { matrix } \ mathbf { e } _ { x } & \ mathbf { e } _ { y } & \ mathbf { e } _ { z } \ \ - x & 0 & 0 \ \ 0 & r _ { 0 } & 0 \ end { matrix } } \ right | = f ( x - x _ { a } ) \, \ mathbf { e } _ { z } - r _ { 0 } x \, \ mathbf { e } _ { z } = - { \ frac { fx _ { a } } { l } } ( l - x ) \, \ mathbf { e } _ { z } \,. } thanks to the equilibrium, the internal bending moment due to external forces to the left of x must be exactly balanced by the internal turning force obtained by considering the part of the beam to the right of x m + m x z = 0. { \ displaystyle \ mathbf { m } + \ mathbf { m } _ { xz } = \ mathbf { 0 } \,. } which is clearly the case.


this combinator may be used in implementing curry's paradox. the heart of curry's paradox is that untyped lambda calculus is unsound as a deductive system, and the y combinator demonstrates this by allowing an anonymous expression to represent zero, or even many values. this is inconsistent in mathematical logic.


in number theory, lemoine's conjecture, named after emile lemoine, also known as levy's conjecture, after hyman levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.


in the ims it is possible for a user to have multiple terminals ( e. g. a mobile phone, a computer ) or application instances ( e. g. video telephony, instant messaging, voice mail ) that are identified with the same public identity ( i. e. sip uri ). therefore, a mechanism is needed in order to route requests to the desired device or application. that is what a globally routable user agent uri ( gru ) is : a uri that identifies a specific user agent instance ( i. e. terminal or application instance ) and it does it globally ( i. e. it is valid to route messages to that user agent from any other user agent on the internet ). these uris are constructed by adding the gr parameter to a sip uri, either to the public sip uri with a value that identifies the user agent instance, or to a specially created uri that does not reveal the relationship between the gruu and the user's identity, for privacy purposes. they are commonly obtained during the registration process : the registering user agent sends a uniform resource name ( urn ) that uniquely identifies that sip instance, and the registrar ( i. e. s - cscf ) builds the gruu, associates it to the registered identity and sip instance and sends it back to the user agent in the response. when the s - cscf receives a request for that gruu, it will be able to route the request to the registered sip instance.


if this presupposition is satisfied, { \ displaystyle \ sim } passes along its overt argument's ordinary denotation while " resetting " its focus denotation. in other words, when the presupposition is satisfied, ] o = ] o { \ displaystyle \! ] _ { o } = \! ] _ { o } } and ] f = { ] o } { \ displaystyle \! ] _ { f } = \ { \! ] _ { o } \ } }.


in mathematics, a topological group g is called a discrete group if there is no limit point in it ( i. e., for each element in g, there is a neighborhood which only contains that element ). equivalently, the group g is discrete if and only if its identity is isolated. a subgroup h of a topological group g is a discrete subgroup if h is discrete when endowed with the subspace topology from g. in other words there is a neighbourhood of the identity in g containing no other element of h. for example, the integers, z, form a discrete subgroup of the reals, r ( with the standard metric topology ), but the rational numbers, q, do not. any group can be endowed with the discrete topology, making it a discrete topological group. since every map from a discrete space is continuous, the topological homomorphisms between discrete groups are exactly the group homomorphisms between the underlying groups.


in set theory, an extender is a system of ultrafilters which represents an elementary embedding witnessing large cardinal properties. a nonprincipal ultrafilter is the most basic case of an extender. a ( κ, λ ) - extender can be defined as an elementary embedding of some model m { \ displaystyle m } of zfc− ( zfc minus the power set axiom ) having critical point κ ε m, and which maps κ to an ordinal at least equal to λ. it can also be defined as a collection of ultrafilters, one for each n { \ displaystyle n } - tuple drawn from λ.


the alternative hypothesis corresponds to the position against the defendant. specifically, the null hypothesis also involves the absence of a difference or the absence of an association. thus, the null hypothesis can never be that there is a difference or an association.


in a paper published in 1982, benioff further developed his original model of quantum mechanical turing machines. this work put quantum computers on a solid theoretical foundation. richard feynman then produced a universal quantum simulator. building on the work of benioff and feynman, deutsch proposed that quantum mechanics can be used to solve computational problems faster than classical computers, and in 1994, shor described a factoring algorithm that is considered to have an exponential speedup over classical computers. after benioff and his peers in the field published several more papers on quantum computers, the idea began to gain traction with industry, banking, and government agencies. the field is now a fast - growing area of research that could have applications in cybersecurity, cryptography, quantum system modeling and more.


the algorithm was first published in 1944 by kenneth levenberg, while working at the frankford army arsenal. it was rediscovered in 1963 by donald marquardt, who worked as a statistician at dupont, and independently by girard, wynne and morrison. the lma is used in many software applications for solving generic curve - fitting problems. by using the gauss – newton algorithm it often converges faster than first - order methods. however, like other iterative optimization algorithms, the lma finds only a local minimum, which is not necessarily the global minimum.


proving that such a system is thermodynamically stable is called the stability of matter problem and it is very difficult due to the long range of the coulomb potential. stability should be a consequence of screening effects, but those are hard to quantify. let us denote by h n, k = − i = 1 n δ x i 2 − k = 1 k δ r k 2 m k − i = 1 n k = 1 k z k | x i − r k | + 1 ≤ i < j ≤ n 1 | x i − x j | + 1 ≤ k < m ≤ k z k z m | r k − r m | { \ displaystyle h _ { n, k } = - \ sum _ { i = 1 } ^ { n } { \ frac { \ delta _ { x _ { i } } } { 2 } } - \ sum _ { k = 1 } ^ { k } { \ frac { \ delta _ { r _ { k } } } { 2m _ { k } } } - \ sum _ { i = 1 } ^ { n } \ sum _ { k = 1 } ^ { k } { \ frac { z _ { k } } { | x _ { i } - r _ { k } | } } + \ sum _ { 1 \ leq i


rp is defined for sets s1 and s2 of cardinal number n and s3 of cardinal number n - 1 as : rp ( s1, s2 ) iff ( s3 ⊂ s1, s3 ⊂ s2 ) meaning that s1 and s2 each have all the pitch - classes of s3 ( transposed or inverted ), plus one. he pc similarity relation rp is not especially significant when taken alone, since by that measure a given set may be similar to many others. when rp is combined with the similarity measures, however, a considerable reduction is effected.


in mobile telephony a bearer service is a link between two points, which is defined by a certain set of characteristics. whenever user equipment ( ue ) is being provided with any service ( cs / ps service ), the service has to be associated with a radio bearer specifying the configuration for layer 2 and physical layer in order to have its qos clearly defined. radio bearers are channels offered by layer 2 to higher layers for the transfer of either user or control data. in other words, layer 2 offers to the upper layers the service of information transmission between the ue and the utran by means of the radio bearers ( rbs ) and signaling radio bearers ( srbs ). therefore, the service access points between layer 2 and upper layers are rbs.


in software development, test effort refers to the expenses for ( still to come ) tests. there is a relation with test costs and failure costs ( direct, indirect, costs for fault correction ). some factors which influence test effort are : maturity of the software development process, quality and testability of the testobject, test infrastructure, skills of staff members, quality goals and test strategy.


some functional elements, described using a software language, may actually be implemented as hardware ( fpga, asic ) hardware views – describes the hardware engineering aspects of the system, hardware design, selection and implementation of all of the physical components to be assembled into the system. there may be many of these views, each specific to a different engineering discipline. communications protocol view – describes the end to end design of the communications protocols and related data transport and data management services, shows the protocol stacks as they are implemented on each of the physical components of the system.


in present - day vocabulary, the term cast steel is almost always used in its sense referring to steel castings. between the late 19th and mid 20th centuries, this was not always true, which is worth understanding if one is reading historical documents ; see cast steel for details.


in the following, label is an optional identifier terminated by a colon, and block is a sequence of one of more perl statements surrounded by braces. all looping constructs except for the c - style for - loop can have a continue block that is executed after each iteration of the loop body, before the loop condition is evaluated again. label for ( expr1 ; expr2 ; expr3 ) block this is the so - called c - style for loop. the first expression is evaluated prior to the first loop iteration.


in multilinear algebra, the tensor rank decomposition or the r a n k − r { \ displaystyle rank - r } decomposition of a tensor is the decomposition of a tensor in terms of a sum of minimum r { \ displaystyle r } r a n k − 1 { \ displaystyle rank - 1 } tensors. this is an open problem. canonical polyadic decomposition ( cpd ) is a variant of the rank decomposition which computes the best fitting k { \ displaystyle k } r a n k − 1 { \ displaystyle rank - 1 } terms for a user specified k { \ displaystyle k }.


in papers published since 2008, asjp has employed a similarity judgment program based on levenshtein distance ( ld ). this approach was found to produce better classificatory results measured against expert opinion than the method used initially. ld is defined as the minimum number of successive changes necessary to convert one word into another, where each change is the insertion, deletion, or substitution of a symbol. within the levenshtein approach, differences in word length can be corrected for by dividing ld by the number of symbols of the longer of the two compared words.


that is, a node is given a high hub score by linking to nodes that are considered to be authorities on the subject. the hub score and authority score for a node is calculated with the following algorithm : start with each node having a hub score and authority score of 1. run the authority update rule run the hub update rule normalize the values by dividing each hub score by square root of the sum of the squares of all hub scores, and dividing each authority score by square root of the sum of the squares of all authority scores. repeat from the second step as necessary.


two octads intersect ( have 1's in common ) in 0, 2, or 4 coordinates in the binary vector representation ( these are the possible intersection sizes in the subset representation ). an octad and a dodecad intersect at 2, 4, or 6 coordinates. up to relabeling coordinates, w is unique. the binary golay code, g23 is a perfect code.


in mathematical morphology, a structuring element is a shape, used to probe or interact with a given image, with the purpose of drawing conclusions on how this shape fits or misses the shapes in the image. it is typically used in morphological operations, such as dilation, erosion, opening, and closing, as well as the hit - or - miss transform. according to georges matheron, knowledge about an object ( e. g., an image ) depends on the manner in which we probe ( observe ) it. in particular, the choice of a certain structuring element for a particular morphological operation influences the information one can obtain.


since we continue to use a g - 1 coding scheme, it is in fact the −1 coded group that will not produce data, hence the fact that we are least interested in that group. a code of 0 is assigned to all other groups. the b values should be interpreted such that the experimental group is being compared against the mean of all groups combined ( or weighted grand mean in the case of weighted effects coding ).


in number theory, a prime triplet is a set of three prime numbers in which the smallest and largest of the three differ by 6. in particular, the sets must have the form ( p, p + 2, p + 6 ) or ( p, p + 4, p + 6 ). with the exceptions of ( 2, 3, 5 ) and ( 3, 5, 7 ), this is the closest possible grouping of three prime numbers, since one of every three sequential odd numbers is a multiple of three, and hence not prime ( except for 3 itself ).


in mathematics, a ( b, n ) pair is a structure on groups of lie type that allows one to give uniform proofs of many results, instead of giving a large number of case - by - case proofs. roughly speaking, it shows that all such groups are similar to the general linear group over a field. they were introduced by the mathematician jacques tits, and are also sometimes known as tits systems.


in networks with unit capacities, a much stronger time bound holds. each blocking flow can be found in o ( e ) { \ displaystyle o ( e ) } time, and it can be shown that the number of phases does not exceed o ( e ) { \ displaystyle o ( { \ sqrt { e } } ) } and o ( v 2 / 3 ) { \ displaystyle o ( v ^ { 2 / 3 } ) }. thus the algorithm runs in o ( min { v 2 / 3, e 1 / 2 } e ) { \ displaystyle o ( \ min \ { v ^ { 2 / 3 }, e ^ { 1 / 2 } \ } e ) } time. in networks that arise from the bipartite matching problem, the number of phases is bounded by o ( v ) { \ displaystyle o ( { \ sqrt { v } } ) }, therefore leading to the o ( v e ) { \ displaystyle o ( { \ sqrt { v } } e ) } time bound. the resulting algorithm is also known as hopcroft – karp algorithm. more generally, this bound holds for any unit network — a network in which each vertex, except for source and sink, either has a single entering edge of capacity one, or a single outgoing edge of capacity one, and all other capacities are arbitrary integers.


in spite of the negative theoretical results on the joint spectral radius computability, methods have been proposed that perform well in practice. algorithms are even known, which can reach an arbitrary accuracy in an a priori computable amount of time. these algorithms can be seen as trying to approximate the unit ball of a particular vector norm, called the extremal norm. one generally distinguishes between two families of such algorithms : the first family, called polytope norm methods, construct the extremal norm by computing long trajectories of points.


in mathematics, any vector space v { \ displaystyle v } has a corresponding dual vector space ( or just dual space for short ) consisting of all linear forms on v, { \ displaystyle v, } together with the vector space structure of pointwise addition and scalar multiplication by constants. the dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space. when defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called the continuous dual space. dual vector spaces find application in many branches of mathematics that use vector spaces, such as in tensor analysis with finite - dimensional vector spaces.


if two dice are thrown and their values added, the resulting distribution is no longer uniform because not all sums have equal probability. although it is convenient to describe discrete uniform distributions over integers, such as this, one can also consider discrete uniform distributions over any finite set.


another example is lay, which may be the past tense of lie, but is also an independent verb ( regular in pronunciation, but with irregular spelling : lay – laid – laid ). in fact the past tense verb lay derives from a causative of the verb from which lie derives. the two verbs are sometimes confused, with lay used in the intransitive senses prescriptively reserved for lie.


only o ( n l o g ( n ) ) { \ displaystyle o ( nlog ( n ) ) } operations are needed to detect edges, where n { \ displaystyle n } is the number of pixels. during the following years, other problems have been considered : classification, segmentation, inpainting and super - resolution. this approach can be applied to gray - level or color images.


however, context - free rules cannot express agreement or reference ( anaphora ), where two different parts of the sentence must agree with each other in some way. these can be readily expressed in w - grammars.


a system or application will hit a bottleneck if the work arrives at a comparatively faster pace relative to other processing components. according to the theory of constraints, improving on the occurrences of hot - spot point of the bottleneck constraint improves the overall processing speed of the software. a thought - provoking stipulation of the theory reveals that improving the efficiency of a particular process stage rather than the constraint can generate even more delay and decrease overall processing capabilities of a software. the process of tracking down bottlenecks ( also referred as " hot spots " - sections of the code that execute most frequently - i. e. have the highest execution count ) is called performance analysis. reduction is achieved with the utilization of specialized tools such as performance analyzers or profilers, the objective being to make particular sections of code perform as effectively as possible to improve overall algorithmic efficiency.


in mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. some variants are commonly referred to as square - and - multiply algorithms or binary exponentiation. these can be of quite general use, for example in modular arithmetic or powering of matrices. for semigroups for which additive notation is commonly used, like elliptic curves used in cryptography, this method is also referred to as double - and - add.


reidl " in 1998 extends and proposes a new way to taxonomize information visualization techniques by using the data state model. many of the techniques share similar operating steps that can easily be reused. the data state model not only helps researchers understand the space of design, but also helps implementers understand how information visualization techniques can be applied more broadly ". in 1999 stuart card, jock d. mackinlay, and ben shneiderman present their own interpretation of this pattern, dubbing it the information visualization reference model.


in the case of neighborhood interchangeable algorithm, if we assign the worst case bound to each loop. then for n variables, which have at most d values for a variable, then we have a bound of : o ( n d ( n − l ) ∗ d ) = o ( n 2 d 2 ) { \ displaystyle o ( nd ( n - l ) * d ) = o ( n ^ { 2 } d ^ { 2 } ) }. similarly, the complexity analysis of the k - interchangeability algorithm for a worst case o ( n k − 1 ) { \ displaystyle o ( n ^ { k - 1 } ) }, with ( k − 1 ) { \ displaystyle ( k - 1 ) } - tuples of variables and d k − 1 { \ displaystyle d ^ { k - 1 } }, for ( k − 1 ) { \ displaystyle ( k - 1 ) } - tuples of values, then the bound is : o ( n d n k − l d k − 1 ) = o ( n k d k ) { \ displaystyle o ( ndn ^ { k - l } d ^ { k - 1 } ) = o ( n ^ { k } d ^ { k } ) }.


to oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental representation of a finite field with its group extension to the automorphic forms under which it is invariant. this is accomplished through abstraction to higher dimensional integration, by an equivalence to a certain analytical group as an absolute extension of its algebra. consequently, this allows an analytical functional construction of powerful invariance transformations for a number field to its own algebraic structure.


in the bin packing problem, there are n items with different sizes. the goal is to pack the items into a minimum number of bins, where each bin can contain at most b. a feasible configuration is a set of sizes with a sum of at most b. example : suppose the item sizes are 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, and b = 12. then the possible configurations are : 3333 ; 333 ; 33, 334 ; 3, 34, 344 ; 4, 44, 444. if we had only three items of size 3, then we could not use the 3333 configuration. denote by s the set of different sizes ( and their number ).


in mathematics, rings are algebraic structures that generalize fields : multiplication need not be commutative and multiplicative inverses need not exist. in other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. ring elements may be numbers such as integers or complex numbers, but they may also be non - numerical objects such as polynomials, square matrices, functions, and power series. formally, a ring is an abelian group whose operation is called addition, with a second binary operation called multiplication that is associative, is distributive over the addition operation, and has a multiplicative identity element.


in sorting n objects, merge sort has an average and worst - case performance of o ( n log n ). if the running time of merge sort for a list of length n is t ( n ), then the recurrence relation t ( n ) = 2t ( n / 2 ) + n follows from the definition of the algorithm ( apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists ). the closed form follows from the master theorem for divide - and - conquer recurrences. the number of comparisons made by merge sort in the worst case is given by the sorting numbers.


in mathematics, minkowski's theorem is the statement that every convex set in r n { \ displaystyle \ mathbb { r } ^ { n } } which is symmetric with respect to the origin and which has volume greater than 2 n { \ displaystyle 2 ^ { n } } contains a non - zero integer point ( meaning a point in z n { \ displaystyle \ mathbb { z } ^ { n } } that is not the origin ). the theorem was proved by hermann minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers. it can be extended from the integers to any lattice l { \ displaystyle l } and to any symmetric convex set with volume greater than 2 n d ( l ) { \ displaystyle 2 ^ { n } \, d ( l ) }, where d ( l ) { \ displaystyle d ( l ) } denotes the covolume of the lattice ( the absolute value of the determinant of any of its bases ).


operators had to maintain a steady rhythm, and the usual speed of operation was 30 words per minute. the table " shows the allocation of the baudot code which was employed in the british post office for continental and inland services. a number of characters in the continental code are replaced by fractionals in the inland code. code elements 1, 2 and 3 are transmitted by keys 1, 2 and 3, and these are operated by the first three fingers of the right hand.


the intent is to create standardized rules to maintain data integrity and enforce business rules throughout one or more related applications. some industries use generalized data dictionaries as technical standards to ensure interoperability between systems. the real estate industry, for example, abides by a reso's data dictionary to which the national association of realtors mandates its mlss comply with through its policy handbook. this intermediate mapping layer for mlss'native databases is supported by software companies which provide api services to mls organizations.


a different fairness notion, that can be guaranteed to more than 1 / 2 of the agents in each group, is the ordinal maximin - share approximation. for every integer c, there exists a ( 1 − 1 / 2 c − 1 ) { \ displaystyle ( 1 - 1 / 2 ^ { c - 1 } ) } - democratic 1 - out - of - c mms - fair allocation. these allocations can be found efficiently using a variant of round - robin item allocation, with weighted approval voting inside each group.


in more concrete terms, the uniform word problem can be expressed as a rewriting question, for literal strings. for a presentation p of a group g, p will specify a certain number of generators x, y, z,... for g. we need to introduce one letter for x and another ( for convenience ) for the group element represented by x−1. call these letters ( twice as many as the generators ) the alphabet σ { \ displaystyle \ sigma } for our problem. then each element in g is represented in some way by a product abc... pqrof symbols from σ { \ displaystyle \ sigma }, of some length, multiplied in g. the string of length 0 ( null string ) stands for the identity element e of g. the crux of the whole problem is to be able to recognise all the ways e can be represented, given some relations.


for example, a demand - side policy component may include placing public transit stops near development, in order to maximize walkability. additionally, california state law requires minimum energy conservation levels for all new and / or existing development projects. the seller of a home is required to include information regarding energy conservation retrofitting and thermal insulation in the sales contract. : 133


in quantum computing, classical shadow is a protocol for predicting functions of a quantum state using only a logarithmic number of measurements. given an unknown state ρ { \ displaystyle \ rho }, a tomographically complete set of gates u { \ displaystyle u } ( e. g clifford gates ), a set of m { \ displaystyle m } observables { o i } { \ displaystyle \ { o _ { i } \ } } and a quantum channel m { \ displaystyle m } ( defined by randomly sampling from u { \ displaystyle u }, applying it to ρ { \ displaystyle \ rho } and measuring the resulting state ) ; predict the expectation values tr ( o i ρ ) { \ displaystyle \ operatorname { tr } ( o _ { i } \ rho ) }. a list of classical shadows s { \ displaystyle s } is created using ρ { \ displaystyle \ rho }, u { \ displaystyle u } and m { \ displaystyle m } by running a shadow generation algorithm. when predicting the properties of ρ { \ displaystyle \ rho }, a median - of - means estimation algorithm is used to deal with the outliers in s { \ displaystyle s }.


in the first version of the aks primality test paper, a conjecture about sophie germain primes is used to lower the worst - case complexity from o ( log12n ) to o ( log6n ). a later version of the paper is shown to have time complexity o ( log7. 5n ) which can also be lowered to o ( log6n ) using the conjecture. later variants of aks have been proven to have complexity of o ( log6n ) without any conjectures or use of sophie germain primes.


in quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance t is a metric on the space of density matrices and gives a measure of the distinguishability between two states. it is the quantum generalization of the kolmogorov distance for classical probability distributions.


the finnish pig latin is called kontinkieli ( " container language " ). after each word you add the word kontti " container ", then switch the first syllables, so every sentence is converted to twice as many pseudo - words. for example, " wikipedia " " wikipedia kontti " " kokipedia wintti ".


in mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. for example, the number of times a given polynomial has a root at a given point is the multiplicity of that root. the notion of multiplicity is important to be able to count correctly without specifying exceptions ( for example, double roots counted twice ).


percentile scores and percentile ranks are often used in the reporting of test scores from norm - referenced tests, but, as just noted, they are not the same. for percentile ranks, a score is given and a percentage is computed. percentile ranks are exclusive : if the percentile rank for a specified score is 90 %, then 90 % of the scores were lower. in contrast, for percentiles a percentage is given and a corresponding score is determined, which can be either exclusive or inclusive. the score for a specified percentage ( e. g., 90th ) indicates a score below which ( exclusive definition ) or at or below which ( inclusive definition ) other scores in the distribution fall.


in the 1990s, many of the notable early successes on statistical methods in natural - language programming ( nlp ) occurred in the field of machine translation, due especially to work at ibm research. these systems were able to take advantage of existing multilingual textual corpora that had been produced by the parliament of canada and the european union as a result of laws calling for the translation of all governmental proceedings into all official languages of the corresponding systems of government. there are corpora in non - european languages as well. for example, the national institute for japanese language and linguistics in japan has built a number of corpora of spoken and written japanese.


in statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. the population distance correlation coefficient is zero if and only if the random vectors are independent. thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. this is in contrast to pearson's correlation, which can only detect linear association between two random variables. distance correlation can be used to perform a statistical test of dependence with a permutation test. one first computes the distance correlation ( involving the re - centering of euclidean distance matrices ) between two random vectors, and then compares this value to the distance correlations of many shuffles of the data.


a best - effort network or service does not support quality of service. an alternative to complex qos control mechanisms is to provide high quality communication over a best - effort network by over - provisioning the capacity so that it is sufficient for the expected peak traffic load. the resulting absence of network congestion reduces or eliminates the need for qos mechanisms.


in the algorithm, each sequence of concatenated strong characters is called a " run ". a " weak " character that is located between two " strong " characters with the same orientation will inherit their orientation. a " weak " character that is located between two " strong " characters with a different writing direction will inherit the main context's writing direction ( in an ltr document the character will become ltr, in an rtl document, it will become rtl ).


in order theory, a discipline within mathematics, a critical pair is a pair of elements in a partially ordered set that are incomparable but that could be made comparable without requiring any other changes to the partial order. formally, let p = ( s, ≤ ) be a partially ordered set. then a critical pair is an ordered pair ( x, y ) of elements of s with the following three properties : x and y are incomparable in p, for every z in s, if z < x then z < y, and for every z in s, if y < z then x < z. if ( x, y ) is a critical pair, then the binary relation obtained from p by adding the single relationship x ≤ y is also a partial order. the properties required of critical pairs ensure that, when the relationship x ≤ y is added, the addition does not cause any violations of the transitive property. a set r of linear extensions of p is said to reverse a critical pair ( x, y ) in p if there exists a linear extension in r for which y occurs earlier than x. this property may be used to characterize realizers of finite partial orders : a nonempty set r of linear extensions is a realizer if and only if it reverses every critical pair.


in mathematics, the smith – volterra – cantor set ( svc ), fat cantor set, or ε - cantor set is an example of a set of points on the real line that is nowhere dense ( in particular it contains no intervals ), yet has positive measure. the smith – volterra – cantor set is named after the mathematicians henry smith, vito volterra and georg cantor. in an 1875 paper, smith discussed a nowhere - dense set of positive measure on the real line, and volterra introduced a similar example in 1881. the cantor set as we know it today followed in 1883. the smith – volterra – cantor set is topologically equivalent to the middle - thirds cantor set.


for example, an 1871 census in the uk ( the first of its kind, but personal data from other censuses dates back to 1841 and numerical data back to 1801 ) found the average male life expectancy as being 44, but if infant mortality is subtracted, males who lived to adulthood averaged 75 years. the present life expectancy in the uk is 77 years for males and 81 for females, while the united states averages 74 for males and 80 for females. studies have shown that black american males have the shortest lifespans of any group of people in the us, averaging only 69 years ( asian - american females average the longest ).


in mathematics, the notion of polyconvexity is a generalization of the notion of convexity for functions defined on spaces of matrices. let mm×n ( k ) denote the space of all m × n matrices over the field k, which may be either the real numbers r, or the complex numbers c. a function f : mm×n ( k ) → r ∪ { ±∞ } is said to be polyconvex if a ↦ f ( a ) { \ displaystyle a \ mapsto f ( a ) } can be written as a convex function of the p × p subdeterminants of a, for 1 ≤ p ≤ min { m, n }. polyconvexity is a weaker property than convexity. for example, the function f given by f ( a ) = { 1 det ( a ), det ( a ) > 0 ; + ∞, det ( a ) ≤ 0 ; { \ displaystyle f ( a ) = { \ begin { cases } { \ frac { 1 } { \ det ( a ) } }, & \ det ( a ) > 0 ; \ \ + \ infty, & \ det ( a ) \ leq 0 ; \ end { cases } } } is polyconvex but not convex.


in mathematics, a ring class field is the abelian extension of an algebraic number field k associated by class field theory to the ring class group of some order o of the ring of integers of k.


the problem of determining whether a formula in propositional logic is satisfiable is decidable, and is known as the boolean satisfiability problem, or sat. in general, the problem of determining whether a sentence of first - order logic is satisfiable is not decidable. in universal algebra, equational theory, and automated theorem proving, the methods of term rewriting, congruence closure and unification are used to attempt to decide satisfiability. whether a particular theory is decidable or not depends whether the theory is variable - free and on other conditions.


in the japanese kantenji braille, the standard 8 - dot braille patterns 2356, 12356, 23456, and 123456 are the patterns related to braille pattern dots - 1245, since the two additional dots of kantenji patterns 01245, 12457, and 012457 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in the japanese kantenji braille, the standard 8 - dot braille patterns 2367, 12367, 23467, and 123467 are the patterns related to braille pattern dots - 1235, since the two additional dots of kantenji patterns 01235, 12357, and 012357 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


unlike javadoc tags, java annotations can also be embedded in and read from java class files generated by the java compiler. this allows annotations to be retained by the java virtual machine at run - time and read via reflection. it is possible to create meta - annotations out of the existing ones in java.


in mathematical psychology and education theory, a knowledge space is a combinatorial structure used to formulate mathematical models describing the progression of a human learner. knowledge spaces were introduced in 1985 by jean - paul doignon and jean - claude falmagne, and remain in extensive use in the education theory. modern applications include two computerized tutoring systems, aleks and the defunct rath. formally, a knowledge space assumes that a domain of knowledge is a collection of concepts or skills, each of which must be eventually mastered.


in sociology of science, the graphism thesis is a proposition of bruno latour that graphs are important in science. research has shown that one can distinguish between hard science and soft science disciplines based on the level of graph use, so it can be argued that there is a correlation between scientificity and visuality. furthermore, natural sciences publications appear to make heavier use of graphs than mathematical and social sciences. it has been claimed that an example of a discipline that uses graphs heavily but is not at all scientific is technical analysis.


in mathematics, the notion of an ( exact ) dimension function ( also known as a gauge function ) is a tool in the study of fractals and other subsets of metric spaces. dimension functions are a generalisation of the simple " diameter to the dimension " power law used in the construction of s - dimensional hausdorff measure.


given a linear system a x = b { \ displaystyle \ mathbf { a } \ mathbf { x } = \ mathbf { b } } where a is an n × n { \ displaystyle n \ times n } real symmetric sparse square matrix. the cholesky factor l will typically suffer'fill in ', that is have more non - zeros than the upper triangle of a. we seek a permutation matrix p, so that the matrix p t a p { \ displaystyle \ mathbf { p } ^ { t } \ mathbf { a } \ mathbf { p } }, which is also symmetric, has the least possible fill in its cholesky factor. we solve the reordered system ( p t a p ) ( p t x ) = p t b.


testing for failures such as aba can be exceedingly difficult, because the problematic sequence of events is very rare. model checking is an excellent way to uncover such problems. see for instance exercise 7. 3. 3 in " modeling and analysis of communicating systems ".


in the agricultural industry, sodium polyacrylate is used to help plants retain moisture in the soil. it can act as a water reservoir for plants and is commonly used by florists to keep flowers fresh. furthermore, the use of sodium polyacrylate for growing domestic fruit and vegetables has been approved by the u. s. department of agriculture.


in software engineering, many reuse metrics and models are metrics used to measure code reuse and reusability. a metric is a quantitative indicator of an attribute of a thing. a model specifies relationships among metrics.


in quantum computing, modular exponentiation appears as the bottleneck of shor's algorithm, where it must be computed by a circuit consisting of reversible gates, which can be further broken down into quantum gates appropriate for a specific physical device. furthermore, in shor's algorithm it is possible to know the base and the modulus of exponentiation at every call, which enables various circuit optimizations.


particularly in large software systems, any change to the source code may have unintended consequences, potentially introducing new bugs ; thus, a code freeze helps ensure that a portion of the program that is known to work correctly will continue to do so. code freezes are often employed in the final stages of development, when a particular release or iteration is being tested, but may also be used to prevent changes to one portion of a program while another is undergoing development. for example : " physics freeze " means no changes whatsoever will be permitted to the physics portion of the code.


in telecommunications, a message exchange pattern ( mep ) describes the pattern of messages required by a communications protocol to establish or use a communication channel. the communications protocol is the format used to represent the message which all communicating parties agree on ( or are capable to process ). the communication channel is the infrastructure that enables messages to " travel " between the communicating parties. the message exchange patterns describe the message flow between parties in the communication process, there are two major message exchange patterns — a request – response pattern, and a one - way pattern.


in radio network protocols, leader election is often used as a first step to approach more advanced communication primitives, such as message gathering or broadcasts. the very nature of wireless networks induces collisions when adjacent nodes transmit at the same time ; electing a leader allows to better coordinate this process. while the diameter d of a network is a natural lower bound for the time needed to elect a leader, upper and lower bounds for the leader election problem depend on the specific radio model studied.


in mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. the term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology.


in probability, a singular distribution is a probability distribution concentrated on a set of lebesgue measure zero, where the probability of each point in that set is zero.


let g { \ displaystyle g } be a group. then the following is equivalent : g { \ displaystyle g } is abelian. every function on g { \ displaystyle g } is a class function. all irreducible representations of g { \ displaystyle g } have degree 1. { \ displaystyle 1. }


in silico pcr refers to computational tools used to calculate theoretical polymerase chain reaction ( pcr ) results using a given set of primers ( probes ) to amplify dna sequences from a sequenced genome or transcriptome. these tools are used to optimize the design of primers for target dna or cdna sequences. primer optimization has two goals : efficiency and selectivity. efficiency involves taking into account such factors as gc - content, efficiency of binding, complementarity, secondary structure, and annealing and melting point ( tm ). primer selectivity requires that the primer pairs not fortuitously bind to random sites other than the target of interest, nor should the primer pairs bind to conserved regions of a gene family.


in mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive - definite. the conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the cholesky decomposition. large sparse systems often arise when numerically solving partial differential equations or optimization problems.


a definition of distance between any two monads is defined and from this and probabilistic mathematical tools emerges a three - dimensional space. axiomatic pregeometry by perez, bergliaffa, romero and vucetich an assortment of ontological presuppositions describes spacetime a result of relations between objectively existing entities. from presuppositions emerges the topology and metric of minkowski spacetime. cellular networks by requardt space is described by a graph with densely entangled sub - clusters of nodes ( with differential states ) and bonds ( either vanishing at 0 or directed at 1 ). rules describe the evolution of the graph from a chaotic patternless pre - big bang condition to a stable spacetime in the present.


efforts to minimize leakage include the use of strained silicon, high - κ dielectrics, and / or stronger dopant levels in the semiconductor. leakage reduction to continue moore's law will not only require new material solutions but also proper system design. certain types of semiconductor manufacturing defects exhibit themselves as increased leakage.


in the explanations below, any indication of a bit's position is counted from the right ( least significant ) side, advancing left. for example, the binary value 0001 ( decimal 1 ) has zeroes at every position but the first ( i. e., the rightmost ) one.


written test cases should include a description of the functionality to be tested, and the preparation required to ensure that the test can be conducted. a formal written test case is characterized by a known input and by an expected output, which is worked out before the test is executed. the known input should test a precondition and the expected output should test a postcondition.


in order to evaluate the methods a well understood family of languages is chosen, with a reliable dataset. this family is often the ie one but others have been used. after applying the methods to be compared to the database, the resulting trees are compared with the reference tree determined by traditional linguistic methods. the aim is to have no conflicts in topology, for example no missing sub - groups, and compatible dates. the families suggested for this analysis by nichols and warnow are germanic, romance, slavic, common turkic, chinese, and mixe zoque as well as older groups such as oceanic and ie.


any non - zero output indicates the offset error in the converter. that is, if the measurement of ground resulted in an output of 0. 001 volts, one can assume that all measurements will be offset by the same amount and can subtract 0. 001 from all subsequent results. gain error can similarly be measured and corrected internally ( again assuming that there is a constant gain error over the entire output range ).


in mathematical finance, convexity refers to non - linearities in a financial model. in other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative ( or, loosely speaking, higher - order terms ) of the modeling function. geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.


in one restricted but very common sense of the term, a graph is an ordered pair g = ( v, e ) { \ displaystyle g = ( v, e ) } comprising : v { \ displaystyle v }, a set of vertices ( also called nodes or points ) ; e ⊆ { { x, y } x, y ∈ v and x = y } { \ displaystyle e \ subseteq \ { \ { x, y \ } \ mid x, y \ in v \ ; { \ textrm { and } } \ ; x \ neq y \ } }, a set of edges ( also called links or lines ), which are unordered pairs of vertices ( that is, an edge is associated with two distinct vertices ). to avoid ambiguity, this type of object may be called precisely an undirected simple graph. in the edge { x, y } { \ displaystyle \ { x, y \ } }, the vertices x { \ displaystyle x } and y { \ displaystyle y } are called the endpoints of the edge. the edge is said to join x { \ displaystyle x } and y { \ displaystyle y } and to be incident on x { \ displaystyle x } and on y { \ displaystyle y }. a vertex may exist in a graph and not belong to an edge.


sanity testing and smoke testing avoid wasting time and effort by quickly determining whether an application is too flawed to merit more rigorous qa testing, but needs more developer debugging. groups of sanity tests are often bundled together for automated unit testing of functions, libraries, or applications prior to merging development code into a testing or trunk version control branch, for automated building, or for continuous integration and continuous deployment. another common usage of sanity test is to denote checks which are performed within programme code, usually on arguments to functions or returns therefrom, to see if the answers can be assumed to be correct. the more complicated the routine, the more important that its response be checked.


in telecommunication, the term security kernel has the following meanings : in computer and communications security, the central part of a computer or communications system hardware, firmware, and software that implements the basic security procedures for controlling access to system resources. a self - contained usually small collection of key security - related statements that ( a ) works as a part of an operating system to prevent unauthorized access to, or use of, the system and ( b ) contains criteria that must be met before specified programs can be accessed. hardware, firmware, and software elements of a trusted computing base that implement the reference monitor concept.


in programming languages, name resolution can be performed either at compile time or at runtime. the former is called static name resolution, the latter is called dynamic name resolution. a somewhat common misconception is that dynamic typing implies dynamic name resolution. for example, erlang is dynamically typed but has static name resolution.


in some languages, the gender of nouns can mostly be determined by physical ( semantic ) attributes, although there remain some nouns whose gender is not assigned in this way ( corbett calls this " semantic residue " ). the world view ( e. g. mythology ) of the speakers may influence the division of categories. zande has four genders : male human, female human, animal, and inanimate. however, there are about 80 nouns representing inanimate entities which are nonetheless animate in gender : heavenly objects ( moon, rainbow ), metal objects ( hammer, ring ), edible plants ( sweet potato, pea ), and non - metallic objects ( whistle, ball ).


in model checking, a subfield of computer science, a signal or timed state sequence is an extension of the notion of words in a formal language, in which letters are continuously emitted. while a word is traditionally defined as a function from a set of non - negative integers to letters, a signal is a function from a set of real numbers to letters. this allow the use of formalisms similar to the ones of automata theory to deal with continuous signals.


in proof complexity, a frege system is a propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally complete inference rules. frege systems ( more often known as hilbert systems in general proof theory ) are named after gottlob frege.


in mathematics, the minimum rank is a graph parameter mr ( g ) { \ displaystyle \ operatorname { mr } ( g ) } for a graph g. it was motivated by the colin de verdiere graph invariant.


in the united states, the national weather service gives out the advice " turn around, don't drown " for floods ; that is, it recommends that people get out of the area of a flood, rather than trying to cross it. at the most basic level, the best defense against floods is to seek higher ground for high - value uses while balancing the foreseeable risks with the benefits of occupying flood hazard zones. : 22 – 23 critical community - safety facilities, such as hospitals, emergency - operations centers, and police, fire, and rescue services, should be built in areas least at risk of flooding. structures, such as bridges, that must unavoidably be in flood hazard areas should be designed to withstand flooding.


the receiving application may ask for this information to be retransmitted, possibly resulting in congestive collapse or unacceptable delays in the overall transmission. errors sometimes packets are corrupted due to bit errors caused by noise and interference, especially in wireless communications and long copper wires.


in mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme x to a scheme y is a morphism such that the induced map on every stalk is a flat map of rings, i. e., f p : o y, f ( p ) → o x, p { \ displaystyle f _ { p } \ colon { \ mathcal { o } } _ { y, f ( p ) } \ to { \ mathcal { o } } _ { x, p } } is a flat map for all p in x. a map of rings a → b { \ displaystyle a \ to b } is called flat if it is a homomorphism that makes b a flat a - module. a morphism of schemes is called faithfully flat if it is both surjective and flat. two basic intuitions regarding flat morphisms are : flatness is a generic property ; and the failure of flatness occurs on the jumping set of the morphism. the first of these comes from commutative algebra : subject to some finiteness conditions on f, it can be shown that there is a non - empty open subscheme y ′ { \ displaystyle y'} of y, such that f restricted to y ′ is a flat morphism ( generic flatness ). here'restriction'is interpreted by means of the fiber product of schemes, applied to f and the inclusion map of y ′ { \ displaystyle y'} into y. for the second, the idea is that morphisms in algebraic geometry can exhibit discontinuities of a kind that are detected by flatness. for instance, the operation of blowing down in the birational geometry of an algebraic surface, can give a single fiber that is of dimension 1 when all the others have dimension 0.


in the binary number system, each numerical digit has two possible states ( 0 or 1 ) and each successive digit represents an increasing power of two. note : what follows is but one of several possible schemes for assigning the values 1, 2, 4, 8, 16, etc. to fingers, not necessarily the best. ( see below the illustrations. ) : the rightmost digit represents two to the zeroth power ( i. e., it is the " ones digit " ) ; the digit to its left represents two to the first power ( the " twos digit " ) ; the next digit to the left represents two to the second power ( the " fours digit " ) ; and so on.


for example, the graph query does the data inference through the connected relations, instead of repeated full search of the tables in relational database. kg facilitates the integration of new heterogeneous data by just adding new relationships between existing information and new entities. this facilitation is emphasized for the integration with existing popular linked open data source such as wikidata. org.


we will also assume that all rings are unital, and all ring homomorphisms are unital. many authors consider the more general concept of an associative algebra over a commutative ring r, instead of a field : an r - algebra is an r - module with an associative r - bilinear binary operation, which also contains a multiplicative identity. for examples of this concept, if s is any ring with center c, then s is an associative c - algebra.


barbara blackburn, who failed her qwerty typing class in high school, first encountered the dvorak layout in 1938 and then she quickly learned to achieve very high speeds of typing, also she occasionally toured giving speed - typing demonstrations during her secretarial career. she appeared on late night with david letterman on january 24, 1985, but felt that letterman made a spectacle of her. the recent emergence of several competitive typing websites has allowed fast typists on computer keyboards to emerge along with new records, though many of these are unverifiable. some notable, verified records include 255 wpm on a one - minute, random - word test by a user under the username slekap and occasionally bailey, 213 wpm on a 1 - hour, random - word test by joshua hu, 221 wpm average on 10 random quotes by joshua hu, and first place in the 2020 ultimate typing championship by anthony ermollin based on an average of 180. 88 wpm on texts of various lengths.


region extraction : left and right hand detection based on a comparison between them. characteristic extraction : location of the fingertips and to detect if it is a peak or a valley. to classify the point, peaks or valleys, these are transformed to 3d vectors, usually named pseudo vectors in the xy - plane, and then to compute the cross product.


a graph g is k - edge - choosable if every instance of list edge - coloring that has g as its underlying graph and that provides at least k allowed colors for each edge of g has a proper coloring. the edge choosability, or list edge colorability, list edge chromatic number, or list chromatic index, ch ′ ( g ) of graph g is the least number k such that g is k - edge - choosable. it is conjectured that it always equals the chromatic index.


in mathematics, the cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. it was discovered in 1874 by henry john stephen smith and introduced by german mathematician georg cantor in 1883. through consideration of this set, cantor and others helped lay the foundations of modern point - set topology. the most common construction is the cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments.